Here is a draft of a talk I am to give soon.  I was asked to present something that might inspire majors and non-majors, and to do something more like what I would do in a class than what I would do giving a conference paper.  This is the result so far.  It is a  formalization of the sort of thing I might do in an upper-level class.  Since I think of it as a talk and not a paper, it is not bedecked with all the scholarly niceties–footnotes or full footnotes, etc.  Most of the footnotes are really just drawers in which I have stashed useful quotations or (I hope) brief, helpful clarifications.  Comments welcome.