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| | Hyperspace Reality |
 | | Of course, the idea of hyperspace goes way back to Plato (427-347 B.C.), who suggested in his Cave allegory, that we are like prisoners of the 3-d world, identifying ourselves with our 3-d shadows, rather than the hyper-dimensional creatures we really are. |
 | | Hyperspace as a word meaning a space of more than three dimensions was coined in the 1890s by mathematicians, who were exploring the geometries defined by Bernhard Riemann (1826-1866) which were not only non-Euclidean (with any degree of warping--called "curvature"), but also were spaces of any number of dimensions. |
 | | But lower dimensional polytopes are substructures in higher dimensional polytopes, and the Coxeter graphs, which generate the mirrors for these reflections, control, by their hierarchical structure, the embedding of lower dimensional polytopes in the higher dimensional polytopes. |
| www.williamjames.com /sirag.htm (2995 words) |
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