Van de Vijver, G., Salthe, S., Delpos, M.(Eds), 1998: Evolutionary Systems. Kluwer, Dordrecht, p. 319-340

On some Relations between Cognitive and Organic Evolution

Olaf Diettrich

Summary The author suggests that a general theory of evolution should describe both organic and cognitive evolution in a coherent and consistent way. His proposal is basically constructivist, seeing evolution as a step by step development of conditions to which evolution itself becomes subject at a later stage. Reference to an independent and objective outside world bringing about conditions to which the organic and cognitive phenotype has to adapt is no longer applicable in this context since these relevant conditions are brought about by the organisms themselves. This topic will be discussed within the context of the Synthetic Theory. Even the laws of nature are shown to be human specifics as long as they are derived from perceived regularities that can be considered as invariants of phylogenetically developed cognitive operators (Constructivist Evolutionary Epistemology, CEE). An extension of these operators by means of measurement devices would lead to the completion of the classical world picture, if both the cognitive and the physical operators are commutable in the sense of operator algebra (quantitative extensions). Otherwise the physical operators will have invariants which can no longer be described in classical terms and would, therefore, require the formation of non-classical theories (qualitative extensions). Because new devices may developed again and again in the course of experimental physics, the evolution of theories cannot converge towards a "theory of everything" describing definitively the structures of reality. As axioms in mathematical are the equivalents of laws in physics, Gödel's incompleteness theorem is equivalent to the fact that qualitative extensions can never be excluded in physics. The organic analogs to qualitative extensions are those evolutionary or proper actions which may affect their own constraints. The author shows that a description of nature is successful (i.e., will allow predictions) only if it is based on the invariants of those operators of which the covariants represent our actions. Accordingly, in the organic realm: the strategies of assimilation are successful if they are based on the invariants of accommodation.


Largely uncontested is that the evolution of cognitive capabilities has to be regarded as a continuation of organic evolution by different means. For example, Evolutionary Epistemology (EE, Campbell 1973, Lorenz 1966, Riedl 1980, Volmer 1980, Wuketits 1984) is based on the assumption that our cognitive instruments and the categories of our thinking have evolved in ways similar to the evolution of organic tools for life management, tools such as metabolic and homoeostatic instruments or limbs as instruments for locomotion and action.

Within EE, however, the question remains unanswered as to what cognitive instruments have evolved and how. The argument is sometimes used that our cognitive instruments must be outcomes of adaptation to the environment and to the problems presented there, otherwise man could not have survived, and that, therefore, our cognitive phenotype must contain some information about the character of our world. Here Campbell (1973) speaks explicitly of "natural selection epistemology." Most problems, however, can be solved in various ways, and in ways that are often not related to one another. Horses and snakes, for example, although they may have developed in a similar physical environment, have entirely different organs of locomotion and these have no structural element in common.

So the criterion of survivability cannot explain why we have acquired the actual categories of human thinking and perceiving and not others. We cannot say, for example, that our visual perception of space is 3-dimensional because the world itself is 3-dimensional in character, and pre-human simians that did not see the world in 3 dimensions would have been unable to spring from tree to tree. Easy to show is that appropriate and successful survival strategies could well be based on 2- or 4-dimensional space-perceptions, and independent of the number of degrees of freedom actually available. Kinaesthetic animals, as described by Lorenz (1983), show us that even a 1-dimensional space-perception referring to nothing other than the linear context of their 3-dimensional pathways can be a helpful cognitive tool. An ape jumping from tree to tree is by no means obliged to interpret his visual perception in terms of a 3-dimensional perspective (geometrical approach). It could be quite sufficient if he saw his world in a 2-dimensional manner -- as 2- dimensional as the picture at his retina is. In this case, however, the ape is obliged to attribute to his legs a capacity not only for propelling him through the air, but also the capacity, associated with jumping, for effecting changes in the sizes of objects, branches in this case, causing them to become larger, actually changing physically in a characteristic manner (physical approach), knowing that he has to grasp the branch envisaged, which he is seeing, just when its size and position achieve certain typical values. If he has learned to do this, an external observer would find no difference between the ape's movement strategies and those initiated on the basis of 3-dimensional perception. (It is evident that physical theories based on an inborn metatheory saying that objects can be "deformed" not only by means of our hands, but also by means of walking or jumping, would have no similarities with the theories we are used to) 1),2).

Concluding that cognitive structures and instruments are unconditional or arbitrary because they are not, and cannot be derived from external boundary conditions, is mistaken, since internal boundary conditions must also be taken into account. Firstly, there are the developmental constraints of cognitive evolution itself; cognitive as well as organic evolution is subject to what has been evolved before. Cognitive evolution in our time, therefore, would find rather limited degrees of freedom. Further, cognitive instruments exert themselves in continuous co-evolution with organic instruments for meeting organically defined needs and requirements. This means that cognitive systems cannot be explained by reference to what is called their object, but only through their organic genesis. This justifies efforts made to look for a closer relationship between cognitive and organic evolution.

Constructivist Evolutionary Epistemology (CEE)

To understand cognitive evolution from an organic point of view, we start from a constructivist extension (CEE, Diettrich, 1993) of classical evolutionary epistemology (EE). The particularity of the CEE is based on a methodological element used mainly in physics, the so-called operational definition of physical terms.

What does that mean? As is well known, classical physics failed to accommodate the phenomena of quantum mechanics and special relativity primarily because it got involved with a non verifiable syntax brought about by the use of terms that had not been checked as to whether they could be defined by means of physical processes.

In our day to day life this epistemological refinement is not necessary. We have a clear understanding of what the length or the weight of a body means, and we do not need confirmation from a tape measure or a scale for carrying on. The situation, however, is different with microscopic distances that are smaller than the atoms of the tape measure. Here, first of all, we have to decide what kind of experimental facility we will apply in order to define length or momentum. Physicists say that properties are defined as invariants of measurement devices. This even applies to the order in time of events which, under normal conditions, can easily be defined and detected. With very high speeds, however, the topology of events may depend on relative motions.

As this kind of experience may be repeated again and again, it suggests a generalization that can be summarized as follows: properties of whatever kind and of whatever subject have no ontological quality. Instead they are defined by the fact that they are the invariants of certain measurement operators. This contrasts with classical thinking in which properties are used for the objective characterisation of objects. One of the most important properties we usually attribute to properties, namely, independent existence, is based simply on the assumption of their independent ontological quality. In day to day life this is incontestable. The length of a body and its colour exist independently of each other and can be measured separately. This does not necessarily apply in subatomic regions, as we know. The position and momentum of microscopic particles cannot be measured independently of one another. Physicists learned from this that theoretical terms have to be defined operationally, i.e., they have to describe nature by means of theories in which only those terms which are defined by certain experimental facilities are acceptable, rather than by categories which are defined by protophysical common sense.

