THE THIRD CANON OF THOUGHT
A KEY TO THE ENIGMAS OF THE WORLD
Perception of the world by man and by animals. Illusions of animals and their lack of control over perceptions. A world of moving planes. Angles and curves as motion. Third dimension as motion. The two-dimensional appearance, for animals, of our three-dimensional world. Animals as real two-dimensional beings. Lower animals as one-dimensional beings. Time and space of a snail. Time-sense as a nebulous spacesense. Time and space of a dog. Change of the world with a change of the mental apparatus. Proof of Kant's problem. Three-dimensional world as an illusory representation.
We have established the tremendous difference which exists between the mentality of man and that of animals. This difference is bound to have a deep effect on the animal perception of the external world. But how and in what? This is precisely what we do not know and what we must endeavour to establish.
To do this we must return once more to our perception of the world and examine in detail how we perceive it; and then we must see how the world must be perceived by the animal with its limited mental equipment.
First of all we must take note of the fact that, as regards the external aspect and form of the world, our perception is extremely incorrect. We know that the world consists of solids, but we always see and touch only surfaces. We never see or touch a solid. A solid is already a concept, made up of a number of representations put together by means of reasoning and experience. For direct sensation only surfaces exist. Sensations of weight, mass, volume, which we mentally associate with a 'solid', are in reality connected for us with sensations of surfaces. We only know that this sensation of surfaces comes from a solid, but we never sense the solid itself. Maybe it is possible to call the composite sensation of surfaces, weight, mass, density, resistance and so on 'sensation of a solid'. But we are obliged mentally to bind all these sensations into one and to call this general sensation -a solid. We sense directly only surfaces, and then, separately, weight; we never sense the resistance of a solid, as such.
But we know that the world does not consist of surfaces, we know that we see the world incorrectly. We know that we never see the world as it really is, not only in the philosophical sense of this expression, but even in the most ordinary geometrical sense. We have never seen a cube, a sphere, etc., we have always seen only surfaces. Realizing this, we mentally correct what we see. Behind the surfaces we think the solid. But we can never represent a solid to ourselves; we cannot represent a cube or a sphere not in perspective, but from all sides at once.
It is clear that the world does not exist in perspective; yet we are unable to see it in any other way. We see everything only in perspective, i.e. in perceiving it, we distort the world with our eye. And we know that we distort it. We know that it is not as we see it. And mentally we continually correct what the eye sees, substituting the real content for those symbols of things which our sight shows us.
Our sight is a complex faculty. It consists of visual sensations, plus the memory of sensations of touch. A child tries to touch everything he sees -the nose of his nurse, the moon, the dancing spot of reflected sunlight on the wall. He learns only gradually to distinguish between the near and the far bysight alone. But we know that even in mature years we are easily subject to optical illusions.
We see distant objects as flat, i.e. even more incorrectly, for relief is, after all, a symbol indicating a certain property of objects. At a great distance a man is outlined for us in silhouette. This happens because at long range we can never touch anything, and our eye has not been trained to notice the differences in surfaces which, at close range, are felt by the fingertips.*
We are never able to see even a small bit of the external world as it is, i.e. such as we know it to be. We can never see a writing desk or a cupboard simultaneously from all sides, as well as inside. Our eye distorts the external world in a certain way to enable us, in looking about, to determine the position of objects relatively to ourselves. But
* In this connection, observations made on the blind beginning to see are very interesting.
The periodical Slepetz ('The Blind Man') 1912, contains a description, based on direct observation, of how men, blind from birth, learn to see after an operation which has restored their sight.
This is how a youth of seventeen describes his experiences after the restoration of his sight by the removal of a cataract. On the third day after the operation he was asked what he saw; he replied that he saw a vast expanse of light with dim objects moving in it. He did not distinguish these objects. Only after four days did he begin to distinguish them, and only after two weeks, when his eyes became used to the light, did he begin to make a practical use of his sight for the discernment of objects. He was shown all the colours of the spectrum and very quickly mastered them, except the yellow and the green which he kept on confusing for a long time. A cube, a sphere and a pyramid, placed before him, seemed to him a square, a flat disc and a triangle. When a flat disc was placed next to look at the world not from our own point of view is impossible for us. And we are never able to have a correct view of it, a view not distorted by our eyesight.
