Sunday, October 31, 2010

Further Adventures of the Inept Autodidact

It has many times been convincingly demonstrated that I have zero talent for languages. Failed attempts to learn Latin, Russian, German, Spanish, and Japanese litter my history. I, however, am also not one to learn very well from my mistakes, so I am once again attempting Spanish. Rosetta Stone (Latin American) is my main tool here, but I also got this cheap beginning Spanish Reader for my Kindle. I am beginning to suspect that it might not be too current, since its Chapter on the US lists the population as 110 million! Also our money includes \$5,\$10, and \$20 gold pieces as well as \$1000 bills.

What is cool is the fact that I can set my Kindle Spanish-English dictionary as primary and use it to quickly define words that I don't know, or find the conjugations of irregular verbs. It has been a lesson, however, in the limitations of the Kindle interface. I find the five-way navigation button a bit clumsy. A touch screen please.

Focus

Bee's new post is entitled This and That - I was briefly afraid that those might be the new names of epsilon and delta - but it is definitely in the don't miss category for it's pitiful story of an obviously talented lad who just couldn't make up his mind what he wanted to do with himself, switching aimlessly among majors.

I liked Ed, but felt sorry for him, too, because, for all his potential, he lacked focus. He had been a history major in college, and a linguistics minor. On graduating, though, he concluded that, as rewarding as these fields had been, he was not really cut out to make a living at them. He decided that what he was really meant to do was study economics. And so, he applied to graduate school, and was accepted at the University of Wisconsin. And, after only a semester, he dropped out of the program. Not for him. So, history was out; linguistics, out; economics, out. What to do? This was a time of widespread political activism, and Ed became an aide to Senator George McGovern, then running for the presidency on an anti-war platform. He also wrote articles for political journals like the Nation and the New Republic. After some months, Ed realized that politics was not for him, because, in his words, it demanded qualities he did not have, foremost among them common sense. All right, then: history, linguistics, economics, politics, were all out as career choices. What to do? Ed suddenly realized that he was really suited to study mathematics. So he applied to graduate school, and was accepted at Princeton. I met him midway through his first year there--just after he had dropped out of the mathematics department...

If you don't recognize the script by now, you will just have to follow the link to Bee's post - and while you are there don't miss the tale of a medical mystery that could have kept Dr. House busy for an episode or two.

Saturday, October 30, 2010

System and State

The notion of a system and its state is a fundamental one in physical science and engineering. Both the words system and state derive from a Proto Indo European base word meaning to stand, and we use them in senses that have varying degrees of precision. In general, a system is a collection of things that "stand together," and the state of that system is the "way they stand together." In physics, a system might be a single elementary particle, a bottle of gas, a star, or the universe, and by its state we mean mean some collection of variables that specify that state. For an electron, for example, its charge, mass, velocity and position.



In classical physics the state variables tend to be measurable numbers, what the quantum pioneers called c-numbers. Things become more abstract in quantum mechanics. The state of a quantum system is specified by something that we call a ray in Hilbert space. It's worth noting, though, that even the classical description is a big step in abstraction from ordinary speech. A planet or a canonball has a complex description in ordinary speech, but if you want to know where it's going next you need some numbers, like velocity and mass, for example.

We are all forced to do some thinking in numbers: the state of my pocketbook is pretty well characterized by the number of dollars in it, for example. Physical sciences and engineering carry numerical thinking to an extreme, but it's not really enough for the world of the quantum. Physicists didn't go gladly to the Hilbert space description - at any rate many of them didn't. They were forced to it by the counter intuitive behavior of quantum phenomena, especially by quantum system's habit of exhibiting both wave and particle like behavior, and by the uncertainty principle.

Consider the spin of an electron. If we measure that spin it always turns out to be either up or down - never something in between. Could anything be simpler? Here's the rub - in between measurements an electron acts like it's partly spinning up and partly spinning down. If this seems strange and bizarre to you, it seems that way to many physicists too, even those who have spent decades thinking about it. I won't go into the ample evidence that this is the case, but suffice it to say that nobody has been able to make it go away, and plenty have tried, including Einstein and other quantum pioneers.

How do we describe something like that? It turns out that a Hilbert space is a good way to do it. I don't have a simple explanation of what a Hilbert space is (see the link for Wikipedia's discussion) but I will try to give a rough intuitive feel for it. Start by imagining a point in space that we will call the origin. Draw an arrow from that point to some other point in space - that arrow is a vector in our three dimensional space. If we put some coordinate axes in our space, with the zeroes of the axes at our origin, we can label our vector with the coordinates of the head of the arrow - each set of coordinates correspondes to a unique vector and vice versa.

Together all the vectors form a vector space. One important property of vectors is that you can add or subtract them, or multiply them by a constant. For example, if we represent the vector with head at x=1, y=2, and z=1 in our coordinate system by |1,2,1> and similarly another vector by |1,0,1> then we can do arithmetic like so:

|1,2,1> + 2|1,0,1> = |1,2,1>+|2,0,2>=|3,2,3>

which is the vector with head at coordinates 3, 2, and 3. If you have studies some vector algebra, you remember that this geometrically corresponds to stretching the second vector by a factor of two, moving its tail to the head of the first, and then drawing a new vector from the origin to the head of the doubled, displaced, second vector.

