Wednesday, February 29, 2012

truer interpretations of atlas shrugged, part n+1

Karl Smith puts it well:
Hank Rearden says he only cares about making money but this is an obvious lie. Like most male obsessives he cares about steel and about women who care about steel and about nothing else.  
If he made money, so be it. If not, so be it. If metallurgy made you a billionaire he’d be a billionaire. If it made you a homeless crank, he’d be a homeless crank. 
That’s the way obsession works. 
What pisses him off is not taking away his money, its taking away his metal. 
Its funny that intuitively folks pick up on that but then in an effort to defend egoism make up this story about loving money that is actually both less accurate and less compelling.
 It's about personal responsibility, not money grubbing. 

Sunday, February 26, 2012

symmetry is awesome

I heard this cute math puzzle recently (thanks Piotr :)

Three ants start at the vertices of a unit equilateral triangle. Ant 1 always faces ant 2, 2 always faces 3, and 3 always faces 1. They all start walking at the same time towards their target neighbor, at one unit per second. What happens?

Now I'll wait while you figure that one out.

In the meantime, here's another nice symmetry-related thing that Joanna showed me: The surface area on a sphere in between any two parallel slices through the sphere is only dependent on the vertical distance between the slices. So if you slice off the top mile of the Earth, and take out a one mile slice at the equator, those sections have the same surface area.

That's a little surprising, until you realize that since sphere are perfectly symmetric (they have constant curvature in any direction), the circumference of the slice you're taking is shrinking as you move away from the equator at exactly the same rate that it's flattening out, so to speak. That is, three inches "above" (3 inches along the axis of rotation) the equator translates to three inches on the ground, but three inches "below" the north pole translates to a looong way on the ground. And this exactly offsets the fact that the Earth is much bigger around at the equator than the pole.

...(ant spoiler alert)...

Ok back to the ants. By symmetry, they will collide at the center of the triangle. The question is, how long does it take for them to get there? They're spiraling inwards as they turn to keep facing each other, so they don't take a straight route there. But, by symmetry, at every point in time they're still in an equilateral triangle formation, essentially starting from scratch on a slightly smaller and rotated triangle! That means that if you figure out what's going on at the first instant, the same thing applies at every later instant.

From there it's easy. The inward distance from each vertex to the center of the triangle is √3/3. And the component of each ant's velocity that is pointing inward is cos(30)=√3/2. So they will collide in the center in 2/3 of a second.

Update: arithmetic corrected... again.

Thursday, February 23, 2012

Mercury and a 28-hour moon

Yesterday there was an aesthetically nice astronomical coincidence. Even better, I got to observe it from the comfort and convenience of the economics grad student lounge, which has a beautiful view towards the west from the 6th floor of a building up a hill in Berkeley. This means you can see all the way to the western horizon, so you can observe objects that fall right on the cusp of possibility, setting just after the sun itself.

Today Mercury and a 28-hour old moon coincided in this brief window. Mercury by itself is very difficult to observe: since it orbits close to the sun, you can only see it just after sunset or just before sunrise, and even then only rarely, when it's as far away from the sun as it ever appears to us (with the Earth and Mercury forming a right angle with the sun.) The last time I saw it definitively was in 2001 (although I can't say I've often tried; I'm more of a deep sky fan than a solar system buff...)

The same applies to extremely thin crescent moons. A goal of any lunar observer is to pick out the hairline crescent as soon as possible either before or after the new moon, when it passes directly between us and the sun and is momentarily invisible. 28 hours old is definitely not the youngest moon you can observe, but I think it's my personal record, and is definitely sufficiently strikingly beautiful.

So, some pictures:

Mercury and crescent moon side by side over bay, shortly after sunset (about half an hour)

moon through binocular eyepiece

Mercury and moon a little later, as it's getting dark

Jupiter (upper left), Venus (left of middle) and moon sliver (on horizon). Unfortunately Mercury didn't quite get picked up in this exposure, but you could still see it naked eye at the time.

Tuesday, February 21, 2012

preference elicitation

Apparently economists are willing to trade half a thumb for a publication in the AER.

I see two possible interpretations. Either the time trade-off method of preference elicitation is a load of BS, or economists are such boring office-bound people that they have unusually low valuations for thumbs :)

Friday, February 17, 2012

jargon proliferation and literature search

If you have an idea and want to find out what has been done on the subject already, the biggest barrier is knowing what to google. Every discipline comes up with their own terminology, and six academics in the same field working independently will also come up with six different terminologies and then refuse to merge them (stubborn pride, obliviousness, habits, who knows why.)

For example, my research has to do with how people behave morally in part because they want to signal that they are good people. There are so many studies relating to different aspects of this motivation, in economics and psychology and sociology and anthropology and even biology, and they call it everything from "social image" "social pressure" and "social signaling" to "prestige" "self image" "guilt" "shame" "pride" and "reputation" (and probably others I haven't heard of; please clue me in). You can certainly break these categories down into well-defined non-redundant subgroups* but the literature doesn't adhere strictly to any particular such breakdown. And anyway, papers using any of that terminology are of interest, so you want to know it all.

So it goes like this. I start off knowing that "social image" is a term used by economists. I google-scholar that, read a bunch of papers about it, and learn about social pressure and social image and social signaling. My previous reading on models of social preferences informed me of a paper on prestige. I talk to a professor about my research, and he mentions a paper by Benabou and Tirole, and through there I learn about self image and self-signaling models. A footnoted reference there leads to a paper in a sociology journal, and by following another long tree of citations, I learn about guilt, shame, and pride. At some point, the word 'reputation' randomly occurs to me, so I google-scholar that and find another branch of literature.

This is hardly a systematic or reliably comprehensive way to learn something.

I don't suppose that a movement towards terminological standardization is going to be successful, and that won't help with the bootstrap problem of knowing where to start in the first place (sometimes the eclectic terminology is helpful there, since no matter what you google, you'll find something...)

But how about we at least make an effort to mention the alternative terminologies in the introductions to our papers? If even a percentage of papers did this somewhat comprehensively, it would be vastly easier to track down the full literature, because one in five (say) papers we randomly stumbled on would tell us where to look.

It would also be really nice if there were a better visualization for relationships and timelines in the literature. Even simply based on citations. It should be really easy for Mendeley to show you a timeline slash citation web for everything in a library, and suggest related articles... if only the non-standards didn't suck so much that even extracting basic metadata wasn't a Herculean task...

I don't even want to know what people did before google. I guess they didn't have lists of papers in the thousands. Either that or grad school was a horrific tree slaughtering madness...

*I propose the following, for the record: Social image motivates people to be nice in order to avoid shame or gain prestige. Self image motivates people to be nice in order to avoid guilt or gain pride. Social pressure is the welfare-reducing altruism that results from avoiding shame. Reputation is the thing you control strategically during repeated interactions.

Thursday, February 16, 2012

imagine being wrong

Robin Hanson says
[O]ne is supposed to believe that racists are so obviously and extremely crazy that it is impossible for a reasonable person to see things from their point of view. Pretending to believe this signals to your associates confidence in your shared anti-racist position, and so is a signal of group loyalty.
This reminded me of an amusing, although extremely frustrating at the time, incident in a high school literature class discussion in which I ignored (or was oblivious to) this rule long enough to essentially say "I can understand how people who grow up in certain environments can end up racist." Of course, the rest of the class instantly attacked me, with surprising virulence and shocked faces, as a racist (and this false impression lasted longer than the hour...)

Too much group loyalty leads to unproductive conversation. Acknowledging differences between races and sexes doesn't imply racism or sexism. Acknowledging that there are reasons aside from insanity why people might be racist or sexist does not imply racism or sexism. Admitting that different races exist in the first place most certainly doesn't imply racism.

If you want to solve these problems, you have to look them in the eye long enough and honestly enough to understand the complex intertwined factors involved. Economists are particularly good at that. Maybe that's why we're so widely hated :)

Wednesday, February 15, 2012

brainstorming

We know that group brainstorming doesn't work. Yet group brainstorming/open-ended discussion sessions always feel incredibly creative and thought-provoking, which presumably is where its appeal and illusion of effectiveness comes from. But not hard to understand the illusion. If everyone has distinct starting point for their personal brainstorming, allowing everyone to brainstorm separately and combining those insights will lead to a cumulative view that circumscribes those ideas. On the other hand, brainstorming collectively pulls each person away from their starting point towards the group mean, from the start, often before they have a chance to voice each their starting point, let alone go in a different direction.