Relief and perspective -these are the distortions of the objects by our eye.They are an optical illusion, a visual deception. A cube in perspective is only a conventional symbol of a three-dimensional cube. And everything we see is only a conventional image of that conventionally real three-dimensional world which our geometry studies - and not the real world itself. On the basis of what we see, we must guess what it really is. We know that what we see is incorrect, and we think of the world as being different from the way we see it. If we had no doubts about the correctness of our sight, if we knew that the world was such as we saw it, it stands to reason that we would think of it as we see it. In practice, however, we are constantly introducing corrections into what we see.
This capacity of introducing corrections in that which the eye sees necessarily implies the possession of concepts, for corrections are made by means of reasoning, which is impossible without concepts. Without this capacity of correcting what is seen by the eye we would see the world quite differently, i.e. much of what actually exists we would see wrongly, much of what actually exists we would not see at all, and we would see a great deal of what, in reality, does not exist at all. In the first place, we would see an enormous number of nonexistent movements. For direct sensation, every movement of our own is connected with the movement of everything around us. We know that this movement is illusory, but we see it as real. Objects turn round before us, run past us, outstrip one another. Houses, past which we drive slowly, turn about leisurely; if we drive fast, they turn quickly; trees suddenly spring up before us, run away and vanish.
This apparent animation of objects, together with dreams, provided, and still provides, the main food for the fantasy of fairy-tales.
to the sphere, he could not see any difference between them. When asked to describe his first impression of the two figures, he answered that he noticed at once the difference between the cube and the sphere and realized that they were not drawings, but could not derive from them the representation of a square and a circle, until he felt in his fingertips the same sensation as though he had touched a square and a circle. When he was allowed to handle the cube, the sphere and the pyramid, he immediately identified these solids by touch and was very surprised at not having recognized them at once by sight. He had as yet no representation of space, of perspective. All objects appeared flat to him. Although he knew that the nose projected and the eyes were sunk in cavities, the human face also looked flat to his eyes. He was overjoyed at having his sight restored, but in the beginning looking at things tired him; impressions overwhelmed and exhausted him. This is why, while enjoying perfect sight, he at times reverted to touch, as a form of relaxation.
In those cases the 'movements' of objects may be very complex. Look at the strange behaviour of a cornfield seen through the window of your railwaycarriage. It runs up to your very window, stops, turns about slowly and runs to one side. The trees in the wood clearly run at different speeds, outstripping one another. A whole landscape of illusory motion! And what of the sun which still continues, in all languages, to rise and set, and the movement of which was at one time so passionately defended!
This is how it all appears to us. And although we already know that all these movements are illusory, we still see them and are, at times, deceived. How many more illusions we would see if we were unable mentally to unravel the causes which produce them, and were to regard everything as existing exactly as we see it?
I see it, therefore it is.
This assertion is the main source of all illusions. The right way to put it would be: I see it, therefore it is not! Or at any rate: I see it, therefore it is not so!
We can say the latter, but animals cannot. For them whatever they see -is. They have to believe what they see.
How does the world appear to animals?
For animals the world is a series of complex moving surfaces. Animals live in a two-dimensional world; their universe has the appearance and properties of a surface. And on this surface there take place a vast number of movements of the most varied and fantastic character.
Why should the world appear as a surface to animals?
First of all, because it appears as a surface to us.
But we know that the world is not a surface, whereas animals cannot know it. They accept everything as it appears. They cannot correct what the eye sees, or cannot do so to the same degree as we can.
