The very recondite aspects of the Esoteric Philosophy can be approached only after a sufficient foundation of teaching has been laid down, otherwise they would be meaningless. The first chapter of this book served in part as such a foundation, and with the little that has been already covered, we are prepared to take at least the first steps forward into the unspeakably grand teachings about the nature of the Universe of and of Man, which, as has been pointed out, concern chiefly his relation to the Solar System.
We must necessarily pause on the threshold of this further study in order to clarify the picture in some important respects. First of all, it must be made clear that in relating the regular polyhedra to Man's nature and to his place in the Universe, we were dealing with Man as a special case only; but it must be borne in mind that a genuine symbol has universal application. This in fact is the test of the genuineness of any symbol. Can it be applied universally? If it can, then it is a reliable tool, and one of very great value. In selecting such a special case, it was only natural to take that of Man himself because that is the instance that is the most likely to be understood.
The situation is not altogether unlike that of the famous geometrical Proposition of the square son the other sides: c2 = a2 + b2. This is known by virtually every schoolboy. However he does not always realize that this proposition covering the right triangle is only a special case of a general proposition that covers all triangles.
The general proposition states that: In any triangle the square on a side opposite an acute angle (less than 90 degrees) is equal to the sum of the squares on the other two sides, diminished by twice the product of one of those sides by the projection of the other side upon it. Briefly: c2 = a2 + b2 - twice the product of side a and the projection of side b upon side a.
There is no need to present the proof of this here. We need only mention that as the acute angle increases and approaches 90 degrees, the projection of one of the sides upon the other diminishes until the acute angle becomes a right angle, in which case the projection vanishes and there is nothing to subtract from the squares on the sides of the triangle. This makes the special case the simplest one of all, and yet it fits perfectly into the general rule.
This illustration is presented in an effort to bring home to the mind of the student that Man is a special or particular case of a general rule of life in the Universe; and it may well be that like the case of the right triangle in geometry, his case is easier to grasp because certain factors that would make the study of other forms of consciousness more difficult for us to follow, have diminished to the vanishing point and therefore do not enter into the picture where we are concerned. Nevertheless, with increased understanding, the time may come when it will be necessary to learn all of the factors, which go to make up the general picture, and then we shall see exactly where Man fits in. Probably the greatest realization that can come to the student is an actual awareness — not a theoretical grasp, but an awareness that becomes part of his own consciousness — of his identity with Nature.
We are going to make an effort to understand more fully the general picture in what is to follow in this study. It is a remarkable thing that the more we can understand of the particular case, the better equipped are we to grasp the general picture; and, conversely, the better grasp we have of the general picture, the more real does the particular case become to us.
We shall now attempt to show by three illustrations how relative is our own position in the scheme of things. In the first illustration, I shall discuss Zero in its relationship to positive and negative numbers; then the ever-present moment of NOW in its relationship to past and future time; and, finally, for the mathematically minded, some concepts of the curvature of space.
Let us now consider Zero in our system of notation. We tend to imagine that we begin to count at Zero, and from that point we suppose that we can count indefinitely; but we soon learn that negative numbers are also very real. Zero appears to be a sort of line of demarcation between the positive and the negative numbers. However, there is nothing fixed and final about Zero. It is really a mathematical concept. A man, for instance, in a roomful of people, may have nothing in his wallet, and from that standpoint he may represent Zero. However, he may be in a room containing a hundred people and he might be the oldest person in the room. From the standpoint of age he would by no means represent Zero.
So, we may speak of Zero as an illusion, a Mâyâ, as the theosophical student would say. And there are other mâyâs,. The moment called NOW is such an illusion. We may think of it as the line of demarcation between past and future — or could we say negative and positive time?
