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January 24, 2017

Papers Written While Drunk

Posted by Tom Leinster

I’m currently reading a preprint by a deservedly very well-respected and highly-reputed mathematician. It’s enjoyable, inspirational, and wonderful. The ideas that it expresses have been haunting and taunting me for years.

For various reasons, I have the impression that it was not wholly written while the author was wholly sober. That’s OK; I’ll judge the paper for what it is, not on how it was written. But it leads me to wonder: how common is this? In literature, it’s a well-established tradition to the point of cliché. For instance, here’s Ernest Hemingway —

Hemingway in Cuba

— giving a cocktail recipe for difficult political times (1937), “to be enjoyed from 11:00am on”. You can find countless examples of fiction writers enthusing about chemically-assisted escape from the so-called real world.

But mathematics prides itself on sharpness and precision in counterpoint to creativity. We love to say that we’re more creative than poets, but a piece of mathematics is in deep trouble if it’s logically wrong. So where does drugged, drunk or hallucinatory mathematics fit into our mathematicians’ culture?

Posted at January 24, 2017 11:44 PM UTC

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Re: Papers Written While Drunk

I think I understand what you mean by the word “drugged”, but it is important to point out that any theory of how “drugged … mathematics fit into our mathematicians’ culture” will need to distinguish between very different types of drugs. Most mathematicians I know do most of their mathematics while on caffeine, and certainly some mathematicians use more powerful stimulants like amphetamines. The book How the Hippies Saved Physics by David Kaiser documents, among other things, the important role of psychedelics in the creation of modern theoretical physics. This is in addition, of course, to the regularly-scheduled sessions in which mathematics is discussed while using, as Wikipedia puts it, one of the most widely used recreational drugs in the world (second, I think, only to caffeine), specifically the third most popular drink overall, after water and tea.

Posted by: Theo Johnson-Freyd on January 25, 2017 1:10 AM | Permalink | Reply to this

Re: Papers Written While Drunk

Yes, I agree wholeheartedly. Different types of drug have very different effects, and any detailed study would treat them separately.

By the word “drugged” I absolutely include caffeine and alcohol. The legality or otherwise of particular drugs is geographically variable and largely irrelevant (though if a drug’s illegal, it makes a difference to how users of it are treated by others).

Obvious things to cite here are Rényi’s dictum that “a mathematician is a machine for turning coffee into theorems” and Erdős’s amphetamine habit. I hadn’t heard of How the Hippies Saved Physics but have just been reading extracts online; thanks for that.

Posted by: Tom Leinster on January 25, 2017 1:24 AM | Permalink | Reply to this

Re: Papers Written While Drunk

The legality would make a huge difference in terms of how much users would admit publicly they use the stuff. If we’re looking for contemporary examples of mathematicians who talk openly of using illicit drugs to aid them in their mathematics, then about the only example I am aware of is Ralph Abraham.

In more private or semi-private settings, one can hear tell of more examples, but specific cases aren’t easily discussed on a public internet forum, for obvious reasons!

Among contemporary scientists who are (or were) not mathematicians, Carl Sagan and Oliver Sacks wrote somewhat openly about their illicit drug use.

Posted by: Todd Trimble on January 25, 2017 5:47 AM | Permalink | Reply to this

Re: Papers Written While Drunk

Maybe sleep counts as a drug, at least internally.

Perhaps you know the feeling of

Theorems that are only true by night

For me it happens sometimes after working late at night. Then during my sleep I find some remarkable theorem, only to discover when I wake up next morning, that the theorem has become completely false in the light of day. Sometimes I consider to get out of bed and write it down, but I think it is safer to leave it as a dream.

Posted by: Joachim Kock on January 25, 2017 8:35 PM | Permalink | Reply to this

Re: Papers Written While Drunk

Talking of mathematics done asleep, or semi-awake, there’s Michael Harris’s account of Thomason’s dream, and also an account of his own dream.

Posted by: David Corfield on January 26, 2017 7:57 AM | Permalink | Reply to this

Re: Papers Written While Drunk

As far as writing mathematics while “drunk” goes, my own experience is that too much alcohol impairs the concentration too much for me to do any hard mathematics. And I don’t think alcohol produces mathematical inspiration in me, whatever the quantity.

