From: Dickey, Michael F (michael_f_dickey@groton.pfizer.com)
Date: Mon Mar 11 2002 - 08:26:25 MST
-----Original Message-----
From: spike66 [mailto:spike66@attglobal.net]
Sent: Saturday, March 09, 2002 12:31 PM
To: extropians@extropy.org
Subject: Re: Carl Sagan's Contact (was: My Review A.I. the Movie (total sp
oiler I hope))
"I disagree sir. In any universe with any curvature, a circle would still
have 360 degrees, for the circle defines the degree, as well as the radian.
The expansion given would work even in a different space curvature, and they
would derive the same value for pi. Nowthen, if they were to actually
attempt to measure the ratio of the circumference to the diameter, Im not
exactly sure what would happen. spike"
scerir - "in a non-Euclidean space the ratio is < pi, or > pi In GR, for a
'warped' (hyper)surface the ratio is < pi, and it is also possible for pi to
be rational, if I remember well"
Ken - "Pi is a constant that does not change no matter where you are, how
much you weigh, or how fast you are going. It says some things about flat
Euclidean space, and to the extent your observations of the space around do
not match, pi helps you figure out the nature of the curvature"
Assuming that PI is the ratio of the diameter of a circle to its
circumference, then altering the curvature of space time would alter that
ratio, this is a fundamental aspect of general relativity is it not?
Imagine a circle drawn on a piece of paper and a diameter drawn through, the
ratio of the two is some particular number. Imagine that instead of drawing
that circle on a flat piece of paper it is drawn on a sphere (similiar to a
line of lattitude on a globe) If it is a small sphere and the line of
lattitude is the equator of the sphere, the total distance around the circle
may be equal to the circle on the paper, but the radius of the circle must
curve with the sphere, and is not a (comparitively) straight flat line so it
must necessarily be longer when compared with the overall circumference. As
the sphere increases in size, the line of latitude must move up the sphere
to maintain its size, as it does the the radius gets closer and closer to
being the straight line of the flat piece of paper, and thus the ratio of
that radius to the circumference gets changes as well. The curvature of the
sphere the circle is drawn on is analogous to the curvature of space time,
Thus PI changes with the curvature of space time. In the absence of a
gravitational field, I believe there is a net curvature of space time (is
space time curved or flat?) If that is the case, the the geometry of the
space time curvature can be altered to change the ratio of a circle to its
radius and thus hide a number in it (can it be arbitrary?)
"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."
If Elly was figuring this out on a computer, perhaps she modeled a
mathematically perfect circle and compared its circumference with its
diameter with the already known curvature of space time, thus making the
calculation one that is representative of the geommetry of space time, and
not merely an abstract mathematical construct. Altering such a curvature
would probably not effect any organisms evolving in the space-time unless
the curvature was severe.
Regards,
Michael
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