Explaining ideas

In presenting major new ideas in a book such as this, there is a trade-off between trying to explain these ideas directly on their own, and using previous ideas to provide a context. For some readers there is a clear short-term benefit in referring to previous ideas, and in discussing to what extent they are right and wrong. But for other readers this approach is likely just to introduce confusion. And over the course of time the ideas that typical readers know will tend to shift. So to make this book as broadly accessible as possible what I mostly do is in the main text to discuss ideas as directly as I can—but then in these notes to outline their historical context. Occasionally in the main text I do mention existing ideas—though I try hard to avoid fads that I expect will not be widely remembered within a few years. Throughout the book my main goal is to explain new ideas, not to criticize ones from the past. Sometimes clarity demands that I say explicitly that something from the past is wrong, but generally I try to avoid this, preferring instead just to state whatever I now believe is true. No doubt this book will draw the ire of some of those with whose ideas its results do not agree, but much as I might like to do so, I cannot realistically avoid this just by the way I present what I have discovered.