Tom, is there any way you could elaborate on why you have those suspicions about the paper? And was it at all based on things you’ve heard about the author, or is it strictly based on the reading?

Posted by: Todd Trimble on January 26, 2017 1:05 AM | Permalink | Reply to this

Re: Papers Written While Drunk

Well, let me first emphasize that my feeling was tentative (“I have the impression that it was not wholly written while the author was wholly sober”). And face to face, I’m actually quite bad at detecting when other people are under the influence.

But in this case, I think what happened was that as I was reading this preprint, I started remembering some stories I’d heard about the author. It then occurred to me that the words I was reading might have been composed after a drink or two, and suddenly everything made sense: the flitting from subject to subject, the careless mistakes, the rhetorical flourishes. Of course that could just be a writing style — I certainly wouldn’t bet money on my intuition being right.

It’s clear why caffeine is at the heart of mathematical culture. I suppose Erdős’s decades-long amphetamine habit goes in the same general direction (heightened energy and concentration — do air forces still give amphetamine pills to their pilots?). Alcohol doesn’t increase concentration or energy (at least, not mine), but many people do find that a small amount helps with tasks such as speaking a foreign language and writing prose. Maybe the disinhibiting effect could also lead one to make bolder conjectures? But I don’t think I know any instances of this.

Posted by: Tom Leinster on January 26, 2017 8:49 AM | Permalink | Reply to this

Re: Papers Written While Drunk

Thanks. I appreciate this is all very tentative!

What seems interesting is that, if true that the style of the paper is partly attributable to the author having ingested some substances, that nothing was changed after the author reread it. I mean, I assume that the article got second or third looks before being released, and that some of those subsequent looks were while in more sober states of mind.

It sounds like an interesting paper, whatever it is. And it sounds as if it might be a kind of mathematical literary experiment, far from the beaten path of definition-theorem-proof. Jean-Yves Girard is one mathematician whose style strikes me as a little on the wild and experimental side (although I know absolutely nothing of any mind-altering substances he might consume, besides nicotine last I knew).

Posted by: Todd Trimble on January 27, 2017 3:58 AM | Permalink | Reply to this

Re: Papers Written While Drunk

Another example of the intersection of mathematics and drunks is the “drunkard’s walk”.

https://www.britannica.com/topic/random-walk#ref77569

I should also say that some of these famous writers, like Samuel Taylor Coleridge, would pretend that they wrote while under the influence of drugs, so the audience would view their work as containing some special insight or secret knowledge. In reality, nobody can come up with anything good while impaired.

Posted by: Jeffery Winkler on January 26, 2017 4:10 AM | Permalink | Reply to this

Re: Papers Written While Drunk

Well said

Posted by: Fethi Kadhi on January 26, 2017 8:45 AM | Permalink | Reply to this

Re: Papers Written While Drunk

One can argue that a finished piece of mathematics is sharp, precise, and often in some way describes an algorithm or can be followed algorithmically so needs no creativity. Most of the mathematics in the world is not research mathematics and fits here.

But the process of creating / discovering new mathematics is extremely creative, and precision usually comes later. Research mathematics is often not in a finished, polished state (and may never reach that state if not enough people are interested in it).

Posted by: Jonathan Kirby on January 26, 2017 9:48 AM | Permalink | Reply to this

Re: Papers Written While Drunk

I’m reminded of a study I once read about by some music historians who were interested in the popular notion that mental illness contributes to creativity. Specifically, they looked at the work of Robert Schumann, who is believed to have been bipolar. Some version of popular conceptions about mental illness and creativity would suggest that Schumann wrote his best music during manic phases. The scholars used Schumann’s diaries and other records to guess when those phases were and when he was writing which pieces, and used frequency of performance as a proxy for the quality of music.

The conclusion: there was no relationship between the quality of a piece and the state of Schumann’s mental health when he wrote it. He did simply write more music during his manic phases than at other times, but this is amply explained by the more energetic state, not by any idea that he was more inspired at those times.

My personal experience of caffeine and mathematics is similar. There are times when caffeine helps me keep concentrating on mathematics longer, but I don’t believe it helps me think any better.

Posted by: Mark Meckes on January 26, 2017 2:02 PM | Permalink | Reply to this

Re: Papers Written While Drunk

I’m as fond of the effects of a cup of coffee as anyone, but I won’t feel I’ve truly made it until I’ve had a great idea while stepping onto an omnibus.

