The Secret of the Universe, by Nathan R. Wood, [1932], at sacred-texts.com
The Secret of the Universe, by Nathan R. Wood, [1932], at sacred-texts.com
What is the Fourth Dimension?—Is time the fourth dimension?—The principle of the "light-year"—The Multiplication Table of Space, Motion and Time—The formula of the physicist—What you cannot do with space, motion and time—The Absolute Relationships of Space, Motion and Time—In how many dimensions do events occur?—The Formula of the True Relativity.
What is the fourth dimension?
This is not to-day a fantastic question, an idle puzzle. It has never really been so. An eager and deep-seated instinct has asked the question and great significances hover around it.
What is that fourth dimension, which apparently does not exist, but to which reason strongly leads? It comes from motion in space, and its logic is beyond question. We may easily follow the steps of the standard argument:
The motion of a point generates one dimension, or a line, an unbroken series of locations or points. That is very clear. A moving point creates a line.
The second step is equally evident:
The motion of a line or series of points generates a plane, or two dimensions. We can see this also without difficulty. A line moving sideways creates a second dimension.
And the third step is equally clear:
The motion of a plane generates a solid, or three dimensions. This also we easily realize. A plane, of two dimensions, held level, for instance, and moved up and down, creates a third dimension.
But now we come to ground without a chart. What does the motion of a solid generate? Many say "A fourth dimension." That seems to follow out the logic of the first three steps.
But no one has ever experienced a fourth dimension.
Does logic truly run away from reality in this matter? It seems to. Indeed, once started on that way, it seems beyond control. If a fourth dimension, why not a fifth? What would the motion of a four-dimensional figure generate, except a fifth dimension? And why not a sixth and seventh and eighth dimension? Can it be that logic runs out into an endless chain of such dimensions, further and further from reality? Can there really be such a divorce of logic from reality, and of logic based not on uncertain premises, but on the three dimensions of space and of geometry? How can the threefold reality of geometry so suddenly land us, at one move, in a world of ever-increasing unrealities?
Yet surely the motion of three dimensions generates something. The motion, the reality, of one dimension, a line, generates a second dimension. The motion, the reality, of two dimensions, a plane, makes three dimensions. What further reality do three dimensions generate? What is the product of three dimensions? Or if there are other dimensions also, what is the product of all possible dimensions?
That fourth property or "fourth dimension," or, if there are more dimensions, the final property, of space is not time.
Einstein, who roams much in the realm of the fourth dimension, regards time as the "fourth dimension," because,
he says, things happen in three dimensions of space and in one of time. Indisputably things do happen in time as well as in space. Einstein believes that this fourth property or "fourth dimension," or time, is the "continuum," the thing which binds everything, including the dimensions of space, together. A point in "four dimensions," or a thing which happens, he rightly calls an "event," because it must be more than a point, it must be something which happens, in order to have a place in time. And he is sure that things occur in three dimensions of space and in one of time. Equally sure are many of his followers. Indeed much of the fabric of the newest scientific view of the universe, with its overthrow of classical physics, is built up on the assumption that, because things happen in three dimensions of space and also in time, this is a four-dimensional world, with three dimensions of space and one of time. And many announcements in astronomy and physics, scientific in their working out and terminology, are in reality based upon the purely speculative foundation of the theory of "Space-time," and are of no more certain validity than their basic speculation.
And now it is announced that the entire physical universe becomes one single reality,—namely, space,—and that space has swallowed up time, by making time its fourth dimension.
And finally, on the other hand, a new geometry, to embrace all the facts of the physical universe, is projected, with time as a dimension of space set forth as the basis of the new system.
But is time the fourth dimension of space? All of these things depend upon that assumption. Do the evidences which are brought to demonstrate that time is
the fourth dimension of space stand up against the strong wind of common sense or of reason? That is what we have a right to consider for ourselves.
In order to prove that time is the fourth dimension it is very much the thing to-day to point out that when one would measure vast distances in the universe one must go beyond the old space methods and use time units as well as space units of measurement. When we have a vast astronomical distance to be expressed, we call in the aid of time. We say that such a star is a million "light-years" away. We mean by a light-year the distance which light, at the rate of approximately 186,000 miles a second, goes in one year. Does not this prove that time is fundamental in great basic measurements? Does it not mean that time is an essential element of space? Does it not show that time is a "fourth dimension" of space?
