Re: You Don't Have to Be Nuts to Be a Mathematician ...

From: Eckard Blumschein (blumschein_at_et.uni-magdeburg.de)
Date: 07/14/04 

Date: Wed, 14 Jul 2004 10:33:34 +0100

Eckard Blumschein wrote:

>>> Instead you might vote YES for 1/oo=0, tell something really
>>> original, or at least lurk for someone who is both a professor who
>>> is obviously wrong and someone who managed to cheat TV teams,
>>> editors and even less critical stuff. Just a hint: Superluminality
>>> by Nimtz has a profound mathematical fallacy-background. Doesn't it?

> I would rather appreciate couraged mathematicians who are aware of the
> fact that Gaussian pulses are always anticipatory.

The fallacy-background would not be profound if I wasn't formally wrong.
Let me tell to mathematicians what anticipatory means in that context:
Extended from minus infinity to plus infinity. Well, iff a Gaussian
pulse is centered at zero, then this condition can be formally fulfilled
without contradiction to causality. In that case, however, there is no
apparent superluminality.

Let me suggest a second, already a bit more tricky exercise:
B. Gompf, R. Günther, G. Nick, R. Pecha, W. Eisenmanger, Phys. Review
Letters 79, 1405-1408 (1997).
You might find out why the correlational measurement led to erroneous
results.

> Not executable are infinity and zero.

Well, any child will tell me 1-1=0. Who is really stupid enough as to
suspect me being even more stupid? I am just not convinced that we need
a universal meaning of numbers and in particular of zero. We know that
it is impossible to approach a non-existing length of a distance by a
finite number of cuts.

> One cannot really count up to
> infinity. Correspondingly, the continuum cannot really be broken into
> elements of zero size. So I vote for correspondence between zero and
> infinity, no matter that e.g. Smirnov claims the opposite and every
> child has to learn Cantor's notion of countability while one could
> likewise introduce the countably infinitely small: 1/2, 1/2, 1/3, ...
>
> Engineers like me have as a rule ten fingers and are using a decimal
> system as to completely express all reals of concern. Is there really
> any reason to distinguish, in application, between rationals and
> irrationals? I don't think so. I know that the whole set theory intends
> to create a biased paradise of numbers. Even the notation limes x_n for
> n to infinity is misleading in that it is based on Weierstrass's epsilon
> delta notion of infinity.
>
> Do we need the potential infinity? I see it the only justification for a
> neutral zero between positive and negative numbers. Otherwise any point
> along a line might be represented by its approximation (delta below any
> limit) from the left as well as from the right. Well, I could agree with
> abandoning the neutral zero and all related stuff since the potential
> infinity cannot be reached.
>
> Don't we need exclusion of division by the neutral zero? Definitely not.
> Exclusion of the smallest imaginable positive and negative values is
> both necessary and sufficient.
>
> Do we need Zermelo-Fraenkel axioms? Perhaps yes, as to find out what
> must be fundamentally revised in order to purify mathematics from some
> flaws.

Flaws in mathematics?
- Isn't it nonsense to exclude the exact neutral value zero e.g. from
   possible denominators while 1-0.9... is not excluded?
- Isn't it nonsense to split R into R^+, zero, and R^-?
- Isn't it overdue to clarify what is wrong with Buridan's donkey?
- Isn't it a bit exaggerated to consider the complex representation of
   a unilateral function more general? I would rather call it redundant.
- Wasn't at least Nimtz incorrect when he assumed band-limited signals
   and concluded that signals must be unlimited?

Eckard Blumschein

Relevant Pages

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