Man in Search of Himself

Evolution

How does everything in the Universe evolve? Where do things come from, and what is their goal? What is the deeper meaning of life? What is the importance of the phenomenon of man? Here are a number of exciting questions to which the whole of science, the whole of art, and the whole of human religion are not sufficient for an answer.

Moreover, these are questions which must be asked again and again. The answers will, no doubt, be provisional, as each generation formulates its own suggestions in reply to these fundamental problems; yet these answers, however uncertain they may be, are the only dim light whereby we may trace out the path of evolution chosen by Nature.

What Evolves?

In the first place, let us remember that we have been led to make a firm distinction between 'what is', which we have called 'Being' — something that cannot be directly apprehended by nature — and the 'maps' we can make of Being by means of some language or other, the word 'language' being taken in its most general sense, that is to say, a pattern of words, or of conscious thoughts, or of actions.

Clearly, we cannot talk of the 'evolution' of Being; first because Being is indescribable directly in any language; and secondly, because the terms of time and duration could have no meaning when applied to Being. Being must be considered en bloc; it forms a rigid whole in time and space, so that there can be no evolution at the level of Being.

The universe we are all aware of, the particular object of human science, is thus not Being itself, but the expression of Being through language. Let us remind ourselves once again that this is the meaning of the famous words in the Bible: 'In the beginning was the Word'. The universe we apprehend was born of the Word, that is to say, quite literally, of language.

This distinction between Being and the universe, that is to say, between Being and language, must not be confused with the distinction drawn by present-day physics (particularly in Unitary Theory) between the Real and the Known. The Known, we must remember, is man's sensory universe; the Real, on the contrary is the universe underlying man's sensory world. But the Real is still a map, and not the territory itself. It is not 'that which is'; it is not Being. The map of the Real put forward by the physicists today is geometrical, but the Universe is not in itself geometry. Tomorrow, the map may perhaps be in musical terms; but this again will not mean that the Universe, as such, 'is' music.

Moreover, as we have already noted, the languages of the Real and the Known differ from one another. The language of the Known is objective: it is based upon the idea of a known object; but the language of the Real is symbolic, for it groups words together so as to form images of situations having no direct connections with the Known. For example, in the language of the Known, an elementary particle is a small 'object'; and this is how a particle ultimately reveals itself to our senses. But in a symbolic language (in particular that of General Relativity), an elementary particle is a certain 'form' of space-time which can be visualised as an image but never corresponds to direct observation by means of the senses.

The map of the Real proposed by physics has certain principal directions, those of extension and duration. This map can show us the symbolic picture of the Universe as a whole. It may be visualised as the surface of a sphere [Fig. 2] where the parallels represent extension in space and the meridians represent duration. In moving along a line of duration, it is evident that extension (which was practically nil at the pole) begins to increase, and reaches it maximum at the equator. After this point, it diminishes to reach practically zero again at the opposite pole.

But it must be noted that that in such a map of the Real there is no genuine evolution; for this map represents the Universe all in one piece: past, present, and future are all part and parcel of one another, and exist simultaneously. But in the ordinary sense of the word, evolution conceives phenomena as appearing at a present moment and then disappearing into the past. As for the future, it is generally admitted that it comes into existence when it becomes present. The map of the Real, however, gives equal validity (that is, the right to be considered as existing) to phenomena that are located at all points of the space-time continuum, whether they be past (in relation to us), present, or still to come. In this map of the Real there is not, properly speaking, any 'becoming': things simply 'are' once and for all. It is our sensory limitations, our inability to apprehend all points in the Real simultaneously, which forces us to take a cross-section through Reality to arrive at the Known, which gives us the illusion of 'becoming'.

Nevertheless, we come back to the idea of change when we move along the axes of duration; so that the Real does allow a certain place to the idea of evolution, but in an attenuated sense that is not the same as the usual idea of evolution.

It seemed important to make quite sure of what our present knowledge of the Universe enables us to discuss with regard to this problem before we go on to treat the problem of evolution more thoroughly. We have seen in effect that Being is not subject to evolution; that the language of the Real (General Relativity and the Unitary Theory) only allows for a very attenuated idea of evolution, from which all notion of becoming is absent; and finally that it is the language of the Known which provides us with the concept of evolution in its ordinary meaning.

The Limitations of Maps

However, if we recall what was said about religion in chapter 6, we shall see that this is not in fact the true position. In the first place, this map represents only the average physical states of the Universe. At any given moment it describes the whole of space in one single physical state which is the average of all local states.

But even this is not the chief reason why this Relativity map does not yield very fruitful results in the field of evolution. What we are looking for is not so much the evolution of the physical states as that of the psychic states of the Universe (taking the work psychic in its widest sense). The physical state at a particular point is described by Relativity in a geometrical (or symbolic) language as the form of space-time at that point. As we shall soon see more clearly, the psychic state at a particular point is, on the contrary, a problem of the links between this point and the other points of space-time. What is needed, therefore, is a topological rather than a geometrical language. However this may be, General Relativity has nothing to say about the evolution of the psychic state of the Universe.

When we come to consider the matter more carefully, does it not become clear that this psychic state is, in fact, the universe itself? If, as we have tried to show, the universe is nothing but Word, it is in effect first and foremost a structure consisting of the links that exist between one set of points and another set of points.

A picture will enable us to draw out this distinction between the physical and the psychic. The map of the Real, giving us the distribution of the average of the physical states of the universe in space and time, is like the sheet of snow covering a mountain. We know that as we come down the mountain (that is, as time passes), the diameter of the snowy surface increases; we also know that the thickness of the snow decreases. These are all problems of form, and once again the answers are averages for any given height on the mountain.

In this picture, the psychic states and their evolution over the span of time will have to be represented quite differently. We should have to imagine that an avalanche of snow-balls was let loose from the top of the mountain. As they came down the mountain, these snow-balls would continually increase in size. Each ball would pick up snow as it went on, which it would then take on down to the foot of the mountain. A re-grouping is therefore taking place: new connections are being made with the masses of snow picked up all down the mountain (through the whole extent of time), resulting in great rolling spheres. To extend our analogy with the Universe, it might be said that the mountain (representing Being) has at its disposal a substance called snow (representing space-time) in order to express itself in forms (or languages). When these forms are spherical (the language of the universal archetypes), then there may come about an increase in dimensions in the snow-forms (that is, an intensification of the connections in space-time) as they roll down the mountain side (that is, as time passes).

