From: Ken Clements (Ken@Innovation-On-Demand.com)
Date: Sat Mar 09 2002 - 16:45:51 MST
Damien Broderick wrote:
> At 09:26 PM 3/8/02 -0800, Spike wrote:
>
> > pi/4 = 1 - 1/3 + 1/5 - 1/7 ...
>
> In our world. But if 2 pi radians is defined = 360 degrees, what happens
> when a circle has more or fewer than 360 degrees, due to space curvature?
>
Damien, the problem is that, in the book, Ellie does not go out and measure
some aspect of this universe. Instead, she uses computers to look into the
mathematical expansion of pi for a hidden message of Creation. There are some
who consider all of mathematics as exactly that message, with no specific
selection of universe. Recently, Richard Greenblatt (prototypical hacker from
the old MIT days) gave a presentation at a conference I attended, in which he
offered analysis of DNA and RNA sequences going back to protozoa deep in the
earth as proof of the existence of a Creator. I got the same feeling as
reading the end of _Contact_, only worse, because this was supposedly
non-fiction (the audience was visibly uncomfortable, but polite, although some
real biologists gave him questions he could only dance around).
Contrast any form of physical measurement with Archimedes, who started with a
simple hexagon and then allowed the sides to successively bifurcate (fractal
approach) until he had derived the formula for the perimeter of a 96 sided
regular polygon. He then used this to set the value of pi between the
inscribed and circumscribed values of 3.14103 and 3.14271.
The fact that pi is the ratio of the circumference to the diameter of a circle
in flat Euclidean geometry, is just one of its manifold properties. One of the
most far-reaching was discovered by Leonhard Euler circa 1736. He showed that
if you started with the constant e and raised that to the power of the product
of pi and the square root of -1, then added one, you got zero. Mathematicians
tend to wax poetic on this simple arrangement of these five special numbers (
1, 0, i, e, pi ). So, if you go putting a special message in pi, you will also
have to mess with e, because there is no room in any of 1, 0, or i (square root
of -1). But if you mess with e, then the function e to the x power will no
longer be its own derivative. Thus by this route, e comes from the
differential equation x' = x, and pi can derived from e, thanks to Euler, so
circles are not involved, nor is the curvature of space-time.
-Ken
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