Hyperspace

“ Thus it would seem that those who have been most diligent in constructing the hyperspace conception have been the least careful of the logical difficulties which beset the elaboration of their assumptions. ”

“ Hyperspaces which are not spaces at all should not be confounded with real space. But they constitute the substance of non-Euclidean geometry; they are its blood and sinews. Their study is interesting, because of the possibilities of speculation which it offers. No mind that has thought deeply upon the intricacies of the fourth dimension, or hyperspace, remains the same after the process. It is bound to experience a certain sense of humility, and yet some pride born of a knowledge that it has been in the presence of a great mystery and has delved into the fearful deeps of kosmic mind. ”

“ If enthusiasts would be content not to transport the so-called fourth dimensional space out of the sphere of hyperspace and cease trying to speculate upon the results of its interposal into three space conditions, which is in every way a constructual impossibility, there could not be any possible objection to its due consideration. ”

“ A very ingenious argument is used to show how rotation about a plane is thinkable and possible in hyperspace. But with this, as with the entire fabric of hyperspace speculations, dependence is placed almost entirely upon analogous and symbolic conceptions for evidence as to the consistency and rationality of the conclusions arrived at. ”

“ It will perhaps be evident now why in a sense the discovery of the non-Euclidean geometries was a stepping-stone to the consideration of hyperspace; though we should bear in mind that the two conceptions are entirely distinct, neither one being dependent upon the other. The logical conception of non-Euclidean geometry is far more difficult than the abstract notion of the fourth dimension. ”

“ My father has found that by suddenly removing a portion of matter from out of space, the pucker flattens out. If the matter is heavy enough and its removal sudden enough, there is a violent disturbance of space. By planning all the steps carefully my father has succeeded in swinging a section of space on a pivot through an angle of 180 degrees, and causing two portions of space to change places through hyperspace, or as you might express it popularly, through the fourth dimension. ”

“ He concedes that there may be thinking beings, living in our world, whose distribution board has four dimensions, and who do consequently think in hyperspace.
THE NEED OF AN ENLARGED SPACE-CONCEPT It is the contrariety in phenomena already referred to, that is forcing advanced minds to entertain the idea of higher space. Mathematical physicists have found that experimental contradictions disappear if, instead of referring phenomena to a set of three space axes and one time axis of reference, they be referred to a set of four interchangeable axes involving four homogeneous co-ordinates. ”

“ The onus of this treatise is, therefore, to distinguish between what is commonly known as sensible space and that other species of space known as geometric spaces. Also to show that the notion which has been styled hyperspace is nothing more nor less than an evidence of the faint, early outcroppings in the human mind of a faculty which, in the course of time, will become the normal possession of the entire human race. ”

“ The nearest beacon to the broken-down Proxima Centauri Beacon was on one of the planets of Beta Circinus and I headed there first, a short trip of only about nine days in hyperspace.
To understand the importance of the beacons, you have to understand hyperspace. Not that many people do, but it is easy enough to understand that in this non-space the regular rules don’t apply. Speed and measurements are a matter of relationship, not constant facts like the fixed universe. ”

“ There was one hitch: a stable form in normspace could become an unstable one in hyperspace. Without empiric knowledge, it was impossible for anyone going from one universe into the other to tell whether any substance he was carrying or wearing or was would remain stable. If unstable, it could turn into liquid or gas; it could turn into energy and blow up; it could cease to be a solid in any one of a number of ways. ”

“ Hyperspace is the artificial symbol of a higher and more extensive realm of awareness. For it cannot be doubted that to be able to think in the terms of hyperspace, to study the various relations and interrelations upspringing from the original premises, actually to become conscious in the hyperspatial realm thus constructed, requires a different species or quality of consciousness than that required for ordinary thinking. The period covering the rise of artificial spatiality is contemporaneous with the rise of the phenomena identified with the spiritual life of Swedenborg ”

“ The first ships to enter hyperspace had no place to go—and no way to even tell if they had moved. The beacons solved that problem and opened the entire universe. They are built on planets and generate tremendous amounts of power. This power is turned into radiation that is punched through into hyperspace. Every beacon has a code signal as part of its radiation and represents a measurable point in hyperspace. Triangulation and quadrature of the beacons works for navigation—only it follows its own rules. The rules are complex and variable, but they are still rules that a navigator can follow. ”

“ This mode of procedure would serve to clarify many if not all of the hyperspace conceptions for the non-mathematician as well as for the metageometricians themselves, especially those who are unwilling to recognize the utter impossibility of their constructions as applied to perceptual space. We should then cease to have the spectacle of otherwise well-demeanored men committing the error of trying to realize abstractions or abstractionizing realities. ”

“ Ione replied, "part of which is Tony's concrete floor, and part of which comes out of some other dimension. This mass of matter is at one end of a long, bar-like portion of space, the middle of which is pivoted in our world, somewhere in Chicago, and both ends of which are free in hyperspace."
"Then," suggested Phil, "why can't we walk down to the axle on which it is balanced, and step out into Chicago?"
"Because there isn't any matter for us to walk on. We are not able to move about in space, in three dimensions, you know. We can only get around in two dimensions, on the surface of matter." ”

