[FRIAM] two books (perhaps a bit more)

[Jon Zingale]

Dave,

It is good to hear your voice. Sarah is presently
finishing a pair of chemistry classes at UNM.
In classic St. John's style, she is constantly
bringing me the kind of thoughtful questions
which send me diving into books on quantum
mechanics and wishing my group theory were
stronger. Most recently, we attempted to understand
the mechanics of hybridization.

Almost nowhere can I find a clear exposition
connecting the theory (with its Lie groups and
discussions of overtones) to the empirical.
Penrose's book, from what I remember, similarly
falls short. The Baez book
<https://www.amazon.com/GAUGE-FIELDS-KNOTS-GRAVITY-Everything/dp/9810220340>,
which a few of us
formed a reading group around last year, did a
fairly good job of connecting the many ideas
and technologies mathematical physicists use
in developing modern theory. Often the requisite
mathematics is beyond what can be expected for
a PhD in mathematics. However, the text left me
with a feeling of efficacy that I could track down
the needed math and get to work.

Perhaps tangentially (wrt philosophy of science),
there has been some interest around the table here
in reservoir computing, and some of the bold claims
about being able to predict chaotic trajectories
<https://mail-attachment.googleusercontent.com/attachment/u/0/?ui=2&ik=a33a25cbf7&attid=0.1&permmsgid=msg-f:1617592106450468931&th=1672d7735074c043&view=att&disp=inline&sadnir=2&saddbat=ANGjdJ-zXLctoXRpve6kgzzxO-OjAEPIbgA9WwC-xPKH4loEyEuhdwm8ZhXn4L_yzdC9cU8Iv0yIZEUq5__8Z0AMXdihGbHmvSidrDaZd8aggIPRGdpN0xc91Vx7ZZBtrMuV6rG0tPBj-eNyADuZJKYJ0aNnNfxRZ4s3TgZwGB9Tj3jDfFLJFCFaWyo7KxEw5csL5tFGb3xAQz2d8g4r-e_ZDKwJrUT4Bqnzl73cn2NvPbX-v2AtOFi4xpE6Yyd-7pL_bU6iuLD5oyF8RJqmMtRM_bGTMorQbgrq6m617Du-aGKz2NodqSCMmy-TS596IwkFBiUOepBHyUA11T8s6uSW6pNonwbKu0WLJkNAMwXNuyylbnFoLP5ZFtx-PXZGakgknOoNqNsDAfnG_Wg9IODOxxtstFs6NcNRwwaHjBVD1N2Fw2rXt-dyLMmy7PSMRT1EKt4l05axXk0JebhcrPpob9FSfm7uIxTL7DxUpqW_AeZeTnRC5G6ZH0vAPZM-w20cRVvv24dxex7yWGOFneUQRhVqGQlDag4mRYCCta2fC0ghB7yBUs5sF-ak4oSVhyG1cAYHiXS_BvxuXKLYpsHwGGuZL_GHzcAxTwD60Lxqqz2ReEF3x1sy4jMbT2sXQigsse6ZVQs9hUoYGDqL>
in the
Kuromoto-Sivashinsky equations eight Lyapunov
times into the future. While I have some loose sense
for why some standard deep learning techniques
work, the echo-state network approach has been
down-right baffling to me. I mention this for two
reasons. First, I trust your expertise in computing
systems could offer some insight. Second, here is
another moment in the history of science where we
are running to form solid theory in the face of
overwhelming odds, all-the-while the effectiveness
of the empirical is plain as day. I sincerely hope
that as this work is carried out, we manage to do
a better job tracing the development of this knowledge
than was done with the development of quantum
mechanics. Perhaps some text can tell me once and
for all whether the energies associated with orbitals
are a  consequence of spherical harmonics?
What about the geometry of molecular configurations?

Cheers,
Jonathan Zingale
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