Wednesday, March 31, 2010

Climate Sensitivity

I suppose there is a sort of Anna Karenina principle for scientific error: every correct scientific argument is the same, but every erroneous argument is erroneous in its own way, but there are some general strategies: put in some correct stuff, put in some related equations but at the critical moment equate some things that aren't actually equal or derive something from an inappropriate equation. Above all, though, make your argument complicated, so that it's really hard to see exactly where you went wrong.

In this last respect I can't say that ex-Professor Motl's Post is a model, because he's really quite clear in his argument and it's pretty obvious exactly where he goes off the tracks in his calculation of climate sensitivity. Of course he does emit a lot of smoke after that point, but it's way too late too hide the dirty deed by then.

To set the scene, let's remember that CO2 causes planetary warming by increasing the outgoing impedance to radiative heat flow through the atmosphere without much affecting the incoming radiation. Since the amount of solar radiation reaching the Earth's surface is approximately unchanged, the amount of radiation leaving the top of the troposphere has to remain unchanged as well, but the increase in outgoing impedance means that the surface warm up until the temperature gradient is large enough to drive an outgoing heat flow that matches the incoming.

The climate sensitivity parameter attempts quantify the surface temperature change needed to compensate for the increased outgoing impedance in terms of the so called radiative forcing:

The radiative forcing of the surface-troposphere system due to the perturbation in or the introduction of an agent (say, a change in greenhouse gas concentrations) is the change in net (down minus up) irradiance (solar plus long-wave; in Wm-2) at the tropopause AFTER allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values.

Lumo next writes down the Stefan-Boltzman law for the dependence of total radiation on the temperature but makes his first critical error in equating that to the radiative forcing - or at least using the same symbol (RF) for it. This fundamental confusion becomes the source of all his subsequent errors. If all the radiation emitted by the surface reached the top of the atmosphere, this formulation would be correct (and there would be no greenhouse effect), but it doesn't, as Lubos explicitly admits. CO2 and other components of the atmosphere ensure that only a fraction of the outgoing radiation (or more generally, heat - since a lot of the transport is not radiative) reaches the top of the atmosphere. The change in that fraction due to addition of a component (such as CO2) is the radiative forcing.

Despite his first fundamental error, Lumo acknowledges the CO2 impedance and calculates (or at least acknowledges some calculation to get) a radiative forcing due to the CO2, getting approximately the IPCC result. What's been left out at this point are the feedbacks. If CO2 warms the surface of the Earth, that warming will increase the amount of water vapor and methane in the atmosphere. They too will reduce the fraction of outgoing emissions that reach the top of the atmosphere.

Here though, Lumo makes his second and more bizarre error. He appears to assume that the effect of the feedback is to change the shape of the curve of dependence of surface emission upon temperature. Of course it doesn't have any such effect - what it does do is change the impedance of the lower atmosphere to outward radiative heat flow. The S-B law governs emission - not net outflow, and the emission must increase (via increasing surface temperature) to compensate for the decrease in atmospheric transmittance.

Next he wanders off into some deductions from his peculiar error - I'm afraid that I didn't try to follow them.

Words Are Cheap

At least if checking the truth of what you say isn't a priority. Not quite free, though, it seems. According to the following link, it seems that Koch industries, a privately held oil and otherwise diversified conglomerate has spent almost $50 million funding the climate denial industry.
It seems that the Koch brothers have funded most of the usual rascals in the climate change racket: Willie Soon, Sallie Baliunas, Moncton and so on. You can contribute to their cause by buying

...such well-known consumer brands as Dixie cups, Brawny and Quilted Northern paper products, Stainmaster carpet, CoolMax and Lycra.

Tuesday, March 30, 2010

Midnight Math

I made the mistake of drinking coffee tonight and couldn't sleep. Trying to understand math usually works, so I started thinking about the famous formula:

exp(i*x) = cos(x) + i*sin(x)

It seemed to me that that equation combined simplicity and great beauty. So how to understand it? If you realize that exp(i*x) lies on the unit circle in the complex plain at angle x wrt the real axis, it's obvious, but how do you get to that? Comparing the power series works, but somehow appealing to the full machinery of differential calculus seemed like a cheat too. I wanted to understand it in more fundamental terms.

Suppose you multiply a real number a by the imaginary unit i. If you think of a as a point a distance a to to right of zero on the real axis, i*a is a similar distance up the imaginary axis. Similarly, the point a + i*b can be reached from zero by going 'a" to the right and then up 'b'. It thus lies at an angle arctan(b/a) from the real axis at distance sqrt(a^2+ b^2) from zero. If we multiply a complex number z by another complex number a + i*b, the answer is another complex number lengthened by a factor of sqrt(a^2 + b^2) and rotated an angle arctan(b/a) in the counterclockwise direction.

Consider the complex number 1 + i*x/n. Multiply it by anything and you get that rotation by arctan(x/n) and magnification by sqrt(1 + (x/n)^2). If I recall correctly, the fundamental definition of exp(x) is the limit as n->infinity of
[1 + x/n]^n. In the limit as n -> infinity, arctan(x/n) -> (x/n).

[1 + x/n]^n is thus a vector in the complex plain rotated by n angles of arctan(x/n) and length of the product of n factors of sqrt(1 + (x/n)^2), which in the limit as n -> inf becomes rotated by angle x and of length 1 - that is, a point on the unit circle in the complex plain at angle x from the real axis.

I probably should check my work but maybe I can sleep now instead.

A Modest Proposal

I grew up in the Catholic Church and have mostly positive memories of it. I was an altar boy and was never abused by any of our priests nor did I have reason to suspect anybody else was. Some of the nuns were a bit physically abusive, its true, but given the absurd costumes they had to wear, its hard to really blame them.

The big problem with the Catholic Church is its organizational structure: it was patterned on the Roman Empire of Constantine, and wound up with most of the vices of that organizational structure. The Pope was only responding to the character of that institution when he chose to deal with the sexual abuse scandal with secrets, lies and a cover up.

The time has come to move the Church a bit closer to the twenty-first century. A good way to start would be with the Pope's resignation, replacement by a term limited (ten years?)Pope elected by all Bishops - themselves elected by the congregations for limited terms. One of the problems with the current lifetime election system is that the Cardinals don't want to be stuck with some idiot forever, so they usually elect somebody so old that he's pretty much senile already.

And get rid of the stupid celibacy stuff.

Monday, March 29, 2010

Post Washington Post

The Washington Post won the undying enmity of the American right by occasionally reporting some facts, including those that led to the exposure of the crooked doing of Nixon and friends. In recent years, that same Post has labored tirelessly to make amends, mostly by getting rid of competent reporters and replacing them with right wing hack columnists, but I suspect they labor in vain - except for the fact that liberals and other people paying attention now hate them even more than the conservatives do.

