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Barnard College of Columbia University

Project Title

Godelian Incompleteness & A Theory of Everything

Project Summary

A physical Theory of Everything is the greatest ambition consuming theoretical physics. Yet last century we were forced to concede that there will never be a mathematical theory of everything. Kurt Godel, Alan Turing, and Gregory Chaitin proved that our knowledge of numbers themselves is fundamentally incomplete. Most numbers are random, a toss of the coin. There are true relations among the numbers about which we can only prove that we can never prove them.

Many times in the history of physics, theories have been shaped by such profound limits. Einstein proposed a fundamental limit in the speed of light and thereby discovered Relativity. Heisenberg invoked an uncertainty principle in measurements of quantum phenomena and thereby laid a cornerstone for Quantum Mechanics. Alongside these should be listed the profound incompleteness in our knowledge of numbers ? there can never be a mathematical theory of everything. The proposal is to define the limits mathematical incompleteness might set on a physical theory of everything. Just as Relativity emerged from the limit of light's speed and Quantum Theory emerged from the limits of measurement, deep insight into the universe and its origins could emerge by confronting the limit of mathematical incompleteness.

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