At the present day, though science has added to its former treasures many things rich and rare, its wildest admirer would not claim for science a wealth of poetic and imaginative conceptions.

And yet science has one veritable romance,—the Fourth Dimension.

This conception,—at one time an object of wild enthusiasm, at another, the recipient of unmeasured scorn,—arose, it appears, from the analogy of pure mathematics. Mathematicians, besides dealing with the square and cube of a number or a quantity; have, from the remotest times, brought the fourth, fifth, and higher powers also into their conceptions.

Now, while the number, its square and cube, have their visible counterparts in nature,—in the line, the surface, and the solid,—the fourth and higher powers seem to have been long treated as mere handy expressions with no real representatives.

Recently, however, the idea has been mooted that at least the fourth power has its real counterpart in nature, and the properties of a fourth dimension have even been analysed and discussed.

We have not been able to discover the originator of this idea, nor whether or not it was known to the mathematicians of ancient Greece and India. That the old philosophers of India were familiar both with the fact and the theory of the fourth dimension, some of their metaphysical conceptions leave us small room to doubt. The only writer on the subject we intend to mention is Professor Zöllner, whose book, “Transcendental Physics,” is or ought to be familiar to all students of the modern wave of psychism.

Professor Zöllner, having been led by his mathematical investigations to form opinions as to the reality and nature of the fourth dimension of space, was led to connect these views inferentially with the phenomena of spiritualism, then attracting great attention. Supposing the observations of them made by spiritualists to be correct, these phenomena could be explained and reduced to order and intelligibility, in the opinion of Zöllner, on the hypothesis that they were caused by agencies or beings acting in space of four dimensions: space as known to us having three dimensions, length, breadth, and height.

These four-dimensional beings would, argued Zöllner, have the same advantage over us that we would have over the hypothetical dwellers in two-dimensional, or surface space,—the Flat-landers of romance: and the three-dimensional space we inhabit would be as much under their power as two-dimensional space, the surface of a sheet of paper, for example, is under ours.

By means of this advantage they could, he thought, transport any material object directly into the centre of a room, without its passing through any of the boundaries of the room, whether walls, ceiling, or floor: just as we, by virtue of our three-dimensional power, can transport an object, the point of a pencil, for example, into the centre of a two-dimensional room, represented by a square drawn on a sheet of paper, without passing the pencil-point through any of the boundaries of the square, as a two-dimensional being would be compelled to do.

Zöllner did not confine himself to theorising. In support of his proposition he quoted the universal tradition of ghosts and phantoms appearing suddenly in the centre of a room without entering by door, window, or chimney—a habit indicated in their name, apparitions.

Furthermore, in a series of experiments with the celebrated medium Slade, who was sent to Europe by the advice of our esteemed founders, Madame H. P. Blavatsky and Col. Olcott, Zöllner repeatedly had objects transported from and to the centre of the room without passing through the walls; amongst other things, a table of considerable size was thus treated. Other phenomena, usually ascribed to the passage of matter through matter, such as knots being tied on endless strings, or on continuous bands cut from a single sheet of parchment, formed by drawing two concentric circles, and then using the strip of parchment between them; or the interlinking of two wooden rings, each turned in a single piece from a block of wood; or the passage of one such ring to the leg of a table, though both extremities of the leg were larger than the ring; and a series of similar occurrences, Zöllner successfully explained on the hypothesis of the action of four-dimensional agencies. There is one phenomenon in particular which deserves notice from its unique evidential value, for it is such that, if the observations of Professor Zöllner were correct, it could be explained on no possible hypothesis except the action of unknown forces, since it is quite inimitable by mechanical means. It was as follows: at one of the séances with Slade, while Zöllner, Professor Weber and Slade were seated around a table a bluish light suddenly appeared under the table, casting shadow of the table-legs on the four walls, as was observed by Zöllner. The remarkable feature of the phenomenon was this, that while the light manifestly came from a point under the table, and threw well-defined shadows, these shadows were not appreciably larger than the table-legs which cast them.

