New Haven Schools (again), The Death Penalty, and Gratuitous Promotion of Family Members

Two quick notes:

Nathaniel has another piece criticizing the New Haven Promise program. This piece says much of what he has already said but includes a few more direct proposals about what else should be done. Unfortunately, this piece is on National Review Online. While that's an impressive accomplishment, that does make me feel conflicted about linking to it. In general, while NRO does have some worthwhile material, a disturbingly large fraction of it has over the last few years come to resemble a nutshell of what is wrong with the modern conservative movement in the US. For example, considering that NRO is the same place where writer Mike Potemra complained that Star Trek promoted "peace, tolerance, due process, progress" which are much too liberal values. Aside from this issue, as I've discussed before, I think that the problems in the public schools, including New Haven, are more complicated than Nathaniel portrays them.

There is a piece by another member of my family that I can link to with fewer reservations. My father has a deeply personal piece up at the Oxford University Press blog discussing why he has grown to oppose the death penalty. I suspect that his changing views are similar to the general decline in support for the death penalty over the last 20 years. The general support for the death penalty has dropped over time although about two thirds of the US still supports the death penalty (I've seen claims that the US did not have strong support for the death penalty in the 1960s and that the level of support grew for some time before beginning its current downwards trend, but I've never seen data backing this claim up.) There's also evidence that more religious people tend to be more likely to support the death penalty. If that is a causal rather than correlative link, the current drop in support for the death penalty may be due to the general drop in popularity of organized religion over the last few years.

Public Schools, Unions, New Haven Promise, and GPFM

Last week, my alma mater Yale University announced that the university would work together with New Haven to fund "New Haven Promise," a program which would provide funding to New Haven public school students who attend colleges in Connecticut. The program promises scholarships for New Haven public school students with only a few weak restrictions. For example, students with less than 90% attendance rates in highschool are not eligible.

There are a number of possible criticisms of this program. The most serious criticism to me seems to be the simple one that this program is not Yale's job. Alumni donate money to Yale with certain expectations. They might also donate money to other causes. But there is a basic expectation that money that goes to Yale will be used for Yale purposes such as going to scholarships for poor students at Yale, not to students at random other schools in Connecticut.

There are additional problems with this program. My little brother wrote an op-ed in the Yale Daily News arguing that this program would in fact cover up the real issues in the New Haven public school systems which need to be addressed. He argues that the teacher unions and the lazy and incompetent teaching which they allow are much more of a root cause of the problems. I'm not convinced of his claims. I'm especially unconvinced by his line that "Instead of staying after school to tutor or help run an extracurricular, unionized teachers typically leave as soon as the final bell rings" which seems to underestimate the great difficulty that even hard-working teachers need to put up with daily.

However, I do think that more broadly speaking there's a clear problem with unions in our public schools which prevent the removal of all but the most egregiously bad teachers. For example, consider the case of eighth grade science teacher John Freshwater in Mount Vernon, Ohio. Freshwater taught science so badly that other teachers in later years had to specifically reteach Freshwater's students. Freshwater told students that Catholics were not real Christians. Freshwater burned crosses into students' arms using a tesla coil. Despite all these issues, it has taken more than 2 years to have Freshwater removed. Thus, while I don't have enough detailed experience to personally evaluate whether the unions are a problem in New Haven (although my limited anecdotal evidence suggests that they are a problem), it does fit the general pattern of what is going wrong with American public schools.

Nathaniel's piece generated a variety of responses such this one by a New Haven public school teacher, this one by a New Haven alderman, and this one by another Yale student. Nathaniel has responded to the last piece here. All of these pieces are worth reading.

On Almost Commuting Matrices

When mathematicians encounter a binary operation, one of the first things they ask is "when does the operation commute?" That is, given an operation * when does one have A*B=B*A? Some operations always commute. Addition and multiplication in the real numbers are examples of this. Sometimes they commute under certain restricted circumstances. For example, subtraction rarely commutes (1-2 is not the same as 2-1).

In high school, children are often taught about matrices and matrix multiplication. Matrix multiplication seems to be given in part simply to have an example of an operation which has complicated behavior regarding when it commutes. Of course, we can only meaningfully talk about this when the matrices in question are assumed to be square matrices since otherwise the multiplication won't even be defined. However, matrices have other operations which we can do on them other than just matrix addition and multiplication. In particular, we can also multiply a matrix by a scalar.

This raises the following question: When do matrices almost commute? By almost commute, we mean commute up to multiplication by a non-zero scalar. A general result seems difficult. But there is at least one pretty result which can be proven without too much trouble by looking at the eigenvalues and eigenvectors of a pair of matrices:

If cAB=BA for some constant c, and A is invertible, then c is a dth root of unity for some d such that d divides the number of distinct non-zero eigenvalues of B. It isn't that hard to generalize this result slightly with A not invertible. However, one then needs the slightly technical condition that A sends no non-zero eigenvector of B to zero. Note also that this result is most nicely stated in the slightly more restricted symmetric case when both A and B are invertible.

