Show your work

Here’s another comment on that New York Times piece:

“mystery number game …. ‘I’m thinking of a mystery number, and when I multiply it by 2 and add 7, I get 29; what’s the mystery number?’ ”

See, that’s what I mean, the ubiquitous Common Core approach to math teaching these days wouldn’t allow for either “games” or “mystery”: they would insist that your son provide a descriptive narrative of his thought process that explains how he got his answer, they would insist on him drawing some matrix or diagram to show who that process is represented pictorially.

And your son would be graded on his ability to provide this narrative and draw this diagram of his thought process, not on his ability to get the right answer (which in child prodigies and genius, by definition, is out of the ordinary, probably indescribable).

Actually, I do often ask CJ to talk out his process after we do a mystery number.  I share with the commenter the worry of slipping into a classroom regime where students are graded on their ability to recite the “correct” process.  But in general, I think asking about process is great.  For one thing, I learn a lot about how arithmetic facility develops in the mind.  I asked CJ the other night how many candies he could buy if each one cost 7 cents and he had a dollar.  He got the right answer, 14, not instantly but after a little thought.  I asked him how he got 14 and he said, “Three 7s is 21, and five 21s is a dollar and five cents, so 15 candies is a little too much, so it must be 14.”

How would you have done it?

Why aren’t math professors sociopaths?

Great open from Chris Hayes:

Imagine you’re a scientist in some sci-fi alternate universe, and you’ve been charged with creating a boot camp that will reliably turn normal but ambitious people into broken sociopaths more or less willing to do anything.

There are two main traits you’d want to cultivate in your recruits. The first would be terror: You’d want to ensure that the experimental subjects were kept off-­balance and insecure, always fearful that bad things would happen, that they would be humiliated or lose their position and be cast out. But at the same time, it would be crucial that you assiduously inculcate a towering sense of superiority, the belief that the project they happen to be engaged in is more important than anything and that, because of their remarkable skills and efforts, they are among the select few chosen to be a part of it. You’d want to simultaneously make them neurotically insecure and self-doubting and also filled with the conviction that they and their colleagues are smarter and better and more deserving than anyone else.

He’s writing about young investment bankers, whose lives, such as they are, are described in Kevin Roose’s new book “Young Money.”  But doesn’t this boot camp actually describe the Ph.D. experience pretty well?  And if so, why aren’t math professors sociopaths?

I can think of one reason:  in finance, the thing you are trying to do is screw over somebody else.  If you win, someone has lost.  Mathematics is different.  We’re all pushing together.  Not that there’s no competition; but it’s embedded in a fundamental consensus that we’re all on the same team.  Apparently this is enough to hold back the sociopathy, at least for most of us.

Reader survey: in what small way are you weird?

Lots of us are weird in big, noticeable ways, that’s for sure.  But I was looking the other day at a series of photographs of people’s fridges and I realized, you know what’s weird about me?  In a small, barely noticeable way?  I don’t have any beer in my fridge.  I never do.  In fact, I don’t really have any alcohol in the house of any kind.  Maybe a bottle of Trader Joe’s white wine I used a cup of for cooking at one point.  OK, I just looked and there’s a bottle of rum in the back of the cupboard.  Who knows where it came from or how long it’s been there?

It’s not that I don’t drink; I do.  But I don’t drink at home.  For me, beer is for drinking at bars, or at parties.  I would never sit and drink a beer and watch the ballgame, or drink a glass of wine with family dinner.  But I think this is actually slightly weird and almost all people have beer in the fridge.

Reader survey:  in what small way are you weird?

(Note:  this would make an excellent question for OKCathy!)

 

 

 

OKCathy

This week’s Aunt Pythia column features Cathy O’Neil’s take on what questions online daters ought to have to answer in their profiles:

How sexual are you? (super important question)
How much fun are you? (people are surprisingly honest when asked this)
How awesome do you smell? (might need to invent technology for this one)
What bothers you more: the big bank bailout or the idea of increasing the minimum wage?
Do you like strong personalities or would you rather things stay polite?
What do you love arguing about more: politics or aesthetics?
Where would you love to visit if you could go anywhere?
Do you want kids?
Dog person or cat person?
Do you sometimes wish the girl could be the hero, and not always fall for the hapless dude at the end?

