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Martin Ward (martin@ward-hull.demon.co.uk) wrote:
: In article <5hhge0$48q@raven.cc.ukans.edu>, Greffindel
: <ipsifend@eagle.cc.ukans.edu> writes
: >Jonathan Cunningham (jlc@sofluc.demon.co.uk) wrote:
: -- snip --
: >: Be careful if you are determining pi by measuring the ratio of the
: >: circumference of a circle to its diameter: a one tonne weight in a 10 metre
: >: diameter circle will affect the value of pi in about the 24th or 25th
: >: decimal place (general relativity and curvature of space-time etc.). If
: >: you wish to try this, it's worth knowing that the correct value of
: >: pi should be around 3.14159265358979323846264338 in flat space, although
: >: the last two or three digits will be different with the one tonne weight
: >: in place. :-).
: >
: >: Jonathan
: >
: >(thinks) (thinks) (thinks)  You know, that makes sense.  What could
: >you say about the set of weights such that under their influence, the
: >"effective pi" would become rational?  Algebraic? How big a weight
: >would you need to get a "pi" of 4?
: >--Greffindel the Plaid

: Jonathan obviously understands the physics of this better than I do, but
: putting in a weight must *reduce* the local "pi", surely?

Better than I as well, I'm sure.  It also depends on what one is
calling 'pi'.  I'm sure the Leibniz series still converges to the same
result even near neutron stars.  But yes, if space is curved by a
large weight, than the linear distance you'd travel to get from one
point on a circle to its antipode would be longer, therefore the
ratio of the circumference to that would be smaller.  My error--
sorry. :)

: Since there are algebraic and rational numbers arbitrarily close to any
: transcendental number like pi the same would be true of the set of
: values of our central mass.  If we can assign it a random real value
: then most such would leave "pi" transcendental, but we could find
: infinitely many values within any range >0 which make "pi" rational.

: Of course quantum mechanics says, does it not, that masses cannot be
: given an arbitrary real value but only one chosen from a set of discrete
: values....
: -- 

See, that's what I'm wondering.  I suppose the answer is that since
mass is quantised, it makes a huge amount of sense to map the set of
allowable masses to the set of integers, but on the other hand, you
could specifically assign a transcendental 'number' to the smallest
possible unit of mass, and than the masses of all objects would be
transcendental.   *but*, on the other hand, our distortion of pi is
based on measured distances in space, a lot depends (doesn't it?) on
the exact mathematical relation between mass and distortion.


: Martin Ward
: _________________________________________________________________________
: "When *I* use a word", Humpty Dumpty said in rather a scornful tone, "it
:  means just what I choose it to mean - neither more nor less".
: "The question is", said Alice, "whether you *can* make words mean so many
:  different things".
: "The question is", said Humpty-Dumpty, "which is to be master - that's all".

: "Through the Looking-Glass" - Lewis Carroll.
: _________________________________________________________________________

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--Greffindel the Plaid

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