Friday, December 31, 2010

I Knew He Was French...

Paul Krugman reports:

This is too weird not to share: guess who was named by one survey as the most influential left of center European thinker?


The Daily Beast and their panel of MacGeniuses came up with a list of twenty "smartest people of 2010." Nobody I actually know made the list, but I have some opinions on some of them. Of course the really smart people of 2010 are probably toiling in utter obscurity in some math or physics department, but we are sticking with just the public types here.

#15 Christopher Hitchens. A very clever, passionate, and erudite fellow who manages to be wrong about a lot of stuff. If I had to be stuck on a long ocean voyage with only one person to talk to, he would be my choice from this list.

#14 Kanye West. WTF?

#8 Felisa Wolfe-Simon. Probably a good scientist who did some nice work with the arsenic tolerating bacteria, but this story was so absurdly hyped by NASA and the press that it really has become something of an embarassment. The bottom line seems to be that she and colleagues do not seem to have proven metabolic replacement of phosphorus in cellular processes.

#5 J. Craig Ventner. Yes, of course.

#4 Mark Zuckerberg. Well, he is lucky, which as Napoleon noted, is far more important than being good. I'm sure he's also bright, but is Facebook good for anything besides entertaining the idiots with global gossip?

#3 Steve Jobs. If there is such a thing as a business genius, Jobs is the man. Many of the tech zillionaires are mostly lucky, but Jobs really is a guy with vision and artistic temperment. That said, I use an android, not an iphone, and only rarely use my powerbook.

#2 Bill and Melinda Gates. They certainly deserve a lot of credit for trying to put their money to good use in the world. Is that genius? Well, it is virtue.

#1 Jon Stewart. I'm a big fan of this talented entertainer, and his heart is usually in the right place, but he really isn't that smart - or even very well informed. Of course he is well ahead of 95% of politicians and 99% of what passes for television news types.

Thursday, December 30, 2010

Nut-Jobs of the Right, XXIV

Tucker Carlson, who so far as I know is not a vegetarian, thinks Michael Vick should have been executed. This sentiment is probably widely shared by NY Giants fans, but I think that rather, the Eagles' offensive line ought to execute their blocks.

Wednesday, December 29, 2010

The Weather Outside is Frightful

OK, maybe not so much here in southern New Mexico, though I suppose you could get a sunburn if you left your shirt off too long outside - but Europe is having its third tough winter in a row and the eastern US is also in the fridge again. So what does it mean? Proof of global warming or disproof (I couldn't bring myself to say "a refudiation", but I was tempted).

Judah Cohen, a commercial weather forecaster, offers a interesting meteorological theory in the NYT.

Annual cycles like El Niño/Southern Oscillation, solar variability and global ocean currents cannot account for recent winter cooling. And though it is well documented that the earth’s frozen areas are in retreat, evidence of thinning Arctic sea ice does not explain why the world’s major cities are having colder winters.

But one phenomenon that may be significant is the way in which seasonal snow cover has continued to increase even as other frozen areas are shrinking. In the past two decades, snow cover has expanded across the high latitudes of the Northern Hemisphere, especially in Siberia, just north of a series of exceptionally high mountain ranges, including the Himalayas, the Tien Shan and the Altai.

The high topography of Asia influences the atmosphere in profound ways. The jet stream, a river of fast-flowing air five to seven miles above sea level, bends around Asia’s mountains in a wavelike pattern, much as water in a stream flows around a rock or boulder. The energy from these atmospheric waves, like the energy from a sound wave, propagates both horizontally and vertically.

As global temperatures have warmed and as Arctic sea ice has melted over the past two and a half decades, more moisture has become available to fall as snow over the continents. So the snow cover across Siberia in the fall has steadily increased.

As always, for the details you need to read the article, but the argument is that less artic ice cover puts more moisture and hence snow cover in Siberia and that steers the jet stream differently than it was formerly. It sounds plausible, but I wonder how it runs in the weather and climate models. Doubtless we shall learn more over the next decade or so. Meanwhile, you might consider: is a snow blower really a luxury purchase - though it will increase your carbon footprint.

Why It's More Dire in Eire*...

Paul Krugman looks at the housing bubble in Ireland and Nevada...

The populations are similar; the housing bubbles were comparable in their extremity; both currently have roughly 14 percent unemployment.

.... Fiscally, Nevada’s retirees can count on Washington to keep paying their Social Security and Medicare, which amounts to a big transfer into the state now that it’s paying much less in federal taxes.

Oh, and Nevada is in effect getting a federal bank bailout — not so much directly via the FDIC, although there’s some of that, as via Fannie and Freddie: with less than 1 percent of the US population, Nevada is generating more than 5 percent of the F&F losses — losses that are a problem for taxpayers in general, not specifically in Nevada.

So there you have it: optimum currency area theory in action..

Ireland is faced with the combined disadvantages of sharing a currency with Germany but not a budget.

*Yes, I've heard that it's not supposed to rhyme with "fire."

