Logic, determination and predictability.
From Informatics to Natural Sciences
Giuseppe Longo
CNRS et Dépt. d'Informatique.
École Normale Supérieure, Paris
http://www.di.ens.fr/users/longo
Motivations:
Computing is an very original tool and, today, an essential component of any form of scientific
knowledge. Modern Computers and their Theory are the result of a strong mathematical (and
philosophical) commitment: the foundation of Mathematics (and of knowledge) on Arithmetic
(Frege, Hilbert… and the ’30s). Now, Mathematics organizes (physical) phenomena: does the use
of discrete or continuous structures affect intelligibility?
Aim:
After a short historical introduction to the two major “crises” that affected foundations as
“certainty” at the end of the XIX century (Riemann’s geometry and Poincaré’s unpredictability),
we will compare causality in “natural” phenomena (as given by mathematical continua) and in
computing devices (Discrete State Machines). This will allow presenting a distinction, implicit in
Turing’s writings, between computational “imitation” and mathematical “modeling”. A
discussion will then informally introduce some technical ideas concerning the relation between
computational undecidability and dynamical unpredictability.
References (see: http://www.di.ens.fr/users/longo )
Bailly F., Longo G. Mathématiques et sciences de la nature. La singularité physique du vivant. Hermann,
Paris, 2006 (english introduction downloadable)
Downloadable papers :
Giuseppe Longo. Laplace, Turing and the "imitation game" impossible geometry: randomness, determinism and
programs in Turing's test. In Epstein, R., Roberts, G., & Beber, G. (Eds.). The Turing Test Sourcebook.
Springer- Kluwer, 2007.
Francis Bailly, Giuseppe Longo. Randomness and Determination in the interplay between the Continuum and the
Discrete. MSCS, to appear.
Hoyrup M., Kolcak A., Longo G. Computability and the Morphological Complexity of some dynamics on
Continuous Domains, invited survey, TCS, to appear.
Giuseppe Longo, Pierre-E. Tendero. The causal incompleteness of Programming Theory in Molecular Biology.
Under revision for publication in BioEssays.