But it is evident that, since the shadows were clearly defined, the source of light must have been of very small area.

A simple experiment will make this clear. Let a lighted lamp on a table near the centre of the room be turned down till the flame is of very small area; let the hand now be held between the lamp and the wall, close to the lamp. A much enlarged shadow of the hand will be cast on the wall, well-defined in proportion to the smallness of the flame.

If the lamp be now turned up, as the area of the flame increases, the shadow will be seen to grow blurred and indistinct, will, in fact, be surrounded by a penumbra, or partial shadow.

Since the shadows in Zöllner’s experiment were sharply defined, the source of light must have been very small, in fact almost a point.

But it was observed in our experiment with the small lamp flame that when the hand was held near the flame its shadow was very much enlarged. And the nearer the hand is to the wall, the more nearly will its shadow approach its own size, and when its distance from the wall is about one-twentieth of its distance from the flame, the shadow will not be appreciably larger than the hand itself.

To apply this to Zöllner’s experiment: as the shadow of the table-leg on the wall was not appreciably larger than the table-leg which cast it, the light must have been from ten to twenty times farther from the table-leg than the table-leg was from the wall; so that if the table-legs were each five feet from the walls, the source of the light must, from the facts observed by Zöllner’s, have been approximately a luminous point, from fifty to one hundred feet behind each leg of the table. But, under ordinary three-dimensional circumstances, this is manifestly impossible, unless either the table was one or two hundred feet square, or the light came from a point one hundred feet either above or beyond the table, and then separated, so as to appear to three-dimensional understandings to travel in at least four directions at once. Let us return to the fourth dimension, beginning with a few parallels from the inferior dimensions.

Let a sheet of paper represent two-dimensional space. Let a straight line be drawn on it. At any point in this straight line, let a perpendicular be drawn. Here the perpendicular, being on the surface of the paper, is also in two-dimensional space. Now let two other straight lines be drawn, intersecting the first line at the point where the perpendicular meets it. It is evident, as every geometer can demonstrate, that neither of these lines, nor any other lines through the same point, except that first drawn, will be at right angles to the perpendicular so long as it remains on the surface of the paper, that is in two-dimensional space, but that the perpendiculars to the intersecting lines at the point, of intersection will be represented by a series of lines all in different directions. But let the first perpendicular be supposed to be raised upright into three-dimensional space, representing it by a pencil held upright with its point at the point of intersection; it is evident that it is now perpendicular to all the intersecting lines; and the only conception a two-dimensional being could form of this line, represented by the pencil, would be a straight line going in several directions at once; since it is perpendicular to all the intersecting lines, and he perceives that all their perpendiculars go in different directions.

Suppose a beam of light, coming from a point several feet above the paper, so that its rays are sensibly paralled, for small distances. Suppose it to fall on a suitable reflector at the point of intersection, so that it may be spread evenly in every direction from that point along the surface of the paper:—a. right-angled conical mirror would serve this purpose. Now let four circles about half an inch in diameter be drawn at equal distances round the point of intersection, an inch or two from this point. Let a square be drawn round all the circles an inch or two outside them. We have here a two-dtmensional counterpart of Zöllner’s room and table: and it will be manifest that the shadows from the two-dimensional table-legs,—the circles—will fall outwards on the walls, that these shadows will not be appreciably larger than the table-legs,—since the rays casting them are sensibly parallel—and that they will be sharply defined, since the rays come from a point of light—the electric arc for example. Now in order that the light should produce this effect, it was necessary that it should fall from three-dimensional into two-dimensional space, and that its source should be at a distance from that two-dimensional space. The only conception a two-dimensional being could form of this light, would be a beam going in all directions at once.

Now apply this by analogy to Zöllner’s table. Suppose a beam, from a point of intense light, in four-dimensional space, to have fallen on the three-dimensional space we are acquainted with, at a point under Zöllner’s table, about equidistant from all the legs, and to be reflected in all the directions of three-dimensional space by a suitable four-dimensional reflector—as we did with a conical mirror in the two-dimensional space:—it is evident that it would have behaved exactly as the light Zöllner observed did behave, and the direction of the beam could only have been conceived by a three-dimensional being as going in all directions at once.

