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December 1, 2009

Dangerous Knowledge

Posted by John Baez

It’s been around a while, so maybe you’ve already seen it… but I just heard about the BBC documentary called Dangerous Knowledge. According to the summary, it’s about “four brilliant mathematicians — Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing — whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide”. And now you can see it on YouTube.

It sounds fun, or at least fun to complain about. Did Cantor really commit suicide? I thought he died of a heart attack. Was Ludwig Boltzmann a mathematician? I thought he was a physicist. And did Alan Turing commit suicide because his genius drove him insane? I thought it had something to do with the British government convicting him for homosexuality and punishing him by forcing him to take estrogen, which made him grow breasts.

But the documentary is more fun than the summary. I’m watching it right now. It’s charmingly dark and edgy, featuring lines like:

Cantor is wonderful because… it’s so crazy! It’s the equivalent of being on drugs.

What could the greatest mathematician of his century have seen that could have driven him insane?

If you have a friend who’s a goth, and you’re trying to explain to them why you like math, have them watch this.

Here’s the summary from the BBC website:

In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.

The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God’s messenger and was eventually driven insane trying to prove his theories of infinity.

Ludwig Boltzmann’s struggle to prove the existence of atoms and probability eventually drove him to suicide. Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death.

Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

The film also talks to the latest in the line of thinkers who have continued to pursue the question of whether there are things that mathematics and the human mind cannot know. They include Greg Chaitin, mathematician at the IBM TJ Watson Research Center, New York, and Roger Penrose.

Dangerous Knowledge tackles some of the profound questions about the true nature of reality that mathematical thinkers are still trying to answer today.

At least right now, you can watch the show on YouTube:

Part 1.

Part 2

Part 3.

Part 4.

Part 5.

Part 6.

Part 7.

Part 8.

Part 9.

Part 10.

(Thanks to André Joyal and Mike Stay for pointing out this show.)

Posted at December 1, 2009 7:31 PM UTC

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Re: Dangerous Knowledge

What could the greatest mathematician of his century have seen that could have driven him insane?

This old trope again? This is almost as bad as beating down .99999… = 1 again and again.

I posted a relevant excerpt from David Foster Wallace’s excellent book Everything and More shortly after his own felo de se a year ago. As it concludes, “Saying that infinity drove Cantor mad is sort of like mourning St. George’s loss to the dragon: it’s not only wrong, but insulting.”

Posted by: John Armstrong on December 1, 2009 10:56 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Surely I can’t be the only person on the categories mailing list who’s also read this blog post, can I?

And to second JA, anything that reportedly peddles a line in “kerrrraazy maths guys! eh?” does not fill me with confidence.

Posted by: Yemon Choi on December 1, 2009 11:06 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Instead of fighting the old trope of the ‘crazy mathematician’, maybe we should enjoy it and exploit it. First of all, it’s a lot more fun than the trope of the ‘dry and soulless calculator’. Second of all, maybe we can use it to get away with some irresponsible behavior. Artists do that sort of thing all the time. Why can’t we?

Posted by: John Baez on December 1, 2009 11:41 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Most likely that is already the case, could be that you act pretty weird every day and get away with it without realizing it.

Posted by: Tim vB on December 2, 2009 12:34 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Maybe we can use it to get away with some irresponsible behavior. Artists do that sort of thing all the time. Why can’t we?

Because we can’t all snuggle in the cozy bosom of the ivory tower, and those of us on the outside have to convince bottom-line driven hiring managers that a mathematician is not a dangerously unstable and risky investment.

Posted by: John Armstrong on December 2, 2009 12:42 AM | Permalink | Reply to this

Re: Dangerous Knowledge

“managers that a mathematician is not a dangerously unstable and risky” - and what is about managers? Acc. to Hare, Birbaumer and other leading psychopathy experts, dangerously pathological people are highly overrepresented among them, esp. in the financial markets.

Posted by: Thomas on December 2, 2009 1:07 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Tim vB wrote:

Most likely that is already the case, could be that you act pretty weird every day and get away with it without realizing it.

That’s completely false. I do realize that I act pretty weird every day and get away with it! I’m even doing it right now.

That’s one of the great things about academia: certain kinds of behavior are acceptable there that aren’t in most other careers. It carves out a space where otherwise marginal people can live useful and happy lives. Without academia, I might have had to eke out a hand-to-mouth existence doing something like techno music.

John A. wrote:

… we can’t all snuggle in the cozy bosom of the ivory tower, and those of us on the outside have to convince bottom-line driven hiring managers that a mathematician is not a dangerously unstable and risky investment.

