Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Wednesday, June 23, 2010

Pi

In the genre of weird movies, there’s also π (1998) by Darren Aronofsky (who also directed Requiem for a Dream). The story’s main character, Max Cohen, believes that everything in the universe adheres to patterns that can be understood through numbers. At first he’s using his self-made supercomputer to predict the stock market. But then he meets a zealous Hasidic Kabbalist who hopes to decipher god’s code in the Torah through numerical calculations. At the same time, Max has been approached by a Wall Street firm, who offer him a superchip in return for his predictions. His computer prints out a string of 216 numbers, just like his old computer did before breaking down, just as his math mentor had just before he died, and through some epiphany he recognizes the spiral-shaped patter in the number-string. The Kabbalist and the Wall Street firm increase their pressure on Max, which sends him over the edge of sanity.

The film toys with the thin line between genius and insanity – the maddening truth, the truth in madness, like an Arthur Machen story, or a Terry Gilliam film. Perhaps the most profound statement in the movie is the mentor’s admonition, that “as soon as you discard scientific rigor, you are no longer a mathematician, you’re a numerologist.” This film is no advocate for scientific truths, though, as Max suffers from incapacitating migraines, nosebleeds, crippling hallucinations, paranoia, and possibly schizophrenia. In the end he drills a hole in his skull to be at peace – and never again think about numbers and patterns. Apart from the art-house hip black-and-white and the interesting soundtrack, I found the cinematography terribly annoying – what with the handheld shots, the quick cuts, and the extreme close-ups. Nevertheless, for those who wish to contemplate the ultimate truth – and whether to find it through science or mysticism – this may not be the worst way to spend your time.

Monday, April 5, 2010

Horizon: Infinity

Infinity: Does it exist? Mathematically, naturally: in theory you can always continue counting – forever. You can always add one to any number, indefinitely, or multiply it by any number. To express large numbers, we can say ten raised to the power of nine for one billion (one followed by nine zeros); ten raised to the power of one hundred is called a googol (one followed by one hundred zeros), and ten raised to the power of a googol is called a googolplex (a number so large it cannot be written down). But a recent BBC Horizon installment goes beyond the possibility of numerical infinity. Its actual existence, its reality beyond mathematics. A mind boggling matter. Is infinity an invention of the human mind? Abstract nonsense, if you will. Philosophically, infinity is close to divinity. God cannot be finite, cannot be proven to exist. It’s a matter of faith. You have to believe in divinity. But does it enhance your life to believe infinity is real?

If infinity is possible, then anything is possible – even as unlikely as a monkey typing the complete works of Shakespeare. “My bounty is as boundless as the sea, my love as deep; the more I give to thee, the more I have, for both are infinite.” (Romeo & Juliette II:2, 133-135) How unlikely is it? It’s one in 10 with nine million zeros!

Is the universe infinite, and if so, are there an infinite number of parallel universes, too? Is time eternal? Is it cosmologically possible for the universe to be infinite and eternal? Or, to put it differently, if space and time were finite, what’s beyond? If the universe is infinite, there would be an infinite number of planets like earth, with an infinite number of individuals just like you and me. How insignificant does that make us? And the nearest exact copy of us is only two to the power of ten to the power of 118 meters away... Naturally, when speaking about the cosmos, we end up talking about the Big Bang, about the inflation theory of the universe, and before we know it, we hear about the logical conclusion that there are infinitely many infinite universes, infinitely expanding... I hope that, like me, you feel that this isn’t making any intuitive sense. It’s baffling, but infinitely fascinating!