Robert Samuelson has long been the Post's economics columnist. Aside from an undergraduate degree in political science and longevity, his qualifications for that post seem to be that:
(1)He has the same last name as a famous economist, and
(2)He reliably spouts the Republican talking points of the day.

Brad DeLong and Menzie Chinn are not amused.

Shep Smith, Master Ironist

I wouldn't want to get Shephard Smith in trouble with his employers, but is he one of the under appreciated ironists of our time or what? Interviewing the ex-fiancee of the leader or the newly arrested militia/terrorists, the dialog went a bit like this:

Ex f: He thought the government was try to take away his freedoms.

Shep: His second amendment rights?

Ex f: He loved his guns, he was afraid to lose them.

Shep: Has he always been like this?

Ex f: Yes, but especially since Obama was elected. He thought he might be (or bring?) the Anti-Christ.

Next, with the retired FBI conspiracy guy:

FBI: They believe the government is conspiring against them, is going to take their guns.

Shep: Where do they get these ideas?

Sunday, March 28, 2010

Cringe Worthy

I was watching Peggy Noonan vs. George Will on ABC's This Week compete in the Most Pompous Gas Bag event. I think I have to give the nod to Will for his cocksure spouting of self-inconsistent nonsense, but Peggy certainly deserves some sort of honorable mention for her buffoonish tone of psuedo-profundity.

Jake Tapper, btw, wasn't at all bad. He paid attention, brought up some useful points, and asked reasonable questions. I'm still looking forward to Christiane though.

Man vs. Computer

It took almost a half century of development for computer chess programs to reach and top the level of the strongest human players, with a specially built IBM supercomputer beating then world champion Gary Kasparov in 1996. In the end, the decisive factor was not software but increasing hardware speed. Computer processing power has continued to increase, and quite modestly priced computer chess programs running on personal computers can now thrash world champions.

The world's other premier intellectual game, Go, has proven a tougher nut to crack. When IBM's Deep Blue was beating Kasparov, the world's strongest Go programs were still getting huge handicaps (11 stones) from strong amateur children and losing. That's not quite the case any more - they now occasionally beat strong professionals at slightly more modest handicaps (7 stones).

I recently purchased a new copy of The Many Faces of Go 12, one of the strongest computer go programs, and I have the impression that it has now reached the point where it can sometimes offer useful advice to a fairly weak amateur* like myself.

Once upon a time one could not hope to become a master chess player unless you lived in New York, Moscow, or one of a very few other chess capitals. Computer chess has made that obsolete - now all you need is program, laptop, and electricity to give you grandmaster opponents whenever you want. For go, though, that time is still seemingly far in the future. Of course you can play on the internet.

Saturday, March 27, 2010

A Pyramid of Hokum (From Comments)

Motl, in comments, has erected a pyramid of hokum that he claims is isomorphic to the call for AGW action. To wit:

...a pyramid of roughly a dozen of assumptions and all of them need to be true at the same moment for the final conclusion to be justifiable: you need warming to exist, to continue in the future, to be caused by CO2, you need the economy to be able to reduce CO2, to make a difference, and so on.

His notion is the justification that these are independent constraints that are both of dubious truth and necessary to warrant action to prevent anthropogenic global warming. There are really only three points (a)human activity is increasing the CO2 in the atmosphere, (b)increasing CO2 increases temperature, and (c)how much? The first two of these are proven beyond reasonable doubt, and don't depend on statistical arguments. The first depends only on measurement and logic, and the second on the validity of the laws of physics. The third is difficult and the relevant lines of evidence depend on statistical and other arguments, but not in way Motl implies. Instead there are various lines of evidence (models, the historical record, the geological record) each of which give similar and mutually confirmatory evidence.

We can (and must) ask other questions. What is the cost of not acting to control our emissions? What would be the cost of acting?

My own suspicion is that we can't act decisivly in time to do much good. Thanks to the cost of acting and to the mass of lies and distortions propagated by Motl and his fellow propagandists, it seems unlikely that action will be taken. It will be a different planet our descendents (if any) inherit, and likely less hospitable to human life.

Take That, Sandra and Elin!

Via Sullivan we get This experiment from Dan Arielly.

It seems that your particular monkeys are just doing what comes naturally.

Given a choice between spending a token to get their absolute favorite food or spending it to have a choice from a buffet of options, capuchin monkeys will opt for variety.

In fact, they'll even eat a less-preferred food from that buffet when the favorite food is on it. They choose variety for variety's sake.

The implications of this simple experiment shed some light on consumer behavior, Ariely said. Earlier work on variety-seeking has found that people eat 43 percent more M&M candies when there are 10 colors in the bowl instead of just seven. "People choose variety for variety's sake," Ariely said. "They often choose things they don't even like as well just for the variety. We knew about this, so the interesting thing was to figure out how basic it is."

Pretty basic, apparently...

The Dark Night of the Conservative Soul

As the American Conservative movement is increasingly consumed by the genies it let loose, more than a few conservatives are beginning to wonder what happened. David Frum's wife, Danielle Crittenden:

We have both been part of the conservative movement for, as mentioned, the better part of half of our lives. And I can categorically state I've never seen such a hostile environment towards free thought and debate -- once the hallmarks of Reaganism, the politics with which we grew up -- prevail in our movement as it does today. The thuggish demagoguery of the Limbaughs and Becks is a trait we once derided in the old socialist Left. Well boys, take a look in the mirror. It is us now.

An Andrew Sullivan reader looks at and doesn't like how a conservative Catholic site reacts to the latest revelations about the pope's role in the pedophilia coverup:

Something snapped in the Bush years, though. The whole organization (led by Neuhaus) descended deeper and deeper into neocon unreality. Anyway, I was reading something about how the Corner over at National Review, which never stops touting Catholic doctrine when it is convenient to its causes, has been utterly silent on the crushing scandal in Rome. And I thought I would check out First Things' site, which I hadn't been to in a while. It was astonishing.

There are seven blogs there. I scrolled down the first page of all of them. I would estimate that about 80% of the posts were anti-Obama diatribes or links, or anti HCR, or anti Democrats generally. And in those seven blogs' first pages, most of which cover at least two or three days' worth of posts, this is the only mention of the doings in the Vatican -- and you'll never guess who gets the blame.

Andrews's response.

I guess I'm just stupid, because I think someday I won't be surprised at how low these people can go.
I like that phrase: "something snapped in the Bush years." It did. It was the conservative soul.

I think you guys just started noticing the rot during the Bush years. Not that I ever had a whole lot of sympathy for the right, but I think that the current neo-fascist character of the Republican party has more to do with Nixon, Buckley, and McCArthy than it does with Bush and Rove. It was Nixon and friends who saw a bright future in aligning the party with the most racist and rejectionist elements of the South. There is a price to be paid when you make deals with the Devil

Friday, March 26, 2010

Probably So and Probably Not

Lumo has an odd posting on confidence testing. He makes much of the fact that if you multiply a bunch of probabilities close to 1 (say 0.95) times each other you can get a number that's close to zero. This may not be a big shock to those who remember how to multiply. His purported point (I suppose) is that if you have some proposition the truth of which depends on the truth of n independent proposititons each of which is known with probability p, then the we presumably have confidence p^n in the composite proposition.

