[FRIAM] invoking quantum woo (was Book publishing advice needed)

[Jon Zingale]

Roger,

There is a lot of mud here to try to sift through, so I will speak to a
couple of things and otherwise move to let this go. The classical problems
of compass and straightedge geometry were blocked by the tools. Namely, the
requirement that these problems be solved by compass and straight-edge
implies that these geometric problems have solutions that are constructible
via a finite sequence of quadratic extensions of the field of complex
numbers with rational coefficients[Ơ]. The realization of the inability to
generally trisect an angle, in this way, needed to wait for Gauss and more
lucidly the advent of Galois theory (algebra!). This advance was quite a bit
more than geometers simply changing the postulates and turning a crank. We
both agree that uncertainty is a consequence of Fourier analysis, but I go
(perhaps a bit too boldly) further to say that it is a consequence of
Fourier analysis over a given logic context. It is in this way that I feel
we are relying on Fourier analysis like the greeks were relying on compass
and straightedge.

Without exhuming Bethe and Feynman and then performing some clever
necromancy, I am not sure either of us will be able to have our Marshall
McLuhan-Annie Hall moment. I am content to let those sleeping dogs lie, and
to concede that my decade-old memory of that video came with some extra
emotional charge.

As I have pointed to here on Friam in the past, work done on topos theoretic
foundations of quantum mechanics by people like Chris Isham and Fotini
Markopoulou-Kalamara, are moving the theory forward beyond where Bethe,
Feynman, and others left it. A popular science account of this movement can
be found in Lee Smolin's 'Three Roads to Quantum Gravity'[ƣ], for instance.
Because pressing theorems or demanding others read Phd level papers has the
effect of sucking the air from the room, I make no further demands to
digress. The take-home for me, from reviewing recent work as well as my own
long time interest in topos theory, is that points can often be more subtle
than we give them credit.

Anyway, I wish to take a break and open a window in hopes that a
conversation may grow here again soon.

Jon

[Ơ] Three famous problems that we will investigate will be the squaring the
circle, doubling the cube, and trisecting an angle. see:
http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Gao.pdf
or see also:
https://en.wikipedia.org/wiki/Straightedge_and_compass_construction

[ƣ] A book I never got to return to Hywel.



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