I gotta say, thinking back to when I was single, during the second Clinton administration, I don’t think these are the questions I personally would most want to ask of my prospective dates.

On the other hand, I think the questions provide a near-perfect portrait of Cathy!  So let me offer my own suggestion:  maybe profiles shouldn’t have any answers.  Maybe they should just have questions.  And you contact the person whose questions you’d like to answer.

What would your questions be?

 

 

Meeting myself at 17

For something I’m writing I looked up a newspaper article I was interviewed in in, from June 7, 1989.  Here’s what I had to say:

Ellenberg on mathematics: “I always think of it — this is kind of crazy — as a zoo. There are a million different mathematical objects. They are like animals. Some are like each other and some are unalike, and they are all objects . . . . There are things in different guises. The amazing thing is, it all connects. Anything you prove with trig[onometry] is just as true if you do it with algebra . . . . I think it is kind of amazing actually, if you think of it from an emotional point of view.”
On learning math: “My feeling is that a lot of people expect not to be good at math. If you see calculus and trig, to a seventh-grader, they see it as something very difficult and very arcane, when maybe the trick is to relax a little bit . . . . Many things you can understand on two levels. If you look at a novel, a novel can be very hard to interpret, but you can still read it and see what happened. With math, there is no real surface level. It is already written in a sort of obscure language. You don’t have the comforting template. You only have the deep structure, and that can be very off-putting.”
On the practicality of math: “Why is it important to have read any Shakespeare for your everyday life? To tell the truth, I can get through the day without ever using a Shakespeare quote, but I think Shakespeare is useful, and I think math is useful.”

What a strange experience, looking at this.  In a way I seem very mentally disorganized.  But at the same time this is recognizably me.  Unsettling.

Scientists aren’t experts on what makes jokes funny

Ben Lillie:

This week I finally realized what bugged me about the talk I was hearing about the science of science communication: Nothing. The issue is what I wasn’t hearing.

This was catalyzed by a short news item Lauren Rugani linked on twitter. A scientist had run a study where they discovered that sometimes a punchline is funnier if words from the punchline had been mentioned several minutes earlier. From the abstract:

“These findings also show that pre-exposing a punchline, which in common knowledge should spoil a joke, can actually increase funniness under certain conditions.”

This is shocking. Not the conclusion, which is clearly correct. The problem is that the conclusion has been known to comedians for at least the last several thousand years. When I trained in improv comedy the third class was on callbacks, the jargon term for that technique. The entire structure of an improv comedy set is based around variations on the idea that things are funnier if they’re repeated. And yet to the authors it was “common knowledge” that this will spoil a joke. There is a long tradition of people who know, from experience, how this works, and yet the idea of asking them is not evident anywhere in the paper. This is the problem — the sense that the only valid answers come from inside science and the research world.

Yes!  Everybody knows by now that when mathematicians try to do mathematical biology alone, without people with domain knowledge of biology in the room, they do crappy mathematical biology.  “Digital humanities” or “neuroaesthetics” or “culturomics” &c are just the same.  New techniques drawn from science and mathematics are fantastic research tools now, and they’re only getting better, but it seems like a terrible idea to study cultural objects from scratch, without domain experts in the room.

Bertrand Russell was emo

Another entry in the series of “towering early 20th century thinkers were emo” (previously:  B.F. Skinner was emo.)  Bertrand Russell, age 31, writing to his friend Gilbert Murray:

I have been merely oppressed by the weariness and tedium and vanity of things lately: nothing stirs me, nothing seems worth doing or worth having done: the only thing that I strongly feel worth while would be to murder as many people as possible so as to diminish the amount of consciousness in the world. These times have to be lived through: there is nothing to be done with them.

This quote is pretty famous but glancing through his letters, holy cow, I had no idea how brutal Russell’s thoughts were.  Here’s his take on math:

Abstract work, if one wishes to do it well, must be allowed to destroy one’s humanity: one raises a monument which is at the same time a tomb, in which, voluntarily, one slowly inters oneself.

And on marriage:

It is ghastly to watch, in most marriages, the competition as to which is to be torturer, which tortured; a few years, at most, settle it, and after it is settled, one has happiness and the other has virtue.  And the torturer smirks and speaks of matrimonial bliss; and the victim, for fear of worse, smiles a ghastly assent.

All these letters are from the period when his first marriage was breaking up, so maybe he cheered up later?