The question, of course, is who is supposed to have reached such a composite conclusion?

The Lumonator includes a link to a supposed offender but I searched the linked post in vain for any hint that that was the case. My guess is that LM is blowing smoke, as is his wont.

The actual case in climate science is more nearly the opposite of the situation he seems to be implying. There are multiple lines of nearly independent evidence each of which points to anthropogenic global warming. If we could apply Lumo style reasoning to these (and I'm not suggesting that we can) it would work oppositely to Mr. Motl's case. The no AGW null hypotheses, each rejected at the 95% level, would all need to be true for AGW to be rejected, and that involves multiplying a lot of 0.05s together. More to the point is the fact that his implication is backed by no examples of the reasoning he criticizes whatsoever.

Thursday, March 25, 2010

The Kindness of Strangers

Economist Mario Rizzo managed to attract intense derision from Brad DeLong for this:

Why am I tipping the cab driver whom I shall not see again? I tip cabdrivers very small amounts... they really don’t do anything more than drive... they don’t know where things are... there are now all sorts of surcharges... even a tax to support the inefficiently-run mass transit system that I am not taking.... I would really like to not tip.... I often do simply because drivers sometimes say nasty things to you if they don’t get a tip. It is a failing of my psychological make-up to let that bother me. Am I being selfish?... I am not being selfish any more than the driver who wants a tip. The real issue is for me: Is this the best use of my money?... You are not a bad person if you don’t tip taxi drivers much or at all. Just be prepared to tell the voice in your head that it is wrong. And don’t let any possible cab-driver annoyance spoil your day.

Brad thinks this makes him a psychopath but this could be overkill - it's not like he was celebrating mass murder, say. He does seem like a schmuck, though. ("Schmuck", btw, is one of those delightful Yiddish words of colorful (or off-colorful) origin).

More interesting to me was this study, which found:

Around 10,000 years ago, residents of large farming communities had to learn to make fair exchanges with strangers and to retaliate against selfish exploiters, researchers propose in the March 19 Science.

Before the rise of modern agriculture and resulting trade, the researchers contend, people rarely had to behave this way with strangers. During Stone Age days, members of small hunter-gatherer groups exchanged favors only with those they knew.

“Cultural and institutional evolution harnessed and extended our evolved psychology so that we could cooperate and exchange goods in vast communities,” says anthropologist and study director Joseph Henrich of the University of British Columbia in Vancouver.

Markets don't work well without a certain amount of trust. Without that trust, there is too much "friction," as everyone struggles to avoid being cheated. If most people are trustworthy, and cheaters (like Mr. Rizzo) are punished - at least by public obloquy, markets can freely function. There is a certain irony in the fact that those most approving of gaming the system seem to be market worshipping libertarians.

Sunday, March 21, 2010

Megan McArdle is a Crazy Lady

Health care reax from someone who purports to be an economist but is actually living in an alternate reality:

What I hope is that the Democrats take a beating at the ballot box and rethink their contempt for those mouth-breathing illiterates in the electorate. I hope Obama gets his wish to be a one-term president who passed health care. Not because I think I will like his opponent--I very much doubt that I will support much of anything Obama's opponent says. But because politicians shouldn't feel that the best route to electoral success is to lie to the voters, and then ignore them.

h/t Andrew Sullivan

I only quoted the parts that weren't totally dishonest - merely deranged.

Wild Caught

It was deep in the dinner party and and conversation had degenerated to denunciation of farmed salmon. "I only eat wild caught salmon," said D. It happened that B and C had similar feelings about the provenance of shrimp. It proved a popular cause.

Until E added: "I only eat wild caught cattle."

Saturday, March 20, 2010

More Tournament Madness

Ever since economists startled me by dissing tournaments, I have been fascinated by their ubiquity and utility as well as their potential for waste. Of course the whole panoply of life is a tournament of sorts, but let's consider one that was important in the development of the modern world: the invention of aircraft.

We have wanted to join the birds in the air at least since ancient times, but no real progress was made on making machines fly until the beginning of the nineteenth century. Not at all coincidentally that was the same time at which another great tournament was picking up speed - the industrial revolution. In the late 1790s, Sir George Cayley, 6th Baronet, Member of Parliment, and prolific inventor turned his attention to flight. His experiments were models of ingenuity, and he discovered many key principles of lift and flight. He designed and built the first successful manned glider and created the basic aircraft design that is used today.

It took more than another century before the Wright brothers were able to develop true powered flight, but the intervening period saw a great contest that steadily advanced the cause of flight. It was not a cheap contest, costing the lives of several of the pioneers, including the great Otto Lilienthal, but no economist should dare to call this contest wasteful just because in the end there was only one, or rather two, winners. Love for the contest is an intrinsic part of human nature, and that love probably costs us a certain amount of economic waste, but it's also the main driving force behind progress.

The Wright brothers, Lilienthal, and Cayley were not motivated by the prospect of making a buck, but by the dream and the contest. The same is true of the developers of most of the fundamental technologies that made the modern world.

The tournament is a fundamental part of our character, sometimes bearing valuable fruit but also loaded with risk. Financial markets are a tournament too, and taking unreasonable risks may be as much feature as defect - efficient markets and rational actors be damned.

Friday, March 19, 2010

More Favorite Books

Looking back at my history with physics books, e.g., 8,9, and 10 below and so many others, I can see that I would have been a lot better physicist if I had paid more attention. Of course it would have helped if I had been smarter too ...

First, a really important book that I haven't read all of: Darwin's Origin of Species. Despite having read only about half I can assure you that no book has had greater influence on me except maybe Newton's Principia of which I have read zero... You can tell a book is really important if you don't need to read it for it to be a big influence.

I promise I did read all the rest of these books carefully though, or at least most of them...

(1)Godel, Escher, and Bach and Metamagical Themas by Douglas Hofstadter. So many ideas connected into one big idea.

(2)Wonderful Life and several other books by Stephen Jay Gould. Gould is frequently blinded by his prejudices but he's a very fine writer and even his mistakes are instructive. One of the big reasons Chuck's book was so important to me. Others are:

(3)The Selfish Gene, Climbing Mount Improbable, and The Ancestor's Tale by Richard Dawkins. Dawkins is closer to the truth than Gould, but I love to catch his mistakes too - a good one in the first edition of TSG was an argument he tried to have with Astronomer and Science Fiction writer Fred Hoyle. Suffice it to say that Dawkins got his numbers all mixed up - numerics is not a strength for him.

(4)The Lord of the Rings, The Hobbit and The Silmarillion by Tolkien. If reality offends thee, pluck it out, or at least read some good fantasy - a rather rare commodity.

