The unreasonable effectiveness of mathematics

Think about this: In each strategic interaction between humans there exists a set of actions such that, for each of the participants, the action he chooses is the best one possible for him, taking into account everyone else's actions. This fact is astonishing in of itself; but what's even more incredible is that a fact like this happens to be an immediate consequence of an obscure and highly technical theorem of topology. Physicist Eugene Paul Wigner wrote a famous essay titled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences;" but it seems that mathematics is unreasonably effective not just in the natural sciences but in pretty much anything we can think of.

You cannot be a writer if you're unable to think like people you don't like

One of the things that happen to you when your beliefs function as a signal of group loyalty rather than as means of trying to estimate truth is that you're unable to think like your enemies. If your beliefs are signals of how much you care about those who agree with you, then whenever you're summarizing opposing views you are doing it not to discover or describe actual reasons that people who disagree with you have for their beliefs, but to show those who belong to your camp how much you hate and despise those who don't. To put it shortly, the reason you're summarizing opposing views is not to describe but vilify them.

One of my favorite (due to its extremity) case studies of this type of thinking is a Polish Catholic publicist and blogger, Tomasz Terlikowski. It's very instructive to read his polemical pieces. He's completely unable to try and figure out why it is that people may disagree with him on ethical matters, and thus unable to faithfully portray beliefs he's attacking. As a result, he's attacking not actually existing beliefs, but ridiculous strawman constructions designed to show how depraved he thinks his enemies are. It's inconceivable to him that any decent, intelligent person could possibly disagree with Catholic ethics, and thus, in his mind, those who do disagree with it must be stupid and/or intentionally destructive. And so in his essays he assumes that pro-choice advocates simply enjoy killing babies, that all that proponents of assisted suicide want is to relieve themselves of the burden of having to care for their old relatives, that people who advocate for gay rights see it mostly as a means of completely destroying society as we know it, etc.

As I said, Terlikowski's essays are instructive as a very extreme case of inability to "put yourself in someone else's shoes." The down side is that they're truly horrible to read: they are an ungodly mixture of bad writing, bad reasoning and breathtaking, hateful arrogance. (Think Phil Donahue but about 15 IQ points stupider and 10 Wild Turkey shots meaner. Or save yourself some trouble and just think of Bill O'Reilly straight away.) What is incredibly entertaining to read, however, is Terlikowski's fiction. He wrote a novel titled "Operation Shroud" ("Operacja Chusta"). The novel isn't entertaining because it's good; on the contrary, it is I think a strong contender for the title of the worst novel ever written in Polish. But as opposed to spectacularly bad essays, spectacularly bad fiction can be fun to read.

Operation Shroud is "theological-fiction." It's set in second half of the 21st Century Europe in which true Catholicism is persecuted by politically correct and ethically nihilist institutions, both state and religious. At any rate, what it's about isn't as interesting as what makes it so bad. One of the major reasons is that Terlikowski's characters are completely ludicrous. Nothing about them feels like real human beings; they are mostly just carriers of different opinions. And, unsurprisingly, Terlikowski's villains are even less of real people than his protagonists. They are nothing more than caricatures. Which makes sense: since Terlikowski cannot conceive of the possibility that a good-natured and intelligent person would have views different than his own, the villains in his book are either complete, drooling idiots or bona-fide, card-carrying psychopaths--hardly an interesting character study material either way. Terlikowski manages to make even those villains that convert to the side of good look uninteresting: there's nothing about their conversion that feels like an actual inner struggle; since the beliefs they've started out with are nothing but vile stupidity, all they need to do in order to discard them is to "open their eyes" and poof, their old evil self is gone, just like that. There's absolutely no reasoning process or emotional struggle behind the conversion; it's just something that happens, like larva turning into a butterfly.

The entire point of my rant is this: you can't be a good writer if you're unable to think like people who aren't you, including people you disagree with, people you don't like, people who don't share your values, people who are capable of doing things you could never do. You don't need to transform into those people; you can still disagree with them, dislike them, despise them or what have you, but you need to be able to understand them. You need to be able to see why they are the way they are and do the things they do. That's the only thing that will make your characters believable. Shakespeare clearly didn't like Edmund's character in King Lear but boy, did he understand him. And so do we. Since Terlikowski doesn't understand people who disagree with him, his fictional characters that he doesn't like are completely incomprehensible.

