I have a MC that has access to the entire knowledge of humanity (note: This is year 4000s so they have much more than "our humanity"). He needs created another consciousness for himself, this new consciousness has limited capacity which is way smaller than the entire humanities knowledge he has access to, so in the story he compresses this library of knowledge and puts it inside this new consciousness.

For more context he can't expand his capacity with servers or other data storage methods, only the capacity avaible is only that of his new consciousness.

He also doesn't have access to magic.

The main question is, if it is possible to compress knowledge infinitely? If not, what would the roughly smallest ratio you could compress information be?

He can use all science related methods be it digital or material.

Even though I said he is from year 4000s the answer doesn't have to be accessible in 4000s, time period is irrelevant to the question. I just want to know the possibilities.