(5)Guns, Germs, and Steel, by Jared Diamond. A great big picture vision of how and where civilization developed. Diamond argues very convincingly that the development of agriculture and civilization had an awful lot to do with geography. Civilization developed in the Middle East because that was where the domesticable plants and animals were, and spread through Eurasia because the continent's East-West orientation facilitates the spread of agriculture. The Americas were nearly opposite. I like several of his other books as well, including The Third Chimpanzee and Collapse a cautionary tale of the environment.

(6)All of Richard Feynman's books, especially Surely you're Joking and the three big red books. They aren't really suitable for complete beginners, but almost everybody else can profit greatly from them, I think.


Tyler Cowen has been propagating a most influential books meme. His own choices are so serious and intellectual that one might be tempted to suspect a hint of pretension if it were anybody else. The only thing remotely disreputable on it is Ayn Rand in non novelistic garb, though on a reader's prompt he was forced to admit that Fisher's Sixty Memorable Games belonged there.

The comments contain lists from mostly lesser mortals, and a few more get propagated here and here and here.

The problem with such lists, if you can call it that, is that we tend to use them to try to show off - even if we are trying to be honest. My guess is that that doesn't make them much less revelealing. Most of Cowen's listers seemed to include some Any Rand in their lists, though some claimed to have outgrown it. I will stick with what the late Paul Samuelson said about Alan Greenspan - "You can take the boy out of the cult, but you can't take the cult out of the boy."

Anyway, I would like to invite any readers who are willing to submit their lists, and here is mine, which, if nothing else, might serve as a cautionary tale:

(1)Tarzan of the Apes has got to be number one, since this is the first book I can remember. I was a late reader - I couldn't really see very well - and my mother used to read to me, but when my brother was born, she got too busy and told me to read it myself. I read all the Tarzan books, and all the other Edgar Rice Burroughs. Children in my small town were allowed to check out four books from the library every two weeks, so I read mine, my older sister's Nancy Drew books, my younger sister's Bobbsey Twins books and everything else I could find - by this time I had glasses.

(2)The Modern Library Giant Treasury of Science Fiction. SF from the fifties and before. I got interested in science via science fiction.

(3)Three volumes by A D'Abro - early popular accounts of relativity and quantum mechanics. The Decline of Mechanism and The Evolution of Scientific Thought from Newton to Einstein. Science books were few and far between in 1950's Kalispell MT. I don't recall where I found these.

(4)Projective Geometry (author's name not recalled) A math professor sent me this book after I had asked a bunch of D'Abro inspired questions about tensors when he visted our high school. It was the first time it occurred to me that mathematics might be an interesting field of study.

(5)Poincare's popular science books Science and Hypothesis and The Value of Science. Hints of how a real scientist/mathematician thought, and the idea that it wasn't so strange to me.

(6)My high school English teacher believed that there were three sacred books that should be read and reread: Moby Dick, The Brothers Karamazov and War and Peace. Each deeply affected my vision of the world.

(7)Winston's Churchill's History of the Second World War and My Early Life.

(8)Gravitation by Misner, Thorne and Wheeler. Probably would have been a better influence on me if I had worked the problems.

(9)Classical Electrodynamics by John David Jackson. Every sensible American school teaches electrodynamics out of this book. Mine didn't. I blame that fact for my being so dumb about electrodynamics.

(10)Elementary Particle Physics by Stephen Gasiorowicz. This book had a lot to do with me not becoming a theoretical physicist. My QED teacher didn't believe in quantum field theory, or teaching it.

Hmmm? I guess there are some books that influenced me as an adult too. Later, maybe.

Thursday, March 18, 2010

A Friend Like Ben

Andrew Sullivan has been following the latest Roman Catholic sexual abuse scandals in Germany and makes a good case that the Pope is in it up to his navel. Among many other crime of omission, it seems that he heard evidence of child rape by a priest, concealed that evidence from the proper authorities, and made it possible for the priest to rape again.

Here he quotes Hans Kung, a leading Catholic theologian:

In his 24 years as Prefect of the Congregation for the Doctrine of the Faith, from around the world, all cases of grave sexual offences by clerics had to be reported, under strictest secrecy ("secretum pontificum"), to his curial office, which was exclusively responsible for dealing with them. Ratzinger himself, in a letter on "grave sexual crimes" addressed to all the bishops under the date of 18 May, 2001, warned the bishops, under threat of ecclesiastical punishment, to observe "papal secrecy" in such cases.

In his five years as Pope, Benedict XVI has done nothing to change this practice with all its fateful consequences.

Honesty demands that Joseph Ratzinger himself, the man who for decades has been principally responsible for the worldwide cover-up, at last pronounce his own "mea culpa".

As Bishop Tebartz van Elst of Limburg, in a radio address on March 14, put it: "Scandalous wrongs cannot be glossed over or tolerated, we need a change of attitude that makes room for the truth. Conversion and repentance begin when guilt is openly admitted, when contrition1 is expressed in deeds and manifested as such, when responsibility is taken, and the chance for a new beginning is seized upon."

A few previous Popes, including a previous Benedict (the IXth), have resigned. Andrew says its time for another resignation.

Genuinely Creepy

Steve Landsburg reaches genuinely creepy heights in his latest attempt at sensationalism. Witness his title: "In Praise of Genocide" and excerpt below:

...But as the world stands today, I suspect that cultures are worth very little at the margin (that is, we could stand to lose any one culture without missing it very much). There’s only so much you can assimilate in a lifetime, and to a considerable extent, time spent in contact with one culture is time not spent in contact with another.

So I’m not sure why the adjective “genocidal” is so often taken to be pejorative. I’m also not sure there’s any point to condemning some mass murderers more fervently than others, but if we’re going to play that game then I’m inclined to count genocidal intent as a mitigating circumstance.

I really need to stop reading this weirdo - but he is my libertarian archetype.

Wednesday, March 17, 2010

Revolutionary Roads

Why did it take so long for humans to have the Industrial Revolution? is the question asked over at the Marginal Revolution. What do you mean say I? Thirteen point seven-five billion years isn't **that** long. Apparently, though, Tyler and friends interpreted the question slightly differently since they quickly fall to geopolitical and economic speculations.

Like other similar questions, e.g., "why did it take so long to" (a)develop agriculture", (b)evolve a technological species, or (c)get some free oxygen on the planet, the most interesting thing is not the answer, which nobody knows, but the reasoning involved in the deduction. I guess I'm not too impressed with historical/economic factors argument.

My prejudice is to believe that the central fact was preceding scientific revolution of Copernicus, Kepler, Galileo, Newton, and others. Not only were the laws of physics extremely useful for the designers of mechanisms, but probably even more influential was the shift to a fundamental viewpoint in which the Universe was not inexplicable but just a very complicated machine. I don't think it is coincidental that the industrial revolution occurred in the same part of the world as the scientific.

