From: Mike Lorrey (mlorrey@datamann.com)
Date: Tue Mar 12 2002 - 09:04:34 MST
Ken Clements wrote:
>
> I thought I explained this rather carefully, but I guess I was not as helpful as I would have liked. Perhaps I was not clear about the difference between physical space-time and mathematical space. I will try again.
>
> "Dickey, Michael F" wrote:
>
> >
> > >
> > Imagine a circle drawn on a piece of paper ... 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.
>
> I covered the spherical case in my post. Yes, the ratio changes with curvature, but pi does not change. Again, the ratio is simply no longer equal to pi.
When pi is no longer equal to that ratio, how does pi deserve to be
called pi? Pi is defined as that ratio, ergo its value is relative to
the local time space curvature.
>
> > 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?)
> >
>
> It's the other way around. In the absence of a gravitational field it is believed there would be *no* curvature, which is not the case because there is a gravitational field. This is physical space-time, not a constructed mathematical space where ther
e are circles.
Yet the universe's expansion is a process of constant flattening of
space time, ergo the local value of pi is constantly changing along an
asymptotic curve (if the universe is closed) or along a hyperbolic curve
(if the universe is open).
>
> >
> > "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.
> >
>
> A circular path may exist in physical space-time, but a circle does not. A circle *is* a mathematically perfect circle, and in pane geometry its circumference to diameter ratio is pi. Your suggestion would have been better than what was in the book, a
s it would have been based on a physical measurement, your "already known curvature." But Carl did not write that. Had he picked that one, it still would not have worked because the message appears "kilometers downstream of the decimal point" which mean
s the measurement would require at lest several hundreds of thousands of orders of magnitude in resolution. The whole Universe has less than 200 orders of magnitude from top to bottom. (By the way, we know pi to over 200 billion places which, if you wro
te down on paper at 4 mm per digit, would run over 800,000 km. Long enough to go from the earth to the moon and back.)
Distinguishing between flatspace mathematics and curved space reality
does resolve the dillemma, but it is STILL based on a flat space model,
in that such a model does not work in all six classes of M-space.
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