  We recall a variation of a construction due to Laakso \cite{LA}, also used by
Lang and Plaut \cite{LA} of a doubling metric space $X$ that cannot be embedded
into any Hilbert space. We give a more concrete version of this construction
and motivated by the results of Olson \& Robinson \cite{OR}, we consider the
Kuratowski embedding $\Phi(X)$ of $X$ into $L^{\infty}(X)$ and prove that
$\Phi(X)-\Phi(X)$ is not doubling.