“ Is there any more cogent reason, then, for accepting the analyst's conception of a world of hyperspace peopled with ensembles, propositions, spaces of n-dimensionality and other mathetic contrivances than the Inferno of Dante, inhabited by hideous shapes and repellent denizens, the remains of ill-spent earth-lives or Swedenborg's Celestial Realm, wherein dwell numerous beings of celestial character performing various tasks in the work of the world? ”

“ The whole scope of inquiry connected with hyperspace is not an end in itself. It is merely a means to an end. And that is the preparation of the human mind for the inborning of a new faculty and consequently more largely extended powers of cognition. ”

“ But I don't think that we are ordinary matter any more, and apparently our three-dimensional laws no longer govern, now that we are in hyperspace. Inertia is based upon time, of course, so our motion might be all right, even at that. ”

“ Freedom of movement is greater in hyperspace than in our space. The degrees of freedom of a rigid body in our space are 6, namely, 3 translations along and 3 rotations about 3 axes, while the fixing of 3 of its points, not in a straight line, prevents all movement. In hyperspace, however, with 3 of its points fixed, it could still rotate about the plane of those 3 points. A rigid body has 10 possible different movements in hyperspace, namely, 4 translations along 4 axes, and 6 rotations about 6 planes, while at least 4 of its points must be fixed to prevent all movement. ”

“ As portions of our space are bounded by surfaces, plane or curved, so portions of -space are bounded by hyperspace (three-dimensional) .
In our space, a point moving in an unchanging direction generates a straight line.
This straight line (say of units in length) , moving perpendicular to its initial position through the distance a, generates a square.
This square, moving perpendicular to its initial position through the distance , generates a cube. ”

“ In other words, representations of the non-Euclidean magnitudes, cannot be said to be strictly perceptual in the same sense that three-space magnitudes are perceived; for three-space magnitudes are really sense objects while hyperspace magnitudes are not sense objects. They are far removed from the sensuous world and in order to conceive them one must raise his consciousness from the sensuous plane to the conceptual plane and become aware of a class of perceptions which are not perceptions in the strict sense of the word, but superperceptions ”

“ Mathematics shall have failed utterly in the utilitarian aspects of this phase of its latest diversion if it do not justify its claims by crowning its work in the field of hyperspace with a "Kosmometer," an instrument devised for the measurement of the movement of space or a "Zoometer," an instrument devised for the measurement of the passage of life. We should like to encourage inventive minds to turn their attention life-ward and space-ward with the end in view of constructing such an instrument. ”

“ AS non-Euclidean geometry has not become popular enough to find a place in the ordinary college curriculum, and as its discovery preceded any serious consideration of space of more dimensions than three, it seems to me that, before taking up hyperspace proper, it would be well at least to mention the non-Euclidean geometries. ”

“ The principal, if not the only, value possessed by the "summitless hierarchies of hyperspaces" which the mathematician constructs in the world of pure thought is the enrichening and ennobling influence which they exert upon the mind. ”

“ If it can be successfully maintained that final judicative power abides in mathematics in the determination of these questions, then it would be useless to struggle against the fiat of mathematics and mathematicians; verily, we should be compelled to accept nolens volens all that mathematicians have devised about hyperspace and its connotations. ”

“ Life on the Star Lord was the only reality.
She moved through the uncharted realms of hyperspace, travelling in one hour's time as measured by earth watches, more than twenty light years distance, if measured in the units of real space. The ship itself was quiet. The vibration of the takeoff had ended in a moment, and now the passengers could hear no noise and hum of motors, could feel no motion against swelling waves, no battering against a barrier of uneven air. The artificial gravity induced a sense of security as absolute as though the ship were resting on living rock. ”

“ You cannot draw any such line in space as we understand it." If our visitor conceived of the fourth dimension, he would reply to us as we replied to the "flat-land" people: "The problem is absurd and impossible if you confine your line to space as you understand it. But for me there is a fourth dimension in space. Draw your line through that dimension, and the problem will be solved. This is perfectly simple to me; it is impossible to you solely because your conceptions do not admit of more than three dimensions." ”

“ To imagine a space means nothing else than that we imagine an epitome of our “space” experience, i.e. of experience that we can have in the movement of “rigid” bodies. In this sense we can imagine a spherical space.
Suppose we draw lines or stretch strings in all directions from a point, and mark off from each of these the distance r with a measuring-rod. All the free end-points of these lengths lie on a spherical surface. We can specially measure up the area (F) of this surface by means of a square made up of measuring-rods. If the universe is Euclidean, then F = 4πr2 ”

“ The phenomena can be explained in terms of higher space. 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. ”

“ As a fact, the ideal systems of the pure mathematician are customarily defined with an obvious, even though often highly abstract and remote, relation to the structure of our ordinary empirical world. Thus the various algebras which have been actually developed have, in the main, definite relations to the structure of the space world of our physical experience. The different systems of ideal geometry, even in all their ideality, still cluster, so to speak, about the suggestions which our daily experience of space and of matter give us. ”

“ III PHYSICAL PHENOMENA LOOKING FOR THE GREATER IN THE LESS After the assured way in which the author has conducted the reader repeatedly up and down the dimensional ladder, it may be a surprise to learn that physical phenomena offer no irrefragable evidences of hyper-dimensionality. We could not think in higher space if consciousness were limited to three dimensions. The mathematical reality of higher space is never in question: the higher dimensions are as valid as the lower, but the hyper-dimensionality of matter is still unproven. ”