What if the Great Library at Alexandria had not been destroyed, but thrived, remained intact, and grew through the ages? My naive response is that the world would be a better place. However, great learning does not always trump folly. In fact, it may exacerbate folly’s consequences.
No matter what, wouldn’t it be fun to have all those books lost because of hate, violence, ignorance, and folly?
Proofs loom large in elementary number theory for two reasons. First, many of the theorems (including those contained in some of the problems in this book) are so simple to state and so easy to understand that one is deceived into thinking that they must also be easy to prove, and this is not always the case. Also, there is much more variety in the kinds of reasoning invoked than is the case in more elementary mathematics, the latter, more or less by definition, being restricted to material that is both useful and relatively easy to master. It is not merely because number theory is not useful in commerce and engineering that it is not customarily learned before calculus, as it logically could be. The variety of proof techniques sometimes seems so large that students regard number theory as a “bag of tricks,” but of course this is a matter of familiarity. What is a trick the first time one meets it is a device the second time and a method the third time.
William J. LeVeque, Fundamentals of Number Theory
Now, extrapolate to other fields of endeavor.
What do you do with a blog when you are totally bewitched and consumed by math problems? It’s worse than true love.
… WordPress didn’t have such a terribly awful mobile connection. I’d try to blog more Iive if they did.
Some questions nag and persist. Why are there many seemingly easy questions about the numbers 1, 2, 3, 4, … that have not been resolved? I suppose much of mathematics as we know it would not exist if the easy problems to state were also easy to resolve.
I can’t put the question out of mind this week. That leads to another unanswered question: why?
OK, Kids, it’s back to school time. We at State Street know you want to impress your math teacher, so we have come up with some extra credit assignments and questions to do exactly that. Here’s the first one.
Are there any odd perfect numbers? If you find one, show it factored and summed. If there isn’t one, just prove it.
Happy hunting.
It is an old mass paperback book. Its pages are yellowed. A watermark runs through it from a puddle it must have briefly sat in one night. It signifies things found and lost. It scares me. But all things scare me these days. So maybe, it signifies nothing. I really can’t tell.
If scientific truth leaves no room for god, then so much the worse for god. I metabolize and get the urge to pass on my genes. I exist because I was selected by impersonal forces. Compared to the things that have troubled me, that thought is no bother at all.
The blue-backed notebooks, the two pencils and the pencil sharpener (a pocket knife was too wasteful), the marble-topped tables, the smell of cafes cremes, the smell of early morning sweeping out and mopping and luck were all you needed.
A Moveable Feast, Ernest Hemingway
Lookin’ forward to writing tomorrow when the sun comes up. As paltry as my words are, a romance continues between me and them.
Tonight, a warm gentle rain. Thunder crashes occasionally. Lightning flashes. Then more thunder off in the distance.
I recall those summer nights when I was a boy in small Iowa towns back in the days when trains ran by them. Upon going to bed I would hear their whistles as they approached the town. After that, the sound of their wheels rolling along the rails disappearing in the distance. And I would fall asleep to that sound.
I wish I was in the country again listening to the train-song.
The patter of the rain and distant thunder tonight will do though. And the remembrance of what peace is really like. And deep sleep, the kind of sleep where forces embrace you rather than threaten you.
The gloom that fell over my feeble mind from the horrible display of baseball ineptitude put on by the Cubs last night has left me, for I am sitting in the sunshine bathing my balcony as I write this. And the Cards lost last night too. The Cubs remain only two games out.
My mind wanders to the awesome 1963 World Series pitching performance of the Dodgers’ Koufax, Podres, and Drysdale against the Yankees. They shut them down in four straight games. The series ended so quickly most people could not believe it. Koufax and Drysdale were almost unbeatable in those early Sixties years. The morning after they pitched I nearly memorized the boxscore of their games and newspaper reports of their triumphs.
Even when most days seem like days of failure and loss, we find something genuine in the exploits of those who reach almost absolute perfection, then triumph.
I wrote the first draft of a novel last year after swearing I’d never try to write one again. I was in love at the time and being in love, I fell slightly in love with myself, which returned me to the awful notion that I could actually write a novel. With some things I am persistent to the point of stubbornness–like writing novels. After the first draft, I realized how horrible it was. I decided to commit it to the waste basket, then the garbage shoot, but one night while in Paris, sitting alone in the bar of a hotel, an idea chanced upon me as to how I could make it better.
The novel was written in the third person. I decided it should be written in the first person. I meditated on the characters in the novel who would be the best candidate as the narrator. None seemed a possibility. Once again, I wanted to throw it down the garbage shoot.
