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Additional resources for Collapse: Philosophical Research and Development:. Numerical Materialism.
At distances that extremely short our current physics breaks down because spontaneous fluctuations in the quantum vacuum should produce mini45 06_Gregory_Chaitin_FINAL 5/9/06 19:48 Page 46 COLLAPSE I black holes that completely tear spacetime apart. And that is not at all what we see happening around us. So perhaps distances that small do not exist. Inspired by ideas like this, in addition to a priori metaphysical biases in favor of discreteness, a number of contemporary physicists have proposed building the world out of discrete information, out of bits.
Well, I’m thinking of formal axiomatic theories, which are formulated using symbolic logic, not in 36 06_Gregory_Chaitin_FINAL 5/9/06 19:48 Page 37 Chaitin – From Leibniz to Ω any natural, human language. In such theories there are always a finite number of axioms and there are explicit rules for mechanically deducing consequences of the axioms, which are called theorems. An N-bit theory is one for which there is an N-bit program for systematically running through the tree of all possible proofs deducing all the consequences of the axioms, which are all the theorems in your formal theory.
How can we measure how successful it is? Well, using the ideas of information and computation, that’s not difficult to do, and the central idea can even be traced back to Leibniz’s 1686 Discours de métaphysique. COMPUTER E PISTEMOLOGY: WHAT IS A MATHEMATICAL OR SCIENTIFIC THEORY? HOW CAN WE JUDGE WHETHER IT WORKS OR NOT? In Sections V and VI of his Discourse on Metaphysics, Leibniz asserts that God simultaneously maximizes the variety, diversity and richness of the world, and minimizes the conceptual complexity of the set of ideas that determine the world.
Collapse: Philosophical Research and Development:. Numerical Materialism. by Robin James Mackay (Editor)