Bring vor, was wahr ist.
Schreib so, dass es klar ist.
Und verficht’s, bis es mit dir gar ist.
Dangerous Knowledge is a 90-minute long BBC documentary about the lives of four great thinkers: Georg Cantor (1845-1918), Ludwig Boltzmann (1844-1906), Kurt Gödel (1906-1978), and Alan Turing (1912-1954). Cantor founded Set Theory, Boltzmann founded Statistical Mechanics, Gödel’s incompleteness theorems had an immense impact on Mathematical Logic, and Turing was one of the fathers of Computer Science. Why these four scientists? What is the pattern? The answer is that all four of them committed suicide.
The documentary is a bit too sensationalist for my taste. Its message is that these four brilliant minds were driven to madness (and, ultimately, to suicide) due to the earth-shattering nature of their ideas. While one could argue that such a claim is not too far-fetched in the cases of Cantor and Boltzmann, it seems somewhat distasteful when applied to Turing. Turing did not go insane because of the depth of his revolutionary insights. Turing’s homosexuality was viewed as a security problem during the troubled times of the Cold War, and the brutal punishment which he underwent (chemical castration) was probably what led him to take his life. Gödel feared that someone was poisoning his food, and would refuse to eat unless his wife would taste his food first. When his wife was hospitalized for some time, Gödel starved himself to death. Hence, the claim that these four suicides were due to “dangerous knowledge” seems rather crude to me.
On the bright side, the claim that these four geniuses were ahead of their time sounds rather plausible. Cantor’s or Boltzmann’s ideas did not meet fierce resistance because they were technically wrong, but because they challenged the belief that the universe was perfect and orderly. No one wanted to hear about Boltzmann’s work on entropy, because entropy is, by definition, a measure of disorder. As Hilbert’s program tried to fix the inconsistencies in the foundations of Mathematics, Gödel’s incompleteness theorems made Hilbert’s monumental mission “wir müssen wissen, wir werden wissen” seem even harder to accomplish.
In my most humble opinion the times were not yet ripe for theories that imposed limitations on human knowledge. “What about Heisenberg’s uncertainty principle?”, I hear you ask. Good point. Do note that two decades can make a world of difference. Heisenberg’s work was created when Quantum Mechanics was already out of the box. By contrast, Boltzmann had to fight the 19th Century establishment that was still deeply entrenched in the Newtonian paradigm.
If you have a couple of hours, here are the documentary’s videos:
Greg Chaitin and Sir Roger Penrose are included in this documentary, which itself makes it worth watching.
Tags: Alan Turing, Documentaries, Foundations of Mathematics, Georg Cantor, Kurt Gödel, Ludwig Boltzmann, Mathematicians
September 1, 2009 at 06:29 |
This could be seen as part of the ‘evidence’ that he’d gone crazy because of his ‘dangerous knowledge’. The same thing is posited in the book Uncle Petros and Goldbach’s Conjecture. Although the book is fiction, it has quite a bit about real mathematicians. There’s a scene where the main character is taken to a common room, perhaps at Princeton’s Institute for Advanced Study. A strange old man is pointed out, all wrapped up in a winter coat on a warm day. It’s supposedly Kurt Gödel.
September 1, 2009 at 06:34 |
I’m so glad you brought up how Turing died. It’s such a crime. I really enjoyed reading Alan Turing: The Enigma. He helped the Brits save lives by decoding messages that the Germans had encoded using their ‘Enigma Machine’, by developing one of the world’s first computers. He should have been knighted, instead he was persecuted.
September 1, 2009 at 14:31 |
The way Turing was persecuted by his own country was, indeed, truly sickening. He probably would have been treated better by the Nazis if he had been captured during WW2. By the way, there’s this ongoing petition:
Some people ask for Turing’s posthumous knighting.
He did help the Brits crack the Enigma cypher, but (contrary to popular belief) he was not the one who cracked it, actually.
The merit of cracking the Enigma cypher belongs to Polish cryptographers (earlier in the 1930s). After the invasion of Poland by Nazi Germany (on this day, 70 years ago), Polish officers took the knowledge to Britain, and helped the allies win the war. If Britain saved Europe, then Poland may have saved Britain.
September 4, 2009 at 01:55 |
I think the whole idea of “dangerous knowledge” only really persists because it’s a wonderful fictional trope. I can think of perhaps three first-rate mathematicians — Cantor, Grothendieck and maybe Gödel — who seem to have exhibited no pathological behavior before they did their greatest work, and then went more or less crazy afterwards. My impression is that Boltzmann suffered bouts of depression (and maybe mania) from early adulthood. I’m also not counting people like John Nash, who is an exceptional case because he did incredible work very early on and had a somewhat later onset of schizophrenia than the average.
Certainly, though, at least in Cantor’s and Boltzmann’s cases, it would make sense that the stress of criticism from the scientific community would aggravate a preexisting condition if nothing else. This was also perhaps true in a different sense for Galois, Bellesque romanticization aside.