A Disease of Mathematics?
Feb. 13th, 2012 10:25 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
cosmolinguist(Last year I entered a science-writing competition. Nothing came of it. I found what I wrote for that when I was looking for something else on my hard drive yesterday and thought it was all right. Maybe some of you would like to read it? So here it is.)
A lot of us might find it a bit unnerving to think too much about infinity, like looking over a cliff whose edge you’re standing near. Infinity seems fractally strange: the more you look at it, the more every bit of it seems as eerie as the whole thing was at first. It can be downright spooky to think about. But that doesn’t mean it’s sinister.
Recently I watched an episode of Horizon (“To Infinity and Beyond”) and was dismayed to see this wariness of thinking very much about infinity was shoehorned onto the mental illness that so strongly affected the life of Georg Cantor.
Cantor was a 19th-century mathematician who did some groundbreaking work on, among other things, the nature of infinity -- he proved that there were an infinity of infinities, some bigger than others. He was also deeply affected by what now might be considered bipolar disorder, which led to him being hospitalised several times throughout his life.
It's infinity, the documentary wants you to believe, that drove him mad. The narrator intones sinisterly: “Cantor ended his days in an asylum. Was it infinity that drove him there? Who knows? Who can tell?”
These dramatic questions do mathematics, psychiatry and Cantor a great disservice. In truth many people know, because many people can tell that this isn't how infinity works, and this isn't how mental illness works
A sprinkling of drama to spice up the programme might seem harmless, but this seems to either make mathematics seem remote (if it’s the purview of the already-insane) or dangerous (if it makes people insane). Popular science programmes should aim to make maths and science accessible and interesting to non-experts, not to reinforce the distance between themselves and scientists... a distance many would also like to put between themselves and mental illness.
In the next scene, Peter Cameron of Queen Mary, University of London dismisses this unscientific view that there are Things That Man Should Not Wot Of, saying, “[Cantor] faced a lot of opposition from his colleagues. It was possibly that, rather than thinking about infinity itself, that was the trouble.”
Still this diamond of boringly sensible thinking goes disregarded as the rough, sinister tone of the programme continues. Though it soon notes in passing that many people have devoted their studies to infinity: since those people aren’t all mentally ill too, surely infinity neither drives mad anyone who comes near it, nor attracts only people who are already crazy.
One reason depressive or psychotic beliefs can be so scary and damaging is because they can weave themselves seamlessly into a person's life. Tapped phones, TV presenters speaking secret messages directly to oneself, and nefariously-implanted microchips are not ideas that would’ve come about before the age of TVs, telephones, and microchips. The illness is not something apart from you; the mind that breaks is your own.
Thus Cantor’s damaging beliefs might have manifested in the subjects he thought most often and deeply about, but that doesn’t mean his illness were the fault of those ideas. Peter Cameron is right to point out that Cantor’s mental illness was more likely exacerbated not by thinking about infinity, but by the universal contempt for his work.
It is in the nature of scientific thinking to attack new ideas to see if they can stand up to careful scrutiny... but science is done by humans, who can be fragile. Cantor’s ideas about infinity were notoriously called a “disease” from which it was hoped mathematics would recover. He hoped for job offers from prestigious universities, but none came. It was as if Cantor’s mathematical disease was quarantined.
Few of us could feel entirely stable if our life’s work made us outcasts.
People like to explain away mental illness: to claim it is certainly something with clear causes and effects; perhaps a moral judgement too, happening to people who somehow deserve it. These justifications imply that if we are “good” people, and if we learn what to stay away from dangerous ideas, we will be safe.
Otherwise we are left with the uncomfortable realisation that there is no reason that Georg Cantor suffered, rather than someone else. Rather than any of us. We want to be safe from such horrors, we shy away from the prospect of being vulnerable to mental illness, but in truth none of us can guarantee immunity.
If we hide and make excuses for mental illness, our whole society suffers. If we respect and support people who happen to have such illness, society benefits -- as we do from Cantor's work, which has become integral to mathematics, not anything like a disease after all.
A lot of us might find it a bit unnerving to think too much about infinity, like looking over a cliff whose edge you’re standing near. Infinity seems fractally strange: the more you look at it, the more every bit of it seems as eerie as the whole thing was at first. It can be downright spooky to think about. But that doesn’t mean it’s sinister.
Recently I watched an episode of Horizon (“To Infinity and Beyond”) and was dismayed to see this wariness of thinking very much about infinity was shoehorned onto the mental illness that so strongly affected the life of Georg Cantor.
