HPB-SB-8-36

H. P. Blavatsky Scrapbooks

from Adyar archives of the International Theosophical Society

T i

vol. 8, p. 36	volume 8, page 36 vol. title: Vol Four of The Theosophical Society of The Arya Samaj of Arya-wart vol. period: Sept 1878 – Sept 1879 pages in vol.: 350
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< The Scientific Hypothesis Respecting Mediumistic Phenomena (continued from page 8-35) >

mensions. “A science which should teach as possible such views of the dimensions of space,” he says, “would unquestionably be the highest geometry conceivable by human intellect.” I will point out in a few words upon what speculative data this idea of a multiplicity of dimensions has been worked out.

The visible world is recognised by us only through our sensations—the changes which it produces in our organisms. Strictly speaking, it is only these changes that are directly recognisable by us; as to the real substance of things, “the thing per se” (das ding an sich), escapes recognition. And as our conception of space is based not alone on à priori recognitions, but also to a certain extent upon observation, therefore the real nature of space, the absolute space, is incomprehensible to us, and without any logical contradiction we can admit of there being a multiplicity of dimensions.

To such an idea we are led moreover by some of the recognised phenomena in nature. Geometrical figures not distinguishable by our thought (similar in form, size, and the mutual relation of their parts) should not be distinguishable by our sensuous perception either; they must be brought into such relations with us as would make them identical in the effects they produce upon us. This condition is satisfied by planes (or figures of two dimensions), symmetrical figures, but it is not satisfied by equally regular solids (figures which embrace the three dimensions). Two equal triangles can always be made to perfectly fit each other by turning over one of them, i.e., through a process accomplished which involves the aid of a third dimension; but if we move these triangles in a plane only, that is to say, using but two dimensions, we would never succeed in making them fit each other, so that one of these would occupy the place of the other. Similar parts of the body, as, for example, our two hands, were they even as identical in their details as an object is identical with its reflection in a mirror, cannot be made to fit together, however much you may turn them. Here then appears to be a logical contradiction; objects which are intrinsically identical prove incapable of mutual adjustment. To beings whose sensuous perceptions are limited to objects of two dimensions only, the identity of two-dimensional plane figures would appear as equally contradictory as to us appears the identity of three-dimensional solids. If to us this contradiction as regards the two-dimensional identical forms is surmounted, thanks to our cognisance of the third dimensions, then, by a like analogy, it becomes possible to surmount the obstacle offered by the identity (or symmetry) of three-dimensial objects, and to explain it by conceding a fourth dimension to space. Living in a space of three dimensions, born three-dimensional beings, we cannot picture to our sensuous perceptions a space of four dimensions; but by analogy we can conceive of it without any logical contradiction, just as we can conceive of a space with a far greater number of dimensions.

The insufficiency of our habitual idealistic conceptions of space, which make it only of three dimensions, is further shown in the fact that certain propositions cannot be strictly proven by Euclid’s geometry, which does not go beyond the commonly accepted three dimensions of space. This lack of exactness was admitted by our famous mathematician, N. J. Lobatchevsky, and by Hauss, the celebrated German scientist. Upon this fact was built Lobatchevsky’s “Ideal Geometry,” at present so thoroughly worked out by many other scientists, but during the lifetime of its author recognised by none. This is, so to say, the geometry of absolute space.

Having once admitted the logical possibility of many-dimensional spaces, we may expect to find possible in a space of four dimensions such phenomena as would be utterly inconceivable in the space familiar to our senses, as with our knowledge of three dimensions we concede the possibility of phenomena which in a space of two dimensions—a mere plane—would be wholly impossible. And if phenomena explicable only upon the hypothesis of a fourth dimension take place on our earth, then of course that fact testifies to the assistance of a fourth dimension, and so forth.

But what phenomena of this kind might, for example, occur on our earth? This is the very problem which Zollner set himself to solve, and which, with remarkable profundity of thought and intelligence, by a purely speculative method he thus analyses.

First example.—A point capable of moving only in a plane, i.e., by two dimensions, and within a circumscribed two-dimensional area, for instance, a circle manifestly could not be carried beyond the continuous line of that circle without rupturing its continuity. But if this point can avail itself of the third dimension, i.e., move and be lifted out of the plane, then of course it could be carried beyond the circumscribed circle. To us all this is comprehensible; but to a being whose area of vision would be limited to a plane, the lifting of the point would be equivalent to its disappearance—a miracle; whereas, in fact, the point would be passing out of the domain appreciable by the senses of the two-dimensional being. In like manner, reasoning by analogy, we ought to admit the possibility of the removal of this point, by the aid of the fourth dimension, beyond a closed three dimensional area, for instance out of a solid ball. The accomplishment of such a phenomenon, thoroughly comprehensible to four dimensional beings, would to us appear a miracle—something impossible.