One pretty corollary of this result is that if A and B are invertible p x p matrices over the real numbers where p is an odd prime, with all distinct eigenvalues, then A and B are almost commuting if and only if they actually commute.

No Free Lunch, Budgetary Constraints, and Gratuitous Promotion of Family Members

My father has a piece up at the Oxford University Press Blog arguing that both major political parties in the US are pretending to the public that there are painless solution to US budgetary problems. I'm not convinced that the current federal budget situation is as dire as he makes it out to be although I do agree that the state and local budgets in many areas are in very bad shape. However, the essential point seems spot on. Neither the Democrats nor the Republicans are willing to be honest with the voters. And this is clearly not a good situation. I don't see any quick resolution to these issues. I will however be slightly partisan in saying that it is clear that some groups are being more unhelpful than others and that the Tea Partiers are clearly one of the most unhelpful groups in question.

The AFA, Youtube, Christine O’Donnell, and Yale: A Rant About The Modern Right Wing

For a long time, I've believed that the anti-intellectualism of the modern right-wing in the United States is a fringe phenomenon.

However, over the last few months, I have become increasingly convinced that anti-intellectualism is not just a fringe phenomenon but a general trend of the modern conservative movement. The leaders of the movement are either ignorant, anti-intellectual buffoons, or they believe that their base is composed of ignorant, anti-intellectual buffoons.

Prior to coming to this conclusion, I had seen much evidence for this claim that did not convince me. The GSS data show that people who self-identify as liberal on average have larger vocabularies than those who self-identify as conservative. However, this did not convince me. Among other problems, the overall trends in that data are complicated. Vocabulary is correlated not just with increased liberalism but with general political extremism. That is, people more likely to identify with extreme political views are more likely to have a large vocabulary. Moreover, having a small vocab does not mean that one is anti-intellectual. It just means one is less likely to be intellectual.

Moreover, as I've discussed before, by some metrics of political knowledge, Democrats perform on average more poorly than Republicans.

However, the evidence for widespread anti-intellectualism among the American right-wing has now reached proportions which are difficult to deny. It is easy to dismiss Sarah Palin's comments about fruit flies as simple ignorance. And it is easy to dismiss Bobby Jindal's remarks about volcano monitoring as an isolated incident. However, these are not isolated incidences and one can point to many similar instances. Two of the most glaring that I've seen recently are remarks by the American Family Association's head Tim Wildmon and remarks made by Delaware senate candidate Christine O'Donnell.

The American Family Association is a right-wing Christian political group most known for organizing the boycotts that the right-wing periodically directs against companies that they have decided are too gay-friendly. I happen to be on their mailing list and received an email recently which contained the following:

A few months ago, AFA commissioned Christian songwriter/singer Eric Horner to write a moving patriotic song to honor our national motto, "In God We Trust."
Without any fanfare, we posted it on YouTube. The response was so overwhelming that YouTube called us to find out what was going on!

The fact is, the video is patriotic and inspiring, and it shares the message of faith. People love it!

YouTube has told us that if we can get 20,000 people to watch the video, they will feature it on their front page. That means that the tens of millions of people who visit YouTube's website each day will be offered the opportunity to watch the video - a video with a Christian message!

(fonts and formatting as in in original)

So much about this claim is strange that it is difficult to figure out where to start. The text contains outright lies. Youtube does not in general contact people for making popular videos to “find out what was going on!” It is conceivable that there is some threshold where such contact would occur. But that threshold is surely far beyond 20,000 views. In comparison for example, this video of Christopher Hitchens has around 35,000 hits and it is not the most popular such interview with Hitchens. Or to use a more amusing comparison, this extremely NSFW tribute video to Ray Bradbury has around a million views. 20,000 views is not much on Youtube. And anyone who gave minimal thought would realize this. My conclusion must be that the AFA lied . This is nothing less than political conmen fleecing a mark.

The other example was Christine O’Donnell’s recent attack on my alma mater. The Senate candidate, fresh from her prior remarks about scientists engineering ultra-intelligent rats , has now decided that Yale is a bad thing. She tweeted:

My opponent wants to bring Yale values to US Senate. I want to bring liberty, limited government, fiscal sanity.

Now, in fairness, she included a link to an article in the American Spectator which seemed to prompt her remark. That article didn’t criticize her opponent Chris Coon for going to Yale or for Yale values, but for his statement that he wants to bring the values of the Yale Divinity School to the Senate. That article is an attack piece, but like many attack pieces, it does have some truth to it and points out correctly that the Yale Divinity School is more left-wing than the general American population. That’s not the same thing as complaining about Yale in general. But, apparently to Christine O’Donnell, the problem as a whole is “Yale” values. According to O’Donnell, the values of one of the best universities on the planet are inherently bad values. It is difficult to imagine a more anti-intellectual stance short of book-burning. And yet, O’Donnell won the GOP primary for the U.S. Senate against Mike Castle. Castle is reasonable, well-educated and experienced. He has a law degree from Georgetown. He has demonstrated competence for over 20 years in political offices. And yet, he lost in the primary.