Graph of the day

The above is taken from a paper by Norton and Ariely. The authors conducted a survey in which they asked a representative sample of Americans a series of questions about income distribution in the United States. They asked people what they think that distribution actually looks like (this is the "Estimated" part of the graph) as well as what they think it should like (the "Ideal" part), and then pitted the results against the distribution as it actually is. The results are interesting. First, voters are deeply ignorant about the income distribution (they think it's much more egalitarian than it actually is). Second, they think that in a perfect world, the income distribution should be even more egalitarian than their erroneous perceptions of it. And third, there are no significant differences in those beliefs and desires between Democratic and Republican voters. This third finding is extremely surprising to me.

The law of small numbers

I've written once before about a quite common belief that small samples behave just like large samples do. Some time ago I was watching a tennis match which would have been extremely close if not for the fact that one of the players was getting the short end of the stick in terms of bad referee calls. The announcers noticed it but didn't think it was important because, they said, refs aren't biased but simply make random mistakes so "in the long run it all evens out" (i.e. you'll get about as many erroneous calls in your favor as you will against you).

The total number of points an average tennis pro will play during his entire career is a rather large sample, so the claim about things "evening out" is probably true. Still, it's meaningless, even if true. It doesn't matter what happens in the large sample of all the points a player will play during his career; what matters is what happens in a number of small subsamples of those points that we call "matches." The number of points played in a single match is small enough that random mistakes do not have to even out. Or, thinking about it in a slightly different way, even though the total number of points you'll play is large, some of those points will matter a lot more than others. Very close encounters can be decided by five or six key points going one way or the other. If you get unlucky and the refs make five bad calls that cost you a Wimbledon final, what does it matter that at some point in your career you will get five bad calls going in your favor, if those calls are unlikely to be as meaningful?

Just when you thought the Internet couldn't surprise you anymore

catsthatlooklikehitler.com

You can't choose not to signal

Thinking about signaling behavior is extremely depressing. It's bad enough to realize that so much of human behavior and beliefs have different purposes than the face value. What's worse is that it's very hard to find someone you can share your thoughts with. Taking our beliefs and behaviors at face value (especially those beliefs and behaviors that we consider "noble") is a very strong social norm, and there's a good reason for it. A lot of our behavioral norms serve to sort people into those that can be trusted to reciprocate if you do them a favor and those that cannot, and self-deception about those norms is part of how the sorting is done. This means that if you question, or even analyze those norms, most people that you choose to talk to about it will react with distrust or even outright hostility. They'll figure you for someone who's likely to shirk from their social responsibilities, and think that all your elaborate talk about signaling behavior is simply a way for you to rationalize your own selfishness.

1954

Leopold Tyrmand's Dziennik 1954 (or "Diary 1954") is hands down one of the best books I've ever read. It really is a shame it's never been translated into English. It's an incredibly insightful account of daily life in a totalitarian state, less dramatic than The Gulag Archipelago, but in its own way terrifying. It chronicles the first three months of 1954 in the life of an aspiring writer who lives in Warsaw.

The book offers an immensely interesting look into the daily routine of someone who is trying to survive in stalinist Poland while being in profound moral opposition to the cruel regime but completely unable to outwardly express that opposition for fear of career- or even life-ending retribution from the authorities. But on top of vivid description, Tyrmand's book offers some truly great analysis. It's full of incredibly insightful observations about how the system works. For example, it explains why communist propaganda was so crude and obnoxious, even though it was relatively easy for the authorities to make it just a little bit more friendly and attractive to the consumers without risking much. The crudeness wasn't due to incompetence; it was purposeful, because the goal of propaganda was not to persuade people but to demoralize and intimidate them.

