Four-Dimensional Vistas Part 2

Now could it be shown that the two-dimensional symmetry observed in nature is the result of a three-dimensional movement, the right-and left-handed symmetry of solids would by a.n.a.logy be the result of a _four_-dimensional movement. Such revolution (about a plane) would be easily achieved, natural and characteristic, in four s.p.a.ce, just as the a.n.a.logous movement (about a line) is easy, natural, and characteristic, in our s.p.a.ce of three dimensions.

OTHER ALLIED PHENOMENA

In the mirror image of a solid we have a representation of what would result from a four-dimensional revolution, the surface of the mirror being the plane about which the movement takes place. If such a change of position were effected in the const.i.tuent parts of a body as a mirror image of it _represents_, the body would have undergone a revolution in the fourth dimension. Now two varieties of tartaric acid crystallize in forms bearing the relation to one another of object to mirror image. It would seem more reasonable to explain the existence of these two identical, but reversed, varieties of crystal, by a.s.suming the revolution of a single variety in the fourth dimension, than by any other method.

There are two forms of sugar found in honey, dextrose and levulose.

They are similar in chemical const.i.tution, but the one is the reverse of the other when examined by polarized light--that is, they rotate the plane of polarization of a ray of light in opposite ways.

If their atoms are conceived to have the power of motion in the fourth dimension, it would be easy to understand why they differ.

Certain snails present the same characteristics as these two forms of sugar. Some are coiled to the right and others to the left; and it is remarkable that, like dextrose and levulose, their juices are optically the reverse of each other when studied by polarized light.

Revolution in the fourth dimension would also explain the change in a body from producing a right-handed, to producing a left-handed, polarization of light.

ISOMERISM

In chemistry the molecules of a compound are a.s.sumed to consist of the atoms of the elements contained in the compound. These atoms are supposed to be at certain distances from one another. It sometimes happens that two compound substances differ in their chemical or physical properties, or both, even though they have like chemical elements in the same proportion. This phenomenon is called isomerism, and the generally accepted explanation is that the atoms in isomeric molecules are differently arranged, or grouped, in s.p.a.ce. It is difficult to imagine how atoms, alike in number, nature, and relative proportion, can be so grouped as somehow to produce compounds with different properties, particularly as in three-dimensional s.p.a.ce four is the greatest number of points whose mutual distances, six in number, are all independent of each other.

In four-dimensional s.p.a.ce, however, the _ten_ equal distances between any two of _five_ points are geometrically independent, thus greatly augmenting the number and variety of possible arrangements of atoms.

This just escapes being the kind of proof demanded by science. If the independence of all the possible distances between the atoms of a molecule is absolutely required by theoretical chemical research, then science is really compelled, in dealing with molecules of more than four atoms, to make use of the idea of a s.p.a.ce of more than three dimensions.

THE ORBITAL MOTION OF SPHERES: CELL SUB-DIVISION

There is in nature another representation of hyper-dimensionality which, though difficult to demonstrate, is too interesting and significant to be omitted here.

Imagine a helix, intersected, in its vertical dimension, by a moving plane. If necessary to a.s.sist the mind, suspend a spiral spring above a pail of water, then raise the pail until the coils, one after another, become immersed. The spring would represent the helix, and the surface of the water the moving plane. Concentrating attention upon this surface, you would see a point--the elliptical cross-section of the wire where it intersected the plane--moving round and round in a circle. Next conceive of the wire itself as a lesser helix of many convolutions, and repeat the experiment. The point of intersection would then continually return upon its own track in a series of minute loops forming those lesser loops, which, moving circle-wise, registered the involvement of the helix in the plane.

It is easy to go on imagining complicated structures of the nature of the spiral, and to suppose also that these structures are distinguishable from each other at every section. If we think of the intersection of these with the rising surface, as the atoms, or physical units, of a plane universe, we shall have a world of apparent motion, with bodies moving harmoniously amongst one another, each a cross-section of some part of an unchanging and unmoving three-dimensional ent.i.ty.

Now augment the whole by an additional dimension--raise everything one s.p.a.ce. The helix of many helices would become four-dimensional, and superficial s.p.a.ce would change to solid s.p.a.ce: each tiny circle of intersection would become a sphere of the same diameter, describing, instead of loops, helices. Here we would be among familiar forms, describing familiar motions: the forms, for example, of the earth and the moon and of their motion about the sun; of the atom, as we imagine it, the molecule and the cell. For is not the sphere, or ovoid, the unit form of nature; and is not the spiral vortex its characteristic motion, from that of the nebula in the sky to the electron in the atom? Thus, on the hypothesis that our s.p.a.ce is traversing four-dimensional s.p.a.ce, and that the forms of our s.p.a.ce are cross-sections of four-dimensional forms, the unity and harmony of nature would be accounted for in a remarkably simple manner.

The above exercise of the imagination is a good preparation for the next demand upon it. Conceive a dichotomous tree--one that always divides into two branches--to pa.s.s through a plane. We should have, as a plane section, a circle of changing size, which would elongate and divide into two circles, each of which would do the same. This reminds us of the segmentation of cell life observed under the microscope, as though a four-dimensional figure were registering its pa.s.sage through our s.p.a.ce.

