[FOM] Chu Spaces and Music (Ircam, Paris, Friday April 9)
Moreno.Andreatta at ircam.fr
Tue Apr 6 19:26:45 EDT 2010
[Apology for multiple posts. The streaming videos of the afternoon session will be available online and in real time. See below for more information]
Ninth Season of the MaMuX Seminar (Mathematics/Music and relationships to other fields)
IRCAM, salle C. Shannon (morning) and I. Stravinsky (afternoon)
1, place Igor-Stravinsky 75004 Paris, France
(Free entry up to availability of places)
Friday 9th of April 2010 (from 10am to 6pm)
Chu Spaces and Music
Pedagogical Morning Session (salle C. Shannon, niveau -2) :
• 10h - 12h Vaughan Pratt – A Chu Space Tutorial
Afternoon (salle I. Stravinsky) :
• 14h30 - 14h45 Moreno Andreatta & Carlos Agon – Introduction to the session
• 14h45 – 15h30 Paul-André Melliès - Chu Spaces and the construction of a duality
• 15h30 – 16h15 Timothy Porter – The Geometry of Observation
• 17h00 - 17h45 Vaughan Pratt – Evolution of music and speech: a Chu perspective
• Final discussion
Vaughan Pratt (Stanford University) : A Chu space tutorial
Selected topics from Chapters 1-4 of « Chu Spaces », Notes for the School on Category Theory and Applications University of Coimbra [http://boole.stanford.edu/pub/coimbra.pdf]
Paul-André Melliès (CNRS/PPS-Jussieu) : Chu spaces and the construction of a duality
In this tutorial talk, I will review the elegant description of the Chu construction discovered by Pavlovic in the 1990s. In particular, I will explain how to see a Chu space as a canonical solution to the question of extracting a duality from the mere existence of a point (or pole) in a category. I will also relate the Chu construction to other important ideas in logic, this including the Dialectica interprétation by Godel (after ideas by Hyland and de Paiva) together with the dynamic and game-theoretic interpretation of the logical interaction.
Timothy Porter (University of Wales, Bangor) : The Geometry of Observation
We start with a simple situation: an observer makes observations about ‘something’. The observer has a list of attributes and is observing a set of objects, and notes whether objects have particular attributes or not. (This gives a 2-valued Chu space and is general enough for us - for the moment.) The question is how to ‘organise’ the observations with respect to spatial, logical, .... aspects of the situation. We will look at classical constructions of Cech and Vietoris from the 1920s from this general point of view, and then look at a more recent uses of similar constructions in Physics and more generally in Topological Data Analysis. We will also brief look at Formal Concept Analysis, a method from A.I. and its relationship with these ideas.
Vaughan Pratt (Stanford University) : Evolution of music and speech: a Chu perspective
1. Time-tone interference in pitch and rhythm.
2. Common roots of timbre and harmony.
3. Compositionality in composition: the sequential soloist, the parallel orchestra, etc.
The three talks of the afternoon session will be available online and in real time through the "Ircam On Air" service. For instructions, see at the following address : http://video.ircam.fr/index.html.en
This session is organized within the activities of the Exploratory Project Interactions Maths/ST2I called « Geometry of Information and Music », supported by the French National Center of Scientific Research (CNRS). For more information , see: http://recherche.ircam.fr/equipes/repmus/mamux/PEPS-GdIM.html
The complete program of the session, with a list of bibliographical references, is available at:
Music Representation Team
1, place I. Stravinsky
email: Moreno.Andreatta at ircam.fr
Tél: +33 (0)1 44781649
Fax: +33 (0)1 44 78 15 40
More about the MaMuX Seminar at:
More information about the FOM