My campus has a few sculptures on it. One of the neatest is Mark Beltchenko's Sidewalk II. Students describe it as a half-pipe, or a skateboard ramp, in miniature. It's apparently made of two different parts, bolted together. It's made out of A36 steel. I don't know if the primary reference is entirely to the spatial qualities of itself or if it means something beyond its odd curves set on a stage platform. One student said the hole in the center seemed like a wound, and it appeared to her to be a veteran.
Perhaps a mathematician could describe the way in which it seems to be a rectangle transmutating into a triangle. Perhaps mathematics has a language for when one form is changing into another form. It also is somewhat like a wave. Does mathematics have a language for a wave? We used to have a commenter who specialized in describing stochatic waves, but he's drifting away with the tides of time.
We could have asked Colson Tooley, too, the young mathematician and loner who shot himself at the U. of Texas at Austin yesterday. People who knew him were "so surprised." Let's see: a "loner, who never expressed emotion," who had tremendous "math skills," but no social skills. Sounds like the most common pattern imaginable for a rampaging lunatic.
It's almost a recipe for running amok. Why do people get like that? I suppose it's very simple: the repression, or maybe it's the math. I avoid math, and part of this is because I'm afraid of running amok.
I also don't know why people make metal sculptures, but I have the feeling it is more satisfying than doing pure math. Sculptors rarely run amok. I'm not saying that people should not do math, but people who do it, should do other things, too. Something should be set up on campuses for the very brilliant, very shy people who live inside the math building, finding a meaning in equations that escapes the rest of us. Doing math is like trying to find a logical meaning in the universe. We know the result equals 42.
Math is human, but humans aren't math, or can't exclusively be defined in mathematical terms, and neither can the world.
Perhaps a pyramid of 40,000 cannonballs can be described in purely mathematical terms. Perhaps Mark Beltchenko's Sidewalk II can be described in mathematical terms.
But I don't think people are contraptions, or bathyspheres, or sets of equations, although they like to make those things, and math helps us do those things, and helps us plan trips, and watch as Obama makes regular trips to the Treasury building to liberate more loot. This gets many people mad, and they stand on the street in Tea Parties and scream about it. The newspaper says THAT'S CRAZY! People are emotional, and are happier when they have other people around them who can understand their moods, and love them for them, and part of that might mean joining a political party, and howling and hooting over all the trillions. Part of this means being able to communicate the moods. Again, I don't think you can do this in mathematical equations, although understanding what a trillion dollars means, or what a few billion would mean in terms of a wall along the Rio Grande, might be important. Or that Obama has spent more money in his first two years than all the presidents in American History, might be factually true, or it may be an explosive estimate. Maybe this is better expressed in mathematical terms than in poetry. Poetry, or at least a little of it, is a life skill on a smaller scale. It will get you a little love.
Can love be expressed in mathematical terms? I think love is always unique, while math is a kind of universal, in which the numbers always mean the same things to everyone (it doesn't have a subjective aspect, and perhaps frowns on the subjective). No two lovers wish to be treated alike or as seen as alike. Love is anti-mathematical! It isn't even logical!
Long live the uniqueness of love: each love as unique and incommensurable as our fingerprints and as incomprehensible as contemporary sculpture, escaping every attempt at definition.
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Blogrolling is kaput and my Blogroll has gone AWOL, so now I Google LS in order to visit. Couldn't help noticing an LS post from January 2008 about Kronman's Education's End. Great post. It drew an anonymous comment from the Manifest Destiny dude. He left a comment on one of the Krez poems I translated on my blog around the same time. He's got to be a certified schizodelphian. His thought process is clear evidence of justifiable suicide, if he ever gets around to it.
Math and I have never been on very good terms. I ended up in the humanities largely because--against the insistence of my stepfather, who thought I should be an engineer (since my real father was an architect--but since my stepfather thought all art was a little fruity and suspicious, and architecture was almost the same as art) and so thought a straight "engineer" would be best--I was unable to get "beyond" the notorious quadratic equation. Logs, calculus--it all went right over my head. I was never able to "solve" the equations. I'd add and subtract and divide and move pieces back and forth from one side to the other, and end up with something like...a mess. I think I have a reductive mind--which means I'm always looking for simple solutions to complex problems, always remembering that complexity--and shades of grey--are the usual truth.
I don't think math makes people nuts. But people do seem to be divided between those who can apprehend great art and literature, and those whose abilities and insights occur via math. There's not much cross fertilization.
The physicist Richard Feinman said he thought that you couldn't understand anything important or accurate about the world without getting far into mathematics. He taught a course for non-science majors at Caltech, where he tried to seduce non-science minds into a better appreciation of the mysteries and wonders of physics (and math).
I don't think love can save the world. Fewer people would be the best start. Rampaging increase is the single biggest problem on earth.
Kirby asks whether mathematical and poetic ability represent a zero-sum game.
