Part II: Emerging structures
Specific laws for natural evolution
Preface to part II
10. Structures of individuality
11. Physical characters
12. Biotic characters
13. Inventory of behaviour characters
Preface to part II
In part I of Laws for dynamic development I developed Herman Dooyeweerd’s and Dirk Vollenhoven’s idea of modal aspects into the concept of relation frames, of laws determining intersubjective relations and subject-object relations. This should find its necessary complement in Dooyeweerd’s idea of structures of individuality. It is not always clear whether Dooyeweerd considered these structures to apply to the law side (structure for) or to the subject side (structure of) things and events. Because I consider this distinction very important, I introduce the term ‘character’ for the law side: a character will be defined as a set of specific and general laws determining a class of individuals and an ensemble of possibilities. Nevertheless, Dooyeweerd’s term expresses correctly that individuality cannot exist without a lawful structure for. In almost all cases, we can also speak of an actual structure of individual things and events, plants and animals, but as we shall see, the most elementary things like electrons do not have a subjective structure in this sense.
At the law side, natural characters are supposed to be unchangeable, but at the subject side, the structure of things and events may very well be changeable. Therefore, the title of part II is Emerging structures, interpreting the natural evolution of physical and living systems as the gradual realization of characters in the course of time. I shall argue that natural evolution has a necessary random component, but is also made possible and is simultaneously constrained by natural laws.
Chapter 10 develops the concept of a character, discussing numerical, spatial and kinetic characters by way of example. This will be applied more extensively to physical characters (chapter 11), biotic characters (chapter 12), and to the characters of animal behaviour (chapter 13). Chapter 10 combines chapters 1-4 of Een wereld vol relaties (2002; Relations and characters in Protestant philosophy, part IV, 2006; A world full of relations, 2010), whereas chapters 11-13 are adapted from chapters 5-7 of the same book.
Part II, chapter 10
Structures of individuality
10.1. The main subject matter of quantum physics
Quantum physics emerged from atomic physics and, at times, the two are still identified. Meanwhile, quantum formalism has been applied successfully to molecular physics, solid state physics, astrophysics, nuclear physics, and to sub-nuclear or high-energy physics.
From a systematic point of view, quantum physics can be divided into three parts: the wave theory of motion (chapter 7), the theory of probability (chapter 9), and the investigation of the typical characters of material things and events. The quantum mechanical wave theory is basically not different from classical wave theory, except for the – indeed very important – recognition of the relation between energy and frequency, and the recognition of the general, modal character of the wave theory. The quantum theory of probability differs from the classical one because of the possibility of interference, and because of the new insight into the law-subject relation for stochastic processes.
These differences between classical and quantum physics are well-known, and widely discussed. But the third difference, the fact that classical mechanics as a modal theory of motion was unable to account for the typicality of physical things and events, has usually been overlooked. Neither can the modal theory of wave packets or the general theory of probability account for typical structures. To describe the typical characters of atoms and molecules, which came to the physicist’s attention not long before 1900 (after the chemists since John Dalton applied them in their own way (T&E 7.5), a completely different theory was required.
Therefore quantum physics did not really begin with the discovery of Planck’s constant in 1900, nor even with Einstein’s conjecture regarding the quantum nature of light in 1905. Rather, quantum physics began with the study of the atom by the spectroscopists, by Ernest Rutherford, Niels Bohr, Arnold Sommerfeld, and others. Bohr, for example, considered the stability of the atom to be the fundamental problem. By pursuing this problem as the central one, in 1913 and later, Bohr made his most remarkable contributions to the development of quantum physics. He made it clear that atomic stability cannot be accounted for by electrodynamics in the context of classical mechanics.
In this respect Bohr diverted sharply from the views of most of his contemporaries, including Max Planck and Albert Einstein. Planck continuously sought a reconciliation of the new experimental and theoretical results with classical physics, whereas Einstein, in a more revolutionary mood, was searching for a new unified theory embracing both electrodynamics and mechanics which would account for the new phenomena. In contrast, Bohr’s approach alone turned out to be fruitful, and so it is that he should be seen as the principal originator of the new theory.
This does not imply that the contributions of Planck and Einstein are negligeable, for the study of the typical structures depends on an insight into the disclosed modal aspects involved, resulting in the wave theory and in the theory of probability (chapters 7 and 9), both serving as a necessary basis for the theory of typical characters.
Realist and nominalist views on invisible things
Realists freely speak about electrons, atoms, nuclei, etc., assuming their individual reality. These are considered no less real than, e.g., rocks. In objection, nominalist physicists and philosophers would argue that, since one cannot directly observe such species, one should consider these (instrumentally) as theoretical constructs, which existence is not directly given, and therefore is not equivalent to the existence of directly visible or tactile things.
To my knowledge, such considerations are never directed towards the existence of stars and other celestial subjects. Yet the stars can only be seen as point-like sources of light even with the most powerful telescopes. In much the same way also electrons can be seen, e.g., as light spots on a TV-screen. In fact, everything known about stars (their mass, density, volume, chemical constitution, age, etc.) has been discovered in precisely the same way as our knowledge of electrons, atoms, etc. In both cases scientific knowledge is derived from instrumental measurements with the help of experimentally confirmed theories. Thus, if electrons are theoretical constructs, so are the stars.
In the 19th century physicists and philosophers like Ernst Mach and Friedrich Ostwald contested the individual existence of atoms and molecules. However, after Albert Einstein and Marian Smoluchowski gave a theoretical quantitative explanation of Brownian motion, and Jean Perrin used it to determine experimentally Avogadro’s number (the number of molecules in a mole), most physicists and philosophers became convinced of the reality of atoms and molecules.
Currently, it is already possible to obtain photographs of large molecules and even of separate atoms with a field-ion microscope. Thus the boundary has shifted. Just as we now know that the back of the moon exists, so, too, the individual existence of atoms and molecules has become unquestionable. Today, only electrons and other sub-atomic particles are considered, by some, to be mere theoretical constructs, whereas, apparently, nobody doubts the existence of quasars and black holes, except perhaps for some postmodern social-constructivitsts.
The individuality of physically qualified things and events cannot be proved as the result of a theoretical investigation (8.1). In this sense defenders of the theoretical construct argument are right: theories create concepts, not real things and events. Critical realism is empirical, accepting the existence of things on experimental arguments. The question is not whether elementary particles can be observed, but whether experiments show them to interact with other particles.
The idea of individually existing subjects is borrowed from pre-theoretic, daily experience. Atoms, electrons, etc., are not encountered in daily experience and, therefore, their individuality must be inferred by extrapolation. Once the existence of individual atoms or smaller systems has been established (on the basis of a variety of evidence), they should be considered as things which simply are smaller than the smallest things observable with ordinary means. Similarly, stars are considered to be individual subjects on a par with the sun, the only difference being that the earth’s distance from the stars is much greater than that from the sun. In other words, the fact that the existence of atoms and electrons, of stars and galaxies, of quarks and quasars, has been discovered by theoretically aided experiments and observations, does not imply that their existence is of a theoretical nature, but is solely a result of their very minute dimensions or their exceedingly vast distances.
The view that electrons etc. are merely theoretical constructs, if taken consistently, inevitably leads to agnosticism which is an irrefutable world view. Such a view can be countered by the pre-scientific conviction that the individual existence of anything real outside of ourselves is guaranteed by the faithfulness of the Creator to his creation. Herman Dooyeweerd’s concept of structures of individuality became as much characteristic for his Christian philosophy as the concept of modal aspects.
Yet, although the idea of individually existing subjects is borrowed from pre-theoretic, daily experience, common sense did not turn out to be a reliable guide in the investigation of characters. At the end of the 19th century, classical mechanics was considered the paradigm of science. Even then it was clear that daily experience was in the way of the development of electromagnetism, for instance. The many models of the ether were more an inconvenience than a stimulus for research.
When relativity theory and quantum physics unsettled classical mechanics, this led to uncertainty about the reliability of science. At first, the oncoming panic was warded off by the reassuring thought that the new theories were only valid in extreme situations. These situations were, for example, a very high speed, a total eclipse, or a microscopic size. However, astronomy cannot cope without relativity theory, and chemistry fully depends on quantum physics. All macroscopic properties and phenomena of solid-state physics can only be explained in the framework of quantum physics.
Largely, daily experience rests on habituation. In hindsight, it is easy to show that classical mechanics collided with common sense in its starting phase, for instance with respect to the law of inertia (13.1). Action at a distance in Newton’s Principia evoked the abhorrence of his contemporaries, but the 19th-century public did not experience any trouble with this concept. In the past, mathematical discoveries would cause heated discussions, but the rationality of irrational numbers or the reality of non-Euclidean spaces is now accepted almost as a matter of course.
This does not mean that common sense is always wrong in scientific affairs. The irreversibility of physical processes is part of daily experience. In the framework of the mechanist world view of the 19th century, physicists and philosophers have stubbornly but in vain tried to reduce irreversible processes to reversible motion, and to save determinism (8.1). This is also discernible in attempts to find (mostly mathematical) interpretations of quantum mechanics that allow of temporal reversibility and of determinism.
Since the 20th century, mathematics, science and technology dominate our society to such an extent, that new developments are easier to integrate in our daily experience than before. Science has taught common sense to accept that the characters of natural things and events are neither manifest nor evident. The hidden properties of matter and of living beings brought to light by the sciences are applicable in a technology that is accessible for anyone but understood by few. This technology has led to an unprecedented prosperity. Our daily experience adapts itself easily and eagerly to this dynamic development.
The shift from modal to specific laws and characters
In the history of science, a shift is observable from the search for universal laws, via structural laws, toward characters, determining processes besides structures. Even the investigation of structures is less ancient than might be expected. Largely, it dates from the 19th century. In mathematics, it resulted in the theory of groups (2.2), later to play an important part in physics and chemistry. Before the 20th century, scientists were more interested in observable and measurable properties of materials than in their structure. Initially, the concept of a structure was used as an explanans, as an explanation of properties. Later on, structure as explanandum, as object for research, came to the fore. During the 19th century, the atomic theory functioned to explain the properties of chemical compounds and gases. In the 20th century, atomic research was directed to the structure and functioning of the atoms themselves. Of course, people have always investigated the design of plants and animals. Yet, as an independent discipline, biology established itself not before the first half of the 19th century (chapter 12). Ethology, the science of animal behaviour, only emerged in the 20th century (chapter 13).
Mainstream philosophy does not pay much attention to structures. Philosophy of science is mostly concerned with epistemological problems (for instance, the meaning of models), and with the general foundations of science (1.1). A systematic philosophical analysis of characters as defined above is wanting. This is strange, for characters form the most important subject matter of 20th-century research, in mathematics as well as in the physical and biological sciences.
For the generic nature of things, processes and all that, no generally accepted word seems to exist. Mathematicians, physicists, and chemists are concerned with structures and symmetries. Biologists deal with the design of an organism. By characters, they mean the traits that organisms belonging to the same taxon have in common. Zoologists study the body plan of animals, and ethologists speak of patterns of behaviour or programs. Sociologists discuss systems in associations and society. As a common denominator, I adopt the word character for a generic set of laws and/or normative principles and norms characterizing similar things, events, relations, acts, artefacts, or associations. Having several meanings, the term character may give rise to misunderstandings, but the introduction of an entirely new word has disadvantages of their own. I prefer to add a new (though related) meaning to the existing word of character.
As a specific set of laws, a character determines the characteristic features of a specific thing, the conditions for its existence and its possible variations, its coming into being, development and perishing. Many kinds of events and processes have a character of their own. Usually one would define such a character by pointing out its essential properties. I shall not pursue this path. I introduce a character not as the essence of things or the nature of processes, but as the set of laws and/or normative principles and norms determining their internal and external relations. For instance, one can only establish the nature of a living being by looking for its relations to other living beings, to non-living things, and to many kinds of processes.
Characters and relation frames
The philosophy of the cosmonomic idea attempts to order the enormous diversity of characters with the help of sixteen relation frames. Six natural frames precede ten interhuman relationships to be discussed later (14.4). Quantitative and spatial relations, relative motions, physical or chemical interactions, genetic kinship, and informative connections turn out to be subjected to sets of general natural laws. These sets of general laws must be distinguished from the sets of specific laws constituting natural characters.
Each character will be primarily characterized by one of these relation frames. Mathematics studies quantitative, spatial, and kinetic characters, often applied in science. A molecule like DNA has primarily a physical character. Its secondary characteristic is its specific spatial shape, that of a double helix. Its biotic function is a tertiary characteristic, its disposition to play a part in biotic processes. The primary, secondary, and tertiary functioning according to the sixteen relation frames gives rise to a philosophical typology of characters.
Characters are never independent of each other. They are not autonomous. Each character is interlaced with other characters in a specific way. Mathematical symmetries play an important part in physical, chemical, and biotic processes. The character of an atomic nucleus is interlaced with that of electrons into the character of an atom. Characters of molecules are intertwined in the structure of living cells. In particular, it is relevant that the characters of more or less stable things are interlaced with characters of events and processes. Modern science is more concerned with changing than with stable systems.
As a set of natural laws, a natural character determines a subjective class of individuals and sometimes an objective ensemble of possible variations. Individuals may be things, plants or animals, events or processes, including numbers, spatial figures and signals.
The present section reconnoitres the concept of a character. Is it a structure? Why a set of laws? What is meant by a natural law? What is a class? What is an ensemble of possible variations? How does a character differ from a model? What is a specific type of characters?
Structure or character
By introducing the term character for the law side of a typical thing, event, or process, I intend to distinguish it from their subject side, their individuality. In common language, a structure of something is the manner in which a building or organism or other complete whole is actually constructed. This mainly spatial concept is much more restrictive than the structure for something, the concept of a set of laws distinguishing a specific thing from things of a different nature, for this distinction is not merely spatial. Some things like electrons have a character but not a structure. On the other hand, a solid like ice displays several crystalline structures. During its lifetime, an animal may change its structure drastically, according to its invariable character. The character of a thing determines under which circumstances it has a certain spatial structure. Contrary to a structure, a character does not merely express a thing’s spatial composition, but also its properties and its propensities; how it functions; how it comes into being, changes and perishes; its mean life time and its dependence on various circumstances. Moreover, the concept of a character is applicable to the nature of events, processes and relations, whereas structure is not. An event like the lighting of a match lacks a structure, even in common language, but it has a specific character.
A character is definitely more than a structure. Molecules differ because of their structure but even more because of their chemical properties, which belong to their character no less than their structure. Often the structure of a molecule determines its properties, but properties depend on circumstances as well. A material may be combustible above a certain temperature and incombustible otherwise. The structure of a material may depend on circumstances. The character of water implies it being a solid below 0oC, having no structure above 100oC, and in between having the structure of a liquid.
The structure of a living being depends on its age and sometimes on its sex. Distinguishing between character and structure allows one to say that the character of a living being determines the development of its structure, or to say that the sexes differ structurally. The character is the same for both and does not change. As far as the concept of structure applies to the subject side of reality, it can safely be assumed that in the course of the evolution structures emerge, whereas characters remain the same.
Characters sharing laws
A law of nature does not necessarily have a mathematical format, and it is not necessarily fundamental. In the most general sense, I consider each natural regularity to be an instance of a law of nature (T&E 8.6). The hereditary and species-specific behaviour of drakes during courting has a fixed pattern, recognizable for all ducks. As a law this pattern belongs to the character of the birds concerned. Not all natural laws take part in a character. The laws constituting a relation frame are not specific, but generally valid. For instance, it is a general law that the mass of a physical thing is equivalent to its energy, whereas it is a specific law that each electron has a rest mass equal to 9.109*10-31 kg.
A specific law often occurs in more than one character. All electrons have the same rest mass, electric charge, magnetic moment, and lepton number, according to four natural laws. Positrons have the same rest mass and magnetic moment but a different charge and lepton number. Electrons and neutrino’s have the same lepton number but different rest mass, charge and magnetic moment. Electrons, positrons and neutrino’s are fermions, but so are all particles that are not bosons. Therefore, it is never a single law but always a specific set of laws characterizing things or events of a certain kind.
In no way should one conceive of these sets as logical definitions. It is very well possible to define an electron by some properties like its mass and charge. However, such a definition says very little about the natural laws constituting its character. Besides the electron’s mass and charge, these laws concern its spin, magnetic moment, and lepton number as well. From the definition it does not follow that the electron is a fermion; that it has an antiparticle; that an electron can annihilate a positron; or that both belong to the first of three families of leptons and quarks. The laws constituting the character of electrons do not follow from a definition, but were discovered during a century of experimental and theoretical research. One can never be sure of knowing the character of a thing or event completely. In fact, knowledge of most characters is rather incomplete, even if it is possible to define them adequately.
Because a character is a set of laws, it is often possible to distinguish types or families of characters having laws in common. Clearly, fermions and bosons are different types of characters. The characters of leptons and quarks are grouped into three generations. Chemists recognize noble gases and halogens, acids, and bases. From a chemical point of view, all oxygen atoms have the same character, but nuclear physicists discern several isotopes of oxygen, each with its own character. Later on, a hierarchy of physical and chemical characters will be discussed (11.3). With respect to quantitative and spatial characters too, the concept of a hierarchy of characters can be applied (10.5).
A character determines a class of similar individuals
This chapter defines a natural character to be a set of unchangeable natural laws, specifically valid for a class of individuals, both actual and potential. The individual things, events or processes concerned are subject to the character. Individual things or processes cannot be taken apart from the laws valid for them. Conversely, a law expresses itself only in its subjects. Reality is two-sided, having a law-side and a subject-and-object-side. Like two sides of a coin, they cannot be separated from each other (1.3).
It is not easy to tell what makes a certain subject a unity, a totality, or a well-distinguished individual. In our daily experience, it is clear that a plant or an animal is such an individual. Natural experience knows the unity of a thing that comes into being and perishes, that maintains its identity while changing and is recognizable as an individual. However, for scientific purposes natural experience is not a reliable source of information. Common sense is not documented, and it cannot be legitimated in a scientifically justifiable way. Since the 19th century, science has discovered an increasing number of characters and corresponding individuals unknown to everyday experience, such as atoms and molecules, cells and neutron stars.
A class corresponding to a character is not a collection. It is not restricted to a certain number, to a limited place or to an interval of time. A class is no more temporal than the natural laws constituting the class. However, the individual things or events being elements of the class are by no means a-temporal. Each actual collection of similar individuals is a temporal subset of the class. For instance, it may serve as a sample for scientific research. If the sample consists of a single individual, it is an exemplar or specimen of the class. Individual things and events are intrinsically temporal, being unavoidably limited in number, space and time. Their character conditions the existence of the individuals in their temporal circumstances.
The character class, the class corresponding to a character, is complete. This means that each individual satisfying the laws of a character is an element of its character class. However, the members of this class are not necessarily actually existing individuals. In fact, a character class usually contains more potential than actual subjects, as well as past and future individual subjects.
Ensemble of possibilities
A character allows of a certain margin of variation. It provides room for the individuality of the things or events subject to the character. The margin of individual variation is relatively small for spatial and kinetic characters, larger for physically qualified ones, and even more for plants and animals. In order to specify this kind of variation, I borrow the concept of an ensemble from statistical mechanics.
The number of possibilities may be restricted. Besides the character, circumstances dependent on space and time may determine the ensemble of possibilities. Hence, an ensemble is not always a class. It is not always sensible to distinguish a class of individuals from an ensemble of possibilities. Sometimes each individual corresponds exactly with one possibility, such that the ensemble coincides with the character class.
The concept of an ensemble is especially relevant when statistics is applicable, distinguishing a possibility from its realization. This is only meaningful with respect to characters that are physically characterized, whether primary, secondary, or tertiary. The relative frequency by which possibilities are realized is called their probability (chapters 8, 9). This is a mathematical concept anticipating some kind of physical interaction. The theory of probability is extremely important for the study of characters. Sometimes, it is possible to design a theory for an ensemble and to calculate theoretical probabilities. More often, probabilities can only be determined in an empirical way.
The difference between things and events can now be specified. Whereas a thing has objective possibilities, in an event or a process a possibility is realized. A process is a complex of events. A thing is a characteristic unity, it has structural coherence and it maintains its identity during its motion. It has a certain stability and duration of existence. It comes into being, it changes, it generates other things, it influences its environment and it decays. An event is transitive and implies transformation and transport, generation, growth and behaviour.
Because the realization of a possibility always involves physical interactions, there are no quantitatively, spatially or kinetically qualified events. Even motion does not constitute an event but a relation.
The description of a character is usually called a model, although the word model has several other meanings in science. A model represents our knowledge of a character, sometimes our assumed or hypothetical knowledge. Often, a model is a simplified representation of the character, sufficient to solve a particular problem. The solution of the problem may lead us to construct a new model in order to solve other problems and to increase our knowledge of the character. In that case a model is a step in a research program (T&E 9.3).
Sometimes, a model is considered a description. However, in science a model is always a theory, a deductively connected set of propositions, including some law statements. A law statement is a human formulation of a natural law. Newton’s formulation of the law of gravity was different both from Galileo’s before him and Einstein’s after him.
Making the distinction of a natural law from a law statement and the distinction of a character from a model means that the philosophy exposed in this book includes a critical-realistic world view. A realist assumes that characters and other natural laws are part of reality, independent of human experience. On the other hand, scientists formulate law statements and construct models for the benefit of their research. Models are invented, characters are discovered. The natural laws constituting a character are not separated from concrete reality but are intrinsically connected to it. Characters can only be discovered investigating the individual things and processes concerned. This critical-realistic view confirms the empirical method of science. It accords with the Christian philosophical view that natural laws are given by God and can be discovered by humans.
10.3. Types of natural characters
The typology of characters as introduced by the philosophy of the cosmonomic idea will be developed in parts III and IV. It should then become clear whether this typology leads to a better understanding of natural and other characters, their coherence and their meaning. The typology depends on the serial order of the relation frames.
Each character has a primary, a secondary and a tertiary characteristic. Moreover, characters are mutually interlaced. Whereas the relation frames are serially ordered, the characters form a network.
Each character is primarily characterized by one of the relation frames, called the qualifying frame. For instance, periodic motion primarily characterizes a rhythm; interaction qualifies physical things and events; plants are primarily characterized by genetic relations, and animals by informed behaviour. In each character, these relations are specific; for example, a physical interaction may be electromagnetic.
For natural characters, the qualifying relation frame is the last one in which the thing concerned acts as a subject. In subsequent relation frames it is an object. A physically qualified thing like a molecule can only be an object in the relation frames succeeding the physical frame. Also a bird’s nest is not a subject with respect to biotic or psychic laws. It is not a living being, it has no ancestry or progeny, and it does not display behaviour. The bird’s nest is at most a subject to physical laws, whereas through the pair of birds, it is an object with respect to the biotic and psychic laws governing the birds’ behaviour. The birds construct the nest with a clear purpose, and it has a function in their reproduction. Therefore, the physical relation frame does not qualify it primarily as a physical subject. Rather, the psychic relation frame qualifies the bird’s nest primarily as a psychic object for subjective animal behaviour.
In principle, each relation frame qualifies a number of characters. According to a traditional viewpoint, there are only three natural kingdoms. These are the kingdoms of minerals, the kingdom of plants and the animal kingdom. However, I believe there are characters qualified by the quantitative, spatial or kinetic relation frame as well (10.5, 10.6). For instance, a triangle has a spatially qualified structure, whereas waves and oscillations have a kinetic character.
Except if it is quantitatively qualified, I shall secondarily characterize the character of an individual thing or event by the projection of the qualifying relation frame on a preceding one, called the founding frame. As many secondary types correspond with each primary type as relation frames precede the qualifying frame. For physically qualified characters, this means three secondary types of characters, respectively founded in projections on the numerical, the spatial or the kinetic relation frame. For instance, an electron is secondarily characterized by quantitative properties like charge, rest mass and magnetic moment, each having a strictly determined value. These properties characterize electrons and distinguish them from other particles like muons (11.2). The founding relation frame is just as typical for a character as its qualifying frame is.
However, mass, charge, and magnetic moment are physical magnitudes, determining how and to what extent an electron can interact with other things. For a physically qualified character, its quantitative foundation is physical as well. Hence, the secondary characteristic does not concern the preceding relation frame itself, but a projection of the qualifying frame onto the founding one.
Whereas the secondary characteristic concerns properties of things and events, the tertiary one concerns propensities. For instance, an electron has the property of having a fixed charge and rest mass, and it has the propensity to become part of an atom. Sometimes, the characters of two individuals are tuned to each other such that they can be interlaced (10.4). The tertiary characteristic of a thing or event means that as an object it may become a part of another thing or a process. An electron, for instance, is not an iron atom but has the disposition to have an objective function in an iron atom. Hence, the tertiary characteristic concerns a specific subject-object relation. The nomological distinction between a subject and an object refers to some law (1.6). Each iron atom is directly subject to the character of iron atoms. On the other hand, its electrons and the iron nucleus are only as objects subjected to the set of laws for an iron atom. Besides their primary and secondary characteristics, nuclei and electrons have a tertiary characteristic. It is their disposition, tendency or affinity to become part of an atom. They are tuned to the character of the atoms to which they may belong.
A second example concerns the molecules playing a part in a living cell, in particular DNA and RNA molecules. Their primary characteristic is physical, for the so-called biomolecules are qualified by interaction. Their foundation is spatial, and the discovery of the double helix structure of DNA molecules by Francis Crick and James Watson (1953) is rightly considered a big step towards the understanding of the functioning of living cells. Nevertheless, much more interesting is the part these molecules play in biotic processes, like the organized assemblage of macromolecules, the fission of cells, and the development of a multicellular plant. That is their disposition, their tertiary characteristic.
Whereas a (secondary) foundation refers to an earlier relation frame, a (tertiary) disposition often anticipates a later one, either later than the qualifying relation frame, or later than the founding one. The spatial and physical structure of a bird’s nest anticipates the psychically qualified behaviour of the birds using it. The quantitatively foundedcharacter of electrons anticipates the spatially founded characters of atoms. If a character qualified by one relation frame is interlaced with a character qualified by a later frame, the former character has an objective function in the latter one. This is, for instance, the case with the character of (physically qualified) molecules like DNA in the character of (biotically qualified) living cells.
Many a thing or process experienced as a coherent individual unit turns out to be an aggregate of individuals. An individual thing is only an aggregate if it has not a character of its own. Examples are a pebble, a wood, or a herd of goats. A process is an aggregate as well. It is a chain of connected events. For a physicist or a chemist, a plant is an aggregate of widely differing molecules, but for a biologist, a plant is a characteristic whole with a specific character.
It makes sense to distinguish homogeneous from heterogeneous aggregates. A homogeneous aggregate is a coherent collection of similar individuals, for instance a wave packet conducting the motion of a photon or an electron; or a gas consisting of similar molecules; or a population of plants or animals of the same species. A heterogeneous aggregate consists of a coherent collection of dissimilar individuals, for instance a gaseous mixture like air, or an ecosystem in which plants and animals of various species live together.
10.4. Interlacement of characters
Even apart from the existence of aggregates, an individual never satisfies the simple character type described in section 10.3. Because of its tertiary characteristic, each character is interlaced with other characters. On the one side, character interlacement is a relation of dependence, as far as the composed character cannot exist without the characters interlaced in or with it. The character of a molecule exists thanks to the characters of its atoms. On the other hand, character interlacement rests on the disposition of a thing or event to become a part of a larger whole. If it actualizes its disposition, it retains its primary and secondary character largely. Sometimes characters are so strongly interlaced that one had better speak of a dual character. Several types of character interlacement can be distinguished.
First type of interlacement
In the first type of interlacement, the whole has a qualifying relation frame different from those of the characters interlaced in the whole. In part I, chapter 7 this phenomenon was discussed with respect to the wave-particle duality, where the particle character is physically qualified (particles interact with each other, which waves do not) and the wave character is primarily kinetic. As a measure of probability, the wave character anticipates physical interactions.
A second example is the physically qualified character of a DNA molecule being interlaced with the biotic character of a living cell. The molecule is physically qualified, the cell biotically. Their characters cannot be understood apart from each other. The cell is a biotic subject, the DNA-molecule a biotic object, the carrier of the genome, i.e., the ordered set of genes. A cell without DNA cannot exist, whereas DNA without a cell has no biotic function. The cell and the DNA molecule are mutually interlaced in a characteristic subject-object relation.
This type of interlacement occurs in processes as well. For instance, the character of each biotic process is intertwined with that of a biochemical process. The behaviour of animals is interlaced with those of processes in their nervous system (chapter 13).
Second type of interlacement
The second type of interlacement occurs if one or more characters having the same qualifying relation frame but different foundations form a single whole.
For example, the character of an atom is interlaced with the characters of its nucleus and electrons. All these characters are physically qualified. The electron’s character is quantitatively founded, whereas the character of the nucleus is spatially founded like that of the atom. However, in the structure of the atom, the nucleus acts like a unit having a specific charge and mass, as if it were quantitatively founded, like the electrons. The (in this sense) quantitatively founded character of the nucleus and that of the electrons anticipate the spatially founded character of the atom. The nucleus and the electrons have a characteristic subject-subject relation, interacting with each other. Nevertheless, they do not interact with the atom of which they are a part, for they have a subject-object relation with the atom, and interaction is a subject-subject relation.
Third type of interlacement
In the third type of interlacement of characters, there is no anticipation of one relation frame to another. For instance, in the interlacement of atomic groups into molecules all characters are physically qualified and spatially founded. For another example, the character of a plant is interlaced with those of its organs like roots and leaves, tissues and cells. Each has its own biotic character, interlaced with that of the plant as a whole. One finds a comparable hierarchy of characters in two-, three- or more-dimensional spatial figures. A square is a two-dimensional subject having an objective function as the side of a cube.
Characters of processes are interlaced with the characters of the things involved. Individual things come into existence, change and perish in specific processes. Complex molecules come into existence by chemical processes between simpler molecules. A cell owes its existence to the never ending process called metabolism: respiration, photosynthesis, transport of water, acquisition of food, and secretion of waste, dependent on the character of the cell.
Usually processes occur on the substrate of things, and many thing-like characters depend on processes. Quantum physics proves that even the most elementary particles are continuously created and annihilated. The question of which is the first, the thing or the process, has no better answer than that of a chicken and an egg. There is only one cosmos in which processes and things occur, generating each other and having strongly interlaced characters.
When a character is interlaced with another one its properties change without disappearing entirely. If an atom becomes part of a molecule, its character remains largely the same, even if its distribution of charge is marginally adapted.
It is interesting that molecules have properties that the composing atoms do not have. A water molecule has properties which are absent in the molecules or atoms of hydrogen or oxygen. Water vapour is a substance completely different from a mixture of hydrogen and oxygen. This universally occurring phenomenon is called emergence. It plays a part in discussions between reductionists and holists, not only in biology or in anthropology.
Emergence is expressed in the symmetry of a system, for instance. A free atom has the symmetry of a sphere, but this is no longer the case with an atom being a part of a molecule. The atom adapts its symmetry to that of the molecule by lowering its spherical symmetry. The symmetry of the molecule is not reducible to that of the composing atoms. Symmetries (not only spatial ones) and symmetry breaks play an important part in physics and chemistry. Constraints like initial and boundary conditions are possible causes of a symmetry break.
Scientific classification is different from the typology of characters based on universal relation frames. Classification means the formation of sets of characters based on specific similarities and differences. This is possible because each character is a set of laws, which it partly shares with other characters. A set of characters is determined by having some specific laws in common. An example of a specific classification is the biological taxonomy of living beings according to species, genera, etc. Other examples are the classification of chemical elements in the periodic system; of elementary particles in generations of leptons and quarks; and of solids according to their crystalline structure.
Because specific classifications rest on specific laws, the chemical classification of the elements is hardly comparable to the biological classification of species. The general typology of characters developed in this treatise is applicable to widely different branches of natural science and may therefore lead to a deepened understanding of characters. Moreover, the typology provides insight into the coherence and the meaning of characters.
Each individual thing is either a subject or an object with respect to any relation frame in a way determined by its primary, secondary, and tertiary characteristics. Individual things and events present themselves in their relations to other things and events, allowing us to establish their identity.
The meaning of a thing or event can only be found in its connection with other things and events, and with the laws valid for them. In addition, the meaning of a character comes to the fore only if its interlacements with other characters are taken into account. For instance, it is possible to restrict a discussion of water to its physical and chemical properties. Its meaning, however, will only become clear if one includes in the discussion that water is a component of many other materials. Water plays a part in all kinds of biotic processes, and it appeases the thirst of animals and humans. Water has a symbolic function in our language and in many religions. The study of the character of water is not complete if restricted to the physical and chemical properties. Its meaning is quite open if one considers the characteristic dispositions of water as well.
Likewise, the meaning of individual things and events is only clear in their lawful relations with other individuals. These relations are subsumed in relation frames, which are of profound significance for the typology of characters. The meaning of the cosmos is not only found in the religious concentration of humankind to the origin of the creation, but also in the coherence of relation frames and of characters.
Rejection of determinism, essentialism, reductionism, and a priorism
The theory developed in part II of this book rests on the presupposition that a character as a set of laws determines the specific nature of things or processes. Such a set leaves room for individual variation. Hence, the theory is not deterministic (8.1). Reality has both a law side and a subject side that cannot be separated. Both are always present. In each thing and each process, lawfulness besides individuality is present.
The theory of characters is not essentialist either. The primary characteristic of each character is not determined by a property of the thing or process itself. Rather, its relations with other things or processes, subject to the laws of a relation frame, are primarily characteristic of a character. Besides, the secondary and tertiary characteristics concern relations subject to general and specific laws as well. In particular the tertiary characteristic, the way by which a character is interlaced with other characters, provides meaning to the things and processes concerned. Essentialism seeks the meaning (the essence) of characters in the things and events themselves, attempting to catch them into definitions. In a relational philosophy, definitions do not have a high priority.
Next, the theory of characters is not reductionist. This statement may be somewhat too strong, for there is little objection to raise against constitutive reductionism. This conception states that all matter consists of the same atoms or sub-atomic particles, and that physical and chemical laws act on all integration levels. The theory of characters supposes that the laws for physical and chemical relations cannot be reduced to laws for quantitative, spatial, and kinetic relations. It asserts the existence of laws for biotic and psychic relations transcending the physical and chemical laws. It is at variance with a stronger form of reductionism, presupposing that living organisms only differ from molecules by a larger degree of complexity, whether or not supplied by the phenomena of supervenience and emergence. I believe that the phenomenon of character interlacement gives a better representation of reality.
Finally, the theory of characters cannot be argued on a priori grounds. As an empirical theory, it should be justified a posteriori, by investigating whether it agrees with scientific results, as will be seen in the next three chapters, after a brief review of some mathematical characters.
10.5. Numerical and spatial characters
Mathematics knows several structures that I consider quantitative characters. Among these, the character of mathematical groups expressing symmetries is of special interest to natural science, as was argued in part I.
A group is a set of elements that can be combined such that each pair generates a third element. In the world of numbers, such combinations are addition or multiplication (2.2).
The character of a group is primarily numerically qualified. It has no secondary foundation, since no relation frame precedes the numerical one. Because of the phenomenon of isomorphy it has the tertiary disposition to be interlaced with spatial, kinetic, and physical characters.
In part I, chapter 2 we used the idea of groups to investigate modal numerical and spatial relations. Apparently, characters qualified by these aspects can be useful to understand the relation frames themselves. This should not be surprising, because modality and typicality are two sides of the selfsame reality (1.4). Groups are powerful instruments wherever symmetry is at stake. Besides in the relation frames, they are helpful in the understanding of probability, and in the study of characters having an internal symmetrical structure.
Mathematics also studiesspatially qualified characters, like those of triangles or circles. Because these are interlaced with kinetic, physical, or biotic characters, spatial characters are equally important to science. This also applies to spatial relations concerning the position and posture of one figure with respect to another one. A characteristic point, like the centre of a circle or a triangle, represents the position of a figure objectively. The distance between these characteristic points objectifies the relative position of the circle and the triangle. It remains to stipulate the posture of the circle and the triangle, for instance with respect to the line connecting the two characteristic points. A co-ordinate system is an expedient to establish spatial positions by means of numbers.
Spatial relations are rendered quantitatively by means of magnitudes like distance, length, area, volume, and angle. These objective properties of spatial subjects and their relations refer directly (as a subject) to numerical laws and indirectly (as an object) to spatial laws.
Science and technology prefer to define magnitudes satisfying quantitative laws. In order to make calculations with a spatial magnitude, it has to be projected on a suitable set of numbers (integral, rational, or real), such that spatial operations are isomorphic to arithmetical operations like addition or multiplication. This is only possible if a metric is available, a law to find magnitudes and their combinations (3.4).
For many magnitudes, an isomorphic projection on a group turns out to be possible. For magnitudes having only positive values (e.g., length, area or volume), a multiplication group is suitable. For magnitudes having both positive and negative values (e.g., position), a combined addition and multiplication group is feasible. For a continuously variable magnitude, this concerns a group of real numbers. For a digital magnitude like electric charge, the addition group of integers may be preferred. It would express the fact that charge is an integral multiple of the electron’s charge, functioning as a unit.
Every metric needs an arbitrarily chosen unit. Each magnitude has its own metric, but various metrics are interconnected. The metrics for area and volume are reducible to the metric for length. The metric for speed is composed from the metrics of length and time. Connected metrics form a metric system.
If a metric system is available, the government or the scientific community may decide to prescribe a metric to become a norm, for the benefit of technology, traffic and commerce. Processing and communicating of experimental and theoretical results requires the use of a metric system.
The shape of a spatial figure functions as an elementary example of a character. A spatial character has both a primary and a secondary characteristic. The tertiary characteristic plays an increasingly complex part in the path of a specific motion, the shape of a crystal, the morphology of a plant or the body structure of an animal. Besides, even the simplest figures display a spatial interlacement of their characters.
A spatial figure has the profile of a thing-like subject. Its shape determines its character. Consider a simple plane triangle in an Euclidean space. The character of a triangle constitutes a set of widely different triangles, having different angles, linear dimensions, and relative positions. This set is easily distinguished from related sets of e.g., squares, ellipses, or pyramids. Clearly, the triangle’s character is primarily spatially characterized and secondarily quantitatively founded. Thirdly, a triangle has the disposition to have an objective function in a three- or more-dimensional figure.
A triangle is a two-dimensional spatial thing, directly subject to spatial laws. The triangle is bounded by its sides and angular points, which have no two-dimensional extension but determine the triangle’s objective magnitude. Quantitatively, the triangle is determined by the number of its angular points and sides, the magnitude of its angles, the length of its sides and its area.
With respect to the character of a triangle, its sides and angular points are objects, even if they are in another context subjects. Their character has the disposition to become interlaced with that of the triangle.
A triangle has a structure or character because its objective measures are bound, satisfying restricting laws or constraints. Partly this is a matter of definition, a triangle having three sides and three angular points. This definition is not entirely free, for a ‘biangle’ as a two-dimensional figure does not exist and a quadrangle may be considered a combination of two triangles. However, there are other lawlike relations not implied by the definition, for instance the law that the sum of the three triangles equals p, the sum of two right angles. This is a specific law, only valid for plane triangles.
