Friday, January 29, 2010

experiments

Economists study equilibrium states but often forget that it takes time to actually get there in the real world. Of course, this is crucial in experimental economics.

(That sounds mind-numbingly obvious, but I just read in Vernon Smith's autobiography that the early experiments done by ...some guy whose name I forget... were single period bargaining games that he used to show that equilibrium predictions of economic theory have no real bearing on how things work in the real world… Vernon of course replicated it with multiple periods and crashed straight in to the efficient outcome. Then again this was in the 1950's.)

But there are also different types of equilibration. If you put a system in an unstable position, it will take some time to get to the stable equilibrium even if everyone involved knows everything about the system. If you drop a ball into a bowl, it'll roll around a bit before hitting the bottom. And if you put people in a double auction where everyone knows everyone else's utility functions, it'll still take some time to get to the equilibrium price.

More often though, equilibration in economic systems isn't an inevitable fall to a stable point. It's a process of figuring out what on earth is going on. If you put people in a double auction with imperfect information, they test the waters and move around a bit, feeling out the environment. (Based on my personal experience playing these games in college, they don't ever really figure out what is going on, but balanced motivations won't allow the system to budge from the stable point anyway.) It's like dropping a ball in a bowl and before falling, it tries rolling one way or another a bit to figure out which way is down, and even when it gets there, it keeps searching around a bit for a lower point.

Not to say that humans randomly feel things out. Self-interest is more powerful than gravity. To continue abusing the ball in the bowl analogy, it's as though it gets dropped in, tries to first go to the center of the earth, realizes it can't, and settles for the bottom of the bowl.

Tuesday, January 26, 2010

PC terminology

I’ve always tended to roll my eyes at ever-changing political correct labels for groups, figuring there’s no real logic to what name is considered polite at a particular point in time. It seems like names just wear out over time and are replaced by new fresh labels periodically.

So I was surprised to read about one logical change in labels in Vernon Smith’s autobiography, where he talks extensively about his pro civil rights activities and race relations in the 30s through 60s. Apparently the “negro” label was replaced with “black” because it was too formal when compared to the “white” label universally used instead of “Caucasian”. Obviously the derogatory derivative “nigger” is insulting but “negro” became insulting as well since it was also unequal to the label for the majority.

In that light it is pretty hilarious that now “black” is being replaced with “African American”, and likewise “Indian” or even “American Indian” is being replaced with “Native American”. (Not to mention that “blacks” and “African Americans” are not the same groups of people, since many African Americans are white and many blacks aren’t American, and “black” is the relevant title when discussing skin-tone based discrimination and associations.)

What’s even funnier is that (so I hear) many blacks object to the new overly-formal and inaccurate title. PC language is lately more designed to avoid guilt than to avoid insult, judging by how much more crap I hear about racism from privileged white people than from marginalized minorities (Ok, that may have something to do with the city I live in…) There is certainly no logic in the crippled -> disabled -> handicapped -> mobility challenged chain. They all mean the same thing.

Over time, whatever the current terminology is, bigoted people will abuse it for bigoted purposes. The people, not the terminology, need changing.

Sunday, January 24, 2010

"Math class is tough!" -Barbie

Wow, this actually happened as late as 1992; I could've had one!

They should have Ken say "I like girls who stay home and cook!"


(The link, since embedded video doesn't import to facebook...)

Friday, January 22, 2010

institutions and culture

Tyler Cowen on good economic institutions and a culture of education.

I would rephrase "family structure which encourages an obsession with education" with "a success-obsessed culture that also values property rights" more generally, but basically yes, I'd bet a whole lot on the idea that institutions that promote entrepreneurship by creating a safe investment environment (which works when the culture is cooperative by respecting property rights), and a culture of success, are the most important determinants of economic prosperity. I'm firmly on Bill Easterly's side in the Easterly-Sachs debate.

It's not that I'm an expert on economic development, it's just one of those things that seems so utterly banally obvious, I can hardly believe there's a debate at all...

I think people just don't like that answer, because it severely limits what a third party activist can do to help alleviate poverty, and at worse implies that such efforts may be damaging. And everyone thinks they would be so much more successful if only they had a little bit more money now, so of course it would help to throw money at the Sudan.

