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

A celebrated result of Gowers states that for every є>0 there is a graph G such that every є-regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/є. 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.