In the interim, since we last left the story on Logicomix, the Greek Logic graphic novel is currently riding high on success at # 1 on the NY Times bestseller list for paperback graphic novels and has also debuted at #14 on the Indiebound Bestsellers list. The authors are also currently touring the United States (insert map of tour cities). The story of logic, math and madness is catching fever worldwide.
Speaking of fever and as the authors of Logicomix are quoted in the beginning of the making of Logicomix as saying that the journey of the novel began upon the observation that many logicians and mathematicians of the 20th century ended up insane during the course of their lives; do logic and madness go together? Bertrand Russell, the protagonist of Logicomix,himself had a fear of hereditary madness throughout life after his parents died and he moved in with his grandparents at a young age. His Uncle Willy was shut away from the eyes of the world as a violent lunatic and his Aunt Agatha too was a little insane. Math, was then a refuge for young Russell. Is it a complete co-incidence that many of the 20th century mathematicians like Cantor, Godel, John Forbes Nash Jr etc., in a quest for the foundations of mathematics were hospitalized in asylums at one point of their life or another?
Russell Crowe plays John Nash in A Beautiful Mind
Brilliance of any kind has had an element of the eccentricity attached to it but madness doesn’t go together with the study of logic always. Again, many among the logicians of the twentieth century did have a medical history of depression and disorders which revealed themselves during the course of their work.
Richard Zach examines the theme of logic and madness well on the LogBlog. Zach refers to a number of other biographies and books on mathematicians. He writes in response to Frege’s portrayal in Logicomix as a raving lunatic and an anti-semitic in the comic book:
As you can see for yourself, the diaries reveal the very dark side of Frege's political views: reactionary, anti-semitic, anti-catholic, anti-socialist. But: Frege didn't write "increasingly rabid treatises" over "the last decades of his life"—these are diary entries written over two months in the very last year before he died. As far as I can tell, he never advocated a "final solution" to the "Jewish problem" with anything like the meaning that these terms have taken on, and he didn't use this Nazi terminology. There is no indication that he admired Hitler (he opposed the Munich Putsch of 1923), and there's no indication that his anti-semitism was racially motivated or anywhere near the level of the Nazis. But most importantly: He wasn't clinically paranoid. As objectionable as his views are, they were widespread in Germany at the time (Had they not been, Hitler would never have come to power). Moreover, if he had been paranoid, this would, I think, absolve Frege of moral responsibility. After all, we don't hold people morally (or legally) responsible for their actions when they're insane. So: Frege: reactionary anti-semite, but no Nazi, and not insane.
Taking into account that globally several million people are diagnosed as suffering from depressioned and with other mental illnesses/disorders diseases, Zach writes:
The National Institutes of Mental Health puts the percentage of the US population with "serious mental illness" at 6%. What's the percentage of pioneers of logic with a serious mental illness? We've found four, but what's the sample? Let's say Rota had in mind the authors of papers in van Heijenoort's From Frege to Gödel. That's 30, and doesn't even include Tarski, Lukasiewicz, Church, Fraenkel, Gentzen, Turing (all not insane), or many of the less well known people working in foundations at around that time. So: 13% of the pioneers of logic had a serious mental illness. But with a sample of 30, the margin of error has to be huge. I'm no statistician, but using the standard formula, I get a margin of error of ±12% (ok, I know you probably shouldn't use the standard formula for samples this small; if you know stats, help me out, please). This suggests that there's good reason to think that Rota's claim is just wrong: it may very well be pure coincidence.
The logic that Zach presents perhaps stands true for even for a population sample containing comprising artistes with mental disorders. Sheer brilliance and creativity has always gone hand in hand with eccentricity, and rage and fervour. There seems to be inherently a fine line separating the two. But what seems interesting is that the fact that, more than just logic or art being linked linking with madness, genius definitely seems to be have elements of the insane. Often, as discussions on depression have bordered, intense personal suffering often increases a person's sensitivities to broader philosophical questions and reasoning. How true this is, still requires more studies. But a casual examination of the greatest minds reveals high statistics incidence of famous people with a history of depression history. Names include the likes of Art Speigelman, At Linkletter, Van Gogh, Emily Dickinson, Winston Churchill.
Math=madness has become pet subject of writers in current culture; but there's no way to generalise this. And it shouldn't be generalised either.For every Cantor, there's a Van Gogh. Creativity in Math and creativity in Arts is different as far as things go. Many people disagree with the stereotypical treatment that mathematicians and scientists are given in films and literature. In conclusion (at least for this post, as we are entering murky deoths which requires more reearch), one can refer to the Unapologetic Mathematician, where bloggerJohn Armstrong quotes from Everything and More by David Foster Wallace, where the latter speaks of this treatment of mathematicians in popular culture by (Direct lift of quote from Unapologetic) saying:
“In the late nineteenth century, an extraordinary mathematician languished in an asylum. . . . The closer he came to the answers he sought, the further away they seemed. Eventually it drove him mad, as it had mathematicians before him.”
The cases of great mathematicians with mental illness have enormous resonance for modern pop writers and filmmakers. This has mostly to do with writers’/directors’ own prejudices and receptivities, which are in turn functions of what you could call our era’s particular archetypal template. It goes without saying that these templates change over time. The Mentally ill Mathematician seems now in some ways to be what the Knight Errant, Mortified Saint, Tortured Artist, and Mad Scientist have been for other eras: sort of our Prometheus, the one who goes to forbidden places and returns with gifts we can all use but he alone pays for. That’s probably a bit overblown, at least in most cases (Although so is the other, antipodal stereotype of mathematicians as nerdy little bowtied fissiparous creatures. In today’s archetypology, the two stereotypes seem to play off each other in important ways.). But Cantor fits the template better than most. And the reasons for this are a lot more interesting than whatever his problems or symptoms were.
In modern medical terms, it’s fairly clear that G. F. L. P. Cantor suffered from manic-depressive illness at a time when nobody knew what this was, and that his polar cycles were aggravated by professional stresses and disappointments, of which Cantor had more than his share. Of course this makes for less interesting lap copy than Genius Driven Mad By Attempts To Grapple With ∞. The truth, though, is that Cantor’s work and its context are so totally interesting and beautiful that there’s no need for breathless Prometheusizing of the poor guy’s life. The real irony is that the view of ∞ as some forbidden zone or road to insanity—which view was very old and powerful and haunted math for 2000+ years—is precisely what Cantor’s own work overturned. Saying that ∞ drove Cantor mad is sort of like mourning St. George’s loss to the dragon: it’s not only wrong, but insulting.
