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NNTP-Posting-Date: Sun, 23 Jun 2024 21:04:31 +0000
Subject: Re: it's a conceptual zoo out there
Newsgroups: sci.math
References: <v57u7g$rgs$1@dont-email.me> <v594kk$bco0$1@dont-email.me>
 <v59ffh$d4vt$1@dont-email.me>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 23 Jun 2024 14:04:46 -0700
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On 06/23/2024 08:37 AM, sobriquet wrote:
> Op 23/06/2024 om 14:32 schreef FromTheRafters:
>> sobriquet pretended :
>>> 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).
>>>
>>> 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..).
>>>
>>> https://www.youtube.com/watch?v=KiI8OnlBTKs
>>>
>>> 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)?
>>
>> I don't think so because regarding physics there is one goal, to model
>> reality, and I believe only one reality to deal with. With mathematics
>> there are endless abstractions such as the idea of endlessness itself
>> in its many forms.
>
> I think there is still a general trend towards unification in both math
> and science.
> In both cases things get discovered and explored and when things are
> explored in more detail, often connections are discovered between
> seemingly unrelated fields that allow one to come up with a unified
> framework that underlies things that initially seemed unrelated.
>
> https://www.youtube.com/watch?v=DxCWRAT0WKc
>

"Knot Theory is Impossible Without These 9 things" - Di Beo's
https://www.youtube.com/watch?v=DxCWRAT0WKc


Uh, sheet bend, square knot / granny knot, shoelace knot, surgeon's
knot, half-bend, ..., some say knots only exist in 3 and 7 dimensions,
about things like Camille Jordan, though one often finds that
knots are learned as shoelace-tying and fishline-tying and
for merit badges and later the profession of the, "rigger".

Betti numbers, knot-untying is a pretty usual thing, with
regards to mostly getting loose end going, then as with
regards to loops and through, there's something to be
said for crochet and yarn-work, for knot-nets vis-a-vis
bend-ends.

Ah, excuse me, bends are not hitches and hitches are not bends.

https://en.wikipedia.org/wiki/Bend_(knot)
https://en.wikipedia.org/wiki/Hitch_(knot)

There are more "knots" than "tangles". Most
"mathematical knot theory" is "tangles".

In 1881 a paper "On the analytical forms called trees",
Am. Jour. Math., reflects also calling what we'd call
"branchings" or vertices as "knots", like tree knots.

Half-Windsor, full-Windsor. Don't forget Moebius strip.

The "Gordian knot" has a usual sort of approach to
reducing a problem, yet, doesn't fix knots in knots.
I.e., it always removes one knot, yet, on average
doubles the number of knotted lines to un-knot.

"Descriptive Differential Dynamics:  dogma, doubling" - Ross Finlayson
https://www.youtube.com/watch?v=JhfoDJ0M7Tc&list=PLb7rLSBiE7F5_h5sSsWDQmbNGsmm97Fy5&index=20