🚀 go-pugleaf

In article <32893...@cfanews.harvard.edu>,
John Girash <gir...@skyron.harvard.edu> wrote:
>Followup-To: alt.folklore.science
>References: <3288d...@cfanews.harvard.edu> <mumfordE...@netcom.com>
>Distribution: 
>Lines: 94
>X-Newsreader: TIN [UNIX 1.3 950824BETA PL0]
>
>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_,

Nope, you cannot take anything for granted.  You have to prove that in this
"other universe" that 1+1 = 2 (believe it or not, this has actually been
proven in this universe.. I believe the text of the proof spans 3 large
books).  You cannot assume anything about another universe.  You must do the
same thing we've done in this universe, exist in it for a while, study it's
properties, and make rules about how it behaves (pi=circumference/diameter,
1+1 = 2, etc).

If you apply any of the rules we know in this universe to another, you've
already taken your first incorrect step.

>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).

You can define pi any way you like so long as all definitions are consistent
in your universe.. PI = circumference/diameter = 4*(1 - 1/3 + 1/5 - 1/7 ..)
= ln((-1)^sqrt(-1)) (if you want to get weird)

>
>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.
>

No, taking out a ruler and measuring is 'demonstrating'.. proving is
taking what is known and taking logical steps from there to make some-
thing else known.  Btw, ruler measurements are still accurate since a
"straight" ruler in a bent universe would itself bend along the universe's
curves.

>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.

No, that is *the* definition of pi... it was the definition 2000+ years ago
when the symbol pi was still a letter of an in-use alphabet instead of a
mathematical symbol, and it is still the definition today.


-- 
Glenn Lamb - mum...@netcom.com -- Finger mum...@netcom.com for PGP Key.
PGPprint = E3 0F DE CC 94 72 D1 1A  2D 2E A9 08 6B A0 CD 82
Reply address set to mum...@no-spam.netcom.com to fudge USENET scanners.
Be sure to send replies to mum...@netcom.com