<div dir="ltr"><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">Dave,</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333"><br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">It is good to hear your voice. Sarah is presently</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">finishing a pair of chemistry classes at UNM.</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">In classic St. John's style, she is constantly</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">bringing me the kind of thoughtful questions</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">which send me diving into books on quantum</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">mechanics and wishing my group theory were</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">stronger. Most recently, we attempted to understand</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">the mechanics of hybridization.</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333"><br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">Almost nowhere can I find a clear exposition</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">connecting the theory (with its Lie groups and</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">discussions of overtones) to the empirical.</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">Penrose's book, from what I remember, similarly<br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">falls short. The <a href="https://www.amazon.com/GAUGE-FIELDS-KNOTS-GRAVITY-Everything/dp/9810220340">Baez book</a>, which a few of us</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">formed a reading group around last year, did a</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">fairly good job of connecting the many ideas</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">and technologies mathematical physicists use</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">in developing modern theory. Often the requisite<br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">mathematics is beyond what can be expected for</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">a PhD in mathematics. However, the text left me</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">with a feeling of efficacy that I could track down</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">the needed math and get to work.</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333"><br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">Perhaps tangentially (wrt philosophy of science), </div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">there has been some interest around the table here</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">in reservoir computing, and some of the bold claims</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">about being able to <a href="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">predict chaotic trajectories</a> in the</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">Kuromoto-Sivashinsky equations eight Lyapunov</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">times into the future. While I have some loose sense<br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">for why some standard deep learning techniques</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">work, the echo-state network approach has been</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">down-right baffling to me. I mention this for two</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">reasons. First, I trust your expertise in computing</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">systems could offer some insight. Second, here is</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">another moment in the history of science where we</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">are running to form solid theory in the face of</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">overwhelming odds, all-the-while the effectiveness</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">of the empirical is plain as day. I sincerely hope</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">that as this work is carried out, we manage to do</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">a better job tracing the development of this knowledge</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">than was done with the development of quantum</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">mechanics. Perhaps some text can tell me once and</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">for all whether the energies associated with orbitals</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">are a  consequence of spherical harmonics?</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">What about the geometry of molecular configurations?</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333"><br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">Cheers,</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333">Jonathan Zingale</div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333"><br></div><div class="gmail_default" style="font-family:garamond,serif;font-size:small;color:#333333"><br></div></div>