A SPECULATIVE PHILOSOPHY. AS UNFOLDED IN A SEARCH FOR A FOURTH DIMENSION.
BY
T. O. TODD, P.P.G.St.B. (Durham)._________ _________
The purport of the lecturer was to show that matter does not possess a Fourth Dimension, that it is - like time and space - a mode o f consciousness, and that if there be a Fourth Dimension it must be found in the self-expression of consciousness.
________ __________MAN is essentially and intuitively a searcher after Truth. This quest contains all the elements of a noble life and provides for all expressions of the beautiful. Its attainment belongs to no class exclusively, whether such class be of philosophers, scientists, or a religious cult. Each of these special fields yield their own results, but disclose no royal pathway to the Absolute. Each searcher, in the depth of his consciousness, might visionise the necessary qualification for an Absolute, but only to find that his thinking processes demanded release from the captivity of a deadlock finality in which he soon finds himself. Hence the Absolute is undefinable and unconditional. Neither science nor philosophy affords any measure for duration, any standard of quality, or any central position in space for universal computation. Everything considered or worked upon is merely a substitute for the time being, and not regarded as the limit of man's attainments, nor as the circumference of the circle of his mental and physical possibilities. Having no standard of reference, all man's search for truth is based on speculative ideas. Known facts lead him to the speculative field, with the result that he speculates on new premises and then seeks for evidences to support his conclusions. When these evidences fail him he finds other avenues open to his mind, but finds that it is even essential that he work from that which he thinks he knows to be real towards that which he speculates upon as a possibility. To dive at once into the subject under consideration, let it be postulated that the only reality which man can freely and satisfactorily venture upon is the existence of matter, which, being tangible to his present sense condition, he can make subservient to his desires. This tangibility is expressed in terms of Three Dimensions-length, breadth and thickness-all of which terms are merely relative and interchangeable until a standard of approach is recognised. The presence of these three dimensions gives stability, hence substance.
Matter contains so many intricate problems that neither science nor philosophy has been able to solve them. Even to-day the question: What is matter ? remains unanswered. The nearest answer is that which claims it to be "a substance" as differentiated from a mental idea, and therefore a something which appeals to the mind as possessing three dimensions. There are so many unsolved problems of matter that the question arises as to whether it is not possible to discover a Fourth Dimension, which, when discovered, would aid considerably in solving the mysteries of existence. Hence the demand for speculating from the known three dimensions to the unknown Fourth Dimension.
There are so many phenomena finding expression in matter in which the known laws of three dimensions do not seem to play a part, and other phenomena which apparently set at naught our restriction of three dimensions, that there is a valid excuse and even a progressive necessity for taking up this idea seriously. But it is absolutely necessary to have some idea of the possible nature of the new measurement or its direction to enable a search to be made in a reasonable manner. This can only be done by first dealing with the problem of one dimension, followed by a consideration of the second, and succeeded by the third. If this could be done satisfactorily we might perhaps discover the law of dimensional progression. [The use of these words suggests that in referring to an unknown law, or an unrealised dimension, it will be necessary to use words expressive of new ideas, or give elasticity to the meaning of old ones. In the present instance it is difficult at times to discover the best word.] And if that law be discovered, the step from the mental appreciation of a third dimension to the mental comprehension of a Fourth Dimension would be considerably, simplified. Let it be remembered, therefore, at the outset, that as we do not know of one-dimensioned matter, nor of two-dimensioned matter, there is no just reason for assuming that matter may possess a Fourth Dimension, for the objectivity of material existence is amply provided for in the combination of three dimensions in one expression - the material object - nor is it possible to remove one of the dimensions, hence it may be assumed that it is not possible to add one - a Fourth.
A very simple experiment of demonstrating the absence of a Fourth Dimension can be tried with a cube. To assist the eye, let the cube vary in size in each of the three directions-say, 1 x 2 x 3 inches. Each single movement of the cube will give the following changes of dimension :-
If a single movement of the cube makes the three dimensions interchangeable, another single movement should bring .the Fourth Dimension into operation-but it does not appear to do so. The deduction is that matter does not possess a Fourth Dimension, and moreover, that inasmuch as the three dimensions of the cube altered with each movement, the terms length, breadth and height do not belong to the material object, but are simply modes of consciousness.
Length Breadth Height 1 2 3 inches 1 3 2 2 3 1 2 1 3 3 1 2 3 2 1 Many thinkers and experimenters speculate on the possibility of a Fourth Dimension being discoverable inside the material object, and have written works based upon that assumption. Such a search must of necessity be fruitless, for a cube can be penetrated only in the direction of one or more of the three dimensions of matter. If there is a Fourth it must be additional and not proportional, and must carry the mind away from each and all of the three dimensions, as will be demonstrated later.
This clearly shows that if a Fourth Dimension exists it must be something superior to matter, both in mere existence and in quality of expression, and that the search must be made in some other direction. Hence the necessity for breaking up the problem and endeavouring to discover the workable reality of one dimension only, following this by a workable two-dimension conclusiveness, placing matter in its position as the third dimensional condition, and, if possible, deduce a progressive inference as to the nature of a Fourth Dimension.
Geometrically regarded, the quest must begin at a point developed by means of line, plane and solid. In this way are three directions (or dimensions) evolved. A point is defined as having position but no attribute, and is therefore non-material, and in terms of matter is not real-nothingness. And it is from this nothingness that the finite mind must begin its task of perception. To enable the eye to be guided, let the reader draw a straight line between two imaginary points. This is a finite line; but it contains an infinite number of points. Hence we have infinity symbolised in the finite. No matter how long that line be produced from either or both ends its quality remains unchanged. It is simply a line possessing length which is infinite in quality as compared with the points of which it is composed, or of which it is an extension. There can be no progress made in continuing the same line, it is therefore imperative that a new direction be found, and that can only be done by every point in the line making a new departure - or taking a direction away from the line, and each point taking a similar direction - that is, at a right angle to the line. The result is a square, or plane surface. This surface gives length and breadth in combination and indissoluble, for they cannot be divorced. Inasmuch as a line does not possess breadth, the square which does possess breadth represents an infinite number of lines, each line possessing an infinite number of points. Consequently the finite plane mentally symbolises infinity multiplied by infinity. The character of the plane does not improve, and there can be no progress inferred from any extension of the plane as such. If progress towards a new dimension be desired, it must be sought for in a new direction apart from the previously travelled directions which formed the line and the plane. This can only be accomplished by every point and every line which go to form the plane travelling in a new direction. This gives the cube, or what we know as matter, or solidity. A plane possessing no height, and a cube being such because it does possess height, the relationship between the two is again infinite - that is, the finite dimensioned cube contains an infinite number of planes, each plane representing an infinite number of lines, and each line an infinite number of points. Hence in solid matter there is the symbol of infinity multiplied by infinity, and again multiplied by infinity. The result of this reasoning is that the mind must get into deeper touch with the idea of the infinite if a Fourth Dimension is discoverable.
Looking at the three sketches made in following the foregoing argument, it will be seen that a line is erected upon a point, a plane is erected upon a line, a cube is erected upon a plane, and the conclusion must of necessity follow that a Fourth Dimension must be erected upon a material form of some kind, and that matter must form only one aspect of the newly discovered - or to be discovered - extensional existence, or greater reality.
The crux of the problem rests now upon the parts which each of the dimensions play in forming the great reality of existence; or the part that they serve to bring the thinker to a comprehension of what are the great realities which he must make use of in order to secure a fuller development of his own consciousness, and bring himself to that state of perfection of which he innately considers himself capable, for lack of which he likens himself to one stumbling along in the dark, and merely trusting to a providence which he hopes will bring good out of all things.
