Gödel Escher Bach : les brins d'une guirlande éternelle / Douglas Hofstadter ; version française de Jacqueline Henry et Robert French

The title of this large book only hints at its contents, which include such recherché topics as DNA and protein synthesis, Zen Buddhism, Ramanujan and the Church-Turing thesis, the behavior of ants and the sphex wasp, the development of the pianoforte, non-standard models and "supernatural'' numbers, problems of translating Dostoyevsky from the Russian, recursive and r.e. sets. What brings Gödel, Escher, and Bach together is the author's interest in "strange loops'', which transport one "upwards (or downwards) through the levels of some hierarchical system [until] we unexpectedly find ourselves right back where we started'' (p. 10). Such loops are visually realized by M. C. Escher in such disturbing lithographs as "Drawing Hands'', "Ascending and Descending'', and "Reptiles'' (reproduced, along with many others, in this volume). Musical examples can be found in the canons and fugues of J. S. Bach, perhaps most strikingly in the canon at the unison in retrograde motion and the modulating canon at the fifth from "The Musical Offering''. And in logic there are those puzzling paradoxes of self-reference such as "This sentence is false'', which the genius of K. Gödel developed into a proof of the incompleteness of formal arithmetic and stronger systems (a result whose proof and interpretation occupies a central place in this work)... (MathSciNet)

Bibliogr. p. 849-[857]. Index