There is now a great deal of evidence confirming the existence of a very hot and dense early stage of the universe. Much of this data comes from a detailed study of the cosmic microwave background (CMB) - radiation from the early universe that was most recently measured by NASA\'s WMAP satellite. But the information presents new puzzles for scientists. One of the most blatant examples is an apparent paradox related to the second law of thermodynamics. Although some have argued that the hypothesis of inflationary cosmology solves some of the puzzles, profound issues remain. In this talk, Professor Penrose will describe a very different proposal, one that suggests a succession of universes prior to our own. He will also present a recent analysis of the CMB data that has a profound bearing on these issues.