Is “Time” a Dimension of “Space”
Theosophical Quarterly, January, 1920
Let us come gradually to this knotty question, using a series of familiar references as stepping-stones. To begin with, readers of The Occult World will remember the Master K. H. saying:
“I feel even irritated at having to use these three clumsy words—past, present, and future. Miserable concepts of the objective phases of the subjective whole, they are about as ill-adapted for the purpose as an axe for fine carving.”
The commentator on Patanjali, who uses this quotation to illustrate and illumine the thought of the twelfth Sutra of the fourth book, somewhat irreverently surmises that there must be something woefully wrong with words that can so far disturb that high, urbane serenity.
The Sutra in question is translated thus: “The difference between that which is past and that which is not yet come, according to their natures, depends on the difference of phase of their properties;” and there is a certain fitness in quoting, as a commentary on this, the letter of a Master who is, in a sense, the spiritual grandson of Patanjali.
The next reference, the next stepping-stone, is the clear affirmation, by the Master who inspired Light on the Path, that certain of the wiser men of science are the veritable pioneers of humanity, and are breaking down the wall between the manifested and the occult worlds. Add to this many definite indications in The Secret Doctrine; for example that the philosopher Leibniz has, in certain of his speculations, come exceedingly close to the true occult principles.
This series of stepping-stones is intended to lead up to the thought that, in the last ten or fifteen years, pioneers among the men of science have made remarkable progress toward solving the age-old enigma of “Time,” and have gone some distance toward dispelling the mists of “past, present, and future,” which arouse the indignation of the august author of The Occult World letters.
Notable among these recent semi-occult speculations is the so-called Theory of Relativity of the physicist-philosopher Einstein, who appears to be a congener of Leibniz and to possess the same deep and penetrating insight into cosmic riddles. But before we try to illustrate Einstein’s theory, it may be well to use some simple facts that will lead up to the deeper mysteries.
A recipe in a once famous cook-book began with the words “Take a hare!” And this long ago gave rise to the proverb: “First catch your hare and then cook him!” We shall begin in some such way: Take a foot-rule! And we seriously advise every reader who is interested in solving the enigma of Time to make the experiment.
Well, take a foot-rule and a bucket of water. The foot-rule is graduated from 1 to 12 inches. Hold the foot-rule upright above the surface of the water in the bucket, with the 1-inch end near the surface. Still holding the foot-rule perpendicularly, lower it gradually till its end just touches the water. If we suppose the surface of the water to represent consciousness, then, as the foot-rule just touches the water, this consciousness will become aware of it.
Let us consider first the edge of the end of the foot-rule, and, of that edge, the side on which the inch-marks are printed. The edge of the water along that edge of the foot-rule is a very short straight line; it has extension in one direction only: the direction of length. It is a short line of consciousness, just as the slit of the spectroscope is a line of consciousness.
Continue to plunge the foot-rule directly downward into the water, holding your attention on the short line of water past which the inch-marks are descending. If we think of that line of water as a one-dimensional perceiving consciousness, it will be conscious of one inch-mark after another, perceiving successively all the inch-marks from 1 to 12.
For that one-dimensional consciousness, there will have been a series of successive impressions, twelve in number; and its concept of the foot-rule will be a series of consecutive marks, spread out through a certain period of time: the time which it has taken you to plunge the whole length of the foot-rule into the water. In other words, what you are thinking of, and perceiving, as a foot-rule, a linear foot of “space,” will be represented in that one-dimensional consciousness as twelve equal periods of “time.” Your space-consciousness will, in his one-dimensional mind, be represented as a time-consciousness. And he can gain an impression of linear space, length, the kind of space you measure with a foot-rule, only in terms of time, in terms of a series of successive impressions spread out through time.
Now let us suppose his consciousness to expand. Instead of being represented by a line on the water, let it be represented by the whole surface of the water as a perceiving surface; just as the retina of the eye or the skin of the palm is a perceiving surface.
