Wednesday, December 22, 2010

Misconceptions in Math Education

This is worth a read.

The great misconception about mathematics -- and it stifles and thwarts more students than any other single thing -- is the notion that mathematics is about formulas and cranking out computations. It is the unconsciously held delusion that mathematics is a set of rules and formulas that have been worked out by God knows who for God knows why, and the student's duty is to memorize all this stuff. Such students seem to feel that sometime in the future their boss will walk into the office and demand "Quick, what's the quadratic formula?" Or, "Hurry, I need to know the derivative of 3x^2 - 6x +1." There are no such employers.

Mathematics is not about answers, it's about processes.

Apologies for My Absence

My apologies for over a month of silence from Athwart History: Mr. History has moved across the country and started a new job. So things are in some turmoil right now. But with any luck we will be back to regular posting soon!

Wednesday, November 17, 2010

A Modest Proposal

They say that if you tax something, you get less of it. So maybe that's the real benefit of a death tax: less death!

Tuesday, November 16, 2010

Why Have Kids?

The radio today reminded me about happiness studies that consistently show that having kids reduces your happiness. This raises an important question: why bother having kids? It's expensive, for starters. It's inconvenient. If it also, to top it off, makes you less happy, then why do it at all?

I think the answer most parents - myself included - would give is that having kids fulfills a need that can't be met by any other means. There's probably some neurological trigger at work here; there's no need to mysticize it. But that makes it no less real. And it raises another important question: is life really about maximizing happiness?

Most religious people would easily answer no to this question. So let's address it to the non-religious, again like myself. I do not believe that maximizing happiness is the goal of life (as evidence of my belief I offer the fact that I consciously chose to have children). The goal seems to be to have a posterity, to leave something behind after we die. For all of us do at some point come to a realization that we are going to die. That fact is difficult to grasp, but the tragedy is eased by the knowledge that something will succeed us, that we are a part of some larger tapestry. Otherwise, we are simply here for a brief few moments of time and then are gone forever.

There are, of course, other ways to join the tapestry of the world than having children: one can become famous, one can make great friends who will carry our memories, etc. But children are the most reliable route, and the one most accessible to the average person. After all, if everyone were famous, no one would be; by definition this route is accessible only to a very few (particularly when we restrict our view to those who are famous enough to be truly remembered a generation after their deaths; this is a very exclusive club indeed).

Consider two people: One, the pure individual, not necessarily nihilistic, but one focused purely on happiness. He is not necessarily a bad person, or selfish, but by definition is self-centered. Two, the family member, one who has a tightly-knit family, with all its trials and tribulations. Picture in your mind's eye both of their lives at the age of, say, 40 years old. The individual is traveling in Europe with his girlfriend, sampling the best that life has to offer. The family man is rushing home after work because his wife has an outing planned that evening and it is his night to prepare dinner for the kids and put them to bed. Which is happier? We can't see into their heads, of course, but it's easy to imagine that the individual is.

Let us cast our view forward twenty years. Now both men are near retirement. The individual has mastered his golf game and has toured all the major courses. He regales his friends with stories of his travels and adventures. He is the life of every party. The family man's children have grown up and left the house; he has paid a heavy price to put them through college, foregoing many of life's pleasures for this. His kids have developed in different ways: perhaps one is a real success, with many friends and a career. Perhaps another is not on such a positive track. But they remain family nonetheless. Again, the individual appears to have had the happier life.

But now let us move another twenty years into the future. Both men are on their deathbeds. The individual has a few friends who visit him, but most of them are preoccupied with their own families, and many are uncomfortable at the sight of the old man so broken down. The family man, though, has his family: his kids have had kids of their own, so there are grandkids. They come to visit out of love and affection. The old man dies knowing that his life had a purpose, however small in the grand scheme of things. Does the individual?

That is not so clear. He might. It's not my intention to disparage or denigrate this lifestyle choice. But odds are good that this man will realize at some point that his life will end entirely unnoticed. The family man's position is not so much better: his life will end mostly unnoticed: his family is but a tiny drop in an ocean both of time and of space. But the difference between nothing and something can be a vast chasm.

So is the goal of life, then, merely its extension, even if only in memories and deeds? Not quite. The truly fulfilled man does not just seek to be remembered, but to have had an impact. We don't just wants our kids to remember us, but for us to have set them on a certain path, to have prepared them for life and, ultimately, for their own struggle with its meaning. That, perhaps, is the greatest blessing of grandchildren: evidence that the torch has been passed one more generation, that the lessons we taught and the pleasures we forewent were not in vain

Thursday, November 11, 2010

U.S.: Manufacturing Powerhouse

Kevin Williamson has a great article on why we shouldn't scapegoat a low renminbi for our economics troubles. Embedded in his article is a great point, often overlooked, about American manufacturing. You hear people from time to time saying things like: We don't build things in this country any more. Poppycock. Here's Williamson:

Despite all the new competition, the United States remains a manufacturing powerhouse — in fact, the total value of manufacturing output in the United States today is far, far higher than it was in the 1950s. Measured by revenue, profit, or return on investment, U.S. manufacturing is unparalleled, and our factories' output is more than twice China’s. But it is true that many manufacturing jobs have been "lost." They were lost not because U.S. manufacturing can't compete with that of feckless Third World rivals, but because U.S. manufacturing is, to use the technical economics term, awesome. The real productivity of U.S. businesses overall grew at an average rate of 1.5 percent a year from 1973 to 1995, which is a really robust number. But the productivity of U.S. manufacturing businesses grew by 2.5 percent in those same years, which is enormous. As Martin Wolf puts it in Why Globalization Works, that growth in productivity alone would have reduced significantly the number of manufacturing jobs in the United States. Add in the fact that people in affluent societies spend relatively less of their disposable income on manufactured goods and relatively more on services, and that reduction becomes even more dramatic. And so it was. There is an obvious parallel: In very poor societies, large numbers of people are employed in agriculture, and people spend most of their money on food. As they get richer, relatively few work in agriculture, and they spend proportionally little on food. Manufacturing, as Wolf sees it, is the new agriculture. In historical terms, it was not that long ago that 75 percent of the U.S. work force was engaged in farming. Now it's less than 1 percent. But who laments the loss of good farming jobs? (Mostly people who have never worked on a farm, that's who.)

I often ask people to name the country with the largest manufacturing output. China? Japan? Nope. It's the U.S.A. It's worthwhile remembering this.

Monday, November 8, 2010

In Defense of Keith Olbermann

It's hard to avoid a whiff of schadenfreude when hearing about Keith Olbermann's suspension by MSNBC in the wake of the revelation that he donated to three Democratic candidates in contravention of MSNBC policies. But that would be too easy.

What's so wrong about political donations from opinion journalists, really? Is anyone surprised to find that Olbermann favors Democrats? Does anyone think: Hey, maybe this means Olbermann might be less than fair when talking about politics. It's one thing when supposedly objective journalists are caught donating. (Although is any journalist really objective? Question for another day.) But Olbermann, Hannity, Maddow, Huckabee: they are not objective. They are not hired to be objective, they are hired to give opinions.

Opinion journalists, pretty much by definition, operate in the open. They have to talk in order to do their work. They give their opinions as part of the job. So their opinions are already a matter of public record. There would seem to be nothing whatsoever lost by allowing them to donate or otherwise exercise their freedom of political speech.

Unless, of course, their employers want to maintain the fig leaf that they are actually objective journalists. But surely MSNBC doesn't think anyone believes that about Keith Olbermann. Right? Free Olbermann!

Wednesday, November 3, 2010

Welcome to Gridlock

My predictions were fairly accurate. I said +7 in the Senate and +61 in the House. So far it's +5 in the Senate, with Colorado, Washington and Alaska left. Alaska will be a Republican or Independent who caucuses with Republicans. If the other two split evenly, there's your +7. In the House, RealClearPolitics has it +61 with 423 races called. However, here's the bad news for the Democrats: in the remaining 12 races, every one is currently held by a Democrat. So if they split evenly, expect a final pickup of 67 seats in the House. Wow.

But the exact numbers don't really matter at this point. We know that the House will be GOP-controlled, the Senate Democrat-controlled, and of course the White House run by a Democrat. So unless the President tacks sharply to the middle, we can expect gridlock city. The GOP should try to pass useful bills, but will probably serve more of a pressure-generating role: they will need to put some ideas on the table that have not had an airing over the past two years. Ideally, some of these ideas might get passed. But if not, the second-best thing is to win the battle of ideas so that after 2012 conservatism can make some legislative progress.

Tuesday, November 2, 2010

Reid Wins

I was hoping to oust Reid, but this could have a silver lining. Reid is still very unpopular nationwide. Angle would've been problematic at best. And it really doesn't matter much whether the GOP has 47 Senators or 48 or even 49. Frankly, I think if the Democrats were smart, they'd replace Reid after this debacle. Remember after the 2008 elections when people were expecting the GOP to lose seats in 2010 because of all the seats they'd have to defend? We're a long way from there, and Reid is being blamed.


And it's Toomey in Pennsylvania. Fantastic news.

