Proof

Notes on film “Proof” Does Logic Help? Rick Rayfield

Proof was a wonderful play on stages all over the country- it was popular because it was interesting, topical, heady, and easy to stage. The author David Auburn adapted his play for the screenplay with the help of Rebecca Miller. The movie is much larger than the play, but covers the same important ground- the relationships between the characters and especially Kate’s relationship with herself.. The movie adds a great physical feel for the University of Chicago, an epitome of ivory-tower academe to provide insight into the strivings of those in mathematics. The rest of the portrait of Chicago is almost stupidly pretty, like my best memories of 16 years there, living on the lakefront and the modern architecture (none of the best is seen in the film), but not realistic. The house at number 4655 is frankly a bad bad neighborhood, formerly upper class, now ghetto. Hollywood cleaned it up for a few weeks to make a movie. Or shot it in London.

Like the first three films in this series, the action is mostly talking. People trying to convince each other. “He IS a great man”. “I am NOT crazy.” “ You are not crazy.” “ You are no washed up, past your peak.” “ You should move to fun New York City” “ You should drink coffee with milk.” “ You should stop spending the day in bed.” So that’s rhetoric. The way arguments are made, the way we try to persuade people.

Is Robert Llewellyn there because Kate brings him alive in her mind as a rhetorical way of reviewing her past and talking to herself.? He is clearly an internal argument- even more striking on stage where the actor is right there. But is he a voluntary argument that she was conjuring up, a tool for thinking, for making an argument. Or is he an involuntary intruder, confusing and threatening? Crazy actually means cracked, broken into pieces, fractured. Does her father’s appearance after his death make her crazy? Do other people see her interacting with her dead father? (That’s a logical argument.)

That is their first conversation. Is she crazy? This film moves beyond rhetoric in the first argument. It moves into a portrayal of logic. Repeatedly during the film, the conversations are the kind you might expect of a mathematician. They are logical arguments. They do not appeal to experience, to narrative, to expertise, or our other classic methods of rhetoric. They refer to some high level form of thinking, familiar to philosophers and mathematicians, ones which are regarded as high levels of rationality.

He says- “ Crazy people do not ask the question about whether they are crazy. You are asking the question. So you are not crazy.” She ‘works” this logical argument and complains that “It does not make sense.” She disproves his syllogism with a counterexample. “You, dad, are crazy, we all know it. And you are asking the question.”

His response, also with a small delay, is to invoke a special exception, “But I am dead.” This of course has great dramatic effect- on stage and on film. She is talking with a dead person- is this voodoo or psychopathology or poetry? But its other impact is to set a stage for discussion at the level of proving and disproving linguistic statements with the kind of logic employed in mathematical proofs. It raises the question of whether these higher forms of rational discourse are superior, or just the strange ways of geniuses and their ambitious students. What is the place, and cost, or superior mental ability?

Let us return for a moment to our seven classic liberal arts and science. Without specifying a topic, we say the first thing to study is how argument and persuasion are made. Then grammar stresses the importance of precise in our language, so that we communicate clearly, so that what we say has good correspondence with our shared experience in the world. The language has its own logic which must be obeyed for it to do it job in communication. SO we have largely skipped grammar, and land on the third member of the Trivium (Rhetoric, Grammar, and Logic), before we wade into the Quadrivium (Arithmetic, Geometry, Music, and Astronomy). Proof nicely gives us a look at logic, and delves into Arithmetic as well. The relation of geometry and arithmetic may not be clear to you- geometry is done with representations of a perfect world of points, lines, planes, and solids. There is a beautiful correspondence of that mathematical world and the real world, encouraging us to believe we are at the threshold of truth. Freemasons use the letter G as a symbols of both God and Geometry, saying they are the same thing in several senses. If you think God is greater than Geometry, then you reveal your lack of understanding of what the whole of geometry involves. Music is also an expression of approaching the divine. Music is a combination of mathematical ratios, precise harmonies with human emotion. People identify music with sacred experience in religions around the world. Atheists the world over sing sacred music because it approaches the divine in which they do not believe. And who can deny the divinity of studying the stars- at once perfect and beautiful, yet asymmetric and unpredictable? As we move from Rhetoric to Logic, in Proof, we have a movie about human’s ability to approach the truth, to taste the divine.

Does being crazy help to see the brilliant truth of God’s creation, expressed in pure mathematics? Is craziness inherited? Does the ability to see the Divine in new ways peak in young adulthood? If so, why? People ask the same question about the physical performance, their sexual performance, the physical attractiveness. At thirty is it strictly downhill in these areas, with your biological clock ticking?

Back to the film. Watch a listen for the logic. “Just because I am paranoid does not mean that there isn’t anything in your backpack.” “How embarrassing is it if I say that last night was wonderful?” “It’s only embarrassing if I say it was wasn’t.”

If-then. Proof by disproving the opposite. Sensitivity to lack of logical connection. But the proofs are mostly about human relationships- prove that you love me, prove that you are safe living independently, prove that you respect me, prove that you deserve trust, prove that you mean what you say about me. And yes, prove that you wrote this. Is this mathematical proof any more important than the human “proofs’ in our lives.

