How Many Angels Can Dance on the Head of a Black Hole

I will try to explain, in elementary terms, the deep connection between space-time geometry and quantum entropy, uncovered in the work of Bekenstein, Hawking, 't Hooft, Gibbons Jacobson, Fischler, Susskind and Bousso. This leads to the conclusion that many of the fundamental degrees of freedom, which describe our world, are inaccessible to direct local measurement. Indeed, local excitations are constrained low entropy states of the fundamental degrees of freedom. These insights give us clues to the nature of a fundamental theory of quantum gravity, and have implications for early universe cosmology, inflation, and the particle physics at the TeV scale (I won't have time to discuss the last of these claims, which is highly speculative).