My friend Andrew is an advocate of the “spaced repetition” technique for
memorization of a great many facts [1]. The ideas behind this are two-fold:

• When one first “learns” a new fact, it needs to be reviewed frequently in
  order to not forget it. However, with each additional review, the fact can
  be retained longer before a refresher is needed to maintain it in recall.

• Because of this, one can maintain a large, growing body of facts in recall
  through daily review: Each day, one need only review for ten minutes or so,
  covering a small number of facts. The facts included should be sampled from the
  full library in a way that prefers newer entries, but that also sprinkles in
  older facts often enough so that none are ever forgotten. Apps have been
  written to intelligently take care of the sampling process for us.

Taking this framework as correct motivates questioning exactly how far it can
be pushed: Would an infinitely-long-lived, but forgetful person be able to
recall an infinite number of facts using this method? (ldots) Below, we
show that the answer is: YES!

Proof:

We first posit that the number of days (T) that a fact can be retained before
it needs to be reviewed grows as a power-law in (s), the number of times it’s
been reviewed so far,

begin{eqnarray} tag{1}label{1}
T(s) sim s^{gamma},
end{eqnarray}

with (gamma > 0). Wi