I came upon a video recently, titled “Dangerous Knowledge,” produced by the BBC. It profiles the life and times of three mathematicians (Georg Cantor, Kurt Gödel, and Alan Turing) and one scientist (Ludwig Boltzmann). For some reason it drew me in. I can’t embed the video here, but you can watch it by following the link.
The show makes allusions to an atheism which I find difficult to relate to this subject of crumbling certainty, the rise of contradictions or imperfections in logical systems, and the decay of what was thought to be permanent or static. Commentators in the show kept making reference to this idea that “God is dead.” It feels irrelevant to me. The important thing going on in the story is the destruction of the concept of the Newtonian mechanical universe. This is not the destruction of Newton’s theories of motion, but rather people’s misperception of his theories. Perhaps this is a European idea. Their concept of God, as it’s portrayed in the show, seemed to be deeply tied to this idea of certainty. Since these four people (not to mention the world around them) were destroying the idea of certainty, their concept of God was being destroyed as well.
Edit 11/17/2012: This was also about the limits of some of our mental perceptual tools, math and science. I think what drew me to this is it felt closer to the truth–that the notion that mathematics provides clarity, truth, and that our world or Universe are permanent was just a prejudice, which doesn’t hold up against scrutiny; that in fact our notions of truth have limits, and that everything in our world is in flux, constantly in a state of change.
I had heard of Cantor when I read “The Art of Mathematics,” by Jerry King. He talked about how Cantor had come up with this very controversial idea that there were infinities of different sizes, using the mathematical concept of sets. He proved the paradoxical idea, for example, that the infinite set of even (or odd) numbers was the same size as the infinite set of natural numbers.
What’s interesting to me is that through this program you can see a line of thought, beginning with Cantor, running through several decades, to some of the first baby steps of computer science with Turing. Turing’s inspiration for his mathematical concept of the computer (the Turing machine) came from the work of Gödel, and another mathematician named Hilbert. The work of Gödel’s that Turing was specifically interested in was inspired by the paradoxes raised by Cantor.
The video below is from the television production of Breaking the Code, which was originally written as a play by the same name. It’s about Turing’s life and work deciphering the Nazis’ Enigma encoding/decoding system, and his ideas about computing. The TV production puts the emphasis on Turing’s homosexuality and how that put him in conflict with his own government. The play got much more into his ideas about computing. There are a couple scenes in the TV version that talk about his ideas. This is one of them. I think it’s a perfect epilogue to “Dangerous Knowledge”: