🚀 go-pugleaf

References: <3288d...@cfanews.harvard.edu> <mumfordE...@netcom.com>
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mum...@no-spam.netcom.com wrote:
: John Girash <gir...@skyron.harvard.edu> wrote:
: >Followup-To: alt.folklore.science

: >Danny Bersch (ber...@sst.sps.mot.com) wrote stuff 
[omitted for brevity]

: >Oh for Pete's sake, the values of pi and e have nothing to do with "which"
: >universe you're in.  They're mathematical concepts, that'll be the same
: >anywhere that 1+1=2.  They are NOT properties of our (or any other)
universe!
: 
: hehe.. uh.. actually, yeah they are properties of our universe...  not
: only properties of our universe, but the properties that help define
: our universe.  And he's correct, they may not be properties of another
: universe.

: >Pi comes from a lot of different places, one of
: >which is the circumference/diameter ratio _in a flat geometry_.  It is a
: >fundamental mathematical constant, which is a hell of a lot stronger
: >statement even than saying c is a fundamental physical constant.  It is
: >_not_ an approximation IN ANY UNIVERSE.  We don't know what c is in "other"
: >universes, or even if relativity is valid there.  But pi remains pi. It's a
: >horribly anthrocentric attitude that lets you say he ancients "defined" pi.
[...]

: Now back to pi being a constant in every universe... a simple request: prove
: it.  Another universe may have an entirely differently formed space-time
: continuum than our own or may not even have a continuum, but something
: completely different.  How can you claim pi will be the same when the
: structure of the universe will be different?  It seems arrogant to think
: any other universe would be exactly the same as ours.

Um, what exactly do you mean by "prove"?  If you'll grant me that 1+1=2
independent of what universe you're in (mathematics deals with _concepts_,
not with empirically testable theories about the nature of the universe,
that's why it's not a science!) then 2 is 2 and pi is pi.  For example,
I can define pi as:
                   pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...
		   which has nothing to do with geometry.  As I said to an
email replier,
mathematicians (I'm not a mathematician) prefer _not_ to define pi
geometrically, because it arises as a fundamental constant in many other
contexts as well.  But even if you do define it geometrically, the _concept_
of flat space exists in any universe regardless of whether or not that
universe is indeed flat (again, ours is an example).

But I get the feeling that by "prove" you mean you want me to take out a
ruler and measure it.  Well, I'm afraid that not even in our universe will
the circumference/diameter ratio come out to exactly pi, because our
universe is not flat.  In fact, even if you "gave" me a matter-free and
otherwise-curvature-free universe to measure it in, the result still 
wouldn't be pi because the mere presence of me and /or my ruler in that
universe induces a curved geometry in it.

None of which changes the validity of defining pi as "the circumference/
diameter ratio _in a flat geometry_".  But frankly, that's not a definition
as much as a just a statement of fact.

: >j "mainly writing this to change the followups line" g.

: >(*) but you can't even say that Newton was "exact" up until Einstein
: >"discovered" (described is a better word) relativity: once Maxwell
: >quantified classical electrodynamics in 1864 (and thus first introducing
: >"c" to fundamental physics), Newton was in conflict with Maxwell.
: >Einstein was just the first to recognise the conflict's implications
: >and to describe its resolution.

: Newton never was exact.  Newtonian mechanics are close enough (meaning there
: was no technology available to measure the error) to the real values for
small
: relative velocities.

That's the way I prefer to think about it.  But the previous poster took
a differnt attitude which I'll grant is at least arguable.

: Btw, I may be incorrect with this myself.  I remember reading somewhere
: that Newton defined force F = d(mv)/dt (derivative of mass * velocity
: with respect to time).  Since others assumed that mass was a constant,
: they simplified this to F = m * a.  Newton may still have been correct,
: others who built on his work were the incorrect ones.  Can anyone verify
: this?

Yes, F = dp/dt (momentum p does "=" mv classically) does generalise much
better than F=ma and is the way I prefer to think about & teach it (e.g. in
astronomy where objects do transfer mass to & from each other).

My apologies, I tried to redirect followups but either my newsreader or the
local news server is adding a blank line before the line 
"Followup-To: alt.folklore.science" that prevents it from working. 
I'll try to get it fixed.  If followups _do_ work this time I'm going to
add this thread to my colm killfile, and to debate me more you'll have to
go to alf!  (-:

jg

-- 
"don't listen when you're told about the best days in your life      Spirit of
 a useless old expression, it means passing time until you die."      the West
 -----------------------------------------------------------------------------
  -- John Girash --- gir...@cfa.harvard.edu --- http://skyron.harvard.edu/ --