tag:blogger.com,1999:blog-264226589944705290.post5946539444019331146..comments2022-05-19T07:55:48.367-07:00Comments on God Plays Dice: Continued fractions and baseball hitting streaksMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-264226589944705290.post-43911338340894676312008-08-05T07:13:00.000-07:002008-08-05T07:13:00.000-07:00Strogatz is most definitely not a crackpot.Strogatz is most definitely not a crackpot.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-38659504662370243872008-08-04T21:20:00.000-07:002008-08-04T21:20:00.000-07:00The 'physics' arxiv is only for people who are con...The 'physics' arxiv is only for people who are considered crackpots by the establishments. Mathematicians cannot really appreciate the social machinations here.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-81972680527913453912008-08-04T18:06:00.000-07:002008-08-04T18:06:00.000-07:00It's a little silly, but I also gave a rather tenu...It's a little silly, but I also gave a rather tenuous connection between continued fractions and baseball hitting *averages* in the blog post POW-8 and its solution. I'll also mention, since I have continued fractions on my mind, that An Idelic Life has a <A HREF="http://complexzeta.wordpress.com/2008/08/01/an-introduction-to-tuning-and-temperament/" REL="nofollow">new post</A> on musical tuning systems, where continued fractions are used to explain 12-tone and 53-tone scales (the latter being used in some forms of Turkish, Arabic, and Indian music). <BR/><BR/>As for why e has a nice continued fraction whereas pi doesn't: putting aside the fact that there are some cute *non-regular* (or non-simple) continued fractions for pi, I don't have any especially great answer, but my friend James Dolan has a kind of interesting take on related matters. The rough slogan is something like, "there is a bijective correspondence between methods for solving differential equations and ways of defining e," in the sense that if you take a method for solving an ODE (power series, fixed-point methods, separation of variables, etc.) and apply it to y' = y, you get a corresponding definition of e. According to that philosophy, the continued fraction definition of e should correspond to a continued fraction method for solving (at least certain classes of) ODE, like perhaps the Riccati equation. That would be more an answer to the question "who ordered e?" rather than "why didn't anyone order pi?", but I think it's an interesting point of view. <BR/><BR/>- ToddUnknownhttps://www.blogger.com/profile/06052144678256568647noreply@blogger.com