Anti-intellectualism is not at all limited to the GOP. It is becoming increasingly clear that the Obama administration actively interfered with government scientists telling the public how bad the the BP spill really was. Moreover, the Huffington Post, a mainstay of the liberal blogosphere, is filled with proponents of pseudoscience. And they have recently branched out from making absurd medical claims to denying evolution. But even these problems are small compared to the scale and pervasiveness of anti-intellectualism among the current conservative movement.

I don’t know what has happened to the GOP. At this point, the party seems to be engaging in a spiral of anti-intellectualism. There may be a positive feedback loop in that the more intellectuals grow disgusted with the Republican Party, the less incentive Republican candidates have to care about intellectuals. But that cannot be the whole story. Many people who are not intellectuals are not anti-intellectuals. So, I don’t understand what is happening to the Republican Party. But it disturbs me greatly. I’d like to be able to reasonably vote for multiple candidates including moderate Republicans. But as long as these trends continue, I will be forced to keep giving my money, my time, and my vote to Democratic candidates. And when I need to mark down what my politics are in a little box, I’ll answer “liberal” or “progressive” because in the United States right now, putting down anything else is becoming perilously close to writing “I support willful stupidity.”

Jack Chick and Civil Rights

There's a new Jack Chick tract up. This tract is entitled "Stinky" and is about an eponymous demon assigned to go up to the surface for Halloween. Stinky is supposed to find a gift for Satan so that a higher a ranking demon, #3, hopes to use to get a higher position in the diabolical hierarchy. Unfortunately, school has just resumed, so I don't have the time to go discuss the tract in detail. And honestly, as Chick tracts go, it is pretty mediocre. We don't even have the grand Catholic conspiracy appearing in this one. The plot-line is slightly less coherent than usual which also may lend to the mediocrity.

However, just when I thought that Jack Chick might be losing his did stand out. At one point, Stinky is trying to get past an angel so he can continue to tempt some humans. Stinky cries out "I demand my Civil Rights!" to which the angel responds "That doesn't work here, Stinky!" (eccentric formatting as in in the original). As far as I can tell, Jack Chick is attempting to make some sort of political argument here along the lines of "civil rights are a demonic concept." I don't know what to say to that.

Conservapedia, P=NP, and the Fields Medal

Conservapedia, the right-wing, Christian alternative to Wikipedia has once again broken new ground. In previous entries we've discussed Conservapedia's founder Andrew Schlafly self-Godwining and Conservapedia's interesting take on Popperian falsifiability. Others have discussed Conservapedia's objections to special and general relativity. Now, Conservapedia is at it again.

Apparently, Conservapedia has taken a recent interest in mathematics. First, they added to their mainpage a take on the recent reports that Deolalikar had proven that P ≠ NP . Conservapedia announced:

University professors pile on against a non-professor's claim to have solved one of the millennium problems. MIT Assistant Professor Scott Aaronson declares, "Vinay Deolalikar still hasn’t retracted his P≠NP claim, but a clear consensus has emerged that the proof, as it stands, is fatally flawed." He absurdly adds, with a cite to Richard Dawkins, "the only miracle in life is that there are no miracles, neither in mathematics nor in anything else."

But the best of the public, aided by the internet, will inevitably solve more problems than liberal colleges will - just as Grigori Perelman solved another millennium problem. The future belongs to the conservative public.

(internal links and fonts suppressed)

Apparently, Aaronson's decision to quote Richard Dawkins meant that math must be evil. I'll leave it as an exercise to the reader to note some of the other more glaring errors. However, this was not the end of Conservapedia's attack on establishment math for being just too liberal. Shortly after this declaration, an addition about the Fields Medal went up. The Fields Medal, awarded every four years, is for mathematics roughly equivalent to a Noble Prize(there is no Nobel in math). Conservapedia announced a "Conservapedia exclusive":

[T]his Thursday liberals will likely give the coveted Fields Medal -- math's highest honor -- to an underachieving woman and to a communist-trained mathematician from Vietnam. Is the lamestream media holding back stories about this to create a bigger splash on Thursday?

(internal links and fonts suppressed)

It is not clear what "underachieving woman" Conservapedia is thinking of, but apparently the "communist-trained mathematician" is a reference to Ngo Bao Chau, who made headlines last year for proving the Fundamental Lemma of the Langlands program. Apparently Conservapedia believes that the general media cares so much about mathematics that a failure to speculate on who will win the Fields Medal is a sign of a media conspiracy. Why a "communist-trained" mathematician would be a big deal is not clear given thatabout half of the Fields Medal winners have been either from the USSR or trained in the USSR.

