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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