THE ELECTRIC CURRENT

Hinton conceived of an electric current as a four-dimensional vortex.

He declared that on the Higher s.p.a.ce Hypothesis the revolution of the ether would yield the phenomenon of the electric current. The reader is referred to Hinton's book, _The Fourth Dimension_, for an extended development of this idea. What follows is a brief summary of his argument. First, he examines the characteristics of a vortex in a three-dimensional fluid. Then he conceives of what such a vortex would be in a four-dimensional medium of a.n.a.logous properties.

The whirl would be about a _plane_, and the contour of this plane would correspond to the ends of the axis line in the former vortex; and as before, the vortex would extend to the boundary. Every electric current forms a closed circuit: this is equivalent to the hyper-vortex having its ends in the boundary of the hyper-fluid. The vortex with a _surface_ as its axis, therefore, affords a geometric image of a closed circuit.

Hinton supposes a conductor to be a body which has the property of serving as a terminal abutment to such a hyper-vortex as has been described. The conception that he forms of a closed current, therefore, is of a vortex sheet having its _edge_ along the circuit of the conducting wire. The whole wire would then be like the centers on which a spindle turns in three-dimensional s.p.a.ce, and any interruption of the continuity of the wire would produce a _tension_ in place of a continuous revolution. The phenomena of electricity--polarity, induction, and the like--are of the nature of the stress and strain of a medium, but one possessing properties unlike those of ordinary matter. The phenomena can be explained in terms of higher s.p.a.ce. If Hinton's hypothesis be the true explanation, the universality of electro-magnetic action would again point to the conclusion that our three-dimensional world is _superficial_--the surface, that is, of a four-dimensional universe.

THE GREATER UNIVERSE

This practically exhausts the list of accepted and accredited indications of hyper-dimensionality in our physical environment. But if the collective human consciousness is moving into the fourth dimension, such indications are bound to multiply out of all measure.

It should be remembered that in Franklin's day electricity was manifest only in the friction of surfaces and in the thunderbolt.

To-day all physical phenomena, in their last a.n.a.lysis, are considered to be electrical. The world is not different, but perception has evolved, and is evolving.

There is another field, in which some of our ablest minds are searching for evidences of the curvature of s.p.a.ce, the field of astronomy and astro-physics. But into this the layman hesitates to enter because the experts themselves have found no common ground of understanding. The ether of s.p.a.ce is a battlefield strewn with dead and dying hypotheses; gravitation, like multiplication, is vexation; the very nature of time, form and movement is under vivid discussion, in connection with what is known as the Theory of Relativity.

Notwithstanding these counter-currents of speculation, which should make the wise man speak smilingly of his wisdom, this summary remains incomplete without a reference to the pressure of higher s.p.a.ce upon those adventurous minds that essay to deal with the profound problems of the greater universe, and a statement of the reasons for their feeling this pressure. These reasons are well suggested by Professor B.G. Harrison, in his _Popular Astronomy_. He says: "With the idea of a universe of finite dimensions there is the obvious difficulty of the beyond. The truth is that a universe of finite proportions is equally difficult to realize as one of infinite extent. Perhaps the nearest a.n.a.logy to infinity that we can understand lies in our conception of a closed curve. It seems easier to imagine the endless movement of a sphere in a circular path than the case of one travelling in a straight line. Possibly this a.n.a.logy may apply in some way to fourth-dimensional s.p.a.ce, but the manner of its application is certainly not easy to understand. If we would imagine that all co-ordinates of time and s.p.a.ce were curved, and eventually return to the same point, it might bring the ultimate comprehension one degree nearer."

A HINT FROM ASTRONOMY

The physical evidence that our s.p.a.ce is thus curved in higher s.p.a.ce, some have considered astronomy to furnish in what is called the "negative parallax" of certain distant stars. This cannot be pa.s.sed by, though it is too deeply involved with the probable error of the observers themselves to be considered more than an interesting fact in this connection. Every one knows that the difference of angle under which an object is seen from two standpoints is called its parallax. The parallax of the stars--and the consequent knowledge of their distance--is obtained by observing them from opposite points of the earth's...o...b..t around the sun. When a star is within measurable distance, these angles are acute, and the lines from the star to the earth at opposite sides of its...o...b..t converge, therefore. But when these lines, as sometimes happens, appear to be _divergent_, the result is called a _negative_ parallax, and is explainable by higher s.p.a.ce relationships. Obviously, the divergence of the lines would indicate that the object lies _behind_ the observer instead of in front of him. This anomaly can be explained by the curvature of s.p.a.ce in the fourth dimension. If s.p.a.ce is so curved, the path of light itself is curved also, and a man--were his vision immeasurably keen, not to say telescopic--could see the back of his own head! It is not worth while to give this question of negative parallax too much importance, by reason of the probability of error, but in this connection it should be stated that there appears to be an undue number of negative parallaxes recorded.