A Hilbert space is a generalization of a vector space - it can have infinitely many dimensions, for example. We won't need that many for our electron spin state - two will do, but we will need another attribute, because our multiplying constants can be complex numbers. We choose two fundamental vectors |up> (the electrons spin is "completely" up) and |down> (the spin is all down). Then the most general spin state is represented by a up> + b down> where a and b complex numbers. (I won't go into details, but we want to make all vectors of unit length, also).

Part of the point here is that while the measurement can only yield up or down, the general pre-measurement state is more complicated. The additional complexity of the representation is related to the uncertainty in quantum measurements. In general, even a complete knowledge of the state is not enough to determine a measurement, since state vector yields only a probability distribution.

As usual, correction and other improvements are welcomed.

Wednesday, October 27, 2010

Clark's Malthusian World

Malthus had the insight, which also proved crucial for Darwin, that Man and other creatures produce more offspring than can survive to adulthood if the population is to maintain a steady, or nearly steady state. Scarcity of resources ultimately limit the population by increasing the death rate until it matches the birth rate. Gregory Clark, in his book A Farewell to Alms: A Brief Economic History of the World, argues that the vast bulk of the human race has lived in Malthusian equilibrium for all its long history before 1800 and the onset of the industrial revolution.

Modern humans may have numbered no more than 10,000 individuals 70,000 years ago, when the population apparently passed through a major bottleneck, and probably never exceeded a few million during our long careers as hunter gatherers. (This and other population estimates from Wikepedia) Over the next seventy thousand years, our geographic range, technology, and numbers expanded dramatically. By 1800 there were some one billion of us - 100,000 times as many as at the bottleneck and some hundreds of times more than the planet could support as hunter gatherers. Technology was the key factor that made this possible, especially agriculture.

So what did an average individual get out of all this progress? Clark presents the evidence in a plethora of tables, charts, and explanations, and his anwer is unequivocal: nothing much, zero, nada, nichevo. Compared to their stone age ancestors, the average person of of 1800 worked much harder, ate less well, and lived no longer. Malthusian economics had done its work and reduced most to the subsistence level, and that subsistence level was in many ways meaner than that of his stone age ancestor. A few at the top of society did better, of course, and some of them had the leisure to write novels about each other.

Thus economic progress had the ironic effect of allowing more people to live rather worse than the much smaller populations of prehistory. This is what Clark calls the "Malthusian Trap." A few exceptional periods, events, and cultures that temporarily escape the grip both test and illustrate the paradigm. After the Black Death devastated Europe, wiping out a substantial fraction of the population, wages for ordinary workers rose sharply and didn't fall again until population caught up with its pre-plague levels. Certain Polynesian groups maintained high standards of living until the Europeans arrived, mainly because they practiced infanticide on a massive scale and otherwise achieved high death rates through war and violence. The devastating toll of tropical disease gave equatorial Africans relatively large incomes until European medicine arrived to save and impoverish them.

Thus peace, healing the sick, and reducing violence all have counterproductive effects downstream. Ditto charity. More people survive to adulthood, but are poorer because there are more of them competing for the same resources. If you measure economic progress based on the benefit to a median individual in the society, there isn't any, except possibly temporarily.

Clark argues that the industrial revolution changed everything. He has many interesting arguments there, but I will save them for later. A key point though, is that in industrial nations technology progressed so rapidly and peoples incomes rose so much that a demographic transition took place - women started having many fewer children. That seems to be a way out of the Malthusian Trap that's less problematic than war, pestilence, infanticide and murder.

Creepy Travel Commentary From Tyler Cowen

Do other people find Tyler's paragraph below as creepy as I do?

We saw a dead guy on the side of the highway; apparently he was struck down by a passing car. Ill-advised pedestrian walks are a problem for many El Salvadorans in the United States as well. "More guns, less crime" I joked to Alex as we drove through the center city.

Tuesday, October 26, 2010

Arrow's Result

Many of the concepts of economics have a certain resistance to popular explanation. Arnold Kling nominated Arrow's (Nobel winning) Impossibility Theorem as a particular challenge. Tyler Cowen, Alex Tabbarok, and Steve Landsburg each took up the challenge: you can find their stuff at the links - I found them all incomprehensibly cluttered with irrelevant details. The basic notion involved is that when several people set out to choose among a set of alternatives, it's impossible to find a voting system that aggregates individual preferences yet satisfies all of some specified and plausible seeming fair decision rules. This probably won't surprise anybody who has tried to cooperatively plan a Thanksgiving dinner.

As I said, I couldn't follow the reasoning in the links, but Wikipedia is pretty clear, and has both formal and informal statements of problem and proof. Tyler also links to this fairly simple yet detailed proof.

Across the River Cam

Just in case I decide to run for office sometime, I wanted to be able to claim an elite U background, like Christine "I am a muggle" O'Donnell (Oxford, correspondence course, sometime).

I have now been to Harvard. Of course I didn't learn anything, except where to find the restroom near Anna's, nor did I enter any of the other buildings, but I was there for the "Head of the Charles." It's a pretty place, if not very close to my idea of what a University campus ought to look like.