To demonstrate how illusory is the moment of NOW, we have only to look up at the heavens. We do not see the stars as they are now. We see them as they have been in various times in the past. The more distant the star, the more remote is the time in the past when the star was as it now appears to our eyes. Some of the most distant galaxies that have been photographed appear to us as they were many millions of years ago. In fact, not only are they changed from what they appear to be, but they have long since moved from the places that they appear to occupy. This is one reason why space and time are considered to be inseparable.
We may go even a step farther and speak of three inseparables: Space, Time and Motion; and we shall have a beautiful symbol of this in Fig. 5 which shows the three-dimensional Svastika at the center of the Tetraktys. The three arms of the Svastika would then represent Space, Time and Motion.
A broader application of this same principle may be found in Einstein's theory of Relativity, upon which we may touch very briefly here. It is presented as the Special Theory and also as the General Theory of Relativity. The Special Theory deals with uniform motion ( which means constant velocity) in space. To state the concept simply: In uncurved space an object in motion will continue with unchanged direction and velocity unless acted upon by a force. A force acting upon it will cause it to accelerate (speed up) or decelerate (slow down), and may also change its direction.
In the statement of the General Theory, an object free to move in curved space will accelerate at a rate which is a function of the curvature in which it finds itself, unless acted upon by a force. A force will cause it to change its rate of acceleration. We may further expand the idea in our own terms by stating that when a freely moving body does not accelerate, it is only that the curvature of space is nil, as the terms Special and General Theories imply. The former is but a special case of the general structure of space.
Following along the lines of thought that we have expressed above, we may see that uncurved space is like the zero in notation, or the moment of NOW in time. It then stands as the line of demarcation between positively curved space and negatively curved space.
It is easy to become confused about the expression “the curvature of space,” because the word “curvature” immediately brings to mind a geometrical conception. This would be wrong, because space itself does not have geometrical properties. Language is not always specific, as for instance, we speak of high temperatures, a high voice, and a high degree of excitement, and in none of these expressions is the concept of altitude considered at all. So I will give an analogy which admittedly will serve as no more than a pointer toward an understanding of what is meant by a curving or a warping of space within the vicinity of a massive body such as a star.
We may speak of a man as having a warped mind, without attaching physical properties to his mind. The presence of certain physical objects can trigger undesirable reflexes, which indicate a warped condition of his mind. Making allowance for the crudity of the analogy, it serves to bring out the meaning of an expression like the warping or curvature of space within the vicinity of a physical body.
We read much of the “space-time continuum,” and time is usually considered to be a fourth dimension. Now, space as we know it has only three dimensions, and the so-called “dimension of time” should not be considered to be a geometrical property of space. Time, in this sense is really a function of motion, and varies with the velocity of a moving object, as does also its mass. It would be impossible to give space here to a discussion of the Relativity theory. There are books available, which give ample explanations of what is meant, and these may be studied by those interested.
Along the lines of Theosophical teaching, time is an illusion, which seems to be real enough, to be sure. The ultimate reality is Duration, and the concept of time is brought about by our own consciousness as we observe events going on around us.
In like manner, the space of science, which we may call physical space is in itself an illusion, produced by our own consciousness. That is not to say that it does not exist, but rather that we do not perceive it for what it truly is.
Because these ideas are extremely abstruse, it might be well to summarize them as follows:
Human consciousness is derived from Universal Consciousness called The Boundless.
Space is also derived from the Boundless, which we may term SPACE , as including more than one kind of space. Some thinkers who have written about hyperspace have come a little closer to the concept of the Ancient Wisdom that there are many levels of space within SPACE, or the Boundless. Thus, we speak of the spaces of SPACE.
Time is derived from Duration, which is only another aspect of the Boundless. Thus, from the Boundless, we have Duration, SPACE, and Consciousness, from which are again derived, Time-space-motion, which Theosophy also defines as Cosmic Life.
In the light of these considerations, let us return to the concept of curved space.
