From: Ted Davis (email@example.com)
Date: Wed Sep 03 2003 - 16:43:27 EDT
"Irrational" numbers, or "surds" (yes, that's a noun related to the
adjective "absurd," look it up for an interesting moment), were thus named
b/c they did not meet the Greek standard of "rational" mathematics--ie, they
could not be written as the quotients of whole numbers. They were not
thereby related to the harmonic ratios in music (recall that music was once
a branch of mathematics). And, of course, by Euclid's time it was possible
to prove by deduction (using a reductio ad absurdum) that the SQRT(2) is
"irrational" by this definition.
Plato realized that, as a consequence of his geometrical atomism (which used
45-45-90 triangles to make up the square sides of the cubical atoms of earth
and used 30-60-90 triangles to make up the triangular sides of the
tetrahedral, icosahedral, and octagonal atoms of the other three terrestrial
elements), some degree of "irrationality" was built into nature. He
interpreted that thusly: the creative power of the divine craftsman (the
"Demiurgos," a word also found in the book of Hebrews) was limited by the
"recalcitrance" of the matter he had not created. Thus, perfect form was
imposed only imperfectly on matter. Thus, we cannot have a "science" (ie,
genuine demonstrable knowledge) of nature, only a "likely story" or opinion.
We could have a "science" only of the perfect forms themselves.
Or something like that. His picture of the Demiurgos is, IMO, a precursor
of the modern process God, who can't exert absolute power of nature
either--that is, IMO the process God can't determine the nature of nature.
Rather the nature of nature is a given, the God must simply do his best with
what he's got. This is why I think of process theology as Platonistic,
though one can also see it as deeply Aristotelian also (an eternal universe
eternally in the process of becoming).
I hope this isn't all too confusing, and that I haven't misstated something
in the midst of this.
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