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Alfred Russel Wallace : Alfred Wallace : A. R. Wallace :
Russel Wallace : Alfred Russell Wallace (sic)

The Fourth Dimension (S502a: 1894)

Editor Charles H. Smith's Note: A transcendental letter to the Editor printed on page 467 of the 29 September 1894 issue of the British spiritualist journal Light. To link directly to this page connect with: http://people.wku.edu/charles.smith/wallace/S502A.htm

     Sir,--The discussion on this subject seems to me to be wholly founded upon fallacy and verbal quibbles. I hold, not only that the alleged fourth dimension of space cannot be proved to exist, but that it cannot exist. The whole fallacy is based upon the assumption that we do know space of one, two, and three dimensions. This I deny. The alleged space of one dimension--lines--is not space at all, but merely directions in space. So the alleged space of two dimensions--surfaces--is not space, but only the limits between two portions of space, or the surfaces of bodies in space. There is thus only one Space--that which contains everything, both actual, possible, and conceivable. This Space has no definite number of dimensions, since it is necessarily infinite, and infinite in an infinite number of directions. Because mathematicians make use of what they term "three dimensions" in order to measure certain portions of space, or to define certain positions, lines, or surfaces in it, that does not in any way affect the nature of Space itself, still less can it limit space, which it must do if any other kind of space is possible which is yet not contained in infinite Space. The whole conception of space of different dimensions is thus a pure verbal fantasy, founded on the terms and symbols of mathematicians, who have no more power to limit or modify the conception of Space itself than has the most ignorant schoolboy. The absolute unity and all-embracing character of Space may be indicated by that fine definition of it as being "a sphere whose centre is everywhere and circumference nowhere." To anyone who thus thinks of it--and it can be rationally thought of in no other way--all the mathematicians' quibbles, of space in which parallel lines will meet, in which two straight lines can enclose a definite portion of spaces, and in which knots can be tied upon an endless cord, will be but as empty words without rational cohesion or intelligible meaning.

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