Hofstadter, Dennett - The Mind's I

Prelude . . . Ant Fugue 152Pierre de Fermatbranch-or even some individual Theorem-of pure mathematics will have importantrepercussions outside of mathematics. It is quite unpredictable-and this case is a perfectexample of that phenomenon.ACHILLES: Mr. Tortoise's double-barreled result has created a breakthrough in the field ofacoustico-retrieval!ANTEATER: What is acoustico-retrieval?ACHILLES: The name tells it all: it is the retrieval of acoustic information from extremelycomplex sources. A typical task of acoustico-retrieval is to reconstruct the sound which arock made on plummeting into a lake, from the ripples which spread out over the lake'ssurface.CRAB: Why, that sounds next to impossible!ACHILLES: Not so. It is actually quite similar to what one's brain does, when it reconstructsthe sound made in the vocal cords of another person from the vibrations transmitted by theeardrum to the fibers in the cochlea.CRAB: I see. But I still don't see where number theory enters the picture, or what this all hasto do with my new records.ACHILLES: Well, in the mathematics of acoustico-retrieval, there arise many questionswhich have to do with the number of solutions of