The crucial step of CEE is to suggest that not only theoretical terms have to be defined operationally, but also observational terms as well as mathematical and logical terms.

Theoretical terms are defined as invariants of operations represented by physical measurement devices.

Observational terms, comprising both the visually perceived regularities (patterns) and those we condense into theories and into what we call laws of nature, are considered to be invariants of phylogenetically evolved mental cognitive operators. These operators are physiologically implemented somewhere in our brain and can be considered as a kind of cognitive measurement device: measurement objects are the sensorial inputs and measurement results are perceptions, i.e., pictures, and, within these pictures, certain regularities, structures or patterns, rather than numbers or pointer positions. Therefore, the entire system of laws of nature we have derived from these regularities cannot be objective entities but only mental constructs.

In this context the often discussed dichotomy of observational and theoretical terms is reduced to a rather secondary difference: observational terms have developed phylogenetically in the unconscious parts of the human brain, whereas theoretical terms are the outcome of conscious and rational efforts. Nevertheless, observational terms remain privileged as the basic elements of any higher theories; we can modify theories according to observational data, but we can not modify the genetically fixed mental operators and their invariants according to the requirements of special situations.

The operational definition of space, time and causality

The most crucial consequence of what has been said above, is that space, time and causality, which according to Kant are the necessary categories on which all external appearance is based, are not the only possible (and therefore necessary) categories. They are rather the phylogenetically evolved features of human perception and interpretation, defined operationally as invariants of certain actions and transformations. Let us look at this in more detail.

Following Piaget, the spatial metric of our perceptional space (and therefore the topology comprised) is operationally defined by means of motion. The identity of extended subjects, therefore, is defined as an invariant of locomotion (Üxküll: "a body is what moves together as a unit"). This definition is probably the main reason for the major difference between of what we call space and what we call time. Time is said to flow in an irreversible way; no one can retrieve any part of the past. We cannot move back and forth between two points in time. But we can do so quite well between two points in space. If we say we travel from point A to point B and than back again to A, we mean that the A where we started before arriving at B, and the A to which we arrived after leaving B, are not only equal but identical. To say so, however, is possible only if we can distinguish between "equal" and "identical" and if what we call identical is not influenced by our travel. This means that Identity is defined as the invariant of motion. And exactly this is the point. Only on grounds of such a definition can we call a change in spatial positions reversible, or more precisely: only on the basis of such a definition can we distinguish between the repeated return to the same A and travel along a sequence of equal As, i.e. between periodicity in time and space.

In a similar way, locomotion can change the visually perceived environment. We can transform the perception we call "forest" by means of walking, appropriately, into the perception we call "city". But this is not what we are accustomed to saying. More common is to speak in terms of an environment which, apriori, is multidimensional in character, i.e., comprising at the same time several structures which differ, first of all, in what we call their spatial positions. What we achieve, then, by means of our legs, is not a modification of the environment. We just "go" to places consisting of different structures and therefore experience different perceptions. What we call the multiplicity of the world, thus, is defined as invariant to changing our positions in that world. From the functional (and CEE) point of view, mentally generated spatial pictures belong to the most elementary theories we have at our disposal, by means of which we can forecast perceptions when walking - in the same way as the temporal structures stored in our memory inform us on what we can expect when repeating certain actions. So, both the formation of pictures and the formation of memory are first of all modi of extending life competence.

The arrow of time determines the difference between past and future. All efforts to define that arrow by means of an operator failed since every operator already comprises inherently the arrow of time: an operator transforms the status of its object before its application into the status after its application. This means that without a preceding definition of the arrow of time it cannot be said what an operator is doing. A consequence is that in all the endless cases where it is said that the arrow of time has been defined operationally it can be shown that the direction of time was already comprised implicitly in the preconditions of the experiment. A typical example is the following: shaking a box containing black and white balls that have been separated according to colour will always lead to disorder and never again to the original order. In physical terms: entropy will increase in time, never decrease. Entropy therefore seems to operationalise the arrow of time. But in this case, the result will depend on what is done first, separating the balls or shaking them. First separating and then shaking will lead to disorder. First shaking and then separating will lead to order. So beforehand we have to know what the terms 'before' and 'after' mean before we can perform the experiment which is to tell us what before and after mean. Also, the often mentioned thermodynamic concepts cannot help, as one can discover in the specialised literature concerned (see also Diettrich, 1989). If the arrow of time cannot be defined by means of physical operations a mental definition is required using, for example, the content of memory in the following sense: of two perceived events, A and B, A is said to precede B if we can remember A when B happens but not B when A happens. Of course, the past is what we can remember but we cannot remember the future.

In order to constitute causality we must be able to identify patterns of events. If a number of events, say A, B, C, and D follow each other always at typical intervals independent of when the first one occurs (i.e., if the pattern is an invariant of translation in time), then we say that there must be a causal relationship between the events concerned. Otherwise the perceived regularity could not be explained. Causal relations, then, are defined as invariant patterns of time. This, however, requires more than just having a topology of events as provided by our memory. We also must be able to distinguish between shorter and longer intervals of time, i.e. we need a time metric defined by a mental metric-generator implemented physiologically somewhere in our brain. For example, that we say lightning is the cause of thunder but not the contrary, is based on the fact that the time between lightning and the next thunder is usually much shorter and varies less than the time between thunder and the following lightning. But the length of time intervals can be defined only by means of a time metric. The mental time metric-generator is therefore responsible for the causal order established and for the prognostic capability derived from it. This also applies to continuous sequences of events such as the development in time of a mechanical system described by the equation of motion, by means of which we can forecast the future development of the system.3)

Physical extensions of perceptions and algorithmic extensions of mathematical thinking

Typical of most empirical sciences is the use of instruments and measurement devices by means of which we extend the range of natural perception in ways similar to those we use to extend our inborn physical capabilities by means of tools and engines. Here we have to distinguish between two important cases (Diettrich, 1994a).

We will speak of quantitative extensions if the perception operators and the measurement operators are commutable in the sense of operator algebra. In this case both operators will have the same spectrum of invariants. This means that the results of the measurement operations can be presented in the terms of invariants of the inborn cognitive operators, i.e., in terms of our classical world picture.

