As I noted previously, every essay that has been included in the book has been modified, some rather substantially and some minimally (just cleaned up a bit for print publication), so these essays on the blog are to be taken mostly as first drafts and prototypes of what they evolved into. In many cases, new pieces have been added to these essays to flesh them out, given that blogging puts a premium on brevity. The book, though, is also kept brief--coming in at only around 120 pages (about 37,000 words).
The essays from the blog that made it into Dot, Dot, Dot are:
- "On Reality and Logic," an exploration of the difference between logical constructs and the reality we use them to attempt to make sense of.
- The five "Down the Rabbit Hole" essays, which were this blog's first real exploration of the weirdness and difficulty with infinity. These five essays followed me a bit as I explored the topic of infinity deeply for the first time (most mathematicians have no need to do this to the level I was digging) and are the real inspiration, together with "On Reality and Logic" that inspired this work. Incidentally, all of this exploration followed an email discussion I was having with Richard Carrier about uses of infinity in theological-style arguments. Links to follow: DtRH-I, in which I lay out some of the basic sense of the axioms that lead us to consider infinity--and paradoxes that arise already.
- DtRH-II, in which I explore the psychological reasons that we go awry with infinity so easily--kind of the essence of the Dot, Dot, Dot title I chose for the whole book.
- DtRH-III, in which I explore some of the paradoxes related to infinity that arise from accepting some of the strange fringe mathematics that it has led to--particularly leading us to believe that infinity is really just an abstraction.
- DtRH-IV, in which I develop more of the nitty-gritties about probability theory and infinity, particularly focusing on the alluring but problematic concept of "choosing any number at random."
- DtRH-V, in which I pull the series together with a reiteration and deeper development of the ideas at the end of essays I and III in the series, really digging into the axiomatic construction and abstract nature of the beast here.
- "Coming Clean About an Error that Is but Isn't," an admission of a common misuse of infinity that I presented in God Doesn't; We Do, why it matters, and why it doesn't matter for my purposes there.
- "Revisiting My Case that the Existence of God is Infinitely Unlikely," a continuation and clarification of the discussion in "Coming Clean" with a reiteration of my primary point with the argument I made in the fifth chapter of God Doesn't; We Do that God's existence may be said to be infinitely unlikely.
- "About Gödel's Ontological Argument," a discussion pointing out the underlying flaws in modal logic "proofs" of the existence of some "God."
Indeed, at this point, I'm quite convinced that the human mind is not capable of truly grasping the infinite except via the "dot, dot, dot" that brushes almost all of it under the rug--and this is utterly fascinating.