Tuesday, December 28, 2010

Flim-Flam Man

Prof. Steve Landsburg, AKA "The Burg" has a response of sorts to criticism of his "percentage of girls" puzzle from yours truly and Lubos Motl. That response was to challenge Lubos (I am the blogger-who-may-not-be-named) and all comers to a \$15,000 sucker bet. Lubosh has called the bet a "borderline cheat" but I don't see any border at all.

The problem is that the subject of his bet is quite different from the original puzzle and his answer to his new problem is different than his original answer - and, not incidentally, now correct in a certain approximation.

Here is the original problem:

There’s a certain country where everybody wants to have a son. Therefore each couple keeps having children until they have a boy; then they stop. What fraction of the population is female?

Well, of course, you can’t know for sure, because, by some extraordinary coincidence, the last 100,000 families in a row might have gotten boys on the first try. But in expectation, what fraction of the population is female? In other words, if there were many such countries, what fraction would you expect to observe on average?...

It seems to me that Landsburg is pretty clearly indicating that he is talking about a country with plausible country sized reproducing population, e.g. comparable or larger than 100,000. When he did his calculation, though, he initially did it for one family, and claimed that that was a perfectly good surrogate for a country - though he has since apprently changed his tune on that. The problem with that, as Doug Zare and others have pointed out, is that one family is a biased estimator for the population.

Let's take a look at his "new" problem - I call it new because it sure doesn't look like the original to me.

I specified that the answer is to be interpreted in expectation, since the actual fraction of girls could be anything at all due to statistical flukes.

I say the answer depends on the number of families in the country, but in no case is it 50%. Lubos insists that the correct answer is 50%.

Now the best way to settle such a dispute is to go to the mathematics. But since Lubos seems unable to follow the mathematics, the next best way is to run a simulation. So I propose the following terms: We’ll randomly choose five graduate students in computer science from among the top ten American university departments of computer science and have them write simulations for a country starting with, say, four couples, each having one child per year and stopping when they have a boy. We’ll let this run for a simulated 30 years and then compute the fraction of girls in the population.

[Edited to add: If Lubos (or anyone else) prefers to run the simulation till every family is complete (as opposed to a fixed number of years), that's fine with me.

I think this is a ridiculous way to frame a bet, and I doubt that Lubos will bite. If you want to do a simulation, specify the code and let us decide if you capture the problem, not some anonymous grad students. I don't have that kind of cash to play with, and running an internet gambling operation is probably illegal anyway, but let me suggest a more natural formulation of the problem: start with 100,000 families, the number mentioned in your first post.

Monday, December 27, 2010

He'll Be a Dentist...

I had my teeth cleaned the other day. The tech managed to convince me that it was time to expose my head to some more ionizing radiation, so I submitted to X-rays. I had mixed feelings about the fact that they still used film. My previous dentist had gone to a CCD system which, while requiring less radiation per shot, also convinced my idiot tech that it wasn't really necessary to get the shot right the first time, since she could always get a do-over - one good reason I left that dentist.

After the cleaning, the dentist looked at my X-rays and said somewhat wistfully:

"Nothing really terrible happening to any of these teeth on the X-rays."

Afterwards he carefully inspected my wisdom teeth, and said with still more apparent disappointment:

"Nothing really going on to justify pulling them - YET."

Am I getting more paranoid in my old age or does the guy really need that boat payment?

It's Called Civilization

Human culture seems to have undergone some sort of major phase transition when we started living in cities. Progressive citification has only intensified in the last century or so as technology has permitted a smaller and smaller number of farmers to feed the rest of us. So what's so special about cities? Are they more than just a convenient way to stack a lot of people in a small amount of room?

It may not have taken a physicist to intuit the answer, says Jonah Lehrer, writing in the New York Times Magazine, but if you want the insight codified in some equations, a physicist, namely Geoffrey West, is the man.

West used to think about physics, but the cancellation of the Super Collider in 1993 caused him to look for new worlds to think about. His first big score was in biology,

West has been drawn to different fields before. In 1997, less than five years after he transitioned away from high-energy physics, he published one of the most contentious and influential papers in modern biology. (The research, which appeared in Science, has been cited more than 1,500 times.) The last line of the paper summarizes the sweep of its ambition, as West and his co-authors assert that they have just solved “the single most pervasive theme underlying all biological diversity,” showing how the most vital facts about animals — heart rate, size, caloric needs — are interrelated in unexpected ways.

The mathematical equations that West and his colleagues devised were inspired by the earlier findings of Max Kleiber. In the early 1930s, when Kleiber was a biologist working in the animal-husbandry department at the University of California, Davis, he noticed that the sprawlingly diverse animal kingdom could be characterized by a simple mathematical relationship, in which the metabolic rate of a creature is equal to its mass taken to the three-fourths power. This ubiquitous principle had some significant implications, because it showed that larger species need less energy per pound of flesh than smaller ones. For instance, while an elephant is 10,000 times the size of a guinea pig, it needs only 1,000 times as much energy. Other scientists soon found more than 70 such related laws, defined by what are known as “sublinear” equations. It doesn’t matter what the animal looks like or where it lives or how it evolved — the math almost always works.