To sum up: no three-dimensional light could have behaved as this light did behave; and a four-dimensional light would have behaved exactly as this light behaved: the conclusion obviously is, that the light observed by Zöllner was a four-dimensional light.

To return to a point we touched on a moment ago. We dealt with a perpendiculat to aline, and with a perpendicular to a plane: by carrying this idea on, it will be evident that, in four-dimensional space, a perpendicular may be drawn to a solid, and the beam in Zöllner’s experiment was actually perpendicular to the cubical, or approximately cubical, room in which the experiment took place.

To go back a little: all the sensory organs of the body, the retina, tympanum, palate, or skin, are surfaces, that is, two-dimensional: but objects appear to us three-dimensional: further, our mental conceptions are four-dimensional. Let us illustrate this: we cannot see inside a closed opaque box: a four-dimensional being could not only see inside such a box, but could write a message inside. But let us now form a mental image of such a box. Though it appears to our minds opaque, yet we can with the mind’s eye see both the inside and the outside at once; hence—and this is of the first importance—our mental conceptions are four-dimensional.

Hence the mind can conceive a four-dimensional perpendicular to three-dimensional space—the room, for instance,—which would be perpendicular to this room, and would enter three-dimensional space at the point of physical consciousness in the head.

It is an experiment in psychics worth trying, to follow this perpendicular in the other direction.

Let us now come to a simpler experiment in transcendental physics, also from Zöllner’s book. As a straight line can only be drawn in one direction at once on a sheet of paper, so, it is clear a flat-lander could only pour water in one direction in two dimensional space—along a straight line in fact. We, however, in virtue of our three-dimensional superiority are able to spill water from above on a surface, so that it will spread in every direction on that two-dimensional surface, exciting the wondering admiration of any two-dimensional beings who happen to be in the neighbourhood.

By analogy, a dweller in four-dimensional space could pour water into our three-dimensional room, so that it would spill in every direction at once—as it would appear to us—on floor, ceiling and walls.

Now Zöllner actually records such an experiment, and demonstrates, as we have done, its connexion with four-dimensional space.

For in séance with Slade, Zöllner observed a jet of water issuing, apparently from a point near the ceiling which spouted against the walls and the ceiling at the same time; this took place in a sitting-room where no water was kept.

We have hitherto taken the genuineness of Zöllner’s phenomena for granted, and, as far as our theories of the fourth-dimension are concerned, it matters little whether they actually occurred or not since they evidently all might have done so on our hypothesis of four-dimensional agencies.

These phenomena closely resemble those produced by the conscious intention of advanced occultists, so that we may reasonably connect the latter also with the hypothesis of a fourth dimension, in which case there would be reason for believing that the consciousness of an occultist who produces phenomena is four-dimensional.

Further, it has been stated that space has really seven dimensions, that the evolution of each round and principle in man coordinates with the evolution of the perception of a new dimension.

It seems that at present we are passing from three to four-dimensional consciousness. Let us recapitulate.

The sensory surfaces of the body, and hence, our sensations, are two-dimensional, our perceptions of objects are three-dimensional while our conceptions are four-dimensional.

As an infinite number of independent straight lines—one-dimensional spaces—may be drawn on a surface—two-dimensional space—and as an infinite number of independent two-dimensional spaces exist in a three-dimensional space so, we may believe, an infinite number of independent three-dimensional spaces—the space known to us being one—may exist in four-dimensional space, an idea harmonising perfectly with the Indian idea of innumerable lokas filling the universe. Space, being merely a form of Maya, it is evident that its varying dimensions are only phases of perception, and not realities, and that every added conception is a fresh step in our divine unfolding, a new phase of the absorption of the finite in the INFINITE, of the expansion of the unit to the ALL.