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
dimensionlinesis not space at all, but merely directions in space. So the alleged space of two
dimensionssurfacesis not space, but only the limits between two portions of space, or the
surfaces of bodies in space. There is thus only one Spacethat 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 allembracing 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 itand it can be rationally thought of in no other
wayall 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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