Yes, that’s unfortunate.

But anyway, I was just kidding: I’m not really calling for more documentaries promoting the image of mathematicians as dangerously risky nuts. So as long as those managers don’t read the nn-Category Café, you’re probably okay.

Posted by: John Baez on December 2, 2009 3:14 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Actually, I’m not convinced that the hiring managers are so rigid. My impression is there are plenty of them that know the difference between the eccentric character that gets the job done and the unreliable suave personality.

In fact, I would say there are at least a few business managers that are much more open-minded than the typical dean or provost, perhaps because the bottom-line induces a universality of sorts.

Posted by: Minhyong Kim on December 2, 2009 10:20 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Maybe there are plenty of them, but I’ve still been asked at almost every interview something to the extent of “given that you come from a research math background, are you actually able to get anything done?”

Posted by: John Armstrong on December 2, 2009 3:54 PM | Permalink | Reply to this

Re: Dangerous Knowledge

John Armstrong muttered:

I’ve still been asked at almost every interview something to the extent of “given that you come from a research math background, are you actually able to get anything done?”

I don’t think that’s so likely to be about mental instability, though, but about whether someone used to the ivory tower can work with practical requirements, including all the compromises that entails.

Posted by: Tim Silverman on December 2, 2009 4:44 PM | Permalink | Reply to this

Re: Dangerous Knowledge

e.g. deadlines

Posted by: jim stasheff on December 3, 2009 2:55 PM | Permalink | Reply to this

Re: Dangerous Knowledge

I’m not sure if I understand why you object to this question.

The software company I work for does not even invite anyone to an interview who hasn’t a master in computer science. (In case you wonder: I haven’t, I applied at a time when they desperately needed someone).

Why? If you haven’t, it will take too much time to get you up and running. If you have in addition a Ph.D. in, say, physics, that means that it will take too much time to get you up and running, you will expect to be well paid (because you invested in a Ph.D.) and you will get bored pretty soon and leave anyway before you get anything done.

In any case, a question like “given your background, why should we believe that you can get the job done we will pay you for” seems legitimate to me.

Posted by: Tim vB on December 3, 2009 4:47 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Tim, it’s not about “why should we believe that you can do this job?” The question is, “why should we believe that you can deliver anything on time ever?”

But maybe you’re right and getting a Ph.D. in mathematics has made me absolutely unhirable outside of academia for entirely justifiable reasons. Maybe businesses are entirely correct that mathematics and logical problem-solving skills are – in and of themselves – worthless and suited only for the erratic fringe.

And in response to Tim Silverman, I don’t see “absentminded dilettante” as being too far a stereotype from instability.

Posted by: John Armstrong on December 3, 2009 6:24 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Sensing some desperation there - you know that sometimes your personal experience is not a trustworthy source to draw conclusions from? Next time you try everything could be entirely different.

Let me play the career consultant, if our hosts allow me to (I have no idea if anything I write is of any use to you, but I’ll try anyway):
Try to look at it from the other point of view: Your employees complain because they have too much to do, your customers complain because you don’t deliver on time, you realize: You need to hire someone. You look for someone who exactly fits the profile, right? If you can’t get that special someone, you settle for the next best thing. Up to this point the story is pretty much the same, in every part of the world with a working capitalistic economy. Believe me, cultural differences will kick in, but only later in the process.
I apply for the job, which means, I want you to buy my workforce, which means I have to convince you that I am worth your money
Now your personality and experience kicks in: Let’s say after highschool I spend one year travelling Asia. If you did something similar and enjoyed it, good for me. If you went directly to college and consider what I did a waste of time, bad for me (which one is more likely depends highly on country and culture, so I have to consider carefully if I want to emphasize this in my c.v.). If you graduated in math and enjoyed it, good for me (not very likely, in any country or culture). If not, you probably had some bad experience with math, but you desperatly need to hire someone! So you ask some critical questions, based on your past experience. Maybe you even try to take revenge for insults you had to suffer during highschool! But I am prepared and - most important - don’t take anything you say personally…

I don’t want to get this (admittedly very much off topic) post too long, but here is one personal anecdote: Once I had to travel to Stuttgart to the Daimler AG as an IT-consultant, during a chat an employee of Daimler asked me:
“So, by the way, what did you graduate in?”
Me: “Theoretical physics.”
He: “What? I didn’t expect that in the least! I mean, you know, these dudes are freaks! You know what I mean? Did you ever try to talk to one of those guys?”
(Looking me straight in the face all the time. I think it was meant as some kind of compliment).