We can measure in three directions; the quality of our mind enables us to do so. Animals can measure simultaneously only in two directions; they can never measure in three directions at once. This is due to the fact that, having no concepts, they are incapable of keeping in mind the measurements of the first direction while measuring the second and third.
I will explain this more clearly.
Let us imagine ourselves measuring a cube. In measuring a cube in three directions, we must, while measuring in one direction, keep in mind, remember, the two others. But things can only be kept in mind as concepts, i.e. we can remember them only by connecting them with various concepts, by labelling them in one or another way.
Thus, having labelled the first two directions -length and breadth, it is possible to measure the height. Otherwise it could not be done. As representations the first two measurements of a cube are absolutely identical and are bound to merge in our mind into one. An animal has no concepts, so it cannot label the first two measurements of the cube as length and breadth. Therefore, at the moment when it begins to measure the height of the cube, the first two measurements will merge into one. An animal measuring a cube and possessing no concepts but only representations, will resemble a cat I once observed. She dragged her kittens - there were five or six of them - into different rooms and could not collect them together again. She would get hold of one, carry it over to another and put them side by side. Then she would start looking for the third, bring it along and place it with the other two. Then immediately she would seize the first, carry it to another room and put it there beside the fourth; then she would again run to the first room, catch hold of the second and drag it somewhere else to the fifth, and so on. For a whole hour the cat struggled with her kittens, genuinely harassed, but could do nothing. Clearly she had no concepts to help her remember how many kittens there were in all.
It is extremely important to explain to oneself an animal's relationship to the measurement of solids.
The whole point is that animals see nothing but surfaces. (This we can saywith the utmost conviction, since we ourselves see nothing but surfaces.)Seeing only surfaces, animals can represent to themselves only two dimensions. The third dimension, side by side with the first two, can only bethought, i.e. this dimension must be a concept. But animals have no concepts; the third dimension appears also as a representation. Consequently, at the moment of its appearance, the first two representations invariably merge into one. Animals see the difference between two dimensions, but cannot see the difference between three. This difference can only be known. And in order to know that, concepts are necessary.
For animals identical representations are bound to merge into one, just as for us two simultaneous, identical phenomena taking place at one point must merge into one. For animals it would be one phenomenon, just as for us all identical, simultaneous phenomena taking place at one point are one phenomenon.
Thus animals will see the world as a surface, and will measure this surface only in two directions.
How then to explain the fact that, living in a two-dimensional world, or seeing themselves in a two-dimensional world, animals orientate perfectly well in our three-dimensional world? How to explain that a bird flies up and down, straight ahead and sideways, in all three directions; that a horse jumps fences and ditches; that a dog and a cat seem to understand the properties of depth and height together with length and breadth?
In order to explain this we must return once more to the fundamental principles of animal psychology. It has been pointed out earlier that many properties of objects which we remember as the general properties of species and varieties, have to be remembered by animals as the individual properties of objects. In sorting out this enormous store of individual properties preserved in memory animals are helped by the emotional quality connected for them with each representation and each memory of a sensation.
An animal knows, say, two roads as two entirely separate phenomena having nothing in common; one phenomenon, i.e. one road consists of a series of definite representations coloured by definite emotional qualities; the other phenomenon, i.e. the other road, consists of a series of other definite representations, coloured by other qualities. We say that both the one and the other are roads, one leading to one place, the other to another. For the animal the two roads have nothing in common. But it remembers all the sequence of emotional qualities connected with the first road and the second road and so remembers both roads with their turnings, ditches, fences and so on.
Thus the memory of the definite properties of objects which they have seen helps animals to orientate in the world of phenomena. But, as a rule, when faced with new phenomena, animals are much more helpless than man.
Animals see two dimensions. They constantly sense the third dimension but do not see it. They sense it as something transient, as we sense time.
The surfaces which animals see possess for them many strange properties; these are, first of all numerous and varied movements.
It has been said already that all illusory movements must be perfectly real for them. These movements seem real to us also, but we know them to be illusory, as for instance the turning round of a house as we drive past, the springing up of a tree from round the corner, the movement of the moon among the clouds and so on.
