[net.math] 3 2's > 4 4's ?

fen@sri-unix (08/25/82)

I seem to remember a little story about the mathematician P.A.M.Dirac --
goes like this:  It seems that one day some of the professors at the academy
that he was attending were arguing about the same sort of problem -- could
any integer be expressed with an equation involving at most 4 4's?  Upon
hearing the debate, he quickly offered a way to express any (positive)
integer using only 3 2's:

		n = 1/2 [- log  {sqrt(sqrt(sqrt(...(2))))}]
			      2

where there are n (sqrt())'s.  Of course, this is cheating because of the
n sqrt's, but so what?