THE THIRD CANON OF THOUGHT
A KEY TO THE ENIGMAS OF THE WORLD
In what direction may the fourth dimension lie? What is motion? Two kinds of movement -movement in space and movement in time -contained in every motion. What is time? Present past and future. Wundt on sense-cognition. Groping through life. Why we do not see the past and the future. A new extension in space and motion in that space. Two ideas contained in the concept of time. Time as the fourth dimension of space. Impossibility of understanding the idea of the fourth dimension without the idea of motion. The idea of motion and 'time-sense'. 'Time-sense' as the limit (surface) of space sense. Riemann's idea of the translation of time into space in the fourth dimension. Hinton on the law of surfaces. 'Ether' as a surface.
From the analogy between the relation of lower dimensional figures to higherdimensional figures we have established the fact that a four-dimensional body may be regarded as the trace of the movement of a three-dimensional body in a direction not contained in it, i.e. that the direction of motion in the fourth dimension lies outside all the directions possible in a three-dimensional space.
What can this direction be?
In order to answer this question we must see whether we know of any movement in a direction not contained in three-dimensional space.
We know that every movement in space is accompanied by what we maycall movement in time. We know, in addition, that even without moving in space, everything that exists moves eternally in time.
And, equally in all cases, whether we speak of motion or of absence of motion, we have in mind the idea of what was before, what is now, what will be after. In other words, we have in mind the idea of time. The idea of motion, whatever this motion may be, as well as the idea of absence of motion, is indissolubly linked with the idea of time. Any motion or absence of motion takes place in time and cannot take place outside of time. Consequently, before speaking about what motion is, we must answer the question: what is time?
Time is the greatest and the most difficult riddle which confronts mankind.
Kant regards time in the same way as he regards space, as a purely subjective form of our perception. He says that, conditioned as we are by the properties of our perceiving apparatus, we create time as a convenience for perception of the outside world. Reality is continuous and constant. But in order to be able to perceive it, we must break it up into separate moments, i.e. represent it to ourselves as an endless series of separate moments, out of which one and one only exists for us. In other words, we perceive reality as though through a narrow slit. What we see through this slit, we call the present; what we saw but see no longer, we call the past; and what we do not see at all but expect to see, we call the future.
Examining each phenomenon as the outcome of another one, or several others, and this in its turn, as the cause of still another, or others, i.e. examining all phenomena in their mutual functional relationship, we, by this very fact, examine them in time because, quite clearly and distinctly, we first visualize the cause and then the effect - first the action, then its function - and we cannot think of it otherwise. So for us the idea of time is essentially connected with the idea of causation and functional interdependence. Causation cannot exist without time, just as motion or absence of motion cannot exist without time.
But our conception of our 'existence in time' is incredibly muddled and hazy.
First of all let us examine our relation to the past, the present and the future. Usually, we consider the past as no longer existing. It has gone vanished -changed, has become transformed into something else. The future does not exist either. It is not yet. It has not yet come, it is not yet formed. Bythe present we mean the moment of transition from the future into the past, i.e. the moment of the transition of a phenomenon from one non-existence into another. Only during this brief moment does a phenomenon really exist for us; before, it exists as a potentiality, and after, it exists as a memory. But in actual fact this brief moment is a fiction. It has no dimension. On the contrary, we have every right to say that the present does not exist. We can never catch it. That which we manage to catch is always already past!
If we stop at that we shall be forced to admit that the world does not exist. The only thing that exists is some phantasmagoria of illusions, flashing up then vanishing.
As a rule we fail to realize this, and do not see that our usual view of time leads to utter absurdity.
Imagine a foolish traveller going from one town to another and findinghimself half way between the two towns. The foolish traveller thinks that the town he left last week no longer exists now, that only the memory of it remains; the walls are demolished, the towers have fallen, the inhabitants have died or run away. And the town where he is due to arrive in a few days' time does not exist now either, but is being hastilybuilt for his coming and, on the day of his arrival, will be ready, peopled and in working order, but on the day following his departure will be destroyedjust like the first.
This is exactly the way we think about things in time -everything passes, nothing returns! Spring is over, it exists no longer. Autumn has not yet come, it does not exist as yet.
What then does exist?
But the present is a moment impossible to capture, it is continuouslymelting into the past.
Thus, strictly speaking, the past, the future and the present do not exist for us. Nothing exists! Yet we live, feel, think - and something surrounds us. Consequently, there must be some fault in our customary attitude to time. We must try to find this fault.