This analogy must not, of course, be taken literally. Its only point is to provide us with a symbolic language in which to visualise this evolution of the Universe as a result of a continual increase in the psychic network, the links between points in space-time.

As we saw in chapter 2, matter is already 'united' (through the physical fields) with distant points in space-time; and this is the first way in which the universe shares in evolution, and the first way in which Being expresses itself. But when life arrives, this expression is considerably intensified; for through the mnemonic field on the one hand, and the processes of nutrition and reproduction on the other, there is an increase in the inter-connections between points in space-time, and the universe expressed by Being increases.

Then man comes upon the scene. He is a living being capable of projecting his individual psychism to form a new and lasting entity — society. Society's collective consciousness — the sum-total of all the individual consciousnesses through space and time — then becomes an extraordinary extension of the expression of Being. With the coming of society, the universe itself grows at a speed never attained before. That is why, if the whole of humanity were to disappear, the universe itself would shrink to the small proportions it possessed before the appearance of man, in the same way that the expression of the mountain in terms of balls of snow is reduced when the greater part of them melt away.

Expression of Being

This is an important question; for we have seen to what a degree the answer we can give is closely bound up with the language it has been agreed to use. To stress this point once more: language is not some sort of inert modelling clay that can be plastered over things in order to receive their impress. Language, and the postulates on which it must always rest, is a methodology of the classification of phenomena; and in this sense, every language is a different cross-section of Nature. All languages are in principle acceptable (provided they retain a logical structure); but not all languages represent the same 'cross-section' of phenomena. What is needed is a language that provides the widest and most accurate view of these phenomena.

As we have pointed out at length, this is the language of 'generalisation'. Such a language never contradicts the languages that have preceded it; on the contrary, the change of perspective brought about by it enables us to see things in a wider (and yet more precise) setting and so to reconcile the languages previously available for the description of phenomena. This is how the language of a Unitary Theory reconciles the two languages of General Relativity and Quantum Theory, which represent two opposite theses: the wave or the particle; the continuous or the discontinuous.

There are a number of languages that might be used in an attempt to describe evolution. We could choose a teleological language or a mechanistic one; a language using spiritual terms, or a purely materialistic one; a language speaking of a 'guided' evolution, or one that spoke purely in terms of 'chance'.

Are we to choose a language (such as those of Darwin and Lamarck) that describes the evolution of 'macroscopic' beings, that is to say, 'complete' living creatures? Or is it to be, as with our modern biologists, a 'microscopic' language in which we shall be dealing with the evolution of cells and genes, and considering successive mutations? Or — another possibility — should we consider a language like that of Teilhard de Chardin, in which evolution is described in terms of the elaboration of the elementary corpuscles of physics?

In actual fact, we have not much right to choose between these languages. We must choose the most generalising language possible. How, then, is this language to be found?

It would surely seem logical to draw our inspiration once again from the generalisation of language that has taken place in physics. It is true that this discipline is concerned essentially with matter; but surely the progressive stages towards a generalising language should be repeatable in a similar fashion, whether we are dealing with our knowledge of matter or with our knowledge of life and its evolution.

To make certain of this, and so be able to select a generalising language applicable to evolution, let us try to compare the progress made by the languages of physics and evolution respectively.

At the beginning of the nineteenth century, physics and chemistry both used a 'macroscopic' language for describing nature. For example, there was Dalton's language, according to which the chemical elements are made up of a definite arrangement of different atoms. According to this language, all material bodies are combinations of these quite distinct ninety-two elements. As far as evolution is concerned, this language may be compared with the one that derives all existing beings (in their macroscopic state) from certain forms which preceded them. On this basis, a veritable genealogical tree is built up for each species. This, as we have pointed out, was the language used by Lamarck and Darwin.

But in physics, Dalton's language soon began to broaden out. The elements were seen to be in reality made up of elementary corpuscles, notably protons, neutrons, and electrons. The language then became 'microscopic'; the various physical and chemical properties of matter were to be explained in terms of the various ways in which all these corpuscles were put together, and of their movements. This language usually leads on into mechanistic theories in which everything is explained in terms of reactions between corpuscles.

It looks very much as if this stage of progress corresponds to the language of the present-day biologists, at least those who look at evolution in the most 'advanced' light (for many scientific researchers in this field still seem to confine themselves to the 'macroscopic' language of Darwin and Lamarck). Evolution is then essentially mechanistic, and the 'microscopic' elements upon which the theories of evolution are based are those of the cells — genes, mitochondria, DNA, etc. The broad principles prevalent in those mechanistic theories are in this case very like those of cybernetics. According to this language, evolution takes place in such a way that structures are continually increasing their efficacy with regard to the external environment. The same principles of action and reaction, or of 'least action', which guided the mechanistic physicists in their discovery of the laws of nature, recur once again in the mechanistic language of evolution.

What is the next state in the process of language? To find an answer, let us turn once more to physics, where this stage has been largely completed. The discontinuous mechanistic ideas of objects and corpuscles have been replaced by the continuous idea of a field. Whereas the mechanistic language used to talk in terms of objects well and truly located in space and time, the field language replaces the object by the mathematical point (whence a greater accuracy of description), and is concerned with the connections between this point and the whole of space-time (whence a greater breadth of description). This is the path proposed by generalisation; for more than half a century it has been the language of physics, which speaks of electromagnetic fields, gravitational fields, and nuclear fields.

Everything would seem to show that this field language is likely to provide the next step forwards in the language of biology, in particular for the description of biological creatures. In chapter 4, we gave an example of such a language when we introduced the mnemonic field. We showed that in spite of its name, it could be physically and mathematically defined with the same accuracy as prevails among the sciences of so-called inanimate matter. It seemed at this point that a language of this kind, introducing the field concept (that is, the connections between any point and the whole of space-time) was necessary to express the characteristics of so-called 'living' creatures.

