I have included extensive historical notes in this book in part out of respect for what has gone before, in part to provide context for ideas (and to see how current beliefs came to be as they are) and in part because the steps one goes through in understanding things may track steps that were gone through historically. Often in the book my conclusions in a particular field differ in a fundamental way from what has been traditional, and it has been important to me in confirming my understanding to study history and see how the conclusions I have reached were missed before. My discussion of science in this book is generally quite precise, being based among other things on computer experiments that can readily be reproduced. But my discussion of history is inevitably less precise. And while I have gone to considerable effort to ensure that its main elements are correct, ultimate objective confirmation is usually impossible. I have always tried to read original writings—for I have often found that later characterizations drop elements crucial for my purposes, or recast history to simplify pedagogy. But even for pieces of history where the people involved are still alive there are often no primary written records, leaving me to rely on secondary sources and recollections extracted in personal interviews—which are inevitably colored by later ideas and understanding. And while with sufficient effort it is usually possible to give fairly simple explanations for fundamental ideas in science, the same may not be true of their history. Looking at the historical notes in this book one striking feature is how often individuals of significant fame are mentioned—but not for the reason they are usually famous. And perhaps the explanation for this is in part that most of those who one can now see made contributions to the kinds of foundational issues I address were capable enough to have been successful at something—but without the whole context of this book they tended to view the types of results I discuss largely as curiosities, and so never tried to do much with them. Note that in mentioning people in connection with ideas and results, I have tried to concentrate on those who seemed to make the most essential contributions for my purposes—even when this does not entirely agree with traditions or criteria in particular academic fields.