A triangle is a whole with parts. As observed, the relation of a whole and its parts is not to be confused with a subject-object relation. It makes no sense to consider the sides and the angular points as parts of the triangle. With respect to a triangle, the whole-part relation has no structural meaning. In contrast, a polygon is a combination of triangles being parts of the polygon. Therefore, a polygon has not much more structure than it derives from its component triangles. The law that the sum of the angles of a polygon having n sides equals (n-2)p is reducible to the corresponding law for triangles.
Different types of triangles
Two individual triangles can be distinguished in three ways, by their relative position, their relative magnitude, and their different shape. I shall consider two mirrored triangles to be alike.
Relative position is not relevant for the character of a triangle. We could just as well consider its relative position with respect to a circle or to a point as to another triangle. Relative position is the universal spatial subject-subject relation. It allows of the identification of any individual subject. Often, the position of a triangle will be objectified, e.g. by specifying the positions of the angular points with respect to a co-ordinate system.
Next, triangles having the same shape can be distinguished by their magnitude. This leads to the secondary variation in the quantitative foundation of the character.
Finally, two triangles may have different shapes, one being equilateral, the other rectangular, for example. This leads to the primary variation in the spatial qualification of the triangle’s character. Triangles are spatially similar if they have equal angles. Their corresponding sides have an equal ratio, being proportional to the sinuses of the opposite angles.
For any polygon, the triangle can be considered the primitive form. It displays a primary spatial variability in its shape and a secondary quantitative variability in its magnitude. Another primitive form is the ellipse, with the circle as a specific variation.
There are irregular shapes as well, not subject to a specific law. These forms have a secondary variability in their quantitative foundation, but lack a lawlike primary variation regarding the qualifying relation frame.
Like two triangles can be different in three respects, a triangle can be changed in three ways: by displacement (translation, rotation and/or mirroring), by making it larger or smaller, or by changing its shape, i.e., by transformation. A transformation means that the triangle becomes a triangle with different angles or it gets an entirely different shape. Displacement, enlargement or diminishment and transformation are spatial expressions anticipating actual events.
An operator describes a characteristic transformation, if coordinates and functions represent the position and the shape of the figure. The character of a spatial transformation preserving the shape of the figure is interlaced with the character of an operator having eigenfunctions and eigenvalues.
All displacements of a triangle in a plane form a group isomorphic to the addition group of two-dimensional vectors. All rotations, reflections and their combinations constitute groups as well. Enlargements of a given triangle form a group isomorphic to the multiplication group of positive real numbers. (A subgroup is isomorphic to the multiplication group of positive rational numbers).
A separate class of spatial figures is called symmetric, e.g., equilateral and isosceles triangles. Symmetry is a property related to a spatial transformation such that the figure remains the same in various respects. Without changing, an equilateral triangle can be reflected in three ways and rotated about two angles. An isosceles triangle has only one similar operation, reflection, and is therefore less symmetric. A circle is very symmetric, because an infinite number of rotations and reflections transform it into itself.
The theory of groups renders good services to the study of these symmetries. Consider the group consisting of only three elements, I, A and B, such that AB=I, AA=B, BB=A. This becomes transparent if an interpretation of the elements is given. This could be the rotation symmetry of an equilateral triangle, A being an anti-clockwise rotation of p/3, B of 2p/3. The inverse is the same rotation clockwise. The combination AB is the rotation B followed by A, giving I, the identity. Clearly, the character of this group has the disposition of being interlaced with the character of the equilateral triangle. However, this triangle has more symmetry, such as reflections with respect to a perpendicular. This yields three more elements for the symmetry group, now consisting of six elements. The rotation group I, A, B is a subgroup, isomorphic to the group consisting of the numbers 0, 1 and 2 added modulo 3. The group is not only interlaced with the character of an equilateral triangle, but with many other spatial figures having a threefold symmetry, as well as with the group of permutations of three objects. In turn, the character of an equilateral triangle is interlaced with that of a regular tetrahedron. The symmetry group of this triangle is a subgroup of the symmetry group of the tetrahedron.
A group expresses spatial similarity as well. The combination procedure consists of the multiplication of all linear dimensions with the same positive real or rational number, leaving the shape invariant. The numerical multiplication group of either rational or real positive numbers is interlaced with a spatial multiplication group concerning the secondary foundation of figures.
The translation operator, representing a displacement by a vector, is an element of various groups, e.g., the Euclidean group mentioned before. Solid-state physics applies translation groups to describe the regularity of crystals. This implies an interlacement of the quantitative character of a group with the spatial character of a lattice and with the physical character of a crystal. The translation group for this lattice is an addition group for spatial vectors. It is isomorphic to a discrete group of number vectors, which components are not real or rational but integral. The crystal’s character has the disposition to be interlaced with the kinetic wave character of the X-rays diffracted by the crystal. As a consequence, this kind of diffraction is only possible for a discrete set of wave lengths.
The kinetic space for waves is called a medium (and sometimes a field), and the physical space for specific interactions is called a field. For the study of physical interactions, spatial symmetries are very important. For instance, in classical physics this is the case with respect to gravity (Newton’s law), the electrostatic force (Coulomb’s law) and the magnetostatic force. Each of these forces is subject to an inverse square law (T&E 4.3). This law expresses the isotropy of physical space. In all directions, the field is equally strong at equal distances from a point-like source, and the field strength is inversely proportional to the square of the distance. About 1830, Carl-Friedrich Gauss developed a method allowing of calculating the field strength of combinations of point-like sources. He introduced the concept of flux through a surface, popularly expressed, the number of field lines passing through the surface. Gauss proved that the flux through a closed surface around one or more point-like sources is proportional to the total strength of the sources, independent of the shape of that surface and the position of the sources. This symmetry property has some important consequences.
Outside the sphere, a homogeneous spherical charge or mass causes a field that is equal to that of a point-like source concentrated in the centre of the sphere. Within the sphere, the field is proportional to the distance from the centre. Starting from the centre, the field initially increases linearly, but outside the sphere, it decreases quadratically. For gravity, Isaac Newton had derived this result by other means.
For magnetic interaction, physicists find empirically that the flux through a closed surface is always zero. This means that within the surface there are as many positive as negative magnetic poles. Magnetism only occurs in the form of dipoles or multipoles. There is no law excluding the existence of magnetic monopoles, but experimental physics has never found them.
In the electrical case, the combination of Gauss’s law with the existence of conductors leads to the conclusion that in a conductor carrying no electric current the electric field is zero. All net charge is located on the surface and the resulting electric field outside the conductor is perpendicular to the surface. Therefore, inside a hollow conductor the electric field is zero, unless there is a net charge in the cavity. Experimentally, this has been tested with a large accuracy. Because this result depends on the inverse square law, it has been established that the exponent in Coulomb’s law differs less than 10-20 from 2. If there is a net charge in the cavity, there is as much charge (with reversed sign) on the inside surface of the conductor. It is distributed such that in the conductor itself the field is zero. If the net charge on the conductor is zero, the charge at the outside surface equals the charge in the cavity. By connecting it with the ‘earth’, the outside can be discharged. Now outside the conductor the electric field is zero, and the charge within the cavity is undetectable. Conversely, a space surrounded by a conductor is screened from external electric fields.
Gauss’s law depicts a purely spatial symmetry and is therefore only applicable in static or quasi-static situations. James Clerk Maxwell combined Gauss’s law for electricity and magnetism with André-Marie Ampère’s law and Michael Faraday’s law for changing fields. As a consequence, Maxwell found the laws for the electromagnetic field. These laws are not static, but relativistically covariant, as Albert Einstein established.
Spin is a well-known property of physical particles. It derives its name from the now as naive considered assumption that a particle spins around its axis. If the particle is subject to electromagnetic interaction, a magnetic moment accompanies the spin, even if the particle is not charged. A neutron has a magnetic moment, whereas a neutrino has not. Spin is an expression of the particle’s rotation symmetry, and is similar to the angular momentum of an electron in its orbit in an atom. A pion has zero spin and transforms under rotation like a scalar. The spin of a photon is 1 and it transforms like a vector. The hypothetical graviton’s spin is twice as large, behaving as a tensor at rotation. These particles, called bosons, have symmetrical wave functions (11.6). Having a half-integral spin (as is the case with, e.g., an electron or a proton), a fermion’s wave function is antisymmetric. It changes of sign after a rotation of 2p. This phenomenon is unknown in classical physics.
The reality of mathematically qualified typical subjects
The question of whether figures and kinetic subjects are real usually receives a negative answer. The view that only physical things are real is a common form of physicalism.
First, this is the view of natural experience, which appears to accept only tangible matters to be real. Nevertheless, without the help of any theory, everybody recognizes typical shapes like circles, triangles or cubes. This applies to typical motions like walking, jumping, rolling or gliding as well.
Second, reality is sometimes coupled to observability. Now shapes are very well observable, albeit a physical substrate is always needed for any actual observation. Moreover, it would be an impoverishment to restrict our experience to what is directly observable. Human imagination is capable of representing many things that are not directly observable. For instance, people are capable of interpreting drawings of two-dimensional figures as three-dimensional objects. Although a movie consists of a sequence of static pictures, one sees people moving. Even things that have no material existence can be observed, like a rainbow.
Third, the view that shapes are not real is strongly influenced by Plato, Aristotle, and their medieval commentators. According to Plato, spatial forms are invisible, but more real than observable phenomena. In contrast, Aristotle held that forms determine the nature of the things, having a material basis as well. Moreover, the realization of an actual thing requires an operative cause. Hence, according to Aristotle, all actually existing things have a physical character.
In opposition, I maintain that in the cosmos everything is real that answers the laws of the cosmos. Then numbers, groups, spatial figures, and motions are no less real than atoms and stars.
But are these natural structures? It cannot be denied that the concept of a circle or a triangle is developed in the course of history, in human cultural activity. Yet I consider them to be natural characters, which existence humanity has discovered, like it discovered the characters of atoms and molecules.
Reality is a theoretical concept. It implies that the temporal horizon is much wider than the horizon of our individual experience, and in particular much wider than the horizon of natural experience. By scientific research, we enlarge our horizon, discovering characters that are hidden from natural experience. Nevertheless, such characters are no less real than those known to natural experience are.
10.6. Kinetic characters
Periodicity is the distinguishing mark of each primary kinetic character with a tertiary physical characteristic. The motion of a mechanical pendulum, for instance, is primarily characterized by its periodicity and tertiarily by gravitational acceleration. For such an oscillation, the period is constant if the metric for kinetic time is subject to the law of inertia, as follows from an analysis of pendulum motion. The character of a pendulum is applied in a clock. The dissipation of energy by friction is compensated such that the clock is periodic within a specified margin.
Kepler’s laws determine the character of periodic planetary motion. Strictly speaking, these laws only apply to a system consisting of two subjects, a star with one planet or binary stars. Both Newton’s law of gravity and the general theory of relativity allow of a more refined analysis. Hence, the periodic motions of the earth and other systems cannot be considered completely apart from physical interactions. However, in this section I shall abstract from physical interaction in order to concentrate on the primary and secondary characteristics of periodic motion.
Uniform circular motion
The simplest case of a periodic motion appears to be uniform circular motion. Its velocity has a constant magnitude whereas its direction changes constantly. Ancient and medieval philosophy considered uniform circular motion to be the most perfect, only applicable to celestial bodies. 17th-century classical mechanics discovered uniform rectilinear motion to be more fundamental, the velocity being constant in direction as well as in magnitude. Christiaan Huygens assumed that the outward centrifugal acceleration is an effect of circular motion. Robert Hooke and Isaac Newton demonstrated the inward centripetal acceleration to be the cause needed to maintain a uniform circular motion (T&E 3.6).
Not moving itself, the circular path of motion is simultaneously a kinetic object and a spatial subject. The position of the centre and the magnitude and direction of the circle’s radius vector determine the spatial position of the moving subject on its path. The radius is connected to magnitudes like orbital or angular speed, acceleration, period and phase. These quantitative properties allow of calculations and an objective representation of motion.
A uniform circular motion can be constructed as a composition of two mutually perpendicular linear harmonic motions, having the same period and amplitude and a phase difference of one quarter. But then circular uniform motion turns out to be merely a single instance of a large class of two-dimensional harmonic motions. A similar composition of two harmonics – having the same period but different amplitudes or a phase difference other than one quarter – does not produce a circle but an ellipse. One can also make a composition of two mutually perpendicular oscillations with different periods. Now the result is a so-called Lissajous figure, if and only if the two periods have a harmonic ratio, i.e., a rational number. Only then, the path of motion is a closed curve. If the proportion is an octave (1:2), then the resulting figure is a lemniscate (a figure eight). The Lissajous figures derive their specific regularity from periodic motions. Clearly, the two-dimensional Lissajous motions constitute a kinetic character. This character has a primary rational variation in the harmonic ratio of the composing oscillations, as well as a secondary variation in frequency, amplitude and phase. It is interlaced with the character of linear harmonic motion and several other characters. The structure of the path like the circle or the lemniscate is primarily spatial and secondarily quantitatively founded. A symmetry group is interlaced with the character of each Lissajous-figure, the circle being the most symmetrical of all.
In all mentioned characters, a typical subject-object relation determines an ensemble of possible variations. In the structure of the circle, the circumference has a fixed proportion to the diameter. This allows of an unbounded variation in diameter. In the character of the harmonic motion, the period (or its inverse, the frequency) occurs as a typical magnitude, allowing of an unlimited variability in period as well as a bounded variation of phase. Varying the typical harmonic ratio results in an infinite but denumerable ensemble of Lissajous-figures.
Linear harmonic oscillation
A linear harmonic oscillation is quantitatively represented by a harmonic function. This is a sine or cosine function or a complex exponential function, being a solution of a differential equation. This equation, the law for harmonic motion, concerns mechanical or electronic oscillations, for instance. Primarily, a harmonic oscillation has a specific kinetic character. It is a special kind of motion, characterized by its law and its period. An oscillation is secondarily characterized by magnitudes like its amplitude and phase, not determined by the law but by accidental initial conditions. Hence, the character of an oscillation is kinetically qualified and quantitatively founded.
The harmonic oscillation can be considered the basic form of any periodic motion, including the two-dimensional periodic motions discussed above. In 1822, Joseph Fourier demonstrated that each periodic function is the sum or integral of a finite or infinite number of harmonic functions. The decomposition of a non-harmonic periodic function into harmonics is called Fourier analysis.
A harmonic oscillator has a single natural frequency determined by some specific properties of the system. This applies, for instance, to the length of a pendulum; or to the mass of a subject suspended from a spring together with its spring constant; or to the capacity and the inductance in an electric oscillator consisting of a capacitor and a coil. This means that the kinetic character of a harmonic oscillation is interlaced with the physical character of an artefact.
Accounting for energy dissipation by adding a velocity-dependent term leads to the equation for a damped oscillator. Now the initial amplitude decreases exponentially. In the equation for a forced oscillation, an additional acceleration accounts for the action of an external periodic force. In the case of resonance, the response is maximal. Now the frequency of the driving force is approximately equal to the natural frequency. Applying a periodic force, pulse or signal to an unknown system and measuring its response is a widely used method of finding the system’s natural frequency, revealing its characteristic properties.
An oscillation moving in space is called a wave. It has primarily a kinetic character, but contrary to an oscillation it is secondarily founded in the spatial relation frame. Whereas the source of the wave determines its period, the velocity of the wave, its wavelength and its wave number express the character of the wave itself. The wave velocity has a characteristic value independent of the motion of the source. It is a property of the medium, the kinetic space of a wave that specifically differs from the general kinetic space as described by the Galileo or Lorentz group.
A wave has a variability expressed by its frequency, phase, amplitude, and polarization. During the motion, the amplitude may decrease. For instance, in a spherical wave the amplitude decreases in proportion to the distance from the centre.
Waves do not interact with each other, but are subject to superposition. This is a combination of waves taking into account amplitude as well as phase. Superposition occurs when two waves are crossing each other. Afterwards each wave proceeds as if the other had been absent. Interference is a special case of superposition, and is usually only possible if the interfering waves have a common source. Now the waves concerned have exactly the same frequency as well as a fixed phase relation. If the phases are equal, interference means an increase of the net amplitude. If the phases are opposite, interference may result in the mutual extinction of the waves.
Just like an oscillation, each wave has a tertiary, usually physical disposition. This explains why waves and oscillations give a technical impression, because technology opens dispositions. During the 17th century, the periodic character of sound was discovered in musical instruments. The relevance of oscillations and waves in nature was only fully realized at the beginning of the 19th century. This happened after Thomas Young and Augustin Fresnel brought about a break-through in optics by discovering the wave character of light in quite technical experiments (T&E 6.4). Since the end of the same century, oscillations and waves dominate communication and information technology.
Interlacement of oscillations and waves
It will be clear that the characters of waves and oscillations are interlaced with each other. A sound wave is caused by a loudspeaker and strikes a microphone. Such an event has a physical character and can only occur if a number of physical conditions are satisfied. However, there is a kinetic condition as well. The frequency of the wave must be adapted to the oscillation frequency of the source or the detector. The wave and the oscillating system are correlated. This correlation concerns the property they have in common, i.e., their periodicity, their primary kinetic qualification.
Sometimes an oscillation and a wave are directly interlaced, for instance in a violin string. Here the oscillation corresponds to a standing wave, the result of interfering waves moving forward and backward between the two ends. The length of the string determines directly the wavelength and indirectly the frequency, dependent on the string’s physical properties determining the wave velocity. Amplified by a sound box, this oscillation is the source of a sound wave in the surrounding air having the same frequency. In fact, all musical instruments perform according to this principle. The wave is always spatially determined by its wavelength. The length of the string fixes the fundamental tone (the keynote or first harmonic) and its overtones. The frequency of an overtone is an integral number times the frequency of the first harmonic.
A wave equation represents the law for a wave, and a real or complex wave function represents an individual wave. Whereas the equation for oscillations only contains derivatives with respect to time, the wave equation also involves differentiation with respect to spatial co-ordinates. Usually a linear wave equation provides a good approximation for a wave, for example, the equations for the propagation of light, the Schrödinger equation, and the Dirac equation. If j and f are solutions of a linear wave equation, then aj+bf is a solution as well, for each pair of real (or complex) numbers a and b. Hence, a linear wave equation has an infinite number of solutions, an ensemble of possibilities. Whereas the equation for an oscillation determines its frequency, a wave equation allows of a broad spectrum of frequencies. The source determines the frequency, the initial amplitude and the phase. The medium determines the wave velocity, the wavelength and the decrease of the amplitude when the wave proceeds away from the source.
Events having their origin in relative motions may be characteristic or not. A solar or lunar eclipse depends on the relative motions of sun, moon and earth. It is accidental and probably unique that the moon and the sun are equally large as seen from the earth, such that the moon is able to cover the sun precisely. Such an event does not correspond to a character. However, wave motion gives rise to several characteristic events satisfying specific laws.
Willebrord Snell’s and David Brewster’s laws for the refraction and reflection of light at the boundary of two media only depend on the ratio of the wave velocities, the index of refraction. Because this index depends on the frequency, light passing a boundary usually displays dispersion, like in a prism. Dispersion gives rise to various special natural phenomena like a rainbow or a halo, or artificial ones, like Newton’s rings.
If the boundary or the medium has a periodic character like the wave itself, a special form of reflection or refraction occurs if the wavelength fits the periodicity of the lattice. In optical technology, diffraction and reflection gratings are widely applied. Each crystal lattice forms a natural three-dimensional grating for X-rays, if their wavelength corresponds to the periodicity of the crystal lattice according to William Bragg’s law.
These are characteristic kinetic phenomena, not because they lack a physical aspect, but because they can be explained satisfactorily by a kinetic theory of wave motion.
Aggregates of waves form wave packets, perhaps the most important expression of a kinetic subject. Apart from that, wave packets have no internal structure, and little individuality. All moving physical things can be described by a wave packet, which therefore, is mostly a modal kinetic subject. Apart from that, physical things have distinctive physical characters, to be investigated in the next chapter. Wave packets have been extensively discussed in chapters 7-9.
 Meyer-Abich 1965, 14, 15; Weisskopf 1972, 42, 294f; Heilbron, Kuhn 1969. For a different view, see Popper 1967.
 This is existence realism. For realism and nominalism with respect to natural laws, see T&E, 8.6.
 Weisskopf 1972, 35; Cantore 1969, 207ff; Grandy (ed.) 1973.
 Bridgman 1927, 59; Margenau 1950, Chapter 4; Margenau, Park 1967; Toulmin 1953, 120ff. Until circa 1960, these nominalists were mainly of the modernist logical-empiricist branch, to be succeeded by historists and the post-modern social-constructivists.
 Mach 1883, 588-590.
 Einstein 1905-1908.
 Cantore 1969, 210: ‘As far as working physicists are concerned, atomic objects are real because they can be shown experimentally to occur with definite properties of interaction’.
 I am referring here to the so-called many-worlds interpretation, and to the transaction interpretation, see Kastner 2013.
Sklar 1993, 3: ‘… little attention of a systematic and rigorous sort has been paid by the philosophical community to the foundational issues to which even our present, only partially formulated, theory of the constitution of matter gives rise.’
 Achinstein 1971, chapter 1. For the sake of convenience, I shall include mathematical laws like that of Pythagoras among natural laws. Laws are also known as axiom, characteristic, constant, design, equation, metric, pattern, phenomenon, postulate, prescription, principle, prohibition, property, proposition, relation, rule, symmetry, theorem or thesis. Hence, I understand the concept of ‘natural law’ much wider than usual.
 Often, one calls a thing an ‘entity’, meaning ‘essential existence’, i.e., the existence of a thing apart from its properties and other relations. I want to make clear that nothing can exist without its relations, and I shall criticize essentialism, in which ‘entity’ is a key word. Hence, I prefer the neutral word ‘thing’. Sometimes one calls events and processes ‘phenomena’. However, I consider a phenomenon not to be an individual but a character. I distinguish the timeless phenomenon of the rainbow from the temporally and spatially determined occurrence of a rainbow as an individual event.
 I shall consider a class to be unbounded in number, space and time. A collection is bounded in number, space and/or time.
 Tolman 1938, 43: An ensemble of systems is ‘… a collection of systems of the same structure as the one of actual interest but distributed over a range of different possible states.’ The concept of an ensemble is circa 1900 introduced by J.W. Gibbs. In physics, it is sometimes possible to project an ensemble onto an abstract state space.
 For a review of critical realism (Popper, Bunge, Putnam and others), see Niiniluoto 1999; Psillos 1999.
 Dooyeweerd NC I, 108; III, 56, 58, 106-109.
 Dooyeweerd NC III, 79, 83. According to Dooyeweerd NC III, 83, structures qualified by the same modal aspect have the same ‘radical type’ as their law side, and all things and events having structures of the same radical type form a ‘kingdom’ at the subject side. However, the word kingdom is not common in physics or chemistry, whereas biologists distinguish six kingdoms of living beings: two kingdoms of prokaryotes, one kingdom of unicellular and colonial eukaryotes, and the kingdoms of plants, animals, and fungi (12.4).
 Stafleu 1985.
 Dooyeweerd NC, III, 143, 266. Numerical relations do not allow of projections on a preceding relation frame.
 This looks like supervenience, see Charles, Lennon (eds.) 1992, 14-18. The idea of supervenience, usually applied to the relation of mind and matter, says that phenomena on a higher level are not always reducible to accompanying phenomena on a lower level. It is supposed that material states and processes invariantly lead to the same mental ones, but the reverse is not necessarily the case. A mental process may correspond with various material processes. Character interlacement implies much more than supervenience, which in fact is no more than a reductionist subterfuge.
 The theory of emergence states that at a higher level new properties emerge that do not occur at a lower level, the whole is more than the sum of its parts, see Popper 1972, 242-244, 289-295; 1974, 142; Popper, Eccles 1977, 14-31; Mayr 1982, 63-64. In suit of Dobzhansky, Stebbins 1982, 161-167 speaks of ‘transcendence’: ‘In living systems, organization is more important than substance. Newly organized arrangements of pre-existing molecules, cells, or tissues can give rise to emergent or transcendent properties that often become the most important attributes of the system’ (ibid. 167). Besides the emergence of the first living beings and of humanity, Stebbins mentions the following examples the first occurrence of eukaryotes, of multicellular animals, of invertebrates and vertebrates, of warm-blooded birds and mammals, of the higher plants and of flowering plants. According to Stebbins, reductionism and holism are contrary approximations in the study of living beings, with equal and complementary values.
In physics, the planned construction of the superconducting supercollider (SSC) about 1990 gave rise to fierce discussions. Supporters (among whom Weinberg) assumed that the understanding of elementary particles will lead to the explanation of all material phenomena. Opponents (like Anderson) stated that solid state physics, e.g., owes very little to a deeper insight into sub-atomic processes. See Anderson 1995; Weinberg 1995; Kevles 1997; Cat 1998.
 Dooyeweerd NC, III, 107: ‘Nowhere else is the intrinsic untenability of the distinction between meaning and reality so conclusively in evidence as in things whose structure is objectively qualified.’
 Essentialism means the hypostatization of being (Latin: esse), contrary to the view that the meaning of anything follows from its relations to everything else. According to Dooyeweerd, the ‘meaning nucleus’ and its ‘analogies’ with other aspects determine the meaning of each modal aspect. However, this incurs the risk of an essentialist interpretation, as if the meaning nucleus together with the analogies determines the ‘essence’ of the modal aspect concerned. In my view, the meaning of anything is determined by its relations to everything else, not merely by the universal relations as grouped into the relation frames, but by the mutual interlacements of the characters as well.
 Mayr 1982, 60: ‘Constitutive reductionism … asserts that the material composition of organisms is exactly the same as found in the inorganic world. Furthermore, it posits that none of the events and processes encountered in the world of living organisms is in any conflict with the physical or chemical phenomena at the level of atoms and organisms. These claims are accepted by modern biologists. The difference between inorganic matter and living organisms does not consist in the substance of which they are composed but in the organization of biological systems.’ Mayr rejects every other kind of reductionism. ‘Reduction is at best a vacuous, but more often a thoroughly misleading and futile, approachapter’ (ibid. 63).
 However, we have observed already that physical and chemical relations can be projected onto quantitative, spatial and kinetic relations. This explains the success of ‘methodical reductionism’.
 Dawkins 1986, 13 calls his view ‘hierarchical reductionism’, that ‘… explains a complex entity at any particular level in the hierarchy of organization, in terms of entities only one level down the hierarchy; entities which, themselves, are likely to be complex enough to need further reducing to their own component parts; and so on. It goes without saying - … - that the kinds of explanations which are suitable at high levels in the hierarchy are quite different from the kinds of explanations which are suitable at lower levels.’ Dawkins rejects the kind of reductionism ‘… that tries to explain complicated things directly in terms of the smallest parts, even, in some extreme versions of the myth, as the sum of the parts…’ (ibid.).
 Papineau 1993, 10: ‘Supervenience on the physical means that two systems cannot differ chemically, or biologically, or psychologically, or whatever, without differing physically; or, to put it the other way round, if two systems are physically identical, then they must also be chemically identical, biologically identical, psychologically identical, and so on.’ This does not imply reductionism, as Papineau himself illustrates in his chapter 2. See e.g., ibid. 44: ‘…I don’t in fact think that psychological categories are reducible to physical ones.’ According to Papineau, in particular natural selection implies that biology and psychology are not reducible to physics, contrary to chemistry and meteorology (ibid. 47, see also Plotkin 1994, 52, 55; Sober 1993, 73-77). But elsewhere (ibid. 122) Papineau writes: ‘Everybody now agrees that the difference between living and non-living systems is simply having a certain kind of physical organization (roughly, we would now say, the kind of physical organization which fosters survival and reproduction)’, without realizing that this does not concern a physical but a biotic ordering, and that survival and reproduction are no more than natural selection physical concepts.
 In a non-Euclidean space two figures only have the same shape if they have the same magnitude as well, see Torretti 1999, 149. Similarity (to be distinguished from congruence or displacement symmetry) is a characteristic of an Euclidean space. Many regular figures like squares or cubes only exist in an Euclidean space.
 Because each triangle belonging to the character class is a possible triangle as well, the ensemble coincides with the character class.
 In 1872, F.Klein in his ‘Erlangen Program’ pointed out the relevance of the theory of groups for geometry, considered to be the study of properties invariant under transformations, see Torretti 1999, 155.
 A permutation is a change in the order of a sequence; e.g., BAC is a permutation of ABC. A set of n objects allows of n!=1.2.3…. n permutations.
 The translation about a vector a is formally represented by the operation T(a)r=r+a, wherein T(a) is called the translation operator.
 An infinitesimal surface is defined as a vector a by its magnitude and the direction perpendicular to the surface. The flux is the scalar product of a with the field strength E at the same location and is maximal if a is parallel to E, minimal if their directions are opposite. If a ^ E the flux is zero. For a finite surface one finds the flux by integration.
 The proportionality factor depends on the force law and is different in the three mentioned cases.
 Even in Protestant philosophy. Dooyeweerd NC, III, 99: ‘No single real thing or event is typically qualified or founded in an original mathematical aspect.’ Hart 1984, 156: ‘If anything is to be actually real in the world of empirical existence, it must ultimately be founded in physical reality.’ Ibid. 263: ‘Existence is ordered so as to build on physical foundations.’
 The phase (φ) indicates a moment in the periodic motion, the kinetic time (t) in proportion to the period (T): φ=t/T=ft modulo 1. If considered an angle, φ=2πft modulo 2π. A phase difference of ¼ between two oscillations means that one oscillation reaches its maximum when the other passes its central position.
 If the force is inversely proportional to the square of the distance (like the gravitational force of the sun exerted on a planet), the result is a periodic elliptic motion as well, but this one cannot be constructed as a combination of only two harmonic oscillations. Observe that an ellipse can be defined primarily (spatially) as a conic section, secondarily (quantitatively) by means of a quadratic equation between the coordinates [e.g., (x-x0)2/a2+(y-y0)2/b2=1], and tertiary as a path of motion, either kinetically as a combination of periodic oscillations or physically as a planetary orbit.
 This equation, the law for harmonic motion, states that the acceleration a is proportional to the distance x of the subject to the centre of oscillation x0, according to: a=d2x/dt2=-(2pf)2(x-x0) wherein the frequency f=1/T is the inverse of the period T. The minus sign means that the acceleration is always directed to the centre.
 In an isotropic medium, the wavelength λ is the distance covered by a wave with wave velocity v in a time equal to the period T: λ=νT=ν/f. The inverse of the wavelength is the wave number (the number of waves per metre), σ=1/l=f/ν. In three dimensions, the wave number is replaced by the wave vector k, which besides the number of waves per metre also indicates the direction of the wave motion. In a non-isotropic medium, the wave velocity depends on the direction.
 Usually, the wave velocity depends on the frequency as well. This phenomenon is called dispersion. Only light moving in a vacuum is free of dispersion. (The medium of light in vacuum is the electromagnetic field.) The observed frequency of a source depends on the relative motions of source, observer and medium. This is called the Doppler effect.
 Polarization concerns the direction of oscillation. A sound wave in air is longitudinal, the direction of oscillation being parallel to the direction of motion. Light is transversal, the direction of oscillation being perpendicular to the direction of motion. Light is called unpolarized if it contains waves having all directions of polarization. Light may be partly or completely polarized. It may be linearly polarized (having a permanent direction of oscillation) or circularly polarized (the direction of oscillation itself rotating at a frequency independent of the frequency of the wave itself).
 The non-relativistic Schrödinger equation and the relativistic Dirac equation describe the motion of material waves.
Part II, chapter 11
11.1. Unification of physical interactions
Unification has always been an aim of physical science (T&E chapter 7). Until 1930 it was thought that there were only two fundamental kinds of interaction, gravitational and electromagnetic, and it was hoped that they could be unified into a single theory. In fact, for some time general relativity was considered as the basis of a unified field theory, a modal theory within which, supposedly, every kind of interaction could find its place. But soon after 1930, physicists realized that the interaction between protons and neutrons cannot be merely one of an electromagnetic character, since the strong nuclear interaction between nucleons is even independent of their charge. In addition to this strong nuclear interaction, which is clearly irreducible to the electromagnetic one, also a weak nuclear interaction had to be distinguished, which has later been linked with electromagnetic interaction. The discovery of the electron in 1897 provided the study of the structure of matter with a strong impulse, both in physics and in chemistry. Our knowledge of atoms and molecules, of nuclei and sub-atomic particles, of stars and stellar systems, dates largely from the 20th century.
Because of their relevance to secondary types of physical characters, this chapter starts with a summary of the projections of the physical relation frame onto the three preceding ones (11.1). Next, we investigate the characters of physically stable things, founded quantitatively, spatially, or kinetically (11.2-11.4). Sections 11.5 and 11.6 deal with aggregates and statistics. Section 11.7 reviews the dynamic processes of physical development: coming into being, change, and decay.
The existence of physically qualified things and events implies their interaction, the universal physical relation. If something could not interact with anything else it would be inert. It would not exist in a physical sense, and it would have no physical place in the cosmos. The noble gases are traditionally called inert because they hardly ever take part in chemical compounds, yet their atoms are able to collide with each other. The most inert things among subatomic particles are the neutrino’s, capable of flying through the earth with a very small probability of colliding with a nucleus or an electron. Nevertheless, neutrinos are detectable and have been detected.
The universality of the relation frames allows science of comparing characters with each other and to determine their specific relations. The projections of the physical relation frame onto the preceding frames allow us to measure these relations. Measurability is the base of the mathematization of the exact sciences (chapter 3). It allows of applying statistics and designing mathematical models for natural and artificial systems.
The simplest case of interaction concerns two isolated systems interacting only with each other. Thermodynamics characterizes an isolated or closed system by magnitudes like energy and entropy (5.2). The two systems have thermal, chemical, or electric potential differences, giving rise to currents creating entropy. According to the second law of thermodynamics, this interaction is irreversible.
In kinematics, an interactive event may have the character of a collision, minimally leading to a change in the state of motion of the colliding subjects. Often, the internal state of the colliding subjects changes as well. Except for the boundary case of an elastic collision, these processes are subject to the physical order of irreversibility. Frictionless motion influenced by a force is the standard example of a reversible interaction. In fact, it is also a boundary case, for any kind of friction or energy dissipation causes motion to be irreversible.
Energy, force and current
Interaction is first of all subject to general laws independent of the specific character of the things involved. Some conservation laws are derivable from Einstein’s principle of relativity, stating that the laws of physics are independent of the motion of inertial systems (5.3).
Being the physical subject-subject relation, interaction may be analysed with the help of quantitative magnitudes like energy, mass, and charge; spatial concepts like force, momentum, field strength, and potential difference; as well as kinetic expressions like currents of heat, matter, or electricity (chapter 5).
Like interaction, energy, force, and current are abstract concepts. Yet these are not merely covering concepts without physical content. They can be specified as projections of characteristic interactions like the electromagnetic one. Electric energy, gravitational force, and the flow of heat specify the abstract concepts of energy, force, and current.
For energy to be measurable, it is relevant that one concrete form of energy is convertible into another one. For instance, a generator transforms mechanical energy into electric energy. Similarly, a concrete force may balance another force, whereas a concrete current accompanies currents of a different kind. This means that characteristically different interactions are comparable, they can be measured with respect to each other (chapter 3). The physical subject-subject relation, the interaction projected as energy, force, and current, is the foundation of the whole system of measuring, characteristic for astronomy, biology, chemistry, physics, as well as technology. The concepts of energy, force, and current enable us to determine physical subject-subject relations objectively.
It is by no means evident that the concepts of energy, force, and current are the most general projections of interaction. Rather, their dynamic development has been a long and tedious process, leading to a general unification of natural science, to be distinguished from a more specific unification to be discussed presently.
There are many different interactions, like electricity, magnetism, contact forces (e.g., friction), chemical forces (e.g., glue), or gravity. Some are reducible to others. The contact forces turn out to be of an electromagnetic nature, and chemical forces are often reducible to electrical ones.
Besides the general unification discussed above allowing of the comparison of widely differing interactions, a characteristic unification can be discerned. Maxwell’s unification of electricity and magnetism implies these interactions to have the same character, being subject to the same specific cluster of laws and showing symmetry. The fact that they can still be distinguished points to an asymmetry, a break of symmetry. The study of characteristic symmetries and symmetry breaks supplies an important tool for achieving a characteristic unification of natural forces.
Since the middle of the 20th century, physics discerns four fundamental specific interactions. These are gravity and electromagnetic interaction besides the strong and weak nuclear forces. Later on, the electromagnetic and weak forces were united into the electroweak interaction, whereas the strong force is reducible to the colour force between quarks. In the near future, physicists expect to be able to unite the colour force with the electroweak interaction. The ultimate goal, the unification of all four forces is still far away.
These characteristic interactions are distinguished in several ways, first by the particles between which they act. Gravity acts between all particles, the colour force only between quarks, and the strong force only between particles composed from quarks. A process involving a neutrino is weak, but the reverse is not always true.
Another difference is their relative strength. Gravity is weakest and only plays a part because it cannot be neutralized. It manifests itself only on a macroscopic scale. The other forces are so effectively neutralized, that the electrical interaction was largely unknown until the 18th century, and the nuclear forces were not discovered before the 20th. Gravity conditions the existence of stars and systems of stars.
Next, gravity and electromagnetic interaction have an infinite range, the other forces do not act beyond the limits of an atomic nucleus. For gravity and electricity the inverse-square law is valid (the force is inversely proportional to the square of the distance from a point-like source). This law is classically expressed in Newton’s law of gravity and Coulomb’s electrostatic law, with mass respectively charge acting as a measure of the strength of the source. A comparable law does not apply to the other forces, and the lepton and baryon numbers do not act as a measure for their sources. As a function of distance, the weak interaction decreases much faster than quadratically. The colour force is nearly constant over a short distance (of the order of the size of a nucleus), beyond which it decreases abruptly to zero.
The various interactions also differ because of the field particles involved. Each fundamental interaction corresponds to a field in which quantized currents occur. For gravity, this is an unconfirmed hypothesis. Field particles have an integral spin and they are bosons (11.4). If the spin is even (0 of 2), it concerns an attractive force between equal particles and a repulsive force between opposite particles (if applicable). For an uneven spin it is the other way around. The larger the field particle’s rest mass, the shorter is the range of the interaction. If the rest mass of the field particles is zero (as is the case with photons and gravitons), the range is infinite. Unless mentioned otherwise, the field particles are electrically neutral.
In high-energy physics, symmetry considerations and group theory play an important part in the analysis of collision processes. New properties like isospin and strangeness have led to the introduction of groups named SU(2) and SU(3) and the discovery of at first three, later six quarks. Quantum electrodynamics reached its summit shortly after the Second World War, but the other interactions are less manageable, being developed only after 1970. Now each field has a symmetry property called gauge invariance, related to the laws of conservation of electric charge, baryon number and lepton number. The appropriate theory is the standard model, since the discovery of the J/y particle in 1974 explaining successfully a number of properties and interactions of subatomic particles. However, the general theory of relativity is still at variance with quantum electrodynamics, with the electroweak theory of Steven Weinberg and Abdus Salam, as well as with quantum chromodynamics.
These fundamental interactions are specifications of the abstract concept of interaction being the universal physical and chemical relation. Their laws, like those of Maxwell for electromagnetism, form a specific set, which may be considered a character. But this character does not determine a class of things or events, but a class of relations.
