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`_I_ have not,' said the Provincial Mayor.
`It is simply this. That Space, as our mathematicians have it,
is spoken of as having three dimensions, which one may call
Length, Breadth, and Thickness, and is always definable by
reference to three planes, each at right angles to the others.
But some philosophical people have been asking why THREE
dimensions particularlywhy not another direction at right
angles to the other three?and have even tried to construct a
FourDimension geometry. Professor Simon Newcomb was expounding
this to the New York Mathematical Society only a month or so ago.
You know how on a flat surface, which has only two dimensions,
we can represent a figure of a threedimensional solid, and
similarly they think that by models of thee dimensions they could
represent one of fourif they could master the perspective of
the thing. See?'
`I think so,' murmured the Provincial Mayor; and, knitting his
brows, he lapsed into an introspective state, his lips moving as
one who repeats mystic words. `Yes, I think I see it now,' he
said after some time, brightening in a quite transitory manner.
`Well, I do not mind telling you I have been at work upon this
geometry of Four Dimensions for some time. Some of my results
are curious. For instance, here is a portrait of a man at eight
years old, another at fifteen, another at seventeen, another at
twentythree, and so on. All these are evidently sections, as it
were, ThreeDimensional representations of his FourDimensioned
being, which is a fixed and unalterable thing.