The surface of the water, then, represents consciousness with two dimensions; not only the first dimension, length, but the second dimension, breadth also.
Now take the foot-rule and hold it horizontally over the water, with the edge containing the inch-marks close to the water. Gradually lower it to the water until the whole series of inch-marks are just immersed. The consciousness represented by the surface of the water can now perceive the whole series of twelve marks at the same time. What was before a series of consecutive impressions of the twelve inch-marks, is now a single simultaneous impression of all the twelve.
This would all seem to be quite simple and elementary. Yet it is the key to the whole mystery. The addition of a new dimension of consciousness, the passage from line-consciousness to surface consciousness, has transformed a time-impression into a space-impression. What was before successive, containing the element of duration, is now simultaneous, with the element of time eliminated.
One step more: instead of a foot-rule, take a walking-stick, hold it upright over the water and plunge it downward as before. The two-dimensional consciousness represented by the water-surface will perceive a circle, corresponding to the cross-section of the stick where it passes from the air to the water; and, as the stick is plunged down, a series of circles will be perceived, following each other in time. If there be a mind behind that surface-consciousness, then the stick will appear in that mind as an almost endless succession of circles, separated from each other by the element of time. That mind will not be able to gain any idea of the stick except as a succession of circles, with the element of duration holding them together. But you can see the whole stick at once. With your three-dimensional perception, you receive a single, simultaneous impression of the whole stick, its length, its shape, its solidity. Your space-perception takes the place of the time-perception in the mind of the two-dimensional perceiver.
In each of the two illustrations,—the foot-rule and the walking-stick—the addition of a dimension to the perceiving consciousness has transformed a time-perception into a space-perception; what appeared as a succession in the lower-dimensioned consciousness, appears as simultaneous in the higher-dimensioned consciousness.
We can now come a little closer to Einstein. The writer of this note has not yet had the opportunity or the time to plunge deeply into the writings of Einstein himself. For the present, he is under obligations to an able article in The Evening Sun, by Isabel M. Lewis, who is connected with the Nautical Almanac Office of the United States Naval Observatory.
A quotation from this article may be more intelligible, because of our illustrated prelude:
“Following upon the failure of physicists to define the velocity of the earth relative to the ether by experimental means, Einstein announced his hypothesis that it is an impossibility to determine by physical experiments the velocity of the earth relative to the ether; moreover, that an immobile or rigid ether is unthinkable, and that there is no such thing as absolute velocity through space for any body, and that measured time and space do not exist as independent and self-contained concepts, but are always conditioned by the phenomena that they are used to describe.
“It is this phase of the Einstein theory that makes it expressible in terms of the fourth dimensional calculus of Minkowski wherein the distinction between space and time vanishes. The two become complementary and inseparable and cannot exist independently any more than the two components of a force can exist by themselves. They are simply two aspects of a greater construct or entity.”
All this is, of course, very incomplete so far; but it is eminently suggestive, and indicates that the scientists who are following this line of approach are already touching the confines of the occult world, citizenship in which, as we have seen, arouses a certain irritation with the conventional view of “time.”
But let us try to illustrate the matter a little further. We have already taken illustrations that involve space of one, two and three dimensions; let us push on, and see what will happen, if we bring in a fourth dimension in exactly the same way.
First, let us try to explain the term “fourth dimension.”
A straight line on a sheet of white paper represents space of one dimension, length only. It is created by the movement of a point, which has no dimension but simply position; in the case of a ruled pencil line, it is created by the movement of the pencil-point along the edge of the ruler. Now draw on the paper a perpendicular to this line. You have at once a second dimension or direction of space. And the two straight lines together define the surface of the paper, its position as a two-dimensional space, having both length and breadth. Now stand the pencil upright at the point where the two straight lines meet on the paper; this immediately gives you a third dimension or direction of space: height added to length and breadth. You can only stand the pencil upright on the paper because you are able to act in space of three dimensions.