At the cost of disagreeing with what many minds regard as an axiom to-day, one can only say, if one is doubtful, "It does not seem to me to prove what you I say that it proves." Far the fact is that the now common light-year measure of distance does not arise from the nature of distance or of space. It arises entirely from the limitations of our minds. Because we cannot grasp more than a certain number of smaller units of distance, we combine them into larger units for our mental convenience. It is exactly as when, to avoid `too great a number of inches, we say feet, instead of inches, or when, to avoid too great a number of feet, we say miles instead of feet. In time-measurements, also, when seconds grow too many, we say minutes, and
when minutes become too many, we say hours, and when hours multiply too largely, we say weeks, and when weeks add themselves into a great total, we say years. We manufacture larger units to bring the total number better within the grasp of our minds. We manufacture light-years simply as a larger unit of measurement. If the use of time in measuring distance lay in the real nature of measurement of space, we should have to use time in all measurements of space. We should have to use it as a factor in measuring short distances. But we do not use it so at all. We do not use time as a factor in measuring feet or metres, or in measuring miles on the earth. The only people who use it so are those whose mental ability is so low that they cannot compute space distances at all, and who say, "It is so many days' journey," or "so many hours' journey," or "it is as far as a horse would travel between sunrise and sunset," or "as far as a man could walk, carrying a sheep, between moon and moon." Such things, day's journeys of a horse, or month's journeys of a man, or year's journeys of a light-ray, do not mean that time is a dimension of space. They signify simply a greater or less degree of mental inability to grasp large numbers of units of distance. Equally well the savage meets the difficulty by saying, "It is ten times as far as from the mountain range to the distant river," or the scientist by saying, "It is a million times as far as the distance from the earth to the sun," or the mathematician by saying, "It is a trillion miles carried to the 10th power." It is all a matter of constructing larger units of measurement, so as to bring down the total number of units to the
range of our comprehension. It does not at all show that time is a dimension of space.
But the sensible way to settle the question is not by arguing against a mistaken association of time with space. It is by working out and presenting the actual relations. It is useless to argue that time and space are not related. They are related. They are commensurate. They are indeed so commensurate that we can describe one in terms of the other. The trouble is not that this is true. The facts should never give us trouble. The trouble is that it is only a part of the truth. It is only what the triunity of space, motion and time shows of all three of those elements. They are all three commensurate. And it is only through its part in that triunity, and by its connection with space through motion, that time is commensurate with space. It is only through motion that we can measure space and time in connection with each other.
We can measure space by motion and express the result in terms of time.
100 miles covered by a motion of 25 miles an hour, and divided by 25 to get the number of hours, results in an elapsed time of 4 hours. 100 ÷ 25 = 4. Hence the basic rule:
1. Space measured or divided by motion gives time.
The distance, divided by the rate of motion at which you travel, will tell you how long, or how much time, it will take you.
This is the basic rule. Space can be measured by motion in terms of time because motion touches both
space and time and is expressed in terms of both. There is no direct relation between space and time. 100 miles and 4 hours have no connection unless there is motion which covers those miles in those hours and links the two together. The time is related to the space through the motion.
Now this is because motion must always touch both space and time, and be commensurate with both, and with both at once. Motion can be expressed only by both space and time at once. Space can be reckoned by itself,—e. g., "100 miles." Time can be reckoned by itself—e. g., "4 hours." But motion can be reckoned only by space and time, and only by both at once. "A rate of motion of 25 miles" means nothing. "A rate of motion of one hour" means nothing. But "a rate of motion of 25 miles an hour," both space and time at once, is well defined.
And this is the triune relationship which we have already seen,—that motion comes out of space and passes into time and so links space and time together. It is the principle of the space-motion-time universe. The creative power, whose omnipresent outspreading into dimensions is space, emerges into energy and motion, and motion issues in successiveness or time.
Time then is related to space through motion, and only through motion, and only in the triune relation of space-motion-time.
