Re: OT: White Goddess

Ray wrote:
> >   Think of truth and fact like circles and squares -
> >a square is a circle, with sufficient numbers of sides
>
>A square is not a circle; it has exactly four sides (all equal in length).
>The ancients spent many a fruitless hour trying to construct squares and
>circles of exactly the same area.  It can't be done - there's that pesky
>'irrational number' called pi.
Well, you can. It can be proved, but let's just state that a circle can be
of any size, so can a square, so obviously a particular square can have the
same area as a certain circle. The trouble is only that the ratio between
the circle's radius and the square's side-length will be irrational. In the
realm of abstract math this isn't much to worry about, and in the realm of
reality you'll be more worried about pesky things called "atoms" - these
buggers have discreet sizes, hazy edges and statistical locations that'll
make anything built out of them rather less than exact.

The ancients' problem was that they tried to do it using only rational
numbers and only a few, arbitrarily selected "tools" (pen, euclidean 2D
paper/papyrus, compasses and ruler).

                                       Andreas
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