Before leaving this problem of the language applicable to evolution, it would seem desirable also to glance at the stage that comes after the field stage; for this next advance is already taking place in physics with the coming of General Relativity and Unitary Theories. Here, everything is no longer described in terms of fields, but as forms of one single substance, space-time. In chapter 4, we pointed out that the same advance would have to take place in the description of life. The single substance remains space-time (since life also is composed of matter); but the form at any given point is no longer adequate for purposes of description: we must now provide 'the form of forms', that is to say, the general structure obtained by the juxtaposition of these forms in relation to one another in accordance with a definite scheme. The language required for this will be topological, and not just geometrical. For example, the famous Möbius strip, which has only one surface, cannot be described in purely geometrical language: recourse must be had to a topological language.

At this point, we will leave the study of the language appropriate for describing the evolution of the universe (and particularly its psychic evolution). However, we may note for future reference that it would perhaps be over-hasty to expect from now on to talk about this evolution in purely topological language; but it would also seem true that the purely mechanistic and corpuscular language has in fact been superseded when we consider our present-day knowledge in other departments (and notably in physics). We shall accordingly attempt to describe evolution essentially in terms of fields. We shall then note that in order to tackle the problem of living structures (and not simply the evolution of life) at a deeper level, it would seem unavoidable to use a topological language. Let us reiterate that such novel languages are not intended to invalidate, or even to modify, what the old languages have told us: the intention is to move towards generalisation, that is to say, towards a language that will give greater precision and breadth to these old languages, and eventually reconcile them with one another. As we shall see in a moment, once the language of fields has been accepted, there is no longer any reason for opposing the material and the psychic; and once the topological language has been adopted, there is no reason to put the living structure in opposition to the inanimate structure, or man to the animal. We shall go on to study these two important points in succession.

Fields

To make this point clearer, it will be enough to recall what we have already dwelt upon at length in previous chapters. Taken in its simplest form of elementary corpuscle, matter can no longer be defined by modern physics as having an individuality separable from the cosmos. It is a field co-extensive with the universe, this field simply being more intense in the region where the corpuscular aspect of matter is most strongly apparent. In this sense, one can see two elements that are characteristic of matter: the place where there is an intensified field (what is usually called 'matter'); and the connections of this matter with the whole of space-time through nuclear, gravitational, and electromagnetic fields.

The problem of life should be approached in precisely the same way; for life is also composed of matter, and can therefore never be understood apart from space-time by treating it simply in its individual aspect. The living being is also co-extensive with the whole of space-time. It displays the same two characteristic elements as matter: around a 'particle' structure (which naturally differs from that of inanimate matter) there is a field by which the living being is linked to the entire cosmos.

In other words, the equivalent in matter of the psychic element in the living being is constituted by the links between this matter and the whole of space-time effected by the physical fields. But this 'material' psychism is made up of very weak connections; and the great quality of the living structure is to be able considerably to increase this union between the One and the All. With man, this union reaches a climax. The growth of psychic power is therefore equivalent to an increasing union between the One and the All. It will be seen that there is no longer any discontinuity here between matter and mind; even at the level of matter, there is a certain psychic element. This is what Teilhard de Chardin (who had a clear insight into this continuity between matter and man) calls the 'inside' of things, meaning thereby the less obvious part of things, since our sensory apprehension of the universe tends to make us see only the 'outside' of things, that is, their corpuscular and individual aspects. We shall later come back to this evolution of the universe leading to a constantly growing interconnection between the creature and space-time, which shows itself in the form of fields.

First, I should like to show how the topological language disposes both of the gulf that appears to separate matter (which does not 'know') from life (which does), and of the apparent gulf between the latter and man (who 'knows that he knows').

This vast problem can be approached in a mechanistic language, in which case the reasoning will be roughly as follows. The whole matter will be viewed as one of increasing complication of structure. At a certain level of complexity, there will be a 'threshold', and radically different properties will make their appearance. The case will be rather like that of a television set under construction: resistances, capacitors, wires, tubes, etc. must all be put together, and nothing will appear on the screen until the last little connection has been completed when — lo and behold! — the televised picture appears.

This language may be accepted as a first approximation. [We have incidentally made use of it in comparing the 'mechanism' of a living structure with that of a crystalline structure in chapter 4. — JC] But what seems very awkward in this way of looking at phenomena is that the mechanistic language allows us to describe only structures which 'do something' new but which 'are not' anything new. Now, one cannot help thinking that there is a difference of state (and not merely of action) between the creature who 'knows' and the one who 'knows that he knows' (or between matter which 'does not know' and life which 'knows').

This is the point where topological language comes to our aid, for it is really able to express this change of state. The analogy of the Möbius strip is a particularly striking illustration of this point.

Such a band can easily be constructed (See Fig. 4). . Cut out a long strip of paper. First stick the two ends together so as to form a kind of crown. What you then have is a cylindrical surface. The characteristic state of this surface (as of all ordinary surfaces) is to have two distinct sides, an inside and an outside. One might, for example, paint one side blue and the other red, without there being any connection between the blue and the red.

Now let us re-cut our strip of paper and re-stick its two ends, but with the red face against the other blue face: by so doing, we have made a Möbius strip. The figure now has a surface 'state' quite different from its normal state, for the surface of the Möbius strip has only one side. The linking of the red with the blue has radically changed the topology of the strip of paper.

This is no doubt only a very rough analogy; but in the first place it brings out clearly the sense in which we must try to visualise the change of state that takes place when evolution makes the sudden transition from the structure which 'knows' to the structure which 'knows that it knows'. Moreover, we shall see in a moment that this may well be more than a mere analogy when we come to examine the topology of the space occupied by a living cell.

Why is this topological language far superior to the mechanistic language for describing this phenomenon? According to the latter, there is supposed to be some mechanism which creates (for example) the human consciousness (making man able to 'know that he knows'). But if this mechanism exists, it must be localised somewhere in the human body. Where is it? A man remains conscious even if his arms and legs are cut off, and even if part of his trunk is removed. This would suggest that the machinery of consciousness is in the head. But where? It has been thoroughly proved by experiment that a large part of the cortex can be removed without a man ceasing to be conscious, that is, ceasing to be human. Moreover, there does not appear to be any particular part of the brain whose destruction removes consciousness. So the mechanical analogy with the television set (or, more generally, with the cybernetic machine) in support of consciousness loses its validity. For we have only to remove a single part of one of these mechanisms, and the whole affair ceases to function. In the case of consciousness it is clear that we are not dealing with a particular mechanism so much as with a particular form. In the Möbius strip — unlike the mechanisms mentioned above — one can also cut out parts of the whole (as you can with the cortex) without depriving it of its characteristic state of possessing only one side. So the language of topology is the appropriate one to use for this kind of description. This is the language which will make it possible to express the abrupt changes of 'state', the thresholds between the conscious human structure, the living structure, and the material structure.

