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Stretching Angles and Banishing Angels

Geometry, most high school students will attest, is a dull subject. This dullness, however, is not only inescapable but essential. Memorizing theorems and deriving proofs is no fun, but doing such tasks teaches us—as "relevant" and "creative" courses in "communication" or "personal development" do not—that the mind must submit to truth, not the other way around. The only alternative to the tedium of geometry, Latin, physics, and other rigorous subjects is a radical subjectivism in which everyone designs his own curriculum—and universe. Imposed discipline of some sort or licensed solipsism are the only available pedagogical options.

But if discipline begins in drudgery, that is not where it need end. In geometry, for instance, once the essentials have been mastered, a philosophical appraisal of Euclid's founding premises and of conceivable alternatives may lead to exciting and profound insights. The Greeks and the Scholastic& alike recognized that contemplation of geometry leads finally to the divine source of all form. "God," said Plato, "geometrizes always." Unfortunately, most high school and even college teachers never open such horizons to their students. Geometry 1 & 2 lead only to Trigonometry and Computer Science.

Rudy Rucker is a rare mathematician not afraid to pursue the speculative implications of his discipline. In particular,...

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