The key to the biological problem turns out to be limitations of infrastructure. Crudely speaking, the volume that can be carried by a pipe (or blood vessel) scales like the square of the linear size, while the volume to be served scales like the cube. Similar consideration doubtless affect cities, but Lehrer doesn't really share those details.

The most interesting detail that he does share is that people in cities are more productive than those who aren't. There is a scaling law for that too:

The challenge for [co-author Luis] Bettencourt and West was finding a way to quantify urban interactions. As usual, they began with reams of statistics. The first data set they analyzed was on the economic productivity of American cities, and it quickly became clear that their working hypothesis — like elephants, cities become more efficient as they get bigger — was profoundly incomplete. According to the data, whenever a city doubles in size, every measure of economic activity, from construction spending to the amount of bank deposits, increases by approximately 15 percent per capita. It doesn’t matter how big the city is; the law remains the same. “This remarkable equation is why people move to the big city,” West says. “Because you can take the same person, and if you just move them to a city that’s twice as big, then all of a sudden they’ll do 15 percent more of everything that we can measure.”This implied that the real purpose of cities, and the reason cities keep on growing, is their ability to create massive economies of scale, just as big animals do. . .

After analyzing the first sets of city data — the physicists began with infrastructure and consumption statistics — they concluded that cities looked a lot like elephants. In city after city, the indicators of urban “metabolism,” like the number of gas stations or the total surface area of roads, showed that when a city doubles in size, it requires an increase in resources of only 85 percent.

The whole article is recommended for all, especially those interested in economics and its implications for the future of the species.

Thursday, December 23, 2010

Back to "The Burg"

Steve Landsburg brings us this little post-Channukah present:

I think he mangles the logic and presents a totally bogus answer.* Let's read it:

•Here’s the wrong answer: Every birth has a 50% chance of producing a girl. This remains the case no matter what stopping rule the parents are using. Therefore the expected number of girls is equal to the expected number of boys. So in expectation, half of all children are girls. {OK, Compare paragraph below}
•Pretty convincing, eh? So why is it wrong? Well, actually, most of it is right. Every birth has a 50% chance of producing a girl — check. This remains the case no matter what stopping rule the parents are using — check. Therefore the expected number of girls is equal to the expected number of boys — check! But it does not follow that in expectation, half of all children are girls! { Yes, Steve, it does!!}
•To see why not, let me tell you about the families who live on my block. There are 3 families with four girls each (and no boys), and one family with 12 boys (and no girls). Altogether, that makes 12 girls and 12 boys — equal numbers! On average, each family has three girls and three boys. Nevertheless, the fraction of girls in the average family is not 50%. It’s 75% (the average of 100%, 100%, 100%, and 0%).

But Prof L, that's not the question you asked. You asked what fraction of the population was female, not what fraction of the average family was female. The answer to the question you asked *is* 50% just like the fraction of female children on your block is 50%. The question you intended to ask, but didn't is: What is expected value of the fraction of the average family that is girls? The answer to that question is:

0*1/2 + (1/2)*1/4 + (2/3)*1/8+ ... =

UPDATE: Maybe I really should stop picking on Landsburg. A number of his commenters has pointed out exactly what's wrong with his logic, but he still doesn't get it. I thought he was just impossibly stubborn, but maybe he's got a brain block or something. He can't even grasp that the fraction of girls in his (hypothetical) neighborhood (12/24) is equal to 1/2. It still drives me nuts that thousands of dim students treat this guy as an authority.

Here's a nice example of the way Steve deals with a commenter who rather politely and repeatedly failed to "get" his point:

Tom: You are definitely too stupid to think about this problem.

UPDATE II: I was remiss in not linking to Doug Zare's original post at MathOverflow. Note that his answer ((1/2) - 1/4k)(a)differs from the Burg's and (b)is very close to 50% for a country with a plausible number of families k. Both his answer and Landsburg's require that you include biologically impossible cases - families with arbitrarily large numbers of children)

It's worth noting that answers to such questions depend critically on how you translate the real world into math and vice-versa. Landsburg, in my opinion, fails egregiously.

Bad Trippin'

What's up with the recent weather related travel debacle in Europe? Five inches of snow shuts down the biggest airports in Europe. Should we attribute it to a typical failure of those damn European socialists?

Not exactly. Actually this one is more like a typical failure of greedy and short-sighted capitalists. Clive Irving has the story of Heathrow and other British airports.

It seems that after the Brits noticed that airports could be made into shopping malls, they turned airports over to the British Airport Authority, which, despite the name, was a private company, rather than a government entity.

As a result, the BAA became a prized, highly profitable business, much admired beyond the U.K. It caught the eye of an ambitious Spanish multinational—until then a specialist in building highways—called Ferrovial. In 2006 Ferrovial bought control of the BAA.

Then the problems really began. Passengers complained of poor maintenance, filthy toilets, chaotic security lines, and poor communications. The full realization of what Ferrovial was up to came in March, 2008, with the opening of Terminal 5. This supposed state-of-the art building, long delayed because of planning problems, was the scene of embarrassing systems failures in its first weeks—thousands of bags were lost, flights were delayed or canceled, and it became an infamous public-relations disaster for British Airways...

