Regarding lossy comprehension, the argument for that one is straightforward: if you want to be omniscient of something, you need to encode that information somehow (as astral matter, as neurons in a brain, as magnetic charges on a hard disk, as marks on a piece of paper, etc. etc.). But now you have more information about that thing... so you need to encode the encoding somewhere, or you can't be said to be omniscient of the original thing. But if you do that, you have to encode the encoding of the encoding somewhere, etc. etc. etc., leading to an infinite regress, which makes no sense.