thoughts on Gödel's incompleteness theorems

I've been trying to understand Gödel's incompleteness theorems for over seven years. A few months ago I really dug in and understood the mechanics of the proof. But what does it mean? This is a frustrating thing about modern mathematics. Hermann Weyl complained about this very thing, that verifying every step in a proof does not necessarily lead to insight. I get how Gödel's proof works; I can lead you through the coding of sentences into numbers, the simple though long process of defining the analog within arithmetic of deduction within the formal system, the construction of the sentence which "refers to itself," and the ensuing double-contradiction from assuming that sentence is provable or its negation is provable. Yet I remain unsatisfied. What does it mean about the nature of numbers, and formal logic?
I have certain intuitions about it. There's something about the meanings of negation, universal quantification, and the combination of the two, that needs to be explicated. There's something about how logic tries to go "beneath" arithmetic and fails in that attempt; I think that you can't reduce one to the other, and that both are co-present before the embodied subject (my Merleau-Pontyian, hermeneutical best) who has the freedom to creatively interpret one in terms of the other, and neither has a true primacy over the other. There's something about infinity, and giving it a finite symbol, and acting like it's somehow contained in there while at the same time reasoning with it purely as a symbol (which is obviously self-contained and finite).
I keep thinking about it and I should probably stop for now. Push too hard and the gears grind. Rest, let your unconscious knit the brain into a new shape
It's similar to my frustrated resignation to the proof that √2 is irrational. I know that if it were rational you could reduce the fraction it to least terms and either the numerator or denominator would be odd, but then you show how for it to be the square root of 2 both must be even, and that makes a contradiction. But why? Numbers overflow the bounds of certain reductive methods we have to think about them. Maybe it's truly mysterious. But I want a better answer than that. There's some assumptions within logic, perhaps the static nature of classical logic, and that the language of logic needs to be separate from its domain of discourse for excluded middle to hold, and then Merleau-Ponty's idea of the body as a sensing-sensible which finds itself as a thing among things as the condition of possibility for sensibility, and perhaps the undecidable sentence of Gödel is such a sensing-sensible which disrupts the assumptions of classical logic. But I can't work it all out without what mathematicians derogatorily call "hand waving." Some day I'll come up with something.
Playing one brooding Austrian off another, allow me to quote Rilke at length:

 Leave to your opinions their own quiet undisturbed development, which, like all progress, must come from deep within and cannot be pressed or hurried by anything.  Everything is gestation and then bringing forth. To let each impression and each germ of a feeling come to completion wholly in itself, in the dark, in the inexpressible, the unconscious, beyond the reach of one's own intelligence, and await with deep humility and patience the birth-hour of a new clarity: that alone is living the artist's life: in understanding as in creating. There is no measuring with time, no year matters, and ten years are nothing. Being an artist means, not reckoning and counting, but ripening like the tree which does not force its sap and stands confident in the storms of spring without fear that after them may come no summer. It does come. But it comes only to the patient, who are there as though eternity lay before them, so unconcernedly still and wide. I learn it daily, learn it with pain to which I am grateful: patience is everything!

more about Fargo (spoilers)

As I said, I liked Fargo a lot. One thing was circumstantial; I didn't start watching until six episodes had been released, and I watched all six in rapid succession. That’s the way to watch this show. It has some of the most unsatisfying episode endings I’ve ever seen. If you don’t have to wait a week to see the next one, it’s not so bad. But after that sixth episode I had to wait, and that diminished the viewing experience.

Also, the show changed after the sixth episode. At the end of that one, Molly gets shot by Gus, the eternal fuck up. Up till that point the show had been frighteningly cold-eyed about its characters, in a Game of Thrones way, where you half expect  the most sympathetic character to be the next to die, in the worst way. But the follow-up on Molly’s gunshot was so lame. She wasn’t mad at Gus. The bullet “passed right through her,” and she was back at work in like a couple days.

Jesus, as I think about it now, Molly SHOULD have died. After that point in the show she did nothing. She recovered, was horrified that Lester somehow framed his brother while she was out, and then she made that poster of the connections of all the characters, which her boss made her hide. Then she married Gus, got pregnant, and did nothing for the rest of the show except lurk after Lester, and finally get promoted to chief in the finale for being “right for the job” (we were told that in the first episode), and for making that sweet poster (three episodes before). Imagine the pathos if Gus had killed her! That  would have been so much better!