While Ferrovial was loading up the Heathrow stores with all their Christmas goodies it hadn’t bothered to check whether it had enough plows to deal with two runways if, by chance, it happened to snow. Or enough de-icing fluid to get the airplanes out of the gates. Or anything else fundamental to fitness of mission. The cost of that negligence is almost incalculable.

This result is hardly surprising. The fundamental problem, as is usually the case, was a misalignment of incentives and public purposes. Britain has a huge stake in having a functioning transportation system that the world can trust. Ferrovial mostly had a stake in selling single malt whiskies. The free market fanatics believe as a matter of religious principle that the government shouldn't do anything, but sometimes governments do it better, either by direct ownership of the key assets or by close regulation.

Wednesday, December 22, 2010

Speedy Projectiles

When I wrote earlier about viscosity and speedy bullets, Guest flogged me for my explanation of penetrating power. I thought it was about the speed of sound, and he said "pressure" and made me figure out why. That's all in the comments to the linked post.

I knew that speed of sound had to be involved though, so I needed to think that through as well. Here what I came up with while trying to go to sleep the other night.

It is pressure that melts the solid (by compressing the material until the intermolecular forces cease to bind, but the speed of sound is important too. Excess pressure is radiated away at the speed of sound, in the form of sound waves, but when the disturbance (hypervelocity projectile, say) is moving faster than the speed of sound, pressure does not have time to be radiated away. Thus, excess pressure accumulates ahead of the projectile and does its melting work until the projectile slows below sound speed and permits it to radiate away.

All that is momentum based reasoning. Energy can be important too, especially for larger projectiles. It can do its work by heating the target above vaporization temperature.

The Senator Who Lived

Harry Reid has been the target of oppobrium from right and left lately - accused of not being able to lead, follow, or campaign. The upshot of the lame duck makes him look a bit more like the master strategist, though.

Ezra Klein of the WaPo on the lame duck:

Sen. Lindsey Graham summed up the session by saying, "When it's all going to be said and done, Harry Reid has eaten our lunch."

To Whom It May Concern

I apologize for ever implying that Ginny might not be a suitable life partner for HP and that Ron was dull. No doubt Jo Row knows better.

---------Uncle CIP

Tuesday, December 21, 2010

Second Responders

It seems that the administration has praised John Stewart for kicking Congress in the pants hard enough to revive the 9/11 first responders health care bill. Meanwhile, the same President, who campaigned for better health care for our wounded veterans, especially those who are victims of traumatic brain injury (TBI), presides over an administration that continues to deny those veterans the gold standard of that care, cognitive rehabilitation.

The reason for denial is simple: it's expensive. The Pentagon convened a large panel of experts from both civilian and military medicine, and they unanimously recommended cognitive rehabilitation, but the Pentagon didn't like the answer, so they had a pet contractor write a report disagreeing. Every outside expert reviewing the contractor report found it deeply flawed, but with that report in its pocket the Pentagon continues to deny the wounded the best treatments.

NPR and Pro Publica report the details.

Saturday, December 18, 2010

Republicans Hate...

...Hispanics slightly more than they hate gays. But they really hate 9/11 first responders.

... the Senate voted against the cloture vote on the DREAM Act: 55-41.

The Senate on Saturday cleared the way for a final vote on a bill to end the military's "don't ask, don't tell" law, putting the 17-year effort to end the ban on gays in the military just hours from completion.

Senators voted 63 to 33 go proceed to debate on the bill. Fifty-seven members of the Senate Democratic caucus and six Republicans -- Sens. Scott Brown (Mass.), Susan Collins (Maine), Mark Kirk (Ill.), Lisa Murkowski (Alaska), Olympia Snowe (Maine) and George Voinovich (Ohio) -- voted yes. Four senators -- Jim Bunning (R-Ky.), Judd Gregg (R-N.H.), Orrin Hatch (R-Utah) and Joe Manchin III (D-W. Va.) -- did not vote.

Shepard Smith excoriated the Senators who are holding up the so-called "Zadroga Bill" to assist 9/11 first responders who suffer from medical problems as a result of their time at Ground Zero. The bill, which provides \$7 billion for the responders, passed the House but is being held up by Republicans in the Senate.

Friday, December 17, 2010

Viscosity II: String Theory

Non-experts might want to read Viscosity I first.

String Theorist and blogger Joseph Djugashvili has a post on what string theory has to say about viscosity, and in particular, about the ratio of viscosity to entropy density. My first reaction was “Say what?” Why should string theory have anything to say about viscosity? It’s a long post, with several interesting references and a number of the standard boring rants, but I won’t attempt to summarize – go read it yourself.

Getting back to the question, recall that viscosity is all about transverse transfer of momentum. At low energies, transverse forces have a long time to act, so it’s not implausible that viscosities could become arbitrarily large, and they do. Conversely, it’s also not really surprising that transverse momentum transfers should saturate at high energies.