 

 

Mathematics is not terribly individual

From Oswald Veblen’s opening address to the 1950 ICM:

Mathematics is terribly individual.  Any mathematical act, whether of creation or apprehension, takes place in the deepest recesses of the individual mind.  Mathematical thoughts must nevertheless be communicated to other individuals and assimilated into the body of general knowledge.  Otherwise they can hardly be said to exist.  By the time it becomes necessary to raise one’s voice in a large hall some of the best mathematicians I know are simply horrified and remain silent…

The solution will not be to give up international mathematical meetings and organizations altogether, for there is a deep human instinct that brings them about.  Every human being feels the need of belonging to some sort of a group of people with whom he has common interests.  Otherwise he becomes lonely, irresolute, and ineffective.  The more one is a mathematician the more one tends to be unfit or unwilling to play a part in normal social groups.  In most cases that I have observed, this is a necessary, though definitely not a sufficient, condition for doing mathematics.”

This view of mathematics and mathematicians is deeply alien to me.  I experience mathematics as thoroughly communal.  Does this reflect a change in mathematical practice in the last 60 years, or just a difference in temperament between Ozzie and me?

 

Things I don’t know how to do: orient myself in space

The New York Times recently covered the latest paper from the Benbow-Lubinski group at Vanderbilt about factors measurable in youth that correlate with adult achievement.  I always enjoy reading these studies because, as a person who scored well on the math SAT at a young age, I’m in their dataset somewhere.

The new paper finds a small but detectable (positive) effect of spatial ability in children on adult measures like patents granted and papers published in STEM.  I hope I didn’t mess up their z-score too badly, because I stink at spatial ability.  I recently revealed to Dr. Mrs. Q., who was horrified, that when we’re inside the house I can’t tell what direction the wall I’m facing corresponds to in the outside world.  Moreover, if I’m on the ground floor, I can’t tell you what’s directly above me on the top floor, or directly below me in the basement.  This is presumably related to my inability to correctly swipe a credit card at the gas pump.

Interesting fact about spatial ability:  it can be trained by sufficient exposure to first-person shooters.

As for the new paper (full author list: Kell, Lubinski, Benbow, and Steiger) I have some quarrels with it.  Their way of measuring “creativity and innovation” is to split the subjects into

• those who have obtained a patent but have not published a paper
• those who have published a paper in natural science, math, or engineering (aka STEM)
• those who have published a paper in biology in medicine
• those who have publications in the arts, law, the humanities, or social science
• everybody else

I think the binary variable “has published a paper in science” vs. “has not published a paper in science” is a pretty bad proxy for creativity.  It is a much better proxy for “pursued an academic career for at least some point in their life.”

What’s more:  from the New York Times lede

A gift for spatial reasoning — the kind that may inspire an imaginative child to dismantle a clock or the family refrigerator — may be a greater predictor of future creativity or innovation than math or verbal skills, particularly in math, science and related fields, according to a study published Monday in the journal Psychological Science.

you might think having high spatial ability is good for creativity.  But the results are more complicated than that.  People who’d published at least one STEM paper had higher spatial reasoning scores than those who didn’t.  But people with an artistic, literary, legal, or social-scientific publication had lower spatial reasoning scores than the mean.  What the Times ought to have said is that spatial reasoning may have an effect on what kind of creative tasks a kid grows up to undertake.

 

BF Skinner was emo

I’m sorry there’s been so much “young B.F. Skinner” material here but I can’t get enough of this stuff!

In 1926, age 22, living in his parents’ attic, he writes an essay in his notebook called “WHAT I ACHIEVE I DESPISE,” which includes this:

Nothing is worth doing.  But we have the instinct to do, and we should be wise enough to do the thing which is most nearly worth doing.

The world considers me lazy because I do not earn bread.  The world expects of me that I should measure up to its standard of strength, which means that if I “got a job” for eight hours of office work (minus the time spent in being friendly to the other employees, in arranging for a party for the evening, in arguing the merits of a baseball scandal, etc.) [if it] constituted a day and paid me respectable money, I should be a man.  It’s not so much my “being a man” that people desire, it is my being one of them.

I see clearly now that the only thing left for me to do in life is to justify myself for doing nothing.

Pace Tolstoy, unhappy 22-year-olds are all alike.