But the most powerful insight of the book (or, at any rate, the most powerful one to me) was an observation that living in a totalitarian state robs everyone of their identity by making it impossible for anyone to define themselves by themselves. Everyone, whether collaborating with the regime or opposed to it, is forced to define their very own self relative to the system they live in. You can't live in communism and simply ignore it. There is so much injustice, cruelty and lies at every corner of your life that it is impossible for you to not think about it; almost every thought you have is a thus a reaction to something you've seen, heard about or read that you viscerally disagree with. Whether you like it or not, your entire inner life becomes a constant polemic with the communist monstrosity surrounding you; there are almost no thoughts left that are entirely your own. Communism robs you of your thoughts. That realization was extremely painful to Tyrmand; he repeatedly complains that even his diary, which is supposed to be the most intimate, personal form of writing, talks about the horrible reality of stalinism more than anything else. There is a great scene in the book that shows exactly how stalinism devours everyone's soul, even those who hate it. Tyrmand is riding a bus with his girlfriend Bogna (not her real name), a high school senior (I think she's 18 at the time but don't remember for sure). Bogna is talking high school gossip, being all loud and cheerful and youthful. As their bus drives by the infamous Rakowiecka Prison, a place where thousands of innocent people were being held, tortured and executed without charges, Bogna bursts into a particularly loud fit of laughter because of something she's talking about that she thinks is funny. Tyrmand gets infuriated by her lack of sensitivity, yells at her for laughing out loud and reminds her that behind the walls they've just passed innocent people are being tortured as they speak. Bogna looks at him incomprehensibly and then blurts out: 'You know what? You're nuts. You're just as insane as they are. All you ever talk about is what the communists are doing.'

Things depend

xkcd comments on using unconditional probability in situations when what's relevant is conditional probability:

Happens all the time. How many times have you heard someone say "Sure, the probability of winning the lottery may be very small... but someone wins it nonetheless!" Or take a more ominous example: Alan Dershowitz's claim, made during O. J. Simpson's trial, that since less than 1 in a 1000 women abused by their partners are also killed by them, the fact that Simpson abused his wife doesn't make it much more likely that he killed her. Makes me wonder how many people were falsely convicted or acquitted because of erroneous arguments like this not having been exposed.

Double delusion

Some people with a gambling problem tell themselves that if they play long enough they'll eventually win big. For most those people it's a delusion; unless you have an enormous amount of money to use on placing bets, gambling has negative expected returns. I wonder if those people actually create two layers of delusion for themselves: Unconsciously, they enjoy gambling as consumption, for its own sake, but their conscious mind tells them they are doing it for instrumental reasons, to earn money, and on top of that they delude themselves into thinking that they actually can earn money that way?

Where does the something that everything must come from, come from?

In his new book "The Grand Design," Stephen Hawking writes:

Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. (...) It is not necessary to invoke God to light the blue touch paper and set the universe going.

Naturally, the statement caused quite an uproar and a lot of polemics from apologetics. It may just be my bad luck, but quite honestly I have not read one single response to Hawking's claims that would be in any way insightful, or even intelligent for that matter. Every single defender of religion that I've read argued against Hawking using some version of the famous First Cause Argument: Whatever begins to exist has a cause, therefore the Universe has a cause, the "First Cause" of everything there is. Apologetics identify the First Cause with God.

Newsflash: The First Cause argument is logically flawed. As in: it's wrong. It commits the fallacy of "begging the question" or, in much less fancy terms, simply assuming what it's trying to prove. Suppose everything that exists must indeed have a cause. Then it does follow that the Universe must have a cause. But what caused the First Cause? You just assumed that everything must have a cause, so the First Cause must have one too. What is it? The Mother of All Causes? And who's her mother? In other words, if everything that exists must have a creator, then who created the creator? Note that you're not allowed to say that God exists without having to be created because "that's His nature." That's not an argument; it's a hand-wave. We might just as well assume that the Universe created itself out of nothing because "that's its nature."

But some response pieces are even more confused that just relying on the First Cause Argument, and I'll write about one of those. It's an essay by Pawel Lisicki, editor-in-chief of one of the largest daily papers in Poland, "Rzeczpospolita." Referring directly to Hawking's above quote, Lisicki writes

Both creation and spontaneity (...) are concepts that are well-defined only in the realm of personal metaphysics and religion. Only a person, an agent (...) who has free will and ability to reason, can be spontaneous.