Also, apparently Conservapedia is unhappy that after Terence Tao got the Fields Medal four years ago he then endorsed Barack Obama for President, Finally, we come to the detail that forced me to write this blog entry. To deal with this apparent liberal bias and affirmative action in the Fields Medal, Conservapedia is starting its own award for mathematicians, the "ConservaMath Medal." According to the website this Medal is "the merit-based alternative to the Fields Medal, with winners announced at the same time so that real achievement is recognized." I'll let that speak for itself.

Integer Complexity: An Upper Bound Update

It looks like I may have a final upper bound on the integer complexity problem. Recall we defined f(n) to be the minimum number of 1s needed to represent n as a product or sum of 1s. Thus, f(6)=5 because we can write 6=(1+1)(1+1+1). Harry Altman and I have been working on improving the lower and upper bounds on this function. Prior posts about this problem can be found under the label integer complexity. Harry has a large number of posts on the subject also, but they aren't all tagged so I'll just direct readers to the most recent one.

I'm writing this post to announce that we have a tight upper bound for f(n). Prior to our work, it was known that if n ≥ 2, we have 3log2 n ≥ f(n) ≥ 3log3 n. It is clear that the lower bound is hit infinitely often (whenever n is a power of 3). We (and by we I mean mostly Harry) have worked on understanding what n have close to the lowest possible value, and using this to understand other conjectures about f, such as the conjecture that if n=2^a*3^b then the most efficient representation for n is the obvious one. However, I've been also working on improving the upper bound, and whenever I've thought that I've been done improving the upper bound, I've then realized another way to tweak my proof to reduce the upper bound slightly. However, at this point, I'm confident that cannot happen anymore using the techniques in question, barring substantially new insight. Thus, I'm now announcing the new upper bound. We have for n ≥ 2, f(n) ≤ αlog2 n where α = 70/(log_2 102236160)= 2.630853... Note that this constant is just small enough for us to also state the weaker but prettier result that f(n) ≤ (19/5) log n. Unfortunately, the proof in question is very ugly, involving a large amount of case checking as well as nasty calculation of inequalities. I'm in the process of writing up the last bit. If readers are interested I can email people a draft of the proof when it is fully written.

Greece, Civil Unions in Hawaii and the Huffington Post:: Ethical Dilemmas about GPFM

My twin has a piece up at the Huffington Post arguing that the veto of Hawaii's civil union bill by its Governor Lingle was not motivated by the reasons that Lingle gave. I'm having some qualms about linking to the Huffington Post. The website has had a long history of pushing anti-science and fringe medical beliefs, including homeopathy and claims that vaccines cause autism. Most recently, they've branched out into anti-evolution propaganda with a piece by David Klinghoffer of the Discovery Institute claiming that evolution was the root cause of Nazism. These issues with the Huffington Post are discussed in detail in this Salon piece and this statistical analysis. I'm concerned about driving traffic to a website which has such attitudes towards science and the scientific consensus. Moreover, it raises serious questions about their otherwise apparently good political coverage. In particular, if they cannot deal with empirical issues well, why should one think that they can deal with issues involving politics where far more cognitive biases come into play? I'm curious what readers think about this issue.

Meanwhile, I can without any concerns link to my father's recent piece at the Oxford University Press blog which discusses what lessons that the United States should take away from the Greek financial crisis. The piece gives a balanced view about the economic and demographic issues that face the United States today and how they compared to Greece.

Insane Clown Posse and Science: Deliberate Ignorance

Insance Clown Posse is a rap group known for dressing up like clowns and demonstrating proficiency with using the word "fuck" as an adjective or adverb. Their fans, called Juggalos, often border on the fanatical. Recently the group released a song called "Miracles" in which they assert that all sorts of everyday things are miracles. This list includes eclipses, giraffes, magnets, rainbows, butterflies and how children look like their parents.

Warning: the following video is painful. The pain comes not just from the stupidity of the lyrics but the fact that the music just sucks. Watch at your own risk.




By itself, this song might be dismissed as silly. However, the song contains the lyrics "And I don't wanna talk to a scientist/Y'all motherfuckers lying, and getting me pissed." When this song came out, there was a fair bit of uproar. Although science is abused by people everywhere in the political spectrum, it is rare for such a direct attack to occur. Taken together with the fact that every single thing listed in the song was some bit of science that is normally explained before people are in 9th grade, the reaction was predictable and humorous. They included Learn Your Motherf#@kin’ Science: A Textbook for Juggalos(amusing but for the fact that they explain rainbows incorrectly) and Rebecca Watson's imagining of how the song lyrics were devised.