When we were approaching the Harvard square T-stop, I noticed that the guy in front of me looked like a cross between the real and movie Mark Zuckerbergs. Later I figured out that everybody at Harvard looked like Mark Zuckerberg except maybe for the Asians. OK, I'm sure that wasn't really true, but I did feel slightly freakish. Though there were lots of other tourists there to read the three lies and rub the toe of John Harvard's boot.

I stopped by MIT too. I think I can sort of see what Gell-Mann had in mind when he said that when he learned he had been admitted there but not to the school he wanted he contemplated suicide (but refrained on the grounds that he could always commit suicide later, but that the operations didn't commute). A very cute co-ed (do they still use that word) gave us directions to the endless hall, which she asserted was supposed to be "very MIT." It was pretty long, but I seem to recall entering one end and exiting the other - and you could probably walk pretty far without freezing to death in the winter.

Elite-er

Via Kevin Drum, Clair Berlinski's How Elite Are You?

1. Can you talk about "Mad Men?" Not intelligibly.

2. Can you talk about the "The Sopranos?" Not without making a face.


3. Do you know who replaced Bob Barker on "The Price Is Right?" No

4. Have you watched an Oprah show from beginning to end? No

5. Can you hold forth animatedly about yoga? No

5. How about pilates? I think I learned about Pontius Pilate in Catholic School. I don't know his family.

5. How about skiing? I really miss it.

6. Mountain biking? There are a few mountain bikes in my garage, none of which I have ridden lately.

7. Do you know who Jimmie Johnson is? Yeah.

8. Does the acronym MMA mean nothing to you? It didn't.

9. Can you talk about books endlessly? If I could find somebody to listen.

10. Have you ever read a "Left Behind" novel? Eew. No thanks.


11. How about a Harlequin romance? Nope


12. Do you take interesting vacations? They interest me.

13. Do you know a great backpacking spot in the Sierra Nevada? Nope.

14. What about an exquisite B&B overlooking Boothbay Harbor? Never heard of it.

15. Would you be caught dead in an RV? I've been in several RVs.

16. Would you be caught dead on a cruise ship? I have been alive on some cruises.

17. Have you ever heard of of Branson, Mo? Yes

18. Have you ever attended a meeting of a Kiwanis Club? Maybe. My father was a major official.

19. How about the Rotary Club? I was an honorary Rotarian in High School - does that count?

20. Have you lived for at least a year in a small town? Born and raised.


21. Have you lived for a year in an urban neighborhood in which most of your neighbors did not have college degrees? Yes

22. Have you spent at least a year with a family income less than twice the poverty line? Grad school doesn't count, but how about enlisted Army?

23. Do you have a close friend who is an evangelical Christian? Does a brother-in-law count?

24. Have you ever visited a factory floor? Yes. Do booze factories count?

25. Have you worked on one? Sort of.


I'm not sure how to score this, but I'm pretty sure that this proves that I'm a hick, but that's not exactly news.

Outsourcing

Outsourcing my current dismay to Paul Krugman: Falling Into The Chasm.

Monday, October 25, 2010

Supreme Crooks

Maureen Dowd retrospects on the confirmation of Supreme Court Justice Thomas. A new fact has come to light, namely that there apparently were other women willing to testify to Thomas's exploitative sexual proclivities, but who then Senator Biden refused to allow to testify. Dowd also notes that Thomas's wife has shamelessly abused her connection to the Justice for financial gain. Thomas and Scalia both have a history of accepting pricey favors from persons with business before the Court, or likely to have business before it. If they were GS-12 civil servants instead of Justices, they would be out on their ears or in the slammer.

And this is what the American people are about to vote for more of. We may have officially transitioned into the too stupid to survive class.

Thursday, October 14, 2010

Not Dead Yet...

I was recently involved in an exercise simulating an attack by a crazed gunman, which I coped with by locking my door and continuing work. Eventually, though, soldiers in body armor with fake machine guns rousted me out. Because I had a real world broken foot, I was evacuated with the simulated casualties and taken to triage. There I was evaluated and tagged with a ticket proclaiming me Dead/Dying - an especially serious stress fracture, I guess. I kept the souvenier, but I'm not actually dead yet, though I do expect to be travelling and posting very lightly for a couple of weeks.

I have noticed that I seem to have at least occasional readers from five or six continents, and I figure you probably didn't all get here by mistake - though I could be wrong. Anyway, if anybody would like to say something about themselves and why you read my stuff - if you do that is - I would like to hear about it. If you want to share what you like or hate about this site, the subjects I write about you like or not and why, well that would be great too.

Wednesday, October 13, 2010

Burgery in Progress!

Econ Prof Steve Landsburg recently waxed wroth about internet trolls who spend time refuting arguments others never made. Since I think that the gentleman himself tends to indulge in that sort of rhetoric whenever his mind turns to Paul Krugman - pretty often - I thought it only fitting to honor him with the eponymn. It only took a couple of days before he provided us another example: a veritable (Lands)burgery in progress.

The subject of this particular burg is the following graph due to Paul Krugman.