11.2. The character of electrons and other leptons
Ontology, the doctrine of on (or ontos, Greek for being), aims to answer the question of how matter is composed according to present-day insights. Since the beginning of the 20th century, many kinds of particles received names ending with on, like electron, proton, neutron and photon. At first sight, the relation with ontology seems to be obvious. Yet, not many physicists would affirm that an electron is the essence of electricity, that the proton forms the primeval matter, that the neutron and its little brother, the neutrino, have the nature of being neutral, or that in the photon light comes into being, and in the phonon sound. In pion, muon, tauon, and kaon, on is no more than a suffix of the letters π, μ, τ and K, whereas Paul Dirac baptized fermion and boson after Enrico Fermi and Satyendra Bose. In 1833 Michael Faraday, advised by William Whewell, introduced the words ion, kation, and anion, referring to the Greek word for to go. In an electrolyte, an ion moves from or to an electrode, an anode or cathode (names proposed by Whewell as well). In this context, the positive electron is a misnomer. Meant as positon, it received an additional r, possibly under the influence of electron or new words like magnetron and cyclotron, which however are machines, not particles.
Only after 1925 quantum physics and high-energy physics allowed of the study of the characters of elementary physical things. Most characters have been discovered after 1930. But the discovery of the electron (1897), of the internal structure of an atom, composed from a nucleus and a number of electrons (1911) and of the photon (1905) preceded the quantum era. These happen to be typical examples of characters founded in the quantitative, spatial, and kinetic projections of physical interaction, respectively energy, force or field, and current.
An electron is characterized by a specific amount of mass and charge and is therefore quantitatively founded. The foundation is not in the quantitative relation frame itself (because that is not physical), but in the most important quantitative projection of the physical relation frame. This is energy, expressing the quantity of interaction. Like other particles, an electron has a typical rest energy, besides specific values for its electric charge, magnetic moment and lepton number.
Electrons have the character of a wave packet as well, kinetically qualified and spatially founded, anticipating physical interactions (chapter 7). An electron has a specific physical character and a generic kinetic character. The two characters are interlaced within the at first sight simple electron. The combined dual character is called the wave-particle duality. Electrons share it with all other elementary particles, hence it is more modal than typical. As a consequence of the kinetic character and the inherent Heisenberg relations, the position of an electron cannot be determined much better than within 10-10 m (about the size of a hydrogen atom). But the physical character implies that the electron’s collision diameter (being a measure of its physical size) is less than 10-17 m.
Except for quarks, all quantitatively founded particles are leptons, to be distinguished from both baryons (11.3) and field particles (11.4). Leptons are not susceptible to the strong nuclear force or the colour force. They are subject to the weak force, sometimes to electromagnetic interaction, and like all matter to gravity. Each lepton has a positive or negative value for the lepton number (L), which significance appears in the occurrence or non-occurrence of certain processes. Each process is subject to the law of conservation of lepton number, i.e., the total lepton number cannot change. For instance, a neutron (L=0) does not decay into a proton and an electron, but into a proton (L=0), an electron (L=1) and an antineutrino (L=-1). The lepton number is just as characteristic for a particle as its electric charge. For non-leptons the lepton number is 0, for leptons it is +1 or -1.
Leptons satisfy a number of characteristic laws. Each particle has an electric charge being an integral multiple (positive, negative or zero) of the elementary charge. Each particle corresponds with an antiparticle having exactly the same rest mass and lifetime, but opposite values for charge and lepton number. Having a half-integral spin, leptons are fermions satisfying the exclusion principle and the characteristic Fermi-Dirac statistics (11.5).
Three generations of leptons are known, each consisting of a negatively charged particle, a neutrino, and their antiparticles. These generations are related to similar generations of quarks (11.3). A tauon decays spontaneously into a muon, and a muon into an electron. Both are weak processes, in which simultaneously a neutrino and an anti-neutrino are emitted.
The leptons display little diversity, their number is exactly 12. Like their diversity, the variation of leptons is restricted. It only concerns their external relations: their position, their linear and angular momentum, and the orientation of their magnetic moment or spin relative to an external magnetic field.
This description emphasizes the quantitative aspect of leptons. But leptons are first of all physically qualified. Their specific character determines how they interact by electroweak interaction with each other and with other physical subjects, influencing their coming into being, change and decay.
A century of electrons
Electrons are by far the most important leptons, having the disposition to become part of systems like atoms, molecules and solids. The other leptons only play a part in high-energy processes. In order to stress the distinction between a definition and a character as a set of laws, I shall dwell a little longer on hundred years of dynamic development of our knowledge of the electron.
Although more scientists were involved, it is generally accepted that Joseph J. Thomson in 1897 discovered the electron (T&E 9.5). He identified his cathode ray as a stream of particles and established roughly the ratio e/m of their charge e and mass m, by measuring how an electric and/or magnetic field deflects the cathode rays. In 1899 Thomson determined the value of e separately, allowing him to calculate the value of m. Since then, the values of m and e, which may be considered as defining the electron, are determined with increasing precision. In particular Robert Millikan did epoch-making work, between 1909 and 1916. Almost simultaneously with Thomson, Hendrik Lorentz observed that the Zeeman effect (1896) could be explained by the presence in atoms of charged particles having the same value for e/m as the electron. Shortly afterwards, the particles emerging from β-radioactivity and the photoelectric effect were identified as electrons.
The mass m depends on the electron’s speed, as was first established experimentally by Walter Kaufmann, later theoretically by Albert Einstein. Since then, instead of the mass m the rest mass mo is characteristic for a particle. Between 1911 and 1913, Ernest Rutherford and Niels Bohr developed the atomic model in which electrons move around a much more massive nucleus. The orbital angular momentum turned out to be quantized. In 1923 Louis de Broglie made clear that an electron sometimes behaves like a wave, interpreted as the bearer of probability by Max Born in 1926 (9.1). In 1925, Samuel Goudsmit and George Uhlenbeck suggested a new property, half-integral spin, connected to the electron’s intrinsic magnetic moment. In the same year, Wolfgang Pauli discovered the exclusion principle. Enrico Fermi and Paul Dirac derived the corresponding statistics in 1926. Since then, the electron is a fermion, playing a decisive part in all properties of matter (11.3, 11.5). In 1930 it became clear that in β-radioactivity besides the electron a neutrino emerges from a nucleus. Neutrino’s, having a very small rest mass and zero electric charge, were later on recognized as members of the lepton family. β-radioactivity is not caused by electromagnetic interaction, but by the weak nuclear force. Electrons turned out not to be susceptible to strong nuclear forces. In 1931 the electron got a brother, the positron or anti-electron, having the same rest mass, but positive electric charge. This affirmed that an electron has no eternal life, but may be created or annihilated together with a positron. In β-radioactivity, too, an electron emerges or disappears (in a nucleus, an electron cannot exist as an independent particle), but apart from these processes, the electron is the most stable particle known besides the proton. According to Dirac, the positron is a hole in the nether world of an infinite number of electrons having a negative energy (11.6). In 1953 the law of conservation of lepton number was discovered. After the second world war, Richard Feynman, Julian Schwinger and Sin-Itiro Tomonaga developed quantum electrodynamics. This is a field theory in which the physical vacuum is not empty, but is the stage of spontaneous creations and annihilations of virtual electron-positron pairs. Interaction with other (sometimes virtual) particles is partly responsible for the properties of each particle. As a top performance counts the theoretical calculation of the magnetic moment of the electron in eleven decimals, a precision only surpassed by the experimental measurement of the same quantity in twelve decimals. Moreover, the two values differ only in the eleventh decimal, within the theoretical margin of error. Finally, the electron got two cousins, the muon and the tauon.
Since Thomson’s discovery, the concept of an electron has been changed and expanded considerably. Besides being a particle having mass and charge, it is now a wave, a top, a magnet, and a fermion, half of a twin, and a lepton. Yet, few people doubt that we are still talking about the same electron.
What the essence of an electron is appears to be a hard question, if ever posed. It may very well be a meaningless question. But the insight is growing into the laws constituting the electron’s character, determining the electron’s relations with other things and the processes in which it is involved. The electron’s charge means that two electrons exert a force on each other according to the laws of Coulomb and Lorentz. The mass follows from the electron’s acceleration in an electric and/or magnetic field, according to Maxwell’s laws. The lepton number makes only sense because of the law of conservation of lepton number, allowing of some processes and prohibiting others. Electrons are fermions, satisfying the exclusion principle and the distribution law of Fermi and Dirac.
The character of electrons is not logically given by a definition, but physically by a specific set of laws, which are successively discovered and systematically connected by experimental and theoretical research.
The individual existence of an electron
An electron is to be considered an individual satisfying the character described above. A much-heard objection to the assignment of individuality to electrons and other elementary particles is the impossibility to distinguish one electron from another. Electrons are characteristically equal to each other, having much less variability than plants or animals, even less than atoms.
This objection can be retraced to the still influential world view of mechanism. This world view assumed each particle to be identifiable by objective kinetic properties like its position and velocity at a certain time. Quantum physics observes that the identification of physically qualified things requires a physical interaction. In general, this interaction influences the particle’s position and momentum. Therefore, the electron’s position and momentum cannot be determined with unlimited accuracy, as follows from Heisenberg’s relations. This means that identification in a mechanistic sense is not always possible. Yet, in an interaction such as a measurement, an electron manifests itself as an individual.
If an electron is part of an atom, it can be identified by its state, because the exclusion principle precludes that two electrons would occupy the same state. The two electrons in the helium atom exchange their states continuously without changing the state of the atom as a whole. But it cannot be doubted that at any moment there are two electrons, each with its own mass, charge and magnetic moment. For instance, in the calculation of the energy levels the mutual repulsion of the two electrons plays an important part.
The individual existence of a bound electron depends on the binding energy being much smaller than its rest energy. Binding energy is the energy needed to liberate an electron from an atom. It varies from a few eV (the outer electrons) to several tens of keV (the inner electrons in a heavy element like uranium). The electron’s rest mass is about 0.51 MeV, much larger than its binding energy in an atom (13.6 eV). To keep an electron as an independent particle in a nucleus would require a binding energy of more than 100 MeV, much more than the electron’s rest energy of 0,51 MeV. For this reason, physicists argue that electrons in a nucleus cannot exist as independent, individual particles, like they are in an atom’s shell.
In contrast, protons and neutrons in a nucleus satisfy the criterion that an independent particle has a rest energy substantially larger than the bindingenergy. Their binding energy is about 8 MeV, their rest energy is almost 1000 MeV. A nucleus is capable of emitting an electron (this is β-radioactivity). The electron’s existence starts at the emission and eventually ends at the absorption by a nucleus. Because of the law of conservation of lepton number, the emission of an electron is accompanied by the emission of an anti-neutrino, and at the absorption of an electron a neutrino is emitted. This would not be the case if the electron could exist as an independent particle in the nucleus.
More than as free particles, the electrons display their characteristic properties as components of atoms, molecules and solids, as well as in processes. The half-integral spin of electrons was discovered in the investigation of atomic spectra. The electron’s fermion character largely determines the shell structure of atoms. In 1930, Pauli suggested the existence of the neutrino because of the character of β-radioactivity. The lepton number is discovered by an analysis of specific nuclear reactions.
Electrons have the affinity or propensity of functioning as a component of atoms and molecules because electrons share electromagnetic interaction with nuclei. Protons and electrons have the same but opposite charge, allowing of the formation of neutral atoms, molecules and solids. Electric neutrality is of tremendous importance for the stability of these systems. This tertiary characteristic determines the meaning of electrons in the cosmos.
11.3. The quantum ladder
An important spatial manifestation of interaction is the force between two spatially separated bodies. An atom or molecule having a spatially founded character consists of a number of nuclei and electrons kept together by the electromagnetic force. More generally, any interaction is spatially projected on a field.
Sometimes a field can be described as the spatial derivative of the potential energy. A set of particles constitutes a stable system if the potential energy has an appropriate shape, characteristic for the spatially founded structure. In a spatially founded structure, the relative spatial positions of the components are characteristic, even if their relative motions are taken care of. Atoms have a spherical symmetry restricting the motions of the electrons. In a molecule, the atoms or ions have characteristic relative positions, often with a specific symmetry. In each spatially founded character a number of quantitatively founded characters are interlaced.
The first stable system studied by physics is the solar system, in the 16th and 17th century investigated by Nicolas Copernicus, Johannes Kepler, Galileo Galilei, Christiaan Huygens, Isaac Newton and many others. The law of gravity, mechanical laws of motion, and conservation laws determine the character of planetary motion. The solar system is not unique, there are more stars with planets, and the same character applies to a planet with its moons, or to a double star. Any model of the system presupposes its isolation from the rest of the world, which is the case only approximately. This approximation is pretty good for the solar system, less good for the system of the sun and each planet apart, and even less for the system of earth and moon. The character of the solar system and of related stellar systems depends on the attractive force of gravity, and therefore differs strongly from the characters to be discussed presently.
Spatially founded physical characters depending on other interactions than gravity display a large variety. According to the standard model (11.1), these characters form a hierarchy, called the quantum ladder, ascending from quarks to molecules and solids. These characters are especially characterized by their propensity to become part of other systems. At the first rung there are six types of quarks, with their antiquarks grouped into three generations (up and down, strange and charm, bottom and top) related to those of leptons (electron, muon, tauon, with their neutrino’s, see 11.2), as follows from analogous processes. The first generation constitutes common matter, the other two only occur in high energy processes.
Like a lepton, a quark is quantitatively founded, it has no spatial structure. But a quark cannot exist as a free particle. Quarks are confined as a duo in a meson (e.g., a pion) or as a trio in a baryon (e.g., a proton or a neutron) or an antibaryon. Confinement is a tertiary characteristic, but it does not stand apart from the secondary characteristics of quarks, their quantitative properties. Whereas quarks have a charge of 1/3 or 2/3 times the elementary charge, their combinations satisfy the law that the electric charge of a free particle can only be an integral multiple of the elementary charge. Likewise, in confinement the sum of the baryon numbers (for quarks ±1/3 of ±2/3) always yields an integral number. For a meson this number is 0, for a baryon it is +1, for an antibaryon it is -1.
Between quarks the colour force is acting, mediated by gluons. The colour force has no effect on leptons and is related to the strong force between baryons. In a meson the colour force between two quarks hardly depends on their mutual distance, meaning that they cannot be torn apart. If a meson breaks apart, the result is not two separate quarks but two quark-antiquark pairs.
Quarks are fermions satisfying the exclusion principle. In a meson or baryon, two identical quarks cannot occupy the same state. But an omega particle (sss) consists of three strange quarks having the same spin. This is possible because each quark exists in three variants, each indicated by a ‘colour’. For the antiquarks three complementary colours are available. The metaphor of colour is chosen because the colours are able to neutralize each other, like ordinary colours can be combined to appear as white. This can be done in two ways, in a duo by adding a colour to its anticolour, or in a trio by adding three different colours or anticolours. The law that mesons and baryons must be coulorless yields an additional restriction on the number of possible combinations of quarks. A white particle is neutral with respect to the colour force, like an uncharged particle is neutral with respect to the Coulomb force. Nevertheless, an electrically neutral particle may exert electromagnetic interaction because of its magnetic moment. This applies e.g. to a neutron, but not to a neutrino. Similarly, by the exchange of mesons, the colour force manifests itself as the strong nuclear force acting between baryons, even if baryons are ‘white’. Two quarks interact by exchanging gluons, thereby changing of colour.
The 20th-century standard model explains the propensitities of quarks to form composites, but it has no solution to a number of problems. Why only three generations? If all matter above the level of hadrons consists of particles from the first generation, what is the tertiary disposition of the particles of the second and third generation? Should the particles of the second and third generation be considered excited states of those of the first generation? Why does each generation consist of two quarks and two leptons (with corresponding antiparticles)? What is the origin of the mass differences between various leptons and quarks?
The last question might be the only one to receive an answer early in the 21st century, when the existence and mass of the boson predicted in 1964 by Peter Higgs were experimentally established (2012). For the other problems, at the end of the 20th century no experiment is proposed providing sufficient information to suggest a solution.
The characters described depend strongly on a number of natural constants, which value can be established only experimentally, not theoretically. These are the gravitational constant G, the speed of light c, Planck’s and Boltzmann’s constant h and k, and the elementary electric charge e, or combinations like the fine structure constant (2pe2/hc=1/137.036) and the mass ratio of the proton and the electron (1836.104). If the constants of nature would have been slightly different, both nuclear properties and chemical properties would change drastically, and life on earth would have been impossible. So it appears that the laws of nature are ‘fine-tuned’ such as to make stable physical and living systems possible.
The second level of the hierarchy consists of hadrons: baryons having half integral spin and mesons having integral spin. Although the combination of quarks is subject to severe restrictions, there are quite a few different hadrons. A proton consists of two up and one down quark (uud), and a neutron is composed of one up and two down quarks (udd). These two nucleons are the lightest baryons, all others being called hyperons. A pion consists of a quark and an antiquark. As a free particle, only the proton is stable, whereas the neutron is stable within a nucleus. All other hadrons have a very short mean lifetime, a free neutron having the longest (900 sec). Their diversity is much larger than that of leptons and of quarks. Based on symmetry relations, group theory orders the hadrons into sets of e.g. eight baryons or ten mesons.
For a large part, the interaction of hadrons consists of rearranging quarks accompanied by the creation and annihilation of quark-antiquark pairs and lepton-antilepton pairs. The general laws of conservation of energy, linear and angular momentum, the specific laws of conservation of electric charge, lepton number and baryon number, and the laws restricting electric charge and baryon number to integral values, characterize the possible processes between hadrons in a quantitative sense. The fields described by quantum electrodynamics and quantum chromodynamics characterize these processes in a spatial sense, and the exchange of field particles in a kinetic way, as we shall see below (11.4).
Atomic nuclei constitute the third layer in the hierarchy. With the exception of hydrogen, each nucleus consists of protons and neutrons, determining together the coherence, binding energy, stability, and lifetime of the nucleus. The mass of the nucleus is the sum of the masses of the nucleons less the mass equivalent to the binding energy. Decisive is the balance of the repulsive electric force between the protons and the attractive strong nuclear force binding the nucleons independent of their electric charge. In heavy nuclei, the surplus of neutrons compensates for the mutual repulsion of the protons. To a large extent, the exclusion principle applied to neutrons and protons separately determines the stability of the nucleus and its internal energy states.
The nuclear force is negligible for the external functioning of a nucleus in an atom or molecule. Only the mass of the nucleus, its electric charge and its magnetic moment are relevant. Omitting the latter, two diversities in nuclei should be mentioned.
The first diversity concerns the number of protons. In a neutral atom it equals the number of electrons determining the atom’s chemical propensities. The nuclear charge together with the exclusion principle dominates the energy states of the electrons, hence the position of the atom in the periodic system of elements.
The second diversity concerns the number of neutrons in the nucleus. Atoms having the same number of protons but differing in neutron number are called isotopes, because they have the same position (topos) in the periodic system. They have similar chemical propensities.
The diversity of atomic nuclei is represented in a two-dimensional diagram, a configuration space. The horizontal axis represents the number of protons (Z = atomic number), the vertical axis the number of neutrons (N). In this diagram the isotopes (same Z, different N) are positioned above each other. The configuration space is mostly empty, because only a restricted number of combinations of Z and N lead to stable or metastable (radioactive) nuclei. The periodic system of elements is a two-dimensional diagram as well. Dmitri Mendeleev ordered the elements in a sequence according to a secondary property (the atomic mass) and below each other according to tertiary propensities (the affinity of atoms to form molecules, in particular compounds with hydrogen and oxygen). Later on, the atomic mass was replaced by the atomic number Z. However, quantum physics made clear that the atomic chemical properties are not due to the nuclei, but to the electrons subject to the exclusion principle. The vertical ordering in the periodic system concerns the configuration of the electronic shells. In particular the electrons in the outer shells determine the tertiary chemical propensities.
This is not an ordering according to a definition in terms of necessary and sufficient properties distinguishing one element from the other, but according to their characters. The properties do not define a character, as essentialism assumes, but the character (a set of laws) determines the properties and propensities of the atoms.
Atoms and molecules
In the hierarchical order, one finds globally an increase of spatial dimensions, diversity of characters and variation within a character, besides a decrease of the binding energy per particle and the significance of strong and weak nuclear forces. For the characters of atoms, molecules, and crystals, only the electromagnetic interaction is relevant, excluding both gravity and the nuclear forces.
The internal variation of a spatially founded character is very large. Quantum physics describes the internal states with the help of a Hilbert space, having the eigenvectors of the Hamiltonian operator as a base (9.2). A Hilbert space describes the ensemble of possibilities (in particular the energy eigenvalues) determined by the system’s character. In turn, the atom or molecule’s character itself is represented by Schrödinger’s equation. This equation is exactly solvable only in the case of two interacting particles, like the hydrogen atom, the helium ion, the lithium ion, and positronium. In other cases, the equation serves as a starting point for approximate solutions, usually only manageable with the help of a computer.
The number of molecular characters is enormous and no universal classification of molecules exists. In particular the characters in which carbon is an important element show a large diversity.
The molecular formula indicates the number of atoms of each element in a molecule. Besides, the characteristic spatial structure of a molecule determines its chemical properties. The composition of a methane molecule is given by the formula CH4, but it is no less significant that the methane molecule has the symmetrical shape of a regular tetrahedron, with the carbon atom at the centre and the four hydrogen atoms at the vertices. The V-like shape of a water molecule (the three atoms do not lie on a straight line, but form a characteristic angle of 105o) causes the molecule to have a permanent electric dipole moment, explaining many of the exceptional properties of water and ice. Isomers are materials having the same molecular formula but different spatial orderings, hence different chemical properties. Like the symmetry between a left and a right glove, the spatial symmetry property of mirroring leads to the distinction of dextro- and laevo-molecules.
The symmetry characteristic for the generic (physical) character is an emergent property, in general irreducible to the characters of the composing systems. Conversely, the original symmetry of the composing systems is broken. In methane, the outer shells of the carbon atom have exchanged their spherical symmetry for the tetrahedron symmetry of the molecule. Symmetry break also occurs in fields. From quantum field theory, in principle it should be possible to derive successively the emergent properties of particles and their spatially founded composites. This is the synthetic, reductionist or fundamentalist trend, constructing complicated structures from simpler ones. It cannot explain symmetry breaks. The alternative is the analytical or holistic method, in which the symmetry break is explained from the empirically established symmetry of the original character. Symmetries and other structural properties are usually a posteriori explained, and hardly ever a priori derived. However, analysis and synthesis are not contrary but complementary methods.
The possibility of being bound into a larger configuration is a very significant tertiary characteristic of many physically qualified systems, determining their meaning in the cosmos. It is a remarkable fact that in an atom the nucleus acts like a quantitatively founded character, whereas the nucleus itself is a spatial configuration of protons and neutrons kept together by forces. The nucleus itself has a spatially founded character, but in the atom it has the disposition to act as a whole, characterized by its mass, charge and magnetic moment. Similarly, a molecule or a crystal is a system consisting of a number of atoms or ions and electrons, all acting like quantitatively founded particles. Externally, the nucleus in an atom and the atoms or ions in a molecule act as a quantitatively founded whole, as a unit, while preserving their own internal spatially founded structure.
However, an atom bound in a molecule is not completely the same as a free atom. In contrast to a nucleus, a free atom is electrically neutral and it has a spherical symmetry. Consequently, it cannot easily interact with other atoms or molecules, except in collisions. In order to become a part of a molecule, an atom has to open up its tertiary character. This can be done in various ways. The atom may absorb or eject an electron, becoming an ion. A common salt molecule does not consist of a neutral sodium atom and a neutral chlorine atom, but of a positive sodium ion and a negative chlorine ion, attracting each other by the Coulomb force. This is called heteropolar or ionic bonding. Any change of the spherical symmetry of the atom’s electron cloud leads to the relatively weak VanderWaals interaction. A very strong bond results if two atoms share an electron pair. This homopolar or covalent bond occurs in diatomic molecules like hydrogen, oxygen and nitrogen, in diamond and in many carbon compounds. Finally, especially in organic chemistry, the hydrogen bond is important. It means the sharing of a proton by two atom groups.
Climbing the quantum ladder, complexity seems to increase. On second thoughts, complexity is not a clear concept. An atom would be more complex than a nucleus and a molecule even more. However, in the character of a hydrogen atom or a hydrogen molecule, weak and strong interactions are negligible, and the complex spatially founded nuclear structure is reduced to the far simpler quantitatively founded character of a particle having mass, charge, and magnetic moment. Moreover, a uranium nucleus consisting of 92 protons and 146 neutrons has a much more complicated character than a hydrogen molecule consisting of two protons and two electrons, having a position two levels higher on the quantum ladder.
Inward a system is more complex than outward. An atom consists of a nucleus and a number of electrons, grouped into shells. If a shell is completely filled in conformity with the exclusion principle, it is chemically inert, serving mostly to reduce the effective nuclear charge. A small number of electrons in partially occupied shells determines the atom’s chemical propensities. Consequently, an atom of a noble gas, having only completely occupied shells, is less complicated than an atom having one or two electrons less. The complexity of molecules increases if the number of atoms increases. But some very large organic molecules consist of a repetition of similar atomic groups and are not particularly complex. In fact, there does not exist an unequivocal criterion for complexity.
An important property of hierarchically ordered characters is that for the explanation of a character it is sufficient to descend to the next lower level. For the understanding of molecules, a chemist needs the atomic theory, but he does not need to know much about nuclear physics. A molecular biologist is acquainted with the chemical molecular theory, but his knowledge of atomic theory may be rather superficial. This is possible because of the phenomenon that a physical character interlaced in another one both keeps its properties and hides them.
Each system derives its stability from an internal equilibrium that is hardly observable from without. The nuclear forces do not range outside the nucleus. Strong electric forces bind an atom or a molecule, but as a whole it is electrically neutral. The strong internal equilibrium and the weak remaining external action are together characteristic for a stable physical system. If a system exerts a force on another one, it experiences an equal external force. This external force should be much smaller than the internal forces keeping the system intact, otherwise it will be torn apart. In a collision between two molecules, the external interaction may be strong enough to disturb the internal equilibrium, such that the molecules fall apart. Eventually, a new molecule with a different character emerges. Because the mean collision energy is proportional to the temperature, the stability of molecules and crystals depend on this parameter. In the sun’s atmosphere no molecules exist and in its centre no atoms occur. In a very hot star like a neutron star, even nuclei cannot exist.
Hence, a stable physical or chemical system is relatively inactive. It looks like an isolated system. This is radically different from plants and animals that can never be isolated from their environment. The internal equilibrium of a plant or an animal is maintained by metabolism, the continuous flow of energy and matter through the organism.
The hierarchical connection implies that the spatially founded characters are successively interlaced, for example nucleons in a nucleus, or the nucleus in an atom, or atoms in a molecule. Besides, these characters are interlaced with kinetically, spatially, and quantitatively qualified characters, and often with biotically qualified characters as well.
The quantum ladder is not philosophical but has a physical and chemical nature. It is not based on some rational philosophical principles, but has been established in an empirical theoretical and experimental investigation. As an ordering principle, the ladder has a few flaws from a logical point of view. For instance, the proton occurs on three different levels, as a baryon, as a nucleus, and as an ion. The atoms of the noble gases are their molecules as well. This is irrelevant for their character. The character of a proton consists of the specific laws to which it is subjected. The classification of baryons, nuclei or ions is not a characterization, and a proton is not ‘essentially’ a baryon and ‘accidentally’ a nucleus or an ion.
11.4. Individualized currents
I consider the primarily physical character of a photon to be secondarily kinetically founded. A photon is a field particle in the electromagnetic interaction, transporting energy, linear and angular momentum from one spatially founded system to another. Besides photons, nuclear physics recognizes gluons being field particles for the colour force, mesons for the strong nuclear force, and three types of vector bosons for the weak interaction. The existence of the graviton, the field particle for gravity, has not been experimentally confirmed. All these interaction particles have an integral spin and are bosons. Hence, these are not subject to the exclusion principle. Field particles are not quantitatively or spatially founded things, but individualized characteristic currents, i.e., kinetically founded quasiparticles. Bosons carry forces, whereas fermions feel forces.
By absorbing a photon, an atom comes into an excited state, i.e. a metastable state at a higher energy than the ground state. Whereas an atom in its ground state can be considered an isolated system, an excited atom is always surrounded by the electromagnetic field.
A photon is a wave packet, like an electron it has a dual character. Yet there is a difference. Whereas the electron’s motion has a wave character, a photon is a current in an electromagnetic field, a current being a kinetic projection of physical interaction. With respect to electrons, the wave motion only determines the probability of what will happen in a future interaction. In a photon, besides determining a similar probability, the wave consists of periodically changing electric and magnetic fields. A real particle’s wave motion lacks a substratum, there is no characteristic medium in which it moves, and its velocity is variable. Moving quasiparticles have a substratum, and their wave velocity is a property of the medium. The medium for light in empty space is the electromagnetic field, all photons having the same speed independent of any reference system.
Each inorganic solid consists of crystals, sometimes microscopically small. Amorphous solid matter does not exist or is very rare. The ground state of a crystal is the hypothetical state at zero temperature. At higher temperatures, each solid is in an excited state, determined by the presence of quasiparticles.
The crystal symmetry, adequately described by the theory of groups, has two or three levels. First, each crystal is composed of space filling unit cells. All unit cells of a crystal are equal to each other, containing the same number of atoms, ions or molecules in the same configuration. A characteristic lattice point indicates the position of a unit cell. The lattice points constitute a lattice named after Auguste Bravais and representing the crystal’s translation symmetry. Only fourteen types of Bravais lattices are mathematically possible and realized in nature. Each lattice allows of some variation, for instance with respect to the mutual distance of the lattice points, as is seen when the crystal expands on heating. Because each crystal is finite, the translation symmetry is restricted and the surface structure of a crystal may be quite different from the crystal structure.
Second, the unit cell has a symmetry of its own, superposed on the translation symmetry of the Bravais lattice. The cell may be symmetrical with respect to reflection, rotation or inversion. The combined symmetry determines how the crystal scatters X-rays or neutrons, presenting a means to investigate the crystalline structure empirically. Hence, the long distance spatial order of a crystal evokes a long time kinetic order of specific waves.
Third, in some materials we find an additional ordering, for instance that of the magnetic moments of electrons or atoms in a ferromagnet. Like the first one, this is a long-distance ordering. It involves an interaction that is not restricted to nearest neighbours. It may extend over many millions of atomic distances.
The atoms in a crystal oscillate around their equilibrium positions. These elastic oscillations are transferred from one atom to the next like a sound wave, and because the crystal has a finite volume, this is a stationary wave, a collective oscillation. The crystal as a whole is in an elastic oscillation, having a kinetically founded character. These waves have a broad spectrum of frequencies and wavelengths, being sampled into wave packets. In analogy with light, these field particles are called sound quanta or phonons.
Like the electrons in a metal, the phonons act like particles in a box. Otherwise they differ widely. The number of electrons is constant, but the number of phonons increases strongly at increasing temperature. Like all quasiparticles, the phonons are bosons, not being subject to the exclusion principle. The mean kinetic energy of the electrons hardly depends on temperature, and their specific heat is only measurable at a low temperature. In contrast, the mean kinetic energy of phonons strongly depends on temperature, and the phonon gas dominates the specific heat of solids. At a low temperature this increases proportional to T3 to become constant at a higher temperature. Peter Debije’s theory (originally 1912, later adapted) explains this from the wave and boson character of phonons and the periodic character of the crystalline structure.
In a solid or liquid, besides phonons many other quantized excitations occur, corresponding, for instance, with magnetization waves or spin waves. The interactions of quasiparticles and electrons cause the photoelectric effect and transport phenomena like electric resistance and thermo-electricity (T&E 7.5).
The specific properties of some superconductors can be described with the help of quasiparticles. In a superconductor two electrons constitute a Cooper-pair. This is a pair of electrons in a bound state, such that both the total linear momentum and the total angular momentum are zero. The two electrons are not necessarily close to each other. Superconductivity is a phenomenon with many variants, and the theory is far from complete.
Superconductivity is a collective phenomenon in which the wave functions of several particles are macroscopically coherent. There is no internal dissipation of energy. It appears that on a macroscopic scale the existence of kinetically founded characters is only possible if there is no decoherence. Therefore, kinetically founded physical characters on a macroscopic scale are quite exceptional.
11.5. Aggregates and statistics
Three types of physically qualified characters have now been discussed, but this does not exhaust the treatment of matter. The inorganic sciences acknowledge many kinds of mixtures, aggregates, alloys or solutions. In nature, these are more abundant than pure matter. Often, the possibility to form a mixture is restricted and some substances do not mix at all. In order to form a stable aggregate, the components must be tuned to each other. Typical for an aggregate is that the characteristic magnitudes (like pressure, volume and temperature for a gas) are variable within a considerable margin, even if there is a lawful connection between these magnitudes.
Continuous variability provides quantum physics with a criterion to distinguish a composite thing (with a character of its own) from an aggregate. Consider the interaction between an electron and a proton. In the most extreme case this leads to the absorption of the electron and the transformation of the proton into a neutron (releasing a neutrino). At a lower energy, the interaction may lead to a bound state having the character of a hydrogen atom if the total energy (kinetic and potential) is negative. Finally, if the total energy is positive, one has an unbound state, an aggregate. In the bound state the energy can only have discrete values, it is quantized, whereas in the unbound state the energy is continuously variable.
Hence, for an elementary particle (a lepton or a quark) the rest energy has a characteristic value, and internal energy states are lacking. A composite character has internal discrete energy states, whereas in an aggregate the internal energy is continuously variable.
With aggregates it is easier to abstract from specific properties than in the case of the characters of composite systems discussed in section 11.3. Thermodynamics studies the properties of macroscopic physical bodies (5.2). The thermodynamic laws describe the natural laws correctly in the case of interacting systems being close to equilibrium. Otherwise, the currents are turbulent and a concept like entropy cannot be defined. Another restriction follows from the individuality of the particles composing the system. In the equilibrium state, the entropy is not exactly constant, but it fluctuates spontaneously around the equilibrium value. Quantum physics shows energy to be subject to a Heisenberg-relation (7.6). In fact, the classical thermodynamic axioms refer to a continuum, not to the actually coarse matter. Thermodynamics is a general theory of matter, whereas statistical physics studies matter starting from the specific properties of the particles composing a system. This means that thermodynamics and statistical physics complement each other.
An equilibrium state is sometimes called an ‘attractor’, attracting a system from any instable state toward a stable state. Occasionally, a system has several attractors, now called local equilibrium states. If there is a strong energy barrier between the local equilibrium states, it is accidental which state is realized. By an external influence, a sudden and apparently drastic transition may occur from one attractor to another one. In quantum physics a similar phenomenon is called tunneling (11.7).
A homogeneous set of particles having the same character may be considered a quantitatively founded aggregate, if the set does not constitute a structural whole with a spatially founded character of its own (like the electrons in an atom). In a gas the particles are not bound to each other. Usually, an external force or a container is needed to keep the particles together. In a fluid, the surface tension is a connective force that does not give rise to a characteristic whole. The composing particles’ structural similarity is a condition for the applicability of statistics.
It is not sufficient to know that the particles are structurally similar. At least it should be specified whether the particles are fermions or bosons. Consider, for instance, liquid helium, having two varieties. In the most common isotope (He4), a helium nucleus is composed of two protons and two neutrons. The net spin is zero, hence the nucleus is a boson. In a less common isotope (He3), the helium nucleus has only one neutron besides two protons. Now the nucleus’ net spin is ½ and it is a fermion. This distinction (having no chemical consequences) accounts for strongly diverging macroscopic properties of the two fluids.
Each homogeneous gas is subjected to a specific law, called the statistics or distribution function. It determines how the particles are most likely distributed over the available states, taking into account parameters like volume, temperature, and total energy. The distribution function does not specify which states are available. Before the statistics is applicable, the energy of each state must be calculated separately.
The Fermi-Dirac statistics based on Wolfgang Pauli’s exclusion principle applies to all homogeneous aggregates of fermions, i.e., particles having half-integral spin. For field particles and other particles having an integral spin, the Bose-Einstein statistics applies, without an exclusion principle. If the mean occupation number of available energy states is low, both statistics may be approximated by the classical Maxwell-Boltzmann distribution function. Except at very low temperatures, this applies to every dilute gas consisting of similar atoms or molecules. The law of Boyle and Gay-Lussac follows from this statistics. It determines the relation between volume, pressure and temperature for a dilute gas, if the interaction between the molecules is restricted to elastic collisions and if the molecular dimensions are negligible. Without these two restrictions, the state equation of Johannes van der Waals counts as a good approximation (T&E 7.5). Contrary to the law of Boyle and Gay-Lussac, the Van der Waals equation contains two constants characteristic for the gas concerned. It describes the condensation of a gas to a fluid as well as the phenomena occurring at the critical point, the highest temperature at which the substance is liquid.
It is not possible to apply statistics directly to a mixture of subjects having different characters. Sometimes, it can be done with respect to the components of a mixture apart. For a mixture of gases like air, the pressure exerted by the mixture equals the sum of the partial pressures exerted by each component apart in the same volume at the same temperature (Dalton’s law). The chemical potential is a parameter distinguishing the components of a heterogeneous mixture.
A heterogeneous mixture like a solution may be considered to have a spatial foundation, because the solvent is the physical environment of the dissolved substance. Solubility is a characteristic disposition of a substance dependent on the character of the solvent as the potential environment.
Stable characters in one environment may be unstable in another one. Common salt molecules solved in water fall apart into sodium and chlorine ions. In the environment of water, the dielectric constant is much higher than in air. Now the Coulomb force between the ions is proportionally smaller, too small to keep the ions together.
The composition of a mixture, the number of grams of solved substance in one litre water, is accidental. It is not determined by any character but by its history. This does not mean that two substances can be mixed in any proportion whatsoever. However, within certain limits dependent on the temperature and the characters of the substances concerned, the proportion is almost continuously variable.
Even if a system only consists of particles of the same character, it may not appear homogeneous if it exists in two or more different phases simultaneously, for example, the solid, liquid, and vaporous states. A glass of water with melting ice is in internal equilibrium at 0°C. If heat is supplied, the temperature remains the same until all ice is melted. Only chemically pure substances have a characteristic melting point. In contrast, a heterogeneous mixture has a melting trajectory, meaning that during the melting process, the temperature increases. A similar characteristic transition temperature applies to other phase transitions in a homogeneous substance, like vaporizing, the transition from a paramagnetic to a ferromagnetic state, or the transition from a normal to a superconducting state. Addition of heat or change of external pressure shifts the equilibrium. A condition for equilibrium is that the particles concerned move continuously from one phase to the other. Therefore this may be called a homogeneous kinetically founded aggregate.
An important example of a heterogeneous kinetic equilibrium concerns chemical reactions. Water consists mostly of water molecules, but a small part (10-7 at 25oC) is dissociated into positive H-ions and negative OH-ions. In the equilibrium state, equal amounts of molecules are dissociated and associated. By adding other substances (acids or bases), the equilibrium is shifted.
Both phase transitions and chemical reactions are subject to characteristic laws and to general thermodynamic laws, for instance Joshua Gibbs’s phase rule.
11.6. Symmetric and antisymmetric wave functions
Based on the characteristic similarity of the individuals concerned, statistical research is of eminent importance in all sciences. It is a means to research the character of individuals whose similarity is recognized or conjectured. It is also a means to study the properties of a homogeneous aggregate containing a multitude of individuals of the same character.