Also looks like Kirk wins in Illinois!

Fiorina couldn't pull it off in California. Too bad, but not unexpected.

6 Left in the Senate

It's 49-45 in the Senate, with 6 left uncalled: Colorado, Pennsylvania, Nevada, Washington, Illinois and California. Republicans would have to win them all to have a clear 51-seat majority: don't count on that. Currently the GOP leads in PA (Toomey's up 52-48 now!), WA and IL (go Kirk!), but losing everywhere else. If that holds, it'll just match my prediction: a 7-seat pickup.

Early Returns Are In...

Toomey and Sestak separated by 2,000 votes. That one could go late into the night.

CNN just called it for Ron Johnson over Russ Feingold. Yea!!! Earlier today I was cleaning up some old email and realized that I was on a Feingold email list back into 2009. Reading over some of the emails I didn't even see Johnson's name mentioned six or eight months ago. Came out of nowhere and knocked off a Democratic stalwart. That one's got to sting.

Manchin winning in WV - too bad, but we saw that coming. He's been leading consistently in polls the last couple of weeks.

Buck losing in Colorado by 5%. Not good.

Exit polls just coming in from California and Washington - Fiorina down 53-43 and Rossi down 52-46.

And just saw Kirk up 48-47 in Illinois!

Early Election-Day Observations

Concerning the election today, a few early observations:

1. My polling location was nearly empty. I walked in, gave my name, got my card, and voted. No lines whatsoever. Here in blue-state New Jersey, where the biggest race is Little-Pallone, that's no big surprise. But perhaps is reason to hope for Little, a major underdog whose only hope is that her voters are much more enthusiastic than Pallone's.

2. Pallone has been running attack ads over the past week. This must indicate that he's at least a bit worried. If he was running a 30-point lead, he could safely run soft-focus ads talking about how great he is, and not worry about the tiny gnat buzzing around. But he's been forced to go after Little by name. It's probably not fair to say that he's running scared, but he's hearing footsteps.

3. WNYC (my local NPR affiliate) is talking about Christine O'Donnell and her gaffes this election season. A less relevant discussion it would be hard to imagine. Look, Democrats: she's going to lose, and deservedly so. How about talking about some close races?

The Election, Finally

I am going off today to vote for Anna Little in her insurgent campaign against Congressman Frank Pallone. She's an unabashed Tea Partier - here in New Jersey! - and seems like a decent enough sort. I'm no knee-jerk Tea Party supporter. I generally support their ideas, but they've put forth a few really poor candidates. Still, that's partially just because they're inexperienced in the world of politics, and that's not a bad thing. In fact, I'd say it's a good thing, net-net.

Little can't be any worse than Pallone, who - unlike many of his Democrat colleagues - has been campaigning fully in support of Obamacare, the Stimulus, and all the other boondoggles of the 111th Congress. The polling is unclear, but Little might just have a shot. In many ways, while this individual race isn't all that important, it can be a bellwether for the hoped-for Republican surge. For if Little wins, or even is within a point or two, then it's going to be a huge night.

More blogging tonight as polls come in. For now, this is my emblem:

Monday, November 1, 2010

Prediction Time

In the Senate, I'm predicting a 7-seat gain for the GOP. Ignoring the seats with 10-point leads one way or the other, there are 8 seats in play, with 2 locked up for the GOP. Those 8 seats are: California (DEM+3), Colorado (GOP+4), Illinois (GOP+2), Nevada (GOP+4), Pennsylvania (GOP+5), Washington (GOP+1), West Virginia (DEM+3), and Wisconsin (GOP+7), where I'm giving the latest poll results in each case. Many of these polls are within the margin of error, but we can still calculate probabilities for each. Based on these numbers, we can find a joint probability distribution for various levels of GOP pickup.

GOP GainProbability

The median of the distribution is at the high end of a 7-seat GOP pickup. It's certainly pretty likely that we'll have an 8-seat pickup, but playing the odds I'll predict +7.

In the House, it's more complicated since there are a lot more races. Also, polls are sketchier. But let's use the latest Real Clear Politics map to make some estimates. If we plug in some reasonable probabilities corresponding to "likely GOP", "leaning GOP" and "tossup", we get this distribution for GOP seats (here I'm ignoring insignificant tails):

GOP SeatsGOP LeadProbability
Under 2230.07%
Over 2560.08%

The median of the distribution is for the GOP to have 240 seats, representing a 61-seat GOP pickup. There is a 96% chance the GOP will pick up between 50 and 76 seats, and a 90% chance they pick up between 52 and 69 seats. So I think we can count on the GOP having at least a 26-seat majority and it's not impossible for them to attain a 60-seat majority.

Of course, this will do them little good without the Senate or the White House. Those will have to wait until 2012.

Menendez Wants to Allocate Your Collective Wealth

Bob Menendez (D-Cuba) makes the following assertion about tax cuts on ABC's This Week:

You can't talk about spending and being responsible about spending and then spend $4 trillion that you don't have of our collective wealth to the individuals who have the greatest wealth in the country.

I see. According to Sen. Menendez, your money, my money, and your neighbor's money is all collective wealth to be allocated to the poor, the middle-class, or the wealthy as Sen. Menendez and Barack Obama decide. This is the face of the Democratic Party, folks. We've got to eject these clowns posthaste.

Here's the video. The interesting part starts around 9:15:

Monday, October 25, 2010

An Open Letter to NPR

I just received an e-mail from my local NPR affiliate, WNYC, to "double my pledge". This is the e-mail I sent in response:

To Whom It May Concern:

I will not be "doubling my pledge", or indeed renewing my pledge next year when the anniversary rolls around. The reason for my change of heart is the firing of Juan Williams. This was an inexplicable, execrable move that I simply cannot support. Please make it clear to your own management and on up the chain that there is at least a portion of your listenership that does not believe that what Williams had to say was even close to a firing offense, and that firing him as a result illustrates NPR's disrespect and intolerance for opposing viewpoints.


- James

UPDATE: To their credit, WNYC responded. Some boilerplate aside, here's the important part:

As the local New York broadcaster of NPR programming, we are always interested to hear our listeners' comments about their programming content and their organization. However, it is important to understand that our organization does not have influence in the content of NPR programming, with their staff, or in their personnel decisions. We pay NPR for the programming and news that we broadcast and, as such, are separate independent organizations.

It's not directly WNYC's fault that NPR fired Juan Williams. But they're not exactly independent, either. WNYC is part of the NPR family. I don't give money to NPR; I give to WNYC. And it seems perfectly reasonable to cut off funding to WNYC in this case. I want them upset with NPR.

The logic seems to me stronger than when people boycott a company for advertising on a show they find objectionable. The company isn't directly responsible for the show's content, but they know the basic message and can sever the relationship if it grows too burdensome. I'm putting pressure (a tiny amount in my case, but hopefully my case is but one among thousands) on WNYC so that they will pressure NPR.

Friday, October 22, 2010

Solving Linear Equations Just Got Much Faster

In computer science, we measure the efficiency of an algorithm in a couple of ways, but one of the most important is called "asymptotic complexity", usually written in something called big-O notation. This notation captures an algorithm's scalability as the problem size gets larger. For example, an algorithm with O(n) performance takes about twice as long to run if the problem size doubles. An algorithm with O(n^2) performance would take four times as long.

You can get a feel for this without computers. Most of us have sorted books alphabetically before, by title or by author. If you have just a few books, say ten or fewer, you can usually eyeball it and get them sorted without using any special algorithm. What you are really doing here (I think) is a sort of mental version of what we CS types call a "selection sort" - you are finding the alphabetically first book, placing it first, then finding the next one and placing it, and so on. With a small set of books, that works fine. But suppose you have 1,000 books to sort. Now the problem is much harder: you can't store the 1,000 books in your memory, so the only practical way to carry out that algorithm is to pick up the first book at hand and then start checking all other books. As you find one alphabetically earlier, put down the book you're holding and pick up the new one, then continue until you've looked at all the books. The book you're holding is the alphabetically first one, so place it on the shelf. Great! Now repeat another 999 times.

This takes a while. In big-O terms, it's an O(n^2) algorithm, which means that running it for 1,000 books takes about 100^2 = 10,000 times longer than running it for 10 books. Not very practical!

You probably intuitively understand this, because if you were really given the job of sorting 1,000 books, you wouldn't do it this way. An alternate (and much faster) way is to start by sorting the books by first letter: you put all the books with authors starting with A in a pile, all the books with authors starting with B in another pile, and so on. Eventually you have 26 piles, some bigger and some smaller. The average pile size will be 1,000/26, or about 40 books. If you just ran selection sort on the piles, each would take about 4^2 = 16 times longer than sorting 10 books, and you'd have to do it 26 times, so you end up doing 416 times more work than sorting 10 books. But that's a 24x improvement over just running selection sort. (To the detail-oriented: yes, it's true that since the piles are different sizes, you won't actually do quite this well in practice. But you can easily make the large piles small by running our "binning" algorithm on the second letter for those large piles: take the S pile and make new piles for authors starting Sa, Sb, Sc, and so on.) (Also: but what about the time needed to split the the 1,000 books into bins in the first place? The good news here is that deciding which pile to put the books into is easy: just look at the book. So you just look at each book once. That takes some time, but it's not significant compared to the rest of the algorithm, which involves comparing pairs of books. In big-O terms, this is an O(n) contribution to the overall algorithm, so it doesn't change the overall complexity.)

