On Fri, 6 Dec 2002, Prof. Peter Johnstone wrote:
While looking for something else, I came across a reference to a recent book called "The Topos of Music: Geometric Logic of Concepts, Theory and Performance" by G. Mazzola, published by Birkh"auser. Has anyone on the categories list seen this book? If so, can you say whether it is really about toposes and geometric logic as I (and most category-theorists) would understand those terms, or is it just a coincidence of terminology?
Peter Johnstone
To answer my own question, I have now managed to get hold of a copy of the book. It's a very large book (1360 pages, U.K. price 83.5 pounds) -- but I suppose it's not for me to complain about that. The author is indeed attempting to apply topos theory (and quite a lot of other high-powered mathematics) to the analysis of music. Whether there's any substance in it is hard to tell from a qick skim-through: I have a strong suspicion that the whole thing is skilfully crafted from bovine excrement, but I'll need to consult my colleagues in the Music Faculty to see whether they think there's anything in it. I am not cited in the Bibliography (naturally I checked this first!) but the books by Goldblatt and Mac Lane--Moerdijk are both there. Bill Lawvere is cited for ETCS (1964), but not for anything more recent. Alexander Grothendieck is cited for SGA4, and also for a private communication to the author, commenting on the book's German- language predecessor (published 1990): "Das ist wohl schon die Mathematik des 'Neuen Zeitalters'". Composers cited in the Bibliography are, in alphabetical order, Milton Babbitt, J.S. Bach, Pierre Boulez, Claude Debussy, J.J. Fux, Paul Hindemith, Sigfrid Karg-Elert, W.A. Mozart, Arnold Schoenberg, Franz Schubert, Robert Schumann and Anton Webern (I may have missed one or two). Other citations include Aristotle, Francis Bacon, Umberto Eco and (inevitably?) Douglas Hofstadter. Peter Johnstone