Someone on Twitter drew my attention to a BBC4 television documentary by David Malone from 2007 about mathematics. Interested I thought I would give it a whirl, I wish I hadn’t. It’s a sort of biography of Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing so what could go wrong? It’s called Dangerous Knowledge but Dangerous Twaddle would have been more appropriate.

In my opinion it starts off with a real humdinger: atmospheric images with the following dramatic voice over:

Beneath the surface of the world are the rules of science but beneath them there is a far deeper set of rules. A matrix of pure mathematics, which explains the nature of the rules of science and how it is we can understand them in the first place.

Ignoring the fact that I don’t actually agree with this piece of trite metaphysics, the author completely blows it in my opinion because another even more dramatic voice over follows this with the following quote:

To see a World in a Grain of Sand

And a Heaven in a Wild Flower

Hold Infinity in the palm of your hand

And Eternity in an hour

This is of course one of the most well known quotes by William Blake taken from his Auguries of Innocence. Malone is obviously ignorant of Blake’s opinion of the mathematical description of the world.

God forbid that Truth should be confined to Mathematical Demonstrations! (Written as a marginal note to Reynolds’ Discourses.)

Before we get down to the real reason that I’m writing this a couple of things that annoyed me whilst watching this documentary. The author-narrator mispronounces the names of both Leibniz and Dedekind. One would think that if somebody is making a documentary about mathematics and mathematicians they would at least take the trouble to get the names of famous mathematicians right. At the end of the section about Cantor he describes him as the greatest mathematician of his century! Regular readers of this blog will know that I intensely dislike such superlatives in the history of science. Even if I didn’t, is Cantor really the greatest mathematician of the nineteenth century? There’s an awful lot of competition. In the section on Gödel, we get told about his friendship with his fellow Austrian mathematician, Albert Einstein.

Now, I know that trying to keep track of Einstein’s nationality is rather difficult for the non-historian; he had a total of eight different ones including being stateless for five years. However, he was only a citizen of the Austrian Empire from April 1911 to July 1912, as professor at the University of Prague. Eleven months out of a life of 76 years hardly justifies calling him an Austrian.

My real beef with the documentary is contained in a further piece of voice over from the introduction:

… pursued the questions to the brink of insanity and over it.

Basically Malone spends eighty minutes telling the world that if brilliant mathematicians think outside the box it can and will drive them insane! This is quite simply bullshit!

He devotes the largest part of the documentary to Georg Cantor and the invention of set theory. I found his explanations of what Cantor achieved and why he did it totally opaque and I spent quite a lot of time at university studying and understanding it. Malone gives a totally bogus explanation of the continuum hypothesis, which suggests very strongly that he simply doesn’t understand it, and then goes on to explain that it was Cantor’s inability to prove the continuum hypothesis drove him insane. I will return to this.

We then move on to Ludwig Boltzmann and his championing of a probablistic atomic theory when the majority of physicists and philosophers opposed the real existence of atoms. Once again Malone tells us that it was Boltzmann’s science that drove him mad and led him to commit suicide.

Although it is always dubious to make historical diagnoses of illnesses, in particular mental ones, Both Cantor and Boltzmann displayed all of the symptoms of a severe bipolar disorder. Bipolar disorder is not caused by mathematical research or any other work for that matter. A stressful working situation might well aggravate an existing bipolar disorder it won’t cause it. This is as I said, dangerous twaddle.

Malone now accelerates his gallop into the realm of total crap with his segment on Kurt Gödel. Following the usually incorrect statement of Gödel’s incompleteness theorem. People almost invariably leave off the very important final “within the system” in their accounts. What Gödel showed in that we cannot produce a formal logical system within which all true mathematical statements are provable. However this does not mean that the statements that are unprovable within the given system are fundamentally unprovable, as Malone claims in his statement of Gödel. However this is a minor quibble compared to Malone’s central claim. He states that Gödel took up the continuum hypothesis and because he like Cantor was unable to prove it, he too went insane. Now, it is well known that Gödel displayed serious symptoms of mental illness that got increasingly worse as he got older, until he quite literally starved himself to death due to his paranoid belief that somebody was trying to poison him. I’m not a clinical psychiatrist, but I’m more that willing to state that Gödel’s ability or lack of it to solve the continuum hypothesis did not cause his mental illness. Malone, however, seem to be totally unaware that Gödel in fact showed the continuum hypothesis was consistent, i.e. cannot be proved false, with the axioms of Zermelo-Fraenkel set theory. This is one of the major breakthroughs in the history of set theory; far from being frustrated by the continuum hypothesis Gödel produced one of his most important results with it.

Malone closes out his trip through the insane and suicidal mathematical geniuses with none other than Alan Turing. Following up on the usually false claim that Turing invented the computer and a very confusing explanation of Turing’s achievements in meta-mathematics, Malone takes us forward to Turing’s death. He has the British secret service responsible for Turing’s chemical castration following his conviction for indecency, which is just simply crap. Turing was offered a choice between a prison sentence or probation with the hormonal treatment as a condition by the court. He freely chose the later. I’m not even going to enter the discussion of whether he committed suicide or not and if he did why. There has already been enough ink spilt on that particular topic.

Malone made a documentary about four major figures in the history of mathematics, logic and mathematical physics and presents the quite honestly laughable thesis that it was their intellectual audacity and the opposition that they experienced to their theories that drove them insane. This is quite simple put, bullshit. As someone who has experienced, at time quite serious, mental illness I find it quite frightening that an organisation such as the BBC is not only prepared to air such crap but to finance it with obviously comparatively large sums of money. We live in a society where it is extremely difficult to explain to people what mental illness is and such pseudo-psychological bullshit as Malone’s documentary does nothing to help with this problem.