Posted by: Tim vB on December 3, 2009 8:14 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Another anecdote: A former Ph D student of mine has done very well by selling himself as a go-to guy for problems where math might be relevant - not that he knew the math but he knew how to look but, more importantly, he could listen to ‘engineerspeak’ and extract the mathematically relevant part

Posted by: jim stasheff on December 4, 2009 1:26 PM | Permalink | Reply to this

Re: Dangerous Knowledge

There has been one opportunity for me to make a show of my “education”:
Once upon a time we had to program an “algorithm” that was supposed to classify vehicle components, input data were parameters like “complexity”, “function” etc. output parameters were milestones. These would be taken as a starting point to schedule a new model from the first draft up to mass production (to be fast at this is a critical advantage for every company that builds cars).
The algorithm was written down by a math Ph.D. who “did it in a way that is the clearest possible one” and then left. Can you guess what he did? He wrote a ten page tex document full of funny symbols (well, just a bit set theory and algebra).
After I had recovered from a severe fit of laughter I realized that I was the only one in a team of a 100 programmers and managers who could read and understand it.

Posted by: Tim vB on December 4, 2009 2:46 PM | Permalink | Reply to this

Re: Dangerous Knowledge

While we’re on the subject of how people from the world of business are suspicious of those who seem to come from academia, let me just note that it works the other way around, too. If you get a math PhD, maybe teach a while, then go into industry, and then try to get back into academia, it’s very hard!

Every single stereotype that paints academics as unsuitable for work in business has a flip side that comes into play here.

Posted by: John Baez on December 4, 2009 5:54 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Agreed, which is why once you try to switch there’s practically no going back. Or forward, it would seem.

Posted by: John Armstrong on December 4, 2009 6:50 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Among the Ph.D.’s I’ve either supervised or co-supervised, there are three that I know to be working quite happily in non-academic institutions. It seemed to depend a lot on their personality. The majority of people getting their degrees (at any level) from University College where I currently teach seemed to plan on obtaining some kind of employment in the city.

Posted by: Minhyong Kim on December 5, 2009 12:46 AM | Permalink | Reply to this

Re: Dangerous Knowledge

<Maths PhDs outside maths departments>

I should emphasize that I don’t think nobody with a maths PhD is capable of working outside a maths department, or anything at all like that. Although there was a short period in my career when the several maths PhDs I was working with all seemed to exhibit (different) stereotypes of the ivory tower academic, this is not the normal situation and I have worked with many maths PhDs in industry who have been excellent workers.

If I ask an interview candidate about whether they can adjust, I’m not dismissing them a priori as absent-minded buffoons—or I wouldn’t be interviewing them! I just want them to show some awareness that industrical research is not like academic research, and that they have thought about what this means to them. Other than that, bright people who are flexible and keen to learn are of course an asset.

Posted by: Tim Silverman on December 5, 2009 12:58 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Yes, this was essentially my thought as well. Whichever way one happens to be moving, harboring simplistic sterotypes of the other side can hardly be constructive. For one thing, it might induce unnecessarily defensive reactions during an interview!

Posted by: Minhyong Kim on December 5, 2009 3:58 PM | Permalink | Reply to this

Re: Dangerous Knowledge

This reminds me to mention something that slipped my mind, maybe because it is too much a matter of course to me now:
If you get invited to an interview, that means that the bosses very much hope that they can hire you and move on. They are busy!
Nobody will take the time to talk to you to tell you that you are not capable!
The proposition “they invited me to an interview, but did not hire me because I’m a research mathematician” is inconsistent. There must be some other reason.

Posted by: Tim vB on December 5, 2009 4:39 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Presumably it’s not unheard of to take a little poke at a job candidate and see what sort of reaction it provokes. Maybe someone did this to John Armstrong.

Posted by: John Baez on December 5, 2009 5:44 PM | Permalink | Reply to this

Re: Dangerous Knowledge

In case anyone needs more advice after the excellent comments from the two Tims, I thought I’d suggest that Math Ph.D.’s seeking jobs in industry not expect too much compensation at the outset. It’s not your employer’s business to take care of the years you’ve invested in education and you’ll clearly need to work your way up. Happily, in the three cases I mentioned earlier, the ascent took place quite rapidly.

Posted by: Minhyong Kim on December 6, 2009 2:40 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Not to worry. Luckily academics doesn’t offer much compensation either.

Posted by: John Armstrong on December 6, 2009 3:49 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Well, even that point is frequently exaggerated. But mostly, I meant one shouldn’t take offense when the inequalities

Ph.D. \geq MA \geq BA

are contradicted.

