Truth (and beauty), out of the corner of your eye

I'm not sure who the madman is, and I'm still thinking about what it means to dream of Turing machines. A Madman Dreams of Turing Machines is by cosmologist Janna Levin, and it's lovely. Potential madmen dreaming: Kurt Gödel, Alan Turing, and Levin herself. This reader, too. Dreaming, perhaps, of some quintessential truth, just beyond reach.

Kurt Gödel:

He is still all potential. The potential to be great, the potential to be mad. He will achieve both magnificently.

Everyone gathered on this Thursday, the rotating numbers accounting for some three dozen, believe in their very hearts that mathematics is unassailable. Gödel has come tonight to shatter their belief until all that is left are convincing pieces that when assembled erect a powerful monument to mathematics, but not an unassailable one — or at least not a complete one. Gödel will prove that some truths live outside of logic and that we can't get there from here. Some people — people who probably distrust mathematics — are quick to claim that they knew all along that some truths are beyond mathematics. But they just didn't. They didn't know it. They didn't prove it.

Gödel didn't believe that truth would elude us. He proved that it would. He didn't invent a myth to conform to his prejudice of the world — at least not when it came to mathematics. He discovered his theorem as surely as if it was a rock he had dug up from the ground. He could pass it around the table and it would be as real as that rock. If anyone cared to, they could dig it up where he buried it and find it just the same. Look for it and you'll find it where he said it is, just off center from where you're staring. There are faint stars in the night sky that you can see, but only if you look to the side of where they shine. They burn too weakly or are too far away to be seen directly, even if you stare. But you can see them out of the corner of your eye because the cells on the periphery of your retina are more sensitive to light. Maybe truth is just like that. You can see it, but only out of the corner of your eye.

And Alan Turing:

Where is God in 1 + 1 = 2? Nowhere.

Over the coming days and weeks and on into months, he feels the last of his spiritualism evaporate like the cooling remains of a fever. He is left without remorse and wonders how he ever clung to his awkward faith with such emotion. We're just machines. At the age of twenty-three and for the rest of his life he embraces, without reservation, a mathematics that exists independently of it. We are biological machines. Nothing more. We have no souls, no spirits. But we are bound to mathematics and mathematics is flawless. This has to be true.

Where is God in 1 + 1 = 2? There is no God.

[. . .]

To his great surprise his materialism is not so sad. He moves with greater ease and resilience and less fear. It is as though his eyes have suddenly come into focus from a nauseating blur and the whole world looks brilliant. All of his senses have sharpened so that colors and sounds and smells and textures are splendid and vibrant, his experience of them a heart-soaring joy. Every blade of grass glistens. The hard Cambridge wind batters respect out of him. The barren twist of every branch of every tree, even the weak fog of light, the whole of the world sings out to him as though he has never seen or heard anything before. With the sheer pleasure of this tactile awakening, his love of nature intensifies as though he has finally given over to her, wholly and without inhibition. Within days his spiritualism is no more than a mildly embarassing, childish memory. In its place is a calm, impervious materialism — nothing like the sad bleak emptiness he feared. He would have a bad time trying to put it into words. No single word could mean this thing. He would have to write something lengthy with many caveats and tangents and even then he knows he would not successfully express the immediacy or the splendor of the visceral experience. Maybe in another's mind better words would come, but not in his. And so his mind offers him something simple. Only one word comes to him over and again, and it could be only this — a word he doesn't often think to use: "beautiful." It is beautiful.

I won't pretend to know what this book actually means or what it aspires to do, beyond speculating as to the character and thought of these two eccentric minds, but it's quite beautiful. This is a fictional account of the lives of Gödel and Turing. There is no hard math here. The philosophical concepts Gödel and Turing played with are presented quite simply and often tangentially. There is no direct relationship between Gödel and Turing. Turing's work drew on Gödel's ideas, but they never met. But parallels are drawn, perhaps no more complicated than the fact that these are two geniuses firmly detached from reality. The story is told with a cool detachment, which proves to be highly poetic.

Excerpt.
Review by M John Harrison.
Interview (Quirks & Quarks, CBC) (mp3).
Janna Levin.

Related:
Jonathan Lethem and Janna Levin discuss truth and beauty (transcript):

Levin: Something I find particularly interesting is that science, I think, is the last realm in which people talk to each other seriously, with a straight face, about beauty. Visual artists would never say that's a beautiful piece of work, not in really contemporary, cutting-edge art.

Lethem: That's a very difficult phrase. After modernism, beauty is terrifically suspect.

Levin: Right, absolutely. And it's considered kind of provincial to aim for something beautiful. We're not doing pretty pictures here; we're doing something else. But in science, we really hold on to beauty and elegance as the goal because, for reasons that I think nobody fully understands, it's a good criterion for distinguishing what's right from what's wrong. And if something is beautiful and elegant, it's probably right. Occasionally, you'll see something that's so beautiful and so elegant, and it's not right, and you can't believe it's not right.