To go back a little. The straight line is space of one dimension. A perpendicular to this line enters space of two dimensions. The surface of the paper is two-dimensional space. A perpendicular to this surface—the pencil set upright—enters space of three dimensions. If we follow the process one step farther, we shall see that a perpendicular to a three-dimensional space, a solid, must enter a fourth dimension or direction of space. The term, fourth dimension, means no more than that.
But you may object that all this is easier said than done, and that a perpendicular to a solid is unthinkable. But is it so in reality? Let us answer that by trying to think of it.
While reading this, you are probably in a room with four walls, a floor and a ceiling: a typical space of three dimensions. Raise your eyes and look at the wall straight in front of you. The line of your glance is a perpendicular to the surface of the wall, which is a two-dimensional space. Look in succession at each of the four walls, and then at the floor and ceiling. In each case, your line of sight is a perpendicular to that surface. You have half-a-dozen perpendiculars, one for each of the bounding surfaces of your three-dimensional space.
Now close your eyes and think of the room. Imagine it out, with its four walls, its floor and ceiling. You will find that you have in your mind the picture of all six at once; you can mentally look in all the directions at once, and visualize the whole interior of the room. Your mental glance or line of sight is, therefore, perpendicular, not to each of the six surfaces in succession, but to the whole room. It is just the perpendicular to a three-dimensional space, for which we have been looking.
Now, unless you are reading in a garden-house—improbable in January—there is a second room, next to the one you are in. If you are familiar with it, you can, while sitting in your own room, form a mind-picture of the second room also, with its four walls, ceiling and roof. You can, from the centre of your thought, draw a perpendicular to that three-dimensional space also. And you can quite easily think of the two interiors at the same time, superimposing one room on the other, and thus being “in two places at the same time”. Or, as the Dream of Ravan puts it, “Without moving is the travelling on this road . . . Thou shalt experience it!”
To go back a little: When you stood your pencil upright on the paper at the point where the two straight lines meet, the pencil was perpendicular to both lines. And you could, from that point, draw straight lines in every direction of the compass—in strictness, in an infinite number of directions—and your pencil would be perpendicular to them all. In just the same way, you can, sitting quietly in your room, call up the mind-pictures of as many rooms as you please, and look into them all: that is, you can, from the point of your thought, draw lines of sight to each of the rooms, lines which will be perpendicular to all of them at the same time.
It would appear, then, that our reflective mind-operations are habitually four dimensional, and conform to the conditions of a space of four dimensions. Take, for instance, memory.
Bergson showed conclusively, in the book translated with the title Matter and Memory, that it is foolish to think of mind-pictures as being lodged in the physical substance of the brain. He gets them out of the brain, but he does not make it wholly clear where he gets them to. It would seem to be quite evident that they are in a four-dimensional picture gallery; and, therefore, each of the innumerable rooms in that gallery is as near to you as any other, so that you can look with equal ease at any picture, on any wall. Speaking three-dimensionally, all the mind-images are in the same place. But speaking four-dimensionally, they are ranged in admirable order, so that you can immediately pick out any one.
Take a kind of mind-picture that is easily counted—a word. You know a great many thousand words in your own tongue, familiar, literary, scientific and technical words. Each one is as near your vocal perception as any other. They are ranged in four-dimensional order. If you learned a dozen languages in addition to your own, it would be just the same. Each of several hundred thousand words would be equally near the focus of your consciousness.
So it would seem that we are familiar with the fourth dimension; though we may not have recognized the fact. Our minds are there already. If we could drive inward, into and through the mind, so that the mind might be external to our consciousness, as the body now is; the mind would then be a kind of body, or, to put it otherwise, we should be in possession of a mind-body, in which we could quite easily do four-dimensional things like being in two places at once. Perhaps that is what the Dream of Ravan is suggesting.
