Group: alt.philosophy · Group Profile
Author: SeanSean Date: Sep 5, 2008 06:25
"John J" wrote in message
news:XvOdnVhCquWbuVzVnZ2dnUVZ_tLinZ2d@supernews.com...>I cannot speak as an expert in anything at all, but I have studied ideas
>for over fifty years and I once joked that perhaps the ancient Geometers
>had it right - if it cannot be expressed in construction then it is not
>worth pursuing. 22/7 is the constructionist's answer to Pi. It works well
>enough for the Euclidean universe. (Do even rocket scientists use a
>_significant_ depth of precision of PI?)
>
> Perhaps a mathematician can enlighten me - exactly where does Euclid's
> geometry fail - that is, can the failure be described at some specific
> decimal place? Does that point of failure delineate the Euclidean universe
> from .... what?
>
Good queries there. How exact does one need to be, to be rational? Do we
actually live in a rational universe anyway? :-)
One of the consequences of the Pythagorean theorem is that incommensurable
lengths (ie. their ratio is irrational number), such as the square root of
2, can be constructed. A right triangle with legs both equal to one unit has
hypotenuse length square root of 2. The Pythagoreans proved that the square
root of 2 is irrational, and this proof has come down to us even though it
flew in the face of their cherished belief that everything was rational.
According to the legend, Hippasus, who first proved the irrationality of the
square root of two, was drowned at sea as a consequence.[
By all means, drown me at sea if Hayes theory of almost everything is
disproven on the mere innaccuracy of 22/7 for the irrational Pi.
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