Pilate, Truth, and Friday the Thirteenth

by Steven H. Cullinane on Thursday, April 12, 2001

On this Maundy Thursday, as Christians throughout the world gather to celebrate Passover and tell tall tales, let us reflect on the big question scheduled for tomorrow, Friday the Thirteenth:

What is Truth?

Relevant information on the world-wide web may be found in the Google Web Directory under Society>Philosophy>Philosophy of Logic>Truth Definitions. I recommend particularly the "Diamond Theory of Truth" website listed there (http://math16.com). This site discusses two rival theories of truth, drawn from Richard J. Trudeau's 1987 book The Non-Euclidean Revolution: diamond theory (pure mathematics is truth) and story theory (fiction is truth).

The latter doctrine is reminiscent of Orwell's 1984. Unfortunately, its author was a few years late to contribute to that year's Orwellian Festschrift. But every year brings new opportunities for Doublethink, and Trudeau was not alone when his book appeared in 1987. That same year saw the publication of the following passage.

The Story of Diamond Theory

In every civilization and culture, colored tilings and patterns appear among the earliest decorations.... An early paper with remarkable counterchange designs formed by diagonally divided squares -- one-half black, one-half white -- was published by Truchet [1704]. For a more recent treatment, with many illustrations, see Cullinane [1976]. However, all these were more or less "accidental" occurrences, independently reinvented many times.... The only artist who deliberately and consistently tried to investigate colored patterns (more specifically, colored tilings) was M. C. Escher....
-- Tilings and Patterns, by Branko Grunbaum and G. C. Shephard, W. H. Freeman and Company, 1987. These remarks appear on pages 463 and 464; the [1976] reference is to a preprint, "Diamond Theory," named on page 661.

This passage, worthy of an academic Sanhedrin, is, to put it mildly, misleading. For a more accurate account of the mathematical background of my work, see the updated version on the website Diamond Theory.

For those who prefer stories to truth, I recommend the 1998 novel The Magic Circle, by Katherine Neville. Her account of the Last Supper is at least more entertaining than the usual fables.

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