As early as 1860, James Clerk Maxwell applied statistics to an ideal gas, consisting of N molecules, each having mass m, in a container with volume V (8.5). The weakness of Maxwell’s theory was neglecting the mutual interaction of the molecules, for without interaction equilibrium cannot be reached. Ludwig Boltzmann corrected this by assuming that the molecules collide continuously with each other, exchanging energy. He arrived at the same result.
Maxwell and Boltzmann considered one system consisting of a large number of molecules, whereas Joshua Gibbs studied an ensemble of a large number of similar systems. Assuming that all microstates are equally probable, the probability of a macrostate can be calculated by determining the number of corresponding microstates. The logarithm of this number is proportional to the entropy of a macrostate.
Both in classical and in quantum statistics a character as a set of laws determines the ensemble of possibilities and the distribution of probabilities (chapters 8, 9). It allows of individuality, the subject side of a character. Positivist philosophers defined probability as the limit of a frequency in an unlimited sequence of individual cases. In this way, they tried to reduce the concept of probability to the subject side. Of course, the empirical measurement of a probability often has the form of a frequency determination. Each law statement demands testing, and that is only possible by taking a sample. However, this does not justify the elimination of the law-side from probability theory.
An example of a frequency definition of probability is found in the study of radioactivity. A radioactive atom decays independent of other atoms, even if they belong to the same sample. During the course of time, the initial number of radioactive atoms (No) in a sample decreases exponentially to Nt at time t. Many scientists are content with this practical definition. However, a sample is a collection limited in time and space, it is not an ensemble of possibilities.
There are two limiting cases. In the one case, we extend the phenomenon of radioactivity to all similar atoms, increasing Noand Nt infinitely in order to get a theoretical ensemble. The ensemble has two possibilities, the initial state and the final state, and their distribution in the ensemble at time t after to can be calculated. In the other limiting case we take No=1. Now exp.-(t-to)/t is the chance that a single atom decays after t-to sec. This quotient depends on a time difference, not on a temporal instant. As long as the atom remains in its initial state, the probability of decay to the final state is unchanged.
Both limiting cases are theoretical. An ensemble is no more experimentally determinable than an individual chance. Only a collection of atoms can be subjected to experimental research. It makes no sense to consider one limiting case to be more fundamental than the other one. The first case concerns the law side, the second case the subject-side of the same phenomenon of radioactivity.
The concept of probability is applicable to a single particle as well as to a homogeneous set of similar particles, a gas consisting of molecules, electrons or photons. In order to study such systems, since circa 1860 statistical physics has developed various mathematical methods. A distribution function points out how the energy is distributed over the particles, how many particles have a certain energy value, and how the average energy depends on temperature. In any distribution function, the temperature is an important equilibrium parameter.
Classical physics assigned each particle its own state, but in quantum physics, this would lead to wrong results. It is better to design the possible states, and to calculate how many particles occupy a given state, without questioning which particle occupies which state. It turns out that there are two entirely different cases.
In the first case, the occupation number of particles in a well-defined state is unlimited. Bosons like photons are subject to a distribution function in 1924 derived by Satyendra Bose and published by Einstein, hence called Bose-Einstein statistics. Bosons have an integral spin. The occupation number of each state may vary from zero to infinity.
In the other case, each well-defined state is occupied by at most one particle, according to Wolfgang Pauli’s exclusion principle. The presence of a particle in a given state excludes the presence of another similar particle in the same state. Fermions like electrons, protons, and neutrons have a half-integral spin. They are subject to the distribution function that Enrico Fermi and Paul Dirac derived in 1926.
In both cases, the distribution approximates the classical Maxwell-Boltzmann distribution function, if the mean occupation of available states is much smaller than 1. This applies to molecules in a classical gas.
The distinction of fermions and bosons rests on permutation symmetry. In a finite set the elements can be ordered into a sequence and numbered using the natural numbers as indices. For n elements, this can be done in n!=18.104.22.168…n different ways. The n! permutations are symmetric if the elements are indistinguishable. Permutation symmetry is not spatial but quantitative.
In a system consisting of a number of similar particles, the state of the aggregate can be decomposed into a product of separate states for each particle apart. A permutation of the order of similar particles should not have consequences for the state of the aggregate as a whole. However, in quantum physics only the square of a state is relevant to probability calculations. Hence, exchanging two particles allows of two possibilities: either the state is multiplied by +1 and does not change, or it is multiplied by –1. In both cases, a repetition of the exchange produces the original state. In the first case, the state is called symmetric with respect to a permutation, in the second case antisymmetric.
In the antisymmetric case, if two particles would occupy the same state an exchange would simultaneously result in multiplying the state by +1 (because nothing changes) and by –1 (because of antisymmetry), leading to a contradiction. Therefore, two particles cannot simultaneously occupy the same state. This is the exclusion principle concerning fermions. No comparable principle applies to bosons, having symmetric wave functions with respect to permutation,.
Both a distribution function like the Fermi-Dirac statistics and Pauli’s exclusion principle are only applicable to a homogeneous aggregate of similar particles. In a heterogeneous aggregate like a nucleus, they must be applied to the protons and neutrons separately.
The distinction of fermions and bosons, and the exclusion principle for fermions, have a fundamental significance for the understanding of the characters of material things containing several similar particles. To a large extent, it explains the orbital structure of atoms and the composition of nuclei from protons and neutrons.
The exclusion principle in solid state physics
When predicting the wave character of electrons, Louis de Broglie suggested that the stability of the electronic orbit in a hydrogen atom is explainable by assuming that the electron moves around the nucleus as a standing wave. This implies that the circumference of the orbit is an integral number times the wavelength. From the classical theory of circular motion, he derived that the orbital angular momentum should be an integral number times Planck’s reduced constant (h/2p). This is precisely the quantum condition applied by Niels Bohr in 1913 in his first atomic theory.
The atomic physicists at Copenhagen, Göttingen, and Munich considered this idea rather absurd, but it received support from Einstein, and it inspired Schrödinger to develop his wave equation. In a stable system, Schrödinger’s equation is independent of time and its solutions are stationary waves, comparable to the standing waves in a violin string or an organ pipe. Only a limited number of frequencies are possible, corresponding to the energy levels in atoms and molecules. Although one often speaks of the Schrödinger equation, there are many variants, one for each physical character. Each variant specifies the system’s boundary conditions and expresses the law for the possible motions of the particles concerned.
In the practice of solid-state physics, the exclusion principle is more important than the Schödinger equation. This can be elucidated by discussing the model of particles confined to a rectangular box. Again, the wave functions look like standing waves.
In a good approximation the valence electrons in a metal or semiconductor are not bound to individual atoms but are free to move around. The mutual repulsive electric force of the electrons compensates for the attraction by the positive ions. The electron’s energy consists almost entirely of kinetic energy, E=p2/2m, if p is its linear momentum and m its mass.
Because the position of the electron is confined to the box, in the Heisenberg relation Δx equals the length of the box (analogous for y and z). Because Δx is relatively large, Δp is small and the momentum is well defined. Hence the momentum characterizes the state of each electron and the energy states are easy to calculate. In a three-dimensional momentum space a state denoted by the vector p occupies a volume Δp. According to the exclusion principle, a low energy state is occupied by two electrons (because there are two possible spin states), whereas high-energy states are empty. In a metal, this leads to a relatively sharp separation of occupied and empty states. The mean kinetic energy of the electrons is almost independent of temperature, and the specific heat is proportional to temperature, strikingly different from other aggregates of particles.
Mechanical oscillations or sound waves in a solid form wave packets. These bosons are called phonons or sound particles. Bose-Einstein statistics leads to Peter Debije’s law for the specific heat of a solid. At a moderate temperature the specific heat is proportional to the third power of temperature. A similar situation applies to an oven, in which electromagnetic radiation is in thermal equilibrium. According to Planck’s law of radiation, the energy of this boson gas is proportional to the fourth power of temperature. Hence, the difference between fermion and boson aggregates comes quite dramatically to the fore in the temperature dependence of their energy. Amazingly, the physical character of the electrons, phonons, and photons plays a subordinate part compared to their kinetic character. Largely, the symmetry of the wave function determines the properties of an aggregate. Consequently, a neutron star has much in common with an electron gas in a metal.
The existence of antiparticles is a consequence of a symmetry of the relativistic wave equation. The quantum mechanics of Erwin Schrödinger and Werner Heisenberg in 1926 was not relativistic, but about 1927 Paul Dirac found a relativistic formulation. From his equation follows the electron’s half-integral angular momentum, not as a spinning motion as conceived by its discoverers, Samual Goudsmit and George Uhlenbeck, but as a symmetry property (still called spin).
Dirac’s wave equation had an unexpected result, to wit the existence of negative energy eigenvalues for free electrons. According to relativity theory, the energy E and momentum p for a freely moving particle with rest energy Eo=moc2 are related by the formula: E2=Eo2+(cp)2. For a given value of the linear momentum p, this equation has both positive and negative solutions for the energy E. De positive values are minimally equal to the rest energy Eo and the negative values are maximally -Eo. This leaves a gap of twice the rest energy, about 1 MeV for an electron. Classical physics could ignore negative solutions, but this is not allowed in quantum physics. Even if the energy difference between positive and negative energy levels is large, the transition probability is not zero. In fact, each electron should spontaneously jump to a negative energy level, releasing a gamma particle having an energy of at least 1 MeV.
Dirac took recourse to Pauli’s exclusion principle. By assuming all negative energy levels to be occupied, he could explain why these are unobserved most of the time, and why many electrons have positive energy values. An electron in one of the highest negative energy levels may jump to one of the lowest positive levels, absorbing a gamma particle having an energy of at least 1 MeV. The reverse, a jump downwards, is only possible if in the nether world of negative energy levels, at least one level is unoccupied. Influenced by an electric or magnetic field, such a hole moves as if it were a positively charged particle. Initially, Dirac assumed protons to correspond to these holes, but it soon became clear that the rest mass of a hole should be the same as that of an electron.
After Carl Anderson in 1932 discovered the positron, a positively charged particle having the electron’s rest mass, this particle was identified with a hole in Dirac’s nether world. Experiments pointed out that an electron is able to annihilate a positron, releasing at least two gamma particles.
Meanwhile it is established that besides electrons all particles, bosons included, have antiparticles. Only a photon is identical to its antiparticle. The existence of antiparticles rests on several universally valid laws of symmetry. A particle and its antiparticle have the same mean lifetime, rest energy and spin, but opposite values for charge, baryon number, or lepton number.
However, if the antiparticles are symmetrical to particles, why are there so few? (Or why is Dirac’s nether world nearly completely occupied?) Probably, this problem can only be solved within the framework of a theory about the early development of the cosmos.
The band theory for metals and semiconductors
The image of an infinite set of unobservable electrons having negative energy, strongly defeats common sense. However, it received unsolicited support from the so-called band theory in solid-state physics, being a refinement of the earlier discussed free-electron model. The influence of the ions is not completely compensated for by the electrons. An electric field remains having the same periodic structure as the crystal. Taking this field into account, Rudolf Peierls developed the band model. It explains various properties of solids quite well, both quantitatively and qualitatively.
A band is a set of neighbouring energy levels separated from other bands by an energy gap. It may be fully or partly occupied by electrons, or it is unoccupied. Both full and empty bands are physically inert. In a metal, at least one band is partly occupied, partly unoccupied by electrons. An isolator has only full (i.e., entirely occupied) bands besides empty bands. The same applies to semiconductors, but now a full band is separated from an empty band by a relatively small gap. According to Peierls in 1929, if energy is added in the form of heat or light (a phonon or a photon), an electron jumps from the lower band to the higher one, leaving a hole behind. This hole behaves like a positively charged particle. In many respects, an electron-hole pair in a semiconductor looks like an electron-positron pair. Only the energy needed for its formation is about a million times smaller.
Another important difference should be mentioned. The set of electron states in Dirac’s theory is an ensemble. In the class of possibilities independent of time and space, half is mostly occupied, the other half is mostly empty. There is only one nether world of negative energy values. In contrast, the set of electrons in a semiconductor is a spatially and temporally restricted collection of electrons, in which some electron states are occupied, others unoccupied. There are as many of these collections as there are semiconductors. To be sure, Peierls was interested in an ensemble as well. In his case, this is the ensemble of all semiconductors of a certain kind. This may be copper oxide, the standard example of a semiconductor in his days, or silicon, the base material of modern chips. But this only confirms the distinction from Dirac’s ensemble of electrons.
11.7. Coming into being, change and decay
The physically qualified characters discussed so far are mainly thing-like, meaning that their properties (not their propensities) are secondarily characterized by retrocipations on preceding relation frames. In contrast, events have a more anticipatory character. An event is physically qualified if it is primarily characterized by an interaction between two or more subjects. A process is a characteristic set of events, partly simultaneously, partly successively. Therefore, physically qualified events and processes often occur in an aggregate, sometimes under strictly determined circumstances, among which the temperature. In a mixture, physical, chemical and astrophysical reactions lead to the realization of characters. Whereas in physical things properties like stability and life time are most relevant, physical and chemical processes concern the coming into being, change and decay of those things.
In each characteristic event a thing changes of character (it emerges or decays) or of state (preserving its identity). With respect to the thing’s character considered as a law, the first case concerns a subjective event (because the subject changes). The second case concerns an objective event (for the objective state changes). Both have secondary characteristics. I shall briefly mention some examples.
Annihilation or creation of particles is a subjective numerically founded event. Like any other event, it is subject to conservation laws. An electron and a positron emerge simultaneously from the collision of a gamma-particle with some other particle, if the photon’s energy is at least twice the electron’s rest energy. The presence of another particle, like an atomic nucleus, is required in order to satisfy the law of conservation of linear momentum. For the same reason, at least two photons emerge when an electron and a positron destroy each other.
By emitting or absorbing a photon, a nucleus, atom or molecule changes its state. This is a spatially founded objective transformation. In contrast, in a nuclear or chemical reaction one or more characters are transformed, constituting a subjective spatially founded event. In a- or b-radioactivity, a nucleus changes subjectively its character, in g-activity it only changes objectively of its state.
An elastic collision is an event in which the kinetic state of a particle is changed without consequences for its character or its internal state. Hence, this concerns an objective kinetically founded event. In a non-elastic collision a subjective change of character or an objective change of state occurs. Quantum physics describes such events with the help of operators determining the transition probability.
A process is an aggregate of events. In a homogeneous aggregate, phase transitions may occur. In a heterogeneous aggregate chemical reactions occur (11.5). Both are kinetically founded. This also applies to transport phenomena like electric, thermal or material currents, thermo-electric phenomena, osmosis and diffusion. In such processes temperature is always an important parameter. It determines the stability of spatially founded things, and the occurrence of collisions between them.
Constraints on events
Conservation laws are constraints, restricting the possibility of processes. For instance, a process in which the total electric charge would change is impossible. In atomic and nuclear physics, transitions are known to be forbidden or improbable because of selection rules for quantum numbers characterizing the states concerned.
Physicists and chemists take for granted that each process that is not forbidden is possible and therefore experimentally realizable. Several laws of conservation like those of lepton number and baryon number were discovered because certain expected reactions turned out to be impossible. In 1930 Wolfgang Pauli postulated the existence of neutrino’s, because otherwise the laws of conservation of energy and momentum would not apply to b-radioactivity. Experimentally, the existence of neutrinos was not confirmed until 1956.
In common life, a collision may be a rather dramatic event, but in physics and chemistry a collision is just an interaction between two or more subjects moving towards each other, starting from a large distance, where their interaction is negligible. In classical mechanics, this interaction means an attractive or repelling force. In modern physics, it implies the exchange of real or virtual particles like photons.
In each collision, at least the state of motion of the interacting particles changes. If that is all, we speak of an elastic collision, in which only the distribution of kinetic energy, linear and angular momentum over the colliding particles changes. A photon can collide elastically with an electron (this is the Compton effect), but an electron cannot absorb a photon. Only a composite thing like a nucleus or an atom is able to absorb a particle.
Collisions are used to investigate the character of the particles concerned. A famous example is the scattering of a-particles by gold atoms (1911). For the physical process, it is sufficient to assume that the particles have mass and charge and are point-like. It does not matter whether the particles are positively or negatively charged. The character of this collision is statistically expressed in a mathematical formula derived by Ernest Rutherford. The fact that the experimental results (by Hans Geiger and Ernest Marsden) agreed with the formula indicated that the nucleus is much smaller than the atom, and that the mass of the atom is almost completely concentrated in the nucleus. A slight deviation between the experimental results and the theoretical formula allowed of an estimate of the size of the nucleus, its diameter being about 104 times smaller than the atom’s. The dimension of a microscopic invisible particle is calculable from similar collision processes, and is therefore called its collision diameter. Its value depends on the projectiles used. The collision diameter of a proton differs if determined from collisions with electrons or neutrons.
In a non-elastic collision the internal structure of one or more colliding subjects changes in some respect. With billiard balls only the temperature increases, kinetic energy being transformed into heat, causing the motion to decelerate.
In a non-elastic collision between atoms or molecules, the state of at least one of them changes into an excited state, sooner or later followed by the emission of a photon. This is an objective characteristic process.
The character of the colliding subjects may change subjectively as well, for instance, if an atom loses an electron and becomes an ion, or if a molecule is dissociated or associated.
Collisions as a means to investigate the characters of subatomic particles have become a sophisticated art in high-energy physics.
Spontaneous decay became first known at the end of the 19th century from radioactive processes. It involves strong, weak or electromagnetic interactions, respectively in a-, b-, and g-radiation. The decay law of Ernest Rutherford and Frederick Soddy (1902) approximately gives the character of a single radioactive process. This statistical law is only explainable by assuming that each atom decays independently of all other atoms. It is a random process. Besides, radioactivity is almost independent of circumstances like temperature, pressure and the chemical compound in which the radioactive atom is bound. Such decay processes occur in nuclei and sub-atomic particles, as well as in atoms and molecules being in a metastable state. The decay time is the mean duration of existence of the system or the state.
The mean lifetime of spontaneous decay differs widely. The stronger the interaction causing a transition, the faster the system changes. If a particle decays because of the colour force or strong force, it happens in a very short time (of the order of 10-23 to 10-19 sec). Particles decaying due to weak interaction have a relatively long lifetime (10-12 sec for a tauon up to 900 sec for a free neutron). Electromagnetic interaction is more or less between. For a spontaneous electronic transition within an atom, the decay time is of the order of 10-8 sec.
Besides spontaneous ones, stimulated transformations occur. Albert Einstein first investigated this phenomenon in 1916, with respect to transitions between two energy levels of an atom or molecule, emitting or absorbing a photon. He found that (stimulated) absorption and stimulated emission are equally probable, whereas spontaneous emission has a different probability. Stimulated emission is symmetrical with stimulated absorption, but spontaneous emission is asymmetric and irreversible.
A stable system or a stable state may be separated from other systems or states by an energy barrier. It may be imagined that a particle is confined in an energy well, for instance an a-particle in a nucleus. According to classical mechanics, such a barrier is insurmountable if it has a larger value than the kinetic energy of the particle in the well, but quantum physics proves that there is some probability that the particle leaves the well. This is called tunneling, for it looks like the particle digging a tunnel through the energy mountain.
Consider a chemical reaction in which two molecules A and B associate to AB and conversely, AB dissociates into A and B. The energy of AB is lower than the energy of A+B apart, the difference being the binding energy. A barrier called the activation energy separates the two states. In an equilibrium situation, the binding energy and the temperature determine the proportion of the numbers of molecules (NA.NB/NAB). It is independent of the activation energy. At a low temperature, if the total number of A’s equals the total number of B’s, only molecules AB will be present. In an equilibrium situation at increasing temperatures, the number of molecules A and B increases, and that of AB decreases. In contrast, the speed of the reaction depends on the activation energy (and again on temperature). Whereas the binding energy is a characteristic magnitude for AB, the activation energy partly depends on the environment. In particular the presence of a catalyst may lower the activation energy and stimulate tunneling, increasing the speed of the reaction.
The possibility to overcome energy barriers explains the possibility of transitions from one more or less stable system to another one. It is the basis of theories about radioactivity and other spontaneous transitions, chemical reaction kinetics, the emergence of chemical elements and of phase transitions, without affecting theories explaining the existence of stable or quasi-stable systems.
In such transition processes the characters do not change, but a system may change of character. The laws do not change, but their subjects do.
Evolution of the elements
The chemical elements have arisen in a chain of nuclear processes, to be distinguished as fusion and fission. The chain starts with the fusion of hydrogen nuclei (protons) into helium nuclei, which are so stable that in many stars the next steps do not occur. Further processes lead to the formation of all known natural isotopes up to uranium. Besides helium with 4 nucleons, beryllium (8), carbon (12), oxygen (16) and iron (56) are relatively stable. In all these cases, both the number of protons and the number of neutrons is even.
The elements only arise in specific circumstances. In particular, the temperature and the density are relevant. The transition from hydrogen to helium occurs at 10 to 15 million Kelvin and at a density of 0,1 kg/cm3. The transition of helium into carbon, oxygen and neon occurs at 100 to 300 million Kelvin and 100 kg/cm3. Only after a considerable cooling down, these nuclei form with electrons the atoms and molecules to be found on the earth.
Once upon a time the chemical elements were absent. This does not mean that the laws determining the existence of the elements did not apply. The laws constituting the characters of stable and metastable isotopes are universally valid, appearing to be independent of time and place. But the realization of the characters into actual individual nuclei does not depend on the characters only, but on circumstances like temperature as well. On the other hand, the available subjects and their relations determine these circumstances. Like initial and boundary conditions, characters are conditions for the existence of individual nuclei. Mutatis mutandis, this applies to electrons, atoms and molecules as well.
In chapter 10, I discussed quantitative, spatial and kinetic characters. About the corresponding subjects, like groups of numbers, spatial figures or wave packets, it cannot be said that they come into being or decay, except in relation to physical subjects. Only interacting things emerge and disappear. Therefore there is no quantitative, spatial or kinetic evolution comparable to the astrophysical one, even if the latter is expressed in numerical proportions, spatial relations and characteristic rhythms. Because evolution requires physical interaction, it may be called dynamic development.
Although stars have a lifetime far exceeding the human scale, it is difficult to consider them stable. Each star is a reactor in which continuously processes take place. Stars are subject to evolution. There are young and old stars, each with their own character. Novae and supernovae, neutron stars and pulsars represent various phases in the evolution of a star. The simplest stellar object may be the black hole, behaving like a thermodynamic black body subject to the laws of thermodynamics.
These processes play a part in the theory about the astrophysical evolution, strongly connected to the standard model (11.1). It correctly explains the relative abundance of the chemical elements. After the very hot start of the dynamic development of the physical cosmos, about thirteen billion years ago, it has expanded at decreasing temperature. A result is the emergence of structures which can only be realized at moderate temperatures: nuclei, atoms, molecules,and solids; planets with their moons; and ultimately, at one lucky planet, living organisms.
The formation of physical things requires collisions, meaning that it can only occur within a margin of temperature, a margin of mean collision energy. Even the formation of an electron-positron pair requires the interaction of at least two photons, with an energy larger that the rest mass of the two emerging particles. On the other hand, the mean kinetic energy (the temperature) cannot be too high, otherwise the next collision would destroy the newly formed systems. Therefore, the decreasing temperature acts as a random dynamic push for the astrophysical evolution. It also needs a specific dynamic pull, the lawful structure of the systems to be formed. Photons can only form an electron-positron pair subject to the specific laws for leptons, and the same applies to the formation of all characteristic physical things.
The expansion of the universe means that all galaxies move away from each other, the larger the distance, the higher their speed. Because light needs time to travel, the picture astronomers get from galaxies far away concerns states from era’s long past. The most remote systems are at the spatio-temporal horizon of the physical cosmos. In this case, astronomers observe events that occurred shortly after the big bang, the start of the astrophysical evolution.
The real start of the physical universe remains forever behind the horizon of human experience. Astrophysicists are aware that going backwards their theories based on observations may approach the big bang without ever reaching it. The astrophysical theory describes what has happened since the beginning - not the start itself - according to laws discovered in our era. The extrapolation towards the past is based on the supposition that these laws are universally valid and constant. This agrees with the realistic view that the cosmos can only be investigated from within. It is not uncommon to consider our universe as one realized possibility taken from an ensemble of possible worlds, as if it would have a character of its own, which may be doubted. Anyhow, there is no way to investigate these alternative worlds empirically.
11.8. Dynamic development of the hidden structure of matter
Chapter 11 investigated the structures of anorganic matter, and chapters 12 and 13 will do the same with the organic and animal worlds. One of the interesting aspects of this investigation is that most of these structures are recently discovered, being totally unknown for the largest part of human history. Generally speaking, this is because structures concern stable things, screening themselves from outside disturbances. Even the relevance of electricity, long considered to be an obscure property of amber only, was only gradually realized in the 19th century (T&E chapter 5), and nuclear forces were discovered after 1930, less than a century ago. The elementary particles and their composites came to the physicists’ attention since the turn of the 20th century, several decades after the chemists started to investigate the structure of molecules.
It is now generally accepted that anorganic matter indeed has hidden structures to be laid bare by intensive scientific research, but this insight is relatively new. It is not obvious, and it was doubted more often than not. Positivist philosophers believe that there are only phenomena, and that structures are human constructs invented to save the phenomena (using a medieval term), to make these comprehensible. In the course of time, this view has become somewhat incredible, since scientists succeeded in penetrating those structures, both theoretically and in particular experimentally. In this process more and more new phenomena came to light, in part predicted with the help of tentative and imperfect models of these structures. It would be quite unbelievable to accept the idea that constructs for explaining phenomena could create new phenomena, instead of assuming that the hidden structures can be opened up to reveal their properties and propensities.
The search for the hidden structure of the anorganic world opposes the classical rationalistic ideal of science, according to which an explanation should start from well-known, self-evident, directly understandable axioms, which truth should be clear for every right-minded human being. Since the 17th century physics abandoned this ideal of science. There is nothing evident in human knowledge of the creation. Scientists try to find the laws that structure reality, achieving their knowledge by observation and experiment. Yet the search for the hidden structure also yields new phenomena, contrary to the classical empiricist science ideal considering phenomena as given, from which laws should be derived by induction. Most phenomena with which advanced investigators are concerned are opened up by scientific research studying the hidden structures. No less than structures, phenomena are hidden from common knowledge.
Science operates neither rationalistically nor empiristically, though it is both rational and empirical. Whereas rationalism neglects experience, empiricism neglects the human ratio. Both are quite static, considering the world as present, as immediately given to natural experience. For both the natural world is transparent, either for natural thought or for natural experience. The invention of the telescope and the microscope have made science aware that the world is not immediately transparent.
With his telescope Galileo discovered shortly after 1600 mountains on the moon, the phases of Venus, the moons of Jupiter, and much more stars than are visible by the naked eye. These discoveries were met with much resistance. One objection was that it is unthinkable that God would make things invisible without a telescope. What is the use of Jupiter having moons? If God intended people to perceive these moons with a telescope, He would have created people with telescopic eyes. This argument means an absolutistic view of natural experience, sounding weird in modern ears. But about 1600 it was far from evident that beyond the human horizon another world may exist, even after Christopher Columbus had discovered America a century before.
Microscopes, too, led to the discovery of a new world, especially in biology. People like Antoni van Leeuwenhoek and Jan Swammerdam were fascinated by one after another discovery of botanic and zoological phenomena and structures which existence could not have been dreamed of before.
Yet even at the turn of the 20th century positivist philosophers like Ernst Mach believed that atoms do not exist because they were never seen. They ignored that besides telescopes and microscopes also theories and experiments are instruments in the dynamic development of hidden structures. Similarly, behaviourists in psychology maintained that only observable behaviour of individual people and animals is real, such that it makes no sense to speculate about an internal structure explaining behaviour. These once popular views lost adherence quite fast in 20th century natural sciences.
The structure of a system is not simply the sum of its directly manifest properties, as was defended over the centuries by alchemists, positivists and behaviorists. The properties and propensities of any structure are hidden, and can only be found by intensive theoretical and experimental research making phenomena manifest. The character as the law for a hidden structure determines its properties and propensities, not reversely.
To perform science is a responsible activity. People ought not to maintain an arrogant rationalistic or empiricist attitude, as if the world is on their hand. A better attitude is that of wonder and respect, of asking questions, of research into how reality responds to the laws for its dynamic development – because the creation does not depend on humanity. In this questioning attitude people discover that things, plants and animals are creations, replying in their own individual way to their structure given by God.
This questioning attitude is one way by which people distinguish themselves. Only human beings are aware of their responsibility, only they attempt to widen their horizon, and only they ask for the hidden structures, the coherence, the unity, the dynamic development, and the origin of reality.
 Jammer 1966, Chapter 14; Popper 1967, 8,9.
 Groups, spatial figures, waves and oscillations do not interact, hence are not physical unless interlaced with physical characters.
 Pauli postulated the existence of neutrinos in 1930 in order to explain the phenomenon of β-radioactivity. Neutrino’s were not detected experimentally before 1956. According to a physical criterion, neutrino’s exist if they demonstrably interact with other particles. Sometimes it is said that the neutrino is ‘observed’ for the first time in 1956. Therefore one has to stretch the concept of ‘observation’ quite far. In no experiment neutrino’s can be seen, heard, smelled, tasted or felt. Even their path of motion cannot be made visible in any experiment. But in several kinds of experiment, from observable phenomena the energy and momentum (both magnitude and direction) of individual neutrino’s can be calculated. For a physicist, this provides sufficient proof for their existence.
 ‘System’ is a general expression for a bounded part of space inclusive of the enclosed matter and energy. A closed system does not exchange energy or matter with its environment. Entropy can only be defined properly if the system is in internal equilibrium.
 About 1900, the electromagnetic world view (T&E 4.6) supposed that all physical and chemical interactions could be reduced to electromagnetism, see McCormmach 1970a; Kragh 1999, chapter 8. Just like the modern unification program, it aimed at deducing the (rest-) mass of elementary particles from the fundamental interaction, see Jammer 1961, chapter 11.
 SU(3) means special unitary group with three variables. The particles in a representation of this group have the same spin and parity (together one variable), but different values for strangeness and one component of isospin.
 Symmetry is as much an empirical property as any other one. After the discovery of antiparticles it was assumed that charge conjugation C (symmetry with respect to the interchange of a particle with its antiparticle), parity P (mirror symmetry) and time reversal T are properties of all fundamental interactions. Since 1956, it is experimentally established that β-decay has no mirror symmetry unless combined with charge conjugation (CP). In 1964 it turned out that weak interactions are only symmetrical with respect to the product CPT, such that even T alone is no longer universally valid.
 Pickering 1984, chapter 9-11; Pais 1986, 603-611. The J/ψ particle established the existence of charm as the fourth flavour of quarks in 1974. In 1977 the fifth quark was found (bottom), in 1978 the tauon, in 1995 the sixth quark (top).
 Historically the suffix –on goes back to the electron. Whether the connection with ontology has really played a part is unclear. See Walker, Slack 1970, who do not mention Faraday’s ion. The word electron comes from the Greek word for amber or fossilized resin, since antiquity known for its properties that we now recognize as static electricity. From 1874, Stoney used the word electron for the elementary amount of charge. Only in the 20th century, electron became the name of the particle identified by Thomson in 1897. Rutherford introduced the names proton and neutron in 1920 (long before the actual discovery of the neutron in 1932). Lewis baptized the photon in 1926, 21 years after Einstein proposed its existence.
 See Millikan 1917; Anderson 1964; Thomson 1964; Pais 1986; Galison 1987; Kragh 1990; 1999.
 Pickering 1984, 67; Pais 1986, 466: ‘The agreement between experiment and theory shown by these examples, the highest point in precision reached anywhere in the domain of particles and fields, ranks among the highest achievements of 20th-century physics.’
 In a collision between two electrons, the assumption that they do or do not keep their identity leads to different predictions for the result. Experimentally, it turns out that they do not maintain their identity.
 1 keV is 1000 eV; 1 MeV is 1 million electronvolt. 1 eV equals the energy that a particle having the elementary charge gains by proceeding through an electric potential difference of 1 Volt.
 Neutrino’s are stable, their rest mass is very small, and they are only susceptible to weak interaction. Neutrino’s and anti-neutrino’s differ by their parity, the one being left handed, and the other right handed. (This distinction is only possible for particles having zero restmass. If neutrinos have a rest mass different from zero, as some recent experiments suggest, the theory has to be adapted with respect to parity). That the three neutrinos differ from each other is established by processes in which they are or are not involved, but in what respect they differ is less clear. For some time, physicists expected the existence of a fourth generation, but the standard model restricts itself to three, because astrophysical cosmology implies the existence of at most three different types of neutrino’s with their antiparticles.
Weisskopf 1972, 41-51; Pais 1986.
 From scattering experiments of electrons at a high energy, it follows that a proton as well as a neutron has three hard kernels, each with an electric charge of (1/3)e or (2/3)e. Like electrons in an atom, quarks may have an orbital angular momentum besides their spin angular momentum, such that mesons and baryons may have a spin larger than 2/3.
 See Barrow, Tipler 1986, 5, 252-254.
 A free neutron decays into a proton, an electron and an antineutrino. The law of conservation of baryon number is responsible for the stability of the proton, being the baryon with the lowest rest energy. The assumption that this law is not absolutely valid, the proton having a decay time of the order of 1031 years, is not confirmed experimentally.
 This is the so-called time-independent Schrödinger equation, determining stationary states and energy levels.
 Positronium is a short living composite of an electron and a positron, the only spatially founded structure entirely consisting of leptons.
The symmetry of strong nuclear interaction is broken by electroweak interaction. For the strong interaction, the proton and the neutron are symmetrical particles having the same rest energy, but the electroweak interaction causes the neutron to have a slightly larger rest energy and to be metastable as a free particle.
Cat 1998, 288: ‘The unifying symmetry Weinberg seems to propose as a picture of the world as it is can, if true, be neither universal nor complete.’
 In the theory of evolution too, the idea of increasing complexity is widely used but hard to define and to apply in practice, see McShea 1991.
 Even in the ground state at zero temperature the atoms oscillate, but this does not give rise to a wave motion.
 This applies to the superconducting metals and alloys known before 1986, as explained by John Bardeen, Leon Cooper and John Schrieffer. For the ceramic superconductors, discovered since 1986, this explanation is not sufficient.
 This phenomenon is called Bose-condensation. A similar situation occurs in liquid helium below 2.1 K.
 The zero point of energy is the potential energy at a large mutual distance.
 A more detailed explanation depends on the property of a water molecule to have a permanent electric dipole moment. Each sodium or chlorine ion is surrounded by a number of water molecules, decreasing their net electric charge. This causes the binding energy to be less than the mean kinetic energy of the molecules.
The negative logarithm (base 10) of the molar concentration of protons is called the pH-value. For pure water at 25 oC, pH = 7, meaning that one in a half billion molecules are ionized. A water molecule may lose or gain a proton. Most H+-ions are coupled to a water molecule to become H3O+ (hydronium).
 Callen 1960, 206-207. The number of degrees of freedom f is defined as the number of variables (temperature, pressure, and concentration) that can be chosen freely to describe the state of a chemical component. The number of components is r, and between the components c different chemical reactions are possible. The number of different phases is m. Now Gibbs’s phase rule is f=(r+2) -m-c. For the equilibrium of ice, water, and its vapour r=1, m=3, c=0, hence f=0. This means that this equilibrium can exist at only one value for temperature and pressure, the so-called triple point (temperature 273,16 K = 0,01 oC, pressure 611,2 Pascal).
 When at a time to, No radioactive atom of the same kind are left in a sample, then the expected number of remaining atoms at time t equals: Nt=No exp.-(t-to)/t, such that Nt/No=exp.-(t-to)/t. The characteristic constant t is proportional to the well-known half-life time. The law of decay is theoretically derivable from quantum field theory. This results in a slight deviation from the exponential function, too small to be experimentally verifiable, see Cartwright 1983, 118.
 Namely as the proportion exp.-(t-to)/t=[exp.-t/t]/[exp.-to/t].
 Jammer 1966, 338-345.
 An integral spin means that the intrinsic angular momentum is an integer times Planck’s reduced constant, 0, h/2π, 2h/2π, etc. A half-integral spin means that the intrinsic angular moment has values like (1/2)h/2π, (3/2)h/2π. Particles having integral spin are bosons and those having half-integral spin are fermions
 It is by no means obvious that the state function of an electron or photon gas can be written as a product (or rather a sum of products) of state functions for each particle apart, but it turns out to be a quite close approximation.
 For a uniform circular motion with radius r, the angular momentum L=rp. The linear momentum p = h/l according to Einstein. If the circumference 2πr = nl, n being a positive integer, then L=nlp/2π=nh/2π. Quantum mechanics allows of the value L=0 for orbital angular momentum. This has no analogy as a standing wave on the circumference of a circle.
 Klein 1964; Raman, Forman 1969.
 A time-dependent Schrödinger equation describes transitions between energy levels, giving rise to the discrete emission and absorption spectra characteristic for atoms and molecules.
 Momentum space is a three-dimensional diagram for the vector p’s components, px,py and pz. The volume of a state equals Δp=ΔpxΔpyΔpz. In the described model, the states are mostly occupied up till the energy value EF, the ‘Fermi-energy’, determining a sphere around the origin of momentum space. Outside the sphere, most states are empty. A relatively thin skin, its thickness being proportional to the temperature, separates the occupied and empty states.
 Except for very low temperatures, the electrons contribute far less to the specific heat of a solid than the phonons do. The number of electrons is independent of temperature, whereas the number of phonons in a solid or photons in an oven strongly depends on temperature.
 For a gas satisfying the Maxwell-Boltzmann distribution, the energy is proportional to temperature. Some people who got stuck in classical mechanics define temperature as a measure of the mean energy of molecules. Which meaning such a definition should have for a fermion gas or boson gas is unclear.
 Kragh 1990, chapter 3, 5.
 1 MeV (a much used unit of energy) is one million electronvolt, much more than the energy of visible light, being about 5 eV per photon.
 This identification took some time, see Hanson 1963, chapter IX. The assumption of the existence of a positive electron besides the negative one was in 1928 much more difficult to accept than in 1932. In 1928, physics acknowledged only three elementary particles, the electron, the proton and the photon. In 1930, the existence of the neutrino was postulated and in 1932, Chadwick discovered the neutron. The completely occupied nether world of electrons is as inert as the 19th century ether. It neither moves nor interacts with any other system. That is why it is not observable. For those who find this difficult to accept, alternative theories are available explaining the existence of antiparticles.
 In the inertial system in which the centre of mass for the electron-positron pair is at rest, their total momentum is zero. Because of the law of conservation of momentum, the annihilation causes the emergence of at least two photons, having opposite momentum.
 A band is comparable to an atomic shell but has a larger bandwidth.
 Dirac and Heisenberg corresponded with each other about both theories, initially without observing the analogy, see Kragh 1990, 104-105.
 As far as change seems to presuppose motion, only physical events and processes should be called real changes. But each motion means a change of position, and transformations are changes of form.