There were certainly seeds for an industrial revolution in Archimedes and the Muslims, Indians, Chinese, and Koreans, but the soil they fell on evidently did not support them. Why not? Geopolitical, social, religious reasons or other? I'll will put my money on the crucial ingredient being the scientific substrate - not just knowlege of the facts and equations, but the prestige of science and the public fascination with it. These were perfect to encourage an intense burst of experimentation and technolgical progress.

By the dawn of the industrial revolution Britain was a nation of tinkerers. George Caley was inventing the airplane and the caterpillar tractor. Across the water, Ben Franklin was sussing out the nature of electricity. I'm pretty sure that kind of cultural explosion could not have taken place in ancient Greece or any of the other supposed candidates.

Tuesday, March 16, 2010

In The Beginning: Saving

It could be argued that economics began when the first human had the idea to squirrel away some nuts for the winter. Of course squirrels had been doing so for a long time and ants forever, but we are talking people here. We gather or produce in order to consume, but the act of deferring some consumption for the future turns out to have profound consequences. That act of saving is the basis for all the elaboration of human society beyond the hunter-gatherer band. Most importantly, saving turns out to have a potentially multiplicative effect if that saving is used produce the means for greater future production.

That multiplicative effect acts first of all through technology. If we don't spend all of our time gathering food, we can spend some of it making tools which allow us to gather food with less effort, and potentially save even more. For a couple of million years, simple tools were as far as technology could take us. Our peripatetic life style limited our saving to more or less what we could pack around with us, and competition with other humans meant that our superior hunting skills made game scarcer and harder to catch.

Rapid progress really began with agriculture. Once a sedentary lifestyle had been adopted, houses and walls could be used to stash our stuff, including a supply of food for a whole year. Moreover, agriculture tended to require large organized efforts for building irrigation systems and herding domesticated animals. The surpluses now produced could be used to support societal specialists and construct fortifications and other durable structures.

Once regular and somewhat predictable surpluses existed, the human race had begun the practice of capital accumulation. That accumulated capital made possible progress, but it also presented a problem: Who controls and gets the benefits from it. And that is what economics is about.

Sunday, March 14, 2010

The Israel Problem

Andrew Sullivan on our problem with Israel.

Petraeus sees what so much of Washington refuses to see: that Israel's year-long contempt for Obama, initiated by the Gaza campaign, entrenched by Netanyahu's victory and compounded by continued settlements and last week's humiliation of Biden is a problem. More then a problem, Israel's total impunity for its intransigence is becoming a liability for the advance of US interests around the world. Petraeus was so disturbed by a recent trip to the Middle East that he asked a team of top CENTCOM officers to brief Admiral Mullen, and asked that the region be made part of his command:

In my reading of the Israeli reaction to the Biden dust up it seemed that the dominant meme was "the US should mind its own business."

That is indeed a consummation devoutly to be wished. Please and pretty please. All that we need to do is stop sending them several billion dollars each year, stop selling them weapons on any basis other than we would to anybody else, and stop carrying their water in the UN Security Council.

Such a path would be far better for us, and would blunt one of the biggest gripes the Islamic world has with us. It might even be better for Israel. Without us to protect their butts they might even figure out that it might be in their interest to make peace with their neighbors.

Israel is the obnoxious little brother that knows it can get away with anything because big brother is the cock of the walk. Just say: Time to fly on your own, little bro. We wish you well, but your fights are no longer our fights.

Let The Bribery Begin

I guess you can never overestimate how flagrant these guys are willing to be.

How do you spell "quid pro quo?"

Pi Yi Yipee Yay!

Today is Pi day, so my Google tells me. Pi is one of those truly mysterious and magical numbers - *the* mysterious and magical number, in fact. Can we conceive of a universe in which Pi is, say, 22/7? Going to a non-Euclidean geometry wouldn't be good enough, I think, because we would want Pi to be constant as well...

For the clebration, I'm planning to make mine apple, though rhubarb would be nice if I could get it...

Saturday, March 13, 2010

Grant vs. Reagan

For me, Ronald Reagan's name on Smithsonian Institution restrooms would be more than honor enough. More than any other person, Reagan is responsible for the deficit mess we find ourselves in today. As it is, we appear to be stuck with him on the Capital's airport and other assorted junk. The nut jobs who worship him want to put him on the $50 bill, however.

Historian Sean Wilentz, Writing in the New York Times, explains why we should keep Grant right where he is.

RONALD REAGAN deserves posterity’s honor, and so it makes sense that the capital’s airport and a major building there are named for him. But the proposal to substitute his image for that of Ulysses S. Grant on the $50 bill is a travesty that would dishonor the nation’s bedrock principles of union, freedom and equality — and damage its historical identity. Although slandered since his death, Grant, as general and as president, stood second only to Abraham Lincoln as the vindicator of those principles in the Civil War era.

Born to humble circumstances, Grant endured personal setbacks and terrible poverty to become the indispensable general of the Union Army. Although not himself an abolitionist, he recognized from the very start that the Civil War would cause, as he wrote, “the doom of slavery.” Above all, he despised the Southern secessionists as traitors who would destroy democratic republican government, of which, Lincoln said in his first inaugural, there was no “better or equal hope in the world.”

I'm down with all that, except maybe the first sentence. I surely don't want to see Ronnie's smiling face replace him - not that I see a $50 very often anyway.

Entropy: Gravity

Gravity presents some new wrinkles for entropy. Even the classical version has a surprise. John Baez has a very nice discussion of the fundamental details.

If you weren't careful, you might think gravity could violate the 2nd law of thermodynamics. Start with a bunch of gas in outer space. Suppose it's homogeneously distributed. If it's big enough, it will start clumping up thanks to its gravitational self-attraction. So starting from complete disorder, it looks like we're getting some order! Doesn't this mean that the entropy of the gas is dropping?

Well, it's a bit trickier than you might think. First of all, you have to remember that a gas cloud heats up as it collapses gravitationally! The clumping means you know more and more about the positions of the atoms in the cloud. But the heating up means you know less and less about their velocities. So there are two competing effects. It's not obvious which one wins!

Baez proceeds to do the calculations for an only slightly idealized case. I recommend these. They are a nice exercise. Mostly algebra with a bit of mechanics and statistical mechanics, but nothing fancy.

The bottom line is this: as the cloud shrinks under gravitational contraction, the cloud heats up - the molecules move faster in their tighter orbits. John's math shows that the net effect is a decrease in entropy. Meanwhile, kinetic energy has increased, but potential energy has decreased even more. Consequently the cloud has heated up even though it has lost energy. This is opposite to the behavior of familiar thermal systems!

In other words, the specific heat of the cloud is negative! Adding heat cools the cloud and subtracting heat makes it hotter! This fact turns out to be central to star formation as well as to understanding gravity and entropy. In order for a cloud of gas to contract, it needs to be able to give off heat. Sun sized stars typically form in dust clouds, with the dust grains serving as minature radiators to cool the collapsing cloud.

