The Book without a Name

I have finished my project!

I will just reread the last chapter tonight (uh . . . I mean this morning) to proof it, and then I will have it printed.

It has no name yet.

"Truth and Beauty" just doesn't cut it for the audience I am looking to attract.

One suggestion was "Beauty, not the Beast."

My husband had a suggestion the other night that I don't think I'll use but is perhaps closer: "Frost and Fibonnaci: Not So Strange Bedfellows."

I just can't quite hit it. I want something attention-grabbing, light, compelling and descriptive. I'm not asking for much, am I?

Any suggestions?

. . . later (2)

I had a good talk with a fourth grade teacher tonight regarding ideas for my graduate project. I contacted him to try to brainstorm as I have begun working on my prospectus. He sounds very excited and feels his principal and colleagues will be excited as well.

I also have an appointment to speak with the principal of a private school next week. He also sounds very eager to interact with me about that.

I'm feeling very encouraged.As I continue writing, I am doing a lot of reading, and I came across the following in the preface to the book "Think of a Number: Ideas, Concepts, and Problems which Challenge the Mind and Baffle the Experts." The author is a physicist with mathematical leanings who graduated from Magdalen College, Oxford. He describes his defense of his research back in 1961 in which one long-serving fellow of the college, who had seemed annoyed stood to his feet and said, "These Green's functions that I hear you talking so much about, how would you explain one of those to a medieval historian?"

The author commented that that question has haunted him to this day. In his preface he goes on to say:

Firstly . . . someone who claims to understand, and be excited by, any aspect of science (and yes, even mathematics) ought to be able to pass on the essence of that knowledge and enthusiasm to any reaonably intelligent layperson who is interested. Secondly . . . many of the most exciting advances of this kind do lend themselves admirably to just such exposition. And finally, and perhaps most importantly . . . there may be a much wider potential interest 'out there' than anyone suspects -- if only authors would make a serious effort to bridge the verbal chasm between the specialized jargon of the learned journals and the normal vocabulary of the population at large.

That pretty much parallels what I have set forth as the goal of my work.

As of today I have completed Chapter 4: Empowerment. I have a good direction for Chapter 5: Elegance and have basically finished Chapter 6: Surprise, except for polishing it. I hope to complete my writing within the next two weeks.

I am also planning to include an index, which seems like it will be tedious work. Time will tell. That too needs yet to be done - as do the end notes as I continue writing.

Completed so far: introduction, chapters 1-4, afterword, appendix 1, appendix 2, and references.

. . . later

POWER TO THE PEOPLE

Why are the stamps adorned with kings and presidents?
That we may lick their hinder parts and thump their heads.

Well, I have been letting the blog slide as I have focused ever more on my writing.

I really appreciated our meeting last week and found it to be very helpful. I am amazed at how you can turn something around entirely with a change of a single word - for instance:

"empowerment" vs. "power"

"arithmetic" vs. "math"

The power of an appropriate word in an appropriate place is truly amazing - even if it is only subtly different from a seeming synonym.

As we both acknowledged, approaching the concept of elegance is the hardest, but I've made some significant progress in that area. Here too I wrestle with translating from what works in a spoken format to what will work in a written format. I had to throw my old approach to this idea out the window and start fresh.

I imagine the concepts of mathematical and poetic elegance are things that cannot be experienced with fullness through explanation but rather must simply be experienced. I'll just have to explain as best I can and hope some experience comes along with it.

For the most part I have scrupulously avoided "explaining" any poems, but in one instance in this chapter I am allowing myself to take a poem apart and explain it. I realize explaining a poem is along the lines of explaining a joke - it ruins it - but if I ruin just one in order to make others more approachable, that is, perhaps, acceptable.

I'm still concerned that so much of the poetry that I use has death as its theme. It is the one negative comment I have had when speaking on this topic. No matter how many light poems I include, if there is more than one about death people think it is too many. Unfortunately the poem that will work best in my chapter on elegance is "Not Waving but Drowning" by Stevie Smith.

Oh well, at least I found Howard Nemerov's fun poem Power to the People (with which I began this entry). I'm revising chapter one on playfulness to include that - especially pleased to have another playful poem by a "serious" poet.

Week Seven

NOTES ON READING:

Other than dipping into many books for research, my main focus has been Borges and Hofstadter this week. With regard to Borges, I have been reading transcripts of interviews with him, which I have found fascinating. From there I dip into poems and pieces of fiction that he mentions of his own work and of others. In one of the Morgan Lectures (interviews) he gave at Dickinson University, I found this question and answer that are particularly relevant to my work:

Question: Do you think that there is a kind of kinship between poets and mathematicians?

Borges: My mathematics is very slight. But I have read and reread Bertrand Russell. And I think there should be a kinship. And I suppose there is. There is a kinship between all things, especially between poets and mathematicians, and poets and philosophers, who are a measure of poets, I should say.