Consider the case of a bullet smashing into a steel plate. If you have an ordinary bullet, and a reasonably thick plate, as the bullet hits it transfers momentum to the atoms of steel directly in front of it, but the forces holding the plate together transfer momentum transversely allowing the bullet to be slowed to a stop. This process has time to act because ordinary bullets travel slowly compared to the speed of sound in steel – the speed with which the momentum can be distributed throughout the larger plate. When a hypervelocity bullet – one travelling fast compared to the speed of sound in the plate – strikes, the atoms of steel in front of it have no time to call on their neighbors for help, and they just get pushed ahead of the pellet. Thus a small hypervelocity pellet can penetrate inches of steel armor.

Transverse momentum transfer saturation has been an important theme in high energy physics, if what I dimly recall is not too far off. Naïve question: Is it possible that such momentum transfer saturation has to occur if we want to avoid non-renormalizable forces?

Back to string theory:
The key paper cited by Lumo is Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics by P.Kovtun, D.T.Son, A.O.Starinets. The paper has a key result, and a conjecture:

The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of $\hbar/4\pi kB$ for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti--de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

I can’t be trusted to adequately summarize their string theoretic argument, but I will try anyway. (Experts should read the paper themselves, and the curious should consult somebody who understands ST). My understanding is as follows: they consider a strongly interacting quantum field theory which has a holographic dual black brane (in the AdS/CFT sense). They use this duality to compute the transverse components of the stress energy tensor in terms of the graviton absorption cross section on the brane. The entropy density can be computed from the temperature of the brane, and the transverse components give the viscosity.

Their argument applies to a class of quantum field theories. The conjecture is that the viscosity/entropy ratio computed above serves as a lower bound for all (or at least “a wide class”) of fluids. They present an uncertainty principle based argument to support it. Again, my summary can hardly do justice to it, but I think that the most crucial idea is that as the entropy decreases, the ability of transverse modes to transfer momentum does as well.

Finally, they have this discussion argument, also used by Lumo, which looks bogus to me.

Discussion.—It is important to avoid some common misconceptions which at first sight seem to invalidate the viscosity bound. Somewhat counterintuitively, a near-ideal gas has a very large viscosity due to the large mean free path. Likewise, superfluids have finite and measurable shear viscosity associated with the normal component, according to Landau’s two-component theory.

The superfluid component really does have zero viscosity. Of course it also has zero entropy density as well, so the bound isn’t really defined. So let’s not clutter up a perfectly good argument with bogus nonsense.

So did string theory really tell us something important here? Well, at a minimum, it seems to have suggested an important idea, but the fact that they were able to deduce a version of their bound from the uncertainty principle alone hints that the bound may not depend on the field theory – black hole duality. Maybe relativity and quantum mechanics alone sufficiently constrain transverse momentum transfer.

Viscosity I

The most fundamental property of a fluid is (doh!) flow. Under application of a force, a fluid deforms continuously. That doesn’t mean that fluids don’t protest a bit, however. Pushing through a fluid usually produces a resistance – you need to do work to make it flow, and a flowing fluid produces forces on objects that it flows past. Of course fluids have mass, and changing the velocity of a mass requires a force, but I’m not talking about that kind of inertial force at the moment, but about the frictional force a fluid moving at constant velocity exerts on anything it flows past. That frictional quality is called viscosity.

We are familiar with very viscous fluids like honey, and much less viscous fluids, like water and air. Imagine stepping into a shallow but swift flowing stream. You feel a force as you insert your foot. That initial force can be explained purely on inertial grounds – you have forced the stream to change direction to flow around you. If the fluid were frictionless, or perfectly inviscid, that force would be perfectly balanced by an opposite force pushing on the other side of your foot as the stream came together behind it. Real streams don’t behave that way, of course, and you will continue to feel the force of the fluid even after your feet are planted and still.

So how does that friction work? Like other frictional forces, viscous friction (in its most familiar form) transfers momentum in directions transverse to the flow. There is more than one way this can happen. Some viscous fluids contain long chain molecules, or molecules that form temporary structures that extent transversely to the flow, or tend to stick to whatever they flow past. This causes the moving fluid to tug along on adjacent layers as it moves. Air isn’t like that, but it still is viscous, because molecules in the flow are moving randomly in directions transverse to the flow. Thus, if we imagine two layers of fluid moving past each other, molecules moving randomly from one layer to the next carry some of their momentum with them, thus transferring some of the momentum of that layer to the next.

The general concept of viscosity relates the forces on a fluid element (as described by the second rank stress tensor) to the deformation of that fluid element (as described by the second rank rate of deformation tensor) and hence is a fourth rank tensor. Lots of familiar fluids, including water and air, are Newtonian, and the viscosity simplifies to a single number.

One of the more fundamental notions for the mechanics of a viscous fluid is the Reynolds number, which is the ratio of the product of a characteristic length L times a characteristic Velocity divided by the kinematic viscosity (itself the ration of viscosity to density). The kinematic viscosity of air is about 2 x 10^(-5) m^2/s. Hence, for a car of length 5 m. moving at 20 m/s, the Reynolds number is 5x20/(2x10^-5 = 5,000,000. The Reynolds number is important mostly because it tells you the ratio of inertial forces governing fluid flow acting to the viscous forces.

