> More predictive power is always a good goal

But in some cases it is not good enough. If you look for a better explanation and chose gradient descent as your strategy, then you'll come to a local maximum eventually, but not for another explanation.

Arguably, it is hard to look for better explanation if the current one doesn't have a backtrack of failed predictions. One of the possible ways out of this situation is to search for the predictions that fail.

But what I want to say is explanations are not just for prediction. They are needed to build a mental model that then can drive the research. And new model can be built (theoretically) from the first principles. I can't find clean examples for it though. If we look at Einstein for example, he started with a failure to predict. But what he came up at first was Special Relativity which failed utterly with the gravity. Einstein spent like 10 years rewriting gravity to make it work with SR? Failed predictions of his new shiny theory didn't stop him, and it is considered to be good.

> Predictability encodes understanding in a strict information theoretic sense, regardless of our ability as humans to access that understanding.

But it doesn't necessary implies the possibility to move forward. I'm not sure if an analogy with compressed data is a good one, but you don't work with compressed data, you unpack it, and maybe unpack some more and convert to a very inefficient format with regard to the disk space used.

Compressed theory is good to apply it as is, but to refine it you should probably prefer something else.