SYNERGETICS

OCTAPHASE EVERYDAY MIND

In one segment of his TV show Cosmos, Carl Sagan tells a story about how science became differentiated from the metaphysical hocus pocus of Pythagorean numero-magic. One day, the Pythagoreans, playing with their new Law about the sum of the squares giving the square of the hypotenuse, discovered irrational numbers. The right triangle formed by the diagonal of a square of edge-length one has a “square root of two” length (in Synergetics we say “second root” since squares have been booted from center stage) and this strange length does not commensurate with any ordinary fraction derived from simple multiplication only by division of the original unit control length’s segmented “number line.” In other words, a thermometer that uses a root-of-2 control length is inherently incommensurable with one using a standard unit divider. No conversion formula using only rational ratios is extant. Then, the story goes, the Pythagoreans retreated into their caves in perplexity and hid their mathematics out of shame. They were ashamed to admit that nature permitted the irrational, the incommensurable, the eternal turmoil that appears to set up camp in the mind when all hope of a crystal clear omni-rational simple number mathematics is vanquished. The evil principle has won. Pythagoreans could not stomach this evil and so retreated into mysticism. Scientists, on the other hand, bravely set forth to explore the empirical domain of butterflies and atoms, star systems and computers. Scientists were not phased by the prospect of eternal turmoil. Life on Earth looked…