Strike one for monumental ignorance. Spontaneous appearance of things uncaused by an intelligent agent is directly observable. Certain particles have been observed to appear spontaneously, out of absolutely nothing. The price mechanism causes millions of unconnected individual decisions to coordinate into one huge resource-allocating machine which does not have a conscious designer. Further, Lisicki writes

In Christian thought, being able to create something is an attribute of God (...) only through analogy and metaphor can we also talk of human creation. Impersonal, spontaneous creation as a cause that the world exists is a self-contradictory concept.

Strike two for ignorance coupled with pretentiousness. Lisicki says that impersonal spontaneous creation is a self-contradictory concept, and that's because... it's inconsistent with the definition of creation that he is using! In other words, he clearly has no idea what "self-contradictory" even means; he's just pretentiously throwing the term around because it makes him sound all smart and everything. To top things off, the definition he's using makes his reasoning perfectly circular. Effectively, Lisicki's entire argument is this:

I've just assumed that everything that exists has been created. I've also defined "creation" as something only God can do. Therefore, the Universe has been created by God.

That's all of it, really. How completely uncritical of your own beliefs do you have to be to think this is actually a sound argument?

Non sequitur of the month: One of the most bizarre attempts at argument I've seen

It's due to Magda Figurska, a Polish blogger I've written about once before. She commented on a blog post whose author quoted a statistic which says that in the second quarter of 2010, annualized GDP growth in Poland was 3.4%. Figurska wrote: "What you're writing is just like communist propaganda. You write about GDP growth of 3.5% in the second quarter but forget to mention that, in the same quarter, inflation was 3%." So far so bad. Figurska is unaware that the 3.4% annualized GDP growth statistic is already adjusted for inflation (in fact, published GDP statistics always are). That's stunning ignorance, but it isn't a non sequitur just yet. Inevitably, another commenter pointed her mistake out to her, to which she replied: "Really? Then look here. Inflation in Germany 0.00%." (The link she gave was simply a table with a bunch of economic statistics for the second quarter of 2010 for a bunch of countries.)

In other words, the fact that Germany experienced no inflation in April, May and June of 2010 somehow proves that GDP growth statistics are not adjusted for inflation. Other commenters in that thread asked Figurska to elaborate on this rather peculiar inference but she ignored them. So what we're left with is a truly stunning non sequitur.

Have some distance to yourself

A distance of 114 million miles, to be exact.

(The image shows the Earth and the Moon as seen from the MESSENGER spacecraft. The source is NASA.)

A whole different language

I'm constantly amazed at how powerful music is in inducing emotions, and also at the complexity of those emotions. Verbal language, on the other hand, is very inefficient at describing emotional states, which I think prevents us from appreciating what music is capable of--because most of the time we simply can't describe it. Read, for example, a verbal description of a mood of any Chopin piece; it's striking how incredibly shallow it is when compared to the mood you feel when you actually listen to it. You'll read words like "melancholy" or "longing" or whatever--all of which are true but way too general and therefore grossly incomplete. Sure it's melancholy and longing, but of a very specific kind, and for some reason we don't have analytic categories to communicate specific shades of general emotional states. Perhaps there are too many of those shades. Or perhaps communicating them efficiently is for some reason completely unimportant for the functioning of society. Or maybe the "shades" are too subjective--when I see Alice blue, someone else sees carmine pink or something.

Added: The ability to elicit extremely complex and varied emotions is I think a property of music as a language and is independent of its quality. Kitschy music can make me feel things way too complex for words just as readily as truly great music.

Two types of jerks

I wrote once about kindness being more scarce in poorer societies. There's also a difference between richer and poorer societies in terms of how unkindness manifests itself most often.

In general, people who are profoundly selfish (a.k.a. assholes) fall into two categories that I call "brutes" and "brats." Both brutes and brats have no regards for other people's values or feelings and act on self-interest only; where they differ is in how they view their actions. Brutes have no problem bending people to their will in situations where they have the power to do so. They will take advantage of others at every opportunity. They more or less know that doing so is wrong, but they don't care. They figure the world is a tough place and it's either kill or be killed, so they kill if they have to. They do not feel the need to rationalize their assholery; even though they know the difference between right and wrong, they don't have a conscience. Brats, on the other hand, hate to think of themselves as assholes. They mostly recruit from people who at some point in their lives were profoundly spoiled, and because for a long time all their social interactions were based on other people catering to their whims, they concluded that the way of the world is such that they rightfully deserve more than others. They have no conscience either; but, as opposed to brutes, they are completely amoral. They believe deeply that other people are there to serve them and interpret any disagreement as terrible injustice.