So, now you understand how complexity works. We care a lot about the complexity of algorithms that we use all the time. For example, above I talked about sorting, because we sort all the time. You can hardly take two steps in your average code base without tripping over a sort. It turns out that sorting (assuming nothing about the data being sorted) takes O(nlogn) time, meaning that it scales almost linearly: that logn term rises slowly, but it's there. O(nlogn) is slower than O(n), but it's much, much faster than O(n^2). Suppose an algorithm takes 1 second with 1,000 data points. Then an O(n) algorithm would take 1,000 seconds with 1 million data points. An O(nlogn) algorithm would take 3,000 seconds (we'll use base-10 logs here). But an O(n^2) algorithm would take 1 million seconds.

Another problem that comes up a lot in CS (not as much as sorting, but a lot) is solving systems of linear equations. Here the measure of problem size is "number of variables", and we'd like to solve systems with lots of variables: millions, even billions of them. The naive, basic algorithm for solving them is something called Gaussian elimination, and it's an O(n^3) algorithm - that's cubed. As you can imagine, this performs pretty badly with large numbers of variables. With a million variables, an O(n^3) algorithm will run a billion times slower than it would with 1,000 variables. So if you could solve a system of a thousand variables in a microsecond, it would take 1,000 seconds - almost 17 minutes - to solve one with a million variables. There are some algorithms that solve linear systems slightly faster than this, but improvements have been slow.

So along comes these Carnegie Mellon researchers. They've figured out a clever algorithm that reduces the complexity of solving (certain kinds of) systems of linear equations to O(n(logn)^2) time. It's hard to express how huge an advance this is. Take our example above: where solving a system of 1,000 variables takes a microsecond and solving a system of a million variables takes 17 minutes. With the new algorithm, you could solve the larger problem in 9,000 microseconds, which is still just 9 milliseconds. Or you could solve an even larger problem - a billion variables - in just 36 seconds. This is an extraordinary achievement.

Read the whole story here.

UPDATE: I meant to mention this in the original post, but forgot. It's worth worrying a bit about the constant. The problem with "asymptotic complexity" is that it only gives an ordering of runtimes with very large problem sizes. For small problem sizes, the constant, or even constant-time or other lower-order terms, can dominate the actual run-time.

The constant shows up as follows: suppose that algorithm A has runtime of approximately n seconds for problem size n, and that algorithm B has runtime of 10^-10 n^2 for problem size n. Then algorithm A has O(n) complexity and B has O(n^2) complexity. But for problem size n=1,000, A takes 1000 seconds while B takes only 10^-4 seconds. For problem size n=1,000,000, A takes 1,000,000 seconds while B takes 100 seconds. As you can see, B is much faster over a very wide range of problem sizes. So even though B is "slower" in the asymptotic sense, it's probably faster in most real cases.

Lower-order terms can matter, too: suppose algorithm A has runtime of 10^-6 n + 2 seconds, while algorithm B has runtime of 10^-6 n^2 seconds. Both A and B have the same constant. But for problem size n = 1,000, A takes about 2 seconds while B takes 1 second: the added 2 seconds for A (presumably for setup and precomputation, or something) dominates the runtime. For much larger problems, of course, A may still be faster: its asymptotic complexity is O(n) compared to B's O(n^2).

So this new algorithm has great asymptotic complexity, but it's worth waiting until we see the constants, lower-order complexities, and other things (like how well the algorithm fits into cache, how well it can be parallelized, etc.) before considering it a big win.

Thursday, October 21, 2010

Another Entry in the Black Book of Communism

This is truly awful.

A pregnant woman in south China was detained, beaten and forced to have an abortion just a month before her due date because the baby would have violated the country's one-child limit, her husband said Thursday.

Forced abortions are bad enough. But a forced abortion of an eight-month fetus is indistinguishable from murder (even if you don't think the abortion of, say, a one-month fetus is murder). A fetus at that stage is perfectly viable outside the womb. The Chinese cold-bloodedly killed a baby in their mad pursuit of social policy.

NPR Fires Juan Williams

NPR has fired Juan Williams for his remarks about Muslims on The O'Reilly Factor.

Obviously, NPR is within its rights to do so, being a private organization. (Well, sort of. Doesn't NPR receive government funding? The government certainly twists the arms of other organizations that act in ways it doesn't like if they receive funding.) But there is a difference between having a right to do something and something being the right thing to do. You might imagine, from the fact of his termination, that Williams must have said some truly awful things about Muslims. Here's what he said:

But when I get on the plane, I got to tell you, if I see people who are in Muslim garb and I think, you know, they are identifying themselves first and foremost as Muslims, I get worried. I get nervous.

Many Americans share these views. Any why wouldn't they? Muslims are responsible for most plane hijackings around the world, and four particular ones nine years ago that you might remember. Williams isn't making a policy proposal, for crying out loud. He's airing his personal fears. Surely NPR wouldn't fire someone for giving a personal, mainstream opinion. Maybe it was this (which O'Reilly said, but Williams agreed with):

The cold truth is that in the world today jihad, aided and abetted by some Muslim nations, is the biggest threat on the planet.

That's controversial, surely. You could easily disagree with it. But is it a firing offense?

It's a shame that NPR felt the need to take such an extraordinary step about such ordinary statements.


Here's video of Juan Williams' side of things:

If Williams said something bigoted here, we should remember this the next time a person of color admits to experiencing a frisson of fear upon seeing a white policeman. Apparently, such an admission can get you fired from NPR.

The Closing of the American Mind (Jazz Version)

Whenever I listen to my Ella Fitzgerald CD, I want to comment on this. Here are the opening lyrics of the Cole Porter song Just One of Those Things:

As Dorothy Parker once said to her boy friend,
"Fare thee well,"
As Columbus announced when he knew he was bounced,
"It was swell, Isabelle, swell,"
As Abélard said to Héloïse,
"Don't forget to drop a line to me, please,"
As Juliet cried in her Romeo's ear,
"Romeo, why not face the fact, my dear?"

This was written in 1935, the depths of the Depression. At that time, these references were considered intelligible enough to use in popular culture. Can you imagine such a thing today?

Tuesday, October 19, 2010

On Nuclear Accidents

Just read an interesting article by Ed Grabianowski on io9 about nuclear accidents and near-disasters. Couple of quotes:

We spent the Cold War in perpetual fear that the U.S. and U.S.S.R. would start an intentional nuclear conflict. The truth is, we came far closer to blowing ourselves up with nuclear weapons than we ever came to WWIII.... The Russians either lost a nuclear sub, lost a sub with nuclear weapons on board, had a nuclear sub's reactor melt down, or all three roughly every other week.... The sad lesson is that we have less to fear from naked aggression than we do from incompetence and bad engineering.

I don't mean to diminish the danger of nuclear accidents, and certainly there was a learning curve involved here - a very dangerous learning curve (it's notable that all the incidents listed occurred between 1950 and 1979, and all the ones in which radiation was released occurred before 1966). But Grabianowski betrays his own politics with some of these claims. How can he know we came "closer to blowing ourselves up than to WWIII"? There were several incidents that came close to sparking WWIII, too - which was "closer"?

It's tempting to think that, as close as some of these engineering mishaps were, they actually weren't as close as the author thinks. Grabianowski himself points out that the Russians had accidents all the time that never had the dire consequences he imagines (other than Chernobyl). That strikes me as evidence that nuclear engineering is not as prone to actual disaster scenarios as the author thinks.

Grabianowski's closing quote, that we have less to fear from aggression than from incompetence, is utter nonsense. Even restricting our historical view just to nuclear weaponry, it's hard to ignore the fact that far more people have been killed by atomic weapons than by atomic accidents. In fact, it's possible that more people were killed on 9/11 than by Chernobyl, the worst nuclear accident in history. (Wikipedia says: "It is estimated that there will ultimately be a total of 4,000 deaths attributable to the accident, due to increased cancer risk." But these estimates are notoriously unreliable, and impossible to prove. In any case, the numbers are comparable.) The twentieth century witnessed hundreds of millions die as a result of naked aggression, and two or three orders of magnitude less due to engineering mishaps.

The numerical comparison demonstrates the absurdity of the claim. But the philosophy behind it is also wrongheaded. Does Grabianowski believe that our military is more dangerous in peacetime than it is valuable in wartime? Having a nuclear-armed military runs the risk of accident. Building and operating nuclear power plants runs similar risks. But in both cases, there is significant return on this investment. In the field of nuclear technology, it is much easier to imagine disaster scenarios than to actually find them.

