Actually bro, I highly doubt the Universe is spherical. If one is to believe
in the concept of gravity bending space-time, then the Universe would be
more akin to some bubbly, blobby, amorphous structure (see
http://www.sciam.com/1999/0699issue/0699landy.html)
Interestingly enough, you could conceptually have "bubbles" in space-time
which are cut off from the rest of the universe.
Anyway, back to Pi... I think that the major issue is that we look at a
circle and think of some number of units, atoms, particles, whatever...
However, we neglect the fact that a circle isn't constituted of particles...
This seems to been some weird human characteristic, we think of everything
in units (time for example)...
Take the function y=x, there are an infinite number of points on that
line... Even, if I limit the range of x from (-1,1), there are still an
infinite number of points on that line... So even the simple function y=x
has infinite precision, yet I can precisely determine that the length of
that line is 2*sqrt(2).
-----Original Message-----
From: Aaron Blosser [mailto:[EMAIL PROTECTED]]
Sent: Wednesday, February 09, 2000 8:41 AM
To: Mersenne@Base. Com
Subject: RE: Mersenne: pi
> The problem isn't that Pi isn't finite, it's less than 4 so it's finite.
> The problem isn't that it isn't exact.
> The problem is that it can't be represented exactly in decimals which mens
> that when we write the expansion, we'll always have to make do with an
> approximation to the exact value.
Consider this:
Let's assume that the universe is spherical (a logical assumption if we
assume it's the result of a currently expanding explosion xx years ago).
If we were to calculate the radius of this sphere down to a single atomic
width, using some decently expanded version of pi would could come up with
an exact number for the volume of the universe.
What I'm getting at is that at some point, pi reaches a practical limit at
which expanding more decimal points is an abstraction because we could never
measure anything large enough for it to be useful. I mean, c'mon! The
universe is only so big! :-)
Being in a hurry, I don't have the time to figure out how many decimal
places that would be...perhaps someone more adventurous would care to give
it a go.
Aaron
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