<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div><div><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">On Wednesday, October 15, 2014 5:33 AM, Anders Sandberg <<a href="mailto:anders@aleph.se" x-apple-data-detectors="true" x-apple-data-detectors-type="link" x-apple-data-detectors-result="1">anders@aleph.se</a>> wrote:<br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">Michael Roberts<<a href="mailto:mike@7f.com" x-apple-data-detectors="true" x-apple-data-detectors-type="link" x-apple-data-detectors-result="2">mike@7f.com</a>> , 15/10/2014 2:43 AM:<br></span></font></blockquote><blockquote type="cite"><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><br></span></font></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">While on the subject of mathematical works, I found this one to be <br></span></font></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">very interesting: <br></span></font></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><br></span></font></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><a href="http://mitpress.mit.edu/books/functional-differential-geometry" x-apple-data-detectors="true" x-apple-data-detectors-type="link" x-apple-data-detectors-result="4" style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><font color="#000000">http://mitpress.mit.edu/books/functional-differential-geometry</font></a></blockquote></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">Cool. Jack Wisdom's stability analysis of Pluto was what convinced me<br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">that maybe there is something to symplectic methods and other<br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">"hightech" calculations</span></font></blockquote><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><br>I like to think all this knowledge eventually has some payoff. It's just a matter of being imaginative and determined enough to figure out how.<br><br></span><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">rather than just brute forcing it with a high<br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">order Runge-Kutta method.</span></font></blockquote><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><br>Ah, the memories. The horrible memories of diff eq. :)<br><br></span><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">The book is pretty neat in that it mixes<br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">scheme with differential geometry; it feels somewhat exotic and yet<br></span></font></blockquote><blockquote type="cite"><font color="#000000"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">familiar.</span></font></blockquote><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><br>Ever more to play around with here. Don't things usually progress from new discoveries and methods that are clunky/unnatural to ones that seem less intuitive at first, but easier and, in the end, more natural/intuitive? Maybe I'm overgeneralizing. There's also a difference between what's taught to undergrads at one time versus later because, I think, "newer" ideas just take time to work their way from the bleeding edge to the textbook. At least, this is my impression, FWIW.<br><br>Regards,<br><br>Dan</span></div></div></body></html>