How Big is Your Problem?

“... Thus, even if a computer the size of the universe had working parts that were smaller than nucleons, it would contain fewer than 10**125 such parts, and thus computations on problems which require more parts wouldn't be possible. Perhaps surprisingly, there are many such problems, some of them quite ordinary and of practical importance.

A comparably tiny time unit is the amount of time required for light, [...] , to traverse one of the above tiny cubes, whose edges are 10**(-13) centimetres. Taking the universe to be about 15 billion years old, we determine than fewer than 10**42 such units have passed since the begining of time.  Thus, any computer calculation that requires more than 10**42 steps [...] requires more time than the present history of this universe.” 

- J.A. Paulos (1988) Innumeracy, p. 21

(Note: 10**42 approx  2**139.5, so if you have 140 potential regressors all 2**140 regressions are beyond this...)


With deepest appreciation to coauthors, colleagues and teachers.