  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 theory. This idea is developed in the modern
theory of algorithmic information, which deals with the size of computer
programs and provides a new view of Godel's work on incompleteness and Turing's
work on uncomputability. Of particular interest is the halting probability
Omega, whose bits are irreducible, i.e., maximally unknowable mathematical
facts. More generally, these ideas constitute a kind of "digital philosophy"
related to recent attempts of Edward Fredkin, Stephen Wolfram and others to
view the world as a giant computer. There are also connections with recent
"digital physics" speculations that the universe might actually be discrete,
not continuous. This systeme du monde is presented as a coherent whole in my
book Meta Math!, which will be published this fall.
