In referring to an article on the Fourth Dimension in the April and June numbers of the Path, I give the writer full credit for the able way in which he has expounded Mr. Hinton's views. But I must at the same time point out some fallacies in the usual course of reasoning adopted on this subject. The first mistake is to regard "space" as capable of existing independently of matter. Occult Science teaches that "space" (better called "Extension") is one of the several properties of matter, and cannot exist without it. Three-Dimensionality is an attribute of "extension," and is essential to it, so that there can be no extension except in three directions. Mr. Hinton starts with the assumption that matter is three-dimensional, but if the view of occult science be right as above given, it is not matter, but extension, that has this quality. His inquiry may be translated in two ways: "Are there beings possessing extension in two directions?", or, "Are there beings without the property of extension at all?" The answer to the first question is, No; it is essential to extension that it be in three directions. Mr. Hinton's ideal square is impossible, for who can conceive of a square which has only one side and cannot be turned over?
The answer to the second is, There probably are entities without extension, but they are not matter as we know it, and cannot be visualized in any way.
Mr. Hinton's reasoning is very specious, and his deductions from his premises are very correct; but it must be borne in mind that forms are merely symbolical and not real, and should be relegated to the same category as algebraical expressions. Nobody regards quadratic or cubic equations as actually existing entities, but simply as symbolical conceptions, and all reasoning with regard to forms should be treated in the same way. One of his deductions is that to a four-dimensional being all points of a solid are equally accessible. This is an attribute of the astral man with his astral senses, and is coexistent with the abolition of extension, not with the presence of a more developed form of it, as Mr. Hinton holds. Certainly, on reading A New Era of Thought one is impressed with the conviction that the author has arrived at important occult truths by the application of his method, among which is the idea of the unity of the higher self in all men; but I venture to suggest that by means of this arduous system of mental discipline he is developing his astral senses, and that, instead of being able to travel mentally in four directions, he will find that there is no necessity to travel in any direction at all, extension having been entirely abolished.
In conclusion I will quote Secret Doctrine, Vol. 1, p. 251, which your readers will find very suggestive: —
"To begin with, of course the superficial absurdity of assuming that Space itself is measurable in any direction is of little consequence. The familiar phrase ('fourth dimension of Space') can only be an abbreviation of the fuller form — the fourth dimension of Matter in Space! But it is an unhappy phrase even thus expanded, because, while it is perfectly true that the progress of evolution may be destined to introduce us to new characteristics of matter, those with which we are already familiar are really more numerous than the three dimensions. The faculties, or what is perhaps the best available term, the characteristics of matter, must clearly bear a direct relation always to the senses of man. Matter has extension, colour, motion (molecular motion), taste, and smell, corresponding to the existing senses of man, and by the time that it fully develops the next characteristic — let us call it for the moment Permeability — this will correspond to the next sense of man — let us call it 'Normal Clairvoyance'; thus when some bold thinkers have been searching for a fourth dimension to explain the passage of matter through matter, and the production of knots upon an endless cord, what they were really in want of was a sixth characteristic of matter.
The three dimensions belong really to but one attribute or characteristic of matter — extension; and 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. These terms, and the term 'dimension' itself, all belong to one plane of thought, to one stage of evolution, to one characteristic of matter. So long as there are foot-rules within the resources of Cosmos to apply to matter, so long will they be able to measure it three ways and no more; and from the time the idea of measurement first occupied a place in the human understanding, it has been possible to apply measurement in three directions and no more. But these considerations do not in any way militate against the certainty that in the progress of time — as the faculties of humanity are multiplied — so will the characteristics of matter be multiplied also. Meanwhile, the expression is far more incorrect than even the familiar one of the 'Sun setting and rising.'"