GRAVITATION

Gravitation remains a puzzle to science. The tendency of modern physics is to explain all material phenomena in terms of electrons and the ether, but the attempt to account for gravitation in this way is attended with difficulties. In order to cope with these, it seems necessary to a.s.sume that our universe is only a portion of a greater universe. This a.s.sumption readily lends itself to the conception of our universe as a three-dimensional meeting place of two portions of a universe of four dimensions--that is, its conception as a "higher" surface. This is a fundamental postulate of higher s.p.a.ce speculation.

One hypothesis advanced to explain gravitation a.s.sumes the existence of a constant hydrostatic pressure transmitted through the ether. A steady flow of ether into every electron in a gravitating system of bodies would give rise to forces of attraction between them, varying inversely as the square of the distance, according to Newton's law.

But in order to avoid the conception of the continual destruction and creation of ether, it is necessary to a.s.sume a steady flow through every electron between our universe and the greater universe of which it is a.s.sumed to form a part Now because the electrons, in order to receive this flow, must lie on the boundary of this greater universe, the latter must be four-dimensional. Every electron, in other words, must be the starting point of a pathway into--and a terminal point out of--four-dimensional s.p.a.ce. Here we have another familiar higher s.p.a.ce concept.

THE ETHER OF s.p.a.cE

The ether of s.p.a.ce, because it has at last found entrance, must be given a grudging hospitality in these pages, even though the mysterious stranger prove but a ghost. The Relativists would have it that with the acceptance of their point of view the ether may be eliminated; but if they take away the ether, they must give us something in its stead. In whatever way the science of the future disposes of this problem, it must take into account the fact of light transmission. On the theory that the ether is an elastic solid of amazing properties, in which the light waves vibrate _transversely_ to their direction, it a.s.sists the mind to think of the ether as four-dimensional, because then a light wave would be a superficial disturbance of the medium--superficial, but three-dimensional, as must needs be the case with the surface of a four-dimensional solid.

This search for evidences of hyper-dimensionality in the universe accessible to our senses is like looking, not for a needle in a haystack, but for a haystack in a needle--for the greater in the less.

From the purely physical evidences, all that can with certainty be said is that the hypothesis is not inconsistent with the facts of science or its laws; that it is being verified and rendered more probable by the investigations of science; that it is applicable to the description or explanation of all the observed phenomena, and a.s.signs a cause fully adequate to have produced them.

Now there is an order of phenomena that we call psychic. Because they are phenomenal they cannot occur outside of time and s.p.a.ce altogether; because they are psychic they defy explanation in terms of the s.p.a.ce and time of every-day life. Let us next examine these in the light of our hypothesis.

IV TRANSCENDENTAL PHYSICS

ZoLLNER

In the year 1877, Johann Friedrich Zollner, professor of physics and astronomy at the University of Leipsic, undertook to prove that certain (so-called) psychic phenomena were susceptible of explanation on the hypothesis of a four-dimensional s.p.a.ce. He used as ill.u.s.trations the phenomena induced by the medium Henry Slade. By the irony of events, Slade was afterward arrested and imprisoned for fraud, in England. This fact so prejudiced the public mind against Zollner that his name became a word of scorn, and the fourth dimension a synonym for what is fatuous and false. Zollner died of it, but since his death public opinion has undergone a change. There is a great and growing interest in everything pertaining to the fourth dimension, and belief in that order of phenomena upon which Zollner based his deductions is supported by evidence at once voluminous and impressive.

It is unnecessary to go into the question of the genuineness of the particular phenomena which Zollner witnessed. His conclusions are alone important, since they apply equally to other manifestations, whose authenticity has never been successfully impeached. Zollner's reasoning with regard to certain psychic phenomena is somewhat along the following lines.

APPARITIONS

_The intrusion (as an apparition) of a person or thing into a completely enclosed portion of three-s.p.a.ce; or contrariwise, the exit (as an evanishment) out of such a s.p.a.ce_.

Because we lack the sense of four-dimensional s.p.a.ce, we must here have recourse to a.n.a.logy, and a.s.sume three-dimensional s.p.a.ce to be the unsensed higher region encompa.s.sing a world of two dimensions, To a hypothetical flat-man of a two-s.p.a.ce, any portion of his plane surrounded by an unbroken line would const.i.tute an enclosure. Were he confined within it, escape would be impossible by any means known to him. Had he the ability to move in the third dimension, however, he could rise, pa.s.s over the enclosing line without disturbing it, and descend on the other side. The moment he forsook the plane he would disappear from two-dimensional s.p.a.ce. Such a disappearance would const.i.tute an occult phenomenon in a world of two dimensions.

Correspondingly, an evanishment from any three-dimensional enclosure--such as a room with locked doors and windows--might be effected by means of a movement in the fourth dimension. Because a body would disappear from our perception the moment it forsook our s.p.a.ce, such a disappearance would be a mystery; it would const.i.tute an occult phenomenon. The thing would be no more mysterious, however, to a consciousness embracing four dimensions within its ken, than the transfer of an object from the inside to the outside of a plane figure without crossing its linear boundary is mysterious to us.