My stylized and completely subjective observation is that poorer assholes are mostly brutes whereas richer ones are mostly brats (this seems to hold both within- and cross-country). There's also an orthogonal gender divide. Holding income constant, selfish men come in both flavors (though brats are usually outnumbered) whereas almost all selfish women are of the brat variety.

(In case you're wondering: If I'm an asshole, then I'm definitely a brat. Note the conditional nature of the statement though.)

If you can't build 'em, grow 'em

Bill Easterly reminds a classic anecdote (due to David Friedman) illustrating the point that, looking at their effects on the economy, trade and technological progress are the same thing:

There are two technologies for producing automobiles in America. One is to manufacture them in Detroit, and the other is to grow them in Iowa.

How does one manufacture cars in Detroit? I don't know; ask an engineer or whoever it is that knows about stuff like that. How does one grow cars in Iowa? Like this:

First you plant seeds, which are the raw material from which automobiles are constructed. You wait a few months until wheat appears. Then you harvest the wheat, load it onto ships, and sail the ships eastward into the Pacific Ocean. After a few months, the ships reappear with Toyotas on them.

Death metal shows and moral intuition

It's probably a good bet that you've never heard of a Polish death metal band called Behemoth. Until recently, I haven't either (even though they are apparently world-famous in their niche). The reason I've heard of them is because one of their shows in Poland made the news nationwide. During that show, its front man Adam Darski went on a long rant about the evils of Christianity, and concluded it by tearing up the Bible. Publicly offending religious sensibilities is criminalized in Poland, and charges were filed against Darski. I don't know if he was convicted or not, and it isn't really relevant here; the point is that the incident spurred a discussion about how the law should be dealing with, well, situations of this sort.

I remember a TV talk show in which a bunch of Polish celebrities were arguing over Darski's case. One of the participants pointed out that the incident happened during a death metal concert, which meant that it was very unlikely for the audience to contain anyone who would be offended by this sort of thing, and at any rate those who are offended by this sort of thing have a simple choice of avoiding Mr. Darski's live shows. To this, an entertainer and Catholic publicist Wojciech Cejrowski replied that it doesn't matter because "just knowing that someone in my country is disrespecting the Bible like this is enough for me to feel offended."

What should happen in those situations? I feel very strongly that Darski's right to tear up the Bible is much more important than Cejrowski's right to know that no one is tearing up the Bible "in his country." But, to be honest, I am not entirely sure why I think that. I'm big on the efficiency criterion and cost-benefit analysis; but if you assume that the right to publicly tear up the bible is worth $50 to Darski, while the comfort of knowing that tearing up the Bible is prohibited by law is worth $100 to Cejrowski, then cost-benefit analysis says we should ban tearing up the Bible. I'm unwilling to accept this conclusion, though don't have much in way of a rational argument why. The only thing I can think of is that in situations when we're weighing banning things versus allowing things, and in which both alternatives hurt someone, we should err on the side of allowing things. Much of progress is achieved through trial and error, so it seems to me that banning things can have an externality in that many potentially beneficial things will not be tried. But then again, many potentially harmful things will not, either. So this is really just a moral intuition that I have, which makes me feel uncomfortable because moral intuitions are not a good guide of ethical choices. Moral intuitions are often wrong. In fact, some people's moral intuitions are downright repugnant to me.

How your beliefs shape your perceptions: If a tree falls down in Smolensk, how thick is it?

Quick: how thick is the tree in the picture? What I mean is, what is its diameter at the point where it broke? Take a guess and make a mental note of it before you read on. You can click on the picture to enlarge it. Don't overthink it though; just pick a number that seems reasonable to you and move on.

Republicans are much more likely than Democrats to think that Obama is a Muslim who was born in Kenya. This correlation doesn't make any sense to me, and to a whole lot of others. People become Democrats or Republicans because of their values or policy preferences; Obama's faith and place of birth are not a matter of values or preferences. They are a matter of fact. There is no a priori reason why people with different values should have different judgments in factual matters. It really doesn't make any sense whatsoever. The only reason why it doesn't baffle people as it should is because it's something that happens all the time, so we just get used to it and forget how utterly insane it really is.