Space-time and Topology

In order to enlarge upon this most important question, we shall remind ourselves of certain results in geometry and topology. These facts are generally familiar to physicists and mathematicians (particularly those concerned with General Relativity); but we shall see that they are here of special concern to the biologists, since it is a molecule of DNA that will serve as an example (and a fundamental case) of the considerations that follow.

Our purpose in putting forward the topological language for biology is to develop language as a tool of research, perfecting it just as the geometrical language of General Relativity perfected the field language previously used in physics; there is no intention of reverting in any way to the corpuscular (and therefore mechanistic) language used at an earlier stage than the field language.

What does all this amount to? The field language is already a great advance over the corpuscular language; for the latter was concerned with the motions and reactions of objects with finite dimensions (corpuscles) in space and time, whereas the field language describes properties which come into being in a space-time framework at every mathematical point, whose dimensions are zero by definition. The field, expressed as the solution of continuous differential equations, does in fact give the connections between a (mathematical) point and the points round about it. There has thus been some further deepening of our knowledge of phenomena through this choice of a language with a finer edge, able to describe each point instead of each corpuscle. But in the field language, the field is always something superimposed on space-time. The next stage will be to reduce everything to one single substance — space-time itself — the physical properties at any given point being reduced to the form of space-time at that point. This brings us back to General Relativity and its geometrical language. Everything is expressed as curvatures (and directions) of space-time at any particular point. This geometrical language has not only resulted in a greater unity (one single basic concept — space-time), but has produced a description now equally independent of the observer (which was not true of the field language).

But here is the essential point. If the material masses (e.g. molecules) are arranged in a 'curved' space-time, an observer outside the curved zone will see these masses as arranged geometrically in relation to one another along a line that is likewise curved; but this is only a secondary effect, in the sense that it is not because the masses are arranged in space along a curved line that space-time is also curved.

This may seem obvious enough; let us nevertheless give an example to illustrate it, for we shall later on see the importance of these remarks.

Everyone knows that light rays passing near the Sun are bent towards it. Why is this? Well, it is a direct result of General Relativity. The enormous mass of the Sun bends space-time around itself, and this space-time is no longer Euclidean. The light rays follow a 'straight line' in this new space, but as the latter is curved, the light rays are curved too. Let us take particular note of this capacity of electromagnetic radiation to follow the curvature of space, for we shall shortly return to it.

It would be possible (at least in theory) to arrange material masses along the curved trajectory of the light rays, in order to give it material substance. Then an observer on Earth would have a continual view of this curved trajectory (L) in the neighbourhood of the Sun.

Now, let us in thought get rid of the Sun, but let us once more arrange the curved material trajectory L in the same place as before. An observer on Earth would still see the curve L, but he would not be at liberty to deduce from it that space-time was curved along this path; and since we have 'removed' the Sun, space-time would not in fact be curved along L.

What is the moral of all this? It means that we must be particularly careful when using the geometrical language of General Relativity. This geometry refers to space-time, and as soon as one introduces into one's language the notion of corpuscles, one is in fact mixing two languages (something we have learnt to beware of); and we can no longer deduce the geometrical qualities of space-time from the geometrical arrangement of the corpuscles with regard to each other. On the other hand, we can deduce from the geometrical qualities of space-time how a chain of corpuscles would appear to us if they were arranged in a 'straight line' in this curved space-time. We have likewise learnt that electromagnetic radiation always follows the form of space-time.

Having made this clear, let us try to visualise Euclidean space-time in the geometrical language of General Relativity. Such a space is not curved: this would be the case with a space devoid of all energy, and true for practical purposes of a space containing only a small amount of energy. In particular, a space occupied by a molecular chain can be considered in terms of General Relativity as practically Euclidean.

To represent such a space it is convenient to take, for instance, a flat sheet of paper divided into millimetre squares. Each little square millimetre of this paper has the same dimensions; and this represents Euclidean space, whose properties are the same throughout. If we try to wrap this sheet of paper around a sphere, we shall not succeed without distorting it — in which case the little squares on our paper will no longer all have the same dimensions. This is a consequence of the fact that the sphere has a curved surface.

But whenever it is possible to apply our sheet of paper to a surface S, without distorting the squares, we can affirm that this surface S is Euclidean, that is to say, not curved. (Mathematicians would add that S is a 'ruled' surface, because a straight ruler can be laid across it at any point.)

We have just seen that a plane surface is such a Euclidean surface, S. We must now go on to ask ourselves: Can there be other surfaces S which are Euclidean, although not plane?

We can see at once that there are such surfaces. A cylinder is one, for example; for we can make a cylinder out of our sheet of paper without distorting the squares. Thus the surface of a cylinder is still Euclidean, and not curved, in the sense of General Relativity. The Möbius strip in Fig. 4 is another Euclidean surface S; for there too the band could be made of squared paper without distorting the squares.

But then comes the interesting point. If a two-dimensional observer found himself in a two-dimensional space represented by the surface S, he would in each case (if he knew the theory of General Relativity) affirm that his space was Euclidean, whether it be in the form of a plane, a cylinder, or a Möbius strip. Thus the language of General Relativity is insufficient for a complete description of these different spaces S, and we must have recourse to a topological language, and say that these spaces are topologically different, though all are Euclidean: one is a plane, another cylindrical, and the third shaped like a Möbius strip. Let us also note that for an outside observer electromagnetic radiation, which always follows the form of space, would describe different trajectories according to the particular topology.

We have now reached a crucial point in our argument. We have seen that a space which is devoid of energy, or contains only a minimum of energy, is practically Euclidean; but we have also seen that, without losing its Euclidean character, it may also take on varying topologies.