We will speak of qualitative extensions if perception operators and measurement operators are not commutable. Then the results can no longer be presented in a classical manner and require new, non- classical theories that accept classical theories as only approximations in certain borderline cases. As the set of possible measurement devices is, in principle, unlimited, what can never be excluded from considerations is that qualitative extensions of previously established operators will bring about modifications of the previously established world picture and of the theories associated with it. So there will never be a definitive world picture and there will never be a definitive 'theory of everything'. No objective laws of nature will ever be formulated. Those laws that we have, we have 'constructed' in a human-specific way in the course of human evolution; they will never converge towards a definitive set of laws except within the context of a limited set of operators, i.e., if we desist from further experimental research exceeding these limitations. What we actually do when we do science is to construct a world that we then believe we analyze by doing science. In other words: analytical in the sense of deepening our knowledge is characteristic of science only within quantitative extensions.

The notion of a theory of everything is equivalent to the notion of reality being characterized by objective laws of nature. According to what has been said in this paper, such a notion cannot be defined operationally. To require of reality structures that are independent of all human action, i.e., structures that are invariant under all possible operators, would deprive reality of just the specificity necessary for being a non-trivial notation. A non-trivial reality can result, thus, only through being invariant under particular operations. In other words, the operator that is to operationalise the notion of reality has to be commutable with every other possible operator. Unfortunately, only the trivial unity operator meets this requirement. So, what we can operationalise is, at best, a kind of current reality which refers to all the operations applied up to now (rather than to all possible operations), i.e., a reality which reflects all the perceptions and experiences man has ever had. This is just what we do when we speak in ontological terms about a reality which -- according to our current knowledge -- has this or that structure. From this it becomes evident that what we call reality cannot be brought about by adaptation to an independently extant or ontological reality. Under these circumstances we may well ask why, then, did cognitive evolution bring about the category of reality. A possible answer to this question is that we have to immunize our perceptions against doubts and distrust, particularly in situations where quick reactions are required. This is exactly what the notion of reality does. Within our day-to-day realism we consider our perceptions as representations of what is real rather than as the outcome of deliberate cognitive interpretation. In this way, time consuming (and, therefore, possibly dangerous) considerations as to whether these interpretations could be improved on do not arise.4) Thinking in terms of reality can be regarded as a kind of "cognitive burden" incorporated during the course of cognitive evolution. I.e.: in whatever direction our cognitive evolution may proceed, reality remains an irreversible category - similar to the developmental constraints in organic evolution called "genetic burden".

As already mentioned, CEE requires that not only observational terms be defined operationally but also that mathematical and logical terms be so defined. If the cognitive operators generating our perceptions are phylogenetically related to those generating mathematical thinking, then their respective results, i.e., perceived structures and mathematical structures, must evidence certain similarities. This would explain why we can simulate the extrapolation of perceptions (i.e. predictions) by means of mathematical extrapolations (problem of induction, see Diettrich, 1991) and why the mathematics we use is so well suited to the descriptions of what we call nature. In this context Davies (1990) speaks of the 'algorithmical compressibility of the world' (i.e., that in so many cases the obvious complexity of the world can be described by means of rather simple mathematical expressions) and Wigner (1960) of 'the unreasonable effectiveness of mathematics in the natural sciences'.

If there is really a relationship between mathematics and perception as postulated here, then the phenomenon of qualitative extensions must occur also in mathematics (Diettrich, 1994b). Similar to the operators of sense perception which can be experimentally extended, also the operators constituting our elementary mathematical notions and concepts can be extended by higher and more complex mathematical calculi. This is what mathematics does as science. Here, as well, we have to make the same distinction.

We will speak of quantitative extensions if the truth value of the terms achieved can be derived from the axioms used.

We will speak of qualitative extensions if the truth value of the terms achieved cannot be derived from the axioms concerned, although the calculi used are completely based on these axioms. In this case the axioms themselves will have to be extended in order to make the truth value in question derivable. The incompleteness theorem of Gödel states that this can happen again and again.

Qualitative extensions are emergent phenomena which cannot be predicted since, by definition, they cannot be derived from previous knowledge. The blueprints of quantum mechanical devices are entirely classical in character and nothing provoked the idea that the results they may bring about could no longer be interpreted within classical theories. The same applies to mathematics. There is no general criterion telling us whether a given calculus will exceed its own axiomatic basis.

With this, the existence of non-classical theories in physics and the incompleteness theorem of Gödel are homologue cognitive phenomena. Neither is there a definitive set of physical theories (i.e. a theory of everything) explaining and describing all (also future) physical problems, nor is there a definitive set of mathematical axioms determining the truth value of all possible mathematical statements. In other words: there is neither a physical reality in the sense of objective laws of nature, (though laws may be universal in so far men will find them confirmed wherever they may be in the universe) nor is there a mathematical (or 'Platonian') reality in the sense of objective axioms. Both any set of physical theories and any set of mathematical axioms will be incomplete.

The demand that subjects of scientific interest be accepted only if they can be operationally defined has to be applied also to individuals and organisms. It is suggested to base the defining operator on the sum of interactions necessary to constitute the organism or individual. Multicellular organisms, for example, are defined by the interactions between and among their cells. Cells are defined by the interaction between and among their organelles, etc. (see Diettrich, 1989). Accordingly the interactions are what we have to consider as being the units of selection. From the Darwinian point of view the replicator rather is what represents the unit of selection (see Hull, 1988). Further to this, this constructivistic approach (by which the interactions are the units of selection) allows us to define a more general notion of units and individuals in cases where the notion of replicator hardly can be applied. Social groups, for example, are defined by the interaction between their members, biological species by genetic interaction and theories by the interrelation between their statements. We know little up to date about the technical realization of the cognitive operators for pattern recognition. But if it should turn out that they are constructed in a modular way as well, then, from the structuralist point of view, the interaction of elements which themselves are defined by interactions would be the generating principle by means of which any hierarchy in organic, cognitive, cultural and social areas could be described. That a modular concept would also allow a better understanding of the problems of homology has been discussed by Wagner (1995).

Perception and action and their cognitive representation

The task of perception is to allow the formation of theories by means of which we can predict the effects of action. As the effects of action can be presented only in terms of perceptions we can say: by means of perceptions we will find out how perceptions may change under the influence of action. In other words, actions are operators which act upon perceptions.

