## 2002/12/31

**[Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter]**

Further progress in *Gödel, Escher, Bach* has proven delightful. There was this dialogue called “Ant Fugue”, which compared anthills to brains in a rather charming way. The dialogue preceding this one was called “Prelude…”. Makes you wonder at the cleverness of the author in finding an analogy to address a subject that also provides a pun like “Prelude…Ant Fugue”. Oh, and in between there was this pun Lierre de Fourmi, a fictional anthill who discovered the converse, so to speak, of Fermat’s Last Theorem. That n^a + n^b = n^c has an infinite number of solutions when n=2, but no solutions when n>2. This is of course a Diophantine equation, and Lierre de Fourmi supposedly discovered his Well-Tested Conjecture when reading *Arithmetica* by Di of Antus, mirroring the way Fermat thought up his theorem while reading *Arithmetica* by Diophantus. Even more clever that one can create such a pun on Diophantus’ name to reflect all the other ant puns going around…Lierre de Fourmi by the way means “bridge of ants”, which reflects an actual behavior of ants that illustrates Hofstadter’s whole point about anthills. It was really amusing, to say the least.