 The law of decay is given by the exponential function: N(t)=N(t0) exp.–(t-t0)/τ. Herein N(t) is the number of radioactive particles at time t. τ is the characteristic decay time. The better known half-life time equals τ.log 2=0,693 τ. This formula is an approximation because N is not a continuous variable but a natural number. Like all statistical laws, the decay law is only applicable to a homogeneous aggregate.
 This is the decay time in the centre-of-mass system of the moving particle itself. In a particle accelerator these particles move at a speed close to that of light, meaning that their life time as measured in the laboratory is much larger, and measurable in terms of the covered distance.
 Einstein 1917. In stimulated emission, an incoming photon causes the emission of another photon such that there are two photons after the event, mutually coherent, i.e., having the same phase and frequency. Stimulated emission plays an important part in lasers and masers, in which coherent light respectively microwave radiation is produced. Absorption is always stimulated.
 Mason 1991, 50.
 Hawking 1988, chapter 6, 7.
 Mason 1991, chapter 4.
 Because there is a reference system in which the centre of mass of the electron and the positron is at rest, and a photon cannot be at rest, a single photon cannot create a pair.
 Barrow, Tipler 1986, 6-9.
Part II, chapter 12
12.1. The biotic relation frame
No doubt, 1859 was the birth year of modern biology. Charles Darwin and Alfred Wallace were neither the first nor the only evolutionists, and their path was paved by geologists in the preceding century establishing that the earth is much older than was previously perceived, and that many animals and plants living in prehistoric times are now extinct. The publication of Darwin’s On the origin of species by means of natural selection draw much attention, criticism, and approval. In contrast, Gregor Mendel’s discovery in 1865 of the laws called after him, which would become the basis of genetics, was ignored for 35 years. The synthesis of Darwin’s idea of natural selection with genetics, microbiology, and molecular biology constitutes the foundation of 20th-century biology.
This chapter applies the relational character theory, discussed in chapter 10, to living beings and life processes. The genetic relation, leading to renewal and ageing, is the primary characteristic of living subjects (12.1). I investigate successively the characters of organized and of biotic processes (12.2, 12.3), of individual organisms (12.4) and of populations and their dynamic evolution (12.5, 12.6). For the time being, I shall take for granted that a species corresponds to a character. Section 12.7 deals with the question of whether this assumption is warranted.
Life presupposes the existence of inorganic matter, including the characters typified by the relation frames of number, space, motion, and interaction. Organisms do not consist of other atoms than those occurring in the periodic system of chemical elements. All physical and chemical laws are unrestrictedly valid for living beings and life processes. Both in living organisms and in laboratory situations, the existence of organized and controlled chemical processes indicates that biotic processes are not completely reducible to physical and chemical ones. In particular, the genetic laws for reproduction make no sense in a physical or chemical context. Rather, they transcend the physical and chemical laws without denying these.
For the biotic relation frame the genetic law is appropriate. Each living organism descends from another one, and all living organisms are genetically related. This also applies to cells, tissues, and organs of a multicellular plant or animal. Its descent determines the function of a cell, a tissue, or an organ in an organism, as well as the position of an organism in taxonomy. The genetic law constitutes the universal relation frame for all living beings. Empirically, it is amply confirmed, and it is the starting point of major branches of biological research, like genetics, evolution theory, and taxonomy. However, in physical and chemical research, the genetic law only plays a part in biochemistry and biophysics.
The genetic order is more than a static relationship. It has the dynamics of innovation and ageing. Renewal is a characteristic of life, strongly related to sexual or asexual cell division, to growth and differentiation. The individual life cycle of fertilization, germination, growth, reproduction, ageing, and dying is irreversible. Rejuvenation occurs in a series from one generation to the next, and between cells in a multicellular organism. A population goes through periods of rise, blooming, regress, and extinction. Speciation implies innovation as well.
The genetic law is hard to prove
Each living being descends from another living being. The law statement, omne vivum e vivo, is relatively recent. Even in the 19th century, generatio spontanea was accepted as a possibility. Empirical and theoretical research have led to the conviction that life can only spring from life. The theory of evolution does not exclude spontaneous generation entirely, for that would constitute the beginning of the biotic evolution. It might even be possible that the two kingdoms of prokaryotes arose independently. In contrast, there are good reasons to assume that eukaryotic cells have evolved from the prokaryotes, and multicellular plants, fungi, and animals from unicellular eukaryotes.
Most biologists accept a stronger law than omne vivum e vivo. It states that all living beings are genetically related, having a common ancestry. This law, to be called the genetic law, is hard to prove. Paleontological research alone does not suffice to demonstrate that all organisms have the same ancestors, but it achieves support from other quarters. The argument that all living beings depend on the same set of four or five nucleic acids and twenty amino acids is not strong. Perhaps no other building blocks are available. But in eukaryotes these molecules only occur in the laevo variant, excluding the mirror-symmetric dextro variant. These two are energetically equivalent, and chemical reactions (as far as applicable) always produce molecules of the two variants in equal quantities. In the production of amino acids, similar DNA and RNA molecules are involved. In widely differing organisms, many other processes proceed identically. Moreover, all plants, animals, and fungi consist of cells, although there are large differences between prokaryotic and eukaryotic cells, as well as between plant and animal cells. Prokaryotic cells are more primitive and much smaller than eukaryotic cells, and the cell wall is in plants thicker and more rigid than in animals.
The fundamental laws of the universal relation frames cannot be logically derived from empirical evidence, even if this is abundantly available. The laws of thermodynamics, the mechanical conservation laws, and the law of inertia are no more provable than the genetic law. Such fundamental laws function as axioms in a theory, providing the framework for scientific research of characters. In this sense, the genetic law has proved to be as fruitful as the generally valid physical and kinetic laws. This does not mean that such laws are not debatable, or void of empirical content. On the contrary, the law of inertia was accepted in the 17th century only after a centuries long struggle with the Aristotelian philosophy of nature, from which science had to be emancipated. The law of conservation of energy and the second law of thermodynamics were accepted only about 1850 (T&E chapter 7). Similarly, only in the 20th century the genetic law was recognized after laborious investigations. In all these cases, empirically sustained arguments ultimately turned the scale.
With respect to the biotic relation frame, the theory of evolution is as general as thermodynamics is with respect to physical and chemical relations. Both theories concern aggregates, but they are nevertheless indispensable for understanding the characters of individual things and processes. The main axioms of evolution theory are the genetic law and laws for natural selection with respect to populations. In general terms, the theory of evolution explains why certain species can maintain themselves in their environment and others cannot, pointing out the appropriate conditions. In specific cases, the evolution theory needs additional data and characteristic laws, in order to explain why a certain species is viable in certain circumstances. Also in this respect, evolution theory is comparable to thermodynamics.
The genetic law lies at the basis of biological taxonomy
Like plants and fungi, as well as protists and prokaryotes, animals are subject to biotic laws, but I shall assume that they are primarily characterized by another relation frame, to be called psychical. Within their generic psychic character, a specific organic character is interlaced (11.1). Genetic relations primarily characterize all other living beings and life processes. Each biotic process is involved with replication (12.3), and the nature of each living being is genetically determined (12.4). Within an organism, physical and chemical processes have the tertiary disposition to function in biotic processes (12.2). Living beings support symbiotic relations leading to evolution (12.5).
The genetic law is a leading principle of explanation for taxonomy and the modern species concept. The universal relation frames allow us of identifying any thing or event, to establish its existence and change, and to find its temporal relations to other things and events. In principle, the genetic law allows of the possibility to order all organisms into a biological taxonomy. The empirical taxonomy does not originate from human thought but from living nature. Its leading principle is not logical but biological. A logical, i.e., deductive classification is based on a division of sets into subsets, considering similarities and differences. It descends logically from general (the kingdoms and phyla) to specific (the species). In contrast, the biological ordering depends on genetic descent, ascending inductively from species to the higher categories.
The biotic order can be projected on the four preceding ones
Genetic relations can be projected on the preceding relation frames. On the different levels of taxonomy, a species, and a multicellular organism, these mappings can be distinguished as follows.
a. A lineage is a serial projection of the genetic order on the quantitative relation frame. Within a species one finds the linear relation of parent to offspring. Within a multicellular organism the serial order concerns each line of replicating cells. By counting the intermediary specimens, it is possible to establish the genetic relation between two individuals, organs, or cells, that are serially connected.
b. Parallel lineages are mutually connected by common ancestry. Therefore species, organs, or cells having no serial relation may be related by kinship, the genetic relation between siblings, cousins, etc. Kinship of parallel lineages is to be considered a spatial expression of the genetic relation. Each branching means a new species, a new individual, a new organ, or a new cell. In taxonomy, biologists establish kinship between species on the basis of similarities and differences. These concern shape (morphology), way of life (physiology), development of an organism (in particular embryology), the manner of reproduction, and nowadays especially comparing DNA, RNA, or the proteins they produce. Kindred lineages are connected in a cladogram, a diagram showing the degree of kinship between species. If an organism has several descendants, the lineage branches within a species. In sexual reproduction lineages are connected and each organism has two parents, four grandparents, etc. Within an organism cell division causes branching. In a plant, fungus, or animal, recently branched cells lie close to each other. The larger the distance between two cells, the smaller is their kinship.
c. Genetic development may be considered the kinetic projection of the order of renewal and ageing. Temporal relations are recognizable in the generation difference as a biotic measure mapped on kinetic time. It is the time between two successive bifurcations of a species, between the germination of a plant and that of its seeds, or between two successive cell divisions. If timing is taken into account, a cladogram becomes a phylogenetic tree. Between two splits a population evolves. From germination to death an organism develops, and cells differentiate and integrate into tissues and organs.
d. The dynamic force of evolution within a species and the splitting of species consist of competition and natural selection. These may be considered projections of the genetic relation on the physical. Between plants, the competition concerns physical and chemical resources for existence, between fungi and animals organic ones as well. Competition is a repulsive force, to use a physical term. Besides natural selection, accidental processes lead to genetic changes, mostly in small isolated populations. This phenomenon is called ‘random genetic drift’ or ‘inbreeding’ in common parlance. Breeders use it to achieve desirable plant or cattle variations. There are attractive forces as well. Only within a species, sexual reproduction is the most innovative form of replication. Sexual interaction may be considered a specific physical expression of the genetic relation. Within an organism, neighbouring cells influence each other during their differentiation and integration.
These projections give rise to four types, each of organized chemical processes (12.2), biotic processes (12.3), biotically qualified thing-like characters (12.4), and their aggregates (12.5, 12.6).
12.2. The organization of biochemical processes
In each living being, many organized biochemical processes take place, having a function in the life of a cell, a tissue, an organ, or an organism. The term organism for an individual living being points to its character as an organized and organizing unit. The organism has a temporal existence. It emerges when the plant germinates, it increases in largeness and complexity during its development, it ages and after its death it falls apart.
An organized unit is not necessarily a living being. A machine does not live, but it is an organized whole, made after a design. A machine does not reproduce itself and is not genetically related to other machines. Because human persons design a machine, its design cannot be found in the machine itself. In a living organism, the natural design is laid down in the genome, the ordered set of genes based on one of more DNA molecules. The organism transfers the design from cell to cell and from generation to generation. The natural design changes because of mutation at the level of a single cell, because of sexual interaction at the level of organisms, or caused by natural selection at the level of a population. It is bound to general and specific laws determining the conditions under which the design is executable or viable. A design is the objective prescription for a biotic character. It is a chemical character having a tertiary biotic characteristic.
The processes to be discussed in the present section are primarily physically qualified, and some of them can be organized in a laboratory or factory. Their disposition to have a function in biotic processes is a tertiary characteristic (12.3).
a. Molecules are assembled according to a design
Although the concept of a lineage points to a relation between living beings, there is an analogy on the molecular level. This refers to the assemblage of molecules according to a genetic design as laid down in the DNA molecules. The DNA composition is partly species specific, partly it is unique for each individual living being.
The natural design for an organism is laid down in its genome, the genetic constellation of the genes in a specific sequence. The DNA molecules are the objective bearers of the genetic design, which is the genotype determining the phenotype, that is the appearance of a living being. Each organism has its own genome, being the objective expression of the species to which it belongs as well as of its individuality. Like the DNA molecules, the genome is mostly species specific.
A DNA molecule consists of a characteristic sequence of bases (nucleotides) of nucleic acids indicated by the letters A (adenine), C (cytosine), G (guanine) and T (thymine). DNA is the start of the assembly lines of the molecules having a function in life processes. Three nucleotides form the design for one of the twenty possible amino acids. An RNA molecule is a replica of the part of the DNA molecule corresponding to a single gene. Mediated by an RNA molecule each gene designs a polypeptide or protein consisting of a characteristic sequence of amino acids. Some proteins are enzymes acting as catalysts in these and other material transformations.
Although a great deal of the assembly of molecules takes place according to a genetically determined pattern, interaction with the surroundings takes place as well. The environment is first of all the cell plasma, the more or less independent specialized organelles and the cell wall, in which many specific biochemical processes occur. Second, via the cell wall a cell is in contact with the physical and chemical environment. Third, in multicellular organisms the environment includes other cells in the immediate neighbourhood. Finally, only animal cells exert some kind of action at a distance (13.1).
To a large extent, the environment determines which genes or combinations of genes are active, being selectively switched on or off. The activity of genes in a multicellular organism depends on the phase of development. The genome acts in the germination phase differently than in an adult plant, in a root otherwise than in a flower. The genetic constellation determines the growth of an organism. Conversely, the genetic action depends on the development of the plant and the differentiation of its cells.
Therefore, DNA is not comparable to a code, a blueprint, a map or diagram in which the phenotype is represented on a small scale. Rather, it is an extensive prescription, a detailed set of instructions for biochemical processes.
The enormous variation of molecules is possible because of the equality of the atoms and the uniformity of chemical bonding. This is comparable with the construction of machines. It is easy to vary machines if and as far as the parts are standardized and hence exchangeable. This applies to the disparity of organisms as well. The organization of a plant or an animal consists partly of standardized modules, some of which are homologous in widely different organisms. Such modules exist on the level of molecules (there are only 20 different amino acids, with an enormous variation in combinations), genes (standardized combinations of genes), cells (the number of cell types is restricted to several hundreds), tissues and organs. For evolutionary innovations, the existence of exchangeable parts having a different function in different combinations and circumstances is indispensable.
b. The biotic functions of molecules depend on their shape
Although the macromolecules occurring in living beings have an enormous diversity, they have much in common as well. Polymers are chains of monomers connected by strong covalent bonds (12.3). Polysaccharides consist of carbohydrates (sugars), polypeptides are constructed from amino acids, and nucleic acids consist of nucleotides. The lipids (fats, oils and vitamins) constitute a fourth important group of large molecules. Lipids are not soluble in water. Lipids are not characterized by covalent bonds but by the weaker Van der Waals bonding. Phospholipids are the most important molecules in biotic membranes. In the double cell wall the molecules are at one end hydrophilic (attracting water), at the other end hydrophobic (repelling water). In the assembly of polymers, water is liberated, whereas polymers break down by hydrolysis (absorption of water).
All organisms apply the same monomers as building blocks of polymers. In contrast, the polymers, in particular the polypeptides and nucleic acids, are species specific. The twenty different amino acids can be connected to each other in each order and in large amounts. As a consequence, the diversity of proteins and their functions is enormous.
Polymers do not only differ because of their serial composition, but in particular by their spatial shape. Like all molecules, they are primarily physically qualified and secondarily spatially founded. DNA’s double helix structure plays a part in its replication in cell division. Also other macromolecules display several spatial structures simultaneously. For the functioning of a protein as an enzyme, its spatial structure is decisive.
Each biochemical process has to overcome an energy barrier (12.6). Increasing the temperature is not suitable, because it accelerates each chemical process and is therefore not selective enough. Catalysis by specialized proteins (enzymes) or RNA molecules (ribozymes) is found in all organisms. In plants, the enzyme rubisco is indispensable for photosynthesis.
The polymers have various functions in an organism, like energy storage, structural support, safety, catalysis, transport, growth, defence, control, or motion. Only nucleic acids have a function in the reproduction of cells and organisms.
c. Metabolism is a transport process
The genetic development of a living being depends on metabolism. A cell can only live and replicate because of a constant stream of matter and energy through various membranes. A unicellular organism has direct contact with its environment, in which it finds its food and deposits its waste. This also applies to a multicellular organism consisting of a colony of independently operating cells, like many algae. These organisms’ ideal environment is salt water, followed by fresh water and moist situations like mud or the intestines of animals. To colonial organisms, this imposes the constraint that a tissue cannot be thicker than two cells.
Multicellular fungi, plants, or animals need internal transport of food, energy, and waste, requiring cell differentiation, in which, for instance, the photosynthetic cells lie at the periphery of plants. Metabolism is an organized stream of matter through the organism. It allows of life outside water. In the atmosphere, oxygen is better accessible than in water, other materials are less accessible.
The cell wall is not merely a boundary of the cell. Nor is it a passive membrane that would transmit some kinds of matter better than others. Rather, it is actively involved in the transport of all kinds of matter from one cell to another. Membranes have an important function in the organization of biochemical processes, the assemblage of molecules, the transformation of energy, the transport of matter, the transfer of information, and the processing of signals. Hence, the presence of membranes may be considered a condition for life.
Plant cells are close together, and transport takes place directly from one cell to the other one. A plant cell has at least one intracellular cavity enclosed by a membrane. This is a vacuole, mostly filled with water, acting as a buffer storage and waste disposal. Animals have intercellular cavities between their cells. Animal cells are connected by proteins regulating the exchange of molecules and information. These proteins play an important part in the development of the embryo as well.
Passive transport is distinguished from active transport. Passive transport lacks an external source of energy and is caused by diffusion in a chemical solution or by osmosis if the solution passes a membrane. Some substances pass a membrane together with proteins acting as carriers. The concentration gradient is the driving force of diffusion. The size and the electric charge of the molecules concerned and the distance to be travelled also influence the diffusion speed. In particular the distance is a constraint, such that diffusion is only significant within a cell and between two neighbouring cells. To cover larger distances other means of transport are needed.
Active transport requires a source of energy, like adenosine triphosphate (ATP). This transport is coupled to carriers and proceeds against a concentration difference like a pump. Endo- or exocytose in eukaryotic cells is the process in which the cell wall encapsulates the substance to be transported. After the capsule has passed the wall it releases the transported substance. Animal cells have receptors in their wall sensitive for specific macromolecules. Besides, animals have organs specifically designed for transport, for instance by the circulation of blood.
No organism can live without energy. Nearly all organisms derive their energy directly or indirectly from the sun, by photosynthesis. This process transforms water, carbon dioxide, and light into sugar and oxygen. This apparently simple chemical reaction is in fact a complicated and well organized process, only occurring in photosynthetic bacteria and in green plants. The product is glucose (a sugar with six carbon atoms in its molecule), yielding energy rich food for plants and all organisms that feed on plants.
The transformation of energy is a redox reaction. Some molecules oxidize by donating electrons, whereas other molecules reduce by accepting electrons. The first step is glycolysis (transformation of glucose in pyruvate), which does not require oxygen. Most organisms use oxygen for the next steps (cellular respiration). Other organisms are anaerobic, transforming energy by fermentation, which is less efficient. In the absence of oxygen, many aerobic cells switch to fermentation. Because nerve cells are unable to do so, they become easily damaged at a shortage of oxygen. Glycolysis, cellular respiration and fermentation are organized processes with many intermediate steps. The end product consists of ATP and other energy carriers that after transport cede their energy in other chemical reactions.
d. Self-replication of DNA molecules has a function in reproduction
Serving as a starting point for the assemblage of polypeptides, the DNA molecule has a specific spatial structure. It consists of a double helix of two sequences of nucleotides being each other’s complement, because each adenide (A) in one sequence connects to a thymine (T) in the other one and each cytosine (C) in one sequence to a guanine (G) in the other.
If the DNA molecule consists of two such strings it is called diploid. The two halves are not identical, even if they look alike. This structure makes the DNA molecule very stable. An RNA molecule, acting as an intermediary between a gene on the DNA molecule and the assemblage of a polypeptide, is haploid. Consisting of a single helix, it is less stable than DNA. DNA is not always diploid. Many fungi consist of haploid cells. Only during sexual reproduction, their sex cells are diploid.
The DNA molecule itself is not assembled by another molecule. It has a unique way of self-duplication. Preceding a cell division, the diploid helix unfolds itself and the two haploid halves separate. In sexual cell division (meiosis) the next steps differ from those in the far more frequent asexual cell division (mitosis).
Mitosis is the asexual form of reproduction for unicellular organisms. It also occurs in the growth of all multicellular organisms. After the first division of the diploid DNA molecule, each half doubles itself by separating the two sequences and connecting a new complementary base to each existing base. Hence, two new diploid DNA molecules arise, after which the cell splits as well. The daughter cells are genetically identical to the mother cell.
Meiosis, the sexual cell division, is more varied. In a much occurring variant, the DNA remains haploid after the first splitting. As a rule, after the second division four daughter cells arise, each with half the DNA. Either all four are sperm cells or one is an egg cell, whereas the other three die or become organelles in the egg cell. Only after the egg cell merges with a sperm cell of another individual, a new diploid cell arises. This cell has a different composition of DNA, hence a new identity. This is only possible if the two merging DNA halves fit to each other. In most cases this means that the individuals concerned belong to the same species. In prokaryotes meiosis is often a more complicated process than in eukaryotes.
Cell division is not restricted to DNA replication. The membranes are not formed de novo but grow from the existing ones. In particular, the cell wall of the original cell is divided among the daughter cells. Life builds on life.
12.3. The character of biotic processes
Besides the organized biochemical processes there are processes that are typically biotically qualified. In section 12.5, I shall discuss the genetic changes occurring in a population. Important processes for the dynamic development of an individual organism, to be discussed in the present section, are cell division, spatial shaping, growth and reproduction.
The genetic identity of a living organism as a whole is determined by its genetic contents. Its heredity is expressed in the genes and their material basis, the DNA molecules. All cells of a multicellular organism have the same DNA configuration and every two living beings have different DNA molecules, except in the case of asexual reproduction. The genes organize the biochemical processes discussed in section 12.2 as well as the biotic processes to be discussed in section 12.3. The genetic identity as an organizing principle of a living being determines its temporal unity. This unity disappears when the organism dies and disintegrates.
a. Cell division leads to multiplication
Cell division is a biotically qualified process that is quantitatively founded. The cell as a subjective unit multiplies itself. Sexual cell division (preceded by sexual interaction, see below) is distinguished from the more frequent asexual cell division (12.2). In the case of an eukaryotic cell, the nucleus too is divided into two halves. The other cell bodies, the cell plasma, and the cell wall, are shared out to the daughter cells and supplied by new ones.
Many organisms reproduce asexually. The prokaryotes and protists (mostly unicellular eukaryotes) reproduce by cell division. Many plants do so by self-pollination. Now the daughter has the same genetic identity as the parent. In this respect they could be considered two spatially separated parts of the same plant. On the one hand, nothing is wrong with this view. Alaska is an integral part of the United States, though it is spatially separated from the mainland. The primary character determines the temporal unity of an individual, and in the case of a bacterium, a fungus, or a plant, this is its genetic identity. Only after a sexual reproduction the daughter plant is a real new individual, genetically different from its parents and any other individual. On the other hand, this view counters natural experience, accepting a plant as an individual only if it is coherent. Moreover, in asexual reproduction not only the spatial coherence is lost, but all kinds of biochemical and biotic interactions as well. This seems to be sufficient to suppose that asexual reproduction gives rise to a new individual.
No single organism is subject to genetic change. Hardly anything can be found that is more stable than the genetic character and the identity of a living being. From its germination to its death, a plant remains identical to itself in a genetic sense. Only in sexual replication genetic change occurs. Of course, a plant is subject to other changes, both cyclic (seasonal) and during its development in its successive phases of life.
b. Symbiosis is spatially founded
The genetic relation is not the only factor determining the biotic position of a living being. For each plant and every animal, its relation to the environment (the biotope or ecosystem) is a condition of life. First, the environment concerns subject-subject relations. Symbiosis should be considered a spatially founded way of living together. It is found on all levels of life. Within an eukaryotic cell symbiosis occurs between the cell nucleus and the organelles having their own DNA. In multicellular organisms cells form tissues or organs. In an ecosystem, unicellular and multicellular organisms live together, mutually dependent, competitive or parasitic.
Second, each organism has a subject-object relation to the physical and chemical surroundings of air, water, and soil. Just like the organized matter in the plant, the physical environment has a dynamic function in life processes.
Third, the character of plants anticipates the behaviour of animals and human beings. This constitutes an object-subject relation. By their specific shape, taste, colour, and flavour plants are observable and recognizable by animals as food, poison, or places suited for nesting, hunting, and hiding.
c. Organic development and growth are founded in motion
The dynamic development of a plant from its germination to adulthood may be considered a kinetically founded biotic process. It is accompanied by differentiation of cells and pattern formation in tissues, and by relative motion of cells in animals. The growth of a plant is strongly determined, programmed by the genome. In the cell division the DNA does not change, but the genes are differentially switched on and off. During the growth, cells differentiate into various types, influenced by neighbouring cells.
There are other influences from the environment, for a plant only grows if the circumstances permit it. Most seeds never start developing, because the external factors are not favourable. Even for a developing plant, the genotype does not determine the phenotype entirely. The development of the plant occurs in phases from cell to cell, in which the phenotype of the next cell is both determined by its genotype and by the phenotype of the preceding cell and the surrounding cells, as well as by the physical, chemical, and organic environment.
The dynamic development of a plant or animal belongs to the least understood processes in biology. It starts from a single point, fertilization, and expands into a series of parallel but related pathways. Sometimes one pathway may be changed without affecting others, leading to a developmental dissociation. Usually such dissociation is lethal, but if it is viable, it may serve as a starting point for evolutionary renewal.
d. Sexual reproduction as a physically founded process
Sexual reproduction may be considered a primarily biotically qualified process that is secondarily physically founded, like a biotic interaction. Two genetically different cells unite, and the DNA splits before forming a new combination of genes (12.2). By sexual reproduction a new individual comes into being, with a new genetic identity.
Contrary to the growth of a plant, reproduction is to a large extent accidental. Which cells unite sexually is mostly incidental. Usually only sex cells from plants of the same species may pair, although hybridization occurs frequently in the plant kingdom. By their mating behaviour, animals sometimes limit accidents, increasing their chances. Even if a viable combination is available, the probability is small that the seed germinates, reaches adulthood and becomes a fruit bearing plant. Because the ultimate chance of success is small, a plant produces during its life an enormous amount of gametes. On the average and in equilibrium circumstances, only one fruit bearing descendant survives. The accidental nature and abundance of reproduction, supplied with incidents like mutation, is a condition for natural selection. But if it would occur in a similar way during the growth of a plant, no plant would ever reach the adult stage. Dynamic development is a programmed and reproducible process. Sexual reproduction (as well as evolution according to Darwin) is neither.
Fertilization is a biotically qualified process, interlaced with biochemical processes having a biotic function. Moreover, in animals fertilization is interlaced with the psychically qualified mating behaviour that is biotically founded.
12.4. The secondary characteristic of organisms
Because four relation frames precede the biotic one, we should expect four secondary types of biotically qualified thing-like characters. These are, respectively, quantitatively, spatially, kinetically, or physically founded. Each type is interlaced with the corresponding type of biotic processes mentioned in section 12.3. Moreover, the characters of different types are interlaced with each other as well.
a. The character of prokaryotes is quantitatively founded
It seems obvious to consider the cell to be the smallest unit of life. Each living being is either a cell or a composite of cells. However, this conceals the distinction between prokaryotes (bacteria and some algae) and eukaryotes. According to many biologists, this difference is more significant than that between plants and animals. The oldest known fossils are prokaryotes, and during three-quarters of the history of the terrestrial biosphere, eukaryotes were absent. Prokaryotic cells are more primitive and usually smaller than eukaryotic cells. Most prokaryotes like bacteria are unicellular, although some colonial prokaryotes like algae exist. The protists, fungi, plants, and animals consist of eukaryotic cells. A bacterium has only one membrane, the cell wall. An eukaryotic cell has several compartments enclosed by a membrane. Besides vacuoles these are particles like the cell nucleus, ribosomes (where RNA molecules assemble polypeptides), mitochondria (the power stations of a cell), and chloroplasts (responsible for photosynthesis). Prokaryotes have only one chromosome, eukaryotes more than one. Therefore, biologists consider the prokaryotes to belong to a separate kingdom, or even two kingdoms, the (eu)bacteria and the much smaller group of archaebacteria (archaea).
It appears that the chromosomes in an eukaryotic cell have a prokaryotic character, as well as the genetically more or less independent mitochondria and chloroplasts. Having their own DNA, the latter organelles’ composition is genetically related to that of the prokaryotes. Therefore, I consider the character of prokaryotes to be primarily biotic and secondarily quantitative. This may also apply to the characters of the mitochondria, chloroplasts, and chromosomes in an eukaryotic cell, and to the character of viruses as well. None of these can exist as a living being outside a cell, but each has its own character and a recognizable genetic identity. Their character has the tertiary disposition to become interlaced in that of an eukaryotic cell. In eukaryotic organisms, reproduction starts in the prokaryotic chromosomes.
b. Eukaryotes, colonial organisms and tissues are spatially founded
A spatially founded biotic character is characterized by symbiosis (12.3). The symbiosis of prokaryotes in an eukaryotic cell is called endosymbiosis. In the character of an eukaryotic cell several quantitatively founded prokaryotic characters are encapsulated. In turn, eukaryotic cells are the characteristic units of a multicellular fungus, plant, or animal. Each cell has a spatial (morphological) shape, determined by the functions performed in and by the cell.
In colonial plants (thallophytes like some kinds of algae), the cells are undifferentiated. As in colonial prokaryotes, metabolism takes place in each cell independent of the other cells. In higher organisms, eukaryotic cells have the disposition to differentiate and to integrate into tissues and organs. Both in cell division and in growth, cells, tissues, or organs emerge having a specific shape. The spatial expression of an organism is found in its morphology, of old a striking characteristic of living beings. Since the invention of the optical microscope in the 17th century and the electron microscope in the 20th, the structure of a cell is well known.
c. Differentiated organisms and organs have a kinetically founded character
Except for unicellular and colonial organisms, each living being is characterized by its dynamic development from the embryonic to the adult phase. Now the replication of cells leads to morphological and functional differentiation. In a succession of cell divisions, changes in morphology and physiology of cells occur. Their tertiary character takes distance from that of the gametes. This gives rise to differentiated tissues and organs like fibres, the stem and its bark, roots, and leaves. These have different morphological shapes and various physiological functions. In a differentiated plant, metabolism is an organized process, involving many cells in mutually dependent various ways (12.2). Growth is a biotic process (12.3). Differentiation enhances the plant’s stability, fitness and adaptive power.
Differentiation concerns in particular the various functions that we find in a plant. The biological concept of a function represents a subject-object relation as well as a disposition. Something is a biotic object if it has a function with respect to a biotic subject (12.2). Cells, tissues, and organs are biotic subjects themselves. A cell has the disposition to be a part of a spatially founded tissue, in which it has a function of its own. A tissue has an objective function in a differentiated organ. By differentiation the functions are divided between cells and concentrated in tissues. In a differentiated plant, chlorophyll is only found in leaves, but it is indispensable for the whole plant. The leaves have a position such that they catch a maximum amount of light.
Differentiation leads to the natural development from germination to death. The variety in the successive life phases of fertilization, germination, growth, maturing, reproduction, ageing, and natural death is typical for differentiated fungi, plants, and animals.
Although the cells of various tissues display remarkable differences, their kinship is large. This follows from the fact that many plants are able to reproduce asexually by the formation of buds, bulbs, stolons, tubers, or rhizomes. In these processes, new individuals emerge from differentiated tissues of plants. Grafting and slipping of plants are agricultural applications of this regenerative power.
d. Sexual interaction characterizes the highest developed plants
Sexual reproduction appears to be an important specific projection of the genetic relation on the physical and chemical relation frame. This biotic interaction between two living beings is the most important instrument of biotic renewal. All eukaryotic organisms reproduce by sexual cell division (even if some species reproduce by other means most of the time). In prokaryotes, the exchange of genetic matter does not occur by sexual interaction, but by the merger of two individuals. Reproduction is a biotic process (12.3), and the part played by DNA replication is discussed in section 12.2.
In the highest developed plants, sexuality is specialized in typical sexual organs, like flowers, pistils, and stamens. Some plant species have separate male and female specimens. In sexually differentiated plants, the sexual relation determines the genetic cycle, including the formation of seeds. Fertilized seeds can exist some time independent of the parent plant without germinating, for instance in order to survive the winter. Sometimes they are provided with a hard indigestible wall, surrounded by pulp being attractive food for animals. The animal excretes the indigestible kernel, co-operating in the dispersal of the seeds.
In particular, sexual reproduction is relevant for the genetic variation within a population. This variation enhances the population’s adaptability considerably. The genetic kinship between individuals in a population is much less than the genetic relation between cells within an individual organism.
The characteristic distinctions between an egg cell and pollen, between male and female sex organs in bisexual plants, and between male and female specimens in unisexual plants, have a function to prevent the merger of sex cells from the same individual. In bisexual plants self-pollination does occur, but sometimes the genetic cycle is arranged such as to preclude this. Fungi are not sexually differentiated but have other means to prevent self-fertilization. Within each fungus species several types occur, such that only individuals of different types can fertilize each other.
Character interlacement enriches the character types
The distinction of four biotic types of thing-like characters is only the start of their analysis. Real characters almost always consist of an interlacement of differently typed characters.
First, one recognizes the interlacement of equally biotically qualified but differently founded characters. In eukaryotic cells, an interlacement occurs with various organelles having a prokaryotic character. Because the organelles have various functions, this interlacement leads to a certain amount of differentiation. In all multicellular plants, the character of the cells is interlaced into that of a tissue. In differentiated plants, the character of organs is interlaced with those of tissues. This concerns both their morphological structure and their physiological functions. The highest developed plants display an interlacement of cells, tissues, leaves, roots, flowers, and seeds. Together they constitute the organism, the plant’s primary biotic character. The differentiation of male and female organs or individuals is striking.
Second, the biotic organism is interlaced with characters that are not biotically qualified. First of all, these concern the physically qualified characters of the molecules composing the plant (12.2). Besides we find in a plant kinetic characters, typical motions of the plant as a whole or of its parts. An example is the daily opening and closing of flowers, or the transport of water from roots to leaves. Each plant and each of its cells, tissues, and organs have typical shapes. By no means these characters are purely physical, chemical, kinetic, or spatial. They are opened up by the biotic organism in which their characters are encapsulated. Their tertiary biotic disposition is more obvious than their primary qualifying or secondary founding relation frames. They have a function determined by the organism. Unlike cells and tissues, they do not form parts of the organism, as follows from the fact that they often persist some time after the death of the organism. Everybody recognizes the typical structure of a piece of wood to be of organic origin, even if the plant concerned is dead for a long time. Wood is not alive, but its physical properties and spatial structure cannot be explained from physical laws only. Wood is a product of a living being, which organism orders the physically qualified molecules in a typically biotic way.
Third, we encounter the interlacement of the organism with many kinds of biochemical and biotic processes (12.2, 12.3). Whereas physical systems always proceed to an equilibrium state, an organism is almost never at rest. (A boundary case is a seed in a quasi-stable state). Metabolism is a condition for life. Reproduction, development, and growth of a multicellular organism, and the seasonal metamorphosis of perennial plants, are examples of biotic processes. Each has its own character, interlaced with that of the organism.
The typology of characters differs from the biotic taxonomy
A relatively recent taxonomy of living beings still distinguished five kingdoms: monera (prokaryotes); protoctista or protista (unicellular and colonial eukaryotic organisms); fungi; animalia; and plantae. Nowadays the prokaryotes are divided into the kingdoms of (eu)bacteria and archaebacteria or archaea, differing from each other as much as they differ from the eukaryotes. The protists form a set of mutually hardly related unicellular or colonial eukaryotes. Fungi are distinguished from plants by having haploid cells most of the time. Being unable to assimilate carbon, they depend on dead organic matter, or they parasitize plants or animals. DNA research reveals that fungi are more related to animals than to plants.
It cannot be expected that the typology discussed in this section would correspond to the biological taxonomy of species. Taxonomy is based on specific similarities and differences and on empirically found or theoretically assumed lineages and kinship. If the biotic kingdoms in the taxonomy would correspond to the division according to their secondary characteristic, this would mean that the four character types would have developed successively in a single line. In fact, many lineages evolve simultaneously. In each kingdom the actualization of animal phyla or plant divisions, classes, orders, etc. proceeds in the order of the four secondary character types and their interlacements. However, their disparity cannot be reduced to the typology based on the general relation frames.
The biological taxonomy, the division of species into genera, families, orders, classes, phyla or divisions, and kingdoms, is not based on the general typification of characters according to their primary, secondary, and tertiary characteristics. Rather, it is a specific typification, based on specific similarities and differences between species.
Sections 12.2 and 12.3 investigated physical, chemical, and biotic processes based on projections of the biotic relation frame on the preceding frames. Section 12.4, too, was mainly directed to secondary characteristics of biotic subjects. Now a tertiary characteristic will be considered, the disposition of organisms to adapt to their environment. Organisms do not evolve individually, but as a population in a biotope or ecosystem. Section 12.5 discusses the laws for populations and aggregates of populations, whereas section 12.6 treats the genome and the gene pool as objective aggregates.
a. A population is a homogeneous aggregate
A population is a homogeneous aggregate, a spatio-temporally bounded and genetically coherent set of living beings of the same species. Two sets of organisms of the same species are considered different populations, if they are spatially isolated and the exchange of genetic matter is precluded. A population as a whole evolves and isolated populations evolve independently from each other.
A population is a quantitatively founded biotic aggregate, having a number of objective properties open to statistical research, like number, dispersion, density, birth rate, and death rate. These numbers are subject to the law of abundance. Each population produces much more offspring than could reach maturity. The principle of abundance is a necessary condition for survival and evolutionary change. Competition, the struggle for life, sets a limit to abundance.
Being threatened by extinction, small populations are more vulnerable than larger ones. Nevertheless, they are better fit to adaptation. Important evolutionary changes only occur in relatively small populations that are reproductively isolated from populations of the same species. As a ‘founder population’, a small population is able to start a new species. Large, widely dispersed populations are evolutionary inert.
b. A population occupies a niche in a biotope
A biotope or ecosystem is a heterogeneous aggregate. It is a spatially more or less bounded collection of organisms of different species, living together and being more or less interdependent. The biotic environment or habitat of a population consists of other populations of various species.
A biotope is characterized by the symbiosis of prokaryotes and eukaryotes, of unicellular and multicellular organisms, of fungi and plants. Most biotopes are opened up because animals take part in them, and sometimes because they are organized by human interference. Biotopes like deserts, woods, meadows, or gardens are easily recognizable.
A population occupies a niche in a biotope. A niche or adaptive zone indicates the living room of a population. Both physical and biotic circumstances determine a niche, in particular predator-prey relations and the competition about space and food. Each niche is both possible and constrained because of the presence of other populations in the same area. In general, the geographic boundaries of the habitats of different species will not coincide. Therefore the boundary of a biotope is quite arbitrary.