Within classical realism this is described by means of what we call the laws of nature. The effects of our acting, we say, are determined by the laws of nature, and by means of our (natural and experimental) perceiving we acquire knowledge about just these laws. From this the scientific decoding of nature is seen as the crucial prerequisite for mastering nature. Only through knowledge of its laws can we master nature. This is the legitimation for all natural sciences in so far it aims at the exploration of natural laws.

Searching for the laws of nature succeeded whenever it was used for mastering nature. As there are, however, no objective laws (as we have seen), this way despite all its success is not legitimized heuristically. So there must be yet another link between perception and action that does not depend on the intermediate level of objective laws. If, nevertheless, we continue speaking about the laws of nature, we can expect that only those laws will help us predict perceptions and the perceived effects of action but not that they will provide us with objective statements about the world. According to classical understanding, action and perception are two entirely different categories: action refers to the individual's input to the world, whereas perception means the world's input to the individual. With CEE, however, both refer to the same mechanism with the consequence that there is no essential difference between them. This sounds strange but is easy to illustrate. Visualize a hammer. It is an instrument designed primarily to alter certain objects. But a hammer, in its quality as an operator, also has invariants: objects and properties which would resist the hammer's strokes of a given strength. The hammer, then, can be used to measure mechanical properties such as the strength of materials. So, both perceiving and acting mean applying the same operator. The only difference is that, in the case of perceiving, we seek the invariants of the operator in question, i.e., we seek what remains unchanged under the application of the operators, whereas in the case of acting we seek what changes under the operator's influence. Our inborn world picture (i.e., the inborn interpretation of the sensorial input), therefore, depends on the phylogenetic 'decision' about which operators we use to construct the cognitive reference frame and which operators we use to modify what is described within the reference frame. (One of these phylogenetic decisions we have already mentioned: to use locomotion to give our perceptual space a third dimension rather than using it to modify the size of structures in a two- dimensional world.) The decision made about our actual cognitive reference frame, however, was not an evolutionary accident. It rather was made according to a relatively simple scheme as we will see.

In case of a physical measurement (which is an action, of course) the result, in physical parlance, is the invariant of the measuring process. In other words, we use the invariants of a process to describe the effect of just that process, i.e., we describe the covariants of an operator by means of its invariants. This can be generalized into the cognitive area. The actions by means of which we explore the world can be considered as measurements (i.e., as perceptions in the broadest sense). Results of measurements (or, as one could say, the results of our experiences) then are pictures of the world and theories representing what we call the unchangeable and, therefore, the objective world (i.e., what is invariant under all our doing and acting). If we look however for the covariants of our action, i.e. what changes under the influence of our actions, we have to refer to what we said about the relationship between the covariants and invariants of measuring processes: the effect of action can be described only in terms of the invariants of action, i.e., in the terms of our world picture. This is exactly the direct relationship between perception and action we looked for and which does not rely on the concept of an objective world.

If this is true, then the elementary categories of our perception must be the invariants of our most elementary action operators. But what are the most elementary action operators? They are not, as one might think, our hands and the tools guided by hands. They are, rather, our legs. By means of a few appropriate steps, we can change the environment of the room we are in into the environment of a blooming garden. Of course, we could achieve the same also by using our hands if we employ them do the necessary reconstruction work. But this is troublesome and time consuming. So, one of the most important human-specific operators is locomotion. Our world picture, as a result, must be based on the invariants of this operator - and this is indeed the case. The most elementary descriptive category of our world view is the identity of extended objects and spatial structures defined as an invariant of locomotion.

This provokes the assumption that, from a phylogenetic point of view, the categories of description can be understood only through their capability to cope with the covariants of certain operators. From this it follows that the cognitive phenotype was fashioned by evolution not in order to explore the world but, instead, to extend the action possibilities of the organic phenotype.

Spatiality and the spatial metric, as we have seen, are categories that are necessarily defined by the process of motion. On the other hand, motion cannot be explained without the notion of space in which motion takes place. From this it follows that motion itself will have brought about the mental category of spatial structures necessary to deal with motion. Exactly this is what we maintain: what an operator is doing can be explained only in terms of its invariants.

We encountered a similar problem when we dealt with the operational definition of the arrow of time. An operational definition was impossible, because the notion of operators themselves would require a prior definition of the arrow of time. We therefore proposed referring to the memory and to events stored there. But, from the cognitive point of view, events themselves are already operators transferring the status before the event into the status after the event. So events, just as any operator, require the prior definition of the arrow of time. Without a definition of the arrow of time events and all we store in our memory in order to write history remain undefined.

By this, time turns out to be a mental modus which itself needs to have been brought about by operational means. In the same way as the spatial metric was generated by the process of motion (i.e., motion bringing about the category of space which is necessary for describing of motion), the category of time has to have been generated by operators (i.e., operators bringing about the category of time which is necessary for describing what operators are).5) We can conclude: physical actions, and the cognitive operators we use to describe them, are brought about by the same organic operators (i.e., organic tools). Perceived patterns or regularities, and the instruments of mathematical thinking we use to describe them are brought about by the same cognitive operators. So mathematical patterns, perceived patterns and the results of our actions are literally homologue in so far as they have a common ontogenetic root, and this is the reason why they can 'cooperate' so well with one another - as well as the various physiological mechanisms having brought about each other.

Circularity or the reproduction of the cognitive phenotype

The difficulty we have in accepting the notional character of our experiences as human-specific constructs differs with space and with time. As to the notion of space, undoubted (except perhaps by naïve realists) is that the spatial patterns we perceive are not objective in the sense of their being considered pictures of real structures, i.e., the world is not necessarily as what it appears to be. Here, with space, we quite readily attribute to our world picture a reduced objectivity. Not so with time: The recorded time topology of events we consider to be real; the order of events is as we have perceived it, actual. The past is as it was and even God cannot change it a posteriori, we are used to say. Weizsäcker (1985) called this the 'facticity of the past'. Factually, however, events can only be defined as the results of cognitive or scientific interpretations, just as visual patterns can only be defined as invariants of cognitive operators. Events, as such, have as less clearly defined outlines than visual patterns have. A modification of the interpretations of events used (for example, in the presence of a novel theory) may well effect the past. An experiment may have been made in the beginning of this century documenting unambiguously a speed faster than that of light. After the appearance of the theory of relativity, the protocol of the same experiment would have had to be rewritten in using a speed less than that of light. A similar revision would have to be made if evolution would have changed our cognitive operators. But because this has not happened during historical times, the illusion arose of both the facticity of the past and the objectivity of the laws of nature. The allegation that thehistoricity of the world is a human specific artefact is the more problematic as it is based (through CEE) just on what is known about biological evolution, and this deals explicitly with the historical order of phylogenetic events. Said another way: on the one hand our world picture ist the construct of our cognitive and experimental apparatus, on the other hand, just this world picture is what physics and biology refer to, particularly when describing the development of the human brain and the operators established there. What, then, is hen, and what is egg ? Is it the real world we live in and which developed in the course of biotic evolution up to and including the brain's functions, or is it just these brain functions which bring about the picture of a real world as a tool for both articulating and solving our problems ? Formulated differently: are perceptions brought about by nature, or is nature a category brought about by our cognitive apparatus ? This dichotomy is the reason for the frequent accusations which say that the EE is circular in so far as not only the categories of space, time and causality are interpreted in phylogenetic terms but also the notion of reality and nature -- the latter comprising phylogeny itself. So, phylogeny is interpreted by phylogeny, which is circular.

