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