Midweek Thoughts (Week 2.5)

1) In GEB chapter 3 "Figure and Ground," in the last paragraph of the section "Illegally Characterizing Primes," the statement, "Do the holes also have some 'form' in common?" immediately brought Riemann to mind.



2) As I ponder Casti/DePauli on Godel and as I get back into GEB, thoughts of formal systems, thought, AI, human intelligence and incompleteness (this is not a complete list!) are running through my mind and are bringing to mind the following by Emily Dickinson:

The Brain -- is wider than the Sky --
For -- put them side by side --
The one the other will contain
With ease -- and You -- beside --

The Brain is deeper than the sea --
For -- hold them -- Blue to Blue --
The one the other will absorb --
As Sponges -- Buckets -- do --

The Brain is just the weight of God --
For Heft them -- Pound for Pound --
And they will differ -- if the do --
As Syllable from Sound --


Post Script: While typing out this poem, I couldn't help but think of the affinity Dickinson and Hofstadter both have for hyphens!

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.

Week One

NOTES ON READING:

GEB: Strange Loopiness and The Braid:

I had not before been aware of strange loops in music - had been in math and art with things such as Escher's "Drawing Hands" and the Epimenides paradox, but had not connected them. Hofstadter braided these together for me powerfully.

I am continuing to ponder the history of "strange loopiness," attempts at banishing it and the consequences thereof (discussion of Godel's Incompleteness Thm and PM), and the implications of strange loops and human intelligence vs. AI.

Am I correct in understanding that a system without the potential for "strange loops" is necessarily incomplete and that a system with the potential for "strange loops" is necessarily inconsistent?

The MIU system and pq- system are fascinating (what a cool, simple description of isomorphism pq- is). I'm working at the MU puzzle. I have not yet turned MI into MU, and given his succeeding discussion I am not yet sure if it is just really hard or impossible. Clearly it is at least meant to be difficult or he could not follow up on it as he has, expecting the reader not to have solved it. Does this mean it is impossible? I'm not ready to give up on it yet.

I love his "invention" interludes and do hear Lewis Carroll resonating all over the place in the style and content - Zeno too, of course. (Also am remembering the Bach "Inventions" I played as a piano student.)

NOTES ON WRITING:

I'm learning by doing!

One thing I've learned it how hard it is to track down sources of "quotes" and anecdotes that I've been familiar with for years, and things I thought were true are not necessarily so! Two examples:

1) I wanted to use "the fact" that T. S. Eliot said poetry had to be hard. This one I have on good authority, but I cannot find that quote that strongly anywhere - have only found something in his collected essays that say that in our time poems must be "difficult" (i.e. complex), but that this might not always have to be the case. If you can direct me with this, please help!

2) There is a lovely anecdote about Lewis Carroll (aka Charles Lutwidge Dodgson) and Queen Victoria - that she, enamored of his Wonderland works asked to be sent anything else he wrote. She was not amused when sent his next publication, a math text. In researching, I have found that this is an "urban legend," and I am very disappointed!

3) Additionally, I have found that the verse of Edward Lear whom I thought was from Limerick and for whom I thought the poetic form was named, is not actually in the form of a true limerick!

So, there go two - perhaps three things - that I wanted to use in my writing!

A second thing I have found is that it is quite a transition from being a speaker to being a writer. It is a very different medium, and I am having to come up with a new understanding of how to hold the attention of my "audience." This is a more difficult "translation" than I had realized it would be.