Actually, however, no real dichotomy exists as long as there is certainty that perceptions and nature condition one another through generating one another. This certainty is provided by the fact that our cognitive phenotype constructs a world picture which permits an understanding of the genesis of just this cognitive phenotype by means of evolution within the framework of just this world picture. Thus, not only organic ontogenesis but also cognitive evolution have to be understood as circular, autoreproductive processes in the subsequent sense:

In the biotic area the following holds: the epigenetic system of an organism is what determines how the genome's structure is to be interpreted and expressed into the phenotype. Identical reproduction is possible, however, only if the epigenetic system brings about a phenotype comprising the epigenetic system itself.

In the cognitive area the following holds: the cognitive apparatus (and all the science based on it) is what decides how the sensory input is to be interpreted and which world picture will be conveyed. The knowledge acquired in this manner is consistent and reproducible, however, only if the cognitive/scientific apparatus generates a world picture that includes containing the cognitive/scientific apparatus itself.

A genome on its own cannot determine the phenotype in the sense of providing a 'blueprint' - it rather represents one of several levels in the process of autoreproduction -- nor can the sensory input dictate its own interpretation, and, by this, the reactions it will effect. This limitation does not contradict the fact that, within the context of a given organic or cognitive phenotype having a given interpretative machinery, a genetic mutation as well as a new perception may lead to reproducible modifications of our physical constitution or of our theories. This means that, as long as the epigenetic system remains unmodified, a given genetic mutation will always produce the same phenotypic change; and as long as our cognitive apparatus and our scientific theories also remain unmodified, a given sensorial input will always lead to the same reading. What we have to avoid, however, is concluding that what mutations and perceptions initiate is also what they determine. Determinism is possible only within a given scheme of interpretations, i.e., outside qualitative extensions changing interpretations. The same limitations hold for adaptation. Adaptation makes sense only within a context of quantitatively extended acting. Acting will be modified positively in order to better meet the requirements given. The requirements themselves remain unchanged. Qualitatively extended acting, however, will affect the requirements and, by doing this, the relevant boundary conditions (i.e., the selective pressure). Qualitatively extended acting, thus, will become a source of emergent results. The world seen as the sum total of the boundary conditions of our acting is subject to a permanent actualization, as acting aims at changing just these conditions in order to make further and more ample acting feasible. This begins with the organic phenotype which defines the constraints for evolutionary 'acting', which in turn changes the constraints for further evolution (evolution meaning the evolution of its own boundary conditions). And it ends with the cognitive phenotype that defines, through our world picture, which kind of scientific acting is possible due to which the world picture itself may be affected -- a paradigmatic shift in the sense of Kuhn, so to speak. The world as object of adaptation can be defined only for the time between two 'paradigmatic changes', i.e., between two qualitative extensions.

Circularity, a devastating objection for any theory within the context of classical realism, becomes (in the sense explained here) a necessary prerequisite for any complete constructivistic approach. The role of circularity constitutes the key difference between realism (of whatever kind) and constructivism as presented here. Realism requires of life mastering methods consistency with an independent outside world. A 'radically' constructivistic interpretation of the world, however, needs only to reconstruct itself. Hence, the so-called radical constructivism of Von Foerster, Glasersfeld, Maturana and Varela is not genuinely radical. In order to avoid conflict with the well established term 'radical constructivism' one should rather speak in terms of 'complete constructivism' when characterizing CEE.

The various epistemologies mentioned here can be explained more clearly when they are classified according to how they meet their functional requirements:

  1. The most elementary position taken is that cognitive constructs (perceptions) have to delineate correctly the structures of the environment, since the strategies devised to meet the requirements of the environment are believed to be derivable from those structures. This is the basis for most kinds of realism.
  2. In constructivism, as well, cognitive constructs have to contribute to meeting the requirements of the environment, but not necessarily by means of delineating environmental structures.

    Both views, therefore, refer to the requirements of the external world - one in a structural way, the other functionally. The view that scientific theories are pictures of the world and that the laws of nature are rules to be followed by everyone legitimizes the program of empirical sciences searching for the world's structures and requirements.

  3. Complete constructivism (CEE) proceeds on the assumption that not only the ways we see the world and the methods we use to meet the requirements of the world are constructed, but also the requirements of the world themselves, since these requirements - may be cognitive or organic - are not defined by an external world but rather by their previous organic, cognitive or even cultural evolution. For example, our phylogenetic predecessors explicitly designed the law of energy conservation when they "decided" upon which type of physical mechanism should emulate the mental clock defining the metric of time. So, the regularities men perceive and condense to what they call the laws of nature (or reality) represent nothing more than their own previous developmental history. We can use the constructive character of what we perceive to define the difference between actuality (Wirklichkeit) and reality. Actuality is what we can change or construct by means of acting in the literal sense. Reality is what we have constructed by means of evolutionary 'acting'. As the latter is irreversible, reality seems to be universal and therefore objective. In other words: 'home-made' is not only the way we see reality but also reality itself.

Darwinism and CEE have an interesting element in common. Darwinism tries to explain the actual forms of life as the result of evolution. Evolutionary models which fail at doing so will be victimized by selection. Darwinian models, so to speak, apply their own content to themselves. Something similar happens with CEE. It tries to simulate the evolution of stable forms of life. The main criterion of stable living forms is by definition their capacity to reproduce themselves. The same applies for CEE. CEE is stable or 'complete' only if it can reproduce itself in the sense just explained. So CEE as well applies its own content to itself. Selection and autoreproduction can be considered the key concepts constituting the Darwinian and the constructivist approaches respectively. Both approaches represent metatheories which, as such, do not make experimentally verifiable statements through which they could contradict one another. Neither excludes the Darwinian view that the selecting environment is a construct of the organisms concerned (see next section) nor excludes the CEE view that specific constructs can be selected out because they lack coherence with other constructs.

