A short proof of Gowers' lower bound for the regularity lemma

A celebrated result of Gowers states that for every N"> 0 there is a graph G such that every N"-regular partition of G (in the sense of Szemer,di's regularity lemma) has order given by a tower of exponents of height polynomial in 1/N". In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter.