121 citations · 255 across the 32 of their papers we have counts for
32 papers
Algorithmic information theory: Some recollections
G. J. Chaitin
Presents a history of the evolution of the author's ideas on program-size complexity and its applications to metamathematics over the course of more than four decades. Includes sug…
The Halting Probability Omega: Irreducible Complexity in Pure Mathematics
G. J. Chaitin
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity me…
Epistemology as Information Theory: From Leibniz to Omega
G. J. Chaitin
In 1686 in his Discours de Metaphysique, Leibniz points out that if an arbitrarily complex theory is permitted then the notion of "theory" becomes vacuous because there is always a…
How real are real numbers?
G. J. Chaitin
We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Emile Borel (1871-1956).
Irreducible Complexity in Pure Mathematics
G. J. Chaitin
By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to…
Leibniz, Randomness and the Halting Probability
G. J. Chaitin
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputabilit…