Category Archives: psychology

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?

 

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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.

 

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Robert Frost to BF Skinner, 1926

“All that makes a writer is the ability to write strongly and directly from some unaccountable and almost invincible personal prejudice like Stevensons in favor of all being happy as kings no matter if consumptive, or Hardy against God for the blunder of sex, or Sinclair Lewis’ against small American towns, or Shakespeare’s mixed, at once against and in favor of life itself. I take it that everybody has the prejudice and spends some time feeling for it to speak and write from. But most people end as they begin by acting out the prejudices of other people.”

I’m a Frost booster, but I don’t see the stance of being “at once against and in favor of life itself” as sufficiently focused to be called a “prejudice.”

 

 

 

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The helicopter was invented a long time ago

“…she had to stay with him at nursery school every morning for four months, or else he went into a violent frenzy of tears and tantrums.  In first grade, he often vomited in the morning when he had to leave her.  His violence on the playground approached danger to himself and others.  When a neighbor took away from him a baseball bat with which he was about to hit a child on the head, his mother objected violently to the “frustration” of her child.  She found it extremely difficult to discipline him herself…”

“…In a Westchester community whose school system is world famous, it was recently discovered that graduates with excellent high-school records did very poorly in college and did not make much of themselves afterwards.  An investigation revealed a simple psychological cause.  All during high school, the mothers literally had been doing their children’s homework and term papers.  They had been cheating their sons and daughters out of their own mental growth…”

“Whereas in earlier years it had been possible to count on the strong motivation and initiative of students to conduct their own affairs, to form new organizations, to invent new projects either in social welfare, or in intellectual fields, it now became clear that for many studnets the responsibility for self-government was often a burden to bear rather than a right to be maintained… Students who were given complete freedom to manage their own lives and to make their own decisions often did not wish to do so… Students in college seem to find it increasingly difficult to entertain themselves, having become accustomed to depend upon arranged entertainment in which their role is simply to participate in the arrangements already made…”

“…a new and frightening passivity, softness, and boredom in American children… incapable of the effort, the endurance of pain and frustration, the discipline needed to compete on the baseball field, or get into college.”

Today’s overinvolved helicopter parents are robbing kids of the character-building experiences of failure and frustration they need, and raising a generation of incompetent narcissists!

Except of course all this is from Betty Friedan’s The Feminine Mystique, published in 1963.  (The third passage is testimony from the president of Sarah Lawrence, the rest is Friedan herself.)

It’s amazing:  you can open this book to just about any page and find material more relevant to contemporary life than 95% of “how we live now” articles published this month.

 

 

 

 

 

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Salience, purchasing behavior, Franklin Bruno

I like Franklin Bruno a lot, and I even know him a little bit, so naturally I was interested in obtaining the new Human Hearts album, Another  I could have paid for a download of this album at any point in the last several months, but I didn’t.  I could have checked to see if I could listen to it free on Spotify, which I have open on my laptop most of the time, but I didn’t do that either.  (Just checked now — it’s not there.)  But the other day, when I walked into the record store on my block and saw it on the new releases shelf, I bought it.  That’s one thing about physical stores — they give you a reason to buy the thing now, not at some other time, while the continuous and eternal availability of the record online meant that there was no moment at which my desire to hear the new Human Hearts album outweighed my desire to click on whatever else I was clicking on.

I presume there are theorists of this kind of thing.

Anyway, here are some favorite Franklin Bruno tracks.

“Love’s Got a Ghetto”

“Going to Marrakesh,” by the Extra Glenns, which is Bruno together with John Darnielle of the Mountain Goats.

I wanted to link to “Coupon,” which is much noisier and messier than the two above, but I can’t find a publicly available sound file, so you’ll just have to imagine it!

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More on the end of history: what is a rational prediction?

It’s scrolled off the bottom of the page now, but there’s an amazing comment thread going on under my post on “The End of History Illusion,” the Science paper that got its feet caught in a subtle but critical statistical error.

