I'm not an information scientist, so this maybe a lay understanding, but as I understand it there is a limit to how much you could theoretically compress any pi

I'm not an information scientist, so this maybe a lay understanding, but as I understand it there is a limit to how much you could theoretically compress any piece of content without losing information. So take that 4.7 bits per character: well, not every letter is equally likely, so we could construct an encoding which takes frequency into account, but then not every word is equally likely, so we could use that information to make a tighter encoding, and so on. At some point we would reach a theoretical minimum. At that limit, the size of the compressed data has one bit per bit of information. So, scaling back up, the estimate is (and it has to be an estimate, I guess, since we can't construct the actual theoretically smallest encoding) 1.5 bits of information per character. I searched for this value, and didn't spend long figuring out if it was well calculated, so take it with a big googly pinch of salt.