This could have ended there. But Insane Clown Posse managed to dig themselves in into an even deeper hole. In one interview, the interviewer asked them if they knew yet how magnets worked and they replied that they were proud that they did not. They also wrote an official response to criticism of the song in which they made it clear that not only don't like learning but "We feel like these haters are the big dumb, popular jocks ganging up on the little class clown scrub." It isn't clear to me in what universe Insane Clown Posse operates if they think that the people who like science were the "big dumb, popular jocks." I'm also a bit confused by the notion that the people who know things like how a rainbow works are "dumb" but it may just be that I'm too stupid to understand. Similarly, it may be due to my stupidity that I'm wondering how they would be sure to put a comma between "dumb" and "popular" but not between "big" and "dumb." Is big actually an adverb modifying dumb? Is "big dumb" some sort of compound adjective? If only scientists were popular; I suspect that such a world would be a much better place.

This could have ended there but then Insane Clown Posse made another mistake: They had a concert in San Francisco, a city full of nerds. Noisebridge, a volunteer group devoted to science education around San Francisco decided to use the Posse's visit to their fair city as an opportunity to educate the Juggalos. They made a series of posters explaining how various things work, with titles like "Fuckin' butterflies, how do they work?" They then dressed up with Juggalo-style clown facepaint as well as labcoats, and went to the concert. They videotaped the result:



As you can see in the video, the Insane Clown Posse roadcrew had seen the Noisebridge website in advance where they had planned the event. Apparently, the Insane Clown Posse was not happy with these scientists, forced them to leave, and tried to take away their video camera. Now, one might think that this was just the work of an overzealous roadcrew claiming to have authority from the people in charge, but there's the not so tiny detail that one of the Insane Clown Posse members bragged on his Twitter account that they "ran those scientist haters off." I wish I were making that up. If I had seen the phrase "scientist haters" in any other context I would have guessed that it meant people who hate scientists. What we have here are people who are so proud of their ignorance that they actually interfere with other people engaging in a humorous attempt to educate.

Now, what could possibly make this situation worse? If you guessed "Insane Clown Posse claims to be religious" then you win a gold star. The exact nature of the band's religious status is not clear. Although songs include lyrics about murder, cannibalism, and necrophilia, the individuals who commit these actions always suffer at the end. They have a series of songs centering around a Carnival which punishes people, and the last such song contains the lyrics "Truth is we follow GOD, we’ve always been behind Him. The carnival is God and may all juggalos find him! He’s out there!” And did I mention they hate gays? So the Insane Clown Posse apparently, hates science, hates gays, and believes in a deity whose chief job is to punish people. If you're wondering if they self-identify as Christian then you win another gold star.

Still, the level of anti-science attitudes here is shocking. It resembles nothing more than a caricature of what is wrong with contemporary Christianity. I don't think that band's Christianity has anything deeply to do with their anti-science attitude. For example, they haven't come out strongly against evolution. The correlation in this case is to some extent probably incidental. But there is a real lesson here and it is contained in their strange idea that scientists are the "big, dumb jocks." That idea is very divorced from reality. How can someone be so wrong about the world around them? Let me suggest that it is because science is the best method we have of finding out about the nature of reality. It isn't the only one, but it is the most reliable and the one that has given us the most fruit. So, when you take an attitude that is so anti-science and against the minimal knowledge of how basic genetics works, or any of a hundred other subjects, you are going to not have good methods for telling whether your beliefs about reality map accurately to reality. And the more effort you make to deny science, the further divorced from reality you will become, to the point where you believe the nerdy guys who work in the labs and like to understand how things work are actually "big dumb, popular jocks."

Israel and The Flotilla to Gaza: Another Excuse to Promote Family Members

My father has a piece up at the Oxford University Press blog arguing that Israel was justified in its actions regarding the flotilla to Gaza. I'm not convinced by the argument. The situation seems complicated especially in that it is not clear that all the items that Israel is not letting are items that could be used to make weapons. The Israeli blockade has stopped hostilities, but it goes beyond that, effectively preventing the maintenance and rebuilding of Gaza's sewage treatment and power plants (See this summary). If the blockade was narrowly tailored to save Israeli lives it would be more morally defensible.

It seems that given the large amount of shouting about this issue, that this is not a bad opportunity to discuss some unambiguous facts about the current situation.

First, it is clear that the blockade has worked to protect Israeli lives. Rocket attacks from Gaza have become nearly non-existent after the blockade.

Second, it is clear that the motivation for the blockade is not primarily out of racial animosity for the Palestinians, although that may play some part. The evidence for this is that the West Bank, controlled by the moderate Fatah faction, is not under any similar restrictions.

Third, it is not clear, and likely will not become clear for the foreseeable future, who started the fighting on the Mavi Mamara. Eyewitness accounts are conflicting. Note that who started the fighting also has zero connection to whether or not the blockade is morally or legally justifiable.

Fourth, Hamas is refusing to accept the flotilla aid until demands are met. If one believes that this aid is vital, then this is a clear example of Hamas willing to let the people of Gaza suffer to suit its own political aims. However, it is important to keep in mind that this despicable behavior by Hamas is also not relevant to whether the blockade is morally or legally justifiable.

