I'm not sure yet.

What does cousin_it mean by

find the shortest algorithm that outputs the same predictions.

Does this algorithm necessarily model the predictions (in any fashion), or just list them? If the predictions are being modeled -- then they'll either predict or not predict the implied invisible.

If the predictions are not being modeled -- I just don't see how you can get an algorithm to output the right list without an internal model.

This comment on this page is relevant... For example, I think I agree with this:

In this case, the look-up table is essentially the program-that-lists-the-results, and the algorithm is the shortest description of how to get them. The equivalence is because, in some kind of sense, process and results imply each other. In my mind, this a bit like some kind of space-like-information and time-like-information equivalence, or as that between a hologram and the surface it's projected from.