Tuesday, January 19, 2010

economist compliments

"Your utility function is closer to sum than to min."

(Ie, "You appreciate the good in things." Aww.)

***

Unrelatedly, can someone please explain the lyrics to "All You Need Is Love" to me? As far as I can tell it's an inane tautology formed from the converse of the intended statement, and then some nonsense. But since it's one of the best known songs of the century with an extremely clearcut message, I figure I must be missing something... or at least I hope I am, for the sake of humanity's logical abilities.

There's nothing you can do that can't be done
Nothing you can sing that can't be sung
Nothing you can say but you can learn how to play the game
It's easy

Monday, January 18, 2010

economists and money

This is a pretty hilarious description of economist's unique money habits (via MR). It somehow simultaneously points out how regular humans should be more like economists, and how economists should be less lackadaisical about disregarding social customs that they don't understand within their theories.

On the first point, economists usually understand the underpinnings of prices and aren't fooled by the exploitative gimmicks. I would take John Siegfried's lead in paying less for a black car, and Paul Kasriel's in buying off-brand shoes. They know that companies often sell identical products with a different label as a form of indirect price discrimination, and a brand name label on your prescription bottle won't make you feel hundreds of dollars better. And even if Nikes are slightly better quality than other brands, that difference is hugely exaggerated in the pricetag, where you're paying for the Swoosh itself.

Economists are also less subject to "mental accounting" and know that switching from Starbucks to home brew really is offset by being able to buy a bigger house or send your kids to college. A penny saved is a penny earned.

On the other hand, economists often forget that money is not the same thing as happiness; you maximize the latter, not the former. Maybe it's true that my time is most profitably spent working on economics, but I'll be much happier if I invest in a diversified time-use portfolio.

And they don't acknowledge that some sources of happiness are just not fungible. I would not advise copying Betsey Stevenson and Justin Wolfers by paying your friends to hire movers instead of helping carry some furniture. Favors between friends can't be bought. (To be more specific, maybe some types of favors can be translated into monetary terms at a discount, but there are cases, this one included in my opinion, where that rate is negative. If a friend tried to buy me moving help, I would be uncomfortable, decline the offer, and perceive that friend as weird, materialistic, and uncaring. Clearly this does not help our friendship in the way trading favors does.)

And, you can't buy quality time. No, don't try to impersonate Robert Hall by hiring help to decorate your Christmas tree. That's not the point.

(In other words, everyone should find a happy medium and become behavioral economists =)

Friday, January 15, 2010

Random Polynomials

Most of the actual math posts at Quomodocumque are over my head but this is both mostly intelligible and, more importantly, has lots of pretty pictures! (Pretty in an aesthetic and in a mathy way.)

Knock your geeky selves out. *grin* Sometimes I forget how awesome math is.

Wednesday, January 13, 2010

how to count sheep

In other words, a diatribe to make non-nerdy people feel smugly non-crazy, and make nerdy people feel cheerfully less lonely in their compulsive-calculation habits. Don't lie, I know you do it too.

I was raised a victim of the delusion that children need at least 11 or 12 hours of sleep a night, so aside from fine-tuning my night-light vision and becoming likely the first person to ever be elated at OSSM's 11pm bedtime (while my roommate rolled her eyes and said "bedtime? are you kidding me? I haven't had one of those since I was 6"), I became an expert at counting sheep.

The whole point of counting sheep is to occupy your brain just enough to distract from the stuff that normally would keep you awake, but not enough to keep you wake. Obviously counting by the natural numbers is insufficient for this task after about age 7. I can count in the background and maintain several hypothetical conversations in the foreground and mull over some math proofs in the middle ground until 5 in the morning without even yawning.

The next step is counting backwards. That's fine for another day or two of sleep. Around fourth grade I counted backwards from a thousand to 1 several times in one week, and then moved on.

