From: utzoo!decvax!cca!fortune!megatest!fen@sri-unix
Newsgroups: net.math
Title: 3 2's  >  4 4's ?
Article-I.D.: megatest.136
Posted: Wed Aug 25 15:42:28 1982
Received: Wed Sep  8 01:38:54 1982

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?