tag:blogger.com,1999:blog-11295132.post8900790152878369108..comments2015-01-29T07:33:00.087-08:00Comments on A Neighborhood of Infinity: Untangling with Continued Fractions: Part 1Dan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-11295132.post-73396830319097645352008-08-23T14:57:00.000-07:002008-08-23T14:57:00.000-07:00Leon,In answer to (3), what we really want are, I ...Leon,<BR/><BR/>In answer to (3), what we really want are, I think, linear names.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-64158686183611850112008-08-23T13:07:00.000-07:002008-08-23T13:07:00.000-07:00Nice. Although, one thing that strikes me about ...Nice. Although, one thing that strikes me about your monadic abstraction is the naming issue, specifically, names need to be referred to on the R.H.S. of a function once, and only once. So it begs the questions:<BR/><BR/>1. Is there a reasonable or useful interpretation when a name is referred to more than once? <BR/><BR/>2. Similarly, what if a name is introduced but not referred to at all?<BR/><BR/>3. Is there an alternate abstraction that enforces this condition? <BR/><BR/>From reading the comments here, I suspect the answer to #3 is "Conway Notation." Great post, I look forward to reading the rest!Leon Smithhttp://www.blogger.com/profile/06462854866941248768noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-90987840918113535652008-08-23T07:38:00.000-07:002008-08-23T07:38:00.000-07:00leithaus,Only by name.leithaus,<BR/><BR/>Only by name.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-82926181537700757652008-08-22T23:24:00.000-07:002008-08-22T23:24:00.000-07:00Do you know Kassel's Quantum Groups book?Do you know Kassel's Quantum Groups book?leithaushttp://www.blogger.com/profile/01069099703796397027noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-13521073702386828452008-08-22T15:57:00.000-07:002008-08-22T15:57:00.000-07:00leithaus,Almost everything I know about knots come...leithaus,<BR/><BR/>Almost everything I know about knots comes from Kauffman's book "Knots and Physics" (and countless mostly-forgotten seminars from my student days). I don't recall anything about a relationship between Hopf algebras and quandles, at least not a direct one.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-56626136840631883412008-08-22T15:30:00.000-07:002008-08-22T15:30:00.000-07:00So... here's a question for you. How do quandles a...So... here's a question for you. How do <A HREF="http://en.wikipedia.org/wiki/Quandle" REL="nofollow">quandles</A> and Hopf algebras relate to each other? i know you can get a quandle out of a group with conjugation, but i'm fuzzy on the Hopf-crossed widget connection.leithaushttp://www.blogger.com/profile/01069099703796397027noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-56364058974432862792008-08-21T09:37:00.000-07:002008-08-21T09:37:00.000-07:00Your readers may be interested in the application ...Your readers may be interested in the application of rational tangles to biology. For instance the article <A HREF="http://www.math.uiowa.edu/~idarcy/ART/p22atopoREV2.pdf" REL="nofollow">Modeling protein-DNA complexes with tangles (PDF)</A> is a fun introduction.alpheccarhttp://www.blogger.com/profile/14645433315403867431noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-5464998708254172372008-08-20T16:53:00.000-07:002008-08-20T16:53:00.000-07:00leithaus,I can't talk about Conway notation until ...leithaus,<BR/><BR/>I can't talk about Conway notation until I've talked about the classification of rational tangles. Or at least talked a bit more about rational tangles.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-73112692354255024242008-08-20T16:38:00.000-07:002008-08-20T16:38:00.000-07:00i think you should at least make a nod to Conway's...i think you should at least make a nod to Conway's knotation. If you stack cup and cap; and you place them (suitably rotated) side by side, then together with the two crossings you get Conway's knotation combinators. You can get a good description from <A HREF="http://knotplot.com/thesis/" REL="nofollow" TITLE="Rob Scharein's thesis">Rob Scharein's thesis</A>. For that matter, <A HREF="http://knotplot.com/" REL="nofollow" TITLE="knotplot">knotplot</A> is a cool site and a cool tool.leithaushttp://www.blogger.com/profile/01069099703796397027noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-67269361111342670402008-08-17T17:43:00.000-07:002008-08-17T17:43:00.000-07:00Nice teaser.. :)Nice teaser.. :)Arnar Birgissonhttp://www.blogger.com/profile/12073820949049315334noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-77716621986116588632008-08-17T04:52:00.000-07:002008-08-17T04:52:00.000-07:00Your first example of a block:(b,c) <- block (a...Your first example of a block:<BR/>(b,c) <- block (a,b)<BR/>seems to have a typo. I think this should be:<BR/>(c,d) <- block (a,b)logopetriahttp://www.blogger.com/profile/09729458744775918709noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-66463105858383778202008-08-17T00:17:00.000-07:002008-08-17T00:17:00.000-07:00Small typo, I think: the first example should be (...Small typo, I think: the first example should be <I>(c,d) <- block (a,b)</I>.oldtimerhttp://www.blogger.com/profile/08499662138218054059noreply@blogger.com