Someone might object here that it's perfectly reasonable for people with different perceptions of facts to have different values, so the observed correlation may not be so strange after all. If you think Obama is a foreigner and a Muslim, perhaps you're more likely to become a Republican. To this I would object that, in the real world, causality seems to run the other way much more often. Most of the people who have strong beliefs about Obama's spirituality and birthplace chose to be Republicans or Democrats long before they even heard of Barack Obama. It really is very striking: instead of choosing policies that match the facts as they see them, people choose to believe the facts that back up their values-driven policies.

What does all this have to do with a picture of a broken tree? A lot, actually, because it's not just any old tree. This tree has tremendous political importance. According to the Russian Interstate Aviation Committee, which is investigating the recent crash of the Polish presidential airplane near Smolensk, Russia, the tree in the picture is broken because, in the final seconds of its flight, the presidential aircraft has hit it with its left wing. It's hypothesized that the impact caused part of the left wing to snap off, which in turn caused asymmetry of lift, forcing the aircraft into a complete roll to the left, after which it hit the ground inverted, killing everyone on board.

OK, but again, what does all this have to do with facts and values and Obama being born in Kenya? Well, lots of Poles, and some Polish media are convinced that the Smolensk crash was in fact an assassination organized by Russian special ops forces. The "accident vs. assassination" divide cuts deep and seems to be driven mostly by values and preferences just like political ideology cleavages are. At any rate, if you believe in a deliberate act of destruction, you must think that the official story of the airplane losing part of its wing on a tree, rolling to the left and hitting the ground upside down cannot be correct. Most assassination-believers claim that it's impossible for the aircraft to have lost a wing on this particular tree because it isn't thick enough.

Which brings me to my point. As I read discussions between accident- and assassination-believers that go on in Polish blogosphere about whether it is or is not likely that this tree has indeed destroyed the airplane's wing, it's very hard to believe that all those people are talking about the same damn tree. Most assassination-believers claim that the trunk is "at most 40 centimeters [about 16 inches--p] in diameter" where it broke. (I've seen claims going as far as 5.5 inches.) Most accident-believers claim that the diameter is "at least 50 centimeters" [about 20 inches]. All of them are basing their opinions on the same pictures.

So there you have it: values shaping perceptions, and very basic perceptions at that. Here's an idea for a fun experiment. Show the picture above to a large group of people who have never heard of the Smolensk crash, and ask them what they think its diameter is. Then show the same picture to a large group of people half of which are accident-believers and half of which are assassination believers, and ask them the same question. How would the answers differ? I don't know if the mean of the guesses in both groups would be different, quite possibly not. But I think the distributions would be nothing alike. The guesses of the first group would be distributed normally, whereas in the second group they would follow some sort of a bimodal distribution. However, one simple additional twist in the experimental design would make that difference disappear. Go to Smolensk and measure the actual diameter of the tree. (It can be done; the tree is still there.) Once you've obtained the correct answer, gather your two experimental groups and ask them to guess the diameter, but this time tell them that everyone who gets within an inch of the correct answer will be paid $500. You will see bimodality in the second group's guesses disappear as if by magic. You will see both distributions assume a normal shape with roughly the same mean, which will be roughly equal to the true value. Such is the difference between situations in which people form their perceptions of facts in order to signal their preferences, and situations in which people form their perceptions of facts in order to find out what those facts actually are.

To sum things up, and in case you were wondering, my own guess is 50 centimeters, plus or minus 10 centimeters (which is about 20 inches, plus or minus 4 inches). My wife's guess was "a foot an a half," or about 47 centimeters. (She has heard of the Smolensk crash, but didn't know what tree she was looking at.)

Nerdy joke

Via Ed Brayton:

Jesus and his disciples were walking around one day, when Jesus said, "The Kingdom of Heaven is like 3x squared plus 8x minus 9." The disciples looked very puzzled, and finally asked Peter, "What on earth does Jesus mean: 'the Kingdom of Heaven is like 3x squared plus 8x minus 9?'" Peter said, "Don't worry. It's just another one of his parabolas."