At the very beginning we accepted the fact that something exists. We called this something the world. How can the world exist if it does not exist in the past, the present and the future?
As deduced from our ordinary viewpoint of time, we make the world appear like an incandescent streamer of fireworks perpetually shooting up, each spark of which flashes for a moment then is instantly extinguished, never to appear again. Flashes follow one another in close succession; the number of sparks is infinite and the whole produces the effect of flame, although in reality it has no existence.
Autumn has not yet come. It will be, but now it is not. And we never stop to think how that which is not can appear.
We move on a plane and accept as actually existing only the small circle illumined by our consciousness. Everything that lies beyond this circle and beyond our field of vision we reject, and deny its very existence. We move on the plane in one direction. This direction we consider eternal and infinite. But any direction perpendicular to it, any lines we may cross, we refuse to accept as eternal and infinite. We think that they vanish into non-existence as soon as we have crossed them, and that the lines in front of us have not yet emerged from non-existence. If we suppose that we move along a sphere,along its equator or one of its parallels, we shall find that we always accept only one meridian as really existing; those behind us have already disappeared, those in front have not yet come into being.
We go along like a blind man who, with his stick, feels the paving stones, the lamp-posts and the walls of the houses and believes in the real existence of only those things he is touching now. What he has passed has vanished never to return! What he has not yet reached does not exist. The blind man remembers the road he has covered; he expects to find a road in front; but he does not see either forward or backward, because he does not see anything; and also because his instrument of cognition - his stick -has a certain, very small length, and beyond this stick non-existence begins for him.
In one of his books Wundt draws attention to the fact that our vaunted five sense-organs are merely feelers by means of which we touch the world around us. We live by 'feel' -by groping. We never see anything. We always grope for everything. With the help of the telescope, the telegraph, the telephone we perhaps lengthen our feelers, so to speak, but we do not begin to see. To say that we see would be possible only if we knew the past and the present. But we do not see and therefore can never convince ourselves of the existence of that which we cannot feel.
Here we have the reason why we regard as really existing only the circle which our feelers can grasp at a given moment. Beyond this circle there is only darkness and non-existence.
But have we the right to think in this way?
Imagine a consciousness not limited by the conditions of sense-perception. Such a consciousness can rise above the plane on which we move; it can see far beyond the bounds of the circle illumined by our ordinary consciousness; it can see that not only does the line along which we move exist, but also all other lines perpendicular to it which we now cross, or have ever crossed before, or shall cross later. Rising above the plane this consciousness will be able to see the plane, make sure that it actually is a plane and not only a line. Then it will be able to see the past and the future lying side by side and existing simultaneously.
Consciousness not limited by the conditions of sense-perception may outdistance the foolish traveller, climb a hill, and see from afar the town towards which he is going. It can convince itself that this town is not being newlybuilt for his arrival but already exists by itself, quite independently of him. It will be able to look back and see on the horizon the towers of the town which the traveller left, and convince itself that the towers have not fallen down, that the town continues to stand and live as it stood and lived before the coming of the traveller.
Such a consciousness may rise above the plane of time and see the springbehind and the autumn in front, see simultaneously the unfolding flowers and the ripening fruit. It may cure the blind man of his blindness and make him see the road he has covered and the road that lies before him.
The past and the future cannot be non-existent, for, if they do not exist, the present does not exist either. They must exist together somewhere, only we do not see them.
The present, as opposed to the past and the future, is the most unreal of all unrealities.
We must admit that the past, the present and the future do not differ from one another in any way, that the only thing that exists is the present -the Eternal Now of Indian philosophy. But we do not see it, because at every given moment we are only aware of a small fragment of this present; this fragment we regard as actually existing, and deny real existence to everything else.
Once we accept this, our view concerning everything that surrounds us must undergo a great change.
Usually we regard time as an abstraction made by us when observing existent motion; that is to say, we think that in observing motion or changes in the relations between things, and comparing the relations which existed before, which exist now and which may exist in the future, we evolve the idea of time. We shall see later how far this view is correct.
Moreover, our idea of time is composed of the concept of the past, the concept of the present and the concept of the future.
The concepts of the past and the present, although very vague, are uniform. But as regards the future there is a great variety of views.
It is essential for us to examine these theories of the future as they exist in the mind of modern man.
There are two main theories -that of a predestined future and that of a free future.
