Hi Jonathan,
Very interesting and fun essay. I think, were there not such a strict page limit, it would have been interesting to see a deeper study of material v. information from the standpoint of culture. I think that there may be some insights lurking there into how we reach conclusions, particularly in science.
Your points about mathematics are similar to those made by a colleague of mine. He always says that it is about as close to the Platonic ideal as one can get. I guess I just have always seen it in a reverse sort of way, but it doesn't necessarily mean I'm right. I tend to think, though, that while it is clear that some mathematics is clearly "discovered" (counting, arithmetic, apparently even simple algebra according to a recent study of babies), some is "invented" in the sense that a set of logical rules are set down and followed to their conclusion where the rules themselves may have been slightly arbitrary.
Ian