Our ordinary space, in which matter is situated, would appear to be practically a Euclidean plane. Certain 'links' can develop in this space; but it is to be observed that other links remain impossible: for example, a point cannot be linked with itself by means of a straight line. Without bringing in energy (that is to say, while still remaining in Euclidean space), one could imagine matter now disposed in a cylindrical Euclidean space. It is now possible to link up a point with itself by means of a circular line around a section of the cylinder. This circular line is the equivalent of a straight line (the shortest distance) in plane topology. But we must observe that there are still two sides to the surface of a cylinder, and as these do not communicate with one another, no links can be made between the two faces. We then go on — still without importing any energy — to Euclidean topology as represented by the Möbius strip, where the surface consists of a single side; and we have then 'intensified' the possibilities of interconnection.

Moreover, it is perfectly conceivable that space might possess a plane Euclidean geometry in the region occupied by an observer (a man, for example), but in other small regions under observation by this man (a molecular chain of DNA, for instance), space may — for a predetermined reason — be still Euclidean, but have a cylindrical or Möbius strip topology.

Space-time and Biology

In the first place, if material elements (a chain of molecules, for example) were arranged in a space whose local topology was cylindrical, an external observer would see this chain of molecules as an open-ended spiral (which could in the limiting case be reduced to a circle). If this molecular chain were arranged in a Euclidean space with a Möbius strip topology, an external observer would see this chain as a double spiral closed in on itself at the ends. Let us remind ourselves that this curious topology is in fact precisely what has been discovered for the molecular chain of DNA, the structure which is associated with everything that is alive.

On the other hand, if some electromagnetic radiation were to penetrate a Euclidean space of cylindrical topology, it would be as it were 'imprisoned' in this space, since light rays are bound to follow the form of the surface. The same phenomenon would take place even more clearly in a Euclidean topology of the Möbius strip type.

These different consequences flowing from possible modifications in a Euclidean space-time would seem to have considerable repercussions for biology.

For example, let us take the molecular chain of DNA, in which the characteristics of life seem to appear. In chapter 4, we pointed out that the information necessary for life appeared to be storable only in electromagnetic form in the space occupied by the living structure. In the topological language we have just been developing, it is possible to see how that might be so in a space which, though still Euclidean (as General Relativity requires, since a molecule of DNA would not represent a sufficient density of energy to make the space non-Euclidean) nevertheless possessed a cylindrical or Möbius strip topology. We should then likewise understand why we see this molecular chain in the strange form of a double spiral. The problem of creating life 'synthetically' would not, in this case, be reduced simply by producing the molecular chain of DNA in our ordinary Euclidean space (with its plane topology); we should also have to know how to transform the spatial region occupied by the DNA molecule so as to give it its correct topology, the topology with the characteristics necessary for producing life.

Of course, all this needs a great deal of further study. On the one hand, we have broached this aspect of the subject in order to make clear how topological language must be applied. In the first place, it is applicable to space-time, rather than to the mutual topological arrangement of corpuscles, which is only a secondary (though important) aspect. On the other hand, we have been concerned to show the power of language as an instrument of research. I am convinced that the biologists most likely to penetrate furthest into the secrets of life or of the human psyche will be those who take advantage of the progress made by language in physics (particularly by the use of a topological language). They too will base their researches — as in physics — on the possible forms of the single substance constituted by space-time.

Evolution of "the Word"

This description will bring into relief three main stages (we could almost call them three acts). First, Being expresses itself through matter; then through matter and life; then through matter, life, and man. We shall see at the end that a fourth 'act' is probably in course of preparation which will superimpose humanity upon the three forms of Being we have just mentioned.

Present-day physical (and more especially cosmological) theories tell us that when time began everything was at an extremely high temperature (about a million million degrees) and occupied an extremely small volume. Certain modern cosmologists even think that this volume was as small as a single elementary particle (about a millionth of a millionth of a millimetre). As we pointed out in chapter 2, there can have been no material structure at this temperature: everything was simply radiation. And in fact everything was then in a state of chaos: there was as yet no differentiation.

But this state of extremely small dimensions at the beginning of time was destined to undergo rapid change. Physics tells us that even at this early stage, expansion was taking place at the velocity of light. This expansion was to be accompanied by very rapid cooling, which enabled structures to come into being; and it was then that matter was born in the shape of the first elementary corpuscles.

As soon as matter appeared, chaos disappeared; for matter is nothing else but the convergence of the physical fields that are at present known to us — the gravitational, the electromagnetic, and the nuclear. A certain ordering of space-time therefore came into operation immediately. Matter was able to classify physical information reaching it (in the form of fields) from the outside world by reacting to this information in a variety of ways.

It can also be said that with matter there came the Word, that is, the expression of Being, of the undifferentiated; in fact, the universe itself was being born at the same time as matter. It is thus possible to see the immediate emergence, at the very beginning of time, of the characteristics that would go on developing throughout the course of evolution. There is the appearance of interlinking in space-time through the elaboration of structures which are both points of convergence and points of projection for these links; for matter is both the meeting-point and the 'generator' of these physical fields.

From the moment of the appearance of pure matter, the universe could already express itself in a language; but this language was confined to actions, and in practice to motion and physico-chemical reactions.

It is important to be clear that the elementary material particle which made this first language possible was already possessed of a complex and organised structure as compared with primitive and unorganised chaos. There was already a particular topological structure at work, making possible this first transition from chaos to a primitive universe. It is perhaps permissible to claim that this structure was the work of chance; for chance certainly can, just for a moment, produce an organised figure, rather in the same way that a kaleidoscope produces artistic figures. But the fact remains that if this chance figure should persist over the course of time, this would mean that it followed an evolution whose direction was already marked out in the body of Being.

At this point we will resume our picture of the mountain (representing Being), covered with a layer of snow representing the substance that allows it to express itself (space-time). The universe is set in motion like an avalanche of snow let loose from the top of the mountain. All forms of snow-heap are possible, but the only ones to continue in existence and so increase in size as they come down the mountain are those which are spherical in form. This spherical form, and the property it possesses of leading to an increase in dimensions, are due simply to the lie of the land, the 'slope' of the mountain-side corresponding to the evolutionary directions marked out in Being.

