The Theosophist Feb 1967
The Problem of the Fourth Dimension
One Sunday morning at the very beginning of this century, my father was walking across one of the quadrangles of Trinity College, Dublin, when he saw coming towards him the head of the college, Provost George Salmon, a venerable figure with side-whiskers and a formidable reputation for learning and for absentmindedness. Politely my father raised his hat to the great man and received a courteous acknowledgement from him. As he did so, he saw something so curious and interesting that he ran round the block of buildings and contrived to meet the Provost a second time and again exchange greeting with him. This time he watched more carefully and saw that his first impression was indeed correct. The Provost, like the good king Dagobert of French legend, had his trousers on back to front.
What gave curious piquancy to this discovery was the fact that the Provost, a very eminent mathematician, was reputed to be able to think in terms of a fourth dimension of space. My father's discovery therefore provided a basis for lively student speculation as to whether, if one absentmindedly allowed oneself to stray into the fourth dimension, one would come back with one's trousers on back to front. Or would one become a mirror image of oneself?
Some years later the Irish poet, W.B. Yeats, used to show to intimate friends two interlinked wooden rings. Each ring was carved as one piece and was quite unbroken and without a join, and each was made of the wood of a different kind of tree. He claimed that the interlinking of the two rings had been brought about by movement through a fourth dimension phenomena recorded in the history of psychism, including the apport of object apparently through walls and into closed containers.
Attention, however, quickly shifted from discussion of a fourth dimension of space as an explanation of certain external phenomena to discussion about the subjective condition of the observer and the possibility of developing "fourth dimensional sight". One enthusiastic proponent of the fourth dimension ideas was C.H. Hinton, who published several books explaining it. He did not merely describe its implications and the relationship which it might have to the apparently three dimensional world in which we normally presume ourselves to live. He tried to offer exercises and techniques which might help the mind of his reader to adjust itself to the entirely new focus of consciousness which appreciation of a fourth dimension demands. He even caused the publisher to supply, with one of his books, a set of little coloured wooden blocks which could be used to construct what one might describe metaphorically as a three dimensional springboard from which consciousness might take the leap into this entirely new way of understanding space. Few will find Hinton's books light reading.
In the Theosophical Society several prominent members spoke from time to time of an altered appreciation of space as being a concomitant of deepened consciousness. Unconditioned Reality implied unconditioned Space, and therefore, as one ascended through the "planes" of our system, additional dimensions were perceived. The perceiving of a new dimension at each step represented the falling away of a limitation upon consciousness.
Here it should be remembered that wherever a scale of dimension, number, solidity or any other quality, is applied metaphorically to bridging the gap between the conditioned and the unconditioned, the unreal and the real, the "outer" and the "inner", it has always been possible to apply that scale in either direction. Just as different writers, or sometimes the same writer, may choose to number the "planes" or "principles" sometimes from "top" to "bottom" and sometimes from "bottom" to "top," so also there is validity in thinking of the scale from dimensionlessness to multiplicity of dimensions as running either "up" or "down". There is a time honored method of describing the coming of the Universe into existence as beginning with a dimensionless point which moves to make a line; the line moves to make a square; the square moves to make a cube. This would, of course, appear to imply that as we draw closer to the real we shall find dimensions decreasing instead of increasing.
It has to be remembered that in these matters we are always speaking metaphorically, extending our image of the known to indicate the hitherto unknown. What we are describing is not the thing in itself but only the image in our minds. Only confusion can come if we lose sight of this and begin to talk as if the mental image is the thing - in itself and as if one such image can be taken as really contradicting or cancelling another.
There are many perceptive comments on this paradox - a Kantian paradox really - scattered through the writings of Dr. Arundale. On several occasions he pointed out that if one is going to talk about "infinity", it is just as valid to consider it as an infinity of contraction as to think of it as an infinity of expansion. He also described, in his book Kundalini, how his experience of a higher state of consciousness found expression in his brain consciousness as something more intensely solid than the physical and not as something more ethereal; for it had been the natural habit of that brain consciousness to act on the assumption that what is most solid is most real and that what is most real is therefore most solid.