Bear in mind that Krugman is responding to those who said government spending exploded after Obama took office, is explicitly considering only the time after the fall of Lehman (Sept 15, 2008), and is considering all government (federal, state, and local) spending. Krugman points out that there is no explosion of spending in 2009, despite the ramp up of countercyclical programs like unemployment insurance.

Next the critique:


Now, what I’m seeing here is something like a 25% increase in spending under the Bush/Obama policies of the past four years. Which makes me wonder exactly what it would take to count as a surge in Krugman-land.

Notice how the "Burg" has changed the subject from Obama to the mythical President Bush/Obama, and the time period from the last two years to the last almost five. This is textbook burgery, but he isn't done. It seems that some people noticed his change of subject. What to do? Pivot and change the subject again! This time to federal spending only, which, as Krugman has mentioned, has surged in the stimulus and other programs - a surge which has largely been matched by the collaspe in expenditures by state and local governments. Bravo: the Burgmeister is still master of his domain.

If you go to the source at the St. Louis Fed you can gin up a thirty year history of federal spending, which shows a steep but roughly linear increase in the 12 years of Reagan and Bush I, a levelling off in the Clinton years, and an exponential increase beginning with Bush II and continuing to present.

Tuesday, October 12, 2010

First Miner Up!!

Finally some good news from somewhere.

Wagner, Nietzsche and Hitler

Wolfgang accuses me of not knowing much about Nietzsche or Hitler. Perhaps not, but I know a little, and I can google. In particular, he thinks I misunderstand the Nietzschean superman. Let's review a bit of what he said in Zarathustra:

The strong men, the masters, regain the pure conscience of a beast of prey; monsters filled with joy, they can return from a fearful succession of murder, arson, rape, and torture with the same joy in their hearts, the same contentment in their souls as if they had indulged in some student's rag.... When a man is capable of commanding, when he is by nature a "Master," when he is violent in act and gesture, of what importance are treaties to him?...

"The Blond Beast" was another Nietzschean epithet idolized by him and borrowed by Hitler. The "Lords of the Earth" was an FN expression that occurs frequently in Mein Kampf. Nietzsche also prefigured Hitler's "final solution." From The Will to Power:

A doctrine is needed powerful enough to work as a breeding agent: strengthening the strong, paralyzing and destructive for the world weary. The annihilation of the decaying races. Decay of Europe.-The annihilation of slavish evaluations.-Dominion over the earth as a means of producing a higher type.-The annihilation of the tartuffery called 'morality.' The annihilation of suffrage universel; i.e. the system through which the lowest natures prescribe themselves as laws for the higher.-The annihilation of mediocrity and its acceptance (The one sided, individuals – peoples;

Hitler went to the Nietzsche museum and posed for a picture with the bust of the philosopher, but his biggest intellectual inspiration was not Nietzsche, but his friend Richard Wagner. Wagner and Nietzsche shared a hatred of the Christian and Jewish religions, and a profound misanthropy, but Nietzsche did not go along with the full virulence of Wagner's antisemitism, and he broke with Wagner partly over that. After his insanity, though, his pro Wagner and violently anti-semitic sister Elizabeth became his literary executor, thereby contaminating some of his work.

From Wikipedia:

It has been observed that In 1932, Elisabeth Forster-Nietzsche received a rose bouquet from Adolf Hitler during a German premier of Benito Mussolini's 100 Days; in 1934 Hitler and Alfred Rosenberg visited her again, presenting her with a wreath for Nietzsche's grave with the words "To A Great Fighter"; in the same year the Führer posed for a photo gazing into the eyes of a white marble bust of Nietzsche, and was presented by Elisabeth with Nietzsche's favorite walking stick.[26] There can be no doubt that Italian and German fascist regimes were eager to lay claim to Nietzsche's ideas, and to position themselves as inspired by them. In Heinrich Hoffmann's best-selling Hitler as Nobody Knows Him (which sold nearly a half-million copies by 1938) the caption of the photo of Hitler with the bust of Nietzsche read, "The Führer before the bust of the German philosopher whose ideas have fertilized two great popular movements: the National Socialist of Germany and the Fascist of Italy."[27]

Monday, October 11, 2010

David Hasselhoff - Your Car is Ready

Google has the robo-car almost ready to go.

I can't wait.

Anyone driving the twists of Highway 1 between San Francisco and Los Angeles recently may have glimpsed a Toyota Prius with a curious funnel-like cylinder on the roof. Harder to notice was that the person at the wheel was not actually driving.

The car is a project of Google, which has been working in secret but in plain view on vehicles that can drive themselves, using artificial-intelligence software that can sense anything near the car and mimic the decisions made by a human driver.

Riding Rockets: Book Review

If you've ever felt the pull of the romance of space travel, Riding Rockets by R. Mike Mullane is a book I heartily recommend. Mullane was a West Point graduate and Air Force aviator with 134 combat missions in Vietnam when he applied to be an astronaut. He was a flight test engineer, not a pilot, and his astronaut class was the first to include mission specialists selected from flight engineers and civilian scientists.

