Week Two

QUESTION FOR TOM

I am well acquainted with the Cantor middle thirds set, its counter-intuitive properties and the mathematics behind it. I have worked with it for years. My question regards points in the set that are not endpoints. I can wrap my mind around this "numerically" with no problem. Do you have any ideas about how to wrap my head around this geometrically? The set has measure zero and contains no intervals. Every point of this uncountably infinite set of points is an isolated point. How, geometrically, did these non-endpoints get "missed" in the removals?

NOTES ON READING:

My reading has been focused on Godel and the Incompleteness Theorem. I took a tangent from GEB to read the Casti/DePauli book on Godel's life and work. There is much mention there of Wittgenstein and his work "Tractatus Logico-Philosophicus." I'd like to explore that at some point in the future. I'd also like to know more about mathematician L. E. J. Brouwer and his work.

I've spent much more time writing than reading this week. (Note: On the side-bar is a running record of my reading.)

NOTES ON WRITING:

I am chasing all over researching details and subtantiating information for my writing.

I have a rough draft of chapter 1 complete but need to polish it quite a bit.

The manuscript will have 5 chapters connecting mathematics and poetry (and has 3 appendices so far); I will also be including an introduction and end notes. The chapters are entitled:

1) Playfulness
2) Pattern
3) Power
4) Elegance
5) Surprise

This week I'm wrestling particularly with how to separate information I want in the introduction from information I want in the main body of the book. I'm also working to keep focused on a target audience so that my writing is consistently at the same level.

Chapter 1 is entended to be a gentle entry. Poetically, it includes the limerick, Shel Silverstein, and e. e. cummings (as well as a humorous personal story). Mathematically it includes Sudoku, one of Zeno's Paradoxes, FLT, the Konigsberg Bridge Problem, and the chaos game (which I will pick up again later in the book as part of chapter 5 - "surprise."). I've tried to begin with a "hook." I hope it is effective.