V CURVED TIME
TIME FROM THE STANDPOINT OF EXPERIMENT AND OF CONSCIOUS EXPERIENCE
In some moment of "sudden light" what one of us has not been able to say, with Rossetti,
"I have been here before,
But when or how I cannot tell."
Are such strange hauntings of our House of Life due to the cyclic return of time? Perhaps,—but what is time?
Suppose some one should ask you, "What is an hour?" Your answer might be, "It is the interval marked off by the clock-hand between 1 and 2." "But what if your clock is running down or speeding up?" To this you would probably reply, "The clock is set and corrected by the earth, the sun and the stars, which are constant in their movements." But they are not. The earth is known to be running slow, by reason of tide friction, and this is likely to continue until it will revolve on its axis, not once a day, but once a year, presenting always the same face to the sun.
We can only measure time by uniform motion. Observe the vicious circle. Uniform motion means the covering of equal spaces in equal times. But how are we to determine our equal times? Ultimately we have no other criterion save the uniform motion of the clock-hand or the star dial. The very expressions, "uniform motion," "equal times," beg the whole question of the nature of time.
Let us then, in this predicament, consider time not from the standpoint of experiment, but of conscious experience—what Bergson calls "real duration."
Every point along the line of memory, of conscious experience, has been traced out by that unresting stylus we call "the present moment." The question of its rate of motion we will not raise, as it is one with which we have found ourselves impotent to deal. We believe on the best of evidence that the conscious experience of others is conditioned like our own. For better understanding let us have recourse to a homely analogy: let us think of these more or less parallel lines of individual experience in the semblance of the strands of a skein of flax. Now if, at the present moment, this skein were cut with a straight knife at right angles to its length, the cut end would represent the time plane—that is, the present moment of all—and it would be the same for all providing that the time plane were flat But is it really flat? Isn't the straightness of the knife a mere poverty of human imagination? Existence is always richer and more dramatic than any diagram.
"Line in nature is not found;
Unit and universe are round.
In vain produced, all rays return;
Evil will bless and ice will burn."
Undoubtedly the flat time-plane represents with fair accuracy the temporal conditions that obtain in the human aggregate in this world under normal conditions of consciousness, but if we consider our relation to intelligent beings upon distant worlds of the visible universe the conditions might be widely different The time section corresponding to what our straight knife made flat in the case of the flax may be—nay, probably is—strongly curved.
RELATIVITY
This crude analogy haltingly conveys what is meant by curved time. It is an idea which is implicit in the Theory of Relativity. This theory has profoundly modified many of our basic conceptions about the universe in which we are immersed. It is outside the province of this book and beyond the power of its author even so much as to sketch the main outlines of this theory, but certain of its conclusions are indispensable, since they baldly set forth our dilemma in regard to the measurement of space and time. We can measure neither except relatively, because they must be measured one by the other, and no matter how they vary, these variations always compensate one another, leaving us in the same state of ignorance that we were in before.
Suppose that two intelligent beings, one on Mars, let us say, and the other on the earth, should attempt to establish the same moment of time, by the interchange of light signals, or by any other method which the most rigorous science could devise. Assume that they have for this purpose two identically similar and mechanically perfect chronometers, and that every difficulty of manipulation were successfully overcome. Their experiment could end only in failure, and the measure of this failure neither one, in his own place, could possibly know. If, after the experiment, the Martian, chronometer in hand, could be instantly and miraculously transported to the earth, and the two settings compared, they would be found to be different: how different, we do not know.
The reason for the failure of any such experiment anywhere conducted can best be made plain by a crude paraphrase of a classic proposition from Relativity. Suppose it is required to determine the same moment of time at two different places on the earth's surface, as must be attempted in finding their difference in longitude. Take the Observatory at Greenwich for one place, and the observatory at Washington for the other. At the moment the sun is on the meridian of Greenwich, the exact time of crossing is noted and cabled to Washington. The chronometer at Washington is set accordingly, and the time checked back to Greenwich. This message arrives two seconds, say, after the original message was sent. Washington is at once notified of this double transmission interval. On the assumption that HALF of it represents the time the message took to travel from east to west, and the other half the time from west to east again, the Washington chronometer is set one second ahead of the signalled time, to compensate for its part of the loss. When the sun has reached the meridian of Washington, the whole process is repeated, and again as before, half of the time the message has taken to cross and recross the Atlantic is added to the Greenwich record of noon at Washington. The number of hours, minutes, seconds, and fractions of a second between these two corrected records represents the difference in solar time between the two places, and incidentally the same moment of time has been established for both—at least, so it would appear.