Mullane's book is a darn good read for entertainment and an even better one for information. Military aviators aren't exactly famous for opening their brains for the world to view, but his book is strikingly candid and revealing. One of my favorite parts is his story of his childhood obsession with space and his devotion to Willy Ley and Chesley Bonestelle's Conquest of Space. I also fell under that spell and tried my hand at building rockets and making rocket fuel - as a hole burned into our basement ceiling once testified. Mullane, though, had the dedication, talent, and diligence to make it happen, despite a need for glasses that kept him out of pilot training.

The military astronauts, as portrayed by Mullane, are ferociously competitive, fun loving denizens of the planet he calls Arrested Development. The first hard decision he had to make as a NASA employee, he says, was what to wear to work. West Point and a military career meant never having had to make that decision before. Nor had he ever inhabited a workplace that included the female of our species. Political incorrectness came naturally to him and he quickly managed to offend the more hardline feminists in his class, notably Dr. Sally Ride, the first American woman in space.

There are many amusing stories here, both Earthbound and orbiting, and some that are downright hilarious. There is also terror and tragedy, and anger. Much of the anger is directed at NASA mismanagement. That mismanagement, as he saw it, made the astronauts job incredibly frustrating and, at a higher level, led to the destruction of Challenger and Columbia.

Flight into orbit is not a dangerous job, and it's not a very dangerous job - it's an incredibly dangerous job. Even in an optimally designed rocket, the passengers put themselves on top of several million pounds of highly explosive fuel for a trip to a place where nature has a lot of ways of killing them. The space shuttle was not that optimal design. It was both underdesigned and overpromised, both circumstances the result of trying to do too much with too little money.

There were at least three grave design flaws in it. First, it lacked a robust escape module. This fact killed the Challenger crew and possibly killed the Columbia crew. Second, the solid fuel boosters and the external fuel tank were in positions where debris from them could destroy the orbiter. Such an accident killed the Columbia and very nearly killed the Discovery. Hot gases that penetrated the solid fuel booster O-rings blew up the Challenger.

As often happens, these severe design flaws were not enough by themselves to kill the Shuttles. That also required a reckless disregard of the evidence of problems by the NASA management.

Distilled Frenzy

. . . the ideas of economists and political philosophers, both when they are right and when they are wrong, are more powerful than is commonly understood. Indeed the world is ruled by little else. Practical men, who believe themselves to be quite exempt from any intellectual influences, are usually the slaves of some defunct economist. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back............... J M Keynes

A Hitler might be Nietsche distilled, but nowadays the madmen tend to rely on distilled Beck.

Byron Williams, Oakland freeway shooter.

I would have never started watching Fox News if it wasn't for the fact that Beck was on there. And it was the things that he did, it was the things he exposed that blew my mind.

The "Burg"

Steve Landsburg:

The Internet seems to have bred a peculiar subspecies of troll that cheerfully devotes enormous effort to refuting arguments nobody ever made. While they seem to have infinite time to construct these pointless rebuttals, these troll-types seem to have no time at all in which to actually digest the arguments they think they’re rebutting. They start with a guess as to what someone else might have said, and seem all but incapable of entertaining the notion that they might have guessed wrong. Is there a name for these people? “Crank” and “troll” are too general. If it were up to me, we’d reserve the word “Bozo” for this purpose, but it too is already in more general use. We need a new word! Give me your suggestions!

Well, since you did ask: in light of the many pixels he has wasted refuting arguments Paul Krugman never made, I suggest the eponymn "landsburg," or just "burg" for the word he seeks.

LOL

From the Lumonator:

It's organic and carbon is cheaper than silicon because you don't have to deconstruct anyone's microprocessors or artificial breasts to get the stuff.

Lubos is talking about solar panels made of rubrene and being funny, but in fact silicon, despite being quite a bit less abundant in the larger universe than carbon, is several hundred times more abundant in the Earth's crust than carbon, and dirt, or at least sand, cheap. Nice pure crystals for optimal solar panels are not so cheap to manufacture of course.

As a person who has recently considered equipping my house with solar panels I do have to say that efficiency can be an important concern. My roof has a limited amount of real estate suitable for mounting solar panels, so to get the optimal amount of energy I need high efficiency panels even here in relentlessly sunny New Mexico.

Sunday, October 10, 2010

Unions and Merit Pay

Many of the usual suspects are taking a crack at the question of why teachers unions oppose merit pay and what can be done about it. Here, for example, are Megan McArdle, Matt Yglesias, Tyler Cowen, and Bryan Caplan.

To me, they mostly miss the point - though at least one commenter is more astute. Caplan gets my cluelessness award:

I don't doubt that unions tend to oppose merit pay, but the reasons are unclear. Profit-maximizing monopolists still suffer financially if they cut quality; the same should hold for unionized workers. Why not simply jack average wages 15% above the competitive level, and leave relative wages unchanged?

Or to put the puzzle another way: Once you've secured a raise for all the workers in your union, why prevent employers from offering additional compensation for exceptionally good workers?

Megan:

Unions are set up to minimize frictions and maximize benefits for the bottom 55%. That's how they work everywhere--in schools, and out. That's how they have to work. No amount of cajoling, no number of white papers, is going to change that.

