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Category Archives: Mathematics
Resolution of Toom's rule paradox
A few days ago our Ghost Pontiff Dave Bacon wondered how Toom’s noisy but highly faulttolerant 2state classical cellular automaton can get away with violating the Gibbs phase rule, according to which a finitedimensional locally interacting system, at generic points … Continue reading
Posted in General, Mathematics, Physics
5 Comments
Nonchaotic irregularity
In principle, barring the intervention of chance, identical causes lead to identical effects. And except in chaotic systems, similar causes lead to similar effects. Borges’ story “Pierre Menard” exemplifies an extreme version of this idea: an early 20’th century writer … Continue reading
Posted in Mathematics, Physics
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What increases when a selforganizing system organizes itself? Logical depth to the rescue.
(An earlier version of this post appeared in the latest newsletter of the American Physical Society’s special interest group on Quantum Information.) One of the most grandly pessimistic ideas from the 19th century is that of “heat death” according to … Continue reading
Posted in Computer Science, General, Mathematics, Physics, Science
6 Comments
Time After Time
Ole Peters was a postdoc at the Santa Fe Institute during the time I was also a postdoc there. In addition to being a world class windsurfer, Ole likes to think about critical phenomena and stochastic processes. And in the … Continue reading
Posted in Economics, Mathematics
8 Comments
Immanants
Recently computer scientist Leslie Valliant won the ACM’s Turing Award, considered one of the most prestigious prizes in computer science. Valliant is famous for many results, not the least of which are his results on the Permanent of a matrix. … Continue reading
Posted in Computer Science, Mathematics
5 Comments
A Mathematical Definition of News?
Lately I’ve been thinking about the news. Mostly this involves me shouting obscenities at the radio or the internet for wasting my time with news items the depth of which couldn’t drown an ant and whose factual status makes fairy … Continue reading
Mandelbrot 19242010
Benoît B. Mandelbrot, a mathematical maverick and curmudgeon extraordinaire has passed away at the age of 85 (NYTimes obit.) Mandelbrot is most well known for coining the word “fractal” and studying the set which now bears his name, but was … Continue reading
Posted in Caltech, Mathematics, Nature
8 Comments
Tidbits
Penrose reviews Hawking and Mlodinow’s new book The Grand Design. Kim sends along a link to a classic telescope catalogs and manuals Mason Porter, after an inspiring talk with Aaron Clauset and Michelle Girvan (a not uncommon circumstance with these … Continue reading
Posted in Astronomy, Mathematics, Physics, Programming
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Reading List: Graph Isomorphism
Warning: this idiosyncratic list of reading material is in no way meant to be comprehensive nor does is it even guaranteed to focus on the most important papers concerning graph isomorphism. Suggestions for other papers to add to the list … Continue reading
Posted in Computer Science, General, Mathematics, Quantum Computing
14 Comments