Authored by Gregory Chaitin In 1956 Scientific American published an article by Ernest Nagel and James R. Newman entitled “Gödel’s Proof.” Two years later the writers published a book with the same title—a wonderful work that is still in print. I was a child, not even a teenager, and I was obsessed by this little [ Read More ]
Archive for the ‘General Science’ Category
Authored by John Baez I will begin with a thoroughly fictionalized account of the quest in physics to find bigger and bigger symmetry groups. Then I will say a bit about how that quest has led to some interesting applications of category theory. Once upon a time up was up, down was down, so the [ Read More ]
Categories: General Science
Gregory Chaitin | Scientific American 232, No. 5 (May 1975), pp. 47-52 Although randomness can be precisely defined and can even be measured, a given number cannot be proved to be random. This enigma establishes a limit to what is possible in mathematics. Almost everyone has an intuitive notion of what a random number is. [ Read More ]
Categories: General Science
the notions of simplicity, complexity and irreducibility Authored by Gregory Chaitin Abstract We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that comprehension is compression, i.e., explaining many facts [ Read More ]
Categories: General Science
Authored by Gregory Chaitin | for +Plus Magazine Over the millennia, many mathematicians have hoped that mathematics would one day produce a Theory of Everything (TOE); a finite set of axioms and rules from which every mathematical truth could be derived. But in 1931 this hope received a serious blow: Kurt Gödel published his famous [ Read More ]
Categories: General Science
Authored by Gregory Chaitin | International Journal of Theoretical Physics 21 (1982), pp. 941-954 Abstract Gödel’s theorem may be demonstrated using arguments having an information-theoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem [ Read More ]
Categories: General Science