So each person is pushed farther from their comfort zone, and therefore feels thought-provoked, but the overall result is much less diverse.

Friday, February 10, 2012

inefficient time use?

A basic result of microeconomic theory, the equimarginal principle, is that, if you are allocating your resources efficiently (spending your  money in the way that makes you best off), the marginal utility of each good you consume should be the same.

For example, let's say there are only two goods in the world you can buy: apples and hamburgers. The nth dollar you spend on apples gives you 6-n dollars worth of happiness (so buying 2 dollars worth of apples gives you (6-1)+(6-2)=$9 worth of happiness.) The nth dollar you spend on hamburgers gives you 10-2n dollars of happiness (so buying 2 dollars of hamburgers gives you (10-2)+(10-4)=$14 worth of happiness.) If you spend 3 dollars on hamburgers and nothing on apples, the third dollar is getting you an extra $2 of happiness, whereas if you instead bought $2 of hamburgers and $1 of apples, you would get $5 from the apple, so you should reallocate one dollar to apples. More generally, if the last dollar you spend on one thing makes you less happy than you would be if you transferred that dollar to another item, you should do so. Therefore, the last dollar you spend on every good should be the same; i.e. your marginal utility of consumption of every good is the same.

But the same thing applies to time use. Time is another scarce resource that we allocate between many possible activities, so it should be true that the last minute we spend on every activity is equally enjoyable. This is largely ignored (the diminishing returns to experiential utility in time, more generally) when analyzing time use. Hence, you see scholars puzzled by the fact that women in Texas are happiest* when having sex, and yet only 12% do this on a given day for an average of less than 15 minutes per day. Why aren't they, uh, doing it more often?

If the marginal utility of sex is sharply diminishing in time, this isn't surprising at all. No more surprising than that people whose favorite food is fudge only eating an ounce of it at a time. It's true that the first bite of fudge makes them really happy, much more happy than anything else they eat, but it's also true that eating more would be a suboptimal choice.

*Not necessarily the authors of the linked study; I've just seen it referenced in that context several times.

Thursday, February 9, 2012

birth control coverage

Cochrane glosses over the main reason for small, regular health costs being incorporated into health insurance (because people will put off those routine preventative things more if they have to pay for them, but ultimately those preventative things reduce healthcare costs, so the insurance company has an incentive to cover those things - and charge you higher premiums for them - in order to coerce you into using them and reduce its own costs later) but that's not relevant with birth control, so I can forgive the simplification. The article is otherwise great.

Especially since I'm a fan of any professor who posts pdfs of their gated articles on their websites :)

(Link stolen from Mankiw.)

Monday, February 6, 2012

gender gap in sticking with your STEM major

Here's a scary chart* that shows that only white males stick with their plans to major in STEM fields in college:


This paper goes on to show that the racial gap in sticking with STEM majors is entirely explained by preparedness/ability (SAT scores etc); i.e. since affirmative action policies lead black Duke students to underperform their white peers, and since STEM majors are harder than humanities majors, more black students switch to the easier majors. BUT, the male/female gap is not explained in this way (as you might expect, since a majority of the Duke student body is female, and they are therefore definitely not being targeted by affirmative action policies.)

So what the heck is going on with the girls? Stably with respect to all kinds of aptitude/background controls, almost 20% of girls switch from STEM to humanities majors. Is it possible that high school STEM education is so bad that girls don't realize their humanities-leaning preferences until college? Do women care more about grades and therefore lean towards the majors with more grade inflation? (This entanglement between STEM classes, cognitively hard/quantitative classes, and classes with relatively low grade inflation, makes it very hard to distinguish between many of these explanations...) Is the impact of STEM professor gender, known to be at least a contributor to this gender gap, actually large enough to explain most of this away?

There's lot of research on STEM participation/achievement gender gaps but I've seen little that looks at this specific choice to switch from a career in science to the humanities**. That switch is the most interesting piece of the puzzle to me: if girls aren't as good at science or they don't like science, fine, but if they want to be scientists and aren't realizing that dream, the educational system may be failing them.

**Please do send me other papers that I might've missed :)

Update: Correction: 70% of the black student body at Duke is female, not the overall student body.