In addition, many other movements will exist for animals which we do not suspect. Actually a great many objects, completely motionless for us -indeed all objects -must appear to animals as moving. AND IT
IS PRECISELY IN THESE MOVEMENTS THAT THE THIRD DIMENSION OF SOLIDS WILL BE MANIFESTED FOR THEM, i.e. THE THIRD DIMENSION OF SOLIDS WILL APPEAR TO THEM AS MOTION.
Let us try to imagine how an animal perceives objects of the external world.
Let us suppose that a large disc is placed before an animal and, beside it, a large sphere of the same diameter.
Facing them directly at a certain distance, the animal will see two circles. If it starts walking round them, the animal will notice that the sphere remains a circle but the disc gradually narrows and becomes a narrow strip. As the animal continues to move round it, the strip begins to widen and graduallybecomes again a circle. The sphere will not change its form as the animal moves round it, but strange phenomena will begin to occur in it as the animal draws near.
Let us try to understand how the animal will perceive the surface of the sphere as distinct from the surface of the disc.
One thing is certain - it will perceive a spherical surface differently from us. We perceive convexity or sphericity as a property common to many surfaces. Owing to the nature of its mental apparatus, the animal should perceive sphericity as an individual property of the given sphere. What should sphericity look like, taken as an individual property of a given sphere?
We can say with the utmost conviction that sphericity will appear to the animal as a movement of the surface it sees.
When the animal comes near to the sphere, in all probability what happens is something like this: the surface the animal sees springs into rapid motion; its centre projects forward, and all the other points begin to recede from the centre with a velocity proportionate to their distance from the centre (or the square of their distance from the centre).
This is the way in which the animal must sense a spherical surface.
It is reminiscent of the way we sense sound.
At a certain distance from the sphere the animal sees it as a plane. Approaching it and touching some point of the sphere, it sees that the relation of all the other points to that point has changed as compared with what it should be on a plane, as if all the other points have moved, have drawn aside. Touching another point it again sees all the other points withdrawing from it.
This property of the sphere will appear as its motion, as 'vibration'. And indeed the sphere will resemble a vibrating, undulating surface. In the same way any angle of a motionless object must appear as motion to the animal.
The animal can see an angle of a three-dimensional object only if it moves past it, and in that case the object will seem to have turned -a new side has appeared, and the old side has receded or moved aside. An angle will be perceived as a turning, a movement of the object, i.e. as something transient, temporal, i.e. as a change in the state of the object. Remembering the angles met with before -which the animal has seen as the motion of bodies - it will regard them as gone, finished, vanished, belonging to the past.
Of course, the animal cannot reason thus, but it will act as though this was its reasoning.
If the animal could think of phenomena (i.e. angles and curved surfaces) which have not yet entered its life, it would no doubt represent them to itself only in time. In other words, the animal could not allow them any real existence at the present moment when they have not yet appeared. If it could express an opinion about them, it would say that these angles exist as a potentiality, that they will be, but that at present they are not.
For a horse, the comer of a house past which it runs every day, is a phenomenon which recurs in certain circumstances, but which still takes place only in time; it is not a spatial and constant property of the house.
For the animal an angle must be a time-phenomenon, instead of being a spacephenomenon as it is for us.
Thus we see that the animal will perceive the properties of our third dimension as movements and will refer these properties to time, to the past or future, or to the present, i.e. to the moment of transition of the future into the past.
This is an extremely important point and contains the key to the understanding of our own perception of the world; consequently we must examine it in greater detail.