We should be cautious, but not allow our caution to stop us moving at all. Doing nothing, or worse, doing the wrong things, also runs risks. Suppose the Global Warming people are right. Then we should be building nuclear plants at breakneck speed. The risk of accident should be overwhelmed by the risk (according to the most dire claims of the Warmingists) of warming. But in many cases those very environmentalists block nuclear power, preferring pie-in-the-sky plans involving solar or wind power. The result is what no one wants: ever greater dependency on fossil fuels.

Grabianowski probably was not thinking all of these things when he wrote the article. I have no reason to believe that he is a nuclear-power-protesting environmentalist. Nonetheless, his article feeds a nucleophobia that we as a society must learn to get over.

Friday, October 15, 2010

That Living Constitution

I had a discussion earlier in the week with a liberal (he would prefer me to say "progressive") friend of mine who was astonished at my declaration that the left was responsible for judicial activism in the Supreme Court. Surely, he said, the left would merely say the same thing about the right. This was a phenomenon that was universal, and that both sides practiced in an effort to subvert the other, nothing but further evidence that the Court has become politicized.

He's right: the left would say the same thing. But they'd be wrong. Judicial activism - by which I mean judges writing decisions using their own preferences rather than their interpretation of the Constitution - stems from Progressive impatience with Constitutional restraint. We can go over the whole history of this another time, but a Corner post by John Derbyshire really gets to the root of it.

A reader writes to Derb:

let me relate the story to you of Justice Ruth Bader Ginsburg’s visit to my alma mater. (For the record, I was not in attendance at her lecture, but I heard the same story from multiple trusted colleagues). A student asked Justice Ginsburg about the use of the "intermediate scrutiny" test for equal protection review. Intermediate scrutiny is the standard by which courts review challenges to government classifications based on gender. (The court uses "rational basis" review for what it calls "non-suspect" classifications, such as wealth, which is a relatively easy test for the government to pass, and a "strict scrutiny" test for "suspect classifications," such as race, which is a much harder standard for the government to clear). The basis of the question was Justice Ginsburg’s majority opinion in US v. Virginia (the case that forced Virginia Military Institute to become a co-ed institution), in which she applied a version of intermediate scrutiny that had never been applied before and which seemed to many observers much more like a strict scrutiny review (in other words, she held the government to a higher standard than precedent seemed to dictate). The student wanted to know how Justice Ginsburg arrived at the use of this "revised" standard.

Her answer astonishes me to this day. She told those assembled that the justices do not use the analytical framework to reach the results in a given case, but that they decide the result first and then fit the opinion into the existing framework.

(Emphasis mine.)

This is a stunning admission. I do not believe you would hear anything like it from any originalist on the Court.

Wednesday, October 13, 2010

Practical Passwords

According to this article on Web password standards, I am one of the "stupid people" who maintain unsafe password practices. Here are some of the findings and my responses:

"4 in 10 respondents shared passwords with at least one person in the past year."
I haven't done this one, but I've encouraged my wife to give me a couple of her passwords to help debug some problems she's having. I don't think she's making a huge mistake here. How many of those 4 in 10 shared passwords with a trusted loved one?
"Nearly as many people use the same password to log into multiple Web sites, which could expose their information on each of the sites if one of them becomes compromised."
I use the same password all the time (I have about five that I generally use, across dozens of sites requiring a password). Sure, it's true that this means if one site is compromised then so might others. But the person getting that password would have to know which sites, and my usernames on those sites. That's not necessarily all that easy.
"Almost half of all users never use special characters (e.g. ! ? & #) in their passwords, a simple technique that makes it more difficult for criminals to guess passwords."
Not necessarily. Most use of special characters is in "133t" spelling: instead of your password being "password", it'll be "p455w0rd" or something like that. I've written dictionary attack software. Adding 133t spelling adds some words to check, but it's not that big a deal. It's true that a password like "5*(AJS*&1" is hard to crack, but then so is "jka82pma8". Furthermore, most sites lock you out after a small number of wrong guesses, so dictionary attacks aren't really very effective.
"30 percent [of young people] logged into a site requiring a password over public WiFi (vs. 21 percent overall)."
Again, this is no big deal... if you do it over SSL encryption. True, sending a password on an unencrypted public WiFi channel is risky. Don't do that. But your bank's Web site is SSL-encrypted, so don't worry about that.
"And 30 percent remember their passwords by writing them down and hiding them somewhere like a desk drawer."
No less a security guru than Bruce Schneier has endorsed this practice, and I completely agree. Hackers can't hack your desk, or your wallet. You're far better off having hard passwords written down in a fairly secure location than really bad passwords (e.g. "123456") that you can remember.

There are, of course, good password practices and bad. But I'm not convinced that surveys like this really reveal that people are as stupid as they think (they may be, but not for the reasons put forth in the survey).

Having a different password for every site, as they recommend, is a wonderful idea. It's also totally impractical. They're also correct that having a single password you use for every site is also a bad idea. The happy medium is to have a few passwords. Use one you can easily remember for all the stuff you don't care much about: Facebook, Slashdot, etc. Use a somewhat harder one for online stores (and don't trust any online store that makes it easy to retrieve your credit card number). And use your best one - maybe here it makes sense to go the "one per site" route - for online banking and brokerage accounts.

Monday, October 11, 2010

Who is Tom Donilon?

He's the new National Security Advisor, replacing Marine General James Jones. And his appointment demonstrates President Obama's unseriousness about national security. Donilon is a professional lobbyist, not a national security expert (although he has been an Obama advisor on national security since the transition in 2008-09, and worked in Pres. Clinton's state department). Should we take this as a small but clear signal that Obama will not be practicing Clintonian triangulation after he loses control of Congress in November? The appointment of a party hack to a critical post would seem to indicate this.

Friday, October 8, 2010

Congrats to Liu Xiaobo

This year's winner of the Nobel Peace Prize is a poke in the eye of China's Communist regime. Finally!

China is trying to block news of the announcement from its own citizens, using the Great Firewall of China and even radio jamming. They claim to be upset because Liu is a "criminal". But he's no murderer - all he's guilty of is "inciting subversion of state power", which is the sort of crime that in the United States is likely to get you elected. In China they throw you in jail.

I don't know much about Liu's story, but if China is throwing this big a hissy fit about his winning the Nobel Prize, he must be a good choice.

Thursday, October 7, 2010

Joining the Blog Bomb for Geert Wilders

Geert Wilders is currently on trial in the Netherlands for his short film Fitna. The film can be viewed in its entirety here. Please be advised that it contains graphic scenes of violence.

The film depicts Islam in a very bad light. By interspersing verses from the Koran with scenes of Islamic violence and hatred, it creates the impression that they are related. (I suspect there is something to this, by the way. But that is a question I have dealt with in other blog posts.) One of the most damning indictments in the film is its videos of Muslim clerics speaking in Arabic, subtitled in English. As the invaluable Middle Eastern Media Research Institute (MEMRI) has illustrated time and again, it's a common terrorist tactic to say one thing to Western audiences and quite another to Arabic ones. Fitna provides a similar service.

The Netherlands is prosecuting Wilders under its hate speech code. Does the film fall under the purview of the code? Perhaps: I am not an expert on Dutch law, needless to say. But if you believe in freedom of speech (as the Dutch government clearly does not), this film is exactly the sort of thing that must be protected. It is political speech, protest speech. Note that the film has not been attacked as libelous. Inaccuracy is not part of the complaint.

Furthermore, its message is merely that Islam is dangerous and to "stop Islamization". There is no call to answer violence with violence. This is not hatred. It may be wrong; you may disagree with the message. But silencing the messenger is an offense against one of the basic freedoms of Western civilization.

Monday, October 4, 2010

Enviro-Fascists Show Their Colors

This is a real ad promoting an environmentalist carbon-control program. It's "voluntary", but as you can see from the ad, they'd prefer that it wasn't.

The most telling point, I think, comes at the end, when the voice-over actress gets the button treatment. Just goes to show that no matter how much you do, it isn't enough. You have to be 100% committed to environmentalism, all the time, or they want you dead (or, at least, out of the way - let's give them the benefit of the doubt).

It all reflects a very Tom Friedman-esque viewpoint: if only we had more fascism and not so much democracy, we could really get some things done!

Thursday, September 30, 2010

Economist v. Tea Party

The Economist (in the person of its America-desk essayist, Lexington) casts a baleful glance at the Tea Party's reverence for the Constitution.

WOULDN’T it be splendid if the solutions to America’s problems could be written down in a slim book no bigger than a passport that you could slip into your breast pocket? That, more or less, is the big idea of the tea-party movement, the grassroots mutiny against big government that has mounted an internal takeover of the Republican Party and changed the face of American politics.

There is something to this, of course. But Lexington gets a few things wrong, too:

...[T]here is something infantile in the belief of the constitution-worshippers that the complex political arguments of today can be settled by simple fidelity to a document written in the 18th century.

This is simply a straw man, nothing more. Of course the Constitution doesn't contain the answers to all our problems. The point the Tea Partiers are making is twofold: first, that the Constitution is the ultimate law of the land, a meta-law, so to speak, that forms the skeleton from which all our other laws and governmental institutions draw their authority, and that that framework has been increasingly ignored over the past century; second, that returning to Constitutional principles would help restrain or even roll back encroaching government, in particular federal, control over our lives.