The theory of predestination is argued in the following way: it is asserted that every future event is the result of past events and is such as it is and no other, owing to a certain direction of the forces contained in the preceding events. In other words, this means that future events are entirely contained in the preceding ones, and if we were to know the force and direction of all the events which took place before the present moment, i.e. if we knew all the past, then, through this very fact we would know all the future. And it is true that if we have a thorough knowledge of the present moment in all its details, we may, at times, actually forecast the future. But if our forecast does not come true we say that we did not know everything there was, and we actually see in the past some cause which had escaped our observation.
The idea of a free future is based on the possibility of deliberate actions and accidental new combinations of causes. The future is considered either as completely undetermined or only partially determined, because at each moment new forces, new events, new phenomena may arise, which have hitherto lain dormant. These new factors, although not causeless in themselves, are so utterly incommensurable with their causes -for instance a city set ablaze from a single spark - that it is impossible to allow for them or correlate them.
This theory asserts that one and the same action may produce different results; one and the same cause may give rise to different effects. In addition, it puts forward the hypothesis that quite deliberate volitional actions on the part of a man may bring about a complete change in the subsequent events of his own and other people's lives.
Supporters of the predestination theory contend that volitional, deliberate actions also depend on certain causes which make them necessary and unavoidable at a given moment; they contend that there is and can be nothing'accidental'; that the things we call accidental are only those happenings of which we do not see the causes because of our limitations; and that the different effects resulting from causes which appear to us to be the same occur because the causes themselves are really different and only appear to be the same owing to the fact that we do not know them sufficiently well and do not see them sufficiently clearly.
The dispute between the theory of a predestined future and the theory of a free future is an endless dispute. Neither the one side nor the other can put forward anything decisive. And this is so because both theories are too literal, too rigid, too material, and the one excludes the other. Both of them say: 'Either this or that.' The result on the one hand is complete cold predestination: come what may, nothing can be changed -what will be tomorrow has been predestined tens of thousands of years ago; and on the other hand, some sort of life on the point of a needle named the present, surrounded on all sides by the gulf of non-existence -a journey into a countrythat does not yet exist, a life in a world which is born and dies every moment, in which nothing ever returns. These opposite views are both equally wrong,because here, as in many other cases, the truth lies in a unification of these two opposite understandings into one whole.
At every given moment all the future of the world is predestined and existing, but it is predestined conditionally, i.e. there must be one or another future in accordance with the direction of events of the given moment, if no new factor comes in. And a new factor can only come in from the side of consciousness and the will resulting from it. It is important to understand and assimilate this.
In addition, our lack of understanding of the relation between the present and the past hinders us from having a right understanding of the relation of the present to the future. Differences of opinion arise only concerning the future; as regards the past everyone is in agreement that it has passed, that it no longer exists -and that it was such as it was. In this past lies the key to the understanding of the errors in our view of the future. The fact is that, in reality, our relation to the past and the future is much more complex than it appears. In the past, in what is behind us, lies not only what was, but also what could have been. In the same way, in the future lies not only what will be but also all that may be.
The past and the future are equally undetermined; the past and the future equally exist in all their possibilities, and equally exist simultaneously with the present.
By time we mean the distance separating events in the order of their sequence and binding them into different wholes. This distance lies in a direction not contained in three-dimensional space. If we think of this direction as lying in space, it will be a new extension of space.
This new extension fulfils all the requirements we may demand of the fourth dimension on the basis of the preceding arguments.
It is as incommensurable with the measurements of three-dimensional space, as a year is incommensurable with St Petersburg. It is perpendicular to all the three directions of three-dimensional space and is not parallel to any of them.
As a deduction from everything that has gone before we may say that time (as it is usually taken) contains two ideas: the idea of a certain space unknown to us (the fourth dimension), and the idea of movement in this space. Our constant mistake lies in the fact that we never see two ideas in time, but always see only one. As a rule we see in time the idea of motion, but cannot tell from whence, whither, where and in which space. Attempts have been made before to link the idea of the fourth dimension with the idea of time. But in all the theories which attempted to link the idea of time with the fourth dimension there was always the implication of some kind of space in time and of some sort of motion in that space. It is evident that those who built these theories did not understand that, by retaining the possibility of motion, they put forward demands for a new time, for no motion can take place without time. As a result time moves in front of us, like our own shadow, receding as we approach it. All our ideas of motion have become hopelessly confused because, if we imagine a new extension of space and the possibility of movement along this new extension, then immediately time confronts us once more declaring itself just as unexplained as before.