I believe the answer is no, and the proof is most easily established by considering the remarkably large proportion of the population who have no perceptable skills in either. If math and poetry were truly a zero-sum capabilities, it should not be possible to suck at both, but clearly it is.
With that, I'd like to explain why there are so few individuals who have established reputations in both mathematics and poetry. Indeed, the only claimant to both that comes to my mind is Charles Dodgson, the author of "Alice in Wonderland."
Distinctive mathematical and poetic talents are both rare. In the whole history of the world, I doubt that there have been 10,000 mathematicians who are more significant than Dodgson, and likewise I doubt that there have been more than 10,000 poets more significant than him. If we consider only people who have lived to adulthood in the past thousand years, I'd guess the number to be less than 20 billion. So, the odds of being either a great mathematician or a great poet are about 1 in 2 million, where great is defined in terms of being Dodgson's equal or better.
If we assume that mathematical and poetic ability are independent, the expected number of individuals in the past thousand years who are as good or better than Dodgson in both poetry and mathematics would be (1/2x10^6)^2 * 2x10^10 = 1/200, making it statistically unlikely that there would have been anyone with Dodgson's characteristics. The fact that Dodgson has Dodgson's characteristics is therefore evidence that there is a positive correlation between the two capabilities. An analogous argument could be built around my experience in High School. I belonged to a graduating class of about 700 students, and took AP Calculus and AP World Lit during my senior year. Each of those classes had about 30 students, and the overlap between the two was about 50%, i.e., 15 students, IIRC. If these were independent capabilities, you'd expect that the overlap between the courses would have been a mere 2 students, and 15 would have been a tremendously unlikely overlap.
There is another sense, though, in which I think Kirby's thesis does point in the direction of truth. If you want to be a distinguished mathematician (or poet, for that matter), it does not suffice to have outstanding potential. Instead, that potential must be exercised and developed. And here there is a fundamental conflict: time spent developing excellence in one of these dimensions buys very little advantage with respect to the other. Most scholars will therefore make a choice between the two, and devote their efforts into establishing excellence in one field, rather than trying to span two fields that have so little apparent intellectual cross-fertilization.
It would be fun to make a thorough list of those who have topped out in the two categories. Like you, I think it is few, and probably those few would be light verse, or comic verse, writers, since mathematics would, it seem to me, militate against the sensuous, and the overwhelmingly Romantic, in terms of sensibility.
And yet, EA Poe was exactly that: very Romantic, and heavily emotional, and yet quite brilliant in mathematics. He used to make, in addition to stories and poems, puzzles for his readers which required very intensive logic. I don't know if this would place him in the top ten thousand mathematicians. I don't think I can evaluate the math side. I'm probably in the top 20% in terms of math ability within humanity, but this is only because there are huge swaths of the earth where people can't even add. Among Muslim women, probably none of them could even figure out 3X = 9, so X = ?
And many of them can't read. There are 1.2 billion Muslims, and half are women, so I'm ahead of them, only because their leaders won't allow them to participate (Curtis doesn't care).
Another place where double-talent seems to exist is philosophical writers. They are often good in math, and gifted in terms of prose writing (not poetry).
Bishop Berkeley only wrote one poem. It's on one of the gates at UC-Berkeley. He also had an advance or two in mathematics. Does this put him in the top 10,000 in either area? As poet, probably not. Can't evaluate the math side.
Isaac Asimov wrote dirty limericks, I think I recall. He was what is called a polymath, but was he really good at anything?
I would imagine someone like Piet Hein was not too bad in both areas.
I can't imagine the complete poems of the Unabomber, but it would probably be fun to read.
It seems to me that (present company excepted) mathematicians often have a stunted emotional growth. Lewis Carroll's pedophiliac tendencies are probably NOT the norm in the mathematical profession, but I'm wondering if a certain emotional withdrawal from ordinary life is common among very great mathematicians.
Among poets, they tend to have very immature ways in this area, too.
As far as we know, Marianne Moore never kissed anybody.
And then you have the other side where Allen Ginsberg kissed everybody, and was a pedo, too, a full-fledged card-carrying member of NAMBLA.
Really great poetry seems to tax the ability of a person to be emotionally normal. Would you call Sylvia Plath normal as she flopped about on the kitchen floor?
If we were to make a Venn diagram with poets, mathematicians and pedos, how many would fit into the overlap of the three bubbles?
We would have to limit this to people who were in the top ten thousand practicing persons of all time in poetry and math, and yet having this third area, too.
I think Poe again might fit.
His wife was 12 when they first got together I think Craig once told us.
Bertrand Russell probably didn't write any important poems, but there's this same problem of a very emotionally immature person who was gifted as a writer and as a mathematician. Not a ped, though, so I don't think he fits, but he had fits. He scolded his children for being afraid of the dark, which caused them to become goofier than they needed to be.
We'd have to look at this phenomenon from Plato forwards.