Commenter Deinst has been especially good, digging into the paper’s dataset (kudos to the authors for making it public!) and finding further reasons to question its conclusions.  In this comment, he makes the following observation:  Quoidbach et al believe there’s a general trend to underestimate future changes in “favorites,” testing this by studying people’s predictions about their favorite movies, food, music, vacation, hobbies, and their best friends, averaging, and finding a slightly negative bias.  What Deinst noticed is that the negative bias is almost entirely driven by people’s unwillingness to predict that they might change their best friend.  On four of the six dimensions, respondents predicted more change than actually occurred.  That sounds much more like “people assign positive moral value to loyalty to friends” than “people have a tendency across domains to underestimate change.”

But here I want to complicate a bit what I wrote in the post.  Neither Quoidbach’s paper nor my post directly addresses the question:  what do we mean by a “rational prediction?”  Precisely:  if there is an outcome which, given the knowledge I have, is a random variable Y, what do I do when asked to “predict” the value of Y?  In my post I took the “rational” answer to be EY.  But this is not the only option.  You might think of a rational person as one who makes the prediction most likely to be correct, i.e. the modal value of Y.  Or you might, as Deinst suggests, think that rational people “run a simulation,” taking a random draw from Y and reporting that as the prediction.

Now suppose people do that last thing, exactly on the nose.  Say X is my level of extraversion now, Y is my level of extraversion in 10 years, and Z is my prediction for the value of Y.  In the model described in the first post, the value of Z depends only on the value of X; if X=a, it is E(Y|X=a).  But in the “run a simulation” model, the joint distribution of X and Z is exactly the same as the joint distribution of X and Y; in particular, E(|Z-X|) and E(|Y-X|) agree.

I hasten to emphasize that there’s no evidence Quoidbach et al. have this model of prediction in mind, but it would give some backing to the idea that, absent an “end of history bias,” you could imagine the absolute difference in their predictor condition matching the absolute difference in the reporter condition.

There’s some evidence that people actually do use small samples, or even just one sample, to predict variables with unknown distributions, and moreover that doing so can actually maximize utility, under some hypotheses on the cognitive cost of carrying out a more fully Bayesian estimate.

Does that mean I think Quoidbach’s inference is OK?  Nope — unfortunately, it stays wrong.

It seems very doubtful that we can count on people hewing exactly to the one-sample model.

Example:  suppose one in twenty people radically changes their level of extraversion in a 10-year interval.  What happens if you ask people to predict whether they themselves are going to experience such a change in the next 10 years?  Under the one-sample model, 5% of people would say “yes.”  Is this what would actually happen?  I don’t know.  Is it rational?  Certainly it fails to maximize the likelihood of being right.  In a population of fully rational Bayesians, everyone would recognize shifts like this as events with probabiity less than 50%, and everyone would say “no” to this question.  Quoidbach et al. would categorize this result as evidence for an “end of history illusion.”  I would not.

Now we’re going to hear from my inner Andrew Gelman.  (Don’t you have one?  They’re great!)  I think the real problem with Quoidbach et al’s analysis is that they think their job is to falsify the null hypothesis.  This makes sense in a classical situation like a randomized clinical trial.  Your null hypothesis is that the drug has no effect.  And your operationalization of the null hypothesis — the thing you literally measure — is that the probability distribution on “outcome for patients who get the drug” is the same as the one on “outcome for patients who don’t get the drug.”  That’s reasonable!  If the drug isn’t doing anything, and if we did our job randomizing, it seems pretty safe to assume those distributions are the same.

What’s the null hypothesis in the “end of history” paper?   It’s that people predict the extent of personality change in an unbiased way, neither underpredicting nor overpredicting it.

But the operationalization is that the absolute difference of predictions, |Z-X|, is drawn from the same distribution as the difference of actual outcomes, |Y-X|, or at least that these distributions have the same means.  As we’ve seen, even without any “end of history illusion”, there’s no good reason for this version of the null hypothesis to be true.  Indeed, we have pretty good reason to believe it’s not true.  A rejection of this null hypothesis tells us nothing about whether there’s an end of history illusion.  It’s not clear to me it tells you anything at all.

