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January 2001
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The Fourth Dimension by C. Howard Hinton (1904)

Don't be fooled by this "nonfiction" volume's camouflage as a treatise on popular mathematics. It was the twentieth century's first grimoire. Anticipating hypergeometric sf like Henry Kuttner's "Mimsy Were the Borogoves" or Greg Bear's "Tangents," Hinton wasn't satisfied with describing the fourth dimension. He wanted to take us there, and provided maps.

Just as a magus must forge his own ritual tools, Hinton urged readers to build the models that enable lowly 3-space entities to visualize a 4-space tesseract or hypercube. His apparatus comprises 27 differently colored slabs, three sets of 27 colored cubes, and twelve "catalogue cubes" whose varicolored faces, edges and corners are 3-space maps of the tesseract's hyperfaces. A sumptuous fold-out illustration shows the catalogue cubes in all their glory.

By memorizing and visualizing these gaudy shapes in the proper relation and sequence, you supposedly develop an intuitive understanding of the tesseract's 4-space structure. "I think there are indications of such an intuition," said Hinton cautiously. Step by step you grasp the eldritch, unimaginable architecture of H. P. Lovecraft's R'lyeh and other cyclopean relics of the Great Old Ones, while staying safe at home.

Physically safe, anyway. Some experimenters found that programming themselves with those compulsive visual sequences could rot the brain. "They are completely mind-destroying," a Scientific American reader warned after Martin Gardner's column mentioned the Hinton cubes. This victim had broken free from the autohypnotic imagery, but with difficulty. Spying on Cthulhu remains unwise.

Not for nothing do Hinton's alternative verbal mnemonics for tesseract geometry (see Appendix II) include such ritual chants as "3 faces: satan, sanet, satet". . . .

—David Langford

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