This is the sense in which we must understand the structure (or topological form) of the elementary particles, and of matter in general, to be already in some sort a 'creation' of Being, for these structures (which may have been assembled by chance) could not have survived unless they had been in accordance with a 'design' on the part of Being — unless they had been the Word accepted by Being as the expression (or language) to be adopted for the evolution of the universe. And so evolution, a continual blend of chance and non-chance, could run counter to Being only for temporary interludes. In the long run, all roads lead down to the bottom of the evolutionary mountain.

Convergence

We shall pass over the building up of all these material systems, since this is not the heart of our subject. For as all these structures come into being, the interconnections between the points of space-time continue to increase, but the 'state' of pure matter continues to be the same. All these structures, whether microscopic or macroscopic, are only centres of convergence for physical fields; and their only 'language' is that of interactions (motion and reactions).

Nevertheless, from this stage onwards, there are signs of attempts on the part of matter to effect a change of 'state'. Here too we shall not discuss whether or not these attempts are the work of chance. Let us repeat that they may be the result of chance; but only the 'successful' attempts (corresponding, that is, to the evolutionary direction in Being), will survive over the course of time and so continue to develop with rapidity. For a change of 'state' to be successfully attempted, everything we have seen so far suggests that it must consist of an abrupt intensification of the field-links between the points of space-time — although, as we have previously explained, these were no doubt already on the increase in the material structures.

For example, an atom, which is very sensitive to electromagnetic radiation, is more closely linked with the cosmos than is a single neutron. But these increases in 'union' can take place only through matter as a result of certain types of liaison — those which come about through physical fields. For instance, it was impossible for matter alone, without any change of state, to be united with its own past, after the fashion of memory. And yet, without the slightest doubt, these links with the past represent an intensification of the connections within space-time; and if they could once be established, they ought therefore to 'be successful'. But in order to carry through these new connections, and in order to align space-time along the axis of the past, it was necessary for a change to occur in the state of matter for life to come on the scene.

Topological Language and Life

First let us make it quite clear in what sense this topological change of structure must be understood as making possible interconnections which had hitherto not been possible.

For this purpose, let us go back to the Möbius strip. We will first consider a simple paper band stuck together at the sends so as to form a kind of crown, part of a cylinder. Then we can paint one of the faces (say, the 'inside' of the loop) blue, and the other side red. We could go on to construct deeper or shallower bands on this cylindrical model, which could therefore present larger or smaller blue or red surfaces. In our analogy, that would mean that the structure would be more or less linked up with the cosmos through the physical fields (and through these only). But without changing the topology (that is to say, as long as the cylindrical form is preserved), it will never be possible to establish communication between the blue and the red. This kind of interlinking remains impossible.

Next, we construct the Möbius strip topology by cutting through the cylindrical band and twisting one end, so as to link red and blue. It is very simple, and easily done; but it brings about a fundamental difference, for we have now passed from a surface with two sides (a cylinder) to a surface with only a single side (the Möbius strip), and there has been a real change of state, which can be described only in topological language. The 'form' has not been altered (since there is still in both cases a ruled surface), but the 'form' of the 'form' has been modified. Analogically, the Möbius strip is to the cylinder what the living structure is to the material structure. The modification of 'state', due to the topological modification, makes possible connections which were impossible in the previous state, however perfectly the mechanism of interconnections was developed. So life is never a mere extension of matter: it is always something different. There is a real threshold: an object is never 'half-alive'; it is either not alive (that is to say, matter pure and simple); or it is alive: there are no intermediate stages.

What, then, are the essentials of the new properties of life?

We have tried to study this difficult question in the chapter on biology. Whilst matter was a simple convergence of the physical fields, life was destined to be a structure whose organisation made possible the storage of information through the physical fields within its own structure. Thus there came into being a kind of 'memorising' of the intersections between matter and the physical fields. Whereas matter is simply a convergence of the physical fields, the living is also a convergence of the interactions experienced by matter all down the course of time. And so language takes on new dimensions: it is no longer simply made up of interactions, as in the case of matter; it is also compounded of the memory of these interactions. Language has in fact become mnemonic.

This linking of the living structure with the past through memory can also be described in terms of fields. That is why we have given the name of menemonic field to this special structure of space-time within the living element. It is a remarkable fact that our knowledge of space-time shows us that this mnemonic field is also propagated at the speed of light, c, which means that the 'present moment' of the living element is propagated through space-time at this same velocity c.

Matter, as we have already noted, is not only a convergence of the physical fields, but also a 'production- and projection-centre' for these fields. Through nutrition and reproduction, life is also enabled to extend its links through the mnemonic field in the same way as matter. As a convergence-centre for its own field of memory, life also becomes a meeting-point for the other fields characteristic of life, through the nutrition of the living structure. And finally, by means of reproduction, it becomes a projection-centre for the mnemonic field in space and time. Thus life is able to cover space-time with these new unions; and simultaneously, the expression of Being is enlarged through this new language.

It looks then as though Nature tries all possible forms of living structure with the aid of the new mnemonic field at the disposal of evolution — perhaps somewhat by chance, but by a chance once again supervised by Being. That is to say that evolution will give lasting power only to the living creatures or groups which intensify the interconnections between the points of space-time, making full use of all the possibilities of the mnemonic field.

The mnemonic field supplies life with all the information that has been 'memorised', sorting it, no doubt, but not systematically arranging it, and without relating the different items to one another. As a rule, life makes spontaneous (instinctive) use of the particular information that enables it to act as efficaciously as possible (not forgetting the long ancestral memory stretching through space and time). But it is not able to fit in all these pieces of memorised information with one another, which means more particularly that it is not able to perform abstractions. At the vegetable or animal stage, life cannot therefore build up a real language, enabling it to compare the various pieces of information it has memorised. Evolution so far lacks the power to express itself more broadly by being able to take 'cross-sections' of the mnemonic field of life and bring these cross-sections together in a single structure; it lacks a new topological transformation of the structure of life, a change of state in life, leading to an intensification of the connections of space-time. At this point man, who has been slowly prepared first by matter and then by life, suddenly comes upon the scene.

Discontinuity

It is because what distinguishes man from the animal or vegetable can be expressed only in terms of form that it is impossible to localise in the human body any precise point where the typical human consciousness is situated. This is also the reason why there cannot be any consciousness without the underlying support of matter, since no form can exist without a substance to which the form refers. [My italics. — Ed.]