But is it established? That each message took an equal time to travel each way is pure assumption, and happens to be a false one. The accuracy of the result is vitiated by a condition of things to which the Relativists have called attention. Our determination might be defended if Washington and Greenwich could be assumed to remain at rest during the experiments, and some argument might even be made in its favor if we could secure any cosmic assurance that the resultant motion of the earth should be the same when Greenwich signalled its noon to Washington and Washington its noon to Greenwich.
Our present discussion is merely illustrative, or diagrammatic; so we will neglect the velocity of the earth in its orbit round the sun, some forty times greater than that of a cannon ball, and the more uncertain and more vertiginous speed of the whole solar system towards its unknown goal. Let us consider only the rotation of the earth on its axis, the tide-speed of day and night. To fix our idea, this may be taken, in our latitudes, at eighteen thousand miles per day, or perhaps half the speed of a Mauser rifle bullet.
So fast, then, will Washington have been moving to meet the message from Greenwich. So fast will Greenwich have been retreating from Washington's message.
Now the ultimate effect of motion on the time-determination cannot be calculated along any such simple lines as these. Indeed, it cannot be exactly calculated at all, for we have not all the data. But there is certainly some effect. Suppose one rows four miles up a river against a current of two miles per hour, at a rowing speed of four miles per hour. This will take two hours, plainly. The return trip with the river's gift of two miles per hour will evidently require but forty minutes. Two hours and forty minutes for the round trip, then, of eight miles.
Now then, to row eight miles in still water, according to our supposition, would have required but two hours. But, some one objects, the current must help the return trip as much as it hindered the outgoing! Ah, here is the snare that catches rough-and-ready common sense! How long would the double journey have taken if the river current had been faster than our rowing speed? How shall we schedule our trip if we cannot learn the correct speed, or if it varies from minute to minute?
These explanations are necessarily symbolistic rather than demonstrative, but any one who will seriously follow out these lines of thought, or, still better, study the attitude of the hard-headed modern physicist towards our classical geometry and mechanics, cannot fail to realize how conventional, artificial—even phantasmal—are the limitations set by the primitive idea of flat space and straight time.
The inferences which we may draw from our hypothetical experiment are plain. The settings of the two chronometers would be defective, they would not show the same time, but each of them would mark the local time, proper to its own place. There would be no means of detecting the amount of error, since the messages were transmitted by a medium involved with them in their transportation. If only local time can be established, the possibility of a warped time-plane—the curvature of time—is directly opened up. Doubtless it is true that on so relatively minute a scale as is offered by the earth, any deviation from perfect flatness of the time-plane would be so inconsiderable and imperceptible as to make it scientifically negligible; but this by no means follows when we consider our relation to other worlds and other systems.
A similar condition holds with regard to space-distortion. The Theory of Relativity enforces the conclusion that from the standpoint of our conventions in regard to these matters, all bodies involved in transportation undergo a contraction in the direction of that transportation, while their dimensions perpendicular to the transportation remain invariable. This contraction is the same for all bodies. For bodies of low velocity, like the earth, this distortion would be almost immeasurably slight; but great or little, no measuring instruments on the body transporting would ever disclose it, for a measure would undergo the same contraction as the thing measured.
THE SPOON-MAN
These concepts that space and time are not as immutable as they appear: that our universe may suffer distortion, that time may lag or hasten without our being in the least aware, may be made interestingly clear by an illustration first suggested by Helmholtz, of which the following is in the nature of a paraphrase.
If you look at your own image in the shining surface of a teapot, or the back of a silver spoon, all things therein appear grotesquely distorted, and all distances strangely altered. But if you choose to make the bizarre supposition that this spoon-world is real, and your image—the spoon-man—a thinking and speaking being, certain interesting facts could be developed by a discussion between yourself and him.
You say, "Your world is a distorted transcript of the one in which I live."
"Prove it to me," says the spoon-man.
With a foot-rule you proceed to make measurements to show the rectangularity of the room in which you are standing. Simultaneously he makes measurements giving the same numerical results; for his foot-rule shrinks and curves in the exact proportion to give the true number of feet when he measures his shrunken and distorted rear wall. No measurement you can apply will prove you in the right, nor him in the wrong. Indeed he is likely to retort upon you that it is your room which is distorted, for he can show that in spite of all its nightmare aspects his world is governed by the same orderly geometry that governs yours.
The above illustration deals purely with space relations, for such relations are easily grasped; but certain distortions in time relations are no less absolutely imperceptible and unprovable. So far from having any advantage over the spoon-man, our plight is his. The Principle of Relativity discovers us in the predicament of the Mikado's "prisoner pent," condemned to play with crooked cues and elliptical billiard balls, and of the opium victim, for whom "space swells" and time moves sometimes swift and sometimes slow.