My point is, the nihilism of the show let up after that sixth episode and revealed its soft little heart. I for one was disappointed. I’m not a groupie for Game of Thrones but its diabolic mission to slay and rape every sympathetic character makes for suspenseful television. Fargo seemed like it was going that way. The violence in Fargo was genuinely disturbing, and it crescendoed in the sixth episode with the brutal murder of that spray tan guy Chumpf. It was hard to watch, because it was so unfair.

Anyway, I wanted to say good things about the show. Um. I liked the acting, across the board, except for Martin Freeman. He has no emotions, ever. One could say that’s just the character of Lester, but one would be wrong about that. Martin Freeman never has any emotions. A better actor could have made Lester a more compelling character. I can’t think of someone off the top of my head, but William H. Macy is a sufficiently obvious example from the movie.

Anyway, I wanted to say good things. I liked the jump-ahead in time in episode 8. I liked Lester seeing Malvo in Las Vegas, and seeing Malvo play a completely different character. That whole set up at the start of the ninth episode, showing Malvo as a dentist, and Stephen Root’s character, and then his shocking execution of all of them in the elevator. Hell yeah. I liked the first episode a lot. (Except for Molly bringing the paint cans to the dead sheriff’s wife. That was a bit much.)  I liked how Malvo scared Gus at the end of the first episode. Hell yeah. I liked the music, how it suggested the original score but was actually different. I liked the heterogeny of the story structure. One could call it sloppy structure, and perhaps it was, but it was fun. I liked the story with Stavros, largely because Oliver Platt’s acting was fantastic. He found the briefcase of money from the movie and the moment he prayed to God for help, and then believe that God is real. Fantastic! I’d believe it too! Then he puts the money back but fish fall from the sky and kill his son. What does that mean? He yells to heaven, “But I put it back! I put it back!” Questions about God, justice, evil, and the show took an ambiguous stance on those moral questions. Evil and injustice happened constantly in the show, yet also there were miraculous occurrences. What is morality in such a world? Where is God in this situation? These questions were approached with both sensational violence and the light touch of humor, my favorite combination.

Oh, it was good fun. That's all.

Fargo (spoilers)

Last night the first season of Fargo ended. I really, really enjoyed the show, despite several imperfections. In part because I'm such a Coen brothers fan, I found the whole thing inherently interesting. Possibly the best cinematography I've seen on TV.
But, to the complaints. The last episode had a structural flaw that left a bad taste in my mouth. The opening sequence where they say "This is a true story" went like this: Fade from black. The camera moves languidly along tread marks in the snow. Fade out. Fade back in. A toppled snowmobile. Fade out, fade in. A vast stretch of snow, dramatic, jagged mountains in the background. Fade out, fade in. There is a rough hole in the ice, large cracks radiate from all its sides. The camera descends toward the dark water of the hole and fades to black. When it fades back in, we find Lester Nygaard where we left him last episode, in a very different time and place from the ominous snowfield. What was that mysterious opening sequence? Then the events of the episode happen, blah blah, Lester fights with Malvo and survives, Malvo is killed by Gus, and Molly hears the tape of when Lester called Malvo, which means she finally has him dead to rights. Show's basically over. Slowly fade to the indistinct blue-white of snowy ground, and, what's that sound? A whining motor. The camera pans up from the ground and hurtles along from the perspective of a speeding snowmobile. A title tells us we're in Glacier Park, Montana, two weeks later. Cut to: Lester on the snowmobile.
Goodbye all tension or surprise regarding the conclusion of the show and the fate of the main character. I watched the following two minutes not in a state of thoughtful and emotional engagement, but with frustration and disappointment. The problem is this: Lester is not an interesting character. We don't care about him, nor are we supposed to, except with a kind of detached curiosity. Because of his sins (and the fate of his alter ego Jerry Lundegaard in the movie), punishment is a foregone conclusion, death being the most obvious possibility. So the fact that he dies carries no weight in itself. At best, the way he dies could end the show with a bizarre or ironic commentary; but all thought was stultified by the spoiler opening. With no thought and no emotion, what you have is a flat ending to an otherwise great show.
The technique of spoiling the end is not an inherently bad one, but it requires a situation with more emotional involvement. Imagine this: the show begins the same way, with the cryptic sequence of snowmobile and hole in ice. The episode plays out. Fade to white snow, sound of snowmobile, camera hurtles through Glacier Park. Cut to: Molly on the snowmobile. What? No! That can't be! We saw the crashed snowmobile already, the person-sized hole in the ice...is Molly going to die? No! Now, whatever happens, we watch it rapt, saying no no no! This works because we like Molly and we can't believe she dies until we see it.
Even a similar thing would work if the character who died wasn't a good guy and their death wasn't tragic in the moral sense. Consider the death of Gus in Breaking Bad. Gus was the enemy and had to die. Yet Gus was such a fantastic character that you could basically spoil the fact of his death and it served to engage the audience even more. As Gus walked from his car to the retirement home to meet Hector, he was filmed in slow-motion, close-ups, to music appropriate for a climatic Western gunfight. That sequence was nothing except a goodbye to a character we love, not because he's good but because he's a great character. We didn't know for certain, plotwise, how things would turn out for him, but with that cinematic salvo as he literally did nothing but walk into a retirement home, we knew.
I have more to say about Fargo. I'll try to come back and say some good things about it.

