With nearly everything of man’s creating—­be it a bureau or a battleship—­the process is as above described.  First, a pattern to scale; next, an actual linear framework; then planes defining a solid.  Consider almost any of the industries practiced throughout the ages:  they may be conceived of thus in terms of dimensions; for example, those ancient ones 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