 

 

 

 

 

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How many times can dating die?

Dating is dead now, at the hand of Facebook, texting, “hanging out,” and “hooking up,” per the New York Times:

Blame the much-documented rise of the “hookup culture” among young people, characterized by spontaneous, commitment-free (and often, alcohol-fueled) romantic flings. Many students today have never been on a traditional date, said Donna Freitas, who has taught religion and gender studies at Boston University and Hofstra and is the author of the forthcoming book, “The End of Sex: How Hookup Culture is Leaving a Generation Unhappy, Sexually Unfulfilled, and Confused About Intimacy.”

Hookups may be fine for college students, but what about after, when they start to build an adult life? The problem is that “young people today don’t know how to get out of hookup culture,” Ms. Freitas said.

Arthur Levine concurs:

This generation is not very good at face-to-face relationships. The image that comes to mind is two students, sitting in the room they share, angrily texting each other, but not talking. They all want to have intimate relationships, they want to get married and have kids, but that’s hard to do if you don’t know how to talk with another person. Just under half of freshmen said they’d been on a date. Relationships often begin with two people meeting at a party and hooking up. Then the next day they check each other out on Facebook, and if they like what they see they might send a message saying they’re going to a party the next night — but not inviting the other person. And if they both show up, and hook up again, that might go on for a while, and then they’d consider posting on Facebook that they were in a relationship.

Oh, for the old days, before Facebook and the ubiquitous Internet, back in 1998, when everything was different, and when Arthur Levine — yep, the same guy — wrote:

One of the things traditional-age undergraduates have been most eager to escape from is intimate relationships.  Traditional dating is largely dead on college campuses, replaced by group dating, in which men and women travel in unpartnered packs.  Group dating is a practice that provides protection from deeper involvement and intimacy.  One student at Southern Methodist University summed up the dating scene this way:  “I don’t think there is much serious dating until people are seniors.  I mean, people go out a lot but do not want serious relationsips.  There is a lot of sex.  College is about casual sex.”

Students talked a lot about sex.  On a given night the typical pattern is to go to a bar or party off campus, get drunk, and end up back in someone’s room.  One student explained, “People will stand in the bar just waiting to be chosen at the end of the night.”  Developing a sexual relationship that is not intended to be emotional is just another alternative to traditional dating.  It is a pattern repeated all across the country and rationalized by students, who told us repeatedly that they have never seen a successful adult romantic relationship.”

Young people who read my blog, I have an important message for you.  I went to college in the early 1990s.  There was not much “traditional dating.”  Lots of people complained about this, especially in newspaper editorials, and worried about our ability to forge meaningful relationships.  You know what happened to us?  We all figured out how to get married and have kids.  Just so you know.

 

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Blogging as competitive eating

I’m told that one trick to the astonishing feats carried out by world-class competitive eaters is that your satiety sensor is on something like a twenty-minute delay; so you can really pack an immense amount of food into your body before your brain realizes you’re doing something your stomach doesn’t want you to do.

I was talking to a colleague who wants to start a blog and asked for some advice, and I realized that blogging is kind of like this, too.  My math posts are very casual and full of mistakes, and the reason is that my practice is to write a post as soon as it occurs to me — I then have about a half hour before my brain says “Wait, you’re supposed to be working right now.”  So in that half hour I have to write as fast as I can, like Kobayashi smashing hot dogs into his mouth.

Yes, this is me blogging:

Is this a good time to mention that I once drank a gallon of milk in four minutes?  Here are my tips for success at this important task:

  • Filling and chugging and refilling and rechugging a glass, rather than drinking straight from the jug; this makes it more like doing a normal thing ten times in very short succession, rather than the abnormal and stupid thing that you are actually doing;
  • Not knowing it’s supposed to be impossible;
  • Being 16.
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