  We find a countable partition $P$ on\textbf{} a Lebesgue space, labeled
$\{1,2,3...$\}, for any non-periodic measure preserving transformation $T$ such
that $P$ generates $T$ and for the $T,P$ process, if you see an $n$ on time -1
then you only have to look at times $-n,1-n,...-1$ to know the positive integer
$i$ to put at time 0. We alter that proof to extend every non-periodic $T$ to a
uniform martingale (i.e. continuous $g$ function) on an infinite alphabet. If
$T$ has positive entropy and the weak Pinsker property, this extension can be
made to be an isomorphism. We pose remaining questions on uniform martingales.
In the process of proving the uniform martingale result we make a complete
analysis of Rokhlin towers which is of interest in and of itself. We also give
an example that looks something like an i.i.d. process on $\mathbb{Z}^2$ when
you read from right to left but where each column determines the next if you
read left to right.