One of the things this says is that movement through a fluid looks different depending on your size and speed. The smaller you are, and the slower you go, the more “viscous” the fluid looks, in the sense that the viscous forces become more important. Reynolds numbers for large jet aircraft are hundreds of millions, 15,000 or so for a hummingbird, perhaps only 100 for a fruit fly, and maybe 10 or less for the very smallest flying insects of all, some tiny parasitic wasps. Small fish swim at Re = 1 or so, and tiny bacteria at perhaps Re = 10^(-5). These littlest swimmers live in Aristotelian physics – the moment they stop swimming, they stop – no coasting allowed.

Wednesday, December 15, 2010

Economics: Disease and Cure

Humans appear to have been practicing medicine since before civilization. Early medicine was based on a mixture of experience, folklore, and superstition. This or that herb or practice sometimes helped this or that condition. Surgery gradually improved with knowledge of anatomy, and the discovery of bacteria gave insight into the nature of many kinds of disease. Advance beyond superstition and nostrum required understanding of how the machine worked at the cellular level and below, though.

Economics, I think, seems firmly lodged in the era of superstition and nostrum. Neoclassical economics has developed elaborate mathematical models, but they lack predictive power and depend on approximations that are too unrealistic to support them. The first requisite for a scientific approach to a cure is to identify the disease and its process. It’s at this point that neo-classicism meets its most fundamental challenge – its optimization assumptions essentially deny the possibility of disease. In Chicago, the economy always lives in the best of all possible worlds.

No doubt you have noticed that I slipped in a possibly suspicious assumption here: the analogy of the economy to an organism, and moreover the assumption that certain states of the economy were disease states. Certainly the economy, or any national economy, is as much a super-organism as any ant colony, bee hive or termite colony, and it’s entirely reasonable to speak of health and disease in such aggregations.

Paul Krugman has a diagnosis of our current distress, and a suggested cure. The diagnosis is probably not so controversial:

America’s economy isn’t a stalled car, nor is it an invalid who will soon return to health if he gets a bit more rest. Our problems are longer-term than either metaphor implies.

And bad metaphors make for bad policy. The idea that the economic engine is going to catch or the patient rise from his sickbed any day now encourages policy makers to settle for sloppy, short-term measures when the economy really needs well-designed, sustained support.

The root of our current troubles lies in the debt American families ran up during the Bush-era housing bubble. Twenty years ago, the average American household’s debt was 83 percent of its income; by a decade ago, that had crept up to 92 percent; but by late 2007, debts were 130 percent of income.

All this borrowing took place both because banks had abandoned any notion of sound lending and because everyone assumed that house prices would never fall. And then the bubble burst.

What we’ve been dealing with ever since is a painful process of “deleveraging”: highly indebted Americans not only can’t spend the way they used to, they’re having to pay down the debts they ran up in the bubble years. This would be fine if someone else were taking up the slack. But what’s actually happening is that some people are spending much less while nobody is spending more — and this translates into a depressed economy and high unemployment.

What the government should be doing in this situation is spending more while the private sector is spending less, supporting employment while those debts are paid down. And this government spending needs to be sustained: we’re not talking about a brief burst of aid; we’re talking about spending that lasts long enough for households to get their debts back under control. The original Obama stimulus wasn’t just too small; it was also much too short-lived, with much of the positive effect already gone.

It’s true that we’re making progress on deleveraging. household debt is down to 118 percent of income, and a strong recovery would bring that number down further. But we’re still at least several years from the point at which households will be in good enough shape that the economy no longer needs government support.

The cure is the more controversial part. Krugman wants a long term government stimulus. This would inevitably pile up a lot of government debt. It’s a good tradeoff, says Krugman. The government can borrow cheaply right now, and the stimulus would boost the economy enough to make up a big chunk of the lost revenue. The core of the argument is that everybody loses when a large fraction of the work force is idle – the goods they could produce if they were working would make everybody richer.

Saturday, December 11, 2010

The Compromise: Once More

My current opinion is that Obama made several mistakes, but this compromise was not one of them. If a fight was going to be made, it had to be made last Spring or Summer. The Republicans have little incentive to fold right now, and will have even less after the end of this Congress. If there were no tax deal, and no unemployment extension, the drag on the economy would have been very likely to stifle the economy, and it would have been very hard to pin the blame on the Republicans.

That said, the fight has been postponed. Obama's choices are to let the Republicans drive or to prepare for war now. If he's not in full warpaint by this time next year, we are truly screwed.

One thing he said this week scared the hell out of me - somebody asked him about a "line in the sand" and he said that they will find out that he has a lot of lines in the sand. That sounds like a plan for disaster. What we need is for the President to articulate a clear and sensible strategy, speak it plainly, and rally the nation behind it. Idiotic talk about yet to be fined lines of defense is just another type of premature surrender.