With man, there comes into existence the supreme property of life, namely the power to make cross-sections of its mnemonic field, the power to arrange phenomena with respect to one another in these cross-sections, the ability to link up these phenomena with those of neighbouring cross-sections, the capacity to compare these cross-sections with those made by other men or by society. Such possibilities mean the birth of consciousness: man can as it were step back from himself and from things. Not only does he exist, but he can be aware of his existence. Then, by means of human language, a new universe, never hitherto expressed, comes into existence. Henceforward man can not only store knowledge within himself: he can also hand it on to society and, in turn, gather in knowledge from society. Transforming information into human knowledge, he can make it possible for successive generations to add their reflections and experiences together, thus building up this tremendous structure that unites man with the cosmos, supported by the three great pillars of science, art, and religion.

Human knowledge is linked to the universe through the convergence of the cosmos upon man. But, as we have already seen in surveying the earlier stages of evolution, man can also be united with the whole by projection towards the external world. This human capacity, the complement of knowledge, is the capacity to love, taking the word in its most general sense. Not only does it cover charity, affection, sexual love, and friendship, but also scientific or artistic creation — in fact, everything that enables us to give the best of ourselves to others.

We have adopted the field language in order to describe this evolution; and knowledge and love also form connections that are none the less real for being materially invisible. It would therefore seem appropriate to give the name of 'psychic field' to man's capacity to unite himself with the cosmos through knowledge and love. This field is propagated essentially by means of thought, language, and human action. It is another means of expression for Being, a means which has succeeded in giving the universe dimensions out of all proportion to those given it by life before the appearance of man.

As our thoughts run in this fashion on the phenomenon of man in evolution, it needs to be made abundantly clear to all that we are not considering this phenomenon as something limited to our planet, Earth. The whole of physics and astronomy, our whole contemporary knowledge of the world, go to prove that the universe is evolving visibly in the same way in all its regions; and that at any given moment in the course or time, the whole extent of space is seen to be filled with the same phenomena (in terms, or course, of averages). Would anyone who has seen the wide extent of the physical fields that characterise matter throughout the whole universe seriously dare to maintain that the mnemonic field of life or the psychic human field cover only the minute portion of the cosmos in which our own physical existence is lived out? The phenomenon of man and the phenomenon of life (as well as the phenomenon of matter) are means of expression developed by Being in parallel fashion in all the regions of space-time. Man should no more feel himself solitary when face to face with infinite space than a star would feel isolated if it were endowed with the power to scan our skies on a clear summer night. There can be no doubt that the final goal of evolution is to project the radiation of the psychic field belonging to each humanity that occupies a planet across all the interstellar spaces in order to weave a united web of knowledge and love, of such fine texture that in the end the expression of Being will be merged in Being itself.

The Ultimate End?

If evolution as we see it at work on our planet had in the course of the ages confronted us with structures corresponding to a progressive and regular intensification of the inter-connections of space-time, we should certainly have no reason to deny that there might well be, at this present moment, creatures on other planets whose psychic make-up is immeasurably superior to that of man. But as we observe evolution at work, we must once again take note that it does not operate in this manner. Continual variations in these space-time connections can be observed when one considers structures corresponding to the same state and the same topological form — continual variations in the material structures as well as in those of life. Nevertheless, the essential stages of evolution do not consist of these continual variations, but in the crossing of thresholds, where there suddenly appear much more important intensifications of these links.

We have taken note of a first threshold between primitive chaos and matter; then another between matter and life; and finally a third between life and man. We have seen that the crossing of these thresholds is brought about by modifications of structure which can be described only in topological language.

In observing all Nature's efforts to cross these thresholds, we see that she multiplies species, she launches out in all possible directions: and then, suddenly, one attempt succeeds and crosses the threshold. But the uniqueness of this success shows that this forward leap was in correspondence with the evolutionary direction marked out in Being. If this were not the case, there would be a whole series of attempts which would persist, and not this one single successful line from chaos to matter, from matter to life, and from life to man.

In that case — and because Being is also one for the whole universe — it is difficult to avoid the conclusion that the same line runs through all the regions of the cosmos. This has already been proved for the initial transition from chaos to matter, since matter is already seen to be broadcast throughout the whole universe. Why should not this also be true for the next stages? Why should we not expect to find life and, likewise, man — or his psychic counterpart — in all regions of the cosmos?

But let us be quite clear on this point. This does not mean that life as we might find it on other planets will be in all cases like what we know upon Earth, and that there will be dogs, cats, elephants, etc. It is certain that life must in the first instance possess certain characteristics enabling it to adapt itself to the planet where it has developed. In a methane atmosphere, for instance, the same living structures could not be developed as in an atmosphere consisting of air. Again — to look at the question more simply — we find that on our planet fish differ from the land-animals. The same might well be true of a being representing the human stage on another planet who might physically and biologically be utterly different from man on Earth, for he would in the first place have to be adapted to the planet on which he had developed. Nevertheless, the essential qualities distinguishing him from simpler forms of life would consist of a psychism very close to that of man on Earth, for he too would correspond to the third basic stage of evolution according to the pattern of matter, life, and man. In a whole number of aspects, and in the same manner, matter presents the same fields (gravitational, electromagnetic, and nuclear) throughout the universe; life, in a whole number of aspects, presents the same characteristic mnemonic field throughout the universe; humanity, in a whole number of aspects, presents the same characteristic psychic field throughout the universe. For these reasons, it sems highly probable that communication will be possible between these various 'humanities', for they will have at their disposal one and the same psychic language. Moreover, how could one think of evolution as a continual intensification of the links in space-time unless this were necessarily so, unless it were possible that at a certain moment genuine links could be established between all the human races of the cosmos?

Convergence of Diversity

This is not a question of an anthropocentric outlook: it is simply a matter of seeing how evolution proceeds — evolution with an experience extending over millions of years — and then of drawing our conclusions as objectively as possible. We are not just 'imagining': we are trying to see.