And Matt is more focused on the what than the why:

Take, for example, the hot issue of teacher compensation. The traditionalist view is that teachers should get paid more for having more years of experience and also for having more degrees. The reform view is that teachers should get paid more for having demonstrated efficacy in raising student test scores. This is an important debate, but I think it’s really not an ideological debate at all. I think the only reason it’s taken on an ideological air is that unions have a view on the matter and people do have ideological opinions about unions in general. But if we found a place where for decades teachers had been paid based on demonstrated efficacy in raising student test scores, then veteran teachers and union leaders would probably be people who liked that system and didn't want to change to a degree-based system. Because unions are controversial, this would take on a certain left-right ideological atmosphere but it’s all very contingent.

Most of the above misses the point. The most fundamental characteristic of the union is embedded in its name - unity is the whole point. Anything that pits member against member undermines that unity. Unions, consequently, are not about to like merit pay.

That doesn't mean merit pay is a bad idea, or that it can't be implemented in a form that is relatively palatable to teachers. I favor a sort of collective approach, where a whole school gets a merit grade and individual teachers have a say in allocations. In particular, this will give teachers an incentive to improve or get rid of incompetent colleagues and try to imitate the best.

Friday, October 08, 2010

China Syndrome

After decades of explosive economic growth, China is feeling its oats and starting to throw its weight around. No more Mr. Nice China seems the order of the day, so it issues threats against any US action to reduce our massive trade deficit, reasserts old claims to Indian territory, and beats up on Japan.

The West, and the world, made a gigantic bet that if China were brought into the world economic and political community it would learn to play nicely - whatever that means. China has changed itself from a decrepit socialist basket case into an marvel of state capitalism, but it has kept the same old Communist Party apparatus in firm charge. The leaders decided to abandon the Party's rationale for existence but kept the power. That totalitarian grip is evident in the paranoid and vicious reaction to the selection of Liu Xiaobo for the Nobel Peace prize.

So why, exactly, did the US and the world tolerate and encourage the emerging superpower and allow themselves to become so dependent on it? Short term thinking and stupidity played their role, of course, but so did a belief in a kind of Magical Capitalism. Milton Friedman and his followers were convinced that capitalism had this magical power to spread freedom. I don't think that they are necessarily completely wrong, but they overestimated its power. Secure in that magical belief, we outsourced our jobs and mortgaged our country to China. Lenin (or was it Marx) would say that we sold them the rope to hang us with.

About Curvature

What is curvature? We have an intuitive notion that some curves are curvier than others, so how have mathematicians sorted this out?

I have been reading The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions by Shing-Tung Yau and Steve Nadis. It turns out that the notion of curvature, and in particular, Ricci curvature, is fundamental to all the considerations therein. From my deeply shallow and mostly forgotten studies of general relativity I recalled that the Ricci tensor was (a) an index contracted Riemann curvature tensor and (b) an essential component of the Einstein tensor. Neither bit of intellectual flotsam gave me any significant insight into what Ricci curvature really was.

For me to understand something, I need to have a mental picture that can be expressed in familiar notions. The simplest notion of curvature is that we associate with a circle. We have an intuitive notion that a smaller circle is “more curved” than a larger one. We can make this notion precise in terms of the reciprocal of the radius of the circle – if the circle has radius R, its curvature is 1/R.

So what about ellipses, hyperbolas, and random curvy lines, still operating in the Euclidean plane? Again, we can see that this kind of curve, unlike a circle, seems to be more curved in some places than others. Can we fit a circle inside such a curve? It turns out that there are infinitely many curves tangent to a given plane curve at a point, but we can find a “best” one – the so called Osculating (or kissing) circle – the circle that stays closest to the curve near the point in question. I should mention that we are sticking to sufficiently smooth curves here, that is, curves without any corners or gaps – (twice continuously differentiable, to be technical). The curvature of that plane curve is then defined to be the reciprocal of the radius of that kissing circle.

Things get a bit more complicated if we go to three (or more) dimensions. Suppose we have a curve embedded in a two dimensional surface – one like the center of a saddle, for example. Imagine yourself with an ant’s eye view from the center of the saddle (or a person’s eye view from the top of a mountain pass). If you look one direction, the world curves up, but in another, it curves down. It’s obvious that lots of circles could be fitted – and a sphere that fit well in one direction, wouldn’t fit in the other.


So does such a surface need infinitely many “curvatures” to describe it, one for each direction? Fortunately not, if the surface is sufficiently smooth. If so, two principal curvatures suffice. At each point of the surface, one can draw a normal line (or perpendicular) to the surface. If we now imagine cutting the surface with planes containing the normal in every possible way, each plane will slice the surface into a unique plane curve which will have an osculating circle with a center on the normal line. Count curvatures as positive if they lie on one side of the surface (the inside for closed surfaces like spheres) and negative if on the other. The maximum such curvature is one principal curvature and the minimum, the other. Their product is the famous Gaussian curvature. The most remarkable thing about the Gaussian curvature (see link) is the fact that it turns out to depend only on the way distances are measured on the surface, not upon the way the surface is embedded in higher dimensional space. This result is one of the foundational notions of differential geometry.

Are we there (to Ricci curvature) yet? Not quite, but another gas station or two ought to do it.