Then comes counting by multiples, backwards and forwards. Here's where it get's interesting. Some multiples are obviously even easier than counting by 1's. (10s, 5s, etc.) To get rid of those you have to rule out numbers that have common factors with ten (since we live in base 10), because then the last digits in the sequence you're going over will have a shorter cycle, and that's too easy. For example, counting by 4's is just a pattern of 4 8 2 6 0 over and over. And for any multiple of 5, it's just 5 0 5 0... And 2 and 5 are the factors of 10.

You can also rule out anything above, say, 20. The numbers just get too big too fast. It definitely takes more than 40 numbers to put me to sleep, and I don't like keeping four digit numbers in my head. When it stops being a calculation game and starts being a memory game, it either becomes too distracting to let you sleep, or you forget your place and have to start over too frequently.

We can also rule out numbers that are a multiple of 10, plus or minus 1. Those are only a slight improvement over 10 and 1 themselves.

So now we're left with 3, 7, 13, and 17.

All of these will keep you entertained for a while. 3 is too easy on its own because you can mentally check whether you're on track as fast as you can calculate the next number (since the digits have to add up to a multiple of 3. I don't have any idea on the fly if 126 is a multiple of 7 but I definitely know it's a multiple of 3.) The solution to that is to start with 1 or 2 instead of 3.

7 is basically fine.

13 and 17 are refinements on 3 and 7 that add the minor step of adding an extra 10 each time. That'll put you to sleep for an extra couple of days.

Unfortunately, even this runs out of usefulness soon. 10+3 is still too easy and 17 has an annoyingly convenient pattern in which you only have to know the first 6 multiples, and then add 2 to each one (and 100) And then 4 (and 200) etc. (In fact, as far as this type of repeat-plus-a-constant problem goes, 17 is as bad as it possibly gets, since 101 is prime.) Once those six numbers, 0 17 34 51 68 85, are engrained in your head, the game devolves into, at most, adding or subtracting 7. Still, ten years later, I still start with 17's (starting with something other than 0 to make it vaguely more interesting, or going backwards) when mild insomnia hits.

After multiples, there are squares. This was riotous fun in middle school. Not only can you check your work by explicitly multiplying n*n, you can get from n*n to (n+1)*(n+1) by adding n and then n+1. Lots of minor little calculations to do to keep your brain humming along in low gear fairly constantly.

But this too has a problem. The problem is that 24 + 25 + 25 + 26 is exactly 100. So when you go from 24*24=576 to 25*25=625 to 26*26=676... well you see the problem, the last two digits are the same! And of course the symmetry keeps going (23*23=529, 27*27=729, etc.) That is, 25*25=625 is a turning point, after which you just go backwards with different leading digits. (And then you get to 50*50=2500 and start over at the beginning). So you only have to know 25 numbers, easy enough to memorize thoroughly in a few nights, and then repeat. Still, that's a big improvement over the 6 numbers you have to know to count by 17's.

(This habit also had an unexpected benefit on high school math contests, where you somewhat frequently get questions involving square numbers. Sure there's always a smart way to do the problem, but if you have them all memorized at least to 2500, it's faster to just look for the answer in the numbers...)

Beating these patterns into the ground in rotation (like letting land lie fallow) kept me sleeping until sleep deprivation in high school and college eliminated the need for it for a few years, but now, my new favorite is triangular numbers! (Numbers of bowling pins in any sized arrangement. 1, 3, 6, 10, 15, etc.) This again has the nice trait of being calculable both via an easy formula, n*(n+1)/2, and by transitioning from one to the next by adding n+1. It doesn't form a cycle until 100, and that's plenty to put me to sleep. It also gets bigger slower than squares and is a bit harder to backwards engineer which one you're on.

The Fibonacci sequence is ok if you don't care about accuracy. If you screw up once you'll never know (since the non-recursive formula involves square roots of 5...) It also involves a little bit too much memory since you soon have to remember 6 digits to get to the next one, instead of 3.

Digits of irrational numbers requires no brain energy whatsoever, don't even think about it. Unless you're figuring them out as you go, like the square root of 2 or something. I find this much too brain intensive to allow sleep.

Other ideas? I think triangular numbers may be the apotheosis of sheep counting.

Sunday, January 10, 2010

enthusiasm

Exactly!