Lexington points out that the solution to the question of whether gays should marry is not contained in the Constitution, as if this is some indictment of it, or reason we should ignore the document. The Constitution is not meant to answer such questions, of course. It is meant to give us a framework within which we answer them. So when the judicial branch arrogates legislative power to itself, as it has in this and many other modern controversies, Constitutionalists are likely to object. It isn't that the answer is necessarily objectionable (although that is often also the case), but that the way in which it was determined was illegal and weakens the framework in the future.

But it isn't only Lexington's legal/philosophical analysis that is awry. The historical analysis also comes up short.

[The Tea Partiers] say that the framers’ aim was to check the central government and protect the rights of the states. In fact the constitution of 1787 set out to do the opposite: to bolster the centre and weaken the power the states had briefly enjoyed under the new republic’s Articles of Confederation of 1777.

The Constitution of 1787 certainly had the effect of bolstering the executive, but it is also designed to balance the powers: state against federal, legislative against judicial against executive. It's certainly true that Madison and his compatriots had states' rights firmly in mind when crafting the document, and the Tea Partiers are absolutely accurate to argue that a primary reason states have lost so much power is because of unConstitutional abuses.

Finally, Lexington argues that, since we can't know what the founders would have thought of the modern welfare state, or recognized its institutions, we have no choice but to ignore their document. This is disingenuous at best. One reason we have the country we have, one reason it became so unrecognizable to the founders in the first place, is because of Progressive steamrollering of the founding documents. It's perfectly fair to see a restoration of respect for the Constitution as one way to roll back some of those changes.

The modern progeny of the Progressive movement have zero respect for the Constitution. They see it as no impediment at all to the furtherance of government control of our lives, and there are any number of videos showing Nancy Pelosi, Barney Frank, and other Democratic bigwigs baldly asserting as much. Conservatives are not revolutionaries at heart; turning back the clock on a century of Progressive changes (some of which, especially in the field of civil rights, we should keep) is too massive a movement to undertake overnight, and is politically impossible anyway. But to roll back a few things (Obamacare being target number one), to restore a sense that there is resistance to the growth of government: these are practical goals that the Tea Party can achieve. Raising the stature of the Constitution in the minds of the public can only help them do it.

Wednesday, September 29, 2010

Obamacare Wipes Out Health Care For Children

Matthew Shaffer lays out the case for why Obamacare was responsible for wiping out the market in child-only health insurance policies.

Insurers say the blame for their withdrawal lies not with them, nor even with the Obama administration’s general desire to extend health coverage, but rather with a single, hastily written provision of Obamacare. As the bill was being negotiated, insurers accepted that it would prevent them from denying coverage to those with pre-existing conditions, but they assumed that other means of managing risk — such as pricing, co-payments, and restrictions on coverage — would still be available. So insurers were surprised to discover that the law essentially required full “guaranteed issue” and banned price discrimination across the child-only market, regardless of clients’ risk profiles.


[Health Care for America Now (HCAN) communications director Avram] Goldstein thinks that argument is misleading. “When the industry expressed reservations about the rules, the Obama administration accommodated them,” he explains. “HHS Secretary Sebelius and her staff added in the ability for insurers to create open enrollment periods, so that a child who suddenly developed a health problem could not just rush over and buy a policy that would be guaranteed issue. Instead you have to say during the year, when you don’t know if you’re sick, whether you’ll enroll. They tried to accommodate insurers.”

This is true, but insurers still have good reason to be skittish. [America’s Health Insurance Plans] explains insurers’ uncertainty with a thought experiment: Suppose twelve different insurers each had an enrollment period in a different month of the year; then parents could still wait until kids got sick to purchase insurance, because they could simply pick the insurer that was enrolling that particular month.

Shaffer doesn't quite connect the final dots, though. The basic problem is that the goal behind setting up an open enrollment period is at odds with that of providing health care for all. Suppose a parent wants to sign up a kid for a child-only policy. If there are many open-enrollment periods scattered throughout the year (from different insurers), then adverse selection allows the parent to wait until the kid is sick before signing up. If there are few open-enrollment periods, though, then the kid may have to wait an arbitrarily long time before getting covered.

It's a teeter-totter: when one side goes up the other goes down. You can attempt to balance the tension between the two, but you cannot resolve it.

UPDATE: I forgot to link to the article in the original posted. That oversight has been corrected.

Painting Yourself Into a Corner

There are riots in Brussels today as Europeans protest austerity measures by the EU and its national governments. Their "argument", such as it is, might seem reasonable: that the recession was caused by banks pushing the envelope, not by those citizens being affected by austerity, so somehow the austerity measures aren't "fair".

But how do they think governments got so flush in the first place? It was certainly due, at least in part, to a booming economy caused by banks pushing the envelope. During boom times, tax revenues is up. But you have to expect a bust eventually (unless you believed that late '90s bunk about the "end of the business cycle"). Governments didn't save up for the rainy days to come: not just European ones; the U.S. and certain states (I'm looking at you, New Jersey, and don't think I haven't noticed you, California) are just as guilty.

So here's the conundrum. Governments get rich because of an unsustainable bubble they tacitly encouraged. Social spending grew to match revenues. When the bubble burst, tax revenue fell and the increased spending suddenly blew massive holes in budgets worldwide. So austerity measures were necessary to close the holes. Now the people who benefitted from increased spending are pissed: their lollipops are being taken away. But what's the alternative? Current budgets are unsustainable, so where's the revenue to come from? You could raise taxes, but that risks killing the geese that lay the golden eggs.

You could target banks, extract as much tax revenue from them as possible, and enforce regulations and laws to prevent future bubbles. But that runs the same risk: if those banks run out of innovative options, tax revenue from them will wither.

What's happened is that we've painted ourselves into a corner. The only way to get out is to take that first unpleasant step onto the wet paint.

Tuesday, September 28, 2010

Funny to the Left of Me, Angry to the Right

Heard on NPR a few minutes ago: A guest on the Leonard Lopate Show said that the left just can't manage to be angry, while the right can't seem to generate humor. Maybe I'm missing something. The right has Chris Buckley, P. J. O'Rourke, Jonah Goldberg, David Kahane, Glenn Beck, and so on. Who does the left have? A bunch of guys and gals who fall over laughing whenever someone mentions Bu$hitler.

And the left doesn't do angry? The only thing the left does better than angry is pompous, condescending self-righteousness. (The anger comes when you put it like that.)

Monday, September 27, 2010

Vote Nixon!

Here's some footage of the first 1960 Presidential debate between John F. Kennedy and Richard M. Nixon. Nixon sounds like a guy I would vote for in a heartbeat.

Too often in appraising whether we are moving ahead or not, we think only of what the federal government is doing. Now, that isn't the test of whether America moves. The test of whether America moves is whether the federal government, plus the state government, plus the local government, plus the biggest segment of all - individual enterprise - moves.

We have, for example, a Gross National Product of approximately $500 billion. Roughly $100 billion to $125 billion of that is the result of government activity. $400 billion is the result of what individuals do. The reason the Eisenhower administration has moved, the reason we've had the funds locally to build the schools and the hospitals and the highways, to make the progress that we have, is because this administration has encouraged individual enterprise, and it has resulted in the greatest expansion of the private sector of the economy that has ever been witness in an eight-year period.

And that is growth. That is the growth that we are looking for, it is the growth that this administration has supported and that its policies have stimulated.

The Post I've Been Wanting to Write

I've been trying to figure out the right angle on a post for a few weeks, one that talks about the idea that the real problem with the American economy is that we aren't consuming enough. Until we kick-start consumptions, the idea goes, the economy will remain sluggish. (The idea is poppycock, by the way.)

Anyway, I've been pre-empted by Kevin Williamson, who has explicated it better than I could have.

Saturday, September 25, 2010

You Didn't Ask Me But I'm Going To Tell You Anyway

I have what I guess is a pretty un-nuanced, old-fashioned view of Don't Ask Don't Tell. Basically, the purpose of the military is to bring violence upon our enemies. It's not a tool of social policy. If having gays serve openly in the military enhances its ability to do violence, then I'm all for it. If not having them serve openly works better, then I'm all for that. If DADT is the best policy, then... well, you get the picture.

It's possible to take that "best for the military" thing too far, of course. I wouldn't support a policy of executing every tenth man in a platoon that screws up, even if that could be proved, via scientific study, to enhance military effectiveness. But our policy with regard to gays in the military has never been anything like that draconian. If discovered, they are discharged; that's all.

Being gay might be a personal choice, or it might be inherent. There's a big debate about this, and in some cases it might matter which is right. (Personally I suspect it's a bit of both, in different proportions for different people.) In the case of military policy, I don't see how it matters one bit. If it's a choice, then that's one choice that's denied to you, like wearing shorts and sandals on parade, or wearing a nosering and a mohawk. If it's inherent (which is a broader term than "genetic" - it might be inherent due to upbringing), then so are lots of other things that keep people from serving in the military. If you have flat feet, you cannot serve. Why? Because it detracts from military effectiveness.

