  We analyze finite and infinite words coming from the symbolic version of
Chacon's transformation, focusing on distances between such words. Our main
result is that if W = 0010 0010 1 0010 ... is the infinite word usually
associated with Chacon's transformation, then the Hamming distance between W
and any positive shift of W is strictly greater than 2/9; moreover, this bound
is sharp. This yields an alternate proof that Chacon's transformation is
non-rigid and (using King's weak closure theorem) has trivial centralizer.
