Home Newsletter
News Books
Welcome to FreeScience.info Language/Lingua

Books 3054
· Book News
· Most clicked
· Least clicked

Search for a Book
HELP US TO HELP YOU
Add a new Book

From Philosophy to Program Size

book
Language:
Author: G. J. Chaitin (IBM Research)
Url: http://arxiv.org/abs/math/0303352
Format: Ps, Pdf
Year: 2003
Category: History of Physics
Pages: 54
Clicks: 2658

Description
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. 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 Godel. 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 Omega 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, both strongly suggest a quasi-empirical view of mathematics. I.e., 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.

Similar Books
Conoscere Fermi
Quando la Fisica parlava tedesco
Quantum Theory at the Crossroads
Brownian Motion, "Diverse and Undulating"
Searching for an equation: Dirac, Majorana and the others
Renormalization for Philosophers
Babel of Units. The Evolution of Units Systems in Classical Electromagnetism

Home |  Authors | About | Contact Us |  Email 
 Copyright © 2002-2013 FreeScience.info. 

Best viewed with Mozilla 1.X 1024x768
free scientific books