The one-dimensioned restriction of the mind is Time. Each of the remarks regarding a line (supra) can be interpreted in terms of time. Time discloses to the mind the idea of the infinite. It cannot reach out to the end of Time in either direction, and every stretch of the mind leaves it where it was. Every point of Time is as much the infinite as any other past or future. Consequently the Infinite is ours Now. So long as the human mind is restricted by its present conception of Time it will never solve the problem of the Infinite. Whatever it may ultimately do is beyond present predication. There is no standard of Time. Even in the corner of the universe as we know it we are using a Substituted Secret in place of the true knowledge. Our year is 365 days. Mercury's year is equal to but three of our months. Neptune's year is equal to taken from 104 of our years. Certainly these are all one standard, the sun - but we cannot sensibly claim that the sun is the universal standard throughout the whole of creation.
The second dimensional restriction is space, and in dealing with the wonders of space the two-dimensional method is sufficient. As Time can be computed only from given data so Space can be computed only from given data. A base line on the earth, of given length, will enable the astronomer to find the angle at each end of the line, and by this means calculate the position in space of any of the heavenly objects. That position is relative to the Point from which the observation is taken, and distance implies only a straight line. Moreover, the position as a second dimensional restriction can only be decided upon by first observing the first restriction Time, and the observation at each end of the line must be made with due regard to the effluxion of Time. So great are the distances of these heavenly objects that infinitude is postulated by the astronomer, for he cannot get a base line long enough to enable an angle to be produced for some of the objects which come within the scope of his aided vision. The longest line available is that formed by the journey of the earth around the which defines the position of the earth at intervals of six months-say, over 18o millions of miles, and with this base line it is impossible to get an angle for computation. The extent to which computations may be made is stated to be such that if an inch space be divided into a hundred parallel lines, the angle for each line could be recorded at the distance of a mile. The astronomer cannot take us beyond existence of space. Position on the earth itself is also defined by means of two - dimensional restriction - latitude and longitude; and that second dimensional method cannot be exercised until the first dimensional restriction of Time has been recorded and compared with Time recorded at the meridian. Not only is man in the infinite Now, but he is in the infinite Here.
The third dimensional restriction is physical matter or the material body, which carries the attributes of three dimensions in its most perfect and most wonderful form. There is no absolute standard of measurement for matter. Nations differ in their standards. Each standard is a substituted secret until the genuine is discovered. It is not necessary to provide arguments for claiming the immutability and indestructibility of matter. In some form or other it fills all space, so far as investigation can take the mind. We are told that there is no vacuum. But as many have agreed that time and space are only different modes of consciousness, it will be quite safe to follow the philosopher who rules matter out of our socalled reality, and makes it only another mode of consciousness. At all events, each mode of consciousness brings us face to face with the Infinite and the totally inscrutable. If, then, our consciousness is built up out of these modes, is it not safe-for the time being-to assume, as a philosophy, that Consciousness is the Fourth Dimension? that each human being exercising the attribute of progressive consciousness has reached that stage in evolution where he becomes a unit in the Infinite Consciousness? The possibilities opened up by this thought are certainly infinite, and constitute a most valid reason for searching for the Four Dimensions of Consciousness.
As Time can be measured only by reference to Time itself; Space measured only by relation to Space; and Matter only in terms of Matter; so Consciousness can be measured only in terms of Consciousness. The greatest attribute of Consciousness is that of Love. This must be the standard for measuring the individual in relation to himself as the first consideration; to others as the second; to Truth as the third; and to God as the fourth. When man understands his right relationship to each of these four qualities of his Consciousness he will have discovered the Fourth Dimension; and he must work simultaneously in Time, Now; in Space, Here; in Matter, his Body; and thus prepare himself from his own Centre. When he attempts to reach the circumference he cannot materially err, and he may come into possession of the lost secrets much sooner than he anticipated.
[The foregoing is but a brief report of the lecture. There were many references to the Ritual and Symbolism of Freemasonry, which are necessarily omitted.]
Extracted from
The Transactions of
The Author's Lodge No. 3456, E.C.
Vol 1, 1915
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2001-08-01