That's a great saying about the angels and donkeys. I've read that most ancient civilizations had the same kind of view of history. They did not have our notion of progress; rather, they saw mankind as having fallen from a primordial "golden age", and heading pretty much straight downhill ever since. No doubt this was aided by the near-universal agreement among old people that the young generation just doesn't measure up to how people were in the old days.

So if we go back to the "chronophone" thought experiment, Archimedes might have been spectacularly uninterested in information from the future (especially through such a garbled connection). Unlike today where we would assume that future civilizations would be sources of tremendous knowledge and wisdom, he would have imagined a future of near-bestial creatures who had long lost whatever vestiges of grace mankind had still retained in his age.