In case you're wondering, it's a simple joke. You don't need to get to its roots in order to understand it.

Kids are random

We're born with a number of false cognitive intuitions that we shed later in life. Young children (especially those before the age of six) tend to make bizarre cognitive errors in controlled experiments, errors which older children will have learned to avoid. For example, young children tend to believe that pouring liquid from one container to another can change its volume: experiments were done in which kids were presented with a choice of one glass of orange juice out of two, which contained the same amount of juice, but of which one glass was taller than the other, and they almost invariably chose the taller one. What's more, when experimenters showed kids that the volume of liquid in both glasses was the same by pouring juice back and forth from one glass to the other, most kids remained unconvinced and still believed the taller glass had more juice in it.

But there's one specific area that I know of in which kids start off right but then, at about age five, acquire a new intuition, one that is wrong. This area is "mimicking randomness." Adults are notoriously bad at it. For example, when a group of adults is asked to write down a sequence that they think could be a likely result of tossing a fair coin 20 times in a row, they give answers quite different from sequences that are generated by actually tossing a fair coin 20 times in a row. Those differences are systematic, and three of them are repeated by almost everyone: 1) sequences given by participants are much more likely to contain 10 tails than actual random sequences, and much less likely to contain more than 12 or less than 8 tails; 2) they contain much less instances of two or more identical outcomes in a row than true random sequences and 3) the series of same outcomes are noticeably shorter than in actual random sequences; for example, the participants almost never write down sequences containing more than four heads in a row, whereas in true random sequences series of five or even six heads in a row are quite common. In other words, sequences provided by participants resemble the underlying stochastic process much more than sequences that were actually generated by that process. Or, in yet other words, people tend to believe in "the law of small numbers:" that small samples have the same properties as large samples. But what's interesting is that, apparently, people do not start believing in that law until they are older than about five. Most four year olds give sequences which do not exhibit those three systematic mistakes. It's a case of cognitive bias that is learned.

Imma strategize!

If you follow political news in Poland, you'll hear the phrase "The problem of Poland's government has always been a lack of long-term, strategic thinking" about four times a week. The truth is exactly the other way around: there's been way too much strategic thinking going on. According to a report written by deputy minister Jerzy Kwiecinski in 2007, between 1989 and 2006 the Polish government has officially launched a total of 406 strategies, of which 250 were still in effect at the time of his writing.

Because it's beautiful

This post is a propos absolutely nothing. It is about the artistry of the first touch in soccer. Below is a video with a compilation devoted to a very specific element of soccer technique: the "touch-fake," where a player receiving a pass uses just one touch to bring the ball under control and wrong-foot the player who marks him at the same time. Watch and admire. Note especially the very first goal, which I think is one of the most amazing ever scored.

Look, your evidence is rather biased

OK, so this post will not be very productive. I'm just venting. I am so tired of people who try to convince everyone that the world is beautiful and good because look, it's got rainbows and sunsets in the mountains and love and music and Christmas dinners. Have you ever heard of confirmation bias? Why don't you look at pancreatic cancer, a tapeworm, a botfly, mass starvation, the Wola massacre, or Robert Mugabe, and put this stupid argument to bed for once?

Some forecasting

Poland's public debt is on its way to become a problem. The debt-to-GDP ratio is now at about 50%, is rising quickly, and many economists worry that it will soon exceed a threshold of 55%, at which the government and parliament are required by law to enact a budget that would lower this ratio (which, in practice, would mean very large tax hikes and/or spending cuts). Fortunately, according to a forecast recently published by the government, by 2012 the debt-to-GDP ratio will cease rising and stabilize at 54.99%.

Why you can't make a passenger plane out of a bomber

Here's an example of how thinking about economics can be helpful in evaluating claims that, at first sight, don't have much to do with economics. Do you remember the Polish presidential aircraft crash of April 10, 2010? If not, here's what happened. On April 10, 2010, the Polish presidential aircraft, a highly customized version of Tu-154 (a Russian-made commercial airliner that began service in 1972) crashed on approach near a small military airport in Smolensk, Russia, killing all 96 people on board. Among the victims were the President of Poland Lech Kaczynski, his wife, the military joint chiefs of staff, the director of Polish central bank, and many other VIPs.

