I’m not sure I understand exactly how the chronophone works. It sounds a bit like the only useful ideas a person can transmit are ideas that she herself has independently worked out or discovered; in which case not the same ideas but some analogous and similarly useful ideas gets delivered to Archimedes. In this case, I guess I might try to read out some of my research papers, hoping that they contain some useful original insights. It might also work if I transmit ideas that have originated with others but whose merits I have grasped through my own independent judgement.
It seems if you subtract all the information advantages that we moderns have, all that remains in this exercise are the organic qualities of our brains and the amount and quality of intellectual labour that our brains have performed.
Eliezer wrote: “Godel’s Completeness theorem shows that any first-order statement true in all models of a set of first-order axioms is provable from those axioms. Thus, the failure of Peano Arithmetic to prove itself consistent is because there are many “supernatural” models of PA in which PA itself is not consistent; that is, there exist supernatural numbers corresponding to proofs of P&~P.”
This is getting far from the topic but… I really don’t see how Completeness entails anything about PA’s failure to prove itself consistent (much less how it suggests an explanation in terms of “supernatural models”, whatever that is supposed to mean). PA is not expressible as a first-order statement, so Completeness has nothing to say about PA or its limitations.