We can also use time by motion, with space as its result. Using a time of 4 hours, a motion of 25 miles an hour will cover 100 miles. 4 × 25 = 100. That is, for the second rule:
2. Time multiplied by motion gives space.
The time elapsed, multiplied by the rate of motion, will give you the distance you travelled.
This is manifestly the reverse of the first rule. Because space divided by motion gives time, time multiplied by motion gives space again. The quotient multiplied by the divisor gives the original number again. That is what it means. The time multiplied by the motion does not actually produce space. Both motion and time presuppose space. It is simply an arithmetical transaction in which we multiply the quotient by the divisor to get the original dividend, the 4 by the 25 to get the 100 out of which they both came. And the connection of the time with the space, whether we are dividing the space or multiplying the time, is always through the motion. There is no connection between 100 miles and 4 hours, unless motion comes and spans the 100 miles in the 4 hours, and so binds the two together, or in turn multiplies the time to give the original space again. It is the triune formula.
A third relation also issues from the first. Since "space divided by motion gives time," therefore:
3. Space divided by time gives motion.
The distance, divided by the time it took you to cover it, gives you your rate of motion.
A space of 100 miles covered in 4 hours, and divided by the 4 to get the miles for one hour, shows a motion of 25 miles an hour. 100 ÷ 4 = 25.
This does not mean that time measures and divides space as motion does. We cannot measure space by time. We cannot cover 100 miles by 4 hours. They
are not commensurate, that is, they are not commensurate unless motion comes between, and connects them. But "100 miles covered in 4 hours" means "100 miles covered by motion in 4 hours." It was the motion which measured and divided the space and gave the time.
"The space divided by the time gives the motion" simply sets forth then the converse of the basic fact that "the space divided by the motion gives the time." For you can always divide the original number by the quotient to get the divisor. As 100 ÷ 25 = 4, so 100 ÷ 4 = 25. It is an arithmetical transaction. And it expresses again the basic fact that "space measured or divided by motion gives time,"—the triune principle of the space-motion-time universe.
* (The physicist uses the constant formula in his work: v = d/t,—"the velocity = the distance ÷ the time." Or, which means the same thing, "the rate of motion = the space ÷ the time." Or we can put the equation in the other order: d/t = v, "the space ÷ the time = the rate of motion."
We see now, in the light of the universal triunity, and of the triune relations of space, motion and time, the great reason which underlies this working formula of d/t = v, or the space / the time = the rate of motion. It is not
because the time measures and divides the space. We cannot measure or divide space by time. Space and time are not in themselves commensurate. 100 miles has nothing to do with 4 hours, for instance,—unless motion covers that 100 miles in that 4 hours, and links the two together. Then "100 miles ÷ a motion of 25 miles an hour gives a time of 4 hours." "The space ÷ the rate of motion = the time." Or, in terms of the physicist's equation, d/v = t, or t = d/v. That is the basic relationship,—"space ÷ motion gives time,"—without which there are no relationships between space, motion and time. But because d ÷ v = t, or d/v = t, you can, if you have the distance and the time, and want to find the velocity, divide the dividend by the quotient, divide the d by the t, to get the divisor or velocity, v. Then at once you have as a working rule, based on our triune law that space / motion = time, or d/v = t, the reverse rule, dividend/quotient = divisor, or space /time = motion, or the useful tool of the physicist, that d/t = v. The triune law of all things, and of space, motion and time, gives the reason. d/t= v simply because d/v= t;—the distance divided by the time equals the speed, because the distance divided by the speed equals the time.
[paragraph continues] You can always divide the distance by the time and get the velocity,—even though distance and time are not in themselves commensurate, because "the distance or space covered and divided by the velocity or rate of motion gives the time.")
And a fourth rule follows as a consequence of the basic rule. Since "space measured or divided by motion gives time," then you can reverse the process, and find that:
4. "Motion multiplied by time gives space."
The rate of motion, multiplied by the time elapsed, gives you the distance.
A motion of 25 miles an hour, for a time of 4 hours, covers a space of 4 times 25 miles, or 100 miles. The motion multiplied by the time gives the space. 25 × 4 = 100.
