Street fighting mathematics

Physicists have a very unsentimental way of manhandling mathematics. In addition to setting up dimensionally inconsistent equations for order-of-magnitude estimations, they like to take lots of short cuts that make computations fast and easy. For example, in the Hartree atomic unit system, several fundamental quantities are all set equal to 1. Electron mass, electron charge, Planck’s constant, and Coulomb’s constant– all are set to 1. One time, in the middle of a derivation, my plasma physics professor crossed out a 2 and wrote 1, saying, “in plasma physics, 2 is 1; sometimes 10 is 1; 5 is always 1.” Another trick was expressing the number of seconds in a year as pi * 10⁷; this is accurate to better than 0.5%!

The book “Street-fighting Mathematics” by Sanjoy Mahajan (MIT Press) teaches a lot of tricks like these. Plus, Mahajan does an excellent job of training the reader in how to approach physics problems and apply logical shortcuts. Check out some of the material using MIT’s Open Courseware site.