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Updated: May 4, 2025
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."
In this way he arrived at a space-structure which possesses neither the three-dimensionality nor the rectilinear character of so-called Euclidean space a space-picture which, though mathematically consistent, is incomprehensible by the human mind.
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