This obviously does not mean that the 100 mile space exists as the product of the 25 mile motion and the 4 hour time. What it means is that you can multiply the divisor by the quotient and get the original number or dividend. Since the space divided by the motion gives the time, then the motion multiplied by the time will give the space again. It is a matter of arithmetic. It comes from the basic fact that the space divided by the rate of motion gave the time. It expresses and shows in reverse the triune formula of space-motion-time.
These four rules all express the same relationships,—that space is always the source in this triunity,—motion is always next,—motion alone is directly commensurate with space and can measure space,—time always
results when motion measures space,—motion can be measured only in terms of both time and space, which it links together, they are all three then commensurate with each other in this triunity of the three,—but time is commensurate with space and can be related to space only as a part of that triunity, as it is linked with space through motion, or comes from space through motion.
[There are no other such relations between the three. For other operations are not possible. The following paragraphs seem meaningless because to a certain extent they are meaningless. But their impossibility is instructive. Yet you may skip these "cannots" if you will.
You cannot divide motion by time.
"A rate of twenty-five miles an hour divided by four, the number of hours passed," means nothing, and gets no results.
You cannot divide motion by space.
"A rate of 25 miles an hour divided by 100, the number of miles traversed," means nothing at all. If you say "25 ÷ 100 = ¼ miles," it means simply that 1/100 of 25 miles an hour is ¼ mile an hour. But it has no significance in the relations of space, motion and time, any more than the similar facts that 1/200 of 25 miles an hour = ⅛ mile an hour, or that 1/50 of 25 miles an hour = ½ mile an hour. It has nothing to do with one hundred as the number of miles.
And you cannot divide time by space.
"Four hours divided by 100, a certain number of miles," means nothing. You can, it is true, divide the four hours by 100, and get 1/25 of an hour, the time required to go one mile. But it means simply that we
have reduced the dividend, 100 miles, in "100 ÷ 25=4," to one mile by dividing by 100, and so as a matter of arithmetic we must divide the quotient, four hours, by 100 also, and we get 1/25 of an hour. We could equally well divide the 100 by fifty and get two miles, and the four hours by fifty and get 2/25 of an hour. We simply reduce both dividend and quotient by the same ratio, and we chose to divide the 100 miles by 100 in order to reduce the distance to one mile. In reducing the dividend and the quotient by the same ratio we have but stated anew, on a scale 1/100 as large, the formula that "the distance or space ÷ the rate of motion gives the time."
And you cannot divide time by motion.
"Four hours divided by a rate of motion of twenty-five miles an hour" means nothing and accomplishes nothing. You can only multiply the time by the rate of motion, the quotient by the divisor, and get the dividend or distance.
And you cannot multiply space by motion.
"One hundred miles multiplied by a rate of twenty-five miles an hour," would be 2,500 miles, which is arithmetically correct, but an absurdity. You can only divide the one hundred by the twenty-five, and get four, the number of hours elapsed. You can only divide the space by the rate of motion and get the time.
Neither of course can you multiply motion by space.
"Twenty-five miles an hour multiplied by one hundred, the total number of miles traversed," would again be 2,500, this time "2,500 miles an hour," which is again absurd and meaningless.
Neither can you multiply space by time.
"One hundred miles multiplied by four, a certain numbers of hours," means nothing. You can only divide the one hundred miles by four, the number of hours passed in motion, and get the twenty-five miles an hour, the rate of motion.
Neither of course can you multiply time by space.
"Four hours multiplied by one hundred, a certain number of miles," means nothing. There is no connection, no relevancy, between the hours and the miles. It is only when the four hours are the time resulting as a certain motion covers the space of one hundred miles that you can relate the four hours and the one hundred miles to each other. They are related to each other solely through the motion. And then you can only divide the space by the time, the one hundred by the four, and get twenty-five, the miles per hour, because the space was the dividend and the time was the quotient in "the space ÷ the rate of motion = the time."]