Posted by: Minhyong Kim on December 6, 2009 9:24 AM | Permalink | Reply to this

Re: Dangerous Knowledge

A tad more seriously: I would not want to completely pooh-pooh the idea that there’s some relation between certain forms of extreme creativity and certain forms of mental instability. Someone somewhere must have done a serious study of this.

Posted by: John Baez on December 2, 2009 12:01 AM | Permalink | Reply to this

Re: Dangerous Knowledge

I doubt that there is any connection, and this BBC “documentary” is probably one of the most interesting - well, whatever you call it - that’s ever been published about it.
There is of course a vast literature about gifted people who develop mental conditions because they cannot adapt to their environment for various reasons, by specialized therapists/psychologists.

Highly gifted people often act in a way that could look like they have some well known mental condition to the unwary observer.
Example: You are very gifted and therefore start a very ambitious project. You become very enthusiastic about it, telling people “no one has ever tried this before (with success)!” Of course they will not understand why anyone would get this excited about proving a theorem, painting a picture or writing a novel. Then you get stuck and despair.
Most people will get the impression that you suffer from a bipolar disorder (which is very annoying to both you and to anyone who really has a bipolar disorder, to say the least).

Posted by: Tim vB on December 2, 2009 12:50 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Conc. bipolar disorder and creativity, some acquaintances recommended Jamison’s collection of cases “Touched with Fire”. But an other acquaintance, who is a well known neurologist, thinks the data are insufficient to draw conclusions.

Posted by: Thomas on December 2, 2009 3:30 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Here are video lectures from a recent Caltech conference, the 2nd talk by Matilde Marcolli is on bipolarity and creativity. I am very impressed about her strength to hold a talk on visibly very moving and personal issues (e.g. colleague’s and student’s suicides last year).

Posted by: Thomas on June 23, 2010 12:46 PM | Permalink | Reply to this

Re: Dangerous Knowledge

I would not want to completely pooh-pooh the idea that there’s some relation between certain forms of extreme creativity and certain forms of mental instability. Someone somewhere must have done a serious study of this.

This isn’t quite the same issue as you’re talking about, but somewhat related: there is a stereotype that sufferers of bipolar disorder can be particularly creative during their manic phases. The composer Robert Schumann is believed to have had bipolar disorder, and I once read about a case study analysis attempting to check out this stereotype in his case. The researchers used Schumann’s diaries and letters to guess when his manic phases occurred and compared this to which pieces he was working on at the time. Then they attempted to measure the quality of pieces by their frequency of performance (yes, that’s a highly imperfect measure, but what better could you do?).

The conclusion was that Schumann, unsurprisingly, wrote more music during his manic phases (which are typically associated with high energy levels and less sleeping than normal). But they found no correlation at all between the quality of his music and whether it was written in a manic phase.

Of course, if you want to posit the hypothesis that people with bipolar disorder tend to be more creative overall than people without bipolar disorder, then this case study does nothing to disprove that.

Posted by: Mark Meckes on December 2, 2009 2:22 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Even if his writing wasn’t any better during his manic phases, getting a lot of writing done is not of no value. After all, practice might not be sufficient for talent, but it sure is necessary.

Posted by: MPL on December 13, 2009 10:40 PM | Permalink | Reply to this

Re: Dangerous Knowledge

For a milder form correlated ? with creativity:

Posted by: jim stasheff on December 2, 2009 2:27 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Hear hear.

And it’s also an interesting balancing act looking after someone with both Asperger’s and bipolar, who is an artist to boot!

Posted by: David Roberts on December 2, 2009 10:41 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Well yes: Freud, Lacan… For some psychotics, art or science can indeed help handle their so-called symptom.

Which by no way means all psychotics are good artists or scientists; neither that good scientists of artists are necessarily psychotics.

Which also does not mean at all that being a psychotic is being inferior to some phantasized normal person. Lacan often paid tribute to the psychotic’s «rigor».

Posted by: Ergo on December 3, 2009 1:30 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Someone in Iceland found a statistical link between mathematical ability and psychosis. The article appeared in the British Journal of Psychiatry in 2004. I corresponded with the author briefly at the time.

The article can be found here. It was only a rather crude statistical study. I’m not sure if it was followed up.

I certainly feel that mathematics makes me some variety of insane, and don’t know how any mathematicians manage to avoid that.

Posted by: Eugenia Cheng on December 16, 2009 11:56 PM | Permalink | Reply to this

Re: Dangerous Knowledge

A new study on “Psychosis and Academic Performance” (communicated by May-Tzu).

Posted by: Thomas on April 5, 2010 11:16 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Someone once told me this story about a weird renaissance sort of “dangerous knowledge”.

