Differential gears, trains, and automobiles

Kottke refeatured a great video explaining differential gears in automobiles. Namely, how does a car handle the problem of the outside wheel having to travel further than the inside wheel when a car turns a corner if the wheels are connected by a fixed axle?

Well, trains have the same issue, and they do not have differential gears. So how do they  handle that problem, and more importantly, how do trains stay on the track? Who better to explain this than the great Richard Feynman.