Persevere

My favorite Clint Eastwood movie, and one of my all time favorite movies, is the "The Outlaw Josey Wales." In the movie Lone Watie (Chief Dan George) tells Josey (Clint Eastwood) about a trip he made to Washington D. C. with other Cherokees to put their grievances before the President. During their audience they were told, "to endeavor to persevere." Then they were sent home with nothing substantive to show for their trip.

For some odd reason I was reminded of the scene while listening to President Bush's speech about Iraq the other night.

He's Back Too

Kerry Wood returns after two months on the DL. He strikes out nine and gives up one run in six innings. The Cubs go on to beat Milwaukee 3 to 2.

I prove the Riemann Hypothesis in my head while watching the game, but in all the excitement I forget to write down the proof. Now, I cannot remember for the life of me what it was.

Oh well, the Cubs won, and that's the important thing.

Summer with Riemann

I have been trying to understand a few elementary results about the zeta function during the past month. I have learned enough about Riemann's original 1859 paper and its importance to become officially addicted the Riemann Hypothesis. I will occupy part of my time for the next several years trying to understand the dense mathematics, beautiful equations, and esoteric proofs associated with the problem. It usually takes at least two years for my math addictions to run their course.

I recall why I majored in mathematics. I literally could not help myself. I kept wanting to learn a little bit more about math even though I was not particularly good at it compared to my brilliant and hard working peers. The odd thing is that I have probably learned more about math after leaving college than I did while I was there. I have spent my whole life wanting to learn a little bit more.

I have found a way to understand some mathematics in my own way. That is so hard to explain. I suppose it is a little like reading a great writer that you love. You read her the first time, become bewitched even though you only get the gist of what she is saying. Then you return to her over and over again. Eventually you understand her based on your own terms, terms that have meaning for you, metaphors that fit the way you frame the world.

Of course, mathematics is creative, creative in the sense that it too is built starting from basic metaphors and blending them into complex metaphors. I learn the math behind the Riemann Hypothesis based on the metaphors that work for me. That is the fun part of the math for me, creating my own metaphors.

Much has been written about the aesthetics of math. To me math really is beautiful. I am not artistic, but I can do some amateurish math. Math is my paltry artistic outlet.

I recommend "A Mathematician's Apology" by G. H. Hardy. It is a literary classic. You don't need to know any math to appreciate it, for it has only a little in it, and even where it does, anyone who understands arithmetic will understand his two mathematical illustrations of what math is all about.

Hardy worked on the Riemann Hypothesis all his life. He proved infinitely many zeros lie on the critical line. That is a big result, but still far away from proving the Riemann Hypothesis.

A spectacular full moon rose over the lake at the end of the first day of summer. What else happened? Darned if know.

Shelby Foote

Shelby Foote is dead at 88. Another one of my heroes is gone.

He's Back!

Mark Prior returns after missing a month and throws one hit baseball at the Sox. The Cubs beat the White Sox 2 - 0 in a honey of a ball game, nicely played by both sides.

Chicago baseball, get some, baby.

Cubs 6 White Sox 2

Maybe there is a god after all. Roberto Novoa seems to think so.

I just had to try out the new Blogger picture posting feature.

Arithmetic, Certainty, Doubt, and Memory

I have been doing some arithmetic, that is, learning a little about the Riemann zeta function. As the days go by, I remember long forgotten math. But have I remembered or just learned anew? I don't think there is a distinct border between recall and learning anew. I see a pattern or technique and often think it is something I once knew. I could be mistaken though.

1 + 1 = 2. I am certain I remember that. But doubt can always creep in. Maybe, knowing something so simple is innate. I believe child development researchers have shown it plausible. Or is it merely because I have two apples sitting beside my computer as I write, and I have unconsciously worked out the sum anew?

White Sox 6 Dodgers 0

Big Frank hits a two run homer. Another good night at the ballpark.

"To Know One Book Really Well"

My favorite time of the year. The long warm days with books.

Terry Schiavo's Brain

About half of it was left. No surprise really.

Of course, half a brain is not the same as half a loaf of bread.

She was probably having less than half the fun she once had.

Feast Followed by Famine

Marlins 15 Cubs 5. Oh well, there's no crying in baseball.

Cubs 14 Marlins 0

I went to the Cubs game last night at Wrigley. Thank you, Mr. Opportunity, for the ticket.

The Cubs are starting to play reasonably well, so the baseball season is a whole lot better. I can see it now--the Cubs vs. the White Sox in the Red Line World Series.

Don't say it. Even my Cubs and White Sox friends think I'm nuts.

Route 66

This memory was inspired by Raindrops.

Seven years ago I was driving to California on Route 66. When I got to the scorchingly hot Texas Panhandle, I decided I needed to create a mission statement for my life. I came up with this.

"To have easy going fun while doing my own thing in my own time."

