This sounds related to this "proof of induction" by Alexander George. Sample quote:

So, to repeat, it can indeed be proved that there is a rule—the “Hardin-Taylor rule”, I shall call it — that will, for any arbitrarily chosen function f, correctly predict most values of f on the basis of its past be- havior; that is, for most t the rule will correctly predict f(t) on the basis of f’s values at all s< t.