Prof Baez leaves us with the question he started with: if the entropy decreased, what does that say about the second law?

Ritual Humiliations

It now seems almost an Israeli tradition for Netanyahu to subject visiting US leaders to some sort of ritual humiliation or other. Whether this feeds some constituency of his or just his ego, he seems to have calculated that the American government is too weak to effectively respond.

The Americans who are paying attention, I suppose he imagines, are mostly Jews or Christianist apocalypticists who will follow Israel blindly. No doubt a lot of American Jews dislike seeing the US disrespected, and more are dismayed by the increasingly fanatical settler movement that celebrates Baruch Goldstein and the One Shot, Two Kills snipers as heroes, but they are still going to be safe supporters no matter what. The Christianist millenialists, by contrast, celebrate every outrage, since their dearest hope is for war and Armageddon.

For now the calculation must hold, but for how long, I wonder. What if the Bible Belt Christianists were to revert to a historically more standard anti-semitism? What if Americans get tired of seeing their sons come home in boxes from wars that have more to do with Israel's interests than our own?

Until now, Israel has been lucky in its friend (singular) and luckier still in its enemies. The tactics the Palestinians have chosen could hardly have been more advantageous for Israel if they were plotted by the Mossad. The despicable suicide bombing tactic was always too weak to serious damage the Israeli state but was wonderfully effective in arousing US and world contempt for Palestinians.

For now, the American President has far too full a plate to face down both Israel's American allies and the powerful Israel lobby in his own caucus and staff. If that should change, Israel had better hope that Americans have short memories and are uncommonly forgiving of grudges. Otherwise, it might find that the US is still a great power, and Israel is still a rather small one.

Friday, March 12, 2010

History of the Dance, Part Six

"Am I my brother's keeper?" might be considered the central question of Judeo-Christian morality. Opinions, as they say, differ. Perhaps the majority of Americans might say "It depends." Libertarians say "No" and Randites "Hell no!" It seems that rural Mayan villagers are at the opposite (and biblically endorsed) pole.

...most people think actions that lead to harm are worse than omissions (i.e. not doing something) that lead to harm. Think of a doctor killing a patient with a lethal dose, as opposed to letting them die by not administering a life-saving drug.

Most people match this pattern of responding but so far most participants have been from urban, technologically advanced cultures. Now Marc Hauser and his colleague Linda Abarbanell have translated these kinds of moral scenarios and taken them to a rural Mayan community in the highlands of Chiapas in Mexico.

The rural Mayans showed the usual bias for seeing harm caused deliberately in pursuit of a greater good as more forbidden than harm caused as a side-effect in pursuit of that same greater good. But Abarbanell and Hauser's breakthrough finding is that the rural Mayans didn't believe that harm caused by direct contact was worse than indirect harm and they didn't think active harmful acts were morally worse than harmful acts of omission.

The researchers don't think these differences emerged because of translation problems. Choosing to focus on the omission/active harm type situation, the researchers tried out several different scenarios, including one designed for use with children, and always the results were the same. The rural Mayans saw agents as more causally responsible for active harm, they just didn't see them as more morally blameworthy. Moreover, when Abarbanell and Hauser tested a more urban Mayan population, they did show the usual tendency to see harmful acts of omission as less bad, thus suggesting that this difference in moral judgment is specific to the rural community.

The authors speculate that the more intimate community of rural life leads to the more communitarian value structures.

Put me down with the Mayans. That's probably why I so detest libertarian ideas and values. I see this as perhaps the key divide between liberal and libertarian.

Via Marginal Revolution

Nasty, Brutish, and Tall

So how much has mankind benefitted from economic progress? Less than we might like to think. The invention of agriculture seems to have triggered a general decline in human health and loss of four inches or so in stature, probably due mainly to an inferior diet, but also perhaps to the more arduous nature of agricultural existence. Domestication of animals brought in a flood of new diseases, and greater population density facilitated epidemic spread. The general decline in stature didn't really turn around until the twentieth century.

For most of humanity, progress has usually been a bummer. The bad effects can be traced to the fact that economic "progress" triggers increases in population until Malthusian effects grind us down. Because we were originally were adapted to Darwinian competition in a much different world, we are not well suited for either the modern diet or lifestyle.

The only known or plausible way to escape the Malthusian trap is limitation of population. For the first time in human history we have good ways to do this, and much of the world has chosen to do so.

Prehistoric life was indeed nasty and brutish, but humans were well adapted to it. It took a thousand centuries, but a better way is now possible.

Thursday, March 11, 2010

Say What?

From Tyler Cowen.

Adam asks:

If you were offered a true statistic about an alien civilization, but only one, what would it be?

Cowen's choices are rather droll:

How about the real rate of return on capital? The risk premium? The percentage of the population which dies in war each year?

He's not ready to assume that their biology is similar, but they are bound to be capitalists, right?

Does anybody know the answers to any of these questions for Earth? Maybe for the last one.

I'm far from sure that statistics are very relevant unless you know some other things about the underlying variables. But what kind of information about an alien culture would tell us the most? Suppose that you have an hour to look through what appears to be an abandoned alien city. What would you look for to learn about the inhabitants? (Try to name five things).

Tuesday, March 09, 2010

Bashing Insurance Companies

President Obama is going around bashing insurance companies, and the usual suspects are rushing to their defense. The defenders of the insurance companies have a point in that it seems a bit unfair to blame them for doing what is their job to do: maximize profits. Crocodiles eat the unwary and so do health insurance companies - that's their nature. Life, though isn't fair, and it also isn't fair that the insurance companies benefit from a ridiculously organized health care system that wastes trillions and is dangerously unstable. The insurance companies badly want to prevent change in the system which would decrease their monopolistic and other profits, and consequently have spent tens of millions to do so. By doing so, they have chosen to be the enemy, and the leader's duty is to defeat, and if necessary destroy, that enemy.

The insurance companies pretended to be on board with reform, so they also get a charge of duplicity. I won't shed any tears for those crocodillians, even if I do happen to own a bit of their stock.

Monday, March 08, 2010


Paul Krugman reports that the Republicans are strongly pushing the idea that we have high unemployment because we have unemployment benefits. No doubt there are some Americans prepared to buy into this mean spirited and economically unsound idea, but if the Republicans want to fight it out on this ground, I say bring it on. I think entirely too many Americans have seen hardworking friends, neighbors, relatives or themselves spit out of the economy to buy into this latest nastiness of the right.

Sure, there are a few people who would rather collect unemployment than work, but the rules make that fairly difficult, at least for very long. So how about replacing unemployment benefits with a government sponsored job corps, in the fashion of Roosevelt in the 1930's? No doubt the Republicans would love that idea.