Posted by: Thomas on December 2, 2009 12:07 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Yeah, but my friend who is a goth, Sam Nelson, is already a mathematician.

Maybe we need to produce mockmentaries about normal theorem loving mathematicians who live in at the edge of the mountains in suburban communities and make excellent Indian food.

Posted by: Scott Carter on December 2, 2009 12:47 AM | Permalink | Reply to this

Re: Dangerous Knowledge

I’ve noticed that when I do abstract math a lot of time continuously it’s better for me not to think of something like what self-consciousness is. Because if I do it my awareness shunt with itself as having positive feedback. And it affects me very strong so I should quickly switch my thoughts to some neutral topic.

Posted by: quantense on December 2, 2009 9:12 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Here’s a related cartoon (where I found out about the video a while ago):

Abstruse Goose: The Cantor Madness.

Posted by: Perry Wagle on December 8, 2009 8:12 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Before anything else, excuse me for my bad English, I’m trying to improve it. Now, may be I did not paid enough attention at reading the comments but it seems to me that no body answered the questions made by Professor John Baez, I mean: Did those great mathematicians really commit suicide? I’m intrigued.

Posted by: Julio Cesar Salazar on December 12, 2009 4:16 AM | Permalink | Reply to this

Re: Dangerous Knowledge

Those questions were ‘rhetorical questions’. I didn’t really want answers… unless I’m very confused, in which case I would like to be corrected.

Did Cantor really commit suicide? I thought he died of a heart attack.

His MacTutor biography says he died of a heart attack, not suicide! More precisely:

In October 1899 Cantor applied for, and was granted, leave from teaching for the winter semester of 1899-1900. Then on 16 December 1899 Cantor’s youngest son died. From this time on until the end of his life he fought against the mental illness of depression. He did continue to teach but also had to take leave from his teaching for a number of winter semesters, those of 1902-03, 1904-05 and 1907-08. Cantor also spent some time in sanatoria, at the times of the worst attacks of his mental illness, from 1899 onwards. He did continue to work and publish on his Bacon-Shakespeare theory and certainly did not give up mathematics completely. He lectured on the paradoxes of set theory to a meeting of the Deutsche Mathematiker-Vereinigung in September 1903 and he attended the International Congress of Mathematicians at Heidelberg in August 1904.

In 1905 Cantor wrote a religious work after returning home from a spell in hospital. He also corresponded with Jourdain on the history of set theory and his religious tract. After taking leave for much of 1909 on the grounds of his ill health he carried out his university duties for 1910 and 1911. It was in that year that he was delighted to receive an invitation from the University of St Andrews in Scotland to attend the 500th anniversary of the founding of the University as a distinguished foreign scholar. The celebrations were 12-15 September 1911 but:

During the visit he apparently began to behave eccentrically, talking at great length on the Bacon-Shakespeare question; then he travelled down to London for a few days.

Cantor had hoped to meet with Russell who had just published the Principia Mathematica. However ill health and the news that his son had taken ill made Cantor return to Germany without seeing Russell. The following year Cantor was awarded the honorary degree of Doctor of Laws by the University of St Andrews but he was too ill to receive the degree in person.

Cantor retired in 1913 and spent his final years ill with little food because of the war conditions in Germany. A major event planned in Halle to mark Cantor’s 70th birthday in 1915 had to be cancelled because of the war, but a smaller event was held in his home. In June 1917 he entered a sanatorium for the last time and continually wrote to his wife asking to be allowed to go home. He died of a heart attack.

Next question:

Was Ludwig Boltzmann a mathematician? I thought he was a physicist.

According to his biography, “In 1869 Boltzmann was appointed to a chair of theoretical physics at Graz. He held this post for four years and then in 1873 he accepted the chair of mathematics at Vienna. He did not stay very long in any place and after three years he was back in Graz, this time in the chair of experimental physics.”

Most people today consider him a physicist.

He hanged himself while his wife and daughter were swimming, on a holiday with at the Bay of Duino near Trieste. What a terrible thing to do to your family! Poor guy!

And did Alan Turing commit suicide because his genius drove him insane? I thought it had something to do with the British government convicting him for homosexuality and punishing him by forcing him to take estrogen, which made him grow breasts.

Alan Turing died of cyanide poison. Quoting Wikipedia:

On 8 June 1954, Turing’s cleaner found him dead; he had died the previous day. A post-mortem examination established that the cause of death was cyanide poisoning. When his body was discovered an apple lay half-eaten beside his bed, and although the apple was not tested for cyanide, it is speculated that this was the means by which a fatal dose was delivered. An inquest determined that he had committed suicide, and he was cremated at Woking crematorium on 12 June 1954.

