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Mathematical Digest


Short Summaries of Articles about Mathematics
in the Popular Press

"The Truth about Counting," by Brian Rotman. The Sciences, November-December 1997, pages 34-39.

This article is presented in the form of a dialogue between a sage, Kronos, and his mathematical protege, Simplicius. Kronos proposes a new way of looking at arithmetic called "non-Euclidean arithmetic." He argues that computers have given the lie to mathematicians' notions of infinity. Whole numbers do not exist apart from human beings' construction of them, he says, and such construction must be finite because we live in a finite universe. A computer set to count whole numbers will eventually stop after it has exhausted all the energy in the universe, so it is more realistic to devise a system of whole number arithmetic that takes account of this finiteness; this is the basis for "non-Euclidean arithmetic." The article ends with the tongue-in-cheek assertion that these ideas imply that mathematics is socially constructed.

--- Allyn Jackson