Madame Blavatsky touched upon these problems of the relativity of consciousness with respect to a fourth dimension in a teasingly brief passage in The Secret Doctrine (Adyar ed., 1, 295) where she describes the use by scientists, spiritualists and Theosophists in her day of the idea of a "fourth dimension of space " as a "sound but incomplete intuition". She shows how there was confusion between several different notions of what was being discussed - dimension as an attribute of space itself, dimension as an attribute of matter in space, and dimension as an attitude of consciousness perceiving matter in space.
A keen interest in a fourth dimension as a concomitant of the extension of psychic perception and experience was current in Madame Blavatsky 's day. This was given more definition in the Theosophical Society by C. W. Leadbeater in several of his book, particularly The Other Side of Death. He held that, while many psychic people, and many discarnates also, have a view of "astral" phenomena which they are able to interpret in terms of our ordinary three dimensions, a complete and integrated view of that plane involves a fourth dimension of space. He even believed that, for some people of a suitable temperament, the steady pursuit of the effort to realize in consciousness the fourth dimension, using such mental exercises as those suggested by Hinton, could lead to the development of a measure of clairvoyance. Several others have described psychic experiences involving the fourth dimension. Geoffrey Hodson published a little book Experiments in Fourth Dimensional Vision and J.J. van Manen dealt with it in a book describing his own psychic or occult experiences.
The best known work on the fourth dimension, however, is probably the Tertium Organum of P.D. Ouspensky. This combines the objective and subjective approaches to the subject, and it has a peculiar interest to students of The Secret Doctrine because it seems to cast a good deal of light on what may have been meant when Madame Blavatsky speaks of earth's humanity in the Second Round being a "two dimensional" species, an expression which leads on to her more general observations on dimension, already referred to, but which remains itself largely unexplained.
Ouspensky held that an animal has what he described as a two-dimensional view of life. He did not mean, of course, that the animal could not live quite comfortably in a three dimensional world or that a dog could not bury a bone. What he was concerned with was the dog's mental view of what occurs, and he regarded this as fundamentally two dimensional. Ouspensky's explanation of what he meant by two dimensional consciousness is worthy of careful study, unobscured by any preconceptions we may have. His account of the difference between how a horse may be understood to see and interpret a scene, and how a human may do so, is very plausible. He then went on to claim that there is a further view as much beyond the ordinary three dimensional human mental image as that is is beyond the understanding of the horse.
In Ouspensky's exposition, the four dimensional way of seeing and understanding represents a new order of experience which is the next step forward for humanity. He quotes and discusses with respect and sympathy the writings of Hinton, Leadbeater and van Manen on the subject. Some of Ouspensky's observations on dimension have an important bearing on the interpretation of certain descriptions of psychic experience. According to his explanation, our perception of anything or of any event is only one cross section our of myriads of other possible cross-sections of something whose reality our three dimensional consciousness cannot yet perceive. All these other possible cross sections are just as "true" as the one we happen to be able to see. When we are offered some description as a result of , say, clairvoyance in space or time, it may not represent at all the cross section that we might see if we could travel to that scene ourselves or that some scientific instrument might record. Yet it would be quite unjust to say that the clairvoyant was deluded or wholly wrong. It could well be that some of those notable discrepancies in Theosophical literature - such as the "Mars Mercury controversy " which exhibited a marked discord between teachings of Madame Blavatsky and of A.P. Sinnett both based on the teachings of the Masters - can find their resolution only in this way, beyond the scope of the three dimensional mind. Lately the whole questions of a fourth dimension has been in debate again in the Theosophical Society since the publication in 1964 of the book A Geometry of Space and Consciousness by Mr. James S. Perkins, Vice President of the Society. This book places old teachings about man and the universe in a new and refreshing light; and into the picture comes the idea of higher dimensions. Mr. Perkins, however, was quickly taken to task in an article in The Theosophical Journal of March-April , 1965, by Dr. E . Lester Smith, F.R.S, and Dr. E. Tudor Edmunds, who contended that his approach was mathematically inadmissible.
