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On 03/17/2024 05:59 PM, Ross Finlayson wrote:Basically most all the coolest things that areOn 03/17/2024 02:18 PM, LaurenceClarkCrossen wrote:>Callahan, in Euclid or Einstein, says,>
p.222 "he is himself struggling to give, in a hazy way, some kind of
reality to his mathematics by clothing his formulae with some
interpretation or other....clarity ends, and we step into a region of
mistiness and fog. We certainly cannot consider Einstein as one who
shines as a scientific discoverer in the domain of physics, but rather
as one who in a fuddled sort of way is merely trying to find some
meaning for mathematical formulae in which he himself does not believe
too strongly..."
That's "Mathematical Physics".
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Consider for example the Cartanian developments
and Geometric Algebra. Didn't exist. Got figured
out, added to physics, discovered a particle, and
a remarkable virtual anti-particle at that. (That
it's so said the contrivance the configuration the
energy the experiment so found not falsified,
or so it is said and relayed according to the
interpretation of the data.)
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Science is still figuring out there's an
"upper, middle, and lower" sky, that the
Babylonians named in hazy antiquity, that
"peripheral parallax" is still sort of a
toss-up between Fresnel and Huygens.
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Now, Einstein is lionized and that means
beyond even what he deserves, at the same
time he sort of pushes off from his followers
writ large, who if they "know" the theory
probably learned it ten different ways,
most of which giving absurd consequences,
that it's also so, that, Einstein was still
searching for a "total field theory", and
even just a practical "bridge" from the linear
to and from the rotational, "Einstein's bridge",
even out of his later years.
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So, these days, the, "nonconservative", the
"pseudomomentum", the "quasi-invariant",
the "pseudodifferential", these aren't just
names for resonance theory and rest-exchange
and resonance theory and rest-exchange,
they represent conceptual concepts in the
mathematics, that most people sort of naively
have, but don't intuitively formalize.
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Or, if they don't, it's like "well, there
were only three people who know relativity,
Einstein, Eddington, and nobody knows who
else, since then at least two of those are
wrong, so, what it's figured is that Einstein
knows less now than was then".
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The usual idea is "physics has three great
edifices, GR and gravity and QM, somehow
they're all supposed to be one theory".
I imagine you may have heard of the idea
of "crisis" in physics, what it means is
that GR and QM sort of, stop talking to each other,
and gravity isn't in the picture at all.
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Then, how to unify those, seems is going to
require just enough super-classical mathematics,
to result that a fall gravity unites with
strong nuclear force, where "QM is a particle/wave
theory usually with a stochastic interpretation
in the fields a field theory", and "GR/SR is space
and kinetic frame with L-principle, Maxwell's fields
and allowed a non-zero while vanishing cosmological
constant, in the fields a field theory", with
conservation about energy, then that it's unified
the particles to make a continuum mechanics, and
diversified the linear and rotational to make
an orbital mechanics, it seems pretty simple
to describe it this way.
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Then, that it's, "un-linear", has that lots of
things in "the usual derivation" are linear,
linear, linear, and linear again, with regards
to explaining, pretty much to explaining,
"triangle rule", and, "inverse square",
winding around the clock, the sum-of-histories,
the sum-of-potentials.
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Then of course there's interpreting all the
derivations and all the data in that, ...,
though at least it's all already sort of
organized this way.
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https://en.wikipedia.org/wiki/Robert_Hermann_(mathematician)
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I have a couple of these books on jet bundles,
they help explain at least there are more modern
formalisms for the same things.
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Wikipedia quotes Hermann thusly:
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"It is a deeply regrettable fact
that the flow of information back and forth
between "modern" geometric and algebraic mathematics
and classical applied mathematics has been so minimal,
even though there is clearly a solid basis for such
interaction. One of my overall motives in writing my
series of books "Interdisciplinary Mathematics" was
to facilitate this flow...[despite] high structural
and mental barriers to such cross-fertilization."
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