Second example.—If we take a two-dimensional knot, i.e., a thread with a simple loop, the ends passing in opposite directions, in such a case its unbending (under the condition that the thread should not quit the plane occupied by its twist, i.e., that it would move but by two dimensions), becomes possible only by making one of its ends trace a full circle. But if we move the thread also on a third dimension, then its unbending can be accomplished in a far simpler way, without dragging one of its ends around a circle; first of all we will straighten its bend, or the two-dimensional knot, into a letter S, and then we can straighten the thread. By analogy, the formation of the three-dimensional knot becomes possible to us (such as a reef knot) three-dimensional beings, only on condition of our first making a two-dimensional knot, and then tracing a circle with the end of the thread on the inclined plane toward the plane of this two-dimensional knot. But for a four-dimensional being, capable of producing the movements and the bending of the thread by the help of a fourth dimension, the tying of such a knot ought also to be attainable without using the end of the thread for the purpose, on the same principle as for us three-dimensional beings, it is possible to produce a loose coil of two dimensions without employing the end of the thread. In short, a four-dimensional being, or rather, a being having at his command a fourth dimension, should be capable of tying a three-dimensional knot on an endless thread, or, what amounts to the same thing, on a thread whose two ends are tied together and sealed.

And this is the experiment which, after an investigation of over a week of various wonderful phenomena occurring in the presence of Slade, was successfully performed for Zöllner. On a simple cord, the ends of which were securely tied and sealed by himself, four three-dimensional knots were tied in a few minutes in full daylight, and while the Leipzig professor was himself holding the sealed ends of the cord on the table. Thus we have a fact which, to us three-dimensional beings, appears unthinkable and impossible, but which with the hypothesis of a fourth dimension of space finds a logical explanation. And thus, also, in its turn, an hypothesis built on synthetic and à priori inferences finds its corroboration in a mediumistic fact. The test conditions surrounding the experiment are unimpeachable and unassailable. There is no room in them for a scientific negation; it is one of two things—either Zöllner lies, or the fact took place as he describes it.

This experiment in the domain of mediumship has nothing substantially new in it; it belongs to a long series of phenomena which exhibit what is generally described as the passage of matter through matter.

Gellenbach, speaking of Zöllner's experiments in his just published work, “ Individuality in the Light of the Biology and Philosophy of the Present Day,” thus remarks: The progress of events, from Kant's theory of space to Zöllner's realised results, reminds us of the discovery of Neptune. Newton demonstrated the laws of gravitation, Laverrier based on them his speculations, and Kant, through a series of synthetic à priori judgments, recognised the idealism of our conception of space and the possibility of manifold dimensions. Zöllner built on these his speculative deductions, and facts coroborated the latter.

At all events the fact is there, whether the hypothesis will stand or not is a question of time. But that, so far, it covers nearly the whole ground of mediumistic phenomena (including Slade's writings on a slate in a tightly closed place, a phenomena witnessed and vouched for by many persons in St. Petersburg already), is clear to everyone who will take the trouble to carefully examine the evidence.

A Christian Pervent to Buddha

A correspondent, writing under date of July 15, says:—The great event of the year so far, in Siam, has been the conversion to Buddhism of a European Christian, and his formal installation into the priesthood, which took place on the 8th ult. I forbear to give his name, for the simple reason that the man’s vanity is so great that he would be delighted to hear that his name was trumpeted abroad even affixed to so questionable a transaction as this. Not only that, but having renounced the sacrament of his baptism, I doubt whether he is entitled to any of the relics of his once Christianity, even of so trifling a nature as a name. Suffice it say, that in country he is an Austrian, and in sect was a Roman Catholic. He was usually designated among the Siamese, Phr’a Kowtow, a name and title given him in Siam.—China Mail.

<Untitled> (End of the British Empire...)

End of the British Empire Foretold.—A curious East Indian “legend,” treating of the future of the Mogul Empire, and based upon the prediction of a priest, made many years ago, has been put into verse in Dresden, and is now in circulation in that city. It describes how the great Mogul Monarch, Aruugzebe, when following his resolution to extirpate the English from Hindostan, was stopped in his work by a holy Brahman, who held before his face a magic mirror, in which he saw the continued growth of the British power until only a shadow remained of his own. At length the shadow itself was swept away and another imperial throne was set up, with a lady seated in its chair. The priest had given assurance that two hundred years of expiation and servitude were necessary in order to free Hindostan from the evil powers that controlled her destinies, and for that reason all prisoners had been set free by Arungzebe. The legend goes on to say that when the lady becomes seated on the throne, the scene suddenly dissolves in a thunder-clap, and India resumes her sway. The priest’s prediction is well known, says the legend, to the natives of India. The first part of the prophecy, it continues, has been fulfilled already—a woman sits on the Mogul throne, and the fabric of British Empire in the East is now cracking and ready to fall to pieces!—New York Tribune.

The Invisible Land

There was a land that lay beyond my sight For which I vainly searched the great earth through. Thither, right often, my companions flew At day-break, or at noontide, or at night, And never came again. I took my flight, Explored all portions of the globe, yet grew No nearer where that mighty retinue Had fled into the stately fields of light. But once, when evening her dusk sails had spread, And I was sleeping, a swift dream came o’er My spirit, and in it I rising said, “Now is the country mine, long sought before!” And one I heard lament that I was dead; And lo! the land stretched just beside my door!

Editor's notes