CIDEC ÜIK |
Estonian Winter Schools in Computer Science Eesti arvutiteaduse talvekoolid |
EWSCS 2003 EATTK 2003 |

VIII Eesti Arvutiteaduse Talvekool (EATTK)

March 2 - 7, 2003

IBM TJ Watson RC

Yorktown Heights, NY, USA

Most work on computational complexity is concerned with time. However this
course will try to show that program-size complexity, which measures
algorithmic information, is of much greater philosophical significance. In
particular, I'll discuss how one can use this complexity measure to study what
can and cannot be achieved by formal axiomatic mathematical theories. In
particular, I'll show (a) that there are natural information-theoretic
constraints on formal axiomatic theories, and that program-size complexity
provides an alternative path to incompleteness from the one originally used by
Kurt Gödel. Furthermore, I'll show (b) that in pure mathematics there are
mathematical facts that are true for no reason, that are true by accident.
These have to do with determining the successive binary digits of the precise
numerical value of the halting probability for a "self-delimiting" universal
Turing machine. I believe that these meta-theorems (a,b) showing (a) that the
complexity of axiomatic theories can be characterized information-theoretically
and (b) that God plays dice in pure mathematics strongly suggest a
quasi-empirical view of mathematics, i.e., that math is different from physics,
but perhaps not as different as people usually think. I'll also discuss the
convergence of theoretical computer science with theoretical physics, Leibniz's
ideas on complexity, Stephen Wolfram's book *A New Kind of Science*, and
how to attempt to use information theory to define what a living being is.

G. Chaitin. Paradoxes of randomness.

*Complexity*, v. 7, n. 5, pp. 14-21, 2002. [pdf, html]G. Chaitin. Elegant Lisp programs. In C. Calude, eds.,

*People and ideas in theoretical computer science*, pp. 32-52. Springer-Verlag, Singapore, 1999. [html]G. Chaitin. Invitation to algorithmic information theory. In D. S. Bridges, C. Calude, J. Gibbons, S. Reeves, I. Witten, eds.,

*Combinatorics, Complexity & Logic: Proc. of DMTCS'96*, pp. 1-23. Springer-Verlag, Singapore, 1997. [html]G. Chaitin. Meta-mathematics and the foundations of mathematics.

*Bulletin EATCS*, v. 77, pp. 167-179, 2002. [pdf, html]G. Chaitin. On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility. 2002. [pdf, html]

G. Chaitin. Foils, Computer Science Winter School Estonia, March 2003. [html]

E-mail: chaitin@us.ibm.com

URL: http://www.cs.umaine.edu/~chaitin/

http://www.cs.ioc.ee/yik/schools/win2003/

Modified Wednesday, Jun 27, 2018 at 10:24 EEST+0300 by monika@cs.ioc.ee