The simple requirement that information must transfer between brains precludes lossless compression. It is not hard, it is impossible. This is fine. The impossibility stems from the fact that every brain is different. If you took the pattern of neurons firing in my head when I think of the definition of "perturbation" and mapped it to your head you might catch a whiff of gargonzola cheese. Ok maybe not quite that since there are meaningful divisions in the brain, but it wouldn't come out anything like it went in. This is a feature. Miscommunication forces each node to process incoming information and check it for compatibility with priors. (The fact that we do a bad job of it set aside for the moment) Lossless transfer would be 100% uncritical because there is nothing to indicate whether you are the source or the recipient of the information. This is how computer viruses work. They can tailor the payload to a known hardware/software stack. If the transmission happens losslessly then the target will run it uncritically. Lossy compression means that bad ideas can become better ideas as they encounter heads with different perspectives and experiences. It is with enough eyes all bugs are shallow. Identical sets of eyes are useless.