Turing’s mother argued strenuously that the ingestion was accidental, caused by her son’s careless storage of laboratory chemicals. Biographer Andrew Hodges suggests that Turing may have killed himself in an ambiguous way quite deliberately, to give his mother some plausible deniability. Others suggest that Turing was re-enacting a scene from the 1937 film Snow White, his favourite fairy tale, pointing out that he took “an especially keen pleasure in the scene where the Wicked Witch immerses her apple in the poisonous brew.”

Also: “An urban legend holds that the logo of Apple computers is a tribute to Alan Turing, with the bite mark a reference to his method of suicide, something that the company denies.”

I read somewhere that earlier in his life, Turing fantasized about the possibility of suicide by poisoned apple. Anyone know?

But, before reading the summary of this documentay, I’ve never heard anyone claim Turing’s genius drove him insane! That seems implausible.

Posted by: John Baez on December 12, 2009 7:25 AM | Permalink | Reply to this

Re: Dangerous Knowledge

I don’t think that by any stretch Alan Turing’s genius drove him insane. But I (very vaguely) remember sitting in a talk by Andrew Hodges where he said that Turing’s views on science and philsophy (and thus foundational mathematics) were very strongly influenced by trying to “deal with” Christopher Morcom’s death (which affected him very deeply), as breifly hinted at here.

So it could reasonably be said that there was a link the other direction between his emotional sensitivity and the particular choice of his mathematical/philosophical breakthroughs. (One imagines he might have produced some other breakthroughs given different life experiences but they might not “stand out” as much in other fields.)

This doesn’t contradict Todd’s larger point below that such all 4 possible combinations of (genius,hypersensitivity/insanity/whatever) occur.

Posted by: bane on December 12, 2009 3:03 PM | Permalink | Reply to this

Re: Dangerous Knowledge

I recommend the `novel’ (but many incidents with documented sources)
A Madman dreams of Turing machines by Janna Levin

`palpably human portrait of solitary genius’ - Phila Inquirer

Posted by: jim stasheff on December 13, 2009 2:58 PM | Permalink | Reply to this

Re: Dangerous Knowledge

I didn’t think he (John Baez) was asking the question seriously; it was more a rhetorical question whose answer is ‘no’.

Did Kurt Gödel commit suicide because of his genius? I think his death is considered partly attributable to mental illness, specifically paranoia, which led him to refuse to eat anything after his wife Adele died for fear that it was poisoned. That’s suicide in a sense, but I wouldn’t say it was attributable to his genius per se.

Did Alan Turing commit suicide because of his genius? I think John answered this one himself; the answer is almost surely ‘no’. He died by eating a cyanide-laced apple and suicide is presumed, although he left no suicide note. It is widely believed that it had something to do with the treatment imposed on him after being convicted of engaging in homosexual acts (he chose to undergo ‘therapy’ in lieu of a prison sentence, which involved hormonal treatments which caused him to grow breasts among other things, as John has already noted). I don’t think that means he committed suicide because of his genius.

Did Ludwig Boltzmann commit suicide because of his genius? My understanding is that he did in fact commit suicide: not only did he suffer from depressions, but he was a sufferer of excruciating headaches and was going blind, and when he became convinced that he was no longer able to work, took his own life. (I can track down my source of this if need be.) I don’t see that that means he committed suicide because of his genius.

Did Georg Cantor commit suicide because of his genius? I, like John, wasn’t aware that he committed suicide. He did suffer from depression, but again, how is that attributable to his being a genius, exactly? (Rhetorical question; it isn’t necessarily.)

The idea that a thin line separates genius from madness seems to me a well-worn trope, a kind of Romantic myth. There are many extremely gifted people who do not suffer from mental illness, and many who suffer from mental illness who do not possess extraordinary intellects. Somehow though this Promethean myth must strike a very deep chord in a lot of people.

Posted by: Todd Trimble on December 12, 2009 7:51 AM | Permalink | Reply to this

Rimbaud’s deadly legacy; Re: Dangerous Knowledge

I deeply agree with Todd Trimble.

Speaking as someone who’s spent a lifetime tilting at the “Two Cultures” windmill, starting with a double B.S. in Math and English Literature at Caltech, it is precisely a “Romantic myth” that “a thin line separates genius from madness.”

The myth is more insidious and deadly than that. It goes on to assert that the Artist has an active responsibility to push himself/herself into the abyss for the sake or art. What Rimbaud (not himself a Romantic as such) asserted in a letter to a friend, dated 1871: “the Poet makes himself a seer by a long, immense and systematic derangement of all the senses.”

