tag:blogger.com,1999:blog-3722233.post726394211092850748..comments2024-03-28T18:17:00.135-05:00Comments on Computational Complexity: Reflection on the old days- by Joseph KruskalLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-3722233.post-51034609831707561412008-11-20T07:50:00.000-06:002008-11-20T07:50:00.000-06:00Joseph Kruskal says: "I feel certain that science ...Joseph Kruskal says: "I feel certain that science of many kinds is developing much more rapidly than it used to for this reason (except, perhaps, in fields where progress is kept secret for reasons of financial gain)"<BR/><BR/>Hmmm ... it's surprising to me that there have been no comments on Kruskal's provocative conclusion. <BR/><BR/>Maybe that's because Kruskal's conclusion expresses a Great Truth? Meaning, its opposite is true too: increased communication bandwidth leads academic communities to focus upon narrower sets of questions.<BR/><BR/>So perhaps these opposing assertions are <I>both</I> true: maybe we are seeing faster progress on narrower fronts? In which case, the boundary between known and unknown will dynamically evolve a fractal geometry? Via a kind of intellectual Rayleigh-Taylor instability?<BR/><BR/>This resulting picture, in which a description of the evolution of a system is compactly encoded in a description of the (complicated) geometry of its state-space, is very trendy nowadays in many fields of mathematics.<BR/><BR/>Anyway, I enjoyed Kruskal's essay very much.Anonymousnoreply@blogger.com