If we are to consider uncurved space as being a special case only, and that from our standpoint (which is similar to that we held when we considered the moment of NOW as the line of demarcation between past and future time), we may then say that uncurved space seems to be so to us only because of where we stand. It is only because of our position that we see positively curve space on the one hand, and negatively curved space on the other. Thus, what we call uncurved space might well appear to be positively curved from another standpoint, or, again, negatively curved space from yet another. What we call strongly curved space might seem to be uncurved from a totally different standpoint; and we are led to consider the possibility of these different standpoints as being at least as “real” as our own.
All that has gone before has been with the purpose of bringing out the idea that this physical universe is, from the standpoint of the Ancient Wisdom, just such a line of demarcation — or cross-section if you like — within the real Universe which extends infinitely on both sides of the cross-section.
This leads us to the teaching of the existence of innumerable planes of consciousness. These exist endlessly in both directions, above and below the physical universe. The words “above” and “below” are completely inadequate for describing them. One tends to form an erroneous picture in one's mind of a many-storied building. This is why we have gone to some length to present the concept of uncurved space, or again of Zero, as being lines of demarcation in a system which is only relative after all; they owe their importance to the standpoint from which they are viewed.
The teachings of the Ancient Wisdom have not been taken very seriously by many people who consider them too far-fetched and savoring too much of mere speculation. There is one thing, however, that should encourage the theosophical student. This is that there have grown in the minds of some advanced mathematicians many new concepts, which are far removed from our daily experience. These concepts, difficult of comprehension by the layman, are nevertheless accorded a place of respect in the minds of the masses; the difficulty that we have in grasping them has not subjected them to ridicule. This is because the trend of modern thinking is in the direction of science; and when these abstruse concepts are shown to work, it does not worry people that they are not able to understand them.
This should give some support to the theosophical student, and he need not feel diffident about explaining his difficult concepts. They are right in line with modern though, and he may take comfort in knowing that if he cannot make his ideas understood right away, at least he is in good company!
The point that I am trying to get across right now is that the phenomenal universe holds a position analogous to that held by Zero, or the ever present NOW, or again, for the mathematician, uncurved space. Since it is largely a matter of viewpoint, and therefore relative, we might further say that physical man occupies a similarly relative position in the grand scheme of Nature. The planes of consciousness above and below this physical universe are related to the physical plane in the same manner as numbers are related to Zero, or that Time is related to the moment of NOW. Hence the enormous difficulty in grasping what these inner planes are really like.
In mathematics we understand clearly the relationship between numbers and zero. Our understanding is somewhat less when we try to probe into the relationship between time and the eternal NOW. On the relationship between curved space and uncurved space, our ideas are more hazy still, for the reason that we apparently have no direct experience with curved space. However, the fact of the matter is that any object, if allowed to fall freely, moves in curved space. Thus, when a man jumps from an airplane and falls freely for a number of seconds before his chute opens, he is falling in curved space, although he does not stop to think about it. In fact, he does not stop at all, which proves the point!
Now, just as the moment of NOW is a paradox, in the sense that it is so fleeting that it apparently has no duration, yet is nevertheless always with us, the Eternal Now, so it is with human consciousness. It is the eternal part of us that is ever with us, but it is also as fleeting as the moment of NOW. That is because we are forever changing. If it were not so, we would cease to exist: If we remained as we were at some time in the past, we would not be in the present! The Eternal Pilgrim endures for aye, although “his shadows live and vanish.” Thus an entity passes through innumerable finite changes, but there is no such thing as a finite entity. Consciousness is infinite.
One final point may be made. As we explained, although our notions about curved space are very hazy, yet it is easy to move within it by allowing ourselves to fall freely. In somewhat the same way, although our notions about the inner worlds are also extremely hazy, yet it is easy to move within them by merely allowing ourselves to “fall freely,” as we do when asleep, or more completely so in Death. We do this because we free ourselves from the restrictions of the waking consciousness.
All this is really by way of introduction to the deeper lessons, which lie ahead.