The role of mathematics in physics

Submitted by Nicholas C. Darnton (inactive) on Monday, 2/1/2010, at 10:32 AM

A famous article by Eugene Wigner ruminating on the deep connection between mathematics and physics.  Depending on your point of view, this connection is either incredibly profound or completely trivial.  My opinion on this matter fluctuates. 

Martingale

Submitted by Nicholas C. Darnton (inactive) on Friday, 4/17/2009, at 12:10 PM

A nice summary of the martingale (also known as the gambler's ruin) for lay audiences.  This is really mathematics, applied here to the stock market / credit crisis, but it pops up in many other contexts.  In particular, the analysis is identical to first passage calculations that predict the speed of biomolecular motors or the time for a DNA binding protein to locate its binding site, and also to polymer physics descriptions of DNA confinement. 

The article refers to a collaboration between a mathematician, statistician and physicist to decide whether a flipped coin really comes up heads and tails with equal probability.  Many concepts from Physics 16 crop up in course of the collaboration, including projectile motion, angular momentum, air resistance, and experimental uncertainty.

Dogs can do vector calculus

Submitted by Nicholas C. Darnton (inactive) on Thursday, 10/16/2008, at 5:37 PM
Fetch diagram

Surprising but true: dogs can minimize fetch times by performing vector calculations.  To test this, a dog retrieved a stick by running some distance along shore and then swimming out to the stick; the dog usually chose the shore distance and swimming distance in such a way that it minimized total time-to-fetch. 

I haven't seen any reference to experiments done in moving water, which would reveal whether dogs understand the difference between relative and absolute velocity.  Anyone with a Retriever and transportation to the Connecticut river is encouraged to try it.