Thursday, July 27, 2006

knots, computation, life and space

Well, on Saturday i made breakthrough in travel. Via the wonders of Skype and the graciousness of the conference organizer, Bob Coecke, i presented results on encoding knots as processes in Oxford at the Cats, Kets and Cloisters conference from my home office in Seattle, WA. (Here is an updated version of the slides with many more technical details than i presented at the conference.) There were some technical glitches that made us restart the Skype connection every 5 - 10 mins, and the connection failed to re-establish for the question section. (Bob, posted my email address so that people could mail me questions.) But, despite these inconveniences, i am very hopeful about this way of engaging technically. (In fact, i am currently working with a company that has some technology that could considerably improve this experience.)

i must say that my co-authors have been wonderful! While it is a matter of historical record that i had the original insight, their probing questions, saintly patience with my mathematical ineptitude and diligence and unwillingness to accept anything but highest caliber work has led to a greatly superior offering than what i could have produced on my own. i should also publicly acknowledge the reviewers of 2006's ICALP for pointing out flaws in the way we presented the results in our submission to the conference. i was using the ICALP deadline as a way of forcing myself just to get something written down, and didn't have the highest of expectations for our submission. But, their comments provided a much needed spur to take the presentation of the results to a higher level.

Now, 'knots' and 'computation' make sense in the title of a post about interpreting knots as processes, but why do i mention 'life' and 'space' as well? Well, it turns out that knots are sitting at the confluence of several different lines of research. Another computation angle has Michael Freedman and co using knots to do quantum computation which you can read about at a less technical level in the April 2006 Scientific American article; while biologists are turning to Conway's tangle calculus to reason about folding of genetic material (i'm not as familiar with this line of research as i ought to be, but this might be a starting point); and researchers in (loop) quantum gravity have been making heavy use of knot theory for quite some time. (Check out John Baez's this week's finds to get a sense of what i'm on about.)


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