As we go to still higher dimensions, more ways to curve become possible. Recall that for the two–dimensional surface we took a bunch of planar slices through the surface to get the two principal curvatures and the Gaussian curvature. We can do something analogous in higher dimensions, though for technical reasons we need to operate in the tangent space and its exponential map – concepts which I won’t try to explain – but try to think of the operation as a kind of best approximation to slicing up the space itself. Each slice is a bit of 2-D (2–dimensional) surface, and the sectional curvature is the Gaussian curvature of that 2-D surface. If we know all the sectional curvatures at a point, we know all about the curvature at that point.

Consider the unit vectors tangent to the manifold at a point (unit vectors in the tangent space). For each such unit vector in n dimensional space, there is an n-2 dimensional family of planes containing that unit vector. If we compute the average sectional curvature for all the planes containing the unit vector A, we get Ricci(A,A), the Ricci curvature in direction A. Since the Ricci tensor Ricci(A,B) is bilinear and symmetric, if we know Ricci(A,A) for all A, we can compute Ricci(A,B) for all A and B.

Needless to say, I have left out a lot. I haven't made clear the distinction between intrinsic and extrinsic curvature, and I haven't mentioned that you really need the full Riemann tensor in more than three dimensions. I'm counting on the mathematically literate among my readers to catch the more egregious errors.

Thursday, October 07, 2010

Religious Threats

Many think that the threat of having Sharia imposed upon us by Muslims is serious enough that we must deal with it by expelling them, but let's remember that's not the only religious threat we face.

If the Episcopelians manage to get control of the country, we will all be forced to worship the Queen of England, or, if prediction may be ventured, even Prince Chuck.

Catholics are far worse. They worship a former Nazi who made his bones running the Inquisition - yes that Inquisition - and covering up clerical child abuse. On the positive side, if we ran them out of the country, we would lose some real loser Supreme Court Justices - not you Sylvia. On the negative, depending on how strictly affiliation was judged, my family and I might have to go back to Ireland, or somewhere.

How about Mormons? They are a native religion of America, to be sure. A few words on that subject: Glen Beck, Orin Hatch, and the White Horse prophecy.

If we let the Jews take over - the stuff they haven't already, I mean - and impose their religious laws, say goodby to cheese burgers and Rubens. Ditto the Hindus.

Of course if they throw the Jews out, there goes the rest of my family.

And let's not even mention Baptists and Evangelicals.

So what religions can America safely tolerate? Unitarians, I think, and maybe Buddhists.

Monday, October 04, 2010

Reality Vision

The Social Network is an excellent movie, but it shouldn't be mistaken for reality. Some who have investigated have found some major holes in the factual structure created by writer Aaron Sorkin and director David Fincher's movie. Check for example Luke O'Brien or Nathan Heller in Slate. Heller, who lived a couple of rooms down from Zuckerberg when they were both freshmen, recognizes neither Zuckerberg nor Harvard in the movie:

I recognized their Harvard, but only from Love Story and The Paper Chase, not my experience.

Heller didn't like the movie, but I did and most critics seem to agree. Perhaps the real Harvard and real Zuckerberg are more compelling, or maybe not. The trouble is that a clearly biographical movie that gets a lot of facts wrong is a kind of crime against reality. I'm ambivalent about the result.

Of course maybe fellow Harvies like O'Brien and Heller need to defend their territory. Or maybe Zuckerberg or some other insider will write their version sometime.

State of the Nation

Paul Krugman tells us a lot about where we are today.

A note to Tea Party activists: This is not the movie you think it is. You probably imagine that you’re starring in “The Birth of a Nation,” but you’re actually just extras in a remake of “Citizen Kane.”

True, there have been some changes in the plot. In the original, Kane tried to buy high political office for himself. In the new version, he just puts politicians on his payroll.

I mean that literally. As Politico recently pointed out, every major contender for the 2012 Republican presidential nomination who isn’t currently holding office and isn’t named Mitt Romney is now a paid contributor to Fox News. Now, media moguls have often promoted the careers and campaigns of politicians they believe will serve their interests. But directly cutting checks to political favorites takes it to a whole new level of blatancy.

Arguably, this shouldn’t be surprising. Modern American conservatism is, in large part, a movement shaped by billionaires and their bank accounts, and assured paychecks for the ideologically loyal are an important part of the system. Scientists willing to deny the existence of man-made climate change, economists willing to declare that tax cuts for the rich are essential to growth, strategic thinkers willing to provide rationales for wars of choice, lawyers willing to provide defenses of torture, all can count on support from a network of organizations that may seem independent on the surface but are largely financed by a handful of ultrawealthy families.


There's more. Read it.

A Good Word For Rick

Josh Marshall has a good word for Rick Sanchez.

Sanchez may have been all the things Stewart and friends called him, but he did, it seems, occasionally ask tough questions. Jon Stewart, on the other hand, famously tosses softballs even to guests he pillories when they aren't on stage.

Sunday, October 03, 2010

Afghani-Pakakistan

Our war in Afghanistan seems increasingly disconnected from common sense. When top leaders discuss our war aims they seem to be speaking Martian: "We need to reverse the momentum of the Taliban long enough to stabilize...." "We need to persuade the Pakistanis that we can be counted on..." to do what I have no idea. We are after al Quaeda and the Taliban, but both have moved HQ to Pakistan.