Which of these policies actually is best for the military is not a question I am at all qualified to answer. But it should be the only question being asked. Whether it enhances social justice or something is irrelevant.

Thursday, September 23, 2010

A Death Tax Tale

Once upon a time there was a company. This company was founded during the Great Depression, and survived that turmoil and the World War that followed it. In the 1960s it was bought by a pair of entrepreneurs who thought they could make it even better. And they did. Under their ownership it prospered. Eventually one of these owners died and his family's share was bought back by the company. That was costly, but the company survived it. The company survived other hardships as well: legal troubles, financial market struggles, moves, new products.

The company has been run by this family of entrepreneurs for nearly fifty years now. And after all of this history, it has been forced to sell itself. Why? Has the company been poorly run? Is it drowning in debt and has to find a partner to help pay its creditors?

No. The company generates millions of dollars in profits a year. It has no debt.

What is happening is simple: the second of the pair who acquired the company is aging, and so is his wife. At some point - maybe tomorrow, maybe ten years from now - they will be dead, and the estate tax will kick in. And if that happened, the company would basically be out of business, because while it is a cash cow, it doesn't have the funds to buy back enough stock to allow the family to pay those taxes. Furthermore, such buybacks would radically change the capital structure of the company, with the family possibly losing control. And all for no good reason.

Naturally, the company wants to avoid this outcome. So it is being acquired. The family and the minority shareholders get their payoffs now, and the company will be absorbed by its new partner. While the company has been lucky - the partner has pledged to run the company as a stand-alone operation, and not mess with its corporate operations or culture - they will install a new CEO, and inevitably some changes will be coming. Employees are nervous, and rightly so.

This is the sort of unintended, and injurious, consequence that Republicans talk about when they attack the "death tax." To make matters worse, in this case at least, the government won't even collect the tax. The acquisition will trigger some capital-gains taxable events (I assume - it may even manage to avoid those depending on the specifics of the deal), but those will be timed to coincide with current lower capital-gains tax rates. The 55% estate tax that will go into effect in 2011 (barring new legislation to prevent the sunsetting of the 2001 Bush tax cuts) will collect zero revenues from the company. It's hard to find a purer example of the Laffer curve at work.

Friday, September 10, 2010

Stupid Koran Tricks

So there's this dimwit (whose name I won't honor by putting in print) in Florida who wants to burn a Koran tomorrow. Stupid.

But what's nearly as stupid is the press coverage of it. Years ago, networks figured out that when some drunken sports fan jumps onto the field to make an ass of himself, the thing to do is not to broadcast his antics to millions of viewers across the nation. You studiously don't film it, talk about something else for a few minutes while security takes care of it, then get back to the game.

I suppose it's harder to do that here. This Florida pastor isn't doing anything illegal, so the police won't be hogtying him and marching him off to the drunk tank. And he can make as much noise as he wants to on the Internet and wherever else he can. But why help him by giving him free publicity? I'll do my part by not providing a name or link, although that's spitting in the wind considering that his name, church, and probably blood type are already in all media outlets.

It's kind of sad when the sports media is wiser than the rest of the media.

Thursday, September 9, 2010

On Same-Sex Marriage

I've written before that I find arguments both for and against same-sex marriage to be about equally inane. That leaves me, net-net, against codifying the practice into law, because as a conservative I favor a millennia-old tradition over a newfangled idea unless significant evidence can persuade me otherwise.

National Review's recent editorial "The Case For Marriage" is the best argument I've read to date bolstering my default position. Is there a similarly persuasive case in favor of same-sex marriage? If so, I haven't read it - and as I've said, it would have to be even more persuasive to swing me against tradition.

Tuesday, September 7, 2010

Why is Labor Day a "patriotic" holiday?

On Independence Day we celebrate our founding as a nation - if we're going to have a flag-waving holiday, that's the logical choice. On Memorial Day we celebrate our fallen warriors - so that one makes sense, too. We have two days on which we celebrate specific American heroes - Presidents' Day and Martin Luther King Day - but those evince at most mild patriotic displays. Thanksgiving is traditionally American, but centers more around family than country. New Year's Day is a strictly secular, global holiday; finally, Easter and Christmas are religious, global holidays.

Other than minor holidays like Veteran's Day and Columbus Day, which most of us don't get anyway, that leaves only Labor Day. In my experience, Labor Day is third behind only Independence Day and Memorial Day in patriotic displays. In my town, for example, we have a fireworks display. I see kids wearing American flag clothing in the park.

But Labor Day is not especially American, and the part of it that is has not much to do with founding American values. Labor Day commemorates the bloody breaking of a strike in 1894. Its associations are with the International Labor movement and it is essentially the American version of May Day, which is the international (not American) socialist holiday (and also commemorates a massacre during a 19th-century strike). Labor Day was created as a conciliatory gesture toward the growing labor movement.

So I don't quite understand the fireworks and the flags. USA! USA! We're unionized!

Math Corner

John Derbyshire has another good one up in his August Diary. It's another probability question, this time about cards:

I have an ordinary deck of 52 playing cards. I shuffle it thoroughly. What is the probability that not one card is in its original position?

As often happens, the way to approach this is to look at the conjugate question: what is the probability that at least one card is in its original position? Suppose, for example, that one card is in its original position - we'll call this a stationary card, because it didn't move after shuffling. There are C(52,1) ways to pick this one card, and the other 51 cards can be arranged arbitrarily, so there are 51! ways to arrange them. However, we've done some double-counting here, because some of those 51! include arrangements that have a second stationary card.

It's worth going over this point in some detail, because this is an argument we're going to come back to again. To see what's happening here, it's useful to reduce the number of cards. So let's say there are only 4 cards, numbered 1, 2, 3 and 4. There are, of course, 4! = 24 possible arrangements of these cards. Let's look at all the arrangements with the "1" card in its original position:


Also, let's look at all the arrangements with the "2" card in its original position:


Notice something? The lists aren't distinct. Those first two entries are common to both lists. What we've done is double-count arrangements that contain at least two stationary cards.

We can subtract those back out pretty easily: there are C(52,2) ways to pick two cards, and then 50! arrangements of the other 50 cards. So we'll subtract C(52,2)50! arrangements.

But wait! We've removed too much, because both of the previous sets included arrangements that had at least three stationary cards. Going back to the 4-card example, take a look at the arrangement "1,2,3,4". We originally double-counted it, but then we double-removed it. So to count those arrangements we have to add back in arrangements with at least three stationary cards, and that's C(52,3)49!.

It should be no surprise at this point that this pattern continues. Now we've double counted arrangements with four stationary cards, so we subtract C(52,4)48! of those, at which point we need to add back the ones with five - there are C(52,5)47! of them - and so on. We end up with this many arrangements:

C(52,1)51! - C(52,2)50! + C(52,3)49! - C(52,4)48! + ... + C(52,51)1! - C(52,52)0!

There are 52! total arrangements of 52 cards, so to get the probability, we divide the above expression by 52!. This simplifies down to:

1/1! - 1/2! + 1/3! - 1/4! + ... + 1/51! - 1/52!

But this is the probability of having at least one stationary card, and we wanted the probability of having zero stationary cards, which is:

1 - 1/1! + 1/2! - 1/3! + 1/4! + ... - 1/51! + 1/52!

Reasoning the same way you can see that if you had n cards, the probability would be the first n+1 terms of this series. (It's an interesting fact that the above expression is the first n+1 terms of something called the Taylor series for 1/e, where e is the base of natural logarithms that you may dimly remember from high school or college. For more than 8 or so cards, the difference between the actual probability and 1/e is very small: less than 0.01%.)

Let's look at Derbyshire's second (related) problem:

I have a deck of n cards, numbered from 1 to n. I shuffle the deck thoroughly. Then I turn the cards over one by one. If the k-th card I turn over bears the number k, call that a "match." What is the probability that after going through the whole deck I shall have tallied m matches, where m is some number in the range from zero to n?

Based on the work we did before, this isn't hard at all.

Let's write the number of arrangements of n cards that have m matches (what I earlier called "stationary cards") as A(n,m). Then the probability p(n,m) that Derbyshire seeks is just A(n,m)/n!. Furthermore, we can reason about A(n,m) as follows: Suppose we select m cards and call them the matches. There are C(n,m) ways to make this selection. For each selection, there are A(n-m,0) arrangements of the remaining cards that have no matches. Any combination of a selection of m matches along with an arrangement of n-m cards that have no matches is equivalent to an arrangement of n cards with m matches. So A(n,m) = A(n-m,0)C(n,m).

Furthermore, since p(n,m) = A(n,m)/n!, we can write p(n,m) = A(n-m,0)C(n,m)/n! = p(n-m,0)C(n,m)(n-m)!/n! = p(n-m,0)/m!. Since our solution to the first problem gave us p(n,0) for every n, we now know how to calculate p(n,m) for every n and m.

Thursday, August 26, 2010

Senate Math Update

Way back on December 16, 2009, I posted a very simplistic analysis showing that the GOP had roughly 3 chances in 5 of picking up Senate seats, about 1 in 6 of losing seats, and just a 1% chance at picking up 6 or more seats. I called this "things looking moderately up for the GOP".