Posted by: Tom Leinster on January 26, 2017 3:32 PM | Permalink | Reply to this

Re: Papers Written While Drunk

There is the story that Paul Erdos was bet that he could not go without amphetamines for a month or so. He abstained and won the bet but he stated that progress in mathematics was set back by that period of time he abstained.

Posted by: Mark Thomas on January 26, 2017 5:59 PM | Permalink | Reply to this

Re: Papers Written While Drunk

Maybe worth mentioning the famous case of Kary Mullis (https://en.wikipedia.org/wiki/Kary_Mullis), who claimed to have invented the PCR technique, which is hugely important in biology, while on LSD. Like other examples, it’s impossible to know how true this is, or whether he would have done the same work without the drug.

It would be cool if someone had done a proper controlled study of some kind. I would be surprised if no one had…

Posted by: Daniel on January 26, 2017 6:17 PM | Permalink | Reply to this

Re: Papers Written While Drunk

My friends in computer science tell me that the Ballmer peak is not entirely a joke.

Posted by: Blake Stacey on January 26, 2017 8:02 PM | Permalink | Reply to this

Re: Papers Written While Drunk

Maybe math is one of those fields where drugs are best left out of the equation. There are going to be outliers, but out of the hundreds of famous mathematicians, if we can only point to one or two such as Erdos, then I think caffeine is probably as far as most of us will want to take it.

If the path of most greats is one of sobriety, then I’ll follow in their footsteps, as they show us the way. The Dionysus in me finds this topic interesting and I would love it if professional mathematicians came out in droves and said, “At night after work, we smoke a little marijuana or have a cocktail and mathematical truths and insights occasionally flow out of this”, then I would be on board.

But my Apollonian nature says, “Ye shall know a tree by the fruit it bears”. What habits produce good mathematics? Then I look at productive mathematicians and ask what are they doing? Maybe one of the few things I can point out is that they all seem relatively ‘square’, a 1960’s American colloquialism for someone who is mostly or completely abstinent from drugs and alcohol.

This is all speculation from my part, that is, I have no idea the reality of many these mathematician’s lives. Perhaps as someone mentioned earlier, behind closed doors and away from the scrutiny of a civilization that embraces prohibition, there is more than meets the eye…

Posted by: adam dreaver on January 28, 2017 2:58 AM | Permalink | Reply to this

Re: Papers Written While Drunk

Regarding caffeine, as a one-time heavy user who quit about 25 years ago, my experience jibes with the conclusions of this paper:

“Effects of caffeine on performance and mood: withdrawal reversal is the most plausible explanation” JE James and PJ Rogers, Psychopharmacology (Berl), 2005 Oct;182(1):1-8. Epub 2005 Jul 2.

https://www.ncbi.nlm.nih.gov/pubmed/16001109

Appropriately controlled studies show that the effects of caffeine on performance and mood, widely perceived to be net beneficial psychostimulant effects, are almost wholly attributable to reversal of adverse withdrawal effects associated with short periods of abstinence from the drug.

Once you’re caffeine-tolerant, you absolutely need it to function normally, but the spectacular difference between how a caffeine-tolerant person functions with and without coffee is more a measure of how badly they underperform without it than of how well they perform with it.

Posted by: Greg Egan on January 28, 2017 8:19 AM | Permalink | Reply to this

Re: Papers Written While Drunk

I’m reminded of Richard Borcherds: “I was over the moon when I proved the moonshine conjecture. I sometimes wonder if this is the feeling you get when you take certain drugs. I don’t actually know, as I have not tested this theory of mine.”

Posted by: Dan Piponi on January 31, 2017 1:44 AM | Permalink | Reply to this

Re: Papers Written While Drunk

How about in the way mathematics is represented artistically? I’m under the impression that its usually its logical precision and rigor is emphasised - so geometric forms, lines, little colour, repetition: cubism or bauhaus comes to mind; but perhaps a 60s psychedelic aesthetic could be applied. I’m not quite sure how, but it could be interesting to see some of Eschers drawings done in this style.

Fractals when I first saw them looked pretty trippy and psychedelic too.

Posted by: Mozibur Ullah on February 4, 2017 6:15 AM | Permalink | Reply to this

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