Meanwhile our troops continue to take casualties fighting an enemy embedded in the population. It's asymmetric warfare, they tell us. I wonder at our leaders grasp of the concept.

Meanwhile the Pakistanis play a curious double game - a double game that everybody recognizes. On the one hand, they give us secret permission to assassinate al Quaeda leaders, on the other they publically protest it. They actively harrass our supply lines when we get to aggressive in our pursuit.

How about we give them a stark choice - hand over the people we want or face war. Not an invasion, just destruction of every aspect of their economy?

Human Nature

Kevin Drum is looking for fundamental aspects of human nature that people don't pay enough attention to. I'm sure that there are a long list but he offers these two for a start:


1.Loss aversion: people really, really hate to lose something they already have and will forego even favorable risks to avoid it.

2.Regression to the mean: an especially strong performance is likely to be followed by a weaker performance and vice versa.

I'm going to ignore the second, because it seems to me to be both obvious and misleading. Obvious in the sense that your best day ever is likely to be better than most of the next days. Misleading in the sense that extraordinary performance is often an excellent predictor of very good future performance. I'm especially interested in those that run counter to the fundamental assumptions of classical economics, and the first fits that bill.

Kevin's commenters offer a number of elaborations on that idea. One is that we tend to strongly prefer a sure thing to a chance at more - a bird in the hand is better than two in the bush. Most people offered the choice of a 10,000 dollar sure thing or a fifty-fifty chance at $30,000 will pick the sure thing.

Another commenter points to this Wikipedia article on cognitive biases.

My belief is that these so-called cognitive biases have their explanation in two fundamental facts: first, humans are selected by evolution not for profit maximization but for survival and reproduction maximization and second, our brains have limited computational power.

Human Sacrifice

If we can stop worrying about the threat of Shariah for a moment, spare some worry cells for the growing threat posed by Druids. As you may recall, they were fond of burning to death human victims in their sacrifice rituals. It seems that they have already been recognized as an official religion in Britain - I don't think we do that here, but they have got to be a major threat.

Of course whoever wrote the story is some kind of ....

You can now breathe easily Lord of the Rings fans, for Druidry, the ancient belief that worships deities that assume different forms in nature, was recognized as a religion in Britain for the first time Saturday and granted charitable status.


WTF? I don't think LOTR has much in common with Druidry.

This Week: Town Hall

Christianne Amanpour hosted a town hall on Islam in America on ABC's this Week. It was a very good event, with lots of points of view represented, several of them of them idiots like Gary Bauer and Junior Graham. It was a little discouraging to watch their tactics and see how effective they were. The basic technique is equating all members of a group with the worst members of the group, or the worst deeds of a member.

It's an amazingly effective technique - not surprisingly, since that's been the way we have started wars for millenia. Thankfully there were some members who spoke clearly for the Constitution and American values. Unfortunately, appeals to reason have little power over those who are hysterical over the prospect that American Muslims are about to introduce stoning for adultry in the US. Perhaps they should worry about the Christians and Jews among us - it's their Bible that the Muslims got it from.

Saturday, October 02, 2010

The Social Network

Who thought a movie about intellectual property could be so gripping. Jesse Eisenberg is spectacular as Mark Zuckerberg.

Rick Sanchez and John Stewart

The WaPo covers CNN's firing of Rick Sanchez.

"White folks usually don't see it. But we do -- those of us who are minorities and women see it sometimes, too, from men in authority." Sanchez paraphrased what he said a CNN executive had once said to him: "I really don't see you as an anchor, I see you more as a reporter. I see you more as a John Quiñones -- you know, the guy on ABC. . . . Now, did he not realize that he was telling me. . . . An anchor is what you give the high-profile white guys, you know. . . . To a certain extent Jon Stewart and [Stephen] Colbert are the same way. I think Jon Stewart's a bigot."

Later in the interview, Dominick noted Stewart is Jewish, which he said is "a minority as much as you are."

"Very powerless people," Sanchez said, with a laugh. "He's such a minority, I mean, you know. . . . Please, what are you kidding? . . . I'm telling you that everybody who runs CNN is a lot like Stewart, and a lot of people who run all the other networks are a lot like Stewart, and to imply that somehow they -- the people in this country who are Jewish -- are an oppressed minority? Yeah." In the audio, which circulated online Friday, Sanchez's sarcasm was evident.

Now nobody at CNN cares if Rick disses Stewart, who has made something of a crusade of mocking Sanchez for years. But he hit the death rail when he, in response to a question, implied that Jews are not an oppressed minority in the TV business. Mocking your bosses has been a business no no for a while.

I've been a fan of the Daily Show for years, but Jon Stewart is starting to evolve into one of the sanctimonius types he mocks. O'Reilly was on the other day and Stewart made a big thing of O'Reilly greeting him with less than gentlemanly hospitality. I mean come on, Jon, you make a living (a damn good living) mocking people and tryingto crush, burn, and destroy them, and you expected to be treated like a longlost brother? You've been trying to kill Sanchez for years. You succeeded - he's dead for TV. Congratulations or whatever.