You should read Stephen Wolfram, The Second Law. He has a useful perspective on what can be predicted (computed) by an observer and what can't, it is more helpf

You should read Stephen Wolfram, The Second Law. He has a useful perspective on what can be predicted (computed) by an observer and what can't, it is more helpful than thinking about things in terms of compression. His views on physics-in-the-world phenomena are not correct, to be clear, but the mental models are useful.