Each niche is occupied by at most one population. This competitive exclusion principle is comparable to Pauli’s exclusion principle for fermions (12.2, 12.4). If a population that would fit an occupied niche invades an ecosystem, the result is a conflict ending with the defeat of one of the two populations. Sooner or later, some population will occupy an empty niche.
If the physical or biotic environment changes, a population can adapt by genetically evolving or by finding another niche. If it fails it becomes extinct.
c. A biotope is in dynamic equilibrium
In each biotope, the populations depend on each other. Each biotope has its food chains and cycles of inorganic material. Fungi living mainly off dead plants form a kingdom of recyclers. Many bacteria parasitize living plants or animals, which, conversely, often depend on bacteria. Sometimes the relation is very specific. For instance, a lichen is a characteristic symbiosis of a fungus and a green or blue alga.
The biotic equilibrium in an ecosystem may change by physical causes like climatic circumstances, by biotic causes like the invasion of a new species, or by human intervention. Like a physical equilibrium, the biotic balance has a dynamic character. If an ecosystem gets out of balance, processes start having the disposition to repair equilibrium or to establish a new equilibrium.
Sometimes the ecological equilibrium has a specific character, if two populations are more or less exclusively dependent on each other, for instance in a predator-prey relation. If the prey increases its number, the number of predators will grow as well. But then the number of prey will decrease, causing a decrease of predators. In such an oscillating bistable system, two ‘attractors’ appear to be active (5.5).
d. A population evolves
Individual organisms are not susceptible to genetic change, but populations are subject to evolutionary change. Besides competition, the driving force of this dynamic development is natural selection, the engine of evolution. With each genotype a phenotype corresponds, the external shape and the functioning of the individual plant. Rather than the genotype, the phenotype determines whether a plant is fit to survive in its environment and to reproduce. Fitness depends on the survival value of an individual plant at short term, and on its reproduction capability and the viability of its offspring. Fitness is a long-term measure for the ability of a population to maintain and reproduce itself.
Natural selection concerns a population and acts on the phenotype. It has the effect that ‘the fittest survives’, as Herbert Spencer would have it. The struggle for life is a process taking place mostly within a population, much less between related populations (if occupying overlapping niches), and hardly ever between populations of different species.
But the evolution of a population depends on the environment, including the evolution of other populations. The phenomenon of co-evolution means that several lineages evolve simultaneously and mutually dependently. An example is the evolution of seed eating birds and seed carrying plants. The plant depends on the birds for the dispersion of its seeds, whereas the birds depend on the plants for their food. Sometimes, the relation is very specific.
Besides co-evolution, biologists distinguish divergent and convergent evolution of homologous respectively analogous properties. Homology concerns a characteristic having a common origin. In related species, its function evolved in diverging directions. Analogy concerns a characteristic having a corresponding function but a different origin. The emergence of analogous properties is called convergent or parallel evolution. The stings of a cactus are homologous to the leaves of an oak, but analogous to the spines of a hedgehog. The wings of a bird and a bat are homologous to each other, but analogous to the wings of an insect. Light sensitivity or visual power emerged at least forty times independently, hence analogously, but the underlying photoreceptors may have arisen only once, they appear to be homologous.
12.6. The gene pool
The insight that populations are the units of evolution is due to Charles Darwin and Alfred Wallace. It is striking that they could develop their theory of evolution without knowledge of genetics. Besides populations being subjective aggregates of living beings, in the biotic evolution objective aggregates play a part. These objective aggregates consist of genes. Six years after Darwin’s publication of The origin of species (1859), Gregor Mendel discovered the laws of heredity. These remained unnoticed until 1900, and only some time later they turned out to be the necessary supplements to the laws for populations.
Some populations reproduce only or mostly asexually (12.7). In section 12.6, I restrict myself to populations forming a reproductive community, a set of organisms reproducing sexually. Within and through a population, genes are transported, increasing and decreasing in number.
a. The genome is an ordered set of genes
The genetic identity of each living being is laid down in its genome, the ordered set of genes (12.2). The genes do not operate independent of each other. Usually, a combination of genes determines a characteristic of the organism. In different phases of development, combinations of genes are simultaneously switched on of off. The linear order of the genes is very important. The number of genes is different in different species and may be very large. They are grouped into a relatively small number of chromosomes, each chromosome corresponding to a DNA molecule. The human genome consists of 23 chromosome pairs and about 30,000 genes. The genes take only 5% of the human DNA, the rest is ‘junk-DNA’, which function was not very clear at the end of the 20th century. A prokaryote cell has only one chromosome. In eukaryotes, genes occur in the cell nucleus as well as in several organelles, such as the mitochondria. The organelles are considered encapsulated prokaryotes (12.4).
Genes are not subjectively living individuals like organisms, organs, tissues, cells, or even organelles. They have an objective function in the character of a living cell. A genome should not be identified with the DNA molecules forming its material basis, neither a gene with a sequence of bases. Confusion arises from using the same word for a sequence of nucleotides in a DNA molecule and its character, the pattern. In all cells of a plant the DNA molecules have the same pattern, the same character, which is called the plant’s genome. Likewise, a gene is not a sequence of nucleotides, nor a particle in a physical or chemical sense, but a pattern of design. The same gene, the same pattern can be found at different positions in a genome, and at the same locus one finds in all cells of a plant the same pair of genes. Each gene is the design for a polypeptide, and the genome is the design of the organism.
The biotic character of the genome is interlaced with the chemical character of DNA molecules. The genome or genotype determines the organism’s hereditary constitution. The phenotype is developed according to the design expressed in the genome. Both phenotype and genotype refer to the same individual organism.
Nevertheless, genes have their own objective individuality. In asexual cell division, the genome remains the same. The parent cell transfers its genetic individuality to the daughter cells. In sexual reproduction, objective individual genes are exchanged and a new subjective individual organism emerges.
b. The population is the carrier of a gene pool
A population is characterized by the possibility to exchange genes. Although the members of the population belong to the same species, they are genetically differentiated. In a diploid cell, a DNA molecule consists of a double helix. At each position or locus there are two genes. These genes may be identical (homozygote) or different (heterozygote). Different genes that can occupy the same locus in different organisms in a population are called alleles. Some alleles dominate others. The distribution of the alleles over a population determines their genetic variation, satisfying Mendel’s laws in simple cases. In sexual reproduction, the pairs of genes separate, in order to form new combinations in the new cell (12.3).
At any time, the gene pool is the collection of all genes present in the population. The exchange of alleles in sexual reproduction leads to changes in the frequencies within the gene pool, but does not change the genes themselves. For change, several other mechanisms are known, such as mutation, crossing-over, and polyploidy. Usually, the location of the genes does not change. It is a specific property of the species. Hence, the way genes co-operate is also specific for a species.
A population in which sexual reproduction occurs without constraints is subject to the statistical law of Godfrey Hardy and Wilhelm Weinberg (1908): on a certain locus in the genome the frequency of the alleles in the gene pool in a stable population is constant, generation after generation. Only selective factors and hybridization with another population may disturb the equilibrium. Hybridization between related species or different populations of the same species give rise to a new species or race if three conditions are met. First, the hybrids are fertile. Second, there is a niche available in which the hybrids are better adapted than the original population. Third, the new combination of genes becomes isolated and sufficiently stabilized to survive.
Observe that the organisms determine the frequency of the genes in the pool. The character of each gene is realized in DNA. Still, it makes no sense to count the number of DNA molecules in a population, because DNA is found in each cell and most cells have no significance for the gene pool. Even the number of gametes is irrelevant for calculating the gene frequency. The frequency of genes in the pool is the weighed frequency of the organisms in the population, being the carriers of the gene concerned. For instance, if at a certain locus a gene occurs once in 10% of the organisms and twice in 10%, the gene has a frequency of 15% in the gene pool, because each locus contains two alleles. By natural selection, the frequency of a gene may increase or decrease, depending on the fitness of the organisms in the population.
c. The gene pool may change very fast
Because of external circumstances, the gene pool may change very fast. Within a few generations, the distribution of a gene pair AB may change from 90% A, 10% B into 10% A, 90% B. This means that a population is able to adapt itself to changes in its habitat, and to increase its chances of survival and reproduction. In a radical environmental change (in particular if a part of the population is isolated), hereditary variation within a species may give rise to the realization of a new species. Hence, adaptation and survival as concepts in the theory of evolution do not concern individual organisms (being genetically stable), but populations. Only populations are capable of genetic change.
Natural selection as such is not a random process, but it is based on at least two random processes, to wit mutation and sexual reproduction. Which alleles combine in mating rests on chance. The enormous amounts of cells involved in reproduction compensate for the relatively small chance of progress.
d. The phenotype is the target of natural selection
The phenotype (not the genotype) determines the chance of survival of an organism in its environment. The phenotype is the coherent set of the functions of all parts of the organism, its morphology, physiology, and its ability to reproduce. The genotype generates the phenotype, whereby development and environment factors play an additional but important part. Natural selection advances some phenotypes at the cost of others, leading to changes in the gene pool. Together with changes in the genes themselves, natural selection induces small changes in each generation to accumulate to large changes after a large number of generations.
The received theory of evolution emerged shortly before 1940 from a merger of Darwin’s theory of natural selection with genetics and molecular biology. It presupposes that evolution occurs in small steps. Major changes consist of a sequence of small changes. In many cases, this is an acceptable theory. Nevertheless, it would be honest to admit that there is no biological explanation available for the emergence of prokaryotes (about three billion years ago); of eukaryotes (circa one billion years ago); of multicellular organisms (in the Cambrium, circa 550 million years ago); of sexual reproduction; of animals; and of the main animal phyla, plant divisions, classes, and orders. At the end of the 20th century, the empirical evidence available from fossils and DNA sequencing is not sufficient to arrive at theories withstanding scientific critique.
12.7. Does a species correspond with a character?
A natural character is defined as a set of laws determining an ensemble of possibilities besides a class of individuals (10.2). A class and an ensemble are not restricted in number, space, and time. They do not change in the course of time and do not differ at different places. A population is not a class but a collection. Hence, it does not correspond to a character. The question of whether a species corresponds to a character is more difficult to answer. ‘There is probably no other concept in biology that has remained so consistently controversial as the species concept.’ Philosophers interpreting the concept of a natural kind in an essentialist way rightly observe that a biotic species does not conform to that concept. However, the idea that a character is not an essence but a set of laws sheds a different light on the concept of a species. The main problem appears to be that insufficient knowledge is available of the laws determining species. Instead, one investigates the much better accessible subject and object side of these unknown laws.
Generally speaking, biologists are realists, because they consider a species to be a natural set. Each living being belongs to a species, classified according to a variety of practical criteria, which do not always yield identical results. Besides, there are quite a few theoretical definitions of a species. The distinction between operational criteria used in practice and theoretical definitions is not always sharp. Practice and theory are mutually dependent. However, not distinguishing them gives rise to many misunderstandings.
Criteria to distinguish species from each other are grouped into genealogical (or phylogenetic), structural, and ecological criteria. This corresponds more or less to a division according to primary, secondary, and tertiary characteristics.
Species can be distinguished because they show distinctive, specific properties. These are regular, therefore lawlike. This is not merely interesting for biologists. In particular in sexual relationships, animals are able to distinguish other living beings from those of their own kind.
Primary criteria to distinguish species are genealogical
The biological taxonomy is based on empirical or theoretically established lineages. A population is a segment of a lineage. A taxon (for instance, a species, genus, family, order, or phylum) is defined as a set of organisms having a common ancestry. A monophyletic taxon or clade comprises all and only organisms having a common ancestry. Birds and crocodiles are monophyletic, both apart and together. A set of organisms lacking a common ancestry is called polyphyletic. Such a set, like that of all winged animals, is not suited for taxonomy. A taxon consisting of some but not all descendants of a common ancestor is called paraphyletic. For instance, reptiles have a common ancestry, but they share it with the birds, which are not reptiles. Opinions differ about the usefulness of paraphyletic taxons.
The biological taxonomy clearly presupposes genetic relations to constitute a general biotic relation frame. Descent providing the primary, genealogical criterion for a species has two important consequences.
The first consequence is seldom explicitly mentioned, but always accepted. It is the assumption that an individual living being belongs to the same species throughout its life. (It may change of population, e.g., by migration.) This means that species characteristics cannot be exclusively morphological. In particular the shape of multicellular fungi, plants, and animals changes dramatically during various phases of life. The metamorphosis of a caterpillar into a butterfly is by no means an exception. The application of similarities and differences in taxonomy has to take into account the various phases of life of developing individuals.
Second, as a rule each living being belongs to the same species as its direct descendants and parents. Therefore the dimorphism of male and female specimens does not lead to a classification into different species. A very rare exception to this rule occurs at the realization of a new species. A minimal theoretical definition says that a species necessarily corresponds to a lineage, starting at the moment it splits off from an earlier existing species, and ending at its extinction.
If this minimal definition would be sufficient as well as necessary, a species would be a collection, like a population bounded in number, space, and time. But this definition cannot be sufficient, because it leaves utterly unclear what the splitting of a species means. Branching alone is not a sufficient criterion, because each lineage branches (an organism has various descendants, and in sexual replication each organism has two parents, four grandparents, etc.). According to the primary criterion alone, the assumption that all organisms are genetically related would mean that either all organisms belong to the same species, or each sexual reproduction leads to a new species. Hence, additional secondary and perhaps tertiary criteria are needed to make clear, which kind of branching leads to a new species.
Secondary and tertiary criteria to distinguish species
The most practical criteria are structural. It concerns similarities and differences based on the DNA-structure (the genotype), besides the shape (morphology), and processes (physiology, development), making up the phenotype. In DNA and RNA research, biologists look at similarities and differences with respect to various genes and their sequences, taking into account the locus where they occur. The comparison of genes at different loci does not always give the same results. Hence people should be cautious with drawing conclusions. It should be observed that DNA and RNA research is usually only possible with respect to living or well-conserved cells and only establishes more or less contemporary relations. This also applies to other characteristics that cannot be fossilized, like behaviour. Non-contemporary similarities and differences are mostly restricted to morphological ones. For the agreement between various related species, homologies are very important (12.6).
Many biologists accept as a decisive distinction between species the existence of a reproductive gap between populations. Within a species, individuals can mate fruitfully with each other, whereas individuals of different species cannot. This concerns a subject-subject relation. According to this definition, horses and donkeys belong to different species. A horse and a donkey are able to mate, but their offspring, the mules, are not fertile. The mentioning of populations is relevant. The reproduction gap does not concern individuals but populations.
Sometimes, a population A belongs to the same species as population B, B ditto with C, but C does not with respect to A. Hence, the concept of a species according to this criterion is not always transitive. The possibility to mate and having fertile descendants is only relevant for simultaneously living members of a population. Hence it serves as a secondary addition to the primary genealogical criterion, stating that organisms living long after each other (and therefore unable to mate) may belong to the same species. Taking this into account, the mentioned lack of transitivity can be explained by assuming that one of the populations concerned is in the process of branching off. After some time, either A or C may become to belong to an independent species.
The reproduction gap is in many cases a suitable criterion, but not always. First, some species only reproduce asexually. This is not an exception, for they include the prokaryotes (the only organisms during three-quarters of the history of life on earth). Second, many organisms that experts rank to different species are able to fertilize each other. Hybrid populations are more frequent in plants than in animals. The reproductive gap is in animals more pronounced than in plants, because of the animals’ mating behaviour and the corresponding sexual dimorphy.
A tertiary criterion concerns the disposition of a species to find a suitable niche or adaptive zone (12.5). How organisms adapt to their environment leads to the formulation of ecological criteria to distinguish species. This is a relational criterion too, for adaptation does not only concern physical (e.g., climatic) circumstances, but in particular the competition with individuals of the same or of a different species.
A universal concept of a species is not obvious
Biologists and monist biophilosophers look after a universal concept of a species. Supposing that a species corresponds to a character, it should be primarily biotically qualified. No difference of opinion is to be expected on that account. But what should be its secondary characteristic? Considering the analysis in section 12.4, for prokaryotes the quantitative relation frame comes to mind (cell division); for unicellular or colonial eukaryotes the spatial frame (morphological shape and coherence); for differentiated plants the kinetic frame (physiology and development); finally, for sexually specialized plants and animals the physical relation frame (the reproductive gap). A species can only be a universal biotic character if the concept of a species is differentiated with respect to secondary and tertiary characteristics. For instance, the secondary criterion based on the reproductive gap is only applicable to sexually reproducing organisms. The pluralistic concept of a species finds its origin in the fact that all secondary and tertiary criteria are restrictively applicable, whereas the universal primary criterion is necessary but not sufficient.
A species is not an individual
Some philosophers assume that species are comparable with organisms and they consider a species to be a biotic individual. A species comes into being by branching off from another species, and it decays at extinction. Species change during their existence. It is true that these processes depend entirely on the replication of the organisms that are part of the species, but that applies to multicellular organisms as well, whose development and growth depend on the reproduction of their cells.
Organisms belonging more or less simultaneously to the same species form a population. Usually a population is a geographically isolated subset of a lineage, a set of organisms having the same ancestry. Both populations and lineages are temporal collections of individuals, not timeless classes. They are aggregates as well, because their members are genetically related. However, an aggregate is not always an individual, and it is always a set of individuals. If considered as a lineage or population (or a set of populations), a species is a temporal collection of individual organisms, subject to biotic laws. I shall not contest this vision that stresses the subject side of a species. But it does not answer the question of whether a species has a law side as well, corresponding with a character.
Evolution does not exclude the existence of character classes
Both lineages and populations are products of a biotic dynamic evolution. Natural selection, genetic drift, and ecological circumstances explain how lineages emerge, change, and disappear. Geographic isolation explains the existence of various populations belonging to the same species. But natural selection, genetic drift, or geographic isolation does not explain why a group of living beings is viable in the circumstances constituting an adaptive zone. Unavoidably, such an explanation takes its starting point from law statements, whether hypothetical or confirmed. These propositions may very well include the supposition that a lineage and its populations are spatio-temporal subsets of a timeless class, without violating the received facts and theories of evolution and genetics. The character of this class determines an ensemble of possibilities, partly realized in the individual variation occurring in a population.
No more than species, the chemical elements have been realized from the beginning of the universe. Only after the universe was cooled down sufficiently, protons and electrons could form hydrogen and helium. Only after the formation of stars, hydrogen and helium nuclei fused to become heavier nuclei. Nuclear physics provides a quite reliable picture of this chemical evolution (11.7). Doubtless, each isotope satisfies a set of laws constituting a character. I believe that the same applies to biotic species, although the complexity of organisms makes it far more difficult to state in any detail which laws constitute a biotic character.
This leads to the following model. Instead of an ensemble corresponding to a single character, consider a space consisting of all possible configurations of DNA. Each configuration is objectively represented by a sequence of letters A, C, G en T. This configuration space is mostly empty, i.e., the majority of all possible genetic configurations is never realized. A large part is not realizable in any circumstance. Most genetic configurations of DNA would never lead to a viable organism, witness the fact that almost all mutations of existing DNA are lethal.
A DNA configuration organized in genes and their loci into chromosomes is for a large part species specific. Therefore, the realizable configurations can be clustered into relatively small ‘valleys’ in this configuration space, each valley corresponding to a species. Related species lie close together. Within each valley, the configuration varies corresponding to the possible individual genetic differences between the organisms concerned. Each valley is a local optimum (an attractor), separated from other valleys by constraints of a physical, chemical, biotic, or psychic nature. From the fact that more than 99% of all species known from fossil records is extinct, it may be derived that many valleys that have been occupied in the past are no longer inhabited, because a suitable niche is no longer available. Other valleys are occupied by one or more populations. A subset of each valley in configuration space constitutes the gene pool of a population belonging to the species. Simultaneously with the population the gene pool changes, by natural selection. By adapting itself to changing circumstances, a population wanders through the valley.
Sometimes a population will cross a barrier between two neighbouring valleys. This means the realization of a new species. It is called anagenesis if the population migrates as a whole, and cladogenesis if the population distributes itself over two species such that the old valley remains occupied. Darwin was more concerned with anagenesis than with cladogenesis. Biologists distinguish sympatric from allopatric cladogenesis. The splitting of a population causes allopatric cladogenesis in geographically isolated areas like the Galapagos and Hawaii islands. In the sympatric case, the populations are not spatially isolated, but a new niche becomes available. The most occurring cause in plants is polyploidy, the duplication of the number of chromosomes, which does not directly lead to cell division. Usually, polyploidy does not give rise to fertile descendants, but sometimes a new species is realized after a number of generations have reproduced asexually or by self-pollination. More than half of all flowering plants display polyploidy.
The crossing of a barrier has an analogy in the well-known phenomenon of tunneling in quantum physics (11.7). An energy barrier usually separates a radioactive nucleus from a more stable nucleus. This barrier is higher than the energy available to cross it. According to classical mechanics, a nucleus could never cross such a barrier, but quantum physics proves that there is a finite (even if small) probability that the nucleus overtakes the barrier, like a car passes a mountain through a tunnel. A similar event occurs in the formation of molecules in a chemical reaction. In this case, the possibility to overtake the energy barrier depends on external circumstances like the temperature. The presence of a catalyst may lower the energy barrier. In biochemical processes enzymes have a comparable function. The possibility that an individual physical or chemical thing changes of character is therefore a fact, both theoretically and experimentally established. Moreover, in all chemical reactions molecules change of character, dependent on circumstances like temperature.
Similarly, at the realization of a new species, circumstances like climate changes may enhance or diminish the probability of overcoming one or more constraints. A small, geographically isolated population will do that easier than a large, widely dispersed population. Since 1972, biology knows the theory of ‘punctuated equilibrium’. From paleontological sources, Niles Eldredge and Stephen Gould derived that in a relatively short time (compared to much longer periods of stable equilibrium), a major transition from one species to another may occur.
Quantum physics explains the transition from one character to the other by tunneling, but tunneling does not explain the existence of the characters concerned. Natural selection explains how a population moves through a valley (a species) and how a population sometimes migrates to a different valley. But natural selection cannot explain why there are valleys of realizable configurations, and which they are. Natural selection explains why constraints can be overcome, not why there are constraints, or which types of constraints are operative. Natural selection explains changes within species and from one species to the other, but not why there are species, and which species exist. On the contrary, the existence of species is a condition for the action of natural selection. Populations change within a species, and sometimes they migrate from one species to another one, and its motor, its dynamic force, is natural selection. However, natural selection does not explain everything. The success of natural selection is only explicable by assuming that a population after adaptation is in a more stable equilibrium with its environment than before. What is stable or better adapted, why the chances of survival of an organism increase by a change induced by natural selection, cannot be explained by natural selection itself. Natural selection explains why a population changes its gene pool, but it does not explain why the new situation is more viable. To explain this requires research into the circumstances in which the populations live and into the characters that determine the species.
On the one side, the model suggests that the standard theories about evolution, genetics, ecology, and molecular biology do not exclude the possibility that each species corresponds to a character, a set of laws defining an ensemble of possibilities, sometimes (and never exhaustively) realized by a population of organisms. After all, ‘by far the commonest fate of every species is either to persist through time without evolving further or to become extinct.’
On the other hand, the model does not prove that a species corresponds to a character. That would only be empirically demonstrable. The idea that an empirical species is a subset of a class subject to a specific set of laws can only be confirmed by pointing out such laws. For instance, both genetics and development biology look for lawful conditions concerning the constitution of genes and chromosomes determining the phenotype of a viable organism belonging to a species. That is because the biotic expression of a character is a natural design, the genome, objectively laid down in the species-specific DNA.
Natural selection may be considered a random push for the dynamic development of populations of living beings. This development also requires the specific lawful pull of the species concerned.
The question of whether species are constant cannot be answered on a priori grounds
Should we not consider the ascription of an unchangeable and lawful character to species a relapse into essentialism? Essentialism is a theory ascribing a priori an autonomous existence to plants, animals, and other organisms. Their essence is established on rational grounds, preceding empirical experience. Essentialism presupposes the possibility to formulate necessary and sufficient conditions for the existence of each species. The conditions for any species should be independent of the conditions for any other species. This view differs widely from the idea of a character being a specific set of laws. With respect to the subject side, as far as essentialism excludes evolution, the theory of characters is by no means essentialist.
According to Aristotelian essentialism, each species would be autonomous. Biologists and philosophers seem to assume that this paradigm is still applicable to physics and chemistry. But physical things can only exist in interaction with other things, and the actual realization of physically qualified characters is only possible if circumstances permit. For instance, in the centre of the sun no molecules can exist. The astrophysical and chemical theories of evolution assume that physical things emerged gradually, analogous to organisms in the biotic evolution. Nevertheless, it is generally accepted that particles, atoms, molecules, and crystals are subject to laws that are everywhere and always valid.
Physical and chemical things can only exist in interaction with each other in suitable circumstances. Similarly, living organisms can only exist in genetic relations with other organisms, permitting the circumstances. Each living organism would perish in absence of other living beings, and no organism can survive in an environment that does not provide a suitable niche.
My reasons to consider a species to be a character are a posteriori, based on scientific arguments open to empirical research. It is a hypothesis, like any other scientific assumption open to discussion. And it is a hypothesis leaving room for the evolution of a population within a species as well as from one species to another one. It is a hypothesis fully acknowledging Darwin’s great discovery of natural selection. Moreover, this hypothesis recognizes the importance of environmental circumstances both determining possibilities and their realization. The laws are not the only conditions for existence. Physical and ecological circumstances are conditions as well. The realization of species can only occur in a certain order, with relatively small transitions. In this respect, too, the evolution of species does not differ from the evolution of chemical elements.
Although essentialists are able to take circumstances into account, the theory of characters moves ahead. The possibilities offered by a character are not merely realizable if the circumstances permit, but the ecological laws are partly the same as the laws constituting the character of a species. The laws forming a character for one species are not separated from the laws forming the character of another species, or from the laws determining biotic processes. Essentialism supposes that each species can be defined independent of any other species.
It is undeniable that my hypothesis runs counter to the kind of evolutionism that denies the existence of constant laws. From the above discussion it will be clear that I do not criticize Darwin’s theory and its synthesis with genetics and molecular biology. By natural selection, the theory of evolution explains the actual dynamic process of becoming and the evolution of populations. I believe that this theory does not contradict the view that species correspond to unchangeable characters and their ensembles. On the contrary, I believe that the facts corroborate the proposed model better than a radical evolutionism denying the existence of laws. The hypothesis that unchangeable laws dominate the species can be investigated on empirical grounds. This discussion belongs to the competence of empirical science.
The answer to the question of whether a species corresponds to a character does not depend on the acceptance or rejection of the belief that characters – not only biotic species – consist of laws given by God. The empirical approach that I advocate is at variance with the creationist view assuming a priori that the species are unchangeable, rejecting any theory of evolution. Creationism uses the Bible as a source of scientific knowledge preceding and superseding scientific research. It contradicts the view that the problem of whether species correspond to constant characters can only be solved a posteriori, based on scientific research.
A species has a law side and a subject side
For the time being, I am inclined to conclude that a species at the law side corresponds with a biotically qualified character, an unchangeable set of laws. The least one can say is that the recognition of a species or a higher taxonomical unit requires an insight into the regularities which make an organism to belong to that category. At the subject side, a species is realized by a lineage, an aggregate of individual organisms, hence with a collection, bounded in number, space, and time.
Evolution means the subjective realization of species. Natural selection is its motor and explains how species are realized. Whether a species is realizable at a certain place and time depends on the character of the species; on the preceding realization of a related species (on which natural selection acts); on the presence of other species (the ecological environment); and on physical circumstances like the climate (the physical environment).
I have no intention to suggest that the biotic evolution is comparable to the astrophysical and chemical evolution in all respects. I conceive of each evolution as a realization of possibilities and dispositions. But the way by which this occurs is strongly different. For physical and chemical things and events, interaction is decisive, including circumstances like temperature and the availability of matter and energy. The biotic evolution depends on sexual and asexual reproduction, with the possibility of variation and natural selection.
Another difference concerns the reproducibility of evolution. The physical evolution of the chemical elements and of molecules repeats itself in each star and each stellar system. In contrast, it is often stated that the biotic evolution is unique and cannot be repeated. It may be better to assert that the actual course of the biotic evolution is far more improbable than that of the physical and chemical ones. Comparable circumstances – a condition for recapitulation – never or hardly ever occur in living nature. In particle accelerators the astrophysical evolution is copied, the chemical industry produces artificial materials, agriculture improves races, in laboratories new species are cultivated, and the bio-industry manipulates genes. All this would be difficult to explain if one loses sight of the distinction between law and subject.
Natural laws have a place in biology, too
As a character, a biotic design is a set of laws, but for a scientist this does no longer imply a divine designer. Whereas this does not solve the question of the origin of the natural laws, natural science became liberated from too naive views about the observability of divine interventions in empirical reality.
Essentialism survived longest in the plant and animal taxonomy. Until the middle of the 20th century, this considered the system of species, genera, families, classes, orders, and phyla or divisions to be a logical classification. In this classification, each category was characterized by one or more essential properties. Biological essentialism was not a remains of the Middle Ages, but a fruit of the Renaissance. From John Ray to Carl Linnaeus, many realistic naturists accepted the existence of unchangeable species, besides biologists having a nominalist view of species.
The difficulty that some philosophers have with the modern concept of a species can be reduced to a conscious or subconscious allegiance to an essentialist view. The difficulty that some biologists have with the idea of natural law is their abhorrence of essentialism. Therefore, it is important to distinguish essence from lawfulness. The ‘essential’ (necessary and sufficient) properties do not determine a character. Rather, the laws constituting a character determine the objective properties of the things or processes concerned. These properties, represented in an ensemble, may display such a large statistical variation that necessary and sufficient properties are hard to find. Moreover, the laws and properties do not determine essences but relations.
A second reason why some biologists are wary of the idea of natural law is that they (like many philosophers) have a physicalist view of laws. Rightly, they observe that the (now outdated) physical and chemical model of a natural law is not applicable to biology. The theory of evolution is considered a narrative about the history of life, rather than a theory about processes governed by natural laws. But probably biologists will not deny that their work consists of finding order in living nature. The theory of evolution would not exist without the supposition that the laws for life, that are now empirically discovered, held millions of years ago as well. The question of whether other planets host living organisms can only arise if it is assumed that these laws hold there, too.
A third reason may be the assumption that a law only deserves the status of natural law, if it holds universally and is expressible in a mathematical formula. A mathematical formulation may enlarge the scope of a law statement. Yet the idea of natural law does not imply that it has necessarily a mathematical form. Neither should a law apply to all physical things, plants, and animals. Every regularity, every recurrent design or pattern, and every invariant property is to be considered lawful. In particular each character expresses its own specific law conformity. In the theory of evolution biologists apply whatever patterns they discover in the present to events in the past. Hence they implicitly acknowledge the persistence of natural laws, also in the field of biology.
Anyhow, Charles Darwin was not wary of natural laws. At the end of his On the origin of species he wrote:
‘It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms.’
 See Rudwick 2005; 2008.
 Mayr 1982, 56: ‘Except for the twilight zone of the origin of life, the possession of a genetic program provides for an absolute difference between organisms and inanimate matter.’ Ibid. 629: ‘… the existence of a genetic program … constitutes the most fundamental difference between living organisms and the world of inanimate objects, and there is no biological phenomenon in which the genetic program is not involved …’. Jacob 1970, 4: ‘Everything in a living being is centered on reproduction’. Rensch 1968, 35: ‘… “life” is not so much defined by certain single characters but by their combination into individualized, purposefully functioning systems showing a specific activity, limited to a certain life span, but capable of reproduction, and undergoing gradually hereditary alterations over long periods.’
 This does not exclude neoteny and other forms of heterochrony, see Raff 1996, chapter 8.
 Farley 1974; Bowler 1989.
 Ruse 1973, 118-121.
 Monod 1970, 102-103: ‘… from the bacterium to man the chemical machinery is essentially the same … 1. In its structure: all living beings … are made up of … proteins and nucleic acids … constituted by the assembling of the same residues … 2. In its functioning: the same reactions, or rather sequences of reactions, are used in all organisms for the essential chemical operations …’
 Rosenberg 1985, 136-152.
 At the end of the 19th century, energeticists like Ostwald assumed that thermodynamics should be able to explain all physical and chemical processes. Atomic theory and quantum physics made clear that thermodynamics is too general for that. Likewise, in my view, evolution theory is not specific enough to explain biotic characters.
 According to Rosenberg 1985, 137-138, ‘biological entity’, ‘parent of’ and ‘ancestor’ are primitive, undefinable concepts in the following two axioms: ‘No biological entity is a parent of itself. If a is an ancestor of b, then b is not an ancestor of a.’ If the mentioned terms are undefined, the natural numbers satisfy these axioms as well (2.1).
 Panchen 1992, chapter 9.
 Dawkins 1983, 16: ‘If you find something, anywhere in the universe, whose structure is complex and gives the strong appearance of having been designed for a purpose, then that something either is alive, or was once alive, or is an artefact created by something alive.’ Kitcher 1993, 270: ‘Entities have functions when they are designed to do something, and their function is what they are designed to do. Design can stem from the intentions of a cognitive agent or from the operation of selection …’
 In RNA, uracil (U) replaces thymine. The production of uracil costs less energy than that of thymine, which is more stable, see Rosenberg 1985, 38-43. Stability is for DNA more important than for RNA that is assembled repeatedly. Hence, mistakes in the transfer of design are easy to correct. The double helix structure also enhances the stability of DNA. RNA consists of only one series of nucleotides.
 A protein is a large polypeptide. Sometimes the same gene assembles more than one protein. Often a gene occurs more than once in the DNA, its locus determining how the gene co-operates with other genes. Hence, similar genes may have different functions. A direct relation between a gene and a phenotypic characteristic is rare. See Hull 1974, 15-19.
 According to the ‘central dogma of molecular biology’, formulated by Francis Crick, the transfer of information from DNA via RNA (‘transcription’ by mRNA) to the polypeptides (‘translation’ by tRNA) is irreversible. With respect to the first step, the dogma does not apply entirely to viruses, and there are important differences between prokaryotes and eukaryotes. The intervention of RNA is necessary in eukaryotes, because DNA is positioned in the cell nucleus, whereas the assembly of the polypeptides occurs elsewhere (in ribosomes). In prokaryotes, the translation may start before the transcription is finished. In transcription, a third form is produced, rRNA, concentrated in the ribosome, the organelle where the assembly of polypeptides takes place. Because RNA has mostly a transport function, its tertiary characteristic may be called kinetic.
 Epigenesis is the name of the process, in which each phase in the development of a plant or animal is determined by preceding phases, genes and environment, see McFarland 1999, 27-29.
 Dawkins 1986, 295-296; McFarland 1999, 27. The conception of the composition of DNA as a code is a metaphor, inspired by the discovery that the structure of DNA can be written in only four symbols.
 Raff 1996, chapter 10. Ibid. 27: ‘If each new species required the reinvention of control elements, there would not be time enough for much evolution at all, let alone the spectacularly rapid evolution of novel features observed in the phylogenetic record. There is a kind of tinkering at work, in which the same regulatory elements are recombined into new developmental machines. Evolution requires the dissociability of developmental processes. Dissociability of processes requires the dissociability of molecular components and their reassembly.’
 Osmosis occurs if a membrane lets pass a solvent (usually water) but not the solved matter. The solvent moves through the membrane in the direction of the highest concentration of the solved matter. This induces a pressure difference across the membrane that counteracts the transport. In equilibrium, the osmotic pressure in some desert plants can be up to a hundred times the atmospheric pressure.
 In haploid cells, the cell nucleus contains a single string of chromosomes, in diploid cells the chromosomes are paired. Each diploid gene occurs in a pair, except the sex chromosomes, being different in males (XY), equal in females (XX). Each chromosome is a single DNA molecule and consists of a large number of genes. The position of the genes on a chromosome is of decisive significance. On each position (locus) in a chromosome pair, there is at most one pair of genes, being homozygote (equal) or heterozygote (unequal). If in different individuals different genes can occupy the same locus, these genes are called alleles.
 Griffiths, Gray 1994.
 Griffiths, Gray 1994.
 During the 20th century, the attention of biologists was so much directed to evolution and natural selection, that the investigation of individual development processes (in which natural selection does not play a part) receded to the background. The complexity of these processes yields an alternative or additional explanation for the fact that relatively little is known about them. Some creationists take for granted ‘natural’ processes in the development of a human being from its conception, during and after pregnancy, while considering similar processes incomprehensible in evolution. A standard objection is that one cannot understand how by natural selection such a complicated organ like the human eye could evolve even in five hundred million years. However, who can explain the development of the human eyesight in nine months, starting from a single fertilized cell? In both cases, biologists have a broad understanding of the process, without being able to explain all details. (I am not suggesting here that the evolution and the development of the visual faculty are analogous processes.)
 Raff 1996, 260.
 Raff 1996, 23.
 Mayr 1982, 140, 244; Margulis, Schwartz 1982, 5-11; Ruse 1982, 169-171.
 These organelles are about as large as prokaryotic cells. RNA research indicates that mitochondria are genetically related to the purple group and chloroplasts to the cyanobacteria, both belonging to the eubacteria. The most primitive eukaryotes, the archaezoa, do not contain mitochondria of other organelles besides their nucleus. The similarity between prokaryotes and the organelles in eukaryotic cells was first pointed out by Lynn Margulis, in 1965.
 Contrary to bacteria, viruses are not capable of independently assembling DNA, RNA and polypeptides, and they can only reproduce parasitically in a cell. Some viruses can be isolated forming a substance that is only physically and chemically active. Only if a virus enters a cell, it comes to life and starts reproducing. Outside the cell, a virus is primarily physically qualified, having a biotic disposition, to be actualized within a cell. Because a virus mainly transports DNA, its character may be considered to have a (tertiary) kinetic disposition (like RNA). A virus has a characteristic shape differing from the shape of a cell.
 Likewise, an atomic nuleus (having a spatially founded character) acts like a quantitative unit in the character of an atom (11.3).
 Margulis, Schwartz 1982. Up till the sixties, besides the animal kingdom only one kingdom of plants was recognized, including the monera, protista and fungi besides the ‘true’ plants, see Greulach, Adams 1962, 28.
 Hence, a population is not a class but a collection (10.1). It is a spatial cross section of a lineage, which in turn is a temporally extended population, see de Queiroz 1999, 53-54. Besides being genetically homogeneous, a population is also genetically varied, see below.
 Darwin 1859, chapter 3.
 Mayr 1982, 602.
 Purves et al. 1998, chapter 28: ‘Fungi: A kingdom of recyclers.’
 McFarland 1999, 72.
 ‘Survival of the fittest’ is sometimes called circular, see e.g. Popper 1974, 137; Dampier 1929, 319: ‘That which is fit survives, and that which survives is fit’. According to Rosenberg 1985, chapter 6 this circularity is caused by the fact that fitness is a primitive, undefinable concept in the theory of evolution. Fitness is not definable, but it is measurable as reproductive success. See also Sober 1993, 69-73. According to McFarland 1999, 78, this circularity is removed by relating survival to an individual and fitness to its offspring: ‘the fit are those who fit their existing environments and whose descendants will fit future environments … in defining fitness, we are looking for a quantity that will reflect the probability that, after a given lapse of time, the animal will have left descendants’. Fitness is a quantitatively founded magnitude, lacking a metric. Fitness depends on the reproduction of an individual, and on that of its next of kin. This is called ‘inclusive fitness’, explaining the ‘altruistic’ behaviour of bees, for instance.