At the funeral (in Rockefeller chapel where I was a tour guide for four years) the eulogists says it, “The work will endure.” What we leave behind is often judged more important than who we were, who we loved, who loved us, how our human life was lived. This movie is not really about mathematically geniuses with mental illness, it is about the search of each of us for truth in the universe, and human love in our lives. On stage, the whole play takes place on a porch. In our next film, Copenhagen, we will see the whole universe from atoms to galaxies discussed but two Nobel-winning physicist. Guess what- it about human nature, not mother nature. I knew a writer with a modestly successful book titled “Kill Shot” in reference to the characters who play handball for money at private clubs. Meeting him at dinner, I said I had read his book about handball and loved it, since I played handball in college. He was aghast. The book is not about handball, he said. It is about greed.. When Kate interrupts the funeral so rudely, she is actually bringing the human back into a setting that was trying to exemplify the divine in our most brilliant minds.

A few loose ends. Hal’s full teaching load is a bit odd. Chicago prides itself on not using grad students to teach courses, just faculty. So if he has a teaching load, it is as the assistant to a professor. I mention this mainly to point out that often in grad school, you receive tuition and stipend for either work as a teaching assistant or as a research assistant. In some cases, at large state schools mostly, grad students may actually be teaching. Watch where you enroll.

I mentioned Kate’s in-your-face remarks at the funeral. Just before she shocks us with, “I’m glad he’s dead”, she says “Proofs are like music.” My head just rattles. The profound observation of the shared value, rationality, and aesthetics of proofs and music is drowned out by the remark which follows. But is she glad for herself, or is she glad for him hat he is dead and no longer pained by his demons and lack of support and love by colleagues? Or is she once again simply saying some painful because she wants to lash out? You can love her, and you will not be alone. But she has a temper and a bit of a mean streak. Will she mature? Or is she just hurting, and once the pain of that past five years subsides she will be gentler, reasonable, and kind?

Kate says her father is graphomaniac, like a “monkey at a typewriter”. This is an odd phrase, meaning the monkey would turn out gibberish. Except we have a old saying in probability theory, that if you had roomful of monkeys with typewriters, eventually they would by chance turn out a King James Bible. Any reasonable application of real numbers to this make it an unreasonable metaphor for a crazy person working alone at a typewriter. But it sets up in our thinking the idea that maybe you have to be a bit crazy to succeed at the esoteric levels of math and physics, and thus a crazy person is a lot more likely than a roomful of monkeys to come up with something noteworthy.

The mathematical term “i” is the square root of negative one (-1). You cannot imagine a number which when squared gives a negative number. Square a negative number (-2 x -2) and you get a positive number. So “i” is the primoridial imaginary number. All other imaginary number are simply a real number multipled by “i”. This is the silent song the band performs, three minutes of silence, an imaginary song.

The huge prime number Kate knows by memory is real (both as a number and in real life as a prime), but has since been superceded by even larger Germain primes. The web pulls up several sites where math buffs post the newest Germain primes they have found and proven. The most recent ones are January and February 2007. At the time the movie was written, 92305×2*16998+1 was likely the largest Germain prime demonstrated. The web is crawling with math geeks arguing this point. This is their movie. Cheez.

When Hal goes into Kate’s room, he heads to the bookshelf. This gives us the premise that she is highly educated in math. But it is also how people in that community act in each other’s space. They head right for the bookshelves to assess interests, background, common teachers, politics, etc.

Northwestern University is on the opposite side of Chicago from the University of Chicago. It is a fine Big Ten school, with lots of excellent departments. However, UC is usually ranked up with Harvard, MIT, Texas, Berkeley, Oxford, Cambridge, and a handful of other top-class institutions, but all sorts of measures- top-ranked programs, entering SATs, number of journal articles per professors, faculty who belong to the National Academy of Arts and Sciences, Nobel prizes, etc.. For Kate to go to Northwestern is a step down from Chicago. This competition between top schools, and within departments, and between students for the top jobs is legendary in academia. Kate’s lien to Hal, “You have a bit of ground to make up.” may be about gaining trust, but I am pretty sure she means that he is not in her class in mathematical ability. At a high level of intellectual ability there is still pride, but there is also a frank assessment and acceptance of one’s abilities. A person can be pretty insecure and cold to one’s self.

This leads to my final note: Is Kate just hurting for the last five years, or is there some underlying psychopathology? Who are we to say? But she has been nearly autistic and reclusive with pretty clear numbers of days in bed that suggest depression. Does being a math genius make up for that? Does having a logical mind help her overcome her deficiencies? Does the logical, hard-working, imaginative mind she gleaned as her father’s daughter help her overcome her personality? Or is it the other way around?

While we are at it, did anyone notice the issue of whether a deranged person is better kept at home or in a supportive institution? He would have been worse. He might have been better there.

While the film maintains some suspense about the authorship of the proof, I think by the Hollywood ending, it is clear. It is also clear that whatever her problems, she is not going to be labeled and housed by her well-intentioned sister. Does that tell us she is not crazy? With an intellectually inferior partner headed for a second-choice career, she might be better off in New York? Does the author really let you make up you own mind about these issues, or do you just get the false impression that you have found the conclusion yourself. Did logic help?

Grammar, as I wade through these notes, I am irritated by typos, unclear writing, and other evidence of poor grammar. Poor communication gets in the way of meaning. If you are frustrated by bad writing, then you have the pulse of grammar- the importance of and even joy of good clear expression. Clarity takes much time and effort, sometimes even talent. I am posting these film notes with insufficient time to make them clean, and hoping they serve as an example of weak grammar. Hope they are useful anyway.

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