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 fault-tolerant 2-state classical cellular automaton  can get away with violating the Gibbs phase rule, according to which a finite-dimensional locally interacting system, at generic points … Continue reading

Posted in General, Mathematics, Physics | 5 Comments

Non-chaotic 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 | Leave a comment

What increases when a self-organizing 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


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

Posted in Brainstorming, Extralusionary Intelligence, Fragment, Go Ahead, Waste Your Time, Mathematics, Off The Deep End | 16 Comments

Mandelbrot 1924-2010

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


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 | Leave a comment

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

Not True in Any Base

Yes, dear Gray Lady, you certainly sound more sophisticated when you use the word “prime number” in your newspaper. But perhaps you might want to look up the actual meaning of the word before placing those words prominently beside two … Continue reading Continue reading

Posted in Funny Ha Ha, Mathematics | 3 Comments