Re: OT: White Goddess

On Wed, 11 Apr 2001, Yoon Ha Lee wrote:

> On Wed, 11 Apr 2001, Andreas Johansson wrote:
>
> > Eh, seeing that I supposed to be good at math, I should probably know this
> > myself, but what's the difference between a circle and a regular polygon
> > with an infinite number of sides? I definitely recall being told by my math
> > teacher tellin' me they're the same ...
>
> Suppose you have a regular polygon with n sides.  (I think you could get
> by with a weaker condition but this will suffice.)  The "limit" of the
> polygon as n goes to infinity is a circle.
But it isn't a polygon with an infinite number of sides, because the
length of each of those sides would have, perforce, to be zero, which
means that the circumference, being a sum of zeros, would be zero.  As
you say, the number of sides *approaches* infinity, but it is an
asymptotic limit.  A curve is a curve, not a polygon, but a curve can be
approximated by a polygon, if one actually wants to do something
practical.  Approximation is not identity.

> I am not certain what mathematical meaning, if any, "transcended
> infinity" has, though.
Then say "transfinite", in that case.  "Infinity" is not a number.  It is
not a quantity.  It should not be treated as if it were.

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