So far we have considered higher animals: a dog, a cat, a horse. Let us now take a lower animal -a snail for example. We know nothing about its inner life, but we may be sure that its perception is very different from ours. In all probability a snail's sensations of its surroundings are very vague. It probably feels warmth, cold, light, darkness, hunger, and instinctively (i.e. incited by the pleasure-pain guidance) it crawls towards the uneaten edge of the leaf it sits on and draws away from a dead leaf. Its movements are governed by pleasure-pain; it always advances towards the one and retreats from the other. It always moves on one line -from the unpleasant towards the pleasant. And, in all probability, it knows and senses nothing except this line. This line constitutes the whole of its world. All the sensations entering from outside are sensed by the snail on this line of its motion. And these come to it out of time -from potentiality they become actuality. For a snail the whole of our universe exists in the future and the past, i.e. in time. Only one line exists in the present; all the rest lies in time. It is more than probable that a snail is not aware of its own movements; making efforts with its whole body it moves forward towards the fresh edge of the leaf, but it seems to it that the leaf moves towards it, coming into being at that moment, appearing out of time, as the morning appears to us.
A snail is a one-dimensional being.
Higher animals - a dog, a cat, a horse -are two-dimensional beings. To them space appears as a surface, a plane. Everything outside this plane lies for them in time.
Thus we see that a higher animal - a two-dimensional being as compared to a one-dimensional — extracts one more dimension out of time.
The world of a snail has one dimension -our second and third dimensions lie for it in time.
The world of a dog has two dimensions - our third dimension lies for it in time.
An animal may remember all the 'phenomena' it has observed, i.e. all the properties of three-dimensional bodies it has come into contact with, but it cannot know that that which for it is a recurring phenomenon is in reality a permanent property of a three-dimensional body - an angle, or curvature, or convexity.
This is the psychology of the perception of the world by a two-dimensional being.
For it a new sun will rise every day. Yesterday's sun has gone and will never recur again. Tomorrow's sun does not yet exist.
Rostand failed to understand the psychology of 'Chantecler'. The cock could not think that he awakened the sun by his crowing. For him the sun does not go to sleep - it recedes into the past, vanishes, is annihilated, ceases to be. Tomorrow, if it comes, there will be a new sun, just as for us there is a new spring each year. In order to be the sun cannot wake up; it must come into being, be born. An animal (if it could think without losing its characteristic psychology) could not believe in the appearance today of the same sun that was there yesterday. This is human reasoning.
For an animal a new sun rises every morning, just as for us a new morning comes every day, a new spring every year.
An animal is incapable of understanding that the sun is one and the same, whether today or yesterday -EXACTLY AS WE PROBABLY CANNOT
UNDERSTAND THAT THE MORNING IS ONE, AND THE SPRING IS ONE.
The motion of objects which, for us, is not illusory but real, such as the motion of a rotating wheel or a moving carriage and so on, must, for an animal, differ greatly from the motion it sees in all objects which are motionless for us - that motion in the guise of which it sees the third dimension of bodies. This first motion (i.e. motion which is also real for us) must appear to it spontaneous, alive.
And these two kinds of motion will be incommensurable for it.
An animal will be able to measure an angle or a convex surface, although it will not understand its true meaning and will regard it as motion. But it will never be able to measure real motion, i.e. motion which is real for us. To do this it is necessary to have our conception of time and measure all movements in relation to some more constant motion, i.e. compare all movements with one. As an animal has no concepts, it will not be able to do this. Therefore, movements of objects which are real for us will be incapable of measurement, and thus incommensurable with other movements which, for it, are real and capable of measurement, but for us are illusory, constituting in reality the third dimension of bodies.
The latter is inevitable. If an animal senses and measures as motion that which is not motion, it is clear that it cannot apply the same measure to that which is and that which is not motion.
But this does not mean that an animal cannot know the character of movements proceeding in our world and conform to them. On the contrary, we see that an animal orientates perfectly among the movements of objects of our three-dimensional world. In this it is helped by instinct, i.e. capacity, evolved through hundreds of centuries of selection, of performing expedient actions without consciousness of purpose. And an animal discriminates perfectly well between movements happening round it.