Humanism and Terror

Last night I finished Merleau-Ponty's book Humanism and Terror. It's been a longstanding project of mine to understand what the hell Merleau-Ponty is talking about. His politics are an indispensable dimension of his total philosophy, so Humanism and Terror was enlightening for my slog through Phenomenology of Perception. He's a Marxist. Before this, I knew nothing intelligible about Marxism, barring Ayn Randian slander, and personal judgments of my own about the personalities of Marxist types in college. Politics is not a passion for me. As the child of divorced parents who are on opposite ends of the political spectrum, any political position I could take was a losing one. The inability to fall into any party line has been a benefit for me, in my opinion, because I think I have a clearer perspective about politics than almost everyone. I float above them like a ghost while they're dug in the trenches with guns in hand. However, this ghostly ability to pass through walls is crippling: I've never voted. As I said, politics is not a passion, it's a burden. I long for the day I can vote in good conscience.
When it comes to politics, I tend to hate almost everyone. Politics makes people deaf and dumb, stupid and awful, sectarian and inhumane. It's not an accident. The world is full of terrible things, children starving and dying, people profiting from the misery and murder of others, and anyone who sees this should become worked up into a frenzy to stop it. But frenzy never solved anything. That's the paradox of politics. You must have a surgeon's tolerance for blood, or a hitman's.
I sincerely believe that everyone wants the world to be a better place, and what they mean by "a better place" is really the same. But there are different philosophies about how to achieve this better place, and different ways to understand what this better place is, and people, being the specific individuals they are, are born into a specific family, a specific culture, and it teaches them the details of this better world, and they inherit their enemies. Politically, almost everyone is a xenophobe, because as feeling creatures they want to see the world improve and they have precisely one fragile notion of a better world, and literally everything else is a stumbling block to the eradication of evil.
Merleau-Ponty (at the time he wrote Humanism and Terror) is a Marxist, but he's ambivalent. He doesn't effuse praise on every move the Communist Party makes, and he drives home more than any other point the contingency of history. For Merleau-Ponty, contingency is the heart of everything. Every position one takes, every act, has no guarantee of success. He bemoans in the introduction to the book the stupidity of his critics who will not tolerate his ambivalent opinion and willingness to criticize the Communist Party. He reports one communist who said, "To engage in conversation is already to lay down one's arms." Throughout the book Merleau-Ponty describes the dirty reality of revolutionary politics. He is an apologist for communist violence, because he believes violence is the only way to disrupt the violence of liberalism. Liberalism, in his opinion, is a proven evil. Communism has at least the merit of not yet proving that it's evil, and of holding a noble ideal for the future of "more human relations between men." For reasons I don't understand, he sees Marxism as the only hope for the future. He goes so far as to say: "Marxism is not a philosophy of history; it is the philosophy of history and to renounce it is to dig the grave of Reason in history. After that there can be no more dreams or adventures."
Emerging from my own ambivalence, as a teenager I read The Fountainhead and was very moved by what Ayn Rand said. She was my introduction to both philosophy and politics. Nowadays I think Ayn Rand was basically an insane person, but she provided a kind of "square one" for my own politics, in the way I imagine being raised Christian would inform your thinking the rest of your life even after you leave the church. It only enforces my belief that people are born into their political prejudices. I can't help it, when it comes to communism or anti-communism, I will fall toward anti-communism. I don't like that, and that's why reading Humanism and Terror has been so enlightening. The only reason I could even take the book seriously is because I've heard it said that Merleau-Ponty ultimately rejected communism in favor of liberalism. I don't like feeling like I'm stuck in a trench. Merleau-Ponty's description of the proletariat helped me understand how someone could be a Marxist. I can't summarize what he said, but it's a beautiful vision of universal humanity (in a way) and I see how a person could stake their life on it (not that I would.)

