Four-Dimensional Vistas | Page 7

of weaving and basket making. Lines (threads in the one case, rushes in the other) are wrought into planes to clothe a body or to contain a burden. Or think, if you choose, of the modern industry of book-making, wherein types are assembled, impressed upon sheets of paper, and these bound into volumes-- _points, lines, planes, solids_. The book in turn becomes the unit of another dimensional order, in the library whose serried shelves form lines, which, combined into planes, define the lateral limits of the room.
HIGHER--AND HIGHEST--SPACE
These are truisms. What have they to do, it may be asked, with the idea of higher spaces? They have everything to do with it, for in achieving the enclosure of any portion of solid space the limit of known dimensions has been reached without having come to any end. More dimensions--higher spaces--are required to account for higher things. All of the products of man's ingenuity are inanimate except as he himself animates them. They remain as they were made, machines, not organisms. They have no inherent life of their own, no power of growth and renewal. In this they differ from animate creation because the highest achievement of the creative faculty in man in a mechanical way lacks the life principle possessed by the plant. And as the most perfect machine is inferior in this respect to the humblest flower that grows, so is the highest product of the vegetable kingdom inferior to man himself, the maker of the machine; for he can reflect upon his own and the world's becoming, while the plant can only become.
What is the reason for these differences of power and function? According to the Higher Space Hypothesis they are due to varying potencies of movement in the secret causeways and corridors of space. The higher functions of consciousness--volition, emotion, intellection--may be in some way correlated with the higher powers of numbers, and with the corresponding higher developments of space. Thus would the difference between physics and metaphysics become a difference of degree and not of kind. Evolution is to be conceived of as a continuous pushing back of the boundary between representation and reality, or as a conquest of space. We may conceive of space as of an infinite number of dimensions, and of consciousness as a moving--or rather as an expanding--point, embracing this infinity, involving worlds, powers, knowledges, felicities, within itself in everlasting progression.

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. Man's ant-like efforts to establish this as a truth have thus far been vain.
Lest this statement discourage the reader at the very outset, he should understand the reason for such failure. We are embedded in our own space, and if that space be embedded in higher space, how are we going to discover it? If space is curved, how are we going to measure its curvature? Our efforts to do so may be compared to measuring the distance between the tips of a bent bow by measuring along the bow instead of along the string.
Imagine a scientifically-minded threadworm to inhabit a page of Euclid's solid geometry: the evidences of three-dimensionality are there, in the very diagrams underneath his eyes; but you could not show him a solid--the flat page could not contain it, any more than our space can contain a form of four dimensions. You could only say to him, "These lines represent a solid." He would have to depend on his faith for belief and not on that "knowledge gained by exact observation and correct thinking" in which alone the scientist finds a sure ground for understanding.
It is an axiom of science never to look outside three-space horizons for an understanding of phenomena when these can logically be accounted for within those horizons. Now because, on the Higher Space Hypothesis, each space is the container of all phenomena of its own order, the futility, for practical purposes, of going outside is at once apparent. The highly intelligent threadworm neither knows nor cares that the point of intersection of two lines in his diagram represents a point in a space to which he is a stranger. The point is there, on his page: it is what he calls a fact. "Why raise" (he says) "these puzzling and merely academic questions? Why attempt to turn the universe completely upside down?"
But though no proofs of hyper-dimensionality have been found