I still like it.

Szymborska and Riemann

It must be over two years ago since I last studied the Riemann Hypothesis: all nontrivial zeros of the Zeta Function have real part ½. If you know a little about functions, infinite series, and complex analysis, the statement of the conjecture is easy to understand. But its proof or disproof has withstood all assaults since Bernhard Riemann first conjectured it in his classic 1859 paper “On the Number of Primes Less Than a Given Magnitude.”

I don’t know what triggers my interest in mathematics. I think it might be the onset of melancholy when I want most to avoid melancholy. Was it melancholy last week that made me open a book of forbidding mathematics about the problem? No matter, I’m hooked again.

This time, I have resolved to ask my own questions about the zeta function rather than reading books about it. The only tools I have are some half remembered analytic number theory and my trusty old TI-85 scientific calculator.

I’m no fool when it comes to these researches. I know I won’t get far, but I will walk my own miles in my own boots. It saves time. I can work while making a BLT sandwich, or talking to an acquaintance who has no idea what is rolling round my brain. Don’t give me a pop quiz; I won’t pass.

Was it only last week I realized I had not been reading nearly enough poetry? That’s changing. The poetry of Wislawa Szymborska sits beside my calculator.

Poetry—trying to find the nontrivial zeros for the equation of life.

Poetry

While discussing favorite poets with Curtis, I was reminded of this one by Marianne Moore.

Poetry

I, too, hate it.
Reading it, however, with a perfect contempt for it, one discovers in
it, after all, a place for the genuine.

Honey Locust

I like the honey locust trees, the ones with the long sharp hazardous thorns on their trunks. The honey locust grows tall and wide. The sunlight shimmers on the ground beneath its lacy foliage.

The honey locust’s leaves do not fall until November, and trick me into believing it is still summer on Autumn days. It is another kind of thorn they have, the kind that pricks the heart.

Love, forget about it.

I wonder what it would be like to fall in love again even if it hurt me like the other times--no, best to take some good poetry from the bookshelf, walk down to the lake, dangle my feet in the water, let the high summer sun scorch me, and wait for the mood to pass.

I Think Metaphorically. So What?

What does it mean as a practical matter that I think in metaphors? Not much.

My metaphors are mostly unconscious. I cannot know what they are unless I discover them through rigorous scientific investigation. That is something I am not equipped to do. Even if I could through prodigious research catalogue all the metaphors in all the minds at the present moment, those minds create new metaphors by the bushel everyday. I would have to research all minds all the time to keep the catalogue up to date.

As a practical matter, I am stuck with the metaphors I use and create without being aware what they are, and how I am using them.

Metaphor by its very nature creates yet another transcendental infinity, a border which I cannot cross into the realm of certainty.

Blue Jays

To all my Canadian friends, I love you dearly, but will you please stop beating the Cubs!

Math Questions

How many prime numbers are there less than a given number? The Prime Number Theorem says approximately n/log n, a formula so simple and beautiful it defies the imagination.

I go through periods when I am curious about questions like that, periods both pleasurable and accursed.

What would I do with all the time I spent studying mathematics if could have it back?

Most likely, make the same mistake.

The Thinking Is Language Metaphor

The thinking is language metaphor is not apt.

I recall my first rocket and mortar attack in Vietnam. I hear the explosion of the first rocket landing nearby. I run out of the hut with my comrades to the bunker. I am afraid. Somebody really wants to kill me. I am helpless. The enemy is far away. I cannot shoot back. Words do not form in my mind as I recall it.

I think about the Riemann Zeta function. Words do not form in my mind while I think about it.

Language is part of thinking, but hardly the whole. Language must fit our metaphorical way of thinking.

Extraterrestrial Intelligence and Metaphor

Our minds are completely embodied. That is, the mind arises from our neural systems. What does that mean for extraterrestrial intelligence?

We will be lucky if we find any extraterrestrial species whose bodies evolved exactly like our own. Since their bodies are different, their minds will be different. They will think about different things than we do, if they think at all, and that thinking will arise in different ways.

For instance, we think metaphorically. Our brains did not specifically evolve to think metaphorically, but metaphorical thinking did arise when our brains evolved sufficiently to make it possible. The characteristic of our higher intelligence is imagination. We continually create new metaphors, and the metaphors are culturally transmitted.

If we find an extraterrestrial species that we recognize as intelligent, then the species will have neural systems similar to our own, neural systems that allow metaphorical thinking.

That is an unlikely event.

A Little Baseball

A lot of fans of State Street have been sending me e-mail and asking, "what's the scoop on this baseball season?" Here goes.

The White Sox have the best record in baseball. The Cubs have won 6 in a row and moved way up in the standings the past couple of weeks.

This could be the year of every sports fan's dreams: the Red Line World Series.

Are you stoked? I know I am.