We have to admit that by the one term, time, we actually designate two ideas - the idea of a 'certain space' and the idea of 'movement in that space'. But in actual fact this movement does not exist; it only appears to exist because we do not see the space of time. This means that the sensation of motion in time (and there is no motion that is not in time) arises in us because we look at the world through a narrow slit, as it were, and only see the lines of intersection of the plane of time with our three-dimensional space.
Thus we must acknowledge the profound incorrectness of the usual theorythat the idea of time is evolved by us from our observation of motion and is nothing other than the idea of sequence which we observe in motion.
We have to accept the exact opposite: that the idea of motion is evolved by us from the sensation of time or the time-sense, i.e. from the sensation or sense of the fourth dimension of space, but out of an incomplete sensation. This incomplete sensation of time (of the fourth dimension) -sensation through a slit - gives us the sensation of motion, i.e. creates an illusion of motion, which is not actually there, and instead of which, in reality, there is only extension in a direction we are unable to imagine.
Yet another aspect of the question is of great importance. The fourth dimension is connected with 'time' and with 'motion'. But we shall not be able to understand the fourth dimension so long as we do not understand the fifth dimension.
Attempting to look at time as an object, Kant says that it has one dimension; this means he represents time to himself as a line extending from an infinite future into an infinite past. We are aware of one point in this line always only one point. This point has no dimension because what we call the present in the ordinary sense of the word is only the recent past and at times also the immediate future.
This would be correct in relation to our illusory idea of time. But in reality eternity is not an infinite extension of time, but a line perpendicular to time; for, if eternity exists, each moment is eternal. The line of time proceeds in the order of sequence of events according to their causal interdependence - first the cause, then the effect: before, now, after. The line of eternity proceeds in a direction perpendicular to this line.
It is impossible to understand time without forming an idea of eternity, just as it is impossible to understand space without the idea of time.
From the point of view of eternity time in no way differs from the other lines and extensions of space -length, breadth and height. This means that just as space contains things we do not see or, to put it differently, more things exist than those we see, so in time 'events' exist before our consciousness comes into contact with them, and they still exist after our consciousness has withdrawn from them. Consequently, extension in time is extension into an unknown space and, therefore, time is the fourth dimension of space.
We must examine the question of time as a spatial concept, relative to our two data -the universe and our inner life.
The idea of time arises from our cognition of the world through senseperception. It has already been pointed out that, owing to the properties of our sense-perception, we see the world as if through a narrow slit.
This gives rise to several questions.
1 Why does apparent motion exist in the world? In other words, why do we not always see the same thing through this slit? Why do changes take placebehind the slit, which create the illusion of motion, i.e. how and why does the focus of our perception shift from place to place in the world of phenomena? In addition we must not forget that through the same slit through which we see the world we also look at ourselves and see in ourselves changes similar to the changes in everything else.
2 Why can we not enlarge this slit?
It is essential to try and answer these questions.
It should be noted, first of all, that within the limits of our ordinaryobservation, our perception always remains in the same conditions and cannot get out of these conditions. To put it differently, it seems chained to some kind of plane above which it is unable to rise. These conditions or this plane we call matter. Our ordinary inner life proceeds on a definite plane (of consciousness or matter) and never rises above it. If our perception could rise above this plane, it would most certainly see below simultaneously a far greater number of events than it usually sees from its position on the plane. If a man climbs a mountain or goes up in a balloon he sees simultaneously and at once a great many things that it is impossible to see simultaneously and at once when on earth -the movement of two trains towards one another which must result in a head-on collision; the approach of an enemy detachment to a sleeping camp; two towns separated by a mountain ridge and so on. So in this case also, perception rising above the plane of consciousness on which it usually lives should see simultaneously phenomena which for ordinary perception are separated by periods of time.
These would be phenomena which ordinary consciousness never sees together as cause and effect, for instance, work and pay; crime and punishment; the movement of trains towards each other and the collision; the approach of the enemy and the battle; sunrise and sunset; morning and evening; day and night; spring, autumn, summer and winter; the birth and death of a man.
With this ascent the angle of vision will widen, the moment will expand.
If we imagine perception taking place on a level above our consciousness, and possessing a wider angle of vision, this perception will be able to grasp as something simultaneous, i.e. as one moment, all that for us takes place in a certain period of time, a minute, an hour, a day, a month. Within the limits of its moment such a perception will be unable to separate before, now and after; for it, all this will be now. Now will expand.
