Friday, September 18, 2009
The Insidious Agitation of the Ungraspables
When I was sixteen, my best friend and I were working one afternoon in the rectory next door to our school building, sorting files. We started talking, for some reason, about death. Where do you go when you die? How can one's "soul" live on forever? I said that I just could not grasp the idea of infinity--that something can have no end--that it could just go on forever and ever and ever and ever and ever. It did not compute, in my sixteen-year-old brain. It still doesn't.
I remember at one point we stopped talking about it, not because we couldn't find a satisfactory answer but because it just got too ... scary. The more you question one thing, the more you turn and question something else. It was like unravelling a thread on a tightly stitched garment. You risked pulling everything apart if you kept going, weakening its very foundation. In my world then, one didn't question such things; you just believed, as you were told, that some things always were and always will be. Period.
I went home that afternoon and thought about it some more. It totally consumed me. It made my head hurt thinking about it. I think I even clutched my head and screamed. It was the mental equivalent of trying to undo a knot closing in around my throat, unable even to begin to know where to look to untangle it. It was that frustrating.
Yesterday I stumbled upon this 2007 BBC documentary by David Malone in which he looks at four brilliant mathematicians –- Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing, suggesting that their mathematical inquires into the ungraspability of infinity drove them all insane, eventually leading them all to commit suicide (Cantor died alone in an insane asylum; Boltzmann hung himself; Gödel starved himself to death; Turin ate an apple poisoned with cyanide). Other, extenuating circumstances may have contributed to their decisions to end their lives (in Alan Turing's case, his having been convicted of the crime of homosexuality and given body-changing hormones, for example, and there's some question as to whether it was, indeed, a suicide), but they all suffered deeply mentally as a result of their attempts to answer some of these difficult questions.
The film is titled "Dark Knowledge" because any attempt to dislodge certainty is usually met with implacable opposition and hostility. These were men out of their time--they did it anyway, and paved the way for a continuation of the inquiry.
Seeing the film brought to the forefront musings I had pushed aside, which never completely subside for me. How is it that I "know" something that I do not actually know? One can intuit something that later proves to be true, and factually verify the truth of the thing intuited--but can anyone prove the origin, mechanical workings or even existence of intuition itself? And even if this could be proved mathematically, how would one explain it in layman's terms?
Mathematicians trying to explain intuition and infinity.... I was never very good at math. Abysmal, in fact. Ask my former high school Algebra teacher. I preferred words to numbers. But I wish I were--good at it-- I wish I could read the Principia Mathematica (or Wittgenstein or Kant or Hegel) with the ease with which I read fiction or poetry. (They, too, sometimes make my head swim, but for entirely different reasons: literature and art sometimes bring instant euphoria; math and philosophy's euphoria comes often only after a long, hard road toward comprehension. At least for me. Sometimes it has to do with language--the language of math, the language of philosophy. It doesn't communicate as readily as a story or picture.)
Subjects for another day. It's a very thought-provoking film, though.
For anyone interested:
David Malone's documentaries:
• The Flow of Time (1999), on the problem of explaining time in physics
• Testing God (2001), on the clash between science and religion
• Soul Searching (2002), on consciousness
• Voices In My Head (2005), on how science and religion interpret the phenomenon of people hearing disembodied voices
• Dangerous Knowledge (2007), in which he claims that some well-known thinkers have been driven to insanity by mathematical or scientific paradoxes.
• High Anxieties: The Mathematics of Chaos (2008), interviews with David Ruelle (chaos theory), Paul Ormerod (economics), James Lovelock (climate change, metaphors of tipping points or slopes)