Nate Silver's Predictatron, whose sophistication compared to my analysis is roughly that of a Boeing 787 Dreamliner to the Wright Flyer, shows the situation considerably stronger for the GOP: a 20% chance that the GOP picks up ten seats, and only a 3% chance of the GOP losing any net seats. Eight months ago I had the chance of the GOP picking up 10 seats at too low to be meaningful. Silver shows that a good bet would be for the Senate to be a 52-48 or 53-47 split, leaving Democrat, after the upcoming November elections. Considering how uneven the open seats are tilted toward the GOP, this is excellent news.

Tuesday, August 24, 2010

Ayn Rand and the New Man

The desire to have Heaven on Earth is dangerous, but hardly novel. You can trace its philosophical origins back at least to Plato (who promoted, in The Republic, the ideal of philosopher-kings who would rule with perfect wisdom and magnanimity). Its social origins surely stretch as far back as human history records: the earliest governments were organized under "god-kings" who reigned with the legimitacy of literal deities.

In modern times - post-Renaissance - this strain of thought can be traced through the French Revolution, through Marx, to Communism, and still looms like a shadow over the world. In Tom Sowell's terminology, this is the "unconstrained vision": the idea that anything is possible if only human nature can be suitably molded. It is a utopian vision. It promises the moon. And with such incredible promises, equally incredible insults to dignity and humanity have been justified. After all, if one is bringing about utopia, what does it matter (say the utopians) if a few million looters are thrown in the gulag? What does it matter if thousands of opponents are guillotined? One cannot make an omelet without breaking eggs.

By contrast, the "constrained vision" holds that human nature sets certain boundaries which we cannot, as a society, hope to exceed. This view of humanity is that which defined the American experiment. James Madison wrote in Federalist 51:

Ambition must be made to counteract ambition. The interest of the man must be connected with the constitutional rights of the place. It may be a reflection on human nature, that such devices should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary.

Madison does not imagine, as Plato, that human nature might be molded to produce a class of philosopher-kings. Nor does he imagine, as Marx, that history's inevitable progression through capitalism, then Communism, will result in a New Man capable of exquisite anarchy. Rather, he realizes that men are not and will not be angels, and thus we must deal with them as they are, not as we wish they would be.

And this is where Ayn Rand comes in. A champion of some free-market types, Rand is, unfortunately, no less a utopian than Marx. Her chosen utopia is a bit different in style from most, filled with self-interested, omnicompetent heroes and heroines. In a sense, it is more like Homer than Plato. Galt's Gulch is a modern-day Mount Olympus. But therein lies exactly the flaw: populated by Randian demigods, it is almost literally Heaven on Earth. Rand cannot see how to attain her vision for humanity without creating New Men to her liking. And we've seen where that leads. As Whittaker Chambers writes: "To a gas chamber — go!"

Further reading on this subject: Jason Lee Steorts, Whittaker Chambers.

UPDATE: Also read Richard Reinsch's post on the subject.

Separated at birth?

Roger Sterling

Charlie Crist

Chinese Traffic Jam

This traffic jam has now lasted nine days and stretches 62 miles along the Beijing-Tibet expressway.

So much for Tom Friedman's "optimal policies", eh?

Monday, August 23, 2010

Is Modern America Like 16th-Century Spain?

Imagine for a minute that everyone on Earth just had an interesting windfall: every dollar, every euro, every peso and yen and renminbi, just cloned itself. So the total amount of money just doubled instantaneously. Here's the question: is anyone richer?

A moment's thought should convince you that the answer is no. The amount of money has doubled, but the goods that can be bought with that money are no more plentiful. So more money is chasing the same number of goods and services. What we would expect to see is the value of money falling by exactly half, just enough to offset the windfall in cash. At the end of the day, no one is actually any better off.

The situation is a little more complicated when you imagine a windfall in a single nation. There are now two effects we care about: domestic production and imports. More money means that domestic prices will likely rise, for the same reason that they would rise worldwide in the global windfall scenario. But imports would remain cheap, so we would expect an increase in imports. And because domestic prices rose, exported goods become more expensive, and hence exports should fall. As a result, the balance of trade becomes negative: our windfall begins to drain out of the country into other countries.

When you look at 16th-century Spain, that's basically what happened. Spain's New World possessions generated immense amounts of gold and silver - free money! - but did nothing to increase Spain's actual productivity. The results were just as I described: prices of Spanish goods rose, imports went up and exports fell. Spanish gold flowed to other nations. The experts of other nations traveled to Spain to work. The short-term consequences for Spain were largely positive: people were able to consume more and their lives were somewhat easier than they otherwise might have been. (Of course, 16th-century Spain had plenty of problems, too, what with the Inquisition and so on.) The long-term consequences were mostly bad, though, as Spain was left behind by its more cash-starved northern European competitors, and their American colonies, who ultimately leveraged productivity increases into wealth and power on a scale Spain never realized.

So is modern America following the same path as Spain? Obviously we have not discovered a New World filled with riches, poorly protected by feather-clad tribesmen wielding stone weaponry against our armored knights and cannons. But we have greatly increased the store of money in our nation. That volume of money has been sloshing around for over a decade, creating a stock market bubble here, a housing bubble there. Just as in Spain, our balance of trade is highly negative: that money is flowing outward. And just as in Spain, foreigners are flocking to our shores to work.

Here's another crucial link: just as Spain controlled a huge portion of the world supply of the primary currency at the time, so does the United States control the world's reserve currency, the U.S. dollar. In the 16th century, the mercantilist system prevailed, under which your national economy was considered strong if it had a lot of gold and silver in it. These days, gold is a marginal store of value (the total quantity of gold ever mined in the world is about a third of U.S. GDP), but the U.S. dollar can be created in as great a quantity as the U.S. Treasury decides.

It's a common worry that China will stop buying Treasury bonds at some point, and that this will starve us of easy credit. That's a legitimate concern. But the comparison with Spain illustrates an additional long-term danger: that our productivity will be hindered by easy access to cash. The United States is still a far more innovative, flexible economy than Inquisition-era Spain. But why risk it? We need to drain the sloshing overage of cash out of our economy, take the painful lumps that will ensue, and get back to what we do best: producing goods and services for the world.

Wednesday, August 18, 2010

Thinking of Iran

Reading this account of the first post-Communist Rolling Stones concert in Prague, I couldn't help but think of Iran. Will they ever be able to look back at the first post-Islamist concert, maybe by Blurred Vision? My vision gets a blurry thinking about it.

Monday, August 9, 2010

DNA Sequencing: Useless?

Adam Keiper, editor of the excellent journal of science and society The New Atlantis, posts to the Corner about an interview by Craig Venter in which he states that the Human Genome Project has yielded "zero" fruit.

Specific DNA sequencing efforts certainly have yielded fruit. Venter points out that finding a gene that adds only 1-3% to the likelihood of getting some disease is of no clinical value: also true. Keiper takes this further:

For better or for worse, our limited genomic knowledge is already influencing people's decisions about important matters. Some women who learn from DNA tests that they have a genetic susceptibility to breast cancer are electing to undergo mastectomies even though they don’t yet have, and might never develop, the disease.

It's not clear Keiper is applying Venter's numbers to his own conclusions, but if so he's trying to take his argument a bridge too far. The BRCA mutations that have been shown to correlate highly with breast cancer change a woman's likelihood from a baseline of about 6-8% by age 70, to a hefty 85%. That is, if you have the BRCA mutation, you have an 85% chance (better than 5 in 6) of getting breast cancer by age 70. That's a huge result, and it's not surprising that some women found to have the mutation would choose to circumvent the disease by having double mastectomies.

Before women reading this rush off to get genetic testing, I should point out that the BRCA mutation is quite rare - well under 1% of the population - and only a small percentage of breast cancer cases involve it. So in that sense, its clinical value may be small since the test is relatively expensive. But wouldn't a cheap BRCA test be of enormous value to, say, a woman of 30 who was considering starting a family?

The larger point Venter and Keiper make is quite right: the HGP was overhyped. But they go a bit too far to deflate the hype. It did have some value.

Friday, August 6, 2010

The Tea Parties and Racism

This is excellent. Watch the whole thing.

Race relations in the U.S. have significantly diverged from the vision of Martin Luther King, Jr. It's people like this who can restore us to sanity - if that's even possible. Perhaps the single most disappointing thing about Obama's Presidency has been his inability to improve race relations. Videos like this help restore my optimism.

Wednesday, August 4, 2010

Remember the Oil Spill?

That unprecedented environmental disaster seems to have faded a bit.

Just goes to show what Calvin Coolidge once said: if you see ten problems coming down the road, nine of them will roll into a ditch before they get to you.

Monday, August 2, 2010

Banning the Burqa

Claire Berlinski writes a thoughtful and convincing essay on why we should ban the burqa, and now.