But for this to take place it is necessary for us to be able to free ourselves from matter, because matter is nothing other than the conditions of time and space in which we live. The question arises: can consciousness get beyond the conditions of a given material existence without itself undergoing a fundamental change, or without disappearing altogether in the ordinary sense, as the positivists would say?
This is a very debatable question. Later, I shall give examples and arguments in favour of this idea that our consciousness can get out of the conditions of a given materiality. At present I want to establish what should
take place when it does get out.
The result should be precisely the expansion of the moment: all that we perceive in time would become one moment in which the past, the present and the future would be visible all at once. This shows the relativity of motion, inasmuch as for us it depends on the limitations of the moment, and this moment includes only a small pan of the impressions of life we take in.
So we have every right to say that instead of 'time' being deduced from 'motion' it is motion that is sensed owing to time-sense. We have this sense, therefore we sense motion. Time-sense is the sense of successive moments. If we had no time-sense we would not sense motion. But the time-sense itself is the boundary or the surface of our 'space-sense'. Where 'space-sense' ends, 'time-sense' begins. It has been made clear that in its properties 'time' is identical with 'space', i.e. it possesses all the attributes of space extension. Yet we do not feel it as space
extension, but feel it as time, i.e. as something specific, inexpressible in any other
words, indissolubly bound up with motion. This inability to feel time spatially is due to
the fact that our time-sense is a nebulous sense of space; with our time-sense we feel
dimly those new characteristics of space which transcend the sphere of three
What is time-sense and why does the illusion of motion arise? The only way to answer
this question in a more or less satisfactory manner is by studying the forms and levels
of our inner life.
Moreover, our inner life is a complex phenomenon within which there is also constant movement. About the nature of this movement I shall speak later, but it is this movement in us that creates the illusion of movement around us, i.e. movement in the material world.
The well-known mathematician, Riemann, realized that, in regard to this question of higher dimensions, time in some way becomes translated into space, and he regarded the material atom as the entrance of the fourth dimension into three-dimensional space.
In one of his books Hinton has very interesting things to say about the 'law of surfaces':
This relationship of a surface to a solid or of a solid ... to a higher solid, is one which we often meet in nature. A surface is nothing more nor less than the relation between two things. Two bodies touch each other. The surface is the relationship of one to the other.
If our space stands in the same relationship to higher space as does a surface to our space, then our space may well be really a surface, i.e. the place of contact of two spaces of a higher order:
It is a fact worthy of notice, that in the surface of a fluid different laws obtain from those which hold throughout the mass. There are a whole series of facts which are grouped together under the name of surface tensions, which are of great importance in physics, and by which the behaviour of the surfaces of liquids is governed.
And it may well be that the laws of our universe are the surface tensions of a higher
According to Hinton, if we consider the surface as a medium lying between two bodies it would certainly have no weight, but would be a powerful means of transmitting vibrations from one body to another. Moreover it would be unlike any other substance, inasmuch as one could never get rid of it. However perfect a vacuum be made between the two bodies, there would be in this vacuum just as much of this unknown medium (i.e. surface) as there was before. Matter would go freely through this medium. Vibrations of this medium would tear asunder portions of matter. This would tend to show that this medium is unlike any ordinary matter. It possesses properties difficult to reconcile in one and the same substance. Is there anything in our experience which corresponds to this medium? Do we suppose the existence of any medium through which matter freely moves, which yet by its vibrations destroys the combinations of matter -some medium which is present in every vacuum, which penetrates all bodies, and yet can never be laid hold of? The substance which possesses all these qualities is known to us and is called the ether. The properties of the ether are a perpetual object of investigation in science. But in view of all the considerations mentioned earlier, it would be interesting to have a look at the world, supposing that we are not in, but on the ether, and the ether is merelythe surface of contact of two higher-dimensional bodies.*
Here Hinton expresses an extremely interesting thought; he links the idea of ether -which in the 'material' or even the 'energy' views of modern physics remains completely unproductive and leads to a dead end - with the idea of 'time'. For him ether is not a substance but only a 'surface', the 'boundary' of something. But of what? Again not of a substance, but only the limit, the surface, the boundary of one form of perception and the beginning of another. . . .
Here, in a sentence, the walls and fences of the materialistic dead end are broken down, and new and unexplored vistas revealed to our thought.
' C. H. Hinton, A New Era of Thought, London, George Allen & Unwin, 1910, pp. 52, 56, 57.