Recently, the late President's brother and leader of Poland's largest opposition party Jaroslaw Kaczynski, gave an interview in which he talked about the crash and the ongoing investigation thereof. One of the things that Kaczynski is wondering aloud about is the extent of damage suffered by the aircraft's fuselage. The plane did not lose lift until it was 20 meters (about 66 feet) above ground, and yet it completely shattered on impact. Kaczynski suggests that this should not have happened because the design of Tu-154 is based on a Soviet bomber and its fuselage is therefore much stronger than that of a typical airliner.

Now it's certainly true that the presidential Tu-154 was in fact structurally stronger than your average commercial aircraft. VIP planes are highly customized with safety in mind. Air Force One is technically a Boeing 747-200, but it's really modified beyond all recognition. So I am not going to talk about that particular Tu-154; instead, I want to criticize the claim that the structural fuselage strength features of a regular, mass produced Tu-154 are adapted from a bomber. You don't need to know much about aircraft engineering to realize that it's unlikely to be true. All you need to know is that commercial airlines have to be profitable while the air force does not.

Passenger aircraft are designed to be sold to commercial airlines. The airlines have to make a profit operating them. That means the aircraft they use have to be fuel-efficient. An aircraft design that puts too much weight on fuselage strength is likely to make the aircraft too heavy. Too heavy means it's using too much fuel to pay for itself. Bombers, on the other hand, don't have to pay for themselves. Designers of bombers can afford to make them able to withstand high-energy impact. Designers of commercial jets cannot.

The meaning of life

In an interview for the New York Times, Deepak Chopra says:

I was trained as a medical doctor. I went to medical school because I wanted to ask the big questions. Do we have a soul? Does God exist? What happens after death?

Perhaps he should have talked to an academic advisor before applying.

(HT: Kids Prefer Cheese.)

Headbutting in soccer

Remember Zinedine Zidane headbutting Marco Materazzi in the 2006 FIFA World Cup final? Of course you do. Headbutting is actually quite widespread in the game (for anecdotal evidence, see here, here and here). I have trouble understanding why that is though. Why don't they punch instead? The penalty for headbutting someone is the same as for punching them: immediate expulsion from the game. If someone made you mad enough to headbutt them, they probably made you mad enough to punch them, and if you find yourself in a fight, your first instinct is to punch not headbutt anyway.

Corporate-speak: what's it good for?

A Marginal Revolution reader writes them with a great question:

Why does the corporate world use language so inefficiently? Why turn a simple thing like "talking to a client about their needs" into a five-step process (distinguished, no doubt, by an acronym)? Do companies think that they create net value when they brand a common thing like human conversation as a one-of-a-kind, complex process – even after the costs of being opaque, jargonistic, and long-winded are taken into account?

To which Tyler Cowen replies:

People disagree in corporations, often virulently, or they would disagree if enough real debates were allowed to reach the surface. The use of broad generalities, in rhetoric, masks such potential disagreements and helps maintain corporate order and authority. Since it is hard to oppose fluffy generalities in any very specific way, a common strategy is to stack everyone's opinion or points into an incoherent whole. Disagreement is then less likely to become a focal point within the corporation and warring coalitions are less likely to form.

This answer seems unsatisfying to me, mainly because I don't think this use of corporate-speak would justify its costs. Because of its transparent stupidity, corporate-speak is highly demoralizing; your employees aren't going to be very happy if you ask them to show up to work wearing clown suits. In addition to this, corporate-speak is used not only for assertions, but for instructions as well; why would you instruct your employees in such incoherent and inefficient ways?

For more possible answers, see the MR comments. My own hypothesis is that I have no idea.

Department of WTF!?

There have recently been severe storms and occasional flash floods in Poland, which scared the life out of the inhabitants of affected towns, because the terrible flood wave that swept through the country back in May this year is fresh in everyone's memory. People are especially scared that the levees will start overflowing again, just like they did four months ago.

Fear no more though; the probability of that happening again is very low. How low? Well, the director of a nationwide natural disaster warning agency held a press conference about the state of the levees in one of the flooded towns and said that "The probability that they will overflow is nearly zero, meaning it's less than thirty percent."

I'm not making this up. I rewound three times to make sure I've heard it correctly.