I was driving home from Iowa from the Christmas holiday when the notion came to me that all I needed to do was add a first person narrator to the story, one who had not been in the first draft. In January, I commenced to do just that. I finished the second draft about a month ago.
I hated the second draft as much as the first when I finished. The garbage shoot and the second manuscript seemed like best friends. This past week I realized all it needs is a completely new plot. But plots are hard things for my feeble imagination to create.
Now, its back to writing things on scraps of paper about the plot if and when they arrive from who knows where. The Muse jabs me in the ribs every now and then, but not often enough.
I’ll write the third draft of the novel. for what is character and plot and the other elements of fiction? They are fictions themselves. Things we tell ourselves are necessary so we may keep going on.
Some of us never catch up on our reading no matter how hard we try over the span of almost 60 years. Take me, for instance. I am woefully under read in the classics of a sport I have enjoyed most of my life–baseball. Thus, I am newly armed with a stack of books about baseball: Veeck–as in Wreck, Bill Veeck, with Ed Linn, Ball Four, Jim Bouton, The Long Season, Jim Brosnan, The Boys of Summer, Roger Kahn, and The Summer Game, Roger Angell. I will also reread The Image of Their Greatness, Ritter and Honig, and The Glory of Their Times, Ritter, just because they satisfy immensely with each reading.
I’d like to think that our reading interest at any one particular time is one of our personae.
I score a lot of baseball games whether at the park, at home, or in the bar. I use scorecards and 8 1/2 x 11 paper too. I was sitting in the bar on Wednesday May 13 waiting for Cubs/Padres game to start when I got the urge to score the game. Not having paper at hand, I walked to the Walgreen’s on Chicago and Michigan and bought a notebook. I scored the game in the notebook.
I have a system that allows me to capture much of a game on lined notebook paper. When completed it looks like a combination of play-by-play melded with box score even though it does not capture all the events. My notation can’t be deciphered by most since much of it is nonstandard. However it’s perfect for little old indolent me.
I’ve logged a lot of games so far this season in my notebook. The digital age makes it unnecessay to do that kind of thing. You can look up every game up on the Internet and get the details. But using paper and pencil intrigues me still.
You get on these reading jags. Sixties and Seventies nonfiction, or the classics of baseball literature that you are ashamed to admit you have not read even though you announce yourself as the big baseball fan. Or some oldies but goldies you want to read again, those oldies plucked almost at random from the book stack, yet resonating against all odds.
It’s summer and you’re drifting and dreaming like you have not for over a year, and you just don’t care about anything but that, for drifting and dreaming drugs you like the best opiate. You listen to people as if you are observing a fly on the wall. The fly is not all that pretty, but it goes about its purpose, and who are you to argue about its purpose?
And you have not forsaken all philosophy, You might throw Hume’s An Inquiry Concerning Human Understanding onto the bonfire of reading one last time. What other book of philosophy might fit for these days of drifting and dreaming?
The skeptical and what might be the end of innocence defines your soul.
“I’ve been wondering about Dostoyevsky,” I said. “How can a man write so badly, so unbelievably badly, and make you feel so deeply.”
“It can’t be the translation,” Evan said. “She makes the Tolstoi come out well written.”
“I know. I remember how many times I tried to read War and Peace until I got the Constance Garnett translation.”
“They say it can be improved on,” Evan said. “I am sure it can although I don’t know Russian. But we both know translators. But it comes out as a hell of a novel, the greatest I suppose, and you can read it over and over.”
“I know,” I said. “But you can’t read Dostoyevsky over and over. I had Crime and Punishment on a trip when we ran out of books down at Schruns, and I couldn’t read it again when we had nothing to read. I read the Austrian papers and studied German until we found some Trollope in Tauchnitz.”
“God bless Tauchnitz,” Evan said. The whiskey had lost its burning quality and was now, when water was added, simply much too strong.
“Dostoyevsky was a shit, Hem,” Evan went on. “He was best on shits and saints. He makes wonderful saints. It’s a shame we can’t reread him.”
“I am going to try The Brothers again. It was probably my fault.”
“You can read some of it again. Most of it. But then it will start to make you angry. No matter how great it is.”
“Well, we were lucky to have had it to read the first time and maybe there will be a better translation.”
“But don’t let it tempt you, Hem.”
“I won’t. I’m trying to do it so it will make it without you knowing it, and so the more you read it, the more there will be.”
A Moveable Feast, Ernest Hemingway
One place I would like to have been.