In any event, my father's piece makes a pretty strong argument, so go and read.

A Quick Note on the Mojave Cross

Last entry, I talked about the Supreme Court of the United States ruling about the cross in the Mojave desert. The ruling was wrong-headed and I am highly worried about the broader implications of allowing the cross to stand. However, at the moment I'm more worried by recent news that the cross was just stolen. This is not a solution. There are situations where violations of rights are so severe as to merit breaking the law to preserve them. This is unambiguously not one of those situations. Whoever did this should be ashamed of themselves.

A Short Rant on Religious Freedom and the Courts

Two recent events make it all the more clear that religious liberty for all is in jeopardy. Recent events show that even in civilized, Western countries, basic religious freedom, whether for believers, agnostics or atheists hangs by a series of thin threads. Great Britain and the United States provide the two most recent examples.

The United States Supreme Court ruled 5-4 that game playing with transfers of small plots of land allow the federal government to endorse specific religions. Readers are likely familiar with the ongoing case of the war memorial cross in the Mojave desert. The federal government attempted to transfer the land just surrounding the cross to a private veterans group to prevent any issues with the establishment clause. The court decided not just that this game playing was acceptable but that it probably wasn't even necessary. Justice Kennedy wrote:

A Latin cross is not merely a reaffirmation of Christian beliefs. Here, a Latin cross in the desert evokes far more than religion. It evokes thousands of small crosses in foreign fields marking the graves of Americans who fell in battles, battles whose tragedies are compounded if the fallen are forgotten.

Because of course, the fact that fallen soldiers of other religions are buried with other symbols is of course besides the point. And the fact that the commonality of the cross is solely because the US is a majority Christian nation is besides the point. And the fact that some (small) Christian groups are actually uncomfortable with the cross as a religious symbol is also besides the point.

But not to worry, since while the US Supreme Court is busy whittling away at basic separation and church and state, the British are busy destroying the rights of people to say things which offend religion. Apparently leaving anti-religious tracts around in the wrong places in England can get you convicted. After leaving anti-religious tracts in an airport prayer room, Harold Taylor received a six-month suspended sentence and is now not allowed to carry anti-religious leaflets in public. As far as I can tell, the tracts left by Taylor were deeply unfunny cartoons that wouldn't have convinced anyone of anything. Taylor probably needs a few lessons in how to be funny and not just annoying(Jennifer McCreight could likely teach him a thing or two). But that shouldn't be a criminal offense either. At least Taylor's situation would still be unambiguously unacceptable in the United States.

These events highlight how important it is that Obama's next Supreme Court nominee be a strong supporter of free speech. Unfortunately, his previous nominee, Sotomayor, has a mixed record on such issues. Let's hope the next one is better.

On the Coming Singularity

Much has been said in the last few years about an approaching technological Singularity, beyond which humans or humans' descendants will be so far beyond anything we understand today that comparisons would be meaningless. I do not believe that the Singularity is imminent.

What do people mean when they speak of the Singularity? There are a variety of such notions, but most versions of the Singularity focus on self-improving artificial intelligences. The central idea is that humans will not only construct functioning artificial intelligences, but that such AIs will be smarter than humans. Given such entities, technological progress will increase rapidly as the AIs make discoveries and inventions that humans would not. This effect will be self-reinforcing as each successive improvement makes the AIs smarter. There are variations of this idea: Other Singularity proponents, generally described as Transhumanists emphasize genetic engineering of humans or emphasize direct interfaces between the human brain and computers. I am skeptical of a Singularity occurring in the near future.

Certainly Singularitarism is seductive. Variations of it make for great science fiction (Charlie Stross' Eschaton is an excellent example) and some version of the Singularity, especially those that involve humans being downloaded into immortal computers or the like, are appealing. Singularitarism may sometimes border on a religion, but it has the virtue of a minimally plausible eschatology, one that doesn't require the intervention of tribal deities, just optimistic estimates for technological and scientific progress. And to be sure, there are some very smart people such as Eliezer Yudkowsky who take the Singularity very seriously.

The most common criticism of Singularitarism is that we will not develop effective AIs. This argument is unpersuasive. There's no intrinsic physical law against developing AIs; we are making slow but steady progress; and we know that intelligences are already possible under the laws of the universe.We're an example.

While I reject most of the common criticisms of a coming Singularity, I am nevertheless skeptical of the idea for two reasons. First, while human understanding of science and technology has been improving over the last few hundred years, the level of resources it takes today to produce the same increase in understanding has increased dramatically. For example, in the mid 19th century a few scientists could work out major theories about nature, such as the basics of evolution and electromagnetism. Now, however, most major scientific fields have thousands of people working in them, and yet the progress is slow and incremental. There seems to be a meta-pattern that as we learn more we require correspondingly more resources to make corresponding levels of progress. Thus, even if we develop smart AIs, they may not lead to sudden technological progress.