 Darwin 1859, chapter 4.
 Panchen 1992, chapter 4.
 Mayr 1982, 611; Raff 1996, 375-382.
 Dawkins 1976 assumes that the ‘selfish genes’ are the subjects to evolution. But according to Mayr 2000, 68-69: ‘The geneticists, almost from 1900 on, in a rather reductionist spirit preferred to consider the gene the target of evolution. In the past 25 years, however, they have largely returned to the Darwinian view that the individual is the principal target.’ See also Sober 1993, chapter 4.
 Mayr 1982, 62: ‘The claim that genetics has been reduced to chemistry after the discovery of DNA, RNA, and certain enzymes cannot be justified … The essential concepts of genetics, like gene, genotype … are not chemical concepts at all …’
 Ruse 1982, 21, 30, 200-207.
 Mutations may have a physical cause (e.g., radioactivity), or a biotic one (e.g., a virus). Mutations are usually indifferent or even lethal, but sometimes enriching. For every gene, they are very rare, but because there are many genes in an individual and even more in a gene pool, they contribute significantly to the variation within a species. Crossing-over means a regrouping of genes over the chromosomes. Polyploidy means that a DNA molecule consists of more than two strings, on each or some loci there are three genes in stead of two.
 Hull 1974, 57-58; Ridley 1993, 87-92, 131-132. Populations are hardly ever in equilibrium. The relevance of the law of Hardy and Weinberg is that deviations point to equilibrium disturbing factors. In small populations ‘genetic drift’ occurs, changes in the gene pool caused by accidental circumstances.
 Ridley 1993, 42-43. Usually, hybridization is impossible, because the offspring is not viable, or because the offspring is not fertile, or because the offspring has a decreasing fertility in later generations.
 Ridley 1993, 387: ‘A community of interbreeding organisms is, in population genetic terms, a gene pool.’
 The complication that on different loci the same gene may occur is left out of consideration in this example.
 Dawkins 1986, 43, 62.
 Mayr 1982, 251. On the biological species concept, see Mayr 1982, chapter 6; Rosenberg 1985, chapter 7; Ereshefsky 1992; Ridley 1993, chapter 15; Wilson (ed.) 1999.
 Panchen 1992, 337-338 mentions seven species concepts, others count more than twenty, see Hull 1999.
 See de Queiroz, 1999, 64: ‘… the species problem results from confusing the concept of a species itself with the operations and evidence that are used to put that concept in practice.’
 de Queiroz 1999, 77: ‘… the general lineage concept is a quintessential biological species concept: inanimate objects don’t form lineages.’
 de Queiroz 1999; Mishler, Brandon, 1987, 310.
 Ereshefsky 1992, 350; de Queiroz 1999, 60, 63: ‘In effect, the alternative species definitions are conjunctive definitions. All definitions have a common primary necessary property – being a segment of a population-level lineage – but each has a different secondary property – reproductive isolation, occupation of a distinct adaptive zone, monophyly, and so on.’
 For some fossils DNA research is possible. An exceptional record concerns a fossil aged 135 millions years.
 Mayr 1982, 273: ‘A species is a reproductive community of populations (reproductively isolated from others) that occupies a specific niche in nature.’ Mayr, ibid. 272 mentions three aspects of a biotic species. ‘The first is to envision species not as types but as populations (or groups of populations), that is, to shift from essentialism to population thinking. The second is to define species not in terms of degree of difference but by distinctness, that is, by the reproductive gap. And third, to define species not by intrinsic properties but by their relation to other co-existing species, a relation expressed both behaviorally (noninterbreeding) and ecologically (not fatally competing).’
 Mayr 1982, 286: ‘The word “species”… designates a relational concept’.
 Ridley 1993, 40-42.
 Nanney 1999.
 Mating behaviour leads to the ‘recognition species concept’, see Ridley 1993, 392-393.
 According to Hull 1999, 38-39, the concept of a species ought to be universal (applicable to all organisms), practical in use, and theoretically significant. Hull, ibid. 25, observes that monists are usually realists, pluralists being nominalists.
 Dupré 1999. Likewise, the physical concept of natural kinds is not universal. For quantitatively, spatially, and kinetically founded characters, different secondary criteria apply.
 Rosenberg 1985, 204-212; Ridley 1993, 403-404. Hull 1999, 32: ‘when species are supposed to be the things that evolve, they fit more naturally in the category individual (or historical entity) than the category class (or kind).’ Hull assumes a duality: ‘Classes are spatio-temporally unrestricted, whereas individuals are spatio-temporally localized and connected. Given this fairly traditional distinction, we argued that species are more like individuals than classes’ (32-33). Clearly, Hull does not distinguish between aggregates and individuals. For a criticism, see Mishler, Brandon, 1987; de Queiroz, Donoghue, 1988; Sober 1993, 149-159; de Queiroz 1999, 67-68.
 Boyd 1999, 141 identifies ‘… a class of natural kinds, properties and relations whose definitions are provided not by any set of necessary and sufficient conditions, but instead by a “homeostatically” sustained clustering of those properties or relations. It is a feature of such homeostatic property cluster (HPC) kinds (…) that there is always some indeterminacy or “vagueness” in their extensions.’
 Based on an essentialist interpretation, Mayr 1982, 251 turns down the analogy of the species concept in biology with that of mineralogy or chemistry: ‘For a species name in mineralogy is on the whole a class name, defined in terms of a set of properties essential for membership in the class.’
 For each organism, a DNA molecule consisting of a characteristic sequence of nucleotides expresses the genetic ‘code’. There are only four nucleotides in DNA, to wit A (adenine), C (cytosine), G (guanine) and T (thymine). Each gene consists of a large sequence of nucleotides. The number of possible sequences of nucleotides is much larger than the number of individual organisms now and in the past. Individuals with the same genetic configuration are genetically identical and occupy the same position in configuration space. This space is comparable with the morphological space or morphospace discussed by Amundson 1994, e.g. For the sake of argument, I assume this space to be two-dimensional.
 Lauder 1982, 508: ‘Why does the range of extant phenotypes, when mapped onto a theoretical “morphospace”, fill so little of it?’ See also Amundson 1994, 99; Raff 1996, chapter 9.
 In the human genome, 0.1% of the genes are individually different, 99.9% being the same for all human beings. In the so-called junk-DNA, one finds more differences that are individual.
 Mayr 1982, 274: ‘Isolating mechanisms are biological properties which prevent the interbreeding of populations that are actually or potentially sympatric.’ Sober 1996, 76: ‘The word ‘constraint’ has been used in many different ways; biologists talk about mechanical constraints, developmental constraints, phylogenetic constraints, genetic constraints, etc., etc. Underlying this diversity, however, is the idea that constraints limit the ability of natural selection to produce certain outcomes.’ Dawkins 1983, 17: ‘Living things are not just statistically improbable in the trivial sense of hindsight: their statistical improbability is limited by the a priori constraints of design.’ For a review of reproductive constraints, see Ridley 1993, 389. For developmental constraints, see Raff 1996, chapter 9.
 A third form, parapatric cladogenesis, is rather rare, see Ridley 1993, chapter 16; Purves et al. 1999, 472-477.
 According to Stebbins 1982, 16-21 such a transition takes 50,000 years or more, whereas a stable period may last millions of years. See Gould, Vrba 1982; Ridley 1993, chapter 19; Strauss 2009, 487-496..
 Stebbins 1982, 23.
 Evolutionists have a tendency to deny the existence of biotic laws, see e.g. Dawkins 1986, 10-15. Nevertheless, Griffiths 1999 asserts that there are laws valid for taxonomy. Ruse 1973, 24-31 stresses that biology needs laws no less than the inorganic sciences. He mentions Mendel’s laws as an example. And Ereshefsky 1992, 360, observes at least that ‘… there may be universal generalizations whose predicates are the names of types of basal taxonomic units … So though no laws exist about particular species taxa, there may very well be laws about types of species taxa.’ See Stafleu 1999, 2000.
 Toulmin, Goodfield 1965. Mayr 1982, 175-177 observes that in Linnaeus’ taxonomy the genera are defined in an essentialist way. Mayr, ibid. 176 quotes from Linnaeus’ Philosophia Botanica (1751): ‘The ‘character’ is the definition of the genus, it is threefold: the factitious, the essential, and the natural. The generic character is the same as the definition of the genus … The essential definition attributes to the genus to which it applies a characteristic which is very particularly restricted to it, and which is special. The essential definition [character] distinguishes, by means of a unique idea, each genus from its neighbors in the same natural order.’
 Sober 1993, 145-149; Hull 1999, 33; Wilson 1999, 188.
 Dawkins 1986, chapter 1.
 See e.g. Mayr 1982, 260: ‘The essentialist species concept … postulated four species characteristics: (1) species consist of similar individuals sharing in the same essence; (2) each species is separated from all others by a sharp discontinuity; (3) each species is constant through time; and (4) there are severe limitations to the possible variation of any one species.’
 Toulmin, Goodfield 1965, chapter 8; Panchen 1992, chapter 6. Ray and Linnaeus were more (Aristotelian) realist than (Platonic) idealist. Mayr 1982, 38, 87, 304-305 ascribes the influence of essentialism to Plato. ‘Without questioning the importance of Plato for the history of philosophy, I must say that for biology he was a disaster.’ (ibid. 87). Mayr shows more respect for Aristotle, who indeed has done epoch-making work for biology (ibid. 87-91, 149-154). However, Aristotle was an essentialist no less than Plato was.
 Rosenberg 1985, 188: ‘Essentialism with respect to species is the claim that for each species there is a nontrivial set of properties of individual organisms that is central to and distinctive of them or even individually necessary and jointly sufficient for membership in that species.’ The identification of a class by necessary and sufficient conditions is a remnant of rationalistic essentialism, see, e.g., Hull 1999, 33; Wilson 1999, 188. Boyd 1999, 141-142 calls his conception of a species as ‘… a class of natural kinds, properties and relations whose definitions are provided not by any set of necessary and sufficient conditions, but instead by a “homeostatically” sustained clustering of those properties or relations’ a form of essentialism, to be distinguished from the essentialism of Linnaeus etc. Griffiths 1999 contests the view that there are no natural laws (in the form of generalizations allowing of counterfactuals) concerning taxonomy. Definition of a natural kind by properties may have a place in natural history, but not in a modern scientific analysis based on theories, in which laws dominate, not properties.
 Hull 1974, 47; Rosenberg 1985, 190-191.
 Hull 1974, 49; Mayr 1982, 37-43, 846. To the 19th-century physicalist idea of law belonged determinism and causality. However, determinism is past, and causality is no longer identified with law conformity but is considered a physical relation.
 Mayr 2000, 68: ‘Laws and experiments are inappropriate techniques for the explication of such events. Instead, one constructs a historical narrative, consisting of a tentative construction of the particular scenario that led to the events one is trying to explain.’
 Rosenberg 1985, 122-126, 211, 219. ‘But biology is not characterized by the absence of laws; it has generalizations of the strength, universality, and scope of Newton’s laws: the principles of the theory of natural selection, for instance.’ (ibid. 211). About M.B. Williams’ axiomatization of the theory of evolution, (ibid. 136-152, see also Hull 1974, 64-66), Rosenberg observes: ‘None of the axioms is expressed in terms that restrict it to any particular spatio-temporal region. If the theory is true, it is true everywhere and always. If there ever were, or are now, or ever will be biological entities that satisfy the parent-of relation, anywhere in the universe, then they will evolve in accordance with this theory (or else the theory is false).’ (ibid. 152). But concerning the study of what is called in this book ‘characters’, Rosenberg believes that these ‘… are not to be expected to produce general laws that manifest the required universality, generality, and exceptionlessness.’ (ibid. 219). Yes indeed, it concerns specific laws. Evolutionists tend to deny the existence of biotic laws, see e.g. Dawkins 1986, 10-15. However, Ruse 1973, 24-31 stresses that biology is no less than the inorganic sciences in need of laws. He points to Mendel’s laws for an example. Rensch 1968 gives a list of about one hundred biological generalizations. Griffiths 1999 asserts that there are laws valid for taxonomy. Ereshefsky 1992, 360, observes at least that ‘… there may be universal generalizations whose predicates are the names of types of basal taxonomic units … So though no laws exist about particular species taxa, there may very well be laws about types of species taxa.’ For a discussion of the functioning of laws in biology, see Hull 1974, chapter 3.
 Dawkins 1983.
 Darwin 1859, 459.
Part II, chapter 13
Inventory of behaviour characters
13.1. The primary characteristic of animals
The sixth and final relation frame for characters of natural things and processes concerns animals and their behaviour. This, too, is a typical 20th-century subject. In the United States and the Soviet Union, especially positivistically oriented behaviorists were concerned with laboratory research of the behaviour of animals, in particular with their learning ability. Later on, in Europe ethology emerged, investigating animal behaviour in natural circumstances. I shall not discuss human psychology, which witnessed important developments during the 20th century as well. Besides ethology and animal psychology, neurology is an important source of information for chapter 13.
Section 13.1 argues that animals are characterized by goal directed behaviour, implying the establishment of informative connections and control. Section 13.2 discusses the secondary characteristic of animals. Section 13.3 deals with the psychical processing of information, section 13.4 with controlled processes and section 13.5 with their goals. Section 13.6 concludes part II and introduces part III.
A psychical character is a pattern of behaviour or a program, a lawful prescription. This is a scheme of fixed processes laid down in detail, with their causal connections leading to a specified goal. Behaviour has an organic basis in the nervous system and in the endocrine system (13.2), and a physical and chemical basis in signals and their processing (13.3).
No more than the preceding chapter, this inventory of animal behaviour contains anything new from a scientific point of view. Only the ordering is uncommon, as it derives from the philosophy of the cosmonomic idea. The proposed ordering intends to demonstrate that the characters studied in mathematics and science do not merely show similarities. Rather, the natural characters are mutually interlaced and tuned to each other.
For the psychic subject-subject relation, I suggest the ability to make informative and goal directed connections. Psychic control influences organic, physical, chemical, kinetic, spatial, and quantitative relations, but it does not mean their abolishment. On the contrary, each new order means an enrichment of the preceding ones. Physical interactions allow of more (and more varied) motions than the kinetic relation frame alone does. Even more kinds of motion are possible in the organic and psychic worlds. The number of organic compounds of atoms and molecules is much larger than the number of inorganic ones. Organic variation, integration, and differentiation are in the animal kingdom more evolved than in the kingdom of plants. Each new order opens and enriches the preceding ones. By making informative connections, an animal functions organically better than a plant. For this purpose, an animal applies internally its nervous system and its hormones, and externally its behaviour, sustained by its senses and motor organs.
Secondary differences between animals and plants
Animals differ in important respects from plants, fungi, and bacteria. No doubt, they constitute a separate kingdom. The theory of evolution assumes that animals did not evolve from differentiated multicellular plants, but from unicellular protozoans. In the evolutionary order, the plants may have emerged after the animals. The first fossils of multicellular animals occur in older layers than those of differentiated plants. Fungi are genetically more related to animals than to plants. Possibly, the plants branched off from the line that became the animal kingdom. If so, this branching is characterized by the encapsulation of prokaryotes evolving into chloroplasts. The distinctive property of green plants is their ability of photosynthesis, which is completely absent in animals and fungi. Another difference is the mobility of most animals in contrast to the sedentary nature of most plants. Animals lack the open growth system of many plants, the presence of growth points of undifferentiated cells, from which periodically new organs like roots or leaves grow. After a juvenile period of development, an animal becomes an adult and does not form new organs. Animal organs are much more specialized than plant organs.
If asked to state the difference, a biologist may answer that plants are autotroph and animals heterotroph. Plants achieve their food directly from their physical and chemical environment, whereas animals depend partly on plants for their food supply. However, fungi too depend on plants or their remains, and some plants need bacteria for the assimilation of nitrogen. Apart from that, this criterion is not very satisfactory, because it does not touch the primary, qualifying relation frames of plants and animals. It seems to be inspired by a world view reducing everything biological to physical and chemical processes. This view stresses the energy balance, metabolism, and the production of enzymes out of proportion. I believe the distinction between autotroph and heterotroph to be secondary.
Animals are primarily distinguished by their behaviour
A relational philosophy does not look for reductionist or essentialist definitions, but for qualifying relations. The most typical biotic property of all living beings, whether bacteria, fungi, plants, or animals, is the genetic relation, between organisms and between their parts, as discussed in chapter 12. Superposed on this relation, animals have psychic relations between their organs by means of their nervous system, and mutually by means of their observable behaviour. In part, this behaviour is genetically determined; in part, it is adaptable. Obviously, in particular species specific behaviour is genetically determined, because species are biotically qualified characters, if not aggregates (12.7). Different animal species can be distinguished because of their genetically determined behaviour. More differentiated animals have a complex nervous system with a larger capacity for learning and more freedom of action, than simpler animals have.
The taxonomy of the animal kingdom is mostly based on descent and on morphological and physiological similarities and differences. Its methodology hardly differs from that of the plant taxonomy. But there are examples of species that can only be discerned because of their behaviour. When a new animal species is realized, a change of behaviour precedes changes in morphology or physiology. This means that controlled behaviour plays a leading part in the formation of a new animal species. Because of the multiformity of species specific behaviour, there are far more animal species than plant species, and much less hybrids.
However, animals have a lot in common with plants and fungi, too, because their psychic character is interlaced with biotic characters. Conversely, as a tertiary characteristic some plants are tuned to animal behaviour. Flowering and fruit bearing plants have a symbiotic relation with insects transferring pollen, or with birds and mammals eating fruits and distributing indigestible seeds.
The psychically qualified character of an animal comes to the fore in its body plan (morphology) and body functions (physiology), being predisposed for its behaviour. For this purpose, animals have organs like the nervous system, hormonal glands, and sense organs, that plants and fungi lack. Animals differ from plants because of their sensitivity for each other, their aptitude to observe the environment, and their ability to learn. They are sensitive to internal stimuli and external signals. Sometimes, also plants react to external influences like sunlight. But they lack special organs for this purpose and they are not sensitive to each other or to signals. In a multicellular plant, a combination of such reactions may give rise to organized motions, for instance flowers turning to the sun. Animal movements are not primarily organized but controlled. However, control does not replace organization, but superposes it.
Each plant cell reacts to its direct surroundings, to neighbouring cells or the physical and biotic environment. A plant cell only exerts action by contact, through its membranes. Neighbouring animal cells are less rigidly connected than plant cells. There are more intercellular cavities. Animal cells and organs are informatively linked by neurons, capable of bridging quite long distances. An animal exerts action at a distance within its environment as well, by means of its sense organs, mobility, and activity.
A physical system is stable if its internal interactions are stronger than its external interactions. An organism derives its stability from maintaining its genetic identity during its lifetime (12.3). Only sexual reproduction leads to a new genetic identity. For the stability of an animal, internal control by the nervous and hormonal systems is more important than the animal’s external behaviour.
Projections of psychic relations on preceding relation frames
Informative goal-directed connections express the universal psychic subject-subject relation. Animals receive information from their environment, in particular from other animals, and they react upon it. Mutatis mutandis, this also applies to animal organs. Both internally and externally, an animal may be characterized as an information processor. Provisionally, I propose the following projections on the five relation frames preceding the psychic one.
a. As units of information, signals or stimuli quantitatively express the amount of information. A neuron has an input for information and an output for instructions, both in the quantitative form of one or more stimuli. The nerve cell itself processes the information.
b. A behaviour program integrates stimuli into information and instruction patterns. Neurons make connections and distribute information. By their sense organs, higher animals make observations and transfer signals bridging short or large distances. The animal’s body posture provides a spatially founded signal.
c. A net of neurons transports and amplifies information, with application of feedback. Communication between animals could be a kinetic expression of the psychic subject-subject relation.
d. Behaviour requires an irreversible causal chain from input to output, intermitted by programmed information processing. Interpretation, the mutual interaction and processing of complex information, requires a memory, the possibility to store information for a lapse of time.
e. The animal’s ability to learn, to generate new informative links, to adapt behaviour programs, may be considered a projection on the biotic subject-subject relation. Learning is an innovative process, unlearning is a consequence of ageing. In the nervous system, learning implies both making new connections between neurons and developing programs.
The psychic subject-subject relation and its five projections should be recognizable in all psychic characters. They are simulated in computers and automatized systems.
13.2. Secondary characteristics of animals
Animal behaviour has an organic basis in the nervous system. Its character has a genetic foundation. The sense organs are specialized parts of the nervous system, from which they emerge during the development of the embryo. The nervous system controls the animal body and requires observation, registration, and processing of external and internal information. The processing of stimuli, coming from inside or outside the animal body, occurs according to a certain program. This program is partly fixed, partly adaptable because of experience. Consequently, animals react to changes in their environment much faster and more flexibly than plants do. Besides the nervous system, the whole body and its functioning are disposed to behaviour.
a. A unicellular animal has the character of a nerve cell
The basic element of the nervous system is the nerve cell or neuron, passing on stimuli derived from a sensor to an effector. A unicellular animal (a protozoan) has no nerve cells. Rather, it is a nerve cell, equipped with one or more sensors and effectors. An effector may be a cilium by which the animal moves. The simplest multicellular animals like sponges consist only of such cells. A nerve cell in a more differentiated animal is a psychic subject with a character of its own, spatially and functionally interlaced with the nervous system and the rest of the body. The protozoans and the sponges as well as the neurons in higher animals may be considered to be primarily psychically and secondarily quantitatively characterized thing-like subjects. For all multicellular animals, the neurons and their functioning (inclusive their neurochemistry) are strikingly similar, with only subordinate differences between vertebrates and invertebrates.
b. Neurons form a spatially founded network
In a multicellular nervous system, a neuron usually consists of a number of dendrites, the cell body and the axon ending in a number of synapses. Each synapse connects to a dendrite or the cell body of another cell. A dendrite collects information from a sensor or from another neuron. After processing, the cell body transfers the information via the axon and the synapses to other neurons, or to a muscle or a gland. The dendrites collect the input of information that is processed in the cell body. The axon transports the output, the processed information that the synapses transfer to other cells.
In all animals except the most primitive ones like protozoans and sponges, the neurons are distinct from other cells. The other cells may be sensitive for instructions derived from neurons, but they are unable to generate or process stimuli themselves. The neurons make psychic connections between each other and to other cells, sometimes bridging a long distance. The neurons form a network, which character is primarily psychically qualified, secondarily spatially founded. One or more neurons contain a program that integrates simultaneously received stimuli and processes them into a co-ordinated instruction.
Jellyfish, sea anemones, corals, and hydrozoans belong to the phylum of cnidarians (now about 10,000 species, but in the early Cambrium much more numerous). They have a net of neurons but not a central nervous system. The net functions mostly as a connecting system of more or less independent neurons. The neurons inform each other about food and danger, but they do not constitute a common behaviour program. The body plan of cnidarians is more specialized than that of sponges. Whereas the sponges are asymmetrical, the cnidarians have an axial symmetry. They cannot move themselves. Sea anemones and corals are sedentary, whereas jellyfish are moved by sea currents. The nerve net of cnidarians can only detect food and danger. It leads to activating or contracting of tentacles, and to contracting or relaxing of the body. However, even if a jellyfish is a primitive animal, it appears to be more complex than many plants.
c. A differentiated nervous system has bilateral symmetry
In the nervous system, signals follow different pathways. Each signal has one or more addresses, corresponding to differentiated functions.
The behaviour of animals displays several levels of complexity. Sensorial, central, and motor mechanisms are distinguished as basic units of behaviour. Often these units correspond with structures in the nervous system and sometimes they are even recognizable in a single neuron. Only in a net, neurons can differentiate and integrate. Now the three mentioned functions are localized respectively in the sense organs, the central nervous system, and in specialized muscles.
The simplest differentiated net consists of two neurons, one specialized as a sensor, the other as a motor neuron. The synapses of a motor neuron stimulate a muscle to contract. In between, several inter-neurons may be operative, in charge of the transport, distribution, or amplification of stimuli. In the knee reflex, two circuits are operational, because two muscles counteract, the one stretching, the other bending the knee. The two circuits have a sensor neuron in common, sensitive to a pat on the knee. In the first circuit, the sensor neuron sends a stimulus to the motor neuron instructing the first muscle to contract. In the second circuit, a stimulus first travels to the inter-neuron, blocking the motor neuron of the other muscle such that it relaxes.
A differentiated nervous system displays a typical left-right symmetry, with many consequences for the body plan of any animal having a head and a tail. In contrast with the asymmetric sponges and axially symmetric cnidarians, bilateral animals can move independently, usually with the head in front. The bilateral nervous system allowing of information transport is needed to control the motion. The more differentiated the nervous system is, the faster and more variable an animal is able to move. In the head, the mouth and the most important junction (ganglion) of the nerve net are located, in the tail the anus. From the head to the tail stretches a longitudinal chain of neurons, branching out in a net. Sometimes there is a connected pair of such chains, like a ladder. Apparently, these animals are primarily psychically and secondarily kinetically characterized. At this level, real sense organs and a central brain are not present yet, but there are specialized sensors, sensitive for light, touch, temperature, etc.
The simplest bilateral animals are flatworms, having hardly more than a net of neurons without ganglions. A flatworm has two light sensitive sensors in its head enabling it to orient itself with respect to a source of light. Round worms and snails have ganglions co-ordinating information derived from different cells into a common behaviour program. Their reaction speed is larger and their behaviour repertoire is more elaborate than those of flatworms, but considerably less than those of arthropods, e.g.
Progressing differentiation of the nervous system leads to an increasing diversity of animal species in the parallel-evolved phyla of invertebrates, arthropods, and vertebrates. Besides the nervous system, the behaviour, the body plan, and the body functions display an increasing complexity, integration, and differentiation. In various phyla, the evolution of the body plan and the body functions, that of the nervous system and the behaviour, have influenced each other strongly.
Remarkable is an increasing internalization, starting with a stomach. Sponges and cnidarians have only one cavity, with an opening that is mouth and anus simultaneously. The cavity wall is at most two cells thick, such that each cell has direct contact with the environment. Animals with a differentiated nervous system have an internal environment, in cavities which walls are several cells thick. Between neighbouring cells, there are intercellular cavities. In differentiated animals, biologists distinguish four kinds of tissues (with their functions): epithelium (the external surface of the body and its organs, taking care of lining, transport, secretion, and absorption); connective tissue (support, strength, and elasticity); muscle tissue (movement and transport); and nervous tissue (information, synthesis, communication, and control). Vertebrates have an internal skeleton and internal organs like blood vessels, kidneys, liver, and lungs. These may be distinguished according to their ethological functions: information and control (nervous system and endocrine system); protection, support, and motion (skin, skeleton, and muscles); reproduction (reproductive organs); food (digestion and respiration organs); transport and defence (blood, the hart, the blood-vessels, the lymph nodes, the immune system); secretion, water and salts balance (kidneys, bladder, and guts). As far as a plant has differentiated organs (leaves, flowers, roots, the bark), these are typically peripheral, with an outward direction to the acquisition of food and reproduction. Animal organs are internalized. This is compensated for by the formation of specific behaviour organs directed outward. These are the movement organs like feet or fins; catching organs like a beak or the hands; fighting organs like horns or nails; and in particular the sense organs.
d. Manipulation of the environment requires a central nervous system and sense organs
The most interesting capacities of the nervous system emerge from the mutual interaction of neurons. The storage and processing of information requires a central nervous system. Reflexes are usually controlled outside this centre. The peripheral nervous system takes care of the transport of information to the centre and of instructions from the centre to muscles and glands. It is therefore secondarily kinetically characterized. The physically founded storage and processing of information requires specialization of groups of cells in the centre, each with its own programs.
In particular the sensors are grouped into specialized sense organs allowing of the formation of images. The best known example is the eye that in many kinds of animals uses light sensitivity to produce an image of the surroundings. In 1604, Johann Kepler demonstrated how in the human eye image formation as a physical process proceeds, thanks to the presence of a lens. In all vertebrates and octopuses, it works in the same way. The visual image formation does not end at the retina. An important part of the brain is involved in the psychic part of imaging. Besides visual, an image may be tactile or auditive, but now there is no preceding physical image formation comparable to the visual one in the eye.
On this level, chains of successive acts occur, in which different organs and organ systems co-operate, such as in food gathering, reproduction, movement or fighting. Animals have manipulative organs, like teeth and claws. Animals with a central nervous system are primarily psychically and secondarily physically characterized.
e. Animals are capable of learning
In the highest animals’ neocortex, the brain is superposed on the autonomous nervous system. In the latter, the same processes occur as in the entire nervous system of lower animals. With respect to the construction of their nervous system and their behaviour, octopuses, birds, and mammals are comparable. Within the nervous system, a division appears between the routine control of the body and less routine tasks. The neocortex can be distinguished from the ‘old brain’, including the limbic system, that controls processes also occurring in lower animals. In primates, there is a further division of labour between the global, spatio-temporal right half and the more concentrated, analytical and serial left half, which in human beings harbours the speech centre. In the neocortex, the learning capacity of animals is concentrated. The difference between old and new brains, or between left and right half, is not rigorous. It points to the phenomenon that new programs always make use of existing ones.
Learned behaviour called habituation, i.e. an adaptive change in the program caused by experience, occurs both in higher and in lower animals. During habituation a new program emerges that the animal applies in a stimulus-reflex relation. The reverse is dehabituation. A stronger form is sensitivation, learning to be alert for new stimuli.
Instrumental learning, based on trial and error, is biotically founded. It requires imagination besides a sense for cause-effect relations. Only the highest animals are able to learn by experiment (experimental trial and error), in which the animal’s attention is directed to the effect of its activities, to the problem to be solved. Sometimes an AH-Erlebnis occurs. Whether this should be considered insightful learning is controversial.
Sometimes animals learn tricks from each other. Singing birds learn the details of their songs from their parents, sometimes prenatal. Some groups display initiation behaviour. In the laboratory, imitation learning is the imitation of a new or improbable activity or expression for which no instinctive disposition exists. It is a consequence of observing that another animal of the same or a different species performs an act for which it is rewarded.
Mammals, birds, and octopuses have programs that require to make choices. They apply these programs in the exploration of their environment and in playing. Initially, the animal makes an arbitrary choice, but it remembers its choices and their effects. By changing its programs, the animal influences its later choices. The new circumstances need not be the same as in the earlier case, but there must be some recognizable similarity.
Interlacement of characters
Starting from the lowest level, each psychic character has dispositions to interlace with characters at a higher level. Neurons have the disposition to become interlaced into a net that allows of differentiation. The differentiated net may form a central nervous system, at the highest level divided into an autonomous system and a brain. These levels constitute a hierarchy, comparable to the quantum ladder (11.3).
On the one hand, the phenomenon of character interlacement means that the characters having different secondary foundations remain recognizable, on the other hand, it implies an amount of adaptation. A neuron in a net is not the same as a unicellular animal, but it displays sufficient similarities to assume that they belong primarily and secondarily to the same character type. Only the tertiary characteristic is different, because a unicellular protozoan cannot become part of a net of neurons, and because it has sensors and flagellates instead of dendrites and an axon.
The relation between ‘old’ and ‘new’ brains can be understood as a character interlacement as well. In particular, instinctive processes and states like emotions that mammals and birds share with fish, amphibians, and reptiles are located in the limbic system, the ‘reptilian brain’. Hence, the difference between the limbic system in the higher animals and the central nervous system in the lower animals is tertiary, whereas the difference of both with the neocortex is secondary. This character interlacement is not only apparent in the structure of the nervous system. Both the programming and the psychic functioning of the nervous system display an analogous characteristic hierarchy.
13.3. Control processes
Animals are sensitive for their own body, for each other and for their physical and biotic environment. By observing, an animal as a subject establishes relations with its environment, being the object of its observation. Organically, sensors or sense organs bring about observation. The gathering of information is followed by co-ordination, transfer, and processing into instructions for behaviour, via the nervous and endocrine systems. Together, this constitutes a chain of information processing.
I shall distinguish between control processes (13.3), controlled processes (13.4), and psychically qualified behaviour (13.5), each having their specific characters. For information processing, projections on the quantitative up to the biotic relation frames can be indicated, as follows.
a. On/off switching of a program
The simplest form of control is to switch on or off a programmed pattern of behaviour, like an electric appliance is put into operation by an on/off switch. Psychology calls this the release after the reception of an appropriate signal. Each signal and each stimulus must surpass a threshold value in order to have effect. Mathematically, a step function represents the transition from one state to the other. Its derivative is the delta function describing a pulse, the physical expression of a stimulus or signal, kinetically represented by a wave packet (chapter 7). In a neuron, a stimulus has the character of a biotically organized chemical process, called an action potential, in which specific molecules (neurotransmitters) play a part. Hence, the objective psychical character of a signal or a stimulus is interlaced with various other characters.
The simplest form of behaviour consists of a direct relation between a stimulus and a response (e.g., a reflex). It depends on a specific stimulus that switches the program on or off. (The program itself may be quite complex). Often, only the output is called behaviour, but there is an unbreakable connection between input, program, and output. Hence it appears better to consider the whole as a kind of behaviour.
Sometimes a program as a whole is out of operation, such that it is insensitive for a stimulus or signal that should activate it. Hormonal action has the effect that animals are sexually active only during certain periods. Hormones determine the difference between the behaviour of male and female specimens of the same species. Sometimes, female animals display male behaviour (and conversely), if treated with inappropriate hormones. Being switched on or off by hormones, sexual behaviour programs appear to be available to both genders.
b. Stimuli are spatially integrated into a pattern
A spatially founded system of connected neurons receives simultaneous stimuli from various directions and co-ordinates instructions at different positions. The integration of stimuli and reflexes does not require a real memory. ‘Immediate memory’ is almost photographic and it lasts only a few seconds. It allows of the recognition of patterns and the surroundings. The reaction speed is low. Recognition of a spatial pattern requires contrast, the segregation of the observed figure from its background.
Often, a program requires more information than provided by a single signal. The observation of a partner stimulates mating behaviour, whereas the presence of a rival inhibits it. Moreover, internal motivation is required. Aggressive behaviour against a rival only occurs if both animals are in a reproductive phase. Besides stimulating, a stimulus may act relaxing, blocking, numbing, or paralysing.
Via the dendrites, several incoming pulses activate simultaneously the psychic program localized in a single cell body or a group of co-operating neurons. Some pulses act stimulating, others inhibiting. In this case, only the integration of stimuli into a pattern produces an instruction that may be a co-ordinated pattern of mutually related activities as well. Each neuron in a net co-ordinates the information received in the form of stimuli through its dendrites. It distributes the processed information via the axon and synapses to various addresses. Various mechanisms can be combined into more complex behaviour systems, like hunting, eating, sexual or aggressive behaviour. A behaviour system describes the organization of sensorial, central, and motor mechanisms being displayed as a whole in certain situations. In electronics, such a system is called an integrated circuit, in computers it is an independent program.
c. Transport of information
Each neuron transports information via its axon to other cells. In a differentiated nervous system, transport and amplification of information occurs in steps, mediating between the reception of signals and the exertion of instructions. As discussed so far, information exists as a single pulse or a co-ordinated set of pulses. However, the information may consist of a succession of pulses as well. The short-term memory (having duration of 10-15 minutes) allows the animal to observe signals arriving successively instead of simultaneously. The stored information is deleted as soon as the activity concerned is completed.
If an observed object moves, it changes its position with respect to its background, enhancing its contrast. Hence, with respect to its background, a moving object is easier to be observed than a stationary object. Likewise, an animal enhances the visibility of an object by moving its eyes.
Amplification of stimuli makes negative feedback possible. This control process requires a sensor detecting a deviation from a prescribed value (the set point) for a magnitude like temperature. Transformed into a signal, the deviation is amplified and starts a process that counters the detected deviation. For a feedback process, no memory is required.
d. Interpretation requires sense organs and a long-term memory
Psychologists distinguish sensation from perception. Sensations are the basic elements of experience, representing information. Perception is the interpretation process of sensorial information, a new phase between the reception of signals and the exertion of instructions. It allows the animal to observe changes in its environment, other than motions for which a short-term memory is sufficient.
A physically differentiated nervous system may include chemical, mechanical, thermal, optic, acoustic, electric, and magnetic sensors, besides sensors sensitive for gravity or moisture. The sense organs distinguish signals of a specific nature and integrate these into an image, that may be visual, tactile, or auditive, or a combination of these.
An animal having sense organs is capable of forming an image of its environment and storing it in its memory. It is able to make a perceptive connection between cause and effect. This does not mean a conceptual insight into the abstract phenomenon of cause and effect - that is reserved to human beings. It concerns concrete causal relations, with respect to the satisfaction of the animal’s needs of food, safety, or sex. For instance, an animal learns fast to avoid sick making food. An animal is able to foresee the effects of its behaviour, for the best predictor of an event is its cause.
Imaging allows an animal to get an impression of its changing environment in relation to the state of its body. The animal stores the image during some time in its memory, in order to compare it with an image formed at an earlier or later time. This is no one-way traffic. Observation occurs according to a program that is partly genetically determined, partly shaped from earlier experiences, and partly adapts itself to the situation of the moment. Observation is selective: an animal only sees what it needs in order to function adequately.
In observation, recollection, and recognition, comparison with past situations as well as knowledge and expectations play a part. If an animal recognizes or remembers an object, this gives rise to a latent or active readiness to react adequately. Not every circuit reacts to a single stimulus switching it on or off. Stimuli derived from a higher program may control a circuit in more detail. This is only possible in a nervous system having differentiation and perception besides co-ordination, and allowing of transport and storage of information. The long-term memory is located in the central nervous system, requiring specialized areas coupled to the corresponding sense organs.
Recognition based on image formation does not occur according to the (logical) distinction of similarities and differences, but holistic, as a totality, in the form of a Gestalt. Recollection, recognition, and expectation, respectively concerning the past, the present, and the future, give rise to emotions like joy, sorrow, anger, or fear. Images psychically interact with each other or with inborn programs. Emotions act like forces in psychic processes, in which both the nervous and the endocrine system play their parts. Sometimes the cause of behaviour is an internal urge or driving force (the original meaning of ‘instinct’). This waits to become operative as a whole until the animal arrives at the appropriate physiological state and the suitable environment to utter its instinct.
Imaging allows an animal to control its behaviour by its expectations, by anticipations, by ‘feedforward’. The intended goal controls the process. Animals drink not only to lessen their thirst, but also to prevent thirst. Taking into account observations and expectations, animals adapt the set point in a feedback system.
e. Imagination is the highest integration level for observation
Fantasy or imagination is more than processing of information. It is innovative generation of information about situations which are not realized yet. It allows higher animals to anticipate on expected situations, to make choices, to solve problems, and to learn from these. It requires a rather strongly developed brain able to generate information, in order to allow of choosing between various possibilities. At this level, emotions like satisfaction and disappointment occur, because of agreement or disagreement between expectation and reality. In particular young mammals express curiosity and display playful behaviour.
Animals control their learning activity by directing their attention. Attention for aspects of the outer world depends on the environment and on the animal’s internal state. A well-known form of learning in a new born animal is imprinting, for instance the identification of its parents. Sometimes, comparing of experience leads to the adaptation of behaviour programs, to learning based on recognized experiences. Associative learning means the changing of behaviour programs by connecting various experiences. In the conditioned reflex, an animal makes connections between various signals. Repetition of similar or comparable signals gives a learning effect known as reinforcement (amplification by repetition).