Cantor was a 19th-century mathematician who did some groundbreaking work on, among other things, the nature of infinity -- he proved that there were an infinity of infinities, some bigger than others. He was also deeply affected by what now might be considered bipolar disorder, which led to him being hospitalised several times throughout his life.
It's infinity, the documentary wants you to believe, that drove him mad. The narrator intones sinisterly: “Cantor ended his days in an asylum. Was it infinity that drove him there? Who knows? Who can tell?”
These dramatic questions do mathematics, psychiatry and Cantor a great disservice. In truth many people know, because many people can tell that this isn't how infinity works, and this isn't how mental illness works
A sprinkling of drama to spice up the programme might seem harmless, but this seems to either make mathematics seem remote (if it’s the purview of the already-insane) or dangerous (if it makes people insane). Popular science programmes should aim to make maths and science accessible and interesting to non-experts, not to reinforce the distance between themselves and scientists... a distance many would also like to put between themselves and mental illness.
In the next scene, Peter Cameron of Queen Mary, University of London dismisses this unscientific view that there are Things That Man Should Not Wot Of, saying, “[Cantor] faced a lot of opposition from his colleagues. It was possibly that, rather than thinking about infinity itself, that was the trouble.”
Still this diamond of boringly sensible thinking goes disregarded as the rough, sinister tone of the programme continues. Though it soon notes in passing that many people have devoted their studies to infinity: since those people aren’t all mentally ill too, surely infinity neither drives mad anyone who comes near it, nor attracts only people who are already crazy.
One reason depressive or psychotic beliefs can be so scary and damaging is because they can weave themselves seamlessly into a person's life. Tapped phones, TV presenters speaking secret messages directly to oneself, and nefariously-implanted microchips are not ideas that would’ve come about before the age of TVs, telephones, and microchips. The illness is not something apart from you; the mind that breaks is your own.
Thus Cantor’s damaging beliefs might have manifested in the subjects he thought most often and deeply about, but that doesn’t mean his illness were the fault of those ideas. Peter Cameron is right to point out that Cantor’s mental illness was more likely exacerbated not by thinking about infinity, but by the universal contempt for his work.
It is in the nature of scientific thinking to attack new ideas to see if they can stand up to careful scrutiny... but science is done by humans, who can be fragile. Cantor’s ideas about infinity were notoriously called a “disease” from which it was hoped mathematics would recover. He hoped for job offers from prestigious universities, but none came. It was as if Cantor’s mathematical disease was quarantined.
Few of us could feel entirely stable if our life’s work made us outcasts.
People like to explain away mental illness: to claim it is certainly something with clear causes and effects; perhaps a moral judgement too, happening to people who somehow deserve it. These justifications imply that if we are “good” people, and if we learn what to stay away from dangerous ideas, we will be safe.
Otherwise we are left with the uncomfortable realisation that there is no reason that Georg Cantor suffered, rather than someone else. Rather than any of us. We want to be safe from such horrors, we shy away from the prospect of being vulnerable to mental illness, but in truth none of us can guarantee immunity.
If we hide and make excuses for mental illness, our whole society suffers. If we respect and support people who happen to have such illness, society benefits -- as we do from Cantor's work, which has become integral to mathematics, not anything like a disease after all.
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(no subject)
Date: 2012-02-13 10:55 am (UTC)(no subject)
Date: 2012-02-13 04:10 pm (UTC)I don't think it had long-term effects on my mental health, but I was once in a bit of a funny mood walking back from school, thinking about thermodynamics and how energy just keeps going round and round and round in cycles... and then woke up lying on the grass, having apparently fainted. Apparently thinking about infinite cycles does require some kind of safe seating ;)
(no subject)
Date: 2012-02-13 05:52 pm (UTC)I did understand Cantor's diagonal proof for about half an hour, recently -- I finally realized Andrew was assuming I understood something so basic he didn't mention it, and I didn't know it; I've forgotten what that something was now -- but the rest of the time I just get agitated adn it probably has to go on the list of things Andrew can't talk about when it's dark, though not for spookiness so much as frustration :) I can't seem to convince Andrew that I really am as bad at math as I am. He thinks so highly of my intelligence otherwise, and as his is wrapped in in a very logical way of thinking that's well-suited to mathematical ideas, that he really doesn't seem to believe that I am as poor as I am at following along.
Finding out how ideas were developed, and what people were like helps a lot (I find it especially cheering to learn how many fucked up their lives, did badly at school, and generally lived unglamorously and a lot like me! I used to think this sort of life ruled out greatness, but clearly not :D ).
(no subject)
Date: 2012-02-14 03:57 am (UTC)(no subject)
Date: 2012-02-15 02:44 pm (UTC)