Second, we may simply be close to optimizing our understanding of the laws of physics for technological purposes. Many of the technologies we hope to develop may be intrinsically impractical or outright impossible. There may be no room-temperature superconductors. There may be no way to make a practical fusion reactor. As Matt Springer suggested (here and here), we might activate our supersmart AI, and then it may say "You guys seem to have thought things through pretty well. I don't have much to add." This seems to be a common problem with Singularity proponents. It is a common argument by Singularitarians that essentially all challenges can be solved by sufficient intelligence. I've personally seen this argument made multiple times by Singularitarians discussing faster-than-light travel. But if it isn't allowed by the laws of physics than there's nothing we can do. If in a chess game white can force a checkmate in 3 moves, it doesn't matter how smart black is. They'll still lose. No matter how smart we are, if the laws of physics don’t allow something then we won’t be able to do that thing, any more than black will be able to prevent a checkmate by white.

There's a third problem with Singularitarism beyond issues of plausibility: It doesn't tell us what to do today. Even if no one had ever come with the Singularity, we'd still be investigating AI, brain-computer interfaces, and genetic engineering. They are all interesting technologies with potentially have major applications to help us answer fundamental questions about human nature. So in that regard, the Singularity as a concept is unhelpful: It might happen. It might not happen. But it tells us very little about what we should do now.

Newest Skeptics Circle

Over at the Digital Cuttlefish there's a new Skeptics Circle up. It has a lot of good posts. You can tell that it is worth reading because it includes my recent post here on skepticism and the scientific method. So go check it out.

Hank Skinner: What You Can Do.

In an earlier post I briefly discussed the case of Hank Skinner. Skinner is scheduled to be executed in Texas for a murder. It is very likely that Skinner is innocent. For a decade now, Texas has systematically blocked every attempt by Skinner to get DNA testing that could prove his innocence. But there is something you can do. The Innocence Project is trying to get permission for DNA testing. Right now, they need a stay on Skinner's imminent execution. So go send a note to Governor Rick Perry. It only takes a minute and every response helps. I know that I have some readers in Texas. It is important for everyone to contact the governor but if you are a Texas voter it is particularly important. Your voice matters. Don't be silent. We have enough innocent blood on our hands already.

Hat-tip to Katherine for pointing out this petition.

Edit: The Supreme Court has issued a stay on Skinner's execution. However, this may not lead anywhere so this petition could still be relevant.

The Skeptical Movement, Science and Naïve Popperism

Members of the modern skeptical movement frequently emphasize their use of the scientific method. Moreover, when discussing the scientific method and whether a given claim is scientific, members of the skeptical movement frequently emphasize falsifiability and experimentation. Both of these tendencies are problematic.

The organized skeptical movement has done a very good job over the last 30 years promoting skepticism and critical thinking. The movement has helped people understand the deep problems with many superstitions and pseudosciences. However, the skeptical movement’s characterizations both of how the movement functions in regard to science and how science functions are inaccurate. Moreover, the movement tends to exaggerate the degree to which falsifiability matters in science.

Let us first examine the claim that the skeptical movement uses the scientific method. No matter how one characterizes science and the scientific method, a central part of the method is experimentation and observation. However, the vast majority of skeptics will not engage in direct experimentation or observation of data nor in fact should they. For example, in an earlier blog post, I discussed why claims of ghostly interference with electronics were extremely implausible. I didn’t need to engage in any experiments to reach that conclusion. I and the commentators in the thread discussed the matter based on what we reliably knew about the universe (especially how electronics work) and then made logical conclusions based on those results. No part of that process required any use of the scientific method.

If we wanted to investigate the claim in more detail, we might try to do actual experiments. But I can dismiss the claim of ghostly interference with electronics with a high degree of probability without experiments. Similarly, I can dismiss homeopathy without doing experiments or without such experiments having been done by anyone since the theory of homeopathy contradicts basic understanding of how the universe functions. The vast majority of skeptics will never actually use the scientific method, but rather rely on small bits of science and a lot of critical thinking. That’s fine. The movement is doing good work that way. But we need not pretend when talking to people that we’re engaging in science when we aren’t. This is all the more a concern because the emphasis on science distracts from the most important part of skepticism- careful critical thinking.

Skeptics often characterize science poorly. Skeptics frequently emphasize the need for claims to be falsifiable in order for them to be scientific. The philosopher Karl Popper first proposed that the demarcation between science and non-science is falsifiability- the ability to falsify a claim. Thus, in a classical Popperian framework, claiming that there is an invisible, intangible dragon living in my bathroom is not scientific because the claim is not falsifiable.

