Physics, Topology, Logic and Computation: a Rosetta Stone

Posted by John Baez

It’s done!

John Baez and Mike Stay, Physics, topology, logic and computation: a Rosetta Stone.

Learn how category theory serves as a lingua franca that lets us translate between certain aspects of these four subjects… and perhaps, eventually, build a general science of systems and processes! In a nutshell, it goes like this:

object morphism Physics system process Topology manifold cobordism Logic proposition proof Computation data type program \array{ & object & morphism \\ Physics & system & process \\ Topology & manifold & cobordism \\ Logic & proposition & proof \\ Computation & data type & program }

It takes a while to explain the details.

Actually, I’ve come to feel that in academia no project is ever really done. At least, not until you lose interest or die — which, come to think of it, is just an extreme case of losing interest. There’s always room for revising, improving, extending, and otherwise revisiting old projects. This is particularly evident with the rise of electronic media like the arXiv. When you catch the umpteenth typo, do you put up yet another version of your paper or not? It just depends how much you care. There are certainly lots of typos still lurking in this paper, and probably much worse problems. But, we’ve tried to take all your comments into account — sometimes by judiciously not doing anything about them — and I feel they’ve vastly improved the paper. Thanks, all of you! We could never have done it without all you logicians and computer scientists.

Posted at March 11, 2008 5:47 AM UTC