But, distinguishing between two kinds of phenomena -two kinds of motion -an animal is bound to explain one of them by some inner inexplicable property of objects, i.e. it will probably regard that kind of motion as the result of the animation of objects, and will regard moving objects as alive.
A kitten plays with a ball or with its own tail because the ball or the tail runs away from it.
A bear will fight with a beam until the beam throws him off the tree, because in the swinging beam he feels something alive and hostile.
A horse shies from a bush because the bush has suddenly turned round and waved a branch.
In the latter case the bush may not have moved at all - it was the horse that was running. But it appeared to move, therefore it was alive. Probably everything that moves is alive for an animal. Why does a dog bark so furiously at a passing carriage? We do not quite understand it. We do not see how a passing carriage turns, twists and grimaces in the eyes of a dog. It is full of life - the wheels, the roof, the mudguards, the seats, the passengers all this is moving, turning. . . .
Now let us summarize our deductions.
We have established that a man possesses sensations, representations and concepts; that higher animals possess sensations and representations, and lower animals only sensations. We deduced that an animal has no concepts mainly from the fact that it has no words, no speech. We have further established that, having no concepts, animals cannot comprehend the third dimension and only see the world as a surface. In other words they have no means, no instrument, for correcting their wrong sensations of the world. Then we found that, seeing the world as a surface, animals see on this surface a great many movements non-existent for us. That is, all those properties of bodies which we regard as the properties of their three-dimensionality, must appear as movements to them. Thus an angle and a spherical surface must appear to them as motion of the plane. Further, we came to the conclusion that everything which, for us, belongs to the domain of the third dimension as something constant, animals must regard as transient occurrences happening to objects - as time-phenomena.
Thus, in all its relations to the world an animal proves to be completelyanalogous to the unreal two-dimensional being which we have supposed lived on a plane. The whole of our world appears to an animal as a plane through which phenomena are passing, moving according to time or in time.
So we can say that we have established the following: that with a certain limitation of the mental apparatus which perceives the external world, for a subject possessing such an apparatus the whole aspect and all the properties of the world must change. And two subjects, living side by side but possessing different mental apparatuses, must live in different worlds -the properties of the extension of the world must be quite different for them. Moreover, we have seen conditions - not artificial and invented but actually existing in nature, i.e. the mental conditions of the life of animals -in which the world appears as a plane or even as a line.
In other words we have established that the three-dimensional extension of the world depends for us on the properties of our mental apparatus; or, that the world's threedimensionality is not its own property, but merely the property of our perception of the world.
To put it differently, the three-dimensionality of the world is the property of its reflection in our consciousness.
If all this is so, it is clear that we have really proved the dependence of space on space-sense. And, since we have proved the existence of a space-sense lower than ours, by this very fact we have proved the possibility of a space-sense higher than ours.
And we must admit that if a fourth unit of thinking becomes formed in us, as different from the concept as the concept is different from the representation, then, simultaneously with this, there will appear for us in the surrounding world a fourth characteristic which we may call geometrically a fourth direction or a fourth perpendicular, because this characteristic will contain properties of objects perpendicular to all properties known to us and not parallel to any of them. In other words, we shall see or feel ourselves not in a space of three, but of four dimensions, and the surrounding objects as well as our own bodies will reveal the general properties of the fourth dimension which we had not noticed before or which we had regarded as individual properties of objects (or their motion), just as animals regard the extension of objects in the third dimension as their motion.
Having seen or felt ourselves in the world of four dimensions, we shall find that the world of three dimensions has not and never had any real existence, that it was a creation of our fantasy, a phantom, a spectre, a delusion, an optical illusion, anything you like, but not reality.
All this is far from being a 'hypothesis', a supposition; it is an exact fact, as much of a fact as the existence of infinity. For the sake of its own existence, positivism had somehow to do away with infinity or at least to call it a 'hypothesis' which may or may not be true. But infinity is not a hypothesis; it is a fact. And just such a fact is also the multi-dimensionality of space and all that it implies, i.e. the unreality of everything three-dimensional.