that book Freedom

To completely destructure this blog right at the start, I'll write about a book instead of a movie. A few years ago I saw some prominent reviews in different newspapers about Freedom. As far as I knew, it was the first book to be published since the last Harry Potter. It's been long enough now that nice hard copies of it have trickled down to the sales shelves at libraries for like $2. I bought a copy last year ($2) and read the first 60 or so pages. Today I was stuck at the library and saw it on the shelf and killed a little time with it while I ate a bagel. What a stupid book. I hate New Yorker fiction. The author, in line with my criticism of comedy actors in my last post, is not involved in the lives of his characters. He's a creep, he leers at them, but he doesn't truly care. The single best word to describe the book is: gossip. Sarcastic, sentimental, safe, and ultimately it exists for the author to prove something about himself. I particularly don't like know-it-all authors. Creating a character is very difficult, but it's too easy to say "She was this kind of person," as if you can talk about "kinds" of people and not be an asshole.

First post: Neighbors, Jurassic Park

I've wanted to do some kind of writing about movies for a long time and I figure now I should just start a blog and write about movies (and probably TV shows) as I see them. Not sure what it will look like, maybe scanty, but it will reveal itself.

Neighbors

There is obviously a major strain of comedies now from the Judd Apatow lineage, and they're without fail pretty amusing. The actors all seem to be having a good time, and that makes up for deficiencies of plot or character depth or any kind of "meaningful" reason for the movie to exist. Neighbors has nothing going for it except the charm of the performances. Shaggy lack of story structure can be done well when there actually is a satisfying structure carefully hidden beneath the seemingly laid-back surface. Last summer's This Is the End is a good example of a deceptively well-structured story. Neighbors is not. The plot lurches forward in episodes, as the two battling houses (if you want a summary of the plot you can go find it somewhere on the internet) come up with new attacks on each other. A character says "We need to do something." Another character says, "How about this?" The first character says, "Yeah, let's do it!" Then they do it. The fun of the movie is watching the characters execute their schemes, not watching them "think."

Seth Rogen is amusing, but not particularly interesting. All of his characters lack depth. He rarely displays vulnerability or emotions. This is a criticism I have of a lot of comedy actors, where they don't involve themselves in what's happening, but instead constantly remove themselves from the situation in one way or another. (Steve Carell is one example. His emotions never seem real, they're too cartoony, or over-expressive. Martin Freeman is another one, off the top of my head, who has this problem, though his problem is more verbal and under-expressive, like Rogen. He comments on what's happening, but he's rarely really there.)

Jurassic Park
I saw Jurassic Park today at the new(ish) Empirical Theater at OMSI. Holy Christ, what a theater. They got rid of their IMAX dome and replaced it with the biggest god damn movie screen I've ever seen. (Between that and Cinetopia, I now have access to some of the technically best movie theaters in the world. Yay!) Perhaps it was the overwhelming size of the screen, or the density and volume of the sound system, or my girlfriend clutching my arm and thrashing in her seat during the scary parts, or the little kids behind me whimpering, "Mommy, I want to go home...Mommmy, please, I'm scared..." or maybe the movie is just really well made, but whatever the reason, it was one of the most suspenseful, exciting, and scary movie experiences I've ever had. Like, adrenal exhaustion, I-need-to-eat-a-nutritious-meal-right-now-preferably-with-brown-rice-in-it, upon leaving the theater.

The characters were mostly uninteresting. Laura Dern did nothing but smile amiably for the first half, and then grimace and scream during the second half. The main paleontologist guy had no personality except that he inexplicably hates children, and then learns to love them. Jeff Goldblum was there for his excess of personality; he had no plot significance whatsoever, except to utter portentous philosophical things about chaos theory, and then have the camera linger on his sweaty chest. Fortunately the rich Scottish guy who owned the park was not made into a caricature. However thin the characterization was, I was totally engaged by the danger of the dinosaurs. Some of the best suspense you'll find in a movie.