Explain the proof by Vinay Deolalikar that P != NP

Question

Recently there has been a paper floating around by Vinay Deolalikar at HP Labs which claims to have proved that P != NP.

Could someone explain how this proof works for us less mathematically inclined people?

Answer 1

One other way of thinking about it, which may be entirely wrong, but is my first impression as I'm reading it on the first pass, is that we think of assigning/clearing terms in circuit satisfaction as forming and breaking clusters of 'ordered structure', and that he's then using statistical physics to show that there isn't enough speed in the polynomial operations to perform those operations in a particular "phase space" of operations, because these "clusters" end up being too far apart.