Well, what does evolution show us? It would seem that in step with the big evolutionary change, there takes place continuously what might be called 'a convergence of diversity'. Original chaos was nothing but undifferentiated radiation, and so could be considered capable of taking on an infinite number of aspects, which were all potentially present. Matter may, as we know, take on a multitude of aspects: but they are certainly not infinite in number. Life as we see it on Earth is spread abroad in many species; but we can count these species — they are not more than a few hundred thousand. At the human stage, we see diverse varieties of individual, distinguishable in particular by the colour of the skin, stature, hair, etc.; but there is a broad similarity. It looks as though Nature, in proportion as she makes a new evolutionary advance, is obliged to restrict the number of aspects she can give to the entities she produces — rather as though the work of creation was becoming more and more difficult and the growing complexity justified only certain aspects which became steadily smaller in number, thus making it possible to give the new creation the properties needed for the threshold that this stage in evolution had just crossed. It was not a priori impossible for the psychic characteristics of man to have appeared simultaneously in man and in some completely different living species — for example, in a bird or a fish. But we know that nothing of the kind has occurred. True, it is conceivable that these experiments of Nature took place in the remote past, and that man has destroyed the psychic beings who were not like himself; but our present-day palaeontologists, whose observations go back over millions of years, would give the lie to this supposition. Never, they would maintain, has any other being except an individual more or less resembling present-day man left any traces of psychism, such as burial of the dead, the use of fire, the making of tools, etc. There is therefore nothing leading us to believe that the psychic stage represented on Earth by man can have come about in any other region of the universe in forms that are very different from those given by Nature to man upon Earth. The 'convergence of diversity' appears to be a broad evolutionary law and, as such, applicable to the whole cosmos.

There is another problem, quite as important as the preceding one, if not even more so. What is there to show that it will be man as we know him today that will still, in hundreds of millions of years, be the centre of evolution? If evolution has already produced three thresholds (chaos-matter; matter-life; life-man), why should not this crossing of thresholds be continued, and evolution lead on to 'ultra-psychic' beings who will be to present-day man what we are to the animals?

As we shall try to explain, this is both true and false.

From Man to Humanity

Let us carefully observe and note the following facts. Matter did not disappear with the coming of life; indeed, life was built up from the elements of matter, for there is no life without matter. Man, in his turn, did not bring about the disappearance of life; rather his body is built up of living cells, and there can be no man without the kingdom of life to support him.

There can be no doubt that evolution will continue along the same broad lines. The human stage will not disappear with the creation of a new organism constituting a new evolutionary threshold (if this threshold is indeed to come). Rather must we once more affirm that this new organism will of necessity be composed of individual men, precisely as man is necessarily composed of living cells, and the living cell of material particles.

In that case, and if a new stage is to come about through a change of state in evolution, we know that man will figure in it and will even occupy a central position. There will be no super-man without man. In the ultimate analysis, as we have already glimpsed in the preceding chapters, if there is to be a new stage in evolution, this cannot come about by the appearance of an individual who is ultra-psychic as compared with man. This new stage can consist only of a society composed of men, what we have called a new humanity — first a new humanity on Earth, then a larger humanity as links are established with other inhabited worlds.

If there is to be a change of state, a new evolutionary threshold, a topological change which will mean that evolution sails into new seas, when will this take place? This is a point we can scarcely decide; but there is every reason to believe that a united earthly humanity will already be on the way to that 'noosphere' glimpsed by Teilhard de Chardin, a noosphere which could no doubt be considered as already constituting a new stage in evolution.

Does this mean that man will remain static to eternity, that he will remain unchanged in a universe that has crossed new evolutionary thresholds?

Not at all. Here again, we have only to look at the methods of evolution to convince ourselves. For the element belonging to an organised whole does in fact adapt its own characteristics to the final end expressed by this whole. [This has been particularly well brought out by the French biologist H Laborit. See, for example, Du Soleil à l'Homme, Masson, Paris, 1963. — JC] To explain this point a little further: the living cell is made up of material particles; but these particles, by the very fact that they are part of a whole which embodies a change of state as compared with simple matter, possess characteristics that differentiate them from matter pure and simple; and in fact, each of these particles is no longer really matter, for it has become alive. This change of characteristics is due, not to the links (that is, the fields) it can draw upon in the living structure, for these remain the same — the gravitational, the electromagnetic, and the nuclear. The change arises from the fact that these particles are now part of a different topological whole, and that the purpose (and so the characteristics of the whole) has repercussions upon all the elements that go to its making. Take, for instance, a bacterium. It is made up of elementary particles which must be considered to be alive as long as they form part of the bacterium; but remove a part of this bacterium, and you will be confronted with nothing more than a mass of matter which, being separated from the living whole, can no longer be considered alive.

The same observations may be made if one considers the living cell in relation to man. The human ensemble is a topological variety which differs from what is merely alive. For this reason, the characteristics of a living human cell are different from those of lower forms of life as long as they are part of the human whole. A cell of the cortex is not simply a living cell; it is a cell endowed with psychic characteristics as long as it forms an integral part of the human cortex. But if you remove this cell and separate it from the human ensemble, you will simply have a living cell without any psychic characteristics.

This machinery by which evolution operates is therefore extremely important. There can be no doubt that it will continue in the future, since it can be seen to have been at work over thousands of millions of years — over the whole journey from matter to man. What does this mean? Simply that the human element, when it forms part of a humanity representing a real change of state, a new threshold in evolution, will itself be modified in its characteristics. If humanity as a whole is endowed with ultra-psychic characteristics, the individual man, as long as he forms part of this humanity, can likewise be considered as endowed with ultra-psychic characteristics. But if separated from this humanity, he would once more be nothing but a man such as we know today.

We can already descry the broad lines of this transformation in the contemporary world when man as an individual compares his personal knowledge with the wisdom of society. Each person's knowledge, when closely associated with society's whole body of wisdom, is out of all proportion to that of a single man divorced from society as a whole. In the humanity of the future, the three great pillars of knowledge — science, art, and religion — will work harmoniously together, and each will be complementary to the others. Then it will be by no means impossible for the human element to find itself raised to a psychic level that represents a new threshold as compared with the level of life today.

And so evolution shows us the extraordinary and marvellous phenomenon of being able to confer on each element the progress attained on the scale of the whole. In the humanity of tomorrow, man will transcend himself; so will the living cell; so will matter itself; for all will be directly illuminated by the properties and qualities expressed by the highest point of the evolutionary advance.