Re: The Nature of Mathematics - a plea for help
From: Eugene Shubert (http://www.everythingimportant.org)
Date: 11/13/04
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Date: Sat, 13 Nov 2004 10:28:54 -0600
"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrncpa01p.59.dubious@radioactivex.lebesque-al.net...
> Eugene Shubert wrote
> http://groups.google.com/groups?&selm=1d682f9d.0411091348.67c8f998@posting.google.com
> >
> >Will Twentyman and Gene Ward Smith sound like extraordinarily
> >competent mathematicians. They agree with me.
>
> So far, you have validated my hypothesis that you define competent
> by the ease with which you can misconstrue the comments of someone
> into agreement where there is none.
This is your condemnation:
You are confident that Gene Ward Smith and Will Twentyman failed to
answer my opening question. And you believe that you're handling the
evidence honestly.
"Gene Ward Smith" wrote
http://groups.google.com/groups?&selm=e6bf7b03.0411080052.7723ba69@posting.google.com
> "Eugene Shubert" wrote
> http://groups.google.com/groups?&selm=418dc083@sys13.hou.wt.net
>
>> Suppose you begin a derivation by assigning a clear and
>> undisputed physical meaning to real parameters x, x', T, T',
>> and a real constant u. From that reasonable starting point,
>> I claim it's legitimate to pick a real number 1/c and then
>> define a new quantity v by the equation u=v/sqrt(1 -v^2/c^2).
>> The point is to then write everything in the ensuing
>> derivation in terms of v and not u. I also believe it's
>> legitimate to define, without any justification whatsoever,
>> the function gamma(v) = 1/sqrt(1 - v^2/c^2).
>
> There is no requirement to give a physical meaning to any of
> the above, .... You've defined u as a function of v, for real
> v with |v| < c. You can certainly do that if you choose, ...
>
> You are also free to define the function gamma, ... You might
> also consider the transformation r = c arctanh(v/c), "rapidity",
> which has nice additivity properties.
>
> None of this is physics as yet;
______________
Will Twentyman <wtwentyman@read.my.sig> wrote
http://groups.google.com/groups?&selm=418fb1a4_4@newsfeed.slurp.net
>
> Eugene Shubert wrote:
>
> > I have a trivial question concerning mathematics and logic and I
> > would like to receive a resounding answer that is both unanimous
> > and clear from practicing mathematicians and logicians. The cross-
> > posting is for the benefit of the physicists who have read my
> > paper http://www.everythingimportant.org/relativity/special.pdf
>> and are stumbling over its elementary logic. Here's the logic that
>> the physicists find troubling. Suppose you begin a derivation by
> > assigning a clear and undisputed physical meaning to real
>> parameters x, x', T, T', and a real constant u. From that
>> reasonable starting point, I claim it's legitimate to pick a real
>> number 1/c and then define a new quantity v by the equation
>> u=v/sqrt(1 -v^2/c^2). The point is to then write everything
>> in the ensuing derivation in terms of v and not u. I also believe
>> it's legitimate to define, without any justification whatsoever,
>> the function gamma(v) = 1/sqrt(1 -v^2/c^2).
>
> It appears that you are making a definition. That's perfectly ok.
> Next you have to defend any interpretations you may put on
> that definition. I suspect they have an objections someplace
> else.
______________
As you say, you're absolutely certain that you're unaware of any
positive confirmations in my favor in the expert testimony of Gene
Ward Smith and Will Twentyman. I suppose that means that you
also don't recognize any difference between purely positive
confirmations if contrasted to the directly opposite, negative
denials by Tom Roberts.
Look again. Tom Roberts directly contradicts the answers given
by Gene Ward Smith and Will Twentyman in his wrangling with
me. Here is the pertinent exchange:
> The quality of a derivation of the equations of SR is usually judged
> by:
> 1. the simplicity and physical believability of its assumptions, or
> lack thereof.
> and:
> 2. the generality of those assumptions.
> Your derivation is seriously lacking in both of those aspects:
> 1. On page 2 your assumptions for \mu and \gamma are completely
> unsupported,
My official derivation begins on page 4. The assumption that you refer
to (page 2), the principle called change of variables, also called
substitution, is one of the clearest and most useful mathematical
ideas in high school algebra and baby calculus. What's your dispute
with intuitively simple fundamentals? What support do I need and
why is it an unwarranted physical assumption if I label the function
1/sqrt(1 -v^2/c^2) with the Greek letter gamma?
> and are not obvious at all -- these are QUITE unusual assumptions,
> to say the least; why should anybody believe them?
> > Why should anyone believe in the substitution v/c = tanh(theta),
> > which transforms the usual Lorentz transformation to its
> > hyperbolic form?
>
> Because that is not an ASSUMPTION, it is a CONCLUSION.
There are plenty of derivations of the Lorentz Transformation
equations that don't define theta. Take Einstein's tortured derivation
for example (Dover, The Principle of Relativity). And try to find a
mathematician who isn't going to laugh at you. If theta isn't defined
anywhere in a derivation, then you are perfectly free to let theta be
anything that pleases you at any step in a derivation. And even if a
simple substitution/transformation doesn't please some physicists, it
still has every mathematical right to exist.
There is no physical assumption in the mathematical substitution
u=v/sqrt(1 -v^2/c^2).
http://www.everythingimportant.org/viewtopic.php?p=3437#3437
http://www.everythingimportant.org/viewtopic.php?p=3441#3441
Eugene Shubert
http://www.everythingimportant.org/relativity/special.pdf
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