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Re: two books (perhaps a bit more)

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jon zingale

Re: two books (perhaps a bit more)

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, 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 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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Roger Critchlow-2

Re: two books (perhaps a bit more)

I love atomic orbitals, I spent days plotting them out by hand on polar graph paper when I first learned about them.

http://scarc.library.oregonstate.edu/coll/pauling/bond/ is an archive of Linus Pauling papers. Pauling figured out orbital hybridization over 1927-1931. Slater figured it out at about the same time. They submitted papers within a month of each other that were both published in the spring of 1931. Scans of both papers are in the Pauling archive, and there's a slightly breathless narrative that explains how Pauling's version came about. For a more systematic treatment, you could look at Pauling's Introduction to Quantum Mechanics with Applications to Chemistry (thank you Dover Books) first published in 1935.

-- rec --

On Thu, Nov 29, 2018 at 1:58 PM Jon Zingale <[hidden email]> wrote:

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, 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 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

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

jon zingale

Re: two books (perhaps a bit more)

In reply to this post by jon zingale

Roger,

Thanks for the recommendation. Sarah had

bought a copy of Pauling's 'Introduction to

Quantum Mechanics' and it had sat at my

periphery until the other night when I read

your post. In one of those few moments of

invincible lucidity, I managed to read the

first 120 pages, deeply satisfying many of

my curiosities. Pauling's exposition was

surprisingly clear, though I must mention

that he also does not mention the direct

connection between Legendre polynomials

and spherical harmonics (thanks wiki!).

Cheers,

Jonathan Zingale

Nick Thompson

Re: two books (perhaps a bit more)

Hi, John,

I assume you realize that I am not Roger. I am glad you are talking with him. It’s his chemistry book I have, by the way. He sold it to me, over my dead body, for a song. I don’t think people should sell their books. Now that you know it’s rogers, shall I bring it to you when we meet … this afternoon…at three … at Ohoris?

Nick

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

From: Friam [mailto:[hidden email]] On Behalf Of Jon Zingale
Sent: Monday, December 03, 2018 10:58 AM
To: [hidden email]
Subject: Re: [FRIAM] two books (perhaps a bit more)

Roger,

Thanks for the recommendation. Sarah had

bought a copy of Pauling's 'Introduction to

Quantum Mechanics' and it had sat at my

periphery until the other night when I read

your post. In one of those few moments of

invincible lucidity, I managed to read the

first 120 pages, deeply satisfying many of

my curiosities. Pauling's exposition was

surprisingly clear, though I must mention

that he also does not mention the direct

connection between Legendre polynomials

and spherical harmonics (thanks wiki!).

Cheers,

Jonathan Zingale

lrudolph

Re: two books (perhaps a bit more)

You might also enjoy his "The Nature of the Chemical Bond". I acquired my
copy an age or two ago from The Library of Science (remember that???) but
only dipped into to it for the first time about 3 years ago. The book's
contribution to the lucidity of my interaction it far exceeded mine,
unfortunately (I'm a mathematician who never took a course in physics, or
any lab science, after a disastrously poor high school course--although I
still managed somehow to learn, only one age ago, about the Legendre
polynomial/spherical harmonic relationship, not that I've ever had
occasion to make any use of it in my own work!), but even so I came away
with some curiosities satisfied, and I'm sure your experience would be
much better.

> Thanks for the recommendation. Sarah had
> bought a copy of Pauling's 'Introduction to
> Quantum Mechanics' and it had sat at my
> periphery until the other night when I read
> your post. In one of those few moments of
> invincible lucidity, I managed to read the
> first 120 pages, deeply satisfying many of
> my curiosities. Pauling's exposition was
> surprisingly clear, though I must mention
> that he also does not mention the direct
> connection between Legendre polynomials
> and spherical harmonics (thanks wiki!).