# “Basically, you would be able to compute anything you wanted”

The quote that forms the title here comes from Lance Fortnow, a computer scientist at Northwestern University, in an article (here – subscription required) in the current edition of the New Scientist on the $P = NP$ question.

It’s an odd statement for a computer scientist to make – most numbers are transcendental numbers and so are fundamentally incomputable: for instance there are $\aleph_{0}$ (aleph null – the smallest of Cantor’s hypothesised infinities) transcendental numbers between 0 and 1 (or between any range of integers).

But besides that oddity it is actually a very good article – calling the world where $P = NP$ Algorithmica – “the computing nirvana”.

I have written before of how much I hope we do live in Algorithmica, though the consensus is we live in a world of NDAlgorithmica (ND for non-deterministic).

The article’s beauty is that it also examines the states between the two: what if, for instance, we discovered that the class of $P$ problems were identical to the class of $NP$ problems but that we could not find the $P$ algorithm, or that the $P$ algorithm was of such a degree of complexity it “would not amount to a hill of beans”?