Meditation on a Theme by ...

Tyler Cowen.

Looking around at my overflowing bookshelves, my son once said: "I think you have all these books because you are trying to convince other people that you're smart."

After thinking about for a second or two I replied: "No, I think I'm trying to convince myself that I'm smart."

Maybe it would be closer to say that I overestimate my intellectual ability to assimilate the books that I buy. I'm going to guess that the really smart guys in physics don't buy many physics books. Feynman, Fermi, and Landau reputedly rarely read scientific papers - they just needed to hear the idea and then they worked it out for themselves. Math might be a slightly different matter.

Whoever we are though, we rarely lack the instinct to try to impress each other. It's probably a key instinct in our organization as a social species. Feynman and Gell-Mann made spectacles of themselves in their juvenile versions of dominance displays at Caltech Physics colloquia.

I Throw My Hands Up In The Air Sometimes...

I think it's frustration over not being able to get this idiotically addictive Taio Cruz song out of my head...

Thursday, December 09, 2010

Republican Scientists

There hardly exist any, reports Daniel Sarewitz. Only 6 % of scientists self-identify as Republican. There is probably a bigger percentage of blacks in the Ku Klux Klan than that. He wonders why, but Kevin Drum isn't so puzzled:

Of course scientists are hostile toward Republicans. As far as they're concerned, Republicans are troglodytes who don't believe in evolution, don't believe in climate change, want to ban stem cell research, and don't want to fund the NSF. They'd be crazy not to be hostile toward Republicans.

My guess is that relatively few scientists are ideologues of right or left, and that there would be, will be, more Republican scientists as soon as Republicans stop being no nothing dumb shits ... like than's going to happen anytime soon.

Tuesday, December 07, 2010

Compromise II

Despite the bitter complaints of those like Krugman and me who wanted a fight, tax cuts and deficit cutting have been pushed to the 2012 election. There is a logic to this, but there is also a peril. What expectation can there be that the fight will turn out any better then? The logic: this is a fight that the President could not win, with a much more Republican Congress coming in. The peril: if the economy continues to limp, and the Democrats remain as inept as they have been, the same battle will need to be fought two years hence, on more unfavorable political terrain.

TBD: Obama as fox or rabbit. If we are lucky, Krugman (and I) will have to admit that Obama is smarter than we are. Let's hope so.

Monday, December 06, 2010

Presidential Compromise

I don't like it, but at least he got a small stimulus out of it. Kicking this can down the road does not look like a good idea to me. Europe's can kicking looks even worse.

We cannot go on like this. The crisis in the euro zone is the single largest threat to the fragile global recovery we are now seeing. And this is not just a problem for Europe. It matters to us in Britain, as well as to the United States and Asia.

At last year’s Group of 20 meetings in London, the participating countries agreed to stabilize the international banking system and to stimulate the world economy. Further progress was made in Pittsburgh six months later. There was real political will to do what was necessary.

That momentum has now been lost, and it will not be regained without greater involvement from the major economies. Decisive action, confronting the underlying causes of this crisis, is now imperative.

Don't expect leadership from Obama or Merkel.

Sunday, December 05, 2010

Digital Invariance?

Hypothesis: The combined IQ of a smartphone and its owner is an invariant of the motion.

Saturday, December 04, 2010

(Is It Really a Vitamin?)* D

Wolfgang asked:

I try to increase my intake of vitamin D to reduce cancer risk. The best would be long outdoor exposure to the sun. Unfortunately, this would increase the risk of skin cancer. So why can the human body not synthesize this vitamin (without sunlight)? What kind of intelligent design is this?

So what's special about sunlight, in particular, sunlight in the UV? Energetic photons, that's what. My guess is that it's either hard or very inconvenient to store a big enough chunk of energy to complete some crucial part of the synthesis - and sunlight is a widely available resource.

Wikipedia says:

The photosynthesis of vitamin D evolved over 750 million years ago; the phytoplankton coccolithophor Emeliani huxleii is an early example. Vitamin D played a critical role in the maintenance of a calcified skeleton in vertebrates as they left their calcium-rich ocean environment for land over 350 million years ago. "Because vitamin D can only be synthesized via a photochemical process, early vertebrates that ventured onto land either had to ingest foods that contained vitamin D or had to be exposed to sunlight to photosynthesize vitamin D in their skin to satisfy their body’s vitamin D requirement."

It seems that plants and fungi synthesize a different form of Vitamin D which may be used as a sort of sunscreen! In any case, nature seems to have had plenty of time to think about devising alternative strategies for its manufacture, but doesn't seem to have developed them. On the other hand:

The naked mole rat appears to be naturally cholecalciferol deficient as serum 25-OH vitamin D levels are undetectable.[14] Interestingly, the naked mole rat is resistant to aging, maintains healthy vascular function[15] and is the longest lived of all rodents.[16]

*Because we can synthesize it.

Thursday, December 02, 2010

Deep Down Quantum Mechanics

The Born probability law, says Brad DeLong, is the Deepest Mystery of Creation. He follows that up with:

“Let me just say that Eliezer Yudkowsky is a bad man for writing almost-comprehensible weblog posts about them...”