Now let us go back again, and try to get a further hold of the time-space problem. You are at present at a certain point on the surface of the earth. The diurnal rotation of the globe from west to east causes the sun to appear over your eastern horizon, to pass through the meridian, and then to descend to the western horizon. That is a general experience. After the sun sets, stars begin to appear, and for the same reason, make the same journey. So you have the succession of morning, noon and evening, of day and night. It is a time-succession for you, lasting twenty-four hours.
But if, instead of looking with your physical eyes at day and night, you think of them in the roomy chamber of your mind, you will easily be able to imagine the earth, one side turned toward the sun, and the other side turned toward outer space: a bright half and a dark half; day and night both going on at the same time, no longer successive but simultaneous. And it is quite clear that both day and night are thus always going on at the same time. There is no to-day nor to-morrow, no this-morning or last-night. It is perpetually “now,” with half the world lit up and half in darkness, or illumined only by the stars.
We have, therefore, by mentally standing apart from the earth and looking at it from outside, transformed the succession of day and night from a time-aspect to a space-aspect ; from consecutive to simultaneous.
Might it not be possible for a spiritual consciousness to do the same thing, standing apart, not from the outer vesture of life, its days and nights, but from its inner content of experience, and thus to see the succession of past, present and future as a single vision, in the light of eternity? Perhaps this is the reason why every religious system teaches this standing back—detachment?
We saw, a little while ago, that what appears as a succession in a lower-dimensioned consciousness, becomes simultaneous in a higher-dimensioned consciousness. Let us try to apply this.
Let us suppose that a Master, in whom we must postulate a higher-dimensioned consciousness, has a dozen pupils. How can he watch them all, train and guide them all, at one and the same time?
A three-dimensional college-professor can take care of a dozen students by giving his full attention to each in turn. This is strictly comparable to the first perception of the foot-rule as a succession of inch-marks perceived successively throughout a certain duration of time. But, just as, by adding a dimension of consciousness, it was possible and easy to get a view of all twelve inch-marks simultaneously, so it may be possible and easy for the Master, in virtue of a higher-dimensioned consciousness, to hold a dozen pupils in full view simultaneously, giving complete and uninterrupted attention simultaneously to all the twelve. What is possible as a succession for the college professor, may be possible as a simultaneous perception for the Master.
Extend this, and it becomes quite thinkable that a divine consciousness may listen simultaneously to the prayers of ten millions of worshippers and may follow in detail the worship in a million churches at once.
One more thought. Our bodies are three-dimensional, and to our bodies the Theosophical teaching assigns three Principles. Ordinary mental consciousness is in a fourth principle, Kama-Manas. But we have seen that ordinary consciousness, the ordinary operation of mind and memory, is in all probability already four-dimensional, though rarely indeed so recognized.
Have we a suggestion, in the Master, of the presence at once of a fully awakened fifth Principle, Buddhi-Manas, and of a still higher-dimensioned consciousness?
Approach the matter this way. Zöllner was the first to write vividly of the fourth dimension; Bergson saw many four-dimensional truths, though he may not have given them that name; Einstein and his followers are familiarizing us with four-dimensional thought.
Yet something is lacking. We have seen that there is a clear correspondence between certain principles of the higher dimensions and fundamental laws of spiritual life. May we not conclude that the spiritual laws are the reality, while the four-dimensional reasonings are, in the strict sense, “superficial” aspects of spiritual laws? They touch surfaces only; they lack spiritual depth. And, to sum the matter up, may not this spiritual depth be that very “fifth dimension” which we are in search of, the element that is needed, to give spiritual depth to these physical and mathematical speculations?
Bergson has worked wonders. Einstein is working wonders. But what might they not have done, had they added devotion, the religious sense, to their extraordinarily intuitive minds? Instead of having physical aspects of occult laws, we might have had revelations of the everlasting realities of spiritual life. The “fifth dimension” is lacking, the depth given by the awakened fifth Principle, Buddhi-Manas, the power of spiritual light.