"We are such stuff as dreams are made on." Shakespeare, The Tempest

Monday, September 29, 2014

Proof

If you are not careful, you could come away from the film, Proof (2005) as a scientist, for the scientific method enjoys a starring role, albeit mostly in subtle undertones rather than in stark instructional flourishes in Technicolor. Essentially, the message is that confirming proof eludes the human mind and its scientific method. Yet interestingly, the film also captures genius, even if its source cannot be proven.


The film centers around Catherine, the daughter (played by Gwyeth Paltrow) of a brilliant math professor, Robert (played by Anthony Hopkins), who went insane and died; the story takes place just after his death. The dramatic tension is both in terms of relationships and questions of fact. Concerning the former, tension is most salient between Catherine and her visiting sister, Claire. Tension also builds between Catherine and her love-interest, Hal. In flashbacks, we feel tension also between Catherine and her father. Last but certainly not least, Catherine herself is riveted with inner tension, which comes to a major decision whether to go to New York to live with Claire taking care of her or to remain in Chicago to pursue Hal and mathematical notoriety and further advancement. In short, Catherine’s inner conflict lies in whether to buy into the paradigm in which she is deemed crazy or the alternative “story line” in which her apparent craziness is actually a natural reaction to having had to deal with her messed up father and sister.

In terms of questions of fact to be resolved, Hal and Claire seek proof establishing the authorship of the breakthrough mathematical proof written in a notebook locked in Robert’s desk. The handwriting seems to be Robert’s, but it is possible that Catherine’s own resembles his as the two worked closely together on mathematics. Also, it is not clear whether Robert was sufficiently sane to reason through such a momentous proof. Proof is therefore paramount, yet as Hal admits, the author cannot be proved. The film ends with him telling Catherine that in going through the mathematical proof together, the most he could do is prove that she could not have written it. This is none other than the scientific method in action!

In science, alternative hypotheses (i.e., propositions) are eliminated. The elimination can be known with certainty—that is, proved to be false. This is all that science portends; it cannot prove the hypothesis that the scientist asserts. In shooting down alternative explanations, the hypothesis is left standing, but this does not prove it. In trying to figure out who ate the cookies left out on a kitchen counter to cool off, we can eliminate the cat, sister Susie, fat brother Scott and even fat brother Jeff. This does not mean that Skip ate the cookies. That Skip has actually lost weight and is athletic would suggest that he is not the culprit, but this too is not proof. It is possible that the dog Skip (named after the brother) jumped up on the counter and chomped up the chocolate mistakenly taking it for another dog’s poop (this does not mean that the brother known as Skip has the same habit!). In short, eliminating alternative suspects does not prove that Skip is the culprit. Even so, science says we can have greater confidence that Skip is our man. Yet is such confidence warranted? We could be overlooking another alternative entirely. Suppose we are completely unaware that a friend occasionally stops by. The only person who knows is the mother, and she isn’t talking. She would gladly let her son Skip take the rap so she could go on leading a double life.

In the film, eliminating possibilities that Catherine could not have written the proof does not mean that she wrote it. It is possible that both she and her father could have written it. Yet the viewer is left with a distinct answer—that Catherine is indeed the author. In fact, we get to see the very instant in which she had the major insight, while she was reaching in her refrigerator. Seeing genius for what it is—a break-through of ideas past those that had been log-jammed or stymied—is perhaps much more revealing, not to mention satisfying, than whether Catherine actually wrote the proof. The flashback itself functions as proof, though even here this devise is shaky due to the salience of mental illness in the film. In other words, the viewer’s assumption that the flashbacks are meant to reveal what actually happened may be faulty, and thus hardly able to support proof. I submit, therefore, that the film is really about how limited the human mind is. Philosophically, the theme is on the epistemological limits of the human brain. We think we know a lot more than we do.