Status: normal

Head-y
A few weekends ago I went to the hospital. I thought my brain was going to explode. I get migraines quite regularly, and I've learned to cope — some ibuprofen at the first signs and a couple hours' sleep in a dark room as soon as the day-to-day allows will usually head it off. But they've been getting worse over the years.

I'd been battling a virus, even worked from home that Friday, as the effort of wearing something other than pyjamas just seemed a bit much that day. Was it a migraine I felt coming on? The pain of it woke me up; the pain of it had me throwing up for hours; the pain of it had me clutching my head and walking round in circles, scared that my eyeballs might squeeze out or that I'd start bleeding from the ears. This wasn't normal.

Of course, at the emergency room they couldn't simply shoot me up with drugs, much to my chagrin; they had to ascertain what was the matter with me.

Why do you say it's a migraine? Because, well, it's like a migraine, only it's so much worse I thought it might not be. Have you ever been diagnosed with migraine? No. Have you seen a doctor about these headaches? Uh, no. How long have you had these headaches? As long as I can remember. Just how bad are these headaches? I'm pretty much incapacitated for a couple hours — the light is screaming, I want to throw up, sometimes I throw up, I have to sleep it off. Your mother never took you to doctor for these headaches? Uh, no.

Various swabs and bloodwork, extracting a sample from inside my sinuses, some basic neurological tests. A CT scan — more frightening than ever I imagined it to be. I faced it alone, J-F having just then gone off to address the parking situation. Like some wierd ancient relic of technology with a Myst-like drone. I never felt my heart beat so hard. What happens if I move my head? if I twitch? I feel a twitch. My heart is going to leap out of my throat. Will I disintegrate or explode?

All negative.

The doctor can't tell me anything I don't already know: It's "just" a migraine. You obviously have some virus; that must be making it worse. She offers me an intravenous painkiller, but 8 hours on, that seems like overkill. (But oh, I would've killed for some earlier.) She gives me some antiinflammatories and sends me home. I want toast. And I'm unreasonably — it's completely backward! — afraid to sleep.

I've been referred to a migraine clinic.

Child-ish
An xbox 360 has recently been introduced into the household. I am unreasonably upset over the fact that I can't play Fable as a female character. I am unreasonably obsessed with the Ratatouille demo, which is unreasonably hard.

Last weekend, Helena started making valentines for all her classmates. Make a list, select a card, match an envelope, line them up, choose a chocolate, line them up. Write a name, cry, "Mommy, can you write "R" for me?," learn to write "R," select a new card, write "R" perfectly. Add a sticker, add matching stickers to the envelope, cry because they're not symmetrical, find another envelope, write the names all over again, stuff the envelope with a card, a candy, a chocolate, seal it with a sticker heart. We do this for hours. All day. And the next day too. Everything is pink and red.

I've spent every day since telling Helena, really, I think it's too early, we can't deliver them just yet, Valentine's Day isn't for more than another week, no one will even recognize what it's for, wait, didn't you forget someone on your list, you can't take them till they're all ready, you can't take some for some kids and leave one little girl out, that wouldn't be nice, it's still too early, if you take them now what will you have for your friends on Valentine's Day, maybe you should wait. I buy some time: one morning I suggest we take the leftover gummie hearts — we can leave one for everyone in their cubbyhole. She may have finally forgotten about the cards.

Book-ish
I've been reading faster than I can document it. No, not exactly — I'm managing to find time to read, at the expense of sleep, but can't find time or energy to write about it. Which is a shame, because The Painter of Battles, by Arturo Perez-Reverte was extraordinary, even though I don't think it exactly works as a novel; it's a powerful meditation on both art and war, and I recommend it highly.

Also read last week: A Madman Dreams of Turing Machines, by Janna Levin, of which I'd known absolutely nothing but to which I was committed it from the moment I read its title. Madman! Turing machines! Actually it's a fictional account of certain events in the lives of Kurt Goodel and Alan Turing. Geeky mathematicians!

(More on these books after I rein life in and dictate some terms on how my time gets allotted.)

"If the world were to end tomorrow what book would you read today?" is the question posed at Reading Matters. Answer: the book I've just passed the midway mark of: Zig Zag, by José Carlos Somoza, a real page turner! (What if you could, with complex camera arrangements based in string theory, see the past?) That is, the end of the world wouldn't change my reading habits at all, except that I'd probably have no time for reading, what with engaging in wierd and complex craft projects with a 5-year-old and trying to recpture some romance with my other half before it all goes up in smoke, but I'd really, really like to know how this book ends. I should go find out now.