Assimilation and accommodation versus action and perception

According to Piaget, assimilation means modifying or using external data in order to meet internal needs. Accommodation means modifying these internal needs in order to be met more easily. Let us apply the terms assimilation and accommodation to general evolution. According to the synthetic theory, successful evolution means constructing or modifying an organism so that it can satisfy external requirements. Evolution is thereby understood to precede primarily by means of accommodation, from its early commencement through to human technical and scientific achievements for managing life.

However, what evolves are not only internal needs for meeting external requirements but also the competence for acting, i.e. the capacity for modifying the environment, i.e. for modifying external requirements according to previously defined internal needs . Seen in this way, evolution is both accommodation and assimilation -- with an increasing tendency towards assimilation: the more complex and "higher" organisms are, the more difficult it becomes for them to modify the phylogenetically acquired physiological and other basic strategies, and the more likely it is, therefore, that evolution tends toward assimilating strategies, i.e., toward improving the methods for modifying the environment. Warm-blooded animals, for example, do not react to climatic changes by altering their physiologically defined body temperature. Instead they conserve their internal climate by means of better isolation or through higher (internal or external) energy investments. Humans, after all, do not react any longer by means of evolutionary accommodation. Whenever a conflict arises between biologically defined human requirements and the environment, the conflict will be solved at the environment's expense.

One of the most popular methods for changing the environment of all animals is locomotion. Paramecia began early to use locomotion for escaping from adverse local conditions. That the relevant environment and its selection pressure is an artefact of the various species occupying it rather than an objective and external issue was seen already by Waddington (1959, p. 1636): "Animals are usually surrounded by a much wider range of environmental conditions than they are willing to inhabit. They live in a highly heterogeneous 'ambience', from which they themselves select the particular habitat in which their life will be passed. Thus the animal by its behaviour contributes in a most important way to determining the nature and intensity of selective pressures which will be exerted on it. Natural selection is very far from being an external force, as the conventional picture might lead us to believe". Regarded from this aspect, life is a mode of world construction in the sense of Goodmann (1984) rather than a process of exploring the world or of acquiring knowledge about the world as Lorenz (1983) said. In other words, evolution seems to aim at assimilation rather than at accommodation.

Actually, however, this picture is as biased as the pure-accommodation picture because the capacity for acting and reacting does not represent eo ipso a successful assimilation strategy. Strategies, as well as organic features, must accommodate themselves to given external conditions. This is what accommodation strategies aim at -- not to explore the environment and modify one's constitution accordingly, but to improve the capability of changing one's environment in order to meet the requirements of one's constitution. These requirements, however, mean first of all making optimal use of existing assimilation techniques. So, accommodation must orient itself to the techniques available rather than to the environment concerned. The most elementary example is the evolutionary extension of homeostasis for adapting to a larger variety of external data rather than finding special solutions for each special case. Accommodation, therefore, will aim at extending the set of controllable data independent of what is actually required. Whether a species can profit from this strategy or not will depend on whether new conditions or a new environment can be found in which these new achievements will pay off. (A cultural example would be basic research that provides solutions for problems which do not yet exist and which will be successful only if appropriate applications can be identified.) So, the interplay characteristic of evolution is not only that between mutation and selection (supply strategy, defined by the supplies and constraints of the environment) but also that between extension of competence and applicability (demand strategy, defined by the requirements and the possibilities of the organism). If we, nevertheless, want to continue using the notion of environment as the instance which articulates the boundary conditions for physical and evolutionary acting, we have to consider it as a construct in a double sense: (a) by acting in the proper sense we can modify the relevant boundary conditions — for example, by means of external heating we can reduce the demands on internal temperature management; (b) by changing the internal requirements the same environment can come to represent different boundary conditions — for example, by the developing from anaerobic to aerobic respiration, a previously irrelevant content of oxygen in the atmosphere became the key survival factor. More generally we can say that what counts is the 'distance' between organism and environment and this can be reduced at both 'ends'.

Here we have an analogue in cognition. We said that the cognitive phenotype is entirely a construct of the organic phenotype, that was brought about to extend the functional possibilities of the phenotype rather than to 'recognize' the world or to explore what Vollmer called the cognitive niche. Nevertheless, here, as well, we can continue using the notion of environment if we consider it (as we did in the organic case) as being constructed in a double sense. (a) We can displace objects, change our position, practice agriculture or construct streets with traffic lights. By all this we change our environment and if we do this in the interest of our needs we practice assimilation. By this we construct what we call actuality (Wirklichkeit). (b) How we see the environment, which regularities we register and to what 'laws of nature' we will condense them is a matter of our cognitive phenotype. The development of the cognitive operators up to the development of our world picture (including the formation of scientific theories), is, therefore, an act of accommodation to the conditions of actuality brought about by assimilation. Our cognitive environment, thus, is a human-specific construct characterized by the laws of nature as comprised in the notion of reality. It is not nature which tells us how we have to see it (for example, as spatial objects moving in a world of three dimensions). It is rather the phylogenetically emerged mental operators and their invariants which define the regularities we perceive and the laws we derive from them. If we consider that the biological development of these operators has been completed, but not the development of their possible physical extensions by means of novel experimental devices with novel invariants which require novel theories, then we can say that we continue more than ever to construct the object of scientific research, i.e., reality. Reality, in so far it is articulated in terms of laws physicists formulate and try to explore in order to make predictions possible, is a human-specific artefact. What we see depends both on what we do and how we interpret the sensory reflexion of our doing.