Best Actor

The big winners were pathetically grateful. The lines and jokes were merely pathetic. Unfortunately, the Academy apparently could not find actual actors to read them. The scripted lines were awful, and most of the time the delivery was awful as well. Maybe teleprompter reading wasn't covered in acting school.

My personal award for best actor in a role delivering Academy scripted crap would have to go to Ben Stiller. It was almost like he actually knew something about comic timing - unlike, say, Steve Martin and Alec Baldwin.

He also wins for best costume and makeup.

Saturday, March 06, 2010

Hotel Management

Let me depart for the moment from my traditional practice of abusing Steve Landsburg to note that I quite liked his post on countable and uncountable numbers. He briefly discussed the countability of the integers and rationals and presented Cantor's proof of the uncountability of the reals. One of his commenters asked the following:

Imagine that you run the front desk at a hotel with a countably infinite number of rooms. Imagine further that all of the rooms are occupied. A man shows up in the lobby and asks for a room. Can you give him a room?

The answer is yes of course, but it should keep your bell boys busy. Interestingly enough, it's hardly any more trouble to accomodate a countably infinite number more of guests. Still, you have to say that the manager who let this deplorable situation arise made a big mistake. How should he have run his hotel so that he didn't have to move an infinite number of people each time some more guests showed up?

What if he had an uncountably infinite number of rooms (for example, let each room have a real room number between 0 and 1)? Would that have made his job any harder?

Friday, March 05, 2010


Nicholas Carr wonders if Google is making us stupid.

I think his theme is that the instant info gratification provided by Google and the interwebs generally has decreased our attention span to point that we can't think deeply any more - but I didn't actually have the patience to read the whole article...

Over the past few years I’ve had an uncomfortable sense that someone, or something, has been tinkering with my brain, remapping the neural circuitry, reprogramming the memory. My mind isn’t going—so far as I can tell—but it’s changing. I’m not thinking the way I used to think. I can feel it most strongly when I’m reading. Immersing myself in a book or a lengthy article used to be easy. My mind would get caught up in the narrative or the turns of the argument, and I’d spend hours strolling through long stretches of prose. That’s rarely the case anymore. Now my concentration often starts to drift after two or three pages. I get fidgety, lose the thread, begin looking for something else to do. I feel as if I’m always dragging my wayward brain back to the text. The deep reading that used to come naturally has become a struggle.

So maybe we have become impatient with multi-thousand word essays with just one idea...though it seems that nobody seems to have actually studied the phenomenon he posits. He does add:

...So, yes, you should be skeptical of my skepticism...

Why Does Entropy Increase?

Sometimes it’s useful to try to define our terms. Consider an isolated system, such that we have both a macroscopic description (mass, temperature, pressure, etc) and a microscopic description in terms of the microscopic constituents (molecules, whatever) and that each microscopic description can be encoded as a point in gazillion dimensional phase space – one dimension for each microscopic degree of freedom. In general a given macro state will not correspond to a unique micro state, and in fact we can think of an “ensemble” of micro states each of which would correspond to the macro parameters as sort of a blob of fluid in phase space.

The log of the volume of fluid (or number of all possible microstates) corresponding to the given macro state is the entropy of that state. (We divide up the volume of the phase space into a bunch of mini volumes, the number of which becomes the number of states) In a very concrete way, the entropy of the macro state represents what we don’t know about the micro state – that is, the number of (microstate) possibilities for it. If we knew precisely which of these possible micro states was the real one, the entropy would be zero.

If our system is truly isolated, though, there is a theorem of classical mechanics, Liouville’s theorem, which says that time evolution preserves the volume of phase space – which would appear to preclude entropy increase. The conventional explanation is to say that while our original blob of phase fluid doesn’t expand, it develops innumerable fingers penetrating other volumes to become ‘close’ to a much larger volume. If we now “coarse grain,” by re-dividing the volume, and counting as “accessible” each volume that contains a bit of the original phase fluid, then we find entropy has increased. It’s hard to avoid the feeling that we have seen some slight of hand here, though, since coarse grained or no, the undisturbed system should still preserve the memory of its past and original volume.

In practice, though, there never is a truly isolated system, and tiny disturbances can act as a kind of entropic viscosity, smearing the phase fluid through all the phase space it comes near. I said that entropy represents what we don’t know about a system, so the increase in entropy due to outside disturbance can equally be thought of as a leaking away of what we once knew about the system. In a perfectly classical world we could imagine chasing down all that leaking information and somehow keeping our entropy down, but in the relativistic cosmos, information can leak away irretrievably by going over horizons.

There are two kinds of relevant horizons here: black hole boundaries and the cosmic “border” of our observable universe. Because the universe is expanding, and expansion rate increases with distance, there are regions of the universe which we can never hope to reach.

We associate an entropy with these horizons, which at first seems abstract and strange. What though, if we recall that entropy is really just information lost? Then what if the entropy of these horizons is just the information about our universe which has leaked out through them? I’m throwing this up as a speculation – I have no idea whether experts regard this idea as obvious or obviously wrong. I kind of like thinking about these entropies as what the universe has forgotten about itself. If that idea is correct though, should we really expect the black hole information loss “paradox” to have a happy solution?

Hide Your Physics Books

Scott Patterson, author of "The Quants" was on the Daily show and he and John Stewart managed to blame physicists and mathematicians for the great financial meltdown. What crap. If you look at the education of the guys who were actually running AIG and the big five investment banks you find lawyers, MBAs, a Finance PhD, and a couple bridge players, pilots and baseball players, but how many physicists? I couldn't find any.

I'm not saying that the real quants were completely innocent, but the really bad decisions seem to have been made by those who couldn't, or wouldn't take the trouble to understand the risk models and their limitations.

Tournaments in Everything*

---> *with apologies to MR and TC

Despite the disapproval of economists, tournaments are a ubiquitous feature of economic life. The big bopper of tournaments is life itself – Richard Dawkins has pointed out that we all are ultimately just vehicles for our genes to compete in the big tournament of evolution. Tournaments exist at subtler scales as well.

One small but important tournament venue is our own brain. One of its most crucial functions is choosing among alternatives: should I take a nap, or go to the party? Should I have Brussels’ sprouts and ginger ale or beer and pizza? Should I exchange pawns or try to maneuver my knight to the kingside?

It’s a crucial feature of this type of decision that intermediate values are not useful. The proverbial mule who fails to choose starves between the two haystacks. No decision is worse than any decision. Many neural systems have features that enhance this sort of all or nothing behavior: after a buildup of potential, an irreversible act of amplification takes place, committing the system to an alternative and the host organism to a choice.

Some have chosen to see the quantum measurement process in the same terms. A typical quantum mechanical system, for example a silver atom, is in a superposition of angular momentum eigenstates until we run it through our Stern-Gerlach analyzer. At that point it is forced to choose up or down.

