🚀 go-pugleaf

In article <3288d...@cfanews.harvard.edu>, gir...@skyron.harvard.edu (John Girash) writes:
#]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!

A) How do we know this?  Been to any other universes lately?
B) Lemme see; let's multiply through by C.  C + C = 2C.  Hmmmm.
   I wonder what Einstein would say about that.  :^)

#]You've missed Scott's point completely: he's saying that the aerodynamics
#]equations did NOT predict any problem going past the speed of sound, whereas
#]relativity DOES predict that c is an absolute limit.
#]
#]Oh boy, you've again missed something: science seeks to predict, _and_then_
#]to_verify_!  And the energy-vs.-speed aspect of relativity has be demonstrated
#]accurate to something ridiculous like 0.9999999 c by particle accelerators:
#]otherwise, the accelerators _wouldn't work at all_!  It is this _verification_
#]that makes science objective and which ties it to the physical universe,
#]countering what the current anti-objective-science views of many sociologists
#]would have us believe.

I understood the points completely; perhaps I simply failed to make mine
clearly enough.  I am not trying to redefine constants or dispute the
observed correlations between measurements and theory, merely trying to
point out that constants are defined and theories proposed based upon
certain underlying and often unstated assumptions and that those
assumptions necessarily color our perceptions.  Also, note that 
correlations between measurements and theory tend to lend support
but do not *prove* the theory.  Ptolemy's planetary model held up pretty 
well for nearly a millenium.

#]As for your "temporal aspect" to proofs, well, you can improve on proofs and
#]sometimes reverse them with technological advances, but it's damned tough to
#]eliminate disproof.  And there's a hell of a lot of disproof out there to the
#]idea that photons travel at anything other than c in vacuum in _any_
#]reference frame (which is the whole foundation of the c-as-speed-limit idea).

I'm not sure I follow this.  To "disprove" a theory, one need only find a 
single verifiable data point that is contrary to theoretical predictions.
Failure to find such a point does not, by any means, *prove* a theory.

#]: Pi comes from the ratio of the circumference of
#]: a circle to its diameter.  The ancients could have chosen the inverse
#]: ratio and given pi a value nearer 0.31831, and the universe would 
#]: still have unfolded as it should.  EE's tend to use 'j' for the 
#]: "imaginary" axis, rather than 'i'.  Who knows, perhaps the theory
#]: would be easier to learn if we considered the axis to be the frequency
#]: axis rather than a "make-believe" axis.
#]
#]You're just plain wrong.  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.
#]
#]btw, you seem to be confusing the idea of "what pi represents" with
#]"how we choose to communicate that idea".  It's the former that is of
#]relevence to discussions like this; the latter is just semantics
#](e.g. whether sqrt(-1) is called "i" or "j").

I've already been taken to task for my presentation, here; it was late and
it appears that I did not make my points clearly.  Forget the 'i', 'j'
stuff; 'Twas a digression that clouded my point.

First, note that there is no assertion that PI is an approximation.  It is
*defined* as the ratio of the circumference of a circle to its diameter in
a Euclidean coordinate system.  I suspect that we ended up with a symbol 
for it because a bunch of folks a long time ago got tired of saying
"the ratio of the circumference of a circle to its diameter" or its
equivalent in ancient Greek.  It is not coincidental that it shows up
in other places since it is essentially a "fudge-factor" for converting
between linear and angular measurement systems.

As for saying that the ancients "defined" PI, they did, indeed.  And they
could have defined it otherwise without pulling down all of science.

What I had intended was just this:

What we define is largely dependent on what we are trying to measure.
'PI' is just a constant, arbitrarily defined as the ratio of the
circumference of a circle to its diameter;

           C = PI * D ( C = 2 * PI * R)  => (PI == C/D)
       
'PI' is C/D only because 'the ancients' chose to fix the value
of 'D' at one and solve for a constant multiplier greater than 1.
[Remember, we had a group of folks who based their mathematics on what
they could count.  Zero as a counting number was a revolutionary concept.]  
One could just as easily have decided to fix the circumference and
solve for the constant that defined the diameter:

                     D = pi * C  =>  pi == D/C

in which case, 'pi' would have been approximately 
1/3.14159... or 0.31831.... and

           C =  D/PI [ C = (2 * R)/PI ] => Circle
           w = (2*f)/PI                 => Radian frequency
           Trig functions end up defined differently, .................

It would not have been unworkable, just different.

We deal with this kind of effect in EE as a part of life; folks
flipped a coin when choosing the sign convention and we ended
up with current being defined in the opposite direction to 
electron flow.

#](*) 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.

What I said was "Newton was exact for his day."  He had been in the ground
for over a century before Maxwell started publishing; they were hardly 
contemporaries.
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