These include all the possible or impossible combinations of the three,—space, motion and time. Even the impossibilities emphasize the relationship which the four possible combinations so clearly express. This relationship is so self-evident as to be axiomatic:
2. Space therefore, the dividend, can as a matter of arithmetic be divided by time, the quotient,
3. The rate of motion and the time can be multiplied, either one by the other, the divisor multiplied by the quotient, or the quotient multiplied by the divisor, the rate of motion multiplied by the time, or the time multiplied by the rate of motion, with the dividend, the distance or space traversed by that motion in that time, discovered again by the multiplication.
4. Space is the source. It is space which is traversed and measured or divided up by the rate of motion, with time as the result.
5. Motion links space and time together; it emerges from space and issues in time; and it can be measured and expressed only in terms of both space and time.
6. Time is commensurate with space to this extent, and only to this extent, that since time is the product when motion emerges and traverses space, time is commensurate with space through motion.
Two facts stand clear in these relationships:
First, that all these relationships express the absolute formula of triunity, namely, that space is the basis, motion traverses the space, and time is the result.
Second, that time is related to space only through motion, and is not the "fourth dimension" of space. It is, rather, the third factor in the triunity of space, motion and time.
Light-year measurement is in entire harmony with these axioms. The astronomer knows a certain vast distance. It is a distance so vast that the figures benumb the mind, and convey no real impression. He wants to express the distance vividly. He says "We will measure it by motion. A certain motion, the speed of light, moving at a rate of 186,000 miles a second, spends so many years, so many light-years, or years of that motion of light, in covering that space." It is that space measured or divided by that rate of motion of light, with years, or time, as a result. It is the triune formula, "Space measured or divided by motion gives time."
Or let us put it not from the astronomers' point of view but from the hearers' or readers' point of view. Here, then, is a vast distance. We do not know that distance, as the astronomer does. But we do know the speed of light. And we do know how long a year is. And so the astronomer tells us that the speed of light, multiplied by a certain number of years during which that light moves, gives the total distance over which that light has moved. It is the rate of motion which traversed the distance, multiplied by the time elapsed, to give the distance,—the motion multiplied by the time to give the space. It is the triune formula,—"The motion multiplied by the time, the divisor multiplied by the quotient, gives the original space."
It reveals time yet again, very strikingly, not as a "fourth dimension" of space, bound in direct union with space, but rather as having its sole connection
with space through motion, whether it is "space divided by motion gives time" or "the motion multiplied by the time gives the original space;" and as having its only connection with space in the fact that time is the third factor in the vast triunity of space, motion and time.
The theory of relativity has this value, besides others, that it clearly recognizes the great fact of Motion as the essence of all physical things. It realizes that things "happen" rather than merely "exist," and are "events" instead of inert and static things, because they are actions, motions, conjunctions of forces, collisions or propulsions of electrons, with their incredible motion. And of course where motion so exists time enters as an element. For time in the physical world is the successiveness of motion in space.
But it is not correct to say that things occur in three dimensions of space and in one of time, and so to make time a fourth dimension or property of space, even though this is almost an axiom of much present-day thought. It is an evanescent point of view.
For, as a matter of fact, events do not so occur.
They occur in three dimensions of space and in three dimensions of time.
Every event is in future, present and past.
It occurs in present time.
Before its occurrence in present time it is in future time.
After its occurrence in present time it is in past time. It cannot be in time without being in all these three elements of time.
As for those important events which we call thoughts, many of those, which have nothing to do with the outer world, but which are always consecutive, occur in no dimensions of space and in three dimensions of time.
But of things in the physical world, all of which, being motion, do "happen" or "occur," all of them occur in three dimensions of space and in three of time. Time is not the fourth dimension of space. Time in the physical world is, as we have seen, self-evidently the outcome of the relation of space to motion. It is the successiveness of motion in space. It is the third element in that universal triunity of space, matter and time. But it is not a fourth property added to the triunity of space. It is the third property in the greater triunity of space, matter and time. And it is itself a triunity, of future, present and past. For the True Relativity is not a vast and shifting irregularity, a systematized uncertainty. The True Relativity is a vast, invariable, regulated, infinite interplay and triunity of Space, Motion and Time. It is a Triuniverse in the reflection and image of a Triune Creator and Ground of the universe.
154:* The general reader may omit the reading of this parenthesis, if he so prefers.