13.4. Controlled processes
All controlled processes are organized processes as well, and subject to physical and chemical laws. In an organized process (12.2), enzymes are operative, by lowering or heightening energy barriers. Hormones play a comparable stimulating or inhibiting part. Technologists speak of control if a process having its own source of energy influences another process, having a different energy source.
a. A stimulus is controlled information
Like an electron, a stimulus corresponds to a kinetic wave packet, whereas the transport and processing of a pulse have a physical nature. Transport of information occurs by means of an electric current or a chemical process in a nerve. The distribution of hormones from the producing gland to some organ, too, constitutes information transport. In invertebrates, the stimulus has often the form of an electric pulse, in vertebrates it is a chemical pulse (an action potential). Whereas the neurons produce most stimuli, external signals induce stimuli as well. The induction and transport of stimuli happens in a characteristic way only occurring in animals. However, the accompanying characters of a physical pulse and a kinetic wave packet are fairly well recognizable.
b. Co-ordination of stimuli and instructions requires a spatial organization
The body plan of an animal is designed for its behaviour. Complex behaviour requires co-ordinated control by an integrated circuit in the nervous system, usually combined with the endocrine system. A special form of co-ordinated behaviour follows an alarm. This brings the whole body in a state of alertness, sometimes after the production of a shot of adrenalin. The animal’s body posture expresses its emotive state.
c. Controlled motions form an obvious characteristic of animals
Controlled motions recognizable as walking, swimming, or flying, are evidently different from physical or biotic movements, even without specifying their goal. Psychically qualified behaviour is recognizable because of its goal, like hunting or grazing. One of the most important forms of animal behaviour is motion. For a long time, the possibility to move itself was considered the decisive characteristic of animals. Crawling, walking, springing, swimming, and flying are characteristic movements that would be impossible without control by feedback. The animal body is predisposed to controlled motion, such that from fossils it can be established how now extinct animals were moving. Not all movements are intended to displacement, they may have other functions. Catching has a function in the achievement of food, chewing in processing it. Animal motions are possible because animal cells are not rigidly but flexibly connected, having intercellular cavities (unlike plant cells). Muscular tissues are characteristically developed to make moving possible.
Many of the mentioned movements are periodic, consisting of a rhythmic repetition of separate movements. Many animals have an internal psychic clock regulating movements like the heartbeats or the respiration. The circadian clock (circa die = about a day) tunes organic processes to the cycle of day and night. Other clocks are tuned to the seasons (e.g., fertility), and some coastal animals have a rhythm corresponding to the tides.
The more complicated an animal is, the more important the control of its internal environment. Homeostasis is a characteristic process controlled by feedback. Many animals keep their temperature constant within narrow limits. The same applies to other physical and chemical parameters.
Animals with a central nervous system and specialized sense organs control their external behaviour by means of feedback. They are able to react fast and adequately to changes in their environment.
d. Animals control their physical and chemical processes
In particular in higher animals, the nervous system controls almost all processes in some way. Respiration, blood circulation, metabolism and the operation of the glands would not operate without control. The animal controls its internal environment by its nervous system, that also controls the transport of gases in respiration and of more or less dissolved materials in the guts and the blood vessels. Whereas in plants metabolism is an organized process, in animals it is controlled as well.
Internal processes are usually automatically controlled, but in specific actions, an animal can accelerate or decelerate them or influence them in other ways. Animals with sense organs also control external processes like the acquisition of food.
The development of a differentiated animal from embryo to the adult form is a controlled biotic process. The growth of an animal starting from its conception is influenced by the simultaneously developing nervous system. In mammals before the birth, there is an interaction with the mother, via the placenta. Emotions induced by the observation of a partner or a rival control mating behaviour.
e. Genetically determined behaviour is developed during the growth and is adaptable
Many forms of behaviour, such as mating, are genetically programmed. Through the genes, they are transferred from generation to generation. They are stereotype, progressing according to a fixed action pattern. The programming of other forms of behaviour occurs during the individual’s development after its conception. Earlier, I observed that the genome should not be considered a blueprint (12.2). Even in multicellular differentiated plants, the realization of the natural design during the growth is not exclusively determined by the genome, but by the environment of the dividing cell as well. The tissue to which the cell belongs determines in part the phenotype of the new cells. Besides, in animal development during the growth the nervous and endocrine systems play a controlling part. While the nervous system grows, it controls the simultaneous development of the sense organs and of other typically animal organs like the heart or the liver.
Besides the animal body including the nervous system, the programs in the nervous system are genetically determined, at least in part. Partly they are developed during growth. Moreover, animals are capable of changing their programs, to learn from information acquired from their environment. Finally, the exertion of a program depends on information received by the program from elsewhere.
Behaviour programs consist of these four components. Hence, there is no dualism of genetically determined and learned behaviour. Behaviour emerges as a relation of the animal with its environment, as adaptation in a short or a long time. First, by natural selection a population adapts the genetic component to a suitable niche. Next, an individual animal actualizes this adaptation during its development from embryo to adult. Third, its learning capacity enables the individual to adapt its behaviour to its environment much faster than would be possible by natural selection or growth. Fourth, the input of data in the program allows the animal to adapt its behaviour to the situation of the moment.
13.5. Goal-directed behaviour
Behaviour consists of psychically qualified events and processes. It emerges as a chain from stimulus or observation via information processing to response. It is always goal-directed, but it is not goal-conscious, intentional, or deliberate, these concepts being applicable to human behaviour only. Since the 18th century, physics has expelled goal-directedness, but the psychic order is no more reducible to the physical order than the biotic one. Behaviour is goal-directed and its goal is the object of subjective behaviour.
Often an animal’s behaviour is directed to that of an other animal. In that case, besides a subject-object relation, a subject-subject relation is involved. Animal behaviour is observable, both to people and to animals. By hiding, an animal tries to withdraw from being observed. Threatening and courting have the function to be observed. This occurs selectively, animal behaviour is always directed to a specific goal. Courting only impresses members of the same species.
According to the theory of characters various types of behaviour are to be expected, based on projections of the psychic relation frame onto the preceding ones. It has been established that many animals are able to recognize general relations in a restricted sense. These relations concern small numbers (up to 5), spatial dimensions and patterns in the animals’ environment, motions and changes in their niche, causality with respect to their own behaviour and biotic relations within their own population.
For human beings, activity is not merely goal-directed, but goal-conscious as well. In the following overview, I shall compare animal with human behaviour.
a. The unit of behaviour is the reflex
A neuron transforms stimuli coming from a sensor into an instruction for an effector, e.g. a muscle or a gland. Muscles enable the animal’s internal and external movements. The glands secrete materials protecting the body’s health or alerting the animal or serving its communication with other animals. The direct stimulus-response relation occurs already in protozoans and sponges. The reflex, being the direct reaction of a single cell, organ, or organ system to a stimulus, is the simplest form of behaviour. It may be considered the unit of behaviour. Reflexes are always direct, goal-directed, and adapted to the immediate needs of the animal. Whereas complex behaviour is a psychically qualified process, a reflex may be considered a psychically qualified event.
Often, a higher animal releases its genetically determined behaviour (fixed action pattern) after a single specific stimulus, a sign stimulus or releaser. If there is a direct relation between stimulus and response, the goal of a fixed action pattern is the response itself, for instance the evasion of immediate danger.
People, too, display many kinds of reflexes. More than animals, they are able to learn certain action patterns, exerting them more or less ‘automatically’. For instance, while cycling or driving a car, people react in a reflexive way to changes in their environment.
Human beings and animals are sensitive for internal and external states like hunger, thirst, cold, or tiredness. Such psychically experienced states are quantitatively determined. An animal can be more or less hungry, thirsty, or tired, feeling more or less stimulated or motivated to acting. The satisfaction of needs is accomplished by complex behaviour. Taken together, animals apply a broad scale of food sources. Animals of a certain species restrict themselves to a specific source of food, characterizing their behaviour. In contrast, human beings produce, prepare, and vary their food. People do not have a genetically determined ecological niche. Far more than animals, they can adapt themselves to circumstances, and change circumstances according to their needs.
Contrary to the animals themselves, scientists analyse the quantitative aspect of behaviour by a balance of costs and benefits. A positive cost-benefit relation is appropriate behaviour and favours natural selection. Behaviour always costs energy and sometimes gains energy. Behaviour involves taking risks. Some kinds of behaviour exclude others. The alternation of characteristic behaviour like hunting, eating, drinking, resting, and secreting depends on a trade-off of the effects of various forms of behaviour. People, too, deliberate in this way, conscious or subconscious.
Animals of the same species may form a homogeneous aggregate like a breeding colony, an ants’ or bees’ nest, a herd of mammals, a shoal of fish, or a swarm of birds. Such an aggregate is a psychically qualified and biotically founded community, if the animals stay together by communicating with each other, or if the group reacts collectively to signals. (A population of animals as a gene pool is biotically qualified, but mating behaviour is a characteristic psychical subject-subject relation.) Human beings form numerous communities qualified by relation frames other than the psychic one.
b. In a biotope, animals react to each other
An ecosystem is a biotically qualified heterogeneous aggregate of organisms (12.5). The environment of a population of animals, its Umwelt, is psychically determined by the presence of other animals, biotically by the presence of plants, fungi, and bacteria, and by physical and chemical conditions as well. Each animal treats its environment in a characteristic way. In a biotope, animals of different species recognize, attract or avoid each other. The predator-prey relation and parasitism are characteristic examples. The posture of an animal is a spatial expression of its state controlled by its emotions, but it has a goal as well, e.g. to court, to threaten, to warn, or to hide. Characteristic spatially founded types of behaviour are orientation, acclimatization, and defending a territory.
The Umwelt and the horizon of experience of a population of animals are restricted by their direct needs of food, safety, and reproduction. Animals do not transcend their Umwelt. Only human beings are aware of the cosmos, the coherence of reality transcending the biotic and psychic world of animals.
c. The kinetic behaviour of animals is characteristically goal directed
The movements of animals are often very characteristic: resting, sleeping, breathing, displacing, cleaning, flying, reconnoitring, pursuing, or hunting. On a large scale, the migration of birds, fish, and turtles are typical motions. Usually the goal is easily recognizable. An animal does not move aimlessly. Many animal movements are only explainable by assuming that the animals observe each other. In particular animals recognize each other’s characteristic movements. Human motions are far less stereotype than those of animals, and do not always concern biotic and psychic needs.
Communication is behaviour of an individual (the sender) influencing the behaviour of another individual (the receiver). It consists of a recognizable signal, whether electric or chemical (by pheromones), visual, auditive, or tactile. It is a detail of something that a receiver may observe and it functions as a trigger for the behaviour of the receiver. Communication is most important if it concerns mating and reproduction, but it occurs also in situations of danger. Ants, bees, and other animals are capable of informing each other about the presence of food. Higher animals communicate their feelings by their body posture and body motions (‘body language’).
A signal has an objective function in the communication between animals if the sender’s aim is to influence the behaviour of the receiver. A signal is a striking detail (a specific sound or a red spot, the smell of urine or a posture), meant to draw the attention. It should surpass the noise generated by the environment. Many signals are exclusively directed to members of the same species, in mating behaviour or care for the offspring, in territory defence and scaring of rivals. Animal communication is species specific and stereotype. It is restricted to at most several tens of signals. In particular between predators and prey, one finds deceptive communication. As a warning for danger, sound is better suited than visual signals. Smelling plays an important part in territory behaviour. Impressive visual sex characteristics like the antlers of an elk or the tails of a peacock have mostly a signal value.
A signal in animal communication is a concrete striking detail. Only human communication makes use of symbols, having meaning each apart or in combination. Whereas animal signals always directly refer to reality, human symbols also (even mainly) refer to each other. A grammar consists of rules for the inter-human use of language, determining largely the character of a language (16.3, 17.5).
d. Animals manipulate their environment
Often, animal behaviour can be projected on cause-effect relations. Higher animals are sensitive for these relations, whereas human beings have insight in them. Sensory observation, image formation, manipulations, emotions, and conflicts are related forms of behaviour.
The senses allow an animal of forming an image of its environment in order to compare it with images stored in its memory. This enables an animal having the appropriate organs to manipulate its environment, e.g. by burrowing a hole. Characteristic is the building of nests by birds, ants, and bees, and the building of dams by beavers. These activities are genetically determined, hardly adaptable to the environment
The formative activity of animals often results in the production of individual objects like a bird’s nest. Plants are producers as well, e.g. of wood displaying its typical cell structure even after the death of the plant. The atmosphere consisting of nearly 20% oxygen is a product of ages of organic activity. In addition, animals produce manure. From the viewpoint of the producing plant or animal, these are by-products, achieving a relatively independent existence after secretion by some plant or animal. In this respect, wood and manure differ obviously from an individual object like a bird’s nest. A nest has primarily a physical character and is secondarily spatially founded, but its tertiary biotic and psychic dispositions are more relevant. It is produced with a purpose. Its structure is recognizable as belonging to a certain species. The nest of a blackbird differs characteristically from the nest of a robin. However, the nest itself does not live or behave. It is not a subject in biotic and psychic relations, but an object. It is a subject in physical relations, but these do not determine its character. It is an individual object, characteristic for the animals that produce it, fish, birds, mammals, insects, and spiders. The construction follows from a pattern that is inborn to the animal. Usually, the animal’s behaviour during the construction of its nest is very stereotype. Only higher animals are sometimes capable of adapting it to the circumstances. The tertiary psychic characteristic of a nest, its purpose, dominates its primary physical character and its secondary spatial shape.
Manipulating the environment concerns a subject-object relation. The mutual competition, in particular the trial of strength between rivals, may be considered a physically founded subject-subject relation. Both are species-specific and stereotype. Stereotype animal behaviour contrasts with the freedom of human activity, for which human beings are consequently responsible.
e. The purpose of biotically founded behaviour is reproduction
Much animal behaviour has a biotic function, like reproduction and survival of the species. Animals are sensitive for genetic relations. Whether protozoans experience each other is difficult to establish, but their mating behaviour makes it likely. The courting and mating behaviour of higher animals is sometimes strongly ritualized and stereotype. It is both observable and meant to be observed. It has an important function in the natural selection based on sexual preferences. The body plan, in particular the sexual dimorphy, is tuned to this behaviour.
Mating behaviour and care for the offspring are psychically qualified and biotically founded types of behaviour. Animals are sensitive to the members of their species, distinguishing between the sexes, rivals, and offspring. For biotically founded behaviour, the mutual communication between animals is important. Sexually mature animals excrete recognizable scents. In herds, families, or colonies, a rank order with corresponding behaviour is observable. An animal’s rank determines its chance of reproduction.
Human mating behaviour is cultivated, increasing its importance. People distinguish themselves from animals by their sense of shame, one reason to cover themselves with clothing. The primary and secondary sex characteristics are both hidden and shown, in a playful ritual that is culturally determined, having many variations (13.1). Human sexuality is not exclusively directed to biotic and psychic needs and inborn sexual differences. It is expressed in many kinds of human behaviour.
An animal changes its identity by learning
The ability to learn is genetically determined and differs characteristically from species to species. Every animal is the smartest for the ecological niche in which it lives. Its ability to learn changes during its development. In birds and mammals, learning takes place already during the prenatal phase. In the juvenile phase, animals display curiosity, a tendency to reconnoitre the environment and their own capacities, e.g. by playing (acting as if). Usually, a young animal has more learning capability than an adult specimen.
The capacity of learning is hereditary and species specific, but what an animal learns is not heritable. The content of the animal’s learning belongs to its individual experience. Sometimes, an animal is able to transfer its experiences to members of its population.
The genetic identity of a plant or animal is primarily determined by the individual configuration of its genes. The identity is objectively laid down in the configuration of the DNA molecule, equal in all cells of the organism. Only sexual reproduction changes the genetic configuration, but then a new individual comes into existence. In contrast, the identity of an animal is not exclusively laid down in its genetic identity. An animal changes because of its individual experience, because of what it learns. By changing its experience (by memorizing as well as forgetting), the animal itself changes, developing its identity. Even if two animals have the same genetic identity (think of clones or monozygotic twins), they will develop divergent psychic identities, having different experiences. In the nervous system, learning increases the number of connections between neurons and between programs.
The individual variation in the behaviour of animals of the same species or of a specified population can often be statistically expressed. The statistical spread is caused by the variation in their individual possibilities (inborn, learned, or determined by circumstances), as far as it is not caused by measurement inaccuracies. When the statistics displays a maximum (for instance, in the case of a Gauss or Poincaré distribution), the behaviour corresponding to the maximum is called ‘normal’. Behaviour that deviates strongly from the maximum value is called ‘abnormal’. This use of the word normal is not related to norms. However, these statistics can be helpful in finding law conformities, in particular if comparison between various species reveals corresponding statistics.
Animals have a limited sense for regularity
Their learning capacity implies that animals are able to recognize signals or patterns, and to react by adapting their behaviour programs. This means that animals in concrete situations have a sense of regularity. This sense is not comparable to the knowledge of and insight into the universal law conformity that humanity has achieved laboriously. Still, it should not be underestimated. The sense of regularity shared by human beings and animals is a condition for the insight into lawfulness that is exclusively human.
The learning capacity of an animal is restricted to behaviour serving the animal’s biotic and psychic needs. It is an example of the capacity of animals (and plants) to adapt themselves to differing circumstances. In this respect, animals differ from human beings, whose behaviour is not exclusively directed to the satisfaction of biotic and psychic needs.
Besides animal psychology studying general properties of behaviour, ethology is concerned with the characteristic behaviour of various animal species. This does not imply a sharp boundary between animal psychology and ethology. In this chapter, I discussed the general relations constituting the psychic relation frame together with the characters that it qualifies.
Human psychology and psychiatry too are concerned with behaviour, but human behaviour is usually not psychically qualified. Hence, it is not always possible to compare animal with human behaviour. In animals, goal-directed behaviour and transfer of information always concerns psychic and biotic needs like food, reproduction, safety, and survival of the species. In human persons, behaviour may serve other purposes, for instance practicing science.
13.6. Dynamic development in the living world
Until the beginning of the 19th century, evolution did not play an important part in science. Before the rise of historical-critical biblical studies, the teachings of the Bible were accepted without questioning. Charles Darwin’s On the origin of species by means of natural selection (1859) made the question of the origin of characters a controversial part of scientific worldviews. If living beings emerge blindly by natural selection, what then is their meaning?
During the 17th, 18th and early 19th century, a natural law was generally considered to be an expression of God’s will. Supposing that God is knowable from two sources - the Holy Scriptures as word revelation and nature as creation revelation - natural theology welcomed each scientific discovery as a proof of the existence of a beneficial creator. The progress of science confirmed the rationality of the belief in God. In particular the argument of intelligent design was popular. The explanation of the purposefulness of nature required the existence of a goal-directed plan and a purposive designer. This looks like the God of Aristotle as the prime mover or first cause, a rationalist principle of explanation for an ordered creation. Because it does not fit in a determinist mechanical worldview, David Hume and Immanuel Kant distanced themselves from the argument of design, but their views, being strictly philosophical, did not exert much influence on the scientific community. Darwin abandoned the argument of design by explaining the origin of species from evolution based on natural selection, instead of being the product of a divine plan. After the publication of Darwin’s On the origin of species (1859), most biologists accepted evolution as a fact, but Darwin’s theory of natural selection remained controversial during a long time. About 1940, from the synthesis with genetics and molecular biology, a theory of evolution emerged that was accepted by most biologists followed by other scientists. They consider natural selection to be the dynamic force of evolution, which is certainly true, but not sufficient. Genetic relations may be a more important engine of biotic development, and sexual reproduction that of the animal world.
The assumption that natural laws do not change does not exclude the idea of evolution at the subject side. Being clusters of universal laws, characters are not subject to evolution, but their subjects do. This does not appear to pose a problem to the astrophysical theory of evolution. The characters of physical and chemical things and events like molecules and molecular processes are supposed to hold for all times and places, taking into account the fact that physical characters can only be realized in suitable circumstances. With respect to the biological theory of evolution, it is relevant whether species are considered characters and evolution is restricted to populations. In that case, evolution concerns the subjective realization of characters in suitable circumstances, and its theory does not say anything at all about the origin of characters. Evolution as a random process with natural selection as its dynamic force is constrained by the laws determining characters, which are gradually realized into populations.
With respect to physical and chemical characters like those of atoms and molecules, everybody seems to accept that the characters at the law side do not change, but are at the subject side realized when circumstances like temperature and other initial and boundary conditions are favourable (11.7). Biologists assume that the evolution of populations occurs within species, and occasionally between species, such that new species arise (12.5-12.6). This micro-evolution fits very well into the assumption that a species corresponds to a character (12.7). However, the macro-evolution like that of eukaryotes from prokaryotes; of multi-cellular eukaryotes; or of plants, animals and fungi; remains an unsolved problem.
Whereas for physical and chemical characters specific laws are sufficiently known, this is not (yet) the case for species. On a higher taxonomic level, about 35 living animal phyla are known each with its own body plan. A body plan may be considered a morphological expression of the law for the phylum. It is a covering law for the characters of all species belonging to the phylum. It is remarkable that these phyla manifested themselves almost simultaneously (i.e., within several millions of years) during the Cambrium radiation, starting about 550 million years ago. Afterwards, not a single new phylum has arisen, and the body plans have not changed. The evolution of the animal world within the phyla (in particular the vertebrates) is much better documented in fossil records than that of other kingdoms. It shows that it is an open process, which natural history can be investigated, but which future cannot be predicted.
Randomness and lawfulness
Some evolutionists and many of their critics emphasize the occurrence of chance in Darwin’s theory of natural selection, often assuming that chance is at variance with law conformity. In fact, stochastic processes can only occur on the basis of existing characters. Biotic evolution starts from physical characters, and always builds on previous biotic characters. Psychic characters of behaviour have a physical and an organic basis. Chance plays an important part in the reproduction of plants and animals (and therefore in natural selection), but far less in their development after germination. The development of the human eyes after the conception is almost completely determined by natural laws. Also the evolution of eyesight in many parallel lines is not merely a chance process, as both evolutionists and their critics appear to believe. It was guided by pre-established laws. Therefore, the perennial discussion about whether or not this process would be likely is quite fruitless.
As we have seen for the astrophysical and biotic evolution (11.7, 12.7), the dynamic evolution within the animal world requires a random push and a specific pull. The specific pull is again the character of the reproduced animals. The random push is sexual reproduction, in which the animals concerned take an active part in choosing their mates, but which result is still largely a random process, although much less so than in plants and fungi, where hybridization occurs much more often.
Evolutionism versus creationism
The view that natural characters realize themselves successively by evolution belongs to the prevailing scientific worldview (12.7). It should not be identified with evolutionism, considered a reductionist, naturalist, materialist, and exclusive worldview, in which
‘... evolution functions as a myth, ... a shared way of understanding ourselves at the deep level of religion, a deep interpretation of ourselves to ourselves, a way of telling us why we are here, where we come from, and where we are going.’
Therefore it makes sense to distinguish evolutionism as a naturalist worldview applying the concept of evolution everywhere, from evolution as a natural phenomenon, as well as from the theory of evolution as a scientific construction.
Whereas Baruch Spinoza and Albert Einstein identified God with nature or with natural laws, naturalists replace God by nature, attempting to explain everything by natural causes, reducing all regularity to physical laws and natural evolution. Naturalism is a form of reductionism, but apart from that, there appears to be little consensus about its contents. In short, ontological or metaphysical naturalism is the worldview rejecting supernatural interventions in reality, and assuming human life to be completely subject to natural laws. Physicalism, materialism, and evolutionism may be considered variants of ontological naturalism. Epistemological naturalism is weaker. It states that supernatural intervention, if it exists, is unknowable. Even more modest, methodological naturalism states that supernatural intervention, if it exists and is knowable, should not be a principle of explanation in science. Methodological naturalism is probably shared by most scientists. At the other side of the spectrum, some extreme naturalists cross the boundary between a worldview and a religion, by assuming that science proves that there is no supernatural origin of reality and of its laws. Evolutionism assumes that the theory of evolution provides not merely a necessary, but also a sufficient explanation for the emergence of humankind.
Creationism presents itself as a Christian alternative for a supposed atheist or agnostic evolutionism. Foundational creationism uses biblical texts as reliable data for scientific theories, as an authoritative source for empirical knowledge. Creationism rejects the view that evolution is a necessary explanation for the rise of humanity, considering the biblical text as both necessary and sufficient. Whoever rejects that worldview is therefore not committed to atheism or evolutionism. Rejecting creationism, many Christians and other believers accept the theory of evolution as a necessary but not sufficient explanation. They assume that evolution needs an additional explanation to become sufficient. In principle, the philosophy of the cosmonomic idea provides this extension.
 According to a modern definition, animalia are multicellular: ‘An organism is an animal if it is a multicellular heterotroph with ingestive metabolism, passes through an embryonic stage called a blastula, and has an extracellular matrix containing collagen.’ (Purves et al. 1998, 553-554). Within the kingdom of the protista (the set consisting of all eukaryotes that do not belong to the animalia, plantae, or fungi), the unicellular protozoans like flagellates and amoebas do not form a well-defined group. The animalia probably form a monophyletic lineage, which would not be the case if the protozoans were included. Therefore, some biologists do not consider the protozoans to be animals, but others do.
 McFarland 1999, 62-63 divides organisms into producers, consumers, and decomposers. Plants produce chemical energy from solar energy. Animals consume plants or plant eaters. Fungi and bacteria decompose plant and animal remains to materials useful for plants.
 Wallace 1979, 23.
 A signal has an external source, causing a stimulus in a sensor, or an impression on a sense organ. A stimulus may have an internal or an external source. In communication technology, the unit of information is called a bit.
 Hogan 1994, 300-301: ‘The study of behavior is the study of the functioning of the nervous system and must be carried out at the behavioral level, by using behavioral concepts … the output of the nervous system, manifested as perceptions, thoughts, and actions.’
 McFarland 1999, 174: ‘Protozoa, being single-cell systems … seem to be organized along principles similar to those governing the physiology of neurons … the protozoan is like a receptor cell equipped with effector organelles.’
 A sponge (to the phylum Porifera belong about 10.000 species) has no nervous system, no mouth, muscles, or other organs. The cells are grouped around a channel system allowing of streaming water. Each cell is in direct contact with water. A sponge has at least 34 different cell types. The cells are organically but not psychically connected. The even more primitive Placozoa (of which only two species are known) too lack a nervous system (Purves et al. 1998, 632-633).
 Churchland 1986, 36, 76-77.
 There are two kinds of nerve cells, neurons that are connected to each other besides glial cells, supporting the activity of the neurons. In the human brain, glial cells are more numerous than neurons, but I shall only discuss neurons.
 Whether the pre-Cambrian Ediacaran fauna mostly consisted of cnidarians is disputed, see Raff 1996, 72.
 Hogan 1994, 300-301: ‘There may often be a close correspondence between systems defined in structural and functional terms, but this is by no means always the case, and it is very easy for confusion to arise.’
 Margulis, Schwartz 1982, 161. After the conception, every multicellular animal starts its development by forming a blastula, a hollow ball of cells. A sponge is not much more than such a ball.
 Purves et al. 1998, 810.
 Purves et al. 1998, 809-814.
 Other animals, e.g., insects, do not have an eye lens. In vertebrates, the image formation occurs at the backside of the retina, in squids at the front side.
 McFarland 1999, 343-346.
 In the subjective observation space (which is not necessarily Euclidean), an animal observes a number of objects in their mutual relationships, dependent on the animal’s needs. Motion of an object is observed against the background of the observation space. Between some changes (as far as of the animal’s interest), the animal makes a causal connection. Together with its own position and its memory, the observation space constitutes the subjective world of experience of an animal, to be distinguished from its objective environment.
 Although control on the level of genes is very important for animal development, I shall not discuss it.
 McFarland 1999, 204: ‘Sensations are the basic data of the senses … Perception is a process of interpretation of sensory information in the light of experience and of unconscious inference’.
 McFarland 1999, 340.
 The distinction between immediate, short and long term memory does not concern their duration, but their function (on which the duration depends), as described in the text.
 Probably, in animals it concerns always ‘object bound’ emotions, e.g., the fear of an other animal. In human beings one finds anxiety in the I-self relation as well.
 McFarland 1999, 278: ‘The term feedforward … is used for situations in which the feedback consequences of behaviour are anticipated and appropriate action is taken to forestall deviations in physiological state.’
 In a thermostat, the desired temperature is called the ‘set point’. In homeostasis, the set point is constant, in an active control process the set point is continuously adapted.
 About various forms of learning, see Eibl-Eibesfeldt 1970, 251-302; Hinde 1966, chapters 23, 24; Wallace 1979, 151-174; Goodenough et al. 1993, 145; McFarland 1999, part 2.3.
 Hinde 1970, chapter 14.
 Cp. Hebb 1953, 108: ‘We cannot dichotomize mammalian behaviour into learned and unlearned …’ Lehrman 1953 and others criticize Lorenz’s definition of instinctive behaviour to be genetically determined (in contrast to learned behaviour). Each kind of behaviour has inherited, learned and environmental components. See also Hinde 1966, 426: ‘… the innate/learnt type of dichotomy can lead to the ignoring of important environmental influences on development.’
 Since Aristotle, there is a dualism of causal and teleological explanations (‘proximate’ versus ‘ultimate’ causes). By ‘teleology’ is understood both the (biotic) function and (psychic) goal, see Nagel 1977. I restrict goal-directedness to behaviour. Goal-directed behaviour always has a function, but a biotic function is not always goal-directed. Function and purpose presuppose (physical) causality, but cannot be considered causes themselves. Nagel 1961, 402 associates teleological explanations with ‘… the doctrine that goals or ends of activity are dynamic agents in their own realizations … they are assumed to invoke purposes or end-in-views as causal factors in natural processes.’ See Ayala 1970, 38. In order to prevent this association, I shall avoid the term teleology (or teleonomy, see Mayr 1982, 47-51). The goal being the object of animal behaviour cannot be a ‘dynamic agent’. Only the animal itself as a psychic subject pursuing a goal is an agent of behaviour. This is in no way at variance with physical laws.
 Houston, McNamara 1999.
 McFarland 1999, 125-130.
 The study of animals living in groups is called ‘sociobiology’, see Wilson 1975. For quite some time, sociobiology has been controversial as far as its results were extrapolated to human behaviour, see Segerstråle 2000. Sociobiology was accused of ‘genetic determinism’, i.e. the view that human behaviour is mostly or entirely genetically determined. For a critique of sociobiology, see Midgley 1985.
 Goodenough et al. 1993, chapter 17. In communication, structuralists recognize the following six elements: the transmitter, the receiver, the message from transmitter to receiver, the shared code that makes the message understandable, the medium, and the context (the environment) to which the message refers.
 Goodenough et al. 1993, 596: ‘Animal communication signals are not true language because animals do not use signals as symbols that can take the place of their referent and because they do not string signals together to form novel sentences.’
 Darwin 1859, 136-138.
 Plantinga 2011, 5.3.
 Compare Dawkins’ confession, 1986, 5: ‘All appearances to the contrary, the only watchmaker in nature is the blind forces of physics, albeit deployed in a very special way. A true watchmaker has foresight: he designs his cogs and springs, and plans their interconnections, with a future purpose in his mind’s eye. Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind’s eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of watchmaker in nature, it is the blind watchmaker.’
 Toulmin, Goodfield 1965; Lindberg, Numbers 1986; Barrow, Tipler 1986, chapter 2; Bowler 1989.
 Newton 1704, 402-403.
 20th-century physics with its ‘theory of everything’ seduced some people to the search of God in a scientific way, see Hawking 1988; Barrow 1990.
 Recently, the argument of design received a new impulse in the form of the ‘anthropic principle’ (Barrow, Tipler 1986), and in the Platonic idea of intelligent design (Plato 1961, Timaeus,1161 ff). One could be tempted to identify each character with an intelligent design, if one were prepared to accept Platonic idealism. Apparently, adherents to the idea of intelligent design seem to attribute a separate design to any natural kind, without caring very much about the mutual relations between these, which can only be found by studying their law conformity. The idea of characters developed by the philosophy of the cosmonomic idea is much richer than the rather vague idea of intelligent design.
 Mayr 1982, 510-525.
 Mayr 1982, 119-120: ‘The difficulties and misunderstandings were finally resolved during the period between 1936-1947, resulting in a unified evolutionary theory often referred to as the “evolutionary synthesis”… Dobzhansky, Rensch, Mayr, Huxley, Simpson, and Stebbins, among others, showed that the major evolutionary phenomena such as speciation, evolutionary trends, the origin of evolutionary novelties, and the entire systematic hierarchy could be explained in terms of the genetic theory as matured during the 1920s and 30s. Except for shifts in emphasis and for a far more precise analysis of all the various mechanisms, the synthetic theory of evolution is the paradigm of today.’
 Stafleu 2002a, chapter 6.
 Raff 1996, 400: ‘”Body plan” refers to an underlying anatomical organization that defines the members of a clade and is distinct from the anatomical organizations of other clades.’ Ibid. xiv: ‘The major animal body plans first appear in the fossil record in early Cambrian rocks, deposited just over half a billion years ago. Body plans arose rapidly during the radiation of the first animals, but have been conserved since their debuts. Despite the enormous amount of developmental and morphological innovation that has occurred since then within body plans, no new phyla appear to have originated since the Cambrian.’
 Raff 1996, chapter 3.
 Mayr 1982, 611: ‘All that is needed as the starting point for the development of eyes is the existence of light-sensitive cells. Natural selection will then favor the acquisition of any needed auxiliary mechanism. This is why photo-receptors or eyes have evolved independently more than forty times in the animal kingdom.’
 According to Dooyeweerd 1959a, 115, 127, evolution is a subjective process of becoming: The structural principles of created reality are successively realized ‘…during the factual process of becoming… proceeding in the continuity of cosmic time, which warrants an inter-modal coherence of its modal aspects.’ Ibid. 143: ‘It concerns the realization of the most individualized and differentiated structural types in plants and animals. It does not concern the structural types as law or ordering types for the long process of the genesis of the flora and the fauna within the order of time.’
 Plantinga 1991, 682.
 Miller 1999, 53-56. Strauss 2009, 106 distinguishes ‘evolution’ (gradual development within certain limits) from ‘evolutionism’ (general development across all barriers). Strauss 2009, 470-496 is quite critical about evolutionism in this sense, without adhering to creationism.
 Einstein in 1929, quoted in Schilpp (ed.) 1949, 103, 659-660: ‘I believe in Spinoza’s God, who reveals himself in the harmony of all being, not in a God who concerns himself with the fate and actions of men.’
 Papineau 1993, 1-2.
 Plantinga 2011, 6.3.
 Numbers 1986; Plantinga 1991; Livingstone 2009; Scott 2009.
 Lever 1956; Van Till 1986; Barbour 1990; McMullin 1993; John Paul II 1996; Miller 1999; Cunningham 2010; Klapwijk 2008; 2011; Wearne (ed.) 2011. Plantinga 2011 argues that the theory of evolution is more in harmony with theism than with naturalism.
 Dooyeweerd 1959b.
 This view does not contradict the intention of the story of the creation in the first chapters of Genesis. Clouser 1991b, 6-7: ‘Thus the interpretation of the biblical remark that God created Adam “from the dust of the ground” would not be that it is intended as a description of God’s act, but as a comment on Adam’s nature. To be sure, it is by God’s creative activity that humans come into being. But on this interpretation the expression “from the dust of the ground” should not be understood as a description of one causal deed in space and time by which a biologically human being came into existence, but as conveying the fact that part of human nature is that humans are made of the same stuff that the rest of the world is made of. Thus, humans never are, and never can be, more than creatures of God. They are not little bits of divinity stuffed into earthly bodies, which are degraded as “the prison house of the soul.”’
 Mayr 1982, 438: ‘… the claim made by some extremists that man is “nothing but” an animal … is, of course, not true. To be sure, man is, zoologically speaking, an animal. Yet, he is a unique animal, differing from all others in so many fundamental ways that a separate science for man is well-justified.”
 This is a hypothesis, for which no logically conclusive proof exists, and probably cannot exist. In scientific laboratories, evolution cannot be copied. Scientific evidence differs from logical proof. Science does not require logical proof for a hypothesis. It requires scientific evidential material that does not contradict the hypothesis, but corroborates it. During the past two centuries, such evidence has been found in abundance. Moreover, for the above-mentioned hypothesis no scientifically defensible or viable alternative appears to be available.
 Referring to Max Weber, Reynolds 1976, xv writes: ‘If we describe what people or animals do, without inquiring into their subjective reasons for doing it, we are talking about their behaviour. If we study the subjective aspects of what they do, the reasons and ideas underlying and guiding it, we are concerned with the world of meaning. If we concern ourselves both with what people are, overtly and objectively, seen to do (or not to do) and their reasons for so doing (or not doing) which relate to the world of meaning and understanding, we then describe action.’ Dooyeweerd NC, III, 87-89, too speaks of the human act-structure, ‘… the immediate temporal expression of the human I-ness, which transcends the cosmic temporal order.’ (ibid. 88). Dooyeweerd 1942, proposition XIV: ‘By “acts” the philosophy of the cosmonomic idea understands all activities starting from the human soul (or spirit), but functioning within the enkaptic structural whole of the human body. Guided by normative points of view, man is intentionally directed to states of affairs in reality or in his imagination. He makes these states of affairs to his own by relating them to his I-ness.’ [my translation, italics omitted].
 Reynolds 1976, 87: ‘Since man’s neural development consists of essentially the same processes as that of other mammalian species (differing in the much greater extent to which those processes go on, to produce a relatively gigantic brain with a greatly exaggerated frontal portion and a number of other characteristic features) we can expect that our brains too develop along genetically programmed lines. In the case of animals this was postulated because behavioural responses tended to be species specific. Is the same true for man? This is the central question … Without wanting to prejudge the issue, it seems to be the case that some universal responses are clearly present in early life, but that they become less and less clearly evident as childhood proceeds; the conclusion that would appear to follow is that the relatively exaggerated growth of certain brain areas is concerned not so much with behaviour determination and restriction as with the opposite: The keeping open of options for behaviour to be modified and adjusted by conditioning of basic programmes.’
 Whereas fertilization is mostly a random process, the ensuing growth of the organism is to a large extent genetically determined. The probability that a fertilized seed germinates, reaches adulthood and becomes a fruit bearing plant, is very small. Therefore, a plant produces during its life an enormous amount of gametes. On the average and in equilibrium circumstances, only one fertile descendant survives. The accidental nature and abundance of reproduction, as well as incidental random mutations, are conditions for natural selection. But if a similar randomness would occur during the growth of a plant, no plant would ever reach the adult stage. Development is a programmed and reproducible process. Sexual reproduction (as well as evolution according to Darwin) is neither.
 Of course, many human acts are based on a reflex or some other fixed action pattern, wired in the brain. Experiments to point this out cannot prove, however, that this is always the case. For an extensive argument against determinism, see Popper 1982. On page 27-28, Popper argues ‘… that the burden of proof rests upon the shoulders of the determinist.’ See also Popper 1972, chapter 6. Luther and Calvin are often accused of some kind of ‘religious determinism’, because of the doctrine of predestination. However, both invariantly stressed the responsibility of every person for their acts.
 Cunningham 2010, 206-212.