I have seen too many friends drive themselves to failure and death by this pressure.

Yet note that, late in life, Rimbaud rejected this all, and begged to be snailmailed in Africa such things as astrolabes. He spent years in Harar, in Somalia (or Somaliland), which Nicholls, who followed the Rimbaud trail, describes as ‘a long way from anywhere.’ Caltech has postdocs working on “Romantics” just as they have postdocs studying the life of Newton.

We use the phrase “morally equivalent” metaphorically in Math. But this myth is as purely immoral as any that I see taught. I say “Thank you!” to John Baez and others here for speaking truth against suicidal nonsense.

Posted by: Jonathan Vos Post on December 12, 2009 6:41 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

Conc. the ‘Romantic myth’: As far as I know, the romantics tried to connect with the ancient greeks, where that idea came from. I guess it survived mainly because up to the renaissance, “mathematicians” was the name for astrologers, magicians and alchemists, whose tendency to poison themselves by heavy metals should have turned “geniuses” into madmen frequently. Until the 20th century, scholar’s poverty and unhealthy life should have had similar effects on the public perception, e.g. an acquaintance who is historian once told me that ca. 1/3 of university students acquired infections producing madness a few decades later. Understanding “romantic myths” needs a look at what health/age relations then were. It is not surprising that creative people then became disinterested in their personal future and preferred destructive tries to intensify their next few years.

Posted by: Thomas on December 13, 2009 4:27 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

Interesting; I’d not thought of this connection. My own associations when I wrote “Romantic myth” had not much to do with mathematicians per se (even taking ‘mathematician’ in a broad sense, including astrologers and alchemists), but more with the image of the “tortured artist as hero”, as epitomized perhaps by The Sorrows of Young Werther, and including other works associated with so-called Sturm und Drang and early Romantic literature. The genius-madness link would perhaps spring from the idea of the artist as under the spell of, or in thrall to, a kind of divine inspiration, of an almost Dionysiac character, where reason and order are left far, far behind. This general current would be in opposition to tendencies of a more “Apollonian” character (also traceable in some respects to ancient Greek culture) that upheld the virtues of light, order, and reason – values associated with the Enlightenment as well, against which Romanticism can be seen as reacting. Or so I am given to understand.

I really do think that more recent narratives about mathematicians tap into this paradigm, thinking for example of movies like Pi and A Beautiful Mind (despite an opposing idea that mathematics is the province of sober rationality). My guess would be that the BBC documentary, which I haven’t watched, is exploiting similar ideas, of intuition flying so high that it comes crashing down, as in the myth of Daedalus and Icarus.

Posted by: Todd Trimble on December 14, 2009 4:23 AM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

My guess would be that the BBC documentary, which I haven’t watched, is exploiting similar ideas, of intuition flying so high that it comes crashing down, as in the myth of Daedalus and Icarus.

Those who haven't watched the documentary should remember that it is rather more sensible than the summary. Your guess should be that the summary writer was exploiting similar ideas.

Posted by: Toby Bartels on December 14, 2009 5:27 AM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

How could those who haven’t watched the documentary ‘remember’ that it is more sensible than the summary?

Posted by: Todd Trimble on December 14, 2009 3:36 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

Todd objected:

How could those who haven’t watched the documentary ‘remember’ that it is more sensible than the summary?

By remembering that Toby just told us that it is!

Posted by: Tim Silverman on December 14, 2009 4:29 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

Yes, thanks Tim, I know he meant that. ‘Remember’ is synonymous here with ‘be apprised’. It just reminds me of the imperative “recall” in mathematical discourse: how am I supposed to recall something if it’s the first time I’ve heard of it? :-)

(Try to see some humor in this, please.)

Posted by: Todd Trimble on December 14, 2009 6:49 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

How could those who haven’t watched the documentary ‘remember’ that it is more sensible than the summary?

Because John said so earlier in the thread!

Except I see now that he didn't say so; he wrote ‘the documentary is more fun than the summary’. It was only reported on the categories mailing list that the documentary is also more accurate than the summary.

Anyway, now I'm telling you (since I have watched it): the documentary is more accurate and less sensationalistic than its official summary. So now you can remember it, as Tim suggested. (^_^)

Posted by: Toby Bartels on December 14, 2009 8:03 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

Right, I had checked back with John’s original post just to see whether there was something about ‘sensible’ I was supposed to have remembered, and noted the ‘fun’ as you have now. In fact, John wrote that with what I took to be a bemused air, as indicated by the choice quotes, which should by all means be shared with our goth friends. ‘Sensible’ didn’t exactly leap out at me from his description.