NOTES ON WRITING

Since sending on my introduction to you I have honed it further and have something I feel very good about. As I have been reading, I have begun to feel compelled to include an afterword too, one that really reinforces the introduction, so I have begun work on that. I have it entirely fleshed out if not entirely written, but it needs a lot of polishing. I am continuing to write quite globally on the chapters but am hoping to have chapter 2 on pattern in a form I feel I can send to you soon. That chapter feels rather belabored and plodding to me, and I've really struggled with making it lighter and smoother. I hope you will be able to help me with that.

Week Six

I'm still plugging along with writing and revising. My main focus right now is on the introduction and chapter two (Pattern). My bibliography continues to expand. I found a wonderful book today on Pascal's Triangle - a pretty significant treatment by A. W. F. Edwards Sc.D. of Cambridge. I'll be able to use very little of it in my book, but it is giving me a very deep background.





In other reading, I've been looking at Agnesi to Zeno by Sanderson Smith, Emily Dickinson and the Art of Belief by Roger Lundin, and Lives of the Modern Poets by Pritchard - among other works.

I also keep dipping into Hofstadter and Borges and am eager for Hofstadter's new book I am a Strange Loop to come out. Reviews I've read make it sound like it revisits GEB quite significantly.

Week Five

It was good to talk with you Friday and untagle some ideas. I sense some new possibilities particularly in thinking about "Empowered" rather than "Power." I also have some new ideas for the introduction rolling around in my head - given our talk of the challenge this is and the reasons it is a challenge.

I sent on chapter one, the bibliography so far, and end notes. I hope they came through (if not, let me know, and I'll resend), and I am eager to hear your comments.

If you did not read Frank and Ernest for today (Sunday, March 18, 2007), please do and keep it in mind as you read my first chapter. I found it an interesting paradox coincidence!

Week Four

QUESTION FOR TOM: I'm looking for an Einstein quote you mentioned during winter term about Einstein not caring if the test of the bending of light supported Relativity Theory or not - that the theory was still right. I had heard something like this years ago - that Einstein said, "If Relativity Theory is wrong, that's too bad for God." The closest thing I can find is the general quote: "If the facts don't fit the theory, change the facts," but I can't find a legitimate source for it. Do you remember where you came across what you shared along these lines in class?

UPDATE: I find that my writing has become a strange attractor. As I read, nearly every paragraph sends me back to my laptop to add to my writing, which sends me out to research, which brings me back to writing. I think before I plow all the way through any more books I need to just sit down and come to grips with this manuscript in full. I don't think I will be released from the grip of the pull of this strange attractor until I at least have a rough draft of the entire manuscript.

At this point I have a fully complete rough draft of chapter 2 (Pattern) -- tedious figures and all -- which needs a LOT of polishing yet. I have also been working more globally on the rest of the manuscript rather than trying to write from start to finish as I had been doing.

I end chapter 2 (Pattern) with fractals, the grand finale being the M-set. I begin chapter 3 (Power) also with the M-set, expressing that all this beauty and complexity can be generated with a mathematical statement of only 6 characters. Part of the power of mathematical language is its brevity.

Week Three

GENERAL UPDATE:

The rest of the week (since my mid-week post) has felt rather unproductive - not for lack of time or effort - have been up until 1 or 2 in the morning working at this.

I've gotten some new ideas and added to chapter 1 (Playfulness) and polished it. I've fully outlined chapter 2 (Pattern) and have more than a third of it written. What is bogging me down is creating images, of which there are many in this chapter.

I've worked with the drawing program on Word as well as the "paint" program on my computer with little success. I'm embarrassed to admit it, but I created the Pascal's Triangle Modulo 2 above by copying hexagonal graph paper and coloring the first 16 rows by hand, scanning it, uploading it, shrinking it, printing 3 copies, cutting and taping, scanning, uploading, shrinking, printing 3 copies, cutting and taping, scanning, uploading and shrinking.

That's totally PATHETIC and feels like a waste of time; after all that work it also came out crooked, but I don't have access to a better method for creating my own images(not that I know of anyway). For the second half of the week, my readings have consisted of my browsing (side bar) and my research of details for the chapters and checking out the links you sent on.

I appreciate your email and have enjoyed the links you suggested. I'm intrigued by L. E. J. Brouwer. I also especially enjoyed the book review from the New Yorker! What fun! On the poetry site I was not able to find what I was looking for . . . will try again.

When (if?!) things settle down for both of us, I'd like to talk about the non-endpoints in the Cantor set. I've had some new insights in the last couple weeks but need to wrestle with it more, but I guess this is getting ahead of the game as it is supposed to be my next study that is on fractal geometry.

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.