This is what I hated about teenage and college society. The definition of "cool" seems to be "derisive of others' enthusiasm". But the happy people are the ones who are unabashedly enthusiastic. About anything, regardless of importance or popularity*.

Now if you'll excuse me I'm going to go back to grinning at the 21 new maps in my living room and nuzzle the three cats.

*Except video games and reality TV. They are just dumb.

Friday, January 8, 2010

Abrahamic bias

It used to baffle me that Pascal's wager is so widely accepted, or at least, non-instantly rejected. Pascal's wager, to refresh your memory, is the suggestion that you should definitely believe in God just in case he's real. If believe in God and you're right, you get eternal glory. If you're wrong, no harm done. If you don't believe and you're right, again no harm done. But if you're wrong, eternal damnation. When you put it that way, it's an obvious choice.

But of course this begs the question, which God should I believe in? Presumably believing in the wrong one is also a recipe for disaster in the afterlife, even if not as bad as believing in none at all. And does God only care that you believe in him, but not that you do what he wants? If not, you run the additional risk of getting his commandments wrong. If the devil has recently come into power, I doubt he will look too kindly on Protestant prostration.

For any set of beliefs you use Pascal's wager to convince me I should follow, I can exactly invert them and use the same argument in my defense.

The reason this trickery is not immediately dismissed by otherwise intelligent people is that we share a common concept of what God is. In our everyday lives, even among Jews and Muslims and every imaginable flavor of Christianity, we never encounter a serious dispute about what this god guy basically is. It's so engrained we no longer have the imagination to doubt it. And if the God of Abraham was the ONLY possibility, and the details about what foods are allowed and what acts are abominations weren't so relevant, I might take Pascal's word to heart myself.

This bias manifests in other ways as well, one of which is much more relevant to modern faith than some ancient mathematician. That is the bias towards monotheism itself, as the obvious successor to ancient inferior Pagan world views that included hundreds of deities that were even allowed to conflict and take out their differences on the physical world. The debate about God doesn't even consider these faiths. Obviously those people were crazy, say the modern faithful, without stopping to notice that the only (false) logical leg up they have on the Greeks and Romans is that of recent consensus.

The world divides neatly into the monotheisms and the "faithless" religions like Buddhism and Confucianism, along with the straight-up nonreligious. The nonreligious still have such an Abrahamic bias that they don't question this duopoly of positions either. If they did, the might notice that the monotheists actually have a very real logical leg down on the clueless and primitive polytheistic faiths.

The most common cause for a crisis of faith is the incompatibility of a loving, omnipotent God and the horror we see everywhere everyday. Those who manage to cling to faith after an earthquake kills thousands of devout fellow believers can only do so by chalking it up to God's "mysterious ways" (while of course insisting with sudden confidence that the same event is a case of divine punishment when it happens to anyone they don't like). But polytheism doesn't have this problem at all. Sure maybe Zeus is all-loving but his jealous brother got ahold of the reins that day. Oops.

In fact this is so easy and so tempting a solution that even the monotheisms can't completely avoid it. Judaism's God is subject to wrathful mood-swings, Christianity and Mormonism have the devil, Islam has satanic verses and djinns, and Zoroastrianism has opposing good and evil spirits (neither of which is the one god.)

Of course, this still isn't as tempting an explanation as (gasp) plate tectonics, but I'll take it as a first step.

Thursday, January 7, 2010

tiny steps

Scientists (especially mathematicians where the effect is amplified) often say that the nature of research is to beat your head against the wall miserably for eons, and then enjoy a short ecstatic breakthrough.

I would refine that slightly to say that the nature of research is to work hard to identify the tiniest feasible problems that can be answered, spend a lot of time answering them (via the process described above), and then eons later, enjoy a wonderful crystallization process in which all these tiny puzzle pieces start to look like a whole picture.

If you only like epiphanies but not year-long headaches, read the end results in textbooks, but don't be a scientist. And if you only like the crystallization but not the squinting at single pixel sized problems, write literature reviews and overview books, but don't be a scientist.

I actually fairly enjoy all those aspects, but it sure is hard to identify a small enough chunk of something to work on before you can even get started...