
A Fight to Fix Symplectic Geometry - KKKKkkkk1
https://www.quantamagazine.org/20170209-the-fight-to-fix-symplectic-geometry/
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auggierose
Very interesting article, I also recommend reading the comments, as they help
to illuminate the nature of the "fight".

What seems to have happened there is this: A genius used his intuition to
solve a foundational issue, but did not produce an adequate proof that he
actually did. 16 years later others come in and make sure that he does. Now
there is some controversial about who gets credit for the proof and for the
solution of the foundational issue.

There shouldn't be such a controversial. Credit is not a zero-sum game. If
somebody now goes ahead and produces a formal machine-checked framework for
symplectic geometry, that should deserve credit as well: Obviously not for
solving the original problem, but for checking beyond any doubt that the
produced mathematics is solid.

Of course ideas are the life-blood of mathematics, but then again ideas are
the life-blood of any creative human endeavour. What is special about
mathematics are the proofs. So I don't see any problem in giving substantial
credit to people who try to make proofs most rigorous.

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Certhas
I don't know which comments you are referring to exactly, but I would like to
add that the comments by Motl should be taken very, very, very carefully. He
is a climate change denier who believes women are over-represented in STEM. In
fact his blog post on this article is titled: "How feminism helped to poison
and politicize symplectic geometry".

Not a reliable source of judgement by any stretch of the imagination.

Edit: If you start reading the comments make sure you read to the end, where
actual mathematicians are commenting.

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auggierose
I am referring to all the comments.

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thanatropism
I'm doing my thesis in numerics for symplectic flow maps, and was really
excited to see the popular press to somewhat cover the world I'm living in.

I also spent days on end joking about how the new generation of alt-medicine
gurus will be "symplectic holistic healers" and how I want a piece of that.
Out with quantum theory, in with symplectic physics!

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balsam
Hi, I'm just getting started out in this area (background: quantum physics).
Are there review papers or slides you would recommend? For the numerics. I'm
somewhat familiar with Wehrheim and da Silva, but didn't realize that people
were going into numerics already.

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thanatropism
On numerics: there are entire textbooks at a relatively elementary level (no
differential geometry) with titles like "Simulating Hamiltonian dynamics". At
the end of the day, verifying that a discrete map (approximating a Hamiltonian
system) is symplectomorphic is a matter of linear algebra.

On theory: there are a couple of good lectures by Dusa McDuff on YouTube; she
also has a short tutorial-like PDF somewhere googleable.

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mlmlmasd
Has infinite mathematics actually been useful for anything at all? I mean
uncountable infinities, higher cardinalities, etc - not limits, and other
'pseudo-infinite' abstractions. I have never encountered these things applied
to anything other than infinite mathematics for infinite mathematics' sake.
Seems like a waste of time.

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joshuata
Many of the ideas from infinite mathematics interact with finite mathematics
in very interesting ways. For example, the traditional integral is the Riemann
integral which cannot handle sets with too many (uncountably many)
discontinuities. The Lebesgue integral loosens those restrictions by using
measure to guarantee there aren't too many discontinuties. The Lebesgue
integral, in turn, is used to integrate over function spaces, allowing for
techniques like fourier transform and technologies such as mp3 encoding.

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gugagore
Why does encoding of discrete-time signals have to do with Lebesgue integrals?

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imode
title should be "The Fight to Fix Symplectic Geometry".

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dang
Belated thanks—a moderator saw your suggestion and fixed the title earlier
today.