Parents in these neighborhoods ask gynecologists to testify to their daughters’ virginity. Polygamy and forced marriages are commonplace. Many girls are banned from leaving the house at all. According to French-government statistics, rapes in the housing projects have risen between 15 and 20 percent every year since 1999. In these neighborhoods, women have indeed begun veiling only to escape harassment and violence. In the suburb of La Courneuve, 77 percent of veiled women report that they wear the veil to avoid the wrath of Islamic morality patrols. We are talking about France, not Iran.

A clothing ban is highly distasteful. It's possible that one has to live through the consequences of widespread veiling, as Berlinski has (and I haven't), to gain an emotional, not merely intellectual, understanding of the necessity of banning it. I don't think I'm quite there yet, but Berlinski supplies the best argument I've read to date.

Monday, July 26, 2010

The Dad Life

I'm not usually a fan of rap, but this struck a chord:


How ironic that the vast right-wing conspiracy turned out to be a vast left-wing conspiracy. I'm sure we're all very surprised.

Friday, July 23, 2010

Happy Belated Anniversary to Athwart History

Here I'm two weeks late to the first anniversary of Athwart History, which saw its first post on July 9, 2009.

Since then, we've seen the passage of the historic, and historically awful, health care bill (which I commented on extensively), a not-quite-so-bad-but-still-not-good financial regulation bill (which I haven't commented on at all until now), a shocking Democratic defeat in Massachusetts, a Gulf oil spill, and a bunch of random other items of interest.

The summer tends to be slow, and Athwart History is no exception. But as the mid-term election swing into gear, no doubt the commentary will accelerate again.

One bit of personal news: I am in the midst of changing jobs, and also moving across the country. Currently I'm in New Jersey (one state struggling with a fiscal crisis) and I'll be moving to California (another one). So this is an exit frying pan, enter fire sort of thing. I'm excited about California, if for no other reason than the weather, and the new job should be a blast, even though it may impede my ability to post.

The Tuesday Child Problem, Solved

At long last, the solution.

As in the case with flipping two coins, the problem revolves around figuring out what options have been eliminated by the statement of the problem. To review, the statement is that I have two children, one of whom is a born born on a Tuesday. The question is what is the probability that my other child is a boy?

First, I'll do this formally, to show that formal mathematics works just fine to solve problems like this. That is, you don't have to stoop to writing out the various possibilities and then tabulating them, as we did in the coin problem.

There is a formula in probability theory that comes in handy here:

(1) P(X|Y) = P(X and Y) / P(Y)

(The notation P(X|Y) means: the probability that X occurs given that Y has occurred, or in short-hand: the probability of X given Y.)

From (1), by the way, you can get another useful formula:

(2) P(X and Y) = P(Y) P(X|Y)

And since P(X|Y) = P(X) if X and Y are independent, that last formula can be written P(X and Y) = P(X) P(Y) in the case of independence.

Finally, since the "and" operation is commutative (i.e., the order of its operands is irrelevant), we have:

(3) P(Y and X) = P(X) P(Y|X) = P(Y) P(X|Y)

In this case, we want to determine:

P(both my children are boys | one child is a boy born on a Tuesday)

By (1), that's equal to P(both my children are boys and one child is a boy born on a Tuesday) / P(one of my children is a boy born on a Tuesday).

The first probability is clearly equivalent to P(both my children are boys and one of them was born on Tuesday), which by (2) is P(both my children are boys) P(one of my children was born on Tuesday). The first of these is easy to calculate: 1/4. The second is trickier, but the easy way to see it is to imagine that neither was born on Tuesday. Since the likelihood for either not being born on Tuesday is 6/7, the chance that neither was born on Tuesday is just 6/7 squared, or 36/49. That means the chance that at least one was born on Tuesday is 1 - 36/49 = 13/49. So that first factor in our equation above is (1/4)(13/49) = 13/196.

Now let's look at the second factor, P(one of my children is a born born on Tuesday). We can apply similar logic by imagining that neither is. The chance that a single child is a boy born on Tuesday is clearly 1/2 (boy) times 1/7 (born on Tuesday) = 1/14. So the chance that a single child is NOT a boy born on Tuesday is 13/14. Hence the chance that neither of two children is a boy born on Tuesday is 13/14 squared, or 169/196. The chance that at least one child is a boy born on Tuesday is then 1 - 169/196 = 27/196.

Plugging these values back into our original formula, we get the final probability as (13/196) / (27/196) = 13/27. And that is the answer.

Another way to do it (a bit less formally, but still perfectly accurate) is more like the two-coins problem. Let's write B for boy, G for girl, T for Tuesday, and !T for not-Tuesday. Then all possible outcomes for one child can be written like this:


These are not equally likely, of course. P(G) = 1/2, P(BT) = 1/14, and P(B!T) = 3/7. But these add up to 1, and are mutually exclusive, so they must cover every possibility.

So for two children, there are nine possible outcomes:


Again, though, these are not equally likely. But their probabilities are easy to compute since the outcomes are independent. Furthermore, some of these outcomes are not possible since we know that one child is a boy born on Tuesday. So the only outcomes remaining are:

G,BT => (1/2)(1/14) = 1/28
BT,G => (1/14)(1/2) = 1/28
BT,BT => (1/14)(1/14) = 1/196
BT,B!T => (1/14)(3/7) = 3/98
B!T,BT => (3/7)(1/14) = 3/98

The sum of these is 1/28 + 1/28 + 3/98 + 3/98 + 1/196 = 27/196. Two boys show up with probability 3/98 + 3/98 + 1/196 = 13/196. The ratio is 13/27, as before.

Thursday, July 8, 2010

World Cup

So it's Spain v. Holland in the final. I have to admit I'm torn on this one. The Dutch, with their centuries-long ties to England, are the closest to being my countrymen, so sheer familial respect prefers them. But the Spanish side, La Roja, is so great to watch.

Often in games like this I have to start watching and see where my heart finds itself rooting. It usually makes some pre-rational decision of its own. Let's just hope it's a good game... and that it doesn't end in penalty kicks.

Wednesday, July 7, 2010

Math Surprises

Some of the best math problems are the simplest to state. But they can be fiendishly difficult to understand, precisely because their domains are so commonplace. A good example is fairly well known: Suppose I have two coins. One of them is showing heads. What is the probability the other one is also showing heads?

The answer most people jump to is 1/2, since we've had it drilled into us that coins are independent, so the outcome of one shouldn't affect the other. But the phrasing of the question contains a subtle trick. By stating that one of the coins is showing heads, I have eliminated the possibility that both coins are showing tails. But there are actually three remaining possibilities: heads/tails, tails/heads, or heads/heads. In only one of these three are both coins heads, so the answer is in fact 1/3.

The trickiness of the phrasing comes from the fact that when we say that one of the coins is heads, we deliberately don't say which one. We could say equivalently that at least one is showing heads. The probability is the expected 1/2 once we specify ahead of time which coin it is.

Given this preliminary, consider the following problem, which has been making its way around the Web of late:

I have two children, one of whom is a boy born on a Tuesday. What is the probability the other one is a boy? (You can make all the expected simplifying assumptions: no twins, boys and girls born in equal proportions, each day of the week is equally likely, etc. It's a math problem, not an obstetrics exercise.)

I will post the answer in a few days.

Thursday, July 1, 2010

The Bargain

Back in the days of the Clinton White House,
It was said we had two Presidents when we'd only elected one.
Hillary being the other, you see.
Quite a bargain, one might say.

But the Obama administration has given us an even
More attractive package. All in one man:

Ideological consistency
And pragmatism,
And combativeness,
And elitism,
Fiscal discipline
And big-government liberalism,
And logorrhea.

He is extremely moderate about being moderately extreme.
Come to think of it, he is a contradiction.
He contains multitudes.
Ten Presidents for the price of one!

Wednesday, June 30, 2010

Daily Kos Caught Lying

Excuse me this moment of schadenfreude, but this is too rich. Apparently the polling firm Daily Kos contracted with for hundreds of polls in its push to help the Democrats contest the 2010 elections has been caught fabricating its results.

To Kos' credit, he has cut ties with the firm, Research 2000, and renounces any blog posts using their results. This is a BFD of Biden-esque proportions, because the difference of just a few percentage points on a poll, especially one that's been finely sliced and diced into subcategories, can have a big effect on perceptions - which can affect elections.

Wednesday, June 23, 2010

World Cup Tiebreakers

John J. Miller finds it "lame" that there is (or was: the games are over) a possible outcome in which the U.S. and England, tied for 2nd and 3rd place in Group C, would have their positions determined by lottery.

He may not be aware of this, but the same is true in the American football playoff system. There is a series of tiebreakers, the last of which is "coin toss".

This isn't surprising: at some point in any round-robin system, it's possible that two or more teams may tie on any given number of measures. If that happens, something must be introduced to break the tie. You might say: use a one-game playoff, which works fine if two teams tie. But what if three teams tie? That's certainly a possible outcome, and further playoffs may do nothing to resolve the situation. So a coin toss, or lottery, is necessary just to come to a decision. It may be "lame", but it's unavoidable.

Happily, the U.S. and England each won their games and advanced to the knockout round without the need for any lotteries.