Let's try to find a poet-mathematician who was in the top 10,000, and yet who was emotionally normal (by which I mean, had one partner, and the partner was happy with their choice after all was said and done).
Kirby,
Regarding excellence and emotional maturity...
I know some truly outstanding mathematicians. In terms of emotional maturity, they're all over the map. Some are child-like in a bad way -- unaware and unappreciative of the feelings of others, self-centered, manipulative. And some are adults in the good sense -- aware and appreciative of the feelings of others, able to communicate insights into the emotional states of others, forgiving, and even sacrificial if the cause is right.
Why do we see this? Why is it the case, evidently both in mathematics and in poetry, that there are individuals who are viewed as successful in the field, but emotionally stunted? I think it is because true excellence in a desired field often removes the necessity of emotional progress, and making emotional progress is not easy. If *all* you want to be is the best poet, or best mathematician, then there's no need to grow up. Your lack of emotional development will cost you friends, will cost you income, and all of the other things that society values. But if you do not value these things, then it costs you nothing. On the other hand, there are many mathematicians, even superlatively talented and accomplished mathematicians, for whom "being the best mathematician" isn't enough. They want a life, too -- a wife (mathematicians are almost always male), kids, and a few friends to knock back a brew with on a Friday evening. Being capable people, if they want this, then they'll do what they need to in order to have it, which is to say, they'll grow up.
To reduce this to a sound bite, I don't believe that excellence in either poetry or mathematics inhibits emotional growth, but either may eliminate its necessity.
Your argument here makes perfect sense, even if one comment that you made reminded me of another comment made by Larry Summers some summers ago.
Poets come in all sexes. I think some of the better ones (Dickinson, Moore) are women.
Poetry is not at all objective (is math?), but instead represents a singular individual's vision of the world. In many ways that vision has to intersect with a section of the community (I don't think poetry means anything unless it's being read), and it has to have people who say ooh, for it to matter.
Is that true for math, too?
By the way, our poetry contest closes tonight at midnight. Voting is tomorrow.
Kirby,
Your argument here makes perfect sense, even if one comment that you made reminded me of another comment made by Larry Summers some summers ago.
Let me draw a distinction that I believe is important. When I say, "mathematicians are almost always male," I'm making an observation about the state of the world as it is, without any theoretical interpretation. Mr. Summers' well-known difficulties came from making a theoretical interpretation.
Poetry is not at all objective (is math?), but instead represents a singular individual's vision of the world.
I believe that mathematics is in part objective, and in part aesthetic.
By the way, our poetry contest closes tonight at midnight. Voting is tomorrow.
Which contest?
Creed closed last night. There weren't many entries. I'm voting for Curtis. But I'll put that on the thread.
Stu, I think your tweaking of the data towards a purely objective statement is probably safe, but perhaps it's unsafe even to notice such things. The liberal creed now tells us that anybody can do anything they set out to do.
Summers' comment struck me as exposing a flaw in feminist thought: they often assume that women are better because they are always emotionally connected. Might this in turn make them incapable of abstract reasoning over a prolonged period, which requires a certain level of dry objectivity?
One of the major problems with liberal thinking is that they develop a thesis: for instance, both genders are equal. Then they fund studies that approve and seem to support that viewpoint. Anyone who goes against that (IQ differentials between men and women, or between races, for instance) are as anathema to the new consensus as Galileo's notions about the centrality of the sun were to the Pope.
Once you ahve a worldview that makes coherent sense, and you develop a creed around it, anyone who threatens that creed threatens the whole house of cards.
It seemed to me that that is what Summers did.
The National enterprise Institute is of course still on the case:
http://blog.american.com/?p=15203
But there are numerous other studies that suggest that boys and girls are different on this topic, and on many others, as well. This threatens the notion that they are the same, and thus deserving of equal pay.
Equality is the central notion, of course. Anyone who points out disparity therefore is likely to lose favor, and then, funding.
But this in turn threatens the fairness rating of the left.
People now generally perceive academics to be biased. The lacrosse debacle at Duke got such enormoius interest because it highlighted this. The Summers debacle was similar.
Now, when the left pushes anything, people doubt if reality is in favor of the notions of the left. Whether it's global warming, or bailouts, bussing, or redistribution, all these things go into the same basket of doubtful.
The liberal PC church is shattered. I think Obama will be the last fruitcake to arise out of it to achieve any real power. And his power is dwindling and will shortly be arrested, leaving him a lame duck on a substantially smaller pond.
The PC church is something like Christianity without God. They want the radical equality of the early Christians, but for whatever reason, they don't accept any limitations.
This queers everything they do, and everything they say, to the left. It means that we can't think straight. I think people are rightly tired of this, jus as they were rightly tired of the Pope in Luther's day.
This is the real reason behind the Tea Party, and that everyone is storming into it, including the best-educated people in the country (according even to the NY Times).
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