tag:blogger.com,1999:blog-11295132.post8586749370976582988..comments2014-09-11T11:37:51.563-07:00Comments on A Neighborhood of Infinity: Untangling with Continued Fractions: Part 4Dan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-11295132.post-14798153462944455422008-09-21T17:47:00.000-07:002008-09-21T17:47:00.000-07:00leithaus,The failure of the type I moves can be vi...leithaus,<BR/><BR/>The failure of the type I moves can be viewed in terms of <A HREF="http://en.wikipedia.org/wiki/Framed_knot" REL="nofollow">framed knots</A>. It arises naturally when looking at the Chern-Simons model, so there's a deep significance to this 'failure'.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-18368762523921142102008-09-21T13:46:00.000-07:002008-09-21T13:46:00.000-07:00Beautiful. i find it intriguing that the π-calculu...Beautiful. i find it intriguing that the π-calculus model has no trouble with R1 and R2, but has to introduce non-trivial machinery to get R3, while your model gets R2 and R3, but finds R1 more problematic. <BR/><BR/>If you circumscribe a ball around the locus of activity in an R-i move, you see that the laws are about crossings that make no difference to an observer on the outside of that ball. Specifically, if you think of the observer as capable of seeing signal pulses on a wire that is twisted into a knot, the Reidemeister moves will preserve signal patterns on the wires. For example, an observer who has concluded a wire acts as a perfect infinite capacity buffer, will conclude that a loop acts like a wire -- this is the observational content of R1.<BR/><BR/>R1 and R2 treat the introduction/elimination of crossings that do not change the experience of the observer while R3 is about a commutativity property. This commutativity property is very tricky for bisimulation to capture.leithaushttp://www.blogger.com/profile/01069099703796397027noreply@blogger.com