I’m always interested in deep mysteries, and even though I’m not quite ready to endorse Brad’s assessment, it is indeed pretty mysterious. It says that the probability of measuring a certain value for a state variable of a quantum system is proportional to the squared modulus of a complex valued vector. To be slightly less abstract, assume that the variable in question is the location of a particle, in which case the complex valued vector becomes just a complex function, the so-called wave function of the particle.

In classical mechanics we could specify the same position, deterministically, by giving the position and momentum of the particle. If you know only probabilistic information about the classical system, then the probability of some measured value can be computed without any hocus pocus about complex values and squared amplitudes. So what’s going on here?

Let’s move on to the cited Eliezer:

“One serious mystery of decoherence is where the Born probabilities come from, or even what they are probabilities of. What does the integral over the squared modulus of the amplitude density have to do with anything?”

I won’t go into his discussion, because I found it pretty opaque, even though I’m pretty sure I understood exactly what he was talking about, but YMMV. However, his post led in two entirely unexpected directions.

First, clicking on EY’s name led to discussion of Harry Potter and the Methods of Rationality, an elaborate fanfic of which I have become a recent fan. If I’m not mistaken, EY is in fact the author of the same.

A second link led to Robin Hanson, one of those Ayn Randian GWU economists who drive me crazy, and whom, it seems, has a earlier life as a speculator on interpretations of quantum mechanics, notably including the Born rule. I glanced over his papers, but lazy bum that I am decided to check if anybody of note had ever referenced them.

SPIRES came up empty, but Google Scholar found some stuff, including this paper by Brumer and Gong: quant-ph/0604178. They didn’t have much to say about Hanson, but they do have this very interesting claim:

“Considerable effort has been devoted to deriving the Born rule (e.g. that $|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\it classical} mechanics as well.”

And later:

“To demonstrate that the Born rule exists in both quantum and classical mechanics we: (1) recall that both quantum and classical mechanics can be formulated in the Hilbert space of density operators [13, 14, 15, 16, 17, 18], that the quantum and classical systems are represented by vectors and c, respectively, in that Hilbert space, and that and c can be expanded in eigenstates of a set of commuting quantum and classical superoperators, respectively; and show (2) that the quantum mechanical Born rule can be expressed in terms of the expansion coefficient of a given density associated with eigendistributions of a set of superoperators in the Hilbert space of density matrix; and (3) that the classical interpretation of the phase space representation of c as a probability density allows the extraction of Born’s rule in classical mechanics, and gives exactly the same 2 structure as the quantum mechanical Born rule. These results suggest that the quantum mechanical Born rule not only applies to cases of large quantum numbers, but also has a well-defined purely classical limit. Hence, independent of other subtle elements of the quantum theory, the inherent consistency with the classical Born rule for the macroscopic world imposes an important condition on any eigenvalue-eigenfunction based probability rule in quantum mechanics.”

Exobiology OMG: NASA Discovers Little Green Men!

OK, strictly speaking, what they discovered was that some men could turn kind of green if fed a suitable poisonous diet. Or even more strictly speaking, that some bacteria could incorporate some Arsenic instead of Phosphorus and still survive, and, apparently, reproduce. Interesting, but, at least in the press release, it’s not clear that arsenic has taken over the crucial physiological functions of phosphorus either in the DNA or the ATP cycle.

Most disappointing announcement from the government since the last time Obama spoke.

N-Dimensional Chess

Conventional Democratic wisdom, at least until recently, was that Obama was playing 3-dimensional chess, and we peasants just couldn't appreciate the subtlety of his moves. Lately, though, it's starting to look like the man is playing in a couple fewer of dimensions and can't quite figure out why his pawn can't move any more.

Is there any area in which he hasn't disappointed? Even his triumphs, health care and the stimulus, were born crippled and badly advertised.


It's not a secret that my disgust with Obama has been growing, but this crap with Peter Orzag, a former cabinet member deeply involved with the bank bailout, negotiating for a position with Citibank pushed me over the edge. If this isn't a crime, it sure as hell ought to be.

Wednesday, December 01, 2010

Advising the White House

Brad DeLong, on the wise words of a former Chairman of the White House's Council of Economic Advisors:

I think that one of Christie Romer's predecessors as CEA Chair, Stanford economist and Republican Mike Boskin, says it best. Being Chair of the CEA and advising all the political appointees in the White House is, he says, a lot like teaching Econ 1 at Stanford. Only at Stanford your students do their reading, pay attention, and ask deeper and more thoughtful questions.

Greetings From the Transgalactic Ambassador

Only speculation, of course, but NASA claims to have some exo-biology announcement planned for tommorow:

At least one guy seems to be pooh-poohing the sensational:

But Alexis Madrigal, science editor at The Atlantic, disagrees. "I'm sad to quell some of the @kottke-induced excitement about possible extraterrestrial life. I've seen the Science paper. It's not that." he said.

News via Wolfgang.