In strict analogy to the organic case we can say that actuality and reality are the two ends which characterize the cognitive distance between individual and environment. Actuality is the result of our doing (including locomotion), i.e., of assimilation. Reality is the result of our phylogenetically acquired ways of interpreting of experiences with a view to making predictions. So reality is the result of accommodation. As we cannot describe actuality without a previously defined interpretation of our sensory input, we cannot speak of assimilation without accommodation. Just as in the organic context: the results of accommodation (i.e., the actual phenotype) define what certain assimilating activities will mean for the organism concerned. This applies, as well, in the opposite direction: accommodation is not possible without assimilation. We cannot speak of reality and its purpose for making predictions (accommodation) without reference to the object of those predictions, the actions (assimilation). The same argument holds in the organic case: action means the accommodation of assimilation strategies. Action and perception cannot be defined independently of one another. More particularly, it does not make sense to speak in terms of perception or recognition of an independent and objective outside world. In other words: the covariants (effect) of an operator cannot be defined separately from the operator's invariants describing this. This we referred to implicitly when we said that perceiving and acting means applying the same operator and that their only difference lies in whether we ask for the operator's invariants or the operator's covariants. Something very similar holds for accommodation and assimilation. A certain operation can be considered as an act of assimilation if we look for what it may effect in the environment, and as an act of accommodation if we look for how it may change our situation in the environment.

Organic theories

Assimilation strategies, as we have seen, do not aim primarily at controlling a particular situation but rather at expanding the spectrum of controllable situations so as to include, as well, a particular situation. The homeostatic temperature management of warm blooded animals is not designed to compensate for an actual temperature of, say, 5%C, but for all temperatures within certain limits. So, assimilation strategies are synonymous with extensions of acting competence.

The cognitive analog is the formation of theories. The purpose of a theory is not only to predict the result of certain actions for their repetition in the future, but also to extend the spectrum of predictable results of actions exceeding the set of those actually realized. Theories are 'true' for the set of actions leading to results they can predict. Prediction, i.e., the cognitive mastering of various actions (comprising also those not yet realized) is, therefore, an analogue of the control of different external conditions (comprising also those that have not yet occurred), i.e., prediction is the analogue of the extension of action competence. If an action mechanism can control more than just one outside condition, we might call it, in analogy, an 'organic theory'. Organic theories are 'true' for the set of outside conditions they can control. The question arises why the mechanisms actually implemented in organisms are 'true' just for the set of frequently occurring conditions rather than for any others. The answer might be as the following: in the cognitive area we have seen that the covariants of an operator (i.e., the effect of acting) can be described appropriately only in terms of the operator's invariants. The organic analog would be: an acting operator masters a set of outside conditions if and only if these conditions are invariants of the operator concerned — and, by definition, the actual conditions are precisely those. Whenever we speak about outside conditions we formulate them in such a way that they will be relevant for the organism and its activity — the invariants of organic perception, so to speak, in the same way that the objects of our sensory perceptions are defined as invariants of our physical activity.

A typical example is the set of possible outside temperatures which have to be mastered by the organic temperature-management devices. The energy invested in order to stabilize the required inside temperature under the condition of a given outside temperature can be regarded as a measure of the outside temperature, and the heat management device itself as an outside thermometer. In this way the notion of temperature is operationally defined by a certain physiological regulatory mechanism. That this mechanism is able to compensate for varying temperatures is therefore not a matter of phylogenetic adaptation. Rather it is a matter of definition: what we call temperature is what can describe the effect of this particular regulatory mechanism or, in the words used above: operators bring about not only certain effects but also the cognitive tools by means of which their effects can be described.

So, there is no need to wonder why the organism is so well adapted to the world in which it finds itself; the way the world is seen is just a reflex of the requirements and possibilities of that organism. In other words, what we call the world, which is said to guide our adaptive efforts, is rather a phylogenetically developed cognitive model by means of which we explain our reproductive success.

Earlier explained in this paper is that theories are invariants of our perceptional and experimental devices and that new devices which are not commutable with those already extant (qualitative extensions) may lead to novel theories that can no longer be described in terms of their predecessors. The question then arises as to whether or not something equivalent can be said about what we have called organic theories.

I propose to speak of a quantitative extension of an acting operator if that operator brings about a better or more effective mastering of the outside conditions without changing the goal envisaged. Example: a bird species, the members of which live by cracking nuts, may adapt their bills phylogenetically according to the nuts available.

I will speak of a qualitative extension if the extension will change implicitly also the goals previously envisaged, i.e., if the modification concerned leads to new applications in new areas and, therefore, to the transfer into a new niche with new adaptive pressures. If the bills of the (hypothetical) bird species, were to diminish phylogenetically towards an unsuitable size they would no longer be able to crack nuts, but they might well learn to pick the grain they found in their own or in a new biotope. From then on modifications would be evaluated and selected according to their grain-picking power. In other words, the original niche is no longer an invariant of the modified beak and therefore has to be transferred into a new niche. The cognitive analog is the effect of measurement devices on their objects as found in subatomic regions. This problem has been solved by using only those variables which are invariants of the measurement operators applied and which, therefore, will not be affected by the measurements made. The analog of the case discussed here would be a feeding habit that is independent of (and therefore an invariant of) the beak's shape, either due to selecting appropriate food stuffs or due to preparing the foodstuff by means of appropriate tools or techniques (e.g., by rolling hard-shell eggs on stony ground until they break; in this case the beak's shape is largely irrelevant). Another example comes from evolutionary biology: genetic mutations can be called quantitative if they affect only the phenotype and, therefore, are reversible. We will speak of a qualitative mutation if it affects also the epigenetic system that interprets and expresses genomic structures. So there is a kind of co-evolution between genomic structures and their interpretation by the epigenetic system which itself is subject to genomic modifications. This may lead to non-stable recursive processes which have been described as non-linear genetics (Diettrich, 1989, 1992). This means that long-term evolutionary processes can develop their own dynamic, a dynamic that does not need to depend on consecutive genomic mutations or environmental changes. A further example is provided by modular extensions such as multicellularity, i.e., combinations of equal or different elements or techniques evoking novel competencies and capabilities: the combination of manual and visual abilities, as well as the combination of electrostatics, magnetostatics and mechanics into electrodynamics with the novel ability to describe electromagnetic waves (such as light waves). Müller and Wagner (1995) have pointed out the possible importance of modular approaches in developmental biology.


The most promising effort of the constructivist approach proposed here (CEE) aims at a coherent description of organic, cognitive and scientific evolution. However, the price to be paid is high. We have to accept that the laws of nature are phylogenetically acquired human-specific artifacts; that there is no 'natural selection epistemology' (sensu Campbell); that there will be no complete set of physical theories ('theory of everything') and that there will be no meaningful context-free communication (such as that with extraterrestrial beings). On the other side, some explanations are offered that could hardly have been expected from outside CEE: the incompleteness of physical theories and the incompleteness of mathematical axioms discerned by Kurt Gödel have the same cognitive roots; the algorithmic compressibility of the world (which is equivalent to the success of induction) is due to the homology of cognitive mechanisms and the mechanisms of mathematical thinking. Of particular interest is the link between organic and cognitive tools: if cognitive tools are to describe the covariants of an operator (i.e., what the operator effects), they have to be designed in terms of the operator's invariants (a principle which has been re-invented by physicists within Hamilton-Jacoby and quantum mechanical formalism). Cognitive evolution (including the epistemology here applied), therefore, is brought about by organic evolution (and by the evolution of experimental tools) rather than by trial and error and selection. And, vice versa, organic (also experimental) evolution is guided by the possibilities provided by cognitive tools.