The common feature of all these “tournaments” is a bifurcation that transforms a potentiality into an actuality. At the start of the NCAA’s March basketball madness there are sixty-four – at the end, only one. In the case of these sporting events, the eventual choice is almost beside the point. The real point is not the winner but the competition. The winner, like the losers, is a character in the drama, necessary not because we need a winner but because otherwise the drama would lack a plot.

That’s not true for all tournaments. Leadership of most organizations is decided by series of tournaments. Usually it’s hoped that the tournament will choose a good leader, but the choice is the real point. If a leader is needed, some way of choosing a leader is needed, and choice is almost always a tournament.

The goal of the tournament is usually not just to choose, though, but to choose well. Otherwise it could just be a lottery. The problem with tournaments, so the economists tell me, is the waste – all the seemingly pointless efforts of the ultimate losers. The lottery avoids the waste, or most of it, but does nothing about discovery of the best choices. A well designed tournament should somehow try to choose well with minimal waste.

Thursday, March 04, 2010

Unnatural Gas

This story ought to scare the crap out of any rational person.

A section of the Arctic Ocean seafloor that holds vast stores of frozen methane is showing signs of instability and widespread venting of the powerful greenhouse gas, according to the findings of an international research team led by University of Alaska Fairbanks scientists Natalia Shakhova and Igor Semiletov.

Methane is a very potent greenhouse gas. Big releases are thought to be behind the dramatic warming of the PETM, a mass extinction event.

On the positive side, recovery from that only took about 200,000 years.

Via Brad DeLong and Matt Yglesias.

Tuesday, March 02, 2010

Entropy II: Fundamentals

Entropy began as a puzzle. If heat was energy, why was there always some heat wasted when one tried to turn it into mechanical energy? The heat engine was perhaps the master invention of the industrial revolution, but it posed both theoretical and practical problems – I will only worry here about the former. Realization that heat was a form of energy, and computation of the mechanical equivalent of heat, generalized the concept of conservation of energy. This was codified in the First Law of Thermodynamics. That inevitable wasted heat energy in every heat engine showed that this could not be the full story of thermodynamics, though, and investigation of the properties of the waste heat led to the concept of entropy, and the Second Law.

Like pressure and temperature, entropy was a state variable, but its interpretation was obscure. Its fundamental property was that it was non-decreasing. In particular, it could be constant in a reversible (quasi-equilibrium) and adiabatic (no heat transfer) process, but always increased in a non-adiabatic or irreversible process. For a reversible process, the entropy change was the ratio of the heat transferred to the temperature at which the transfer occurred.

Once the interpretation of temperature in terms of the motion of microscopic components of matter became popular, it became natural to search for a microscopic foundation of entropy as well. That discovery, mostly by Boltzmann, is one of the deepest in physics. Entropy, said Boltzmann, is a logarithmic measure of the number of microscopic states available to a system in a give macroscopic state. With this definition, the law of entropy increase can be seen as a matter of probability.

Consider an experiment where we flip a number of coins, say 10. If they are fair coins, each will have equal probability of coming up heads or tails. If we flip the coins all at once, what is the probability that, say, exactly 3 will be heads? The way we do this calculation is to imagine a universe of all possible coin flips and count what fraction of that universe has exactly three heads. There are ten coins, each of which can be either H or T, so there are 2^10 = 1024 possible outcomes. If we remember the binomial expansion, we can see that there are 10!/((10-3)!3!) = 10*9*8/6 = 120 ways that this can happen, so that the probability P(3 heads) = 120/1024 = 15/128.

An analogous idea is used in calculating entropy. The macro state is the analog of total number of heads, and microstates are analogous to possible results of a flip. Consider a box with ten particles moving randomly about in it. Suppose that we quickly insert a partition down the middle so that each particle has an even chance of ending up on either side of the box. Call those that wind up on the right side “heads” and those that wind up on the left “tails.” We won’t calculate all the way to probability here, but we will count the number of possible outcome micro-states corresponding to a given macro outcome. The entropy will then be the logarithm of that number of states.

Suppose all the particles end up on the right hand side (ten “heads”). There is only one way that can happen, so the entropy of that state is log (1) = 0. If three wind up on the RHS (3 “heads”), we have already seen that that can happen in 120 ways so entropy = log (120) = 4.79. In this way we can calculate the entropy of each possible macro-state. We would find that the highest entropies corresponded to the most probable results. The law of entropy increase becomes the probabilistic rule that the system is likely to end up in one of the most probable states. For large N, the state distributions become much more sharply peaked.

An elementary book that gets right to the point of calculating entropy and its consequences is
Kittel and Kroemer

Next: Gravity

For the advanced student: and link therein. Mikey likes it. So far.

Tournament Madness

OK, economists keep telling me that tournaments are inefficient, and I think they may be right, but I can't seem to get one to give me a cogent argument. So I asked my buddy Captain Imperio. CImP, as I call him, doesn't know anything about econ or tournaments, but he does know how to use the interwebs, so this is what he came up with:

People love tournaments. Economists, not so much. Why not?

Consider a certain idealized economic activity, widget manufacture, for example, and that widgets are an item in demand by a great many. By the nature of things, there will be a certain amount of variation in skill at widget manufacture, and the more skillful will crank out more widgets and make a better living than the less skillful. Net income for widget makers will be smooth function of skill, the less skillful will find other ways to make a living, and the number of widgets produced will tend ins invisible handy way to the number demanded by society.

Suppose, on the other hand, that the King desires a gidget. He only wants one, but he wants the best gidget possible, so he sponsors a month-long design contest and promises to pay handsomely (say $1 million) for the very best gidget available. Hundreds of citizens then begin designing and building gidgets in hopes of collecting the prize. At the end of the month, the King selects the winner, pays the designer, and everybody else goes home. This situation, says the economist, is bad, because hundreds of months were wasted designing and building gidgets that nobody wants.

What really really bothers the economist, though, is that this situation undermines the logic of the efficient market. The King was willing to pay big bucks because he really wanted a cool gidget. The gidget designers were willing to invest their time, because they calculated that their expectation of profit = probability of winning x amount of prize (say 1/500 x $1 million = $2000) was better than they could have made making widgets. However, if all concerned had been omniscient ideal market agents, the King would have just handed (say) some money to the one he omnisciently knew was the best gidget designer, gotten the design he wanted, and all the losing competitors would have saved their time and trouble – which looks like a Pareto improvement, that is, a change which makes nobody worse off and some better off.

If the only tournaments around were sporting events or occasional design competitions, this would be no big deal, but in fact tournaments are ubiquitous in the economy. All sorts of activities from hedge fund performance to job promotions to admission to the most desirable kindergarten are structured as tournaments. It is not implausible that the tournament structure of the financial industry contributed to the recent financial collapse.

Tournaments are a real challenge to market fundamentalists, because they suggest that there are situations (lots of them!) where rational actors with limited knowledge can make rational choices that wind up being bad for almost everyone.

Here is a more detailed discussion of the winner-take-all tournament