The summer days roll languidly by. I read A Moveable Feast and Dispatches in short alternating bursts. They are made for that like bookends of a different wood and hue. And I do a little math just so I can learn a little more before I die.
At night, before falling asleep, I lie in bed and pretend I am in a boat upon on a placid sea, the waves rocking it slowly, hugging me until I succumb.
You could be in the most protected space in Vietnam and still know that your safety was provisional, that early death, blindness, loss of legs, arms or balls, major and lasting disfigurement–the whole rotten deal–could come in on the freakyfluky as easily in the so called ways, you heard so many of these stories it was a wonder anyone was left alive to die in the firefights and motor-rocket attacks.
Dispatches, Michael Herr
While searching the book stacks at home last night I came across Herr’s Dispatches. I have not read it in around 35 years, so I decided to try a few pages to see if it was still fresh. Damn, fresh ain’t the word for it. Frenentic, a prose style manic and on the edge. I classify it with the other books from the Sixties and early Seventies that fall in the categories New Journalism and the Nonfiction Novel: books like Capote’s In Cold Blood, Thompson’s Hells Angels, Wolfe’s Electric Cool Aid Acid Test, Mailer’s Armies of the Night, and Pirsig’s The Art of Motorcycle Maintenance.
The best half dozen books to come out of the Vietnam War are Herr’s, Caputo’s A Rumor of War, Kovik’s Born on the Fourth of July, O’Brien’s The Things They Carried, Mailer’s Armies of the Night, and Halberstam’s The Best and Brightest. I judge Dispatches as the best because Herr confurs a near impossible prose style.
Lots of good nonfiction has come from the Iraq War. I now wait for the gritty and wild books written by a new generation who were there and saw things up close and personal.
However, with Dispatches the bar is set very high. Reading it again is blowing me away just as it did the first time.
We can construct an arbitrarily large sequence of composite numbers. When putting that beside the notion that a function as simple as x/log x estimates the number of primes less than x arbitrarily close to square root accuracy, things seem strange.
I guess I don’t really understand questions about primes yet. Immensity always overwhelms my imagination.
It’s grown dark at midday. I can her thunder in the distance.
Raymond Carver’s Collected Poems remains one of my favorite reads. I like his conversational voice that has music woven through it. Geez, I wish I could do that.
She calls me. She says he wasn’t as serious as she thought. She says she was ambivalent in the first place. I tell her hanging out together is still on my agenda. (That’s so cold saying it that way.) Fuck it; she’s no longer in my heart. It ain’t going to happen.
Some people you desire for your whole life. Others fade into blue as swiftly as you can make it happen.
Color her blue. But don’t get me wrong. I’ll always remember her that Sunday afternoon at the coffee shop when she first opened Middlemarch. I’m going to miss discussing it with her, but I barely understand it myself. By the time she is my age and read it several times, she will know much more about it than me.
I hope the children she will eventually have understand just how smart her Mom is.
Sometimes, a simple sentence well crafted will do. Come on, write! People will love you for it.
I’m still playing chess, although not as many games as I did. I’d like to think that my games are of a higher quality, but I am getting my ass kicked by folks who are way better than me.
I do my analysis with the chess set V gave me for my birthday last year. It’s a sort of talisman. A spark of life flows through me each time I touch a piece.
I woke up early so as not to miss the dawn on this longest day. I went to Starbuck’s when they opened early this morning. I sat on the ledge looking out upon State Street. Hardly a soul was out and about that early in the morning. I read part of the New York Times on my iPhone.
After the news bored me, I started thinking about this fictional person who claims she can taste the difference between Bud Light and Miller Lite. I imagined myself possessing a six pack of Bud Light and a six pack of Miller Lite. How could I use those six packs to test whether she really could tell the difference? What kind of experiment could I concoct that would lend some insight?
Two six packs doesn’t seem like much of a sample, but unless I want my test subject to get drunk enough to go home with me, it might have to suffice for the experiment. Let’s face it, we don’t often get to use large samples in our everyday researches, yet we must make decisions given regretable constraints.
My imaginary taster epitomizes one of my interests these days: what kind of knowledge might we glean from small samples of data? What kinds of odds would we demand if we bet on future outcomes of an experiment.
Some people ask the question as to whether God plays dice. Well, if there is a god, she forces us to play dice. That might suffice for all we need to know about God and chance.
I’m out on Twitter and run into this message at the site of a friend. Who posted it I do not know.
I’m a gymnast so I’m very flexible. Ever fucked a girl with her legs behind her head?
Actually, I did on more than one occasion.