This relationship between action and perception (or organic and cognitive development) is the same as the relationship between assimilation (modifying the environment according to previously defined internal needs) and accommodation (modifying the internal constitution and the resulting needs according to externally defined requirements): assimilation aims at changing what cannot be approached by accommodation (i.e., at the invariants of accommodation) and accommodation aims at approaching what cannot be achieved by assimilation (i.e. at the invariants of assimilation). In terms of the action/perception dichotomy, this reads as follows: acting requires the view that what we see of the world has a real (i.e. unchangeable) background. And what we consider as real of the world (such as the laws of nature) requires the view that this cannot be changed by our acting. Assimilation, as long as it is in action, requires a fixed goal which is not modified by accommodation, and accommodation, as long as it is in action, requires a fixed goal which is not modified by assimilation. This is also so in scientific evolution: experimental efforts require a well defined theoretical basis, and theoretical efforts require given experimental facts to which they refer. It is like walking: at the same time we can precede only with one of our legs whereas the other one has to be at rest. We nevertheless can precede over unlimited distances if we change alternately the active and the passive role of our legs. Evolutionary 'walking' in this sense means the endless sequence of what we called qualitative extensions comprising the permanent co-evolution between accommodation and assimilation: tool-inventing and finding applications (in both organic and scientific evolution); perceiving and acting; experiments and their interpretation; general research and the goal defining paradigms. A particular case is the co-evolution between (say organic) units and their interactions. The development of interactions between units may bring about new forms of units which then could develop higher forms of interactions defining higher units etc. as represented within the course of self-organisation, and vice versa.


The author is grateful to Prof. Dr. Gertrudis Van de Vijver, and Dr. Robert W. Kickert for many helpful comments on early drafts of the manuscript, and particularly to the Konrad-Lorenz-Institute for Evolution and Cognition (Austria) and its chairman, Prof. Dr. Rupert Riedl, where the author, as the then guest professor, could develop this paper.


  1. The question whether modifications of visual perceptions should be interpreted geometrically or physically was addressed in another case in physics: the orbits of planets could be considered as the effect of explicit gravitational forces (the physical solution) as well as geodetic lines within a 4-dimensionally curved 3-dimensional space (the geometrical solution within the theory of general relativity). As this is just a different interpretation of the same observations we cannot come to a decision on empirical grounds, nor was adaptation by selection relevant when the cognitive evolution of primates came to decide whether to see the visualized world in 2 or 3 dimensions. In other words: perceptional spaces and systems of categories are purely descriptional systems which may tell us something about how we see the world but which tell us nothing about the world itself. Hence, they cannot be the outcome of adaptation to the world.
  2. An interesting analogon can be constructed to the theory of special relativity. Visualize locally fixed plants that have eyes and can see, living in a world of no motion. For these plants there is no need to distinguish between objects that are small because they are really small, and those that are small due to their greater distance (as we would say). These plants do not know the phenomena of perspective and their world of visual perception is 2-dimensional. As soon, however, as they learn to communicate, they will find out that objects that are small for one observer might well be big for another one. They may, then, construct a theory of relativity of size, saying that size depends on the relative position of the observer -- difficult to understand for someone who is used to live in a 2-dimensional world. The same happened to physicists when empirical evidence forced them to construct the theory of special relativity saying that time intervals depend on the relative motion of the observer -- difficult to understand for someone who is used to live in a Newtonian world. (By the way, this analogon can be even extended: the limitation of all speeds in the 3-dimensional case (vœc) corresponds to the limitation of all lengths in the 2-dimensional case, as these can be defined only by means of the aperture œ 180°)
  3. The specificity of the metric generator has direct effects on the laws of conservation we record in physics (energy, momentum, etc.). Following Noether's theorem, these laws can be derived from the invariance properties of the equation of motion: invariance under a translation in time (i.e., physics is the same yesterday and today) implies the conservation of energy; invariance under translation in space (i.e., physics is the same in America and Europe) implies conservation of momentum; invariance under spatial rotations implies conservation of angular momentum. In other words: from the homogeneity of space follows the conservation of momentum and from the homogeneity of time follows the conservation of energy. What 'homogeneous' means, however, is exclusively a matter of the mental metric-generator concerned. This applies also to the other conservation laws which, therefore, are human specifics rather than objective properties of nature. As will be seen below, the conservation laws constitute what one could call the cognitive reference-frame we use to describe actions and what those actions will bring about. Other conservation laws based on other cognitive operators would effect a different cognitive phenotype, but this would not mean that the methods and life strategies based on other operators would be less consistent or efficient. What is excluded, however, is communication between representatives of different cognitive phenotypes. This may apply to extraterrestrial beings. Though they may well survive with their particular cognitive phenotype, no communication is possible between them and us; and means invested by space research to this end is money thrown down the terrestrial drain. The organic analog is that representatives of different species cannot communicate genetically, i.e., they cannot interbreed.
  4. This is close to what H. A. Simon (1983) called 'restricted rationality' saying that higher animals and men in many cases concentrate their capabilities on solving actual problems while disregarding higher interests and long-term requirements.
  5. The program describing the covariants of operators by means of their invariants is well known and is often used in physics. Within the framework of Hamilton-Jacoby-formalism, the variables of a mechanical system are chosen so that conservation laws (invariants) will apply for them. With this prerequisite cared for, the transformations describing the system's development in time can be found easily and explicitly. On the other hand, the conservation laws themselves can be shown to be generated by the transformations considered. So the canonical total momentum ( in this paper identified, in a more general way, as 'motion') brings about spatial translation, and the total energy (represented by the Hamiltonian) brings about translations in time. Something very similar applies for quantum mechanics. The system's development in time is generated by the Hamiltonian and the eigenvectors of the Hamiltonian constitute the reference frame by means of which this is described. If we replace the physical transformations and operators by their cognitive/mental equivalents we just get what we said: space and time have no independent or ontological quality but are rather products of human-specific operators.


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Version of 5 April 2000