THE ORBITAL MOVEMENT OF TIME
Now if our space is curved in higher space, since such curvature is at present undetectable by us, we must assume, as Hinton chose to assume, that it curves in the minute, or, as some astronomers assume, that its curve is vast. These assumptions are not mutually exclusive: they are quite in analogy with the general curvature of the earth's surface which is in no wise interfered with by the lesser curvatures represented by mountains and valleys. It is easiest to think of our space as completely curved in higher space in analogy with the surface of a sphere.
Similarly, if time is curved, the idea of the cyclic return of time naturally (though not inevitably) follows, and the division of the greater cycles into lesser loops; for it is easier to assign this elliptical movement to time than any other, by reason of the orbital movements of the planets and their satellites. What results from conceptions of this order? Amazing things! If our space is curved in higher space, you may be looking toward the back of your own head. If time flows in cycles, in travelling toward to-morrow you may be facing yesterday.
This "eternal return," so far from being a new idea, is so old that it has been forgotten. Its reappearance in novel guise, along with so many other recrudescences, itself beautifully illustrates time curvature in consciousness. Yugas, time cycles, are an integral and inexpugnable part of Oriental metaphysics. "Since the soul perpetually runs," says Zoroaster, "in a certain space of time it passes through all things, which circulation being accomplished, it is compelled to run back again through all things, and unfold the same web of generation in the world." Time curvature is implicit in the Greek idea of the iron, bronze, silver, and golden ages, succeeding each other in the same order: the winter, seed-time, summer and harvest of the larger year. Astrology, seership, prophecy, become plausible on the higher-time hypothesis. From this point of view history becomes less puzzling and paradoxical. What were the Middle Ages but a forgetting of Greek and Roman civilization, and what was the Renaissance but a remembering of them—a striving to re-create the ruined stage-settings and to re-enact the urbane play of Pagan life. The spirit of the Crusades is now again animate throughout Europe. Nations are uniting in a Holy War against the Infidel de nos jours.
But it is in the individual consciousness that time curvature receives its most striking confirmation—those lesser returns and rhythms to which we give the name of periodicity. Before considering these, however, a fundamental fallacy of the modern mind must be exposed.
MATERIALITY THE MIRROR OF CONSCIOUSNESS
Our vicious habit of seeking the explanation of everything—even thought and emotion—in materiality, has betrayed us into the error of attributing to organic and environic changes the very power by which they are produced. We are wont to think of feeling, the form in which Being manifests to consciousness, as an effect instead of as a cause. When Sweet Sixteen becomes suddenly and mysteriously interesting to the growing boy, it is not because sex has awakened in his body, but because the dread time has come for him to contemplate the Idea of Woman in his soul. If you are sleepy, it is not because the blood has begun to flow away from your brain, but because your body has begun to bore you. Night has brought back the Idea of Freedom, and consciousness chloroforms the thing that clutches it. If you are ill, you grow cold or your temperature rises: it is the signal by which you know that your consciousness is turning toward the Idea of Pain.
Just as a savage looks for a man behind a mirror, we foolishly seek in materiality for that which is not there. The soul determines circumstance: the soul contains the event which shall befall. The organic and environic rearrangements incident to obscure rotations in higher space are like the changes a mirror-image undergoes as an object draws near and then recedes from its plane. This is only a figure of speech, but it is susceptible of almost literal application. Ideas, emerging from the subconscious, appproach, intersect, recede from, and re-approach the stream of conscious experience; taking the forms of aversions and desires, they register themselves in action, and by reason of time curvature, everything that occurs, recurs.
PERIODICITY
We recognize and accept this cyclic return of time in such familiar manifestations of it as Nature affords in periodicity. We recognize it also in our mental and emotional life, when the periods can be co-ordinated with known physical phenomena, as in the case of the wanderlust which comes in the mild melancholy of autumn, the moods that go with waning day, and winter night. It is only when these recurrences do not submit themselves to our puny powers of analysis and measurement that we are incredulous of a larger aspect of the law of time-return. Sleep for example, is not less mysterious than death which, too, may be but "a sleep and a forgetting." The reason that sleep fails to terrify us as death does is because experience has taught that memory leafs the chasm. Why should death bedreaded any more than bedtime? Because we fear that we shall forget. But do we really forget? As Pierre Janet so tersely puts it, "Whatever has gone into the mind may come out of the mind," and in a subsequent chapter this aphorism will be shown to have extension in a direction of which the author of it appears not to have been aware. Memory links night to night and winter to winter, but such things as "the night-time of the spirit" and "the winter of our discontent" are not recognized as having either cause or consequence. Now though the well-springs of these states of consciousness remain obscure, there is nothing unreasonable in believing that they are recrudescences of far-off, forgotten moods and moments; neither is it absurd to suppose that they may be related to the movements and positions of the planets, as night and winter are related to the axial and orbital movements of the earth.
But there are other, and even more interesting, evidences of time curvature in consciousness. These lead away into new regions which it is our pleasure now to explore.