From: spike66 (spike66@attglobal.net)
Date: Fri Mar 08 2002 - 22:26:04 MST
Damien Broderick wrote:
>>It's also hard to see how anyone could put a message into Pi. That
>>is such a simply defined number, how could it have a message?
>>
>My sense of this was that Sagan was using the child's version of pi: the
>ratio of circumference of a circle to its diameter. This is controlled by
>the specific and tweakable geometry of spacetime, no?...Damien Broderick
>
No. Since arctan x = x - x**3/3 + x**5/5 - x**7/7 - ...
For x = 1 in particular, we get the series that nobody except a
mathematician really believes to converge. p i/4 = arctan 1 so pi/4 =
1 - 1/3 + 1/5 - 1/7 ...
This formula would make it impossible to hide messages in the digits of
pi, regardless of the geometry of spacetime. Sagan must have known
this, and thus dropped the notion in the movie.
Nowthen, the longer one ponders the above expansion, the more
strange and wonderful it seems that it should work. Thinking about
it long enough can leave one staring into the abyss. spike
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