Re: it's a conceptual zoo out there

On 06/22/2024 07:58 PM, Ross Finlayson wrote:

On 06/22/2024 06:36 PM, sobriquet wrote:

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In particle physics, people used to refer to the particle zoo since
there was such a bewildering variety of elementary particles that were
being discovered in the previous century.
Eventually things got reduced to a relatively small set of fundamental
fermions and bosons and all other particles (like hadrons or mesons)
were composed from these constituents (the standard model of particle
physics).
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Can we expect something similar to happen eventually in math, given
that there is a bewildering variety of concepts in math (like number,
function, relation, field, ring, set, geometry, topology, algebra,
group, graph, category, tensor, sheaf, bundle, scheme, variety, etc..).
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https://www.youtube.com/watch?v=KiI8OnlBTKs
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Can we kind of distinguish between mathematical reality and mathematical
fantasy or is this distinction only applicable to an empirical science
like physics or biology (like evolution vs intelligent design)?

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It's mostly the milieu of model theory what relates among them.
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Logically then that's mostly relations.
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The "stronger" and "weaker" theories
are both "weaker" and "stronger",
proving more with less, less with more,
less with less, more with more.
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Then "Foundations" has the usual goal of being "a 'the' theory".
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"A Theory"
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https://www.youtube.com/watch?v=WT7yUJYtTz8&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=43
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There still is a "Particle Zoo", there's a "Wave Zoo", too.
"Resonance theory" is above wave theory about "particle-wave"
duality. Energy's conserved, yet it's also in a form, and
the interactions and transitions are various.
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I basically look at it as geometry, arithmetic, algebra,
number theory, topology, and function theory, operator calculus.
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I.e. the discrete is embedded in the continuous.
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Here's some reading including from d'Espagnat and Badiou
about that there really is a "the mathematics" to attain to,
not just poesie and metaphor, yet a real strong lyrical metonymy.
https://www.youtube.com/watch?v=vMF_-HprkZs&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=19
It's a concept.
https://en.wikipedia.org/wiki/Concept
Kind of like Gadamer does, Badiou in his "Second Manifesto"
also arrives at a sort of stronger "amicus Plato".
Well, sort of, ..., for a while.
Then for constant, consistent, complete, and concrete,
for constancy and consistency and diversity and variety,
then for physics in the tendencies and propensities of
the oscillating and restitutive and dissipating and attenuative,
and as for symmetry-flex, quasi-invariance, and continuity laws
for symmetry-breaking, invariance, and conservation laws, that
are fuller symmetries, invariances, and laws.
The Higgs Boson: these days has also for Big Higgs, Little
Higgs, and sort of anti-Higgs, supersymmetr(ies), plural.
So, "unification", where "all energy is the same",
is contrived. Yet, there's still to be said that
the four sorts quantities of physics, arrange each
other about and around, in a field theory,
sum-of-histories, sum-of-potentials.