Anyway, duly noted. I will cast no further aspersions on the documentary before watching it. :-)

Posted by: Todd Trimble on December 14, 2009 10:10 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

I think part of the problem may be this: when I first wrote this blog entry, I kept tinkering with it and changing it for about a day, so some of you may have seen different versions. I think one of these earlier versions said the documentary was more ‘sensible’ than the summary — or something like that.

It certainly is more sensible than the ridiculous summary quoted above! But I decided I didn’t want to get myself in the position of defending a somewhat interesting but somewhat silly documentary. So I wound up saying it was more ‘fun’, hoping that was sufficiently vague and double-edged to avoid offending anyone.

I actually found it quite fun! So, I urge everyone to randomly pick a 10-minute segment and watch it.

(I keep trying and failing to find an online version of one of my favorite New Yorker cartoons. It shows two balding, grumpy, tweedy professors sitting in overstuffed armchairs in an old-fashioned faculty lounge. One of them says to the other: “At least we never stooped to popularizing science!”)

Posted by: John Baez on December 15, 2009 9:02 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

Thomas reported that:

[a] historian once told me that ca. 1/3 of university students acquired infections producing madness a few decades later.

That doesn’t sound right to me. Lots of university students acquired infections that killed them in short order, or left them disabled, disfigured or in pain for decades, but then so did lots of people from all walks of life. I don’t recall a particularly high incidence of madness among scholars from my reading in the history of science. I think I’d have noticed if a third of them went mad.

I guess alchemists would have been in some extra danger of heavy metal poisoning, but I’m not sure this would actually have stood out against the background of industrial accidents and other occupational hazards in the medieval and early modern period.

I’m inclined to agree with Todd, that the trope of ‘insanity of great mathematicians’ is an adaptation of the broader trope of the divine frenzy which produces great revelations, whether religious, oracular, poetic, philosophical or scientific. This can already be found in ancient Greece (for instance, I vaguely recall that Plato discusses a supposed resemblance between madness and poetry somewhere—or maybe it’s between poetry and prophecy; sorry, it’s been a long time and the memory isn’t as clear as I thought when I started this sentence). And one finds similar ideas in other cultures too (revelation through hallucinations, etc).

One partial source of these is, I think, the (accurate) observation that achieving extraordinary things (including extraordinary knowledge) often requires enormously hard and prolonged work which can, if unregulated, drive people to the point of a nervous breakdown; another the belief that extraordinary benefits come (or “ought” to come) at an extraordinary price; a third a supposition that extraordinary achievements are in some way out of the natural order of things, and therefore cannot be achieved by a normal rational human being in the ordinary course of normal activities—that they must come in some sense from outside the person (hence the annoying question, asked more often of novelists than mathematicians: where do you get your ideas from?)

Of course, there is also the fact that a story is often more compelling if it is simple and dramatic rather than—like life—complicated and mundane.

Posted by: Tim Silverman on December 14, 2009 4:50 PM | Permalink | Reply to this

Re: Rimbaud’s deadly legacy; Re: Dangerous Knowledge

Speaking of Rimbaud’s deadly legacy: some of you will remember some of the films dating back to the 80’s on Rimbaud and his intense, restless, tortured existence.

My favorite of these movies is probably “Premier Sang”. In one memorable scene, the police are out to capture the vagabond Rimbaud; his former associate explains to the constable what manner of man they are dealing with:

“If you’re going to fight Rimbaud, you’d better remember one thing.”

“What’s that?”

“Better bring a good supply of body bags.”

:-P

Posted by: Todd Trimble on December 14, 2009 4:03 PM | Permalink | Reply to this

Re: Dangerous Knowledge

Haven’t read the entire thread, but the same fate has been ascribed to Nietzsche, whom some philosophers with a theological bent have claimed succumbed to madness on account of his own denial of any kind of objective value or truth in the universe.

I’m more inclined to think his breakdown was a byproduct of syphilis, with its debilitating effects on the nervous system.

Posted by: rqabrams on December 16, 2009 10:50 PM | Permalink | Reply to this

Re: Dangerous Knowledge

When Pierre Bertaux was director of the french Sûreté, he ordered an investigation and concluded that Nietzsche had no syphilis or other illnesses, but poinsened himself by misusing his “Dr.”-titel for accessing very huge amounts of dangerous drugs. An other interesting, but questionable, idea of Bertaux was that Hölderlin only simulated a mental disorder.

Posted by: Thomas on December 17, 2009 12:34 PM | Permalink | Reply to this

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