This reminded me of questions which arose in my own mind on reading certain passages in Ouspensky. I had found myself wondering whether Ouspensky was not simply playing illicit tricks with indices and, in fact, producing something which was not admissible from the point of view of mathematics. On the other hand I have had brief personal experiences which, while not constituting any proof even to myself, at least make me sympathetic towards the Hinton-Leadbeater-Ouspensky line of thought on the subject. It then occurred to me that Ouspensky could not have expressed himself in any other way. In trying to describe a higher order of experience to people living in terms of a more restricted order of experience, he could use only the language which they had constructed and he was bound to break the rules of mathematics founded upon that more restricted order of experience.
Madame Blavatsky can be quoted in support of nearly any view of the matter. On the one hand she said that the use of the expression "the fourth dimension" was prompted by a "sound but incomplete intuition". And on the other hand she also said that "popular common sense justly rebels against the idea that, under any condition of things, there can be more than three of such dimensions as length, breadth and thickness".
But "popular common sense" is also a manifestation of that mind that is the "slayer of the Real". The "illumined mind" is able to know things in their wholeness and does not have to approach anything divisively in terms of "either-or"; but the "either-or" approach is and has to be the basis of Science and mathematics, the basis of our habitual order of experience, real enough to us but unreal, at least in its values, from the point of view of a higher order of experience.
It would therefore seem that to criticise or attempt to evaluate a higher order of experience by the standards of the mathematics and Science of a lower order of experience must be to use a wrong criterion. It is open of experience must be to use a wrong criterion. It is open to anybody to disbelieve in the reality of any higher order of experience, to reject personally any belief in the validity of the occult; but this is a personal attitude. If we accept even hypothetically the possibility of a higher order of experience, it has to be accepted that, since it is "higher", it cannot be contained or assessed by the methods and standards of a "lower" order of experience.
At the same time whose seek to express something of a higher experience cannot fairly claim to be extending the world with which Science is concerned, for they are bringing in factors which do not at all belong to that world. Ouspensky, like others before him, held that experience of four-dimensional consciousness led to a view of objects and situations which was often in complete disharmony with "common sense". As an example of this, he suggested that it led to a perception that the part is equal to the whole, apparently a sort of macrocosm in microcosm experience.
The fact that one order of experience cannot be conveyed in the terms of another was sometimes referred to in past years by Krishnamurti by saying that the truth cannot be "stepped down". That is to say, it cannot be treated like an electric current that can be put through a transformer. Truth can be known only in terms of the order of experience in which it is true. And this may be linked up with Wittgenstein's teaching, disturbing in its implications, that every statement obeys its own logic.
Thus any attempt to give expression to a higher order of experience is like a work of art, a picture, a poem, a gesture. It is not appropriate to try to analyse it as a whole and connect it precisely with the body of what we already know or think we know. One may perhaps analyse aspects and details; but the totality of it has a quality which necessarily evades analysis.
There is, therefore, this same elusive quality about the whole subject of the fourth dimension. By the conditions which the very hypothesis of a fourth dimension established, it evades complete criticism or analysis by the mathematics developed in a world of three dimensions by minds habituated to the "common sense" of three dimensions.
This is profoundly frustrating to the deep-rooted "either-or" response of the "common sense" discursive mind. That mind wants to ask, "Is there or is there not a fourth dimension?" And it can never have an answer apart from its own experience. It is so easy to conclude that, if we ourselves have not had a certain kind of experience, then any other person who claims to have had it is, at the best, under an illusion. But it could fairly be said that the Theosophical Society was founded upon a rejection of that attitude.
To those who are temperamentally drawn to it, the problem and paradox of the fourth dimension can present in a richly crucial form the whole problem and paradox of the "Occult". Anybody who feels attracted to what is propounded by Hinton, C.W. Leadbeater, Ouspensky, Mr. Hodson or Mr. Perkins on this subject need not to be afraid to pursue it further in meditation and experiment and to lay himself open to the promptings of what Madame Blavatsky designated a "sound" intuition. But it would be unwise to seem in any way to claim that by doing this we are extending the existing structure of three dimensional Science or mathematics.