However, naïve Popperism is not a good description of science as a whole. While falsifiability is a useful approximation of what is often scientific, there are many problems with it as a description of all forms of science. For example, as pointed out by Quine, people can add defensive hypotheses to defend an underlying hypothesis; it is far from clear when such defensive hypotheses are acceptable and when they are not. In Quine’s formulation, a defensive hypothesis is a hypothesis that is added to prevent the falsification of another hypothesis. Thus, for example, to return to the case of an invisible dragon in my bathroom, you could try to test for its presence by searching on spectra other than visible light (such as looking at infrared light). When no evidence is found using that method, I might add the defensive hypothesis that the dragon also doesn’t interact with infrared light. As I add more and more hypotheses to counter each experiment, I prevent my claim from being falsified, but, at any given point, the claim that a dragon is in my bathroom remains falsifiable – in theory at least. In portraying a scientific method which relies completely on falsifiability the skeptical movement ignores issues such as those raised by defensive hypotheses.

Unfortunately, the situation becomes even more complicated because sometimes one can add defensive hypotheses and still do good science. For example, consider the history of our understanding of the solar system. In the early 1600s, astronomers adopted Kepler’s model of the solar system in which planets orbit around the sun in ellipses. Subsequently this model was refined further by Newton whose mechanics gave orbits nearly identical to those of Kepler but slightly more accurate (essentially if there is a single planet around a star then Newtonian mechanics predicts an orbit that is a perfect ellipse. But in fact, gravitational attraction between planets makes the orbits slightly non-elliptical). However, with this very accurate, very precise model, new issues arose. The orbit of the planet Uranus seemed to be slightly off from what it should be. Thus, Alexis Bouvard posited the existence of an as yet unobserved planet, which later became discovered and named Neptune. Bouvard’s hypothetical planet was a defensive hypothesis built to defend the more cherished hypothesis of Newtonian mechanics against being falsified by experimental data. Bouvard’s defensive hypothesis was good science; the defensive hypotheses about my dragon are not. It is not clear how one can easily distinguish between the good defensive hypotheses and the bad ones.

So how do we determine when defensive hypotheses are acceptable and when they are not? Imre Lakatos suggested that we should look to whether a hypotheses is fruitful: hypotheses that lead to interesting predictions and new questions are fruitful; hypotheses that required unproductive defensive hypotheses should be rejected. While I am partial to Lakatos’s viewpoint, such an approach renders the line between science and non-science inherently subjective.

In addition to the problem of defensive hypotheses, there are many other problems with a falsifiability as the sole line between science and non-science. Naïve Popperism is insufficient to describe the borders of science. Skeptics need both a clearer understanding of the scientific method and a clearer understanding of how the skeptical approach relies on science

Jack Chick and Consistent Theology

Two new Jack Chick tracts are up. They are both pretty mediocre. "The Royal Affair" tells the story of David and Bathsheba with a pretty standard threat of hellfire and brimstone at the end. There's nothing of note in the tract other than that Jack Chick apparently thinks that the word "literal" actually means "figurative." (Memo to Jack: David didn't go through a "literal hell." He went through a figurative hell. Figurative and literal have opposite meanings. They are not synonyms.)

The second tract, "Going Down?" is standard Chick tract but with a single interesting twist. It is not uncommon in Chick tracts for someone to have a near-death experience, briefly witness the horrors of hell, and then come back to life knowing about the terrible threat of hell. This tract is an example. However, whenever this happens in a Chick tract, the people who have experienced hell always then accept Jesus as their personal lord and savior. However, in this new tract, the person who experiences hell does not learn about Jesus but rather dies shortly thereafter being dragged back down to hell. Few tracts better illustrate the utterly random nature of the afterlife in Chick's universe: in this case, the return to this world appears to almost be a divine accounting error which doesn't even serve the minimal purpose of saving the individual's soul.

Contemplating this tract also leads to another issue: Chick's theology concerning the immediate afterlife is inconsistent. In most Chick tracts, when people die they stand before Jesus and are judged. In some tracts, such as the above, they are sent immediately to hell. I am aware of no tract in which someone dies and comes before Jesus only to come back to life. In a tiny minority of tracts (such as this one) people who die without Jesus instead go to a temporary realm to wait until they are judged on Doomsday.

Why is Chick's theology of the afterlife so varied? Does he realize how contradictory his various tracts are on this matter? The most obvious hypothesis is that Chick's theology has changed over time. However, there are no chronological trends in which of the three approaches to the afterlife he takes. I suspect that Chick simply does not care about the details of the afterlife that much since the primary issue is being saved or lost; all else is secondary. Thus, a combination of whim and plot-demands control the exact depiction of the afterlife. Given Chick's apparent lack of great intellectualism he may not even have given the matter enough thought to realize the inconsistent nature of his theology.

I do hope that the May tracts are better than this set. It is a big let down given that in January we had a tract about angels fighting werewolves.

Purim and Don't Ask Don't Tell

Today is Purim, the Jewish holiday which celebrates the events recounted in the Book of Esther in which Esther and Mordechai stop Haman's plans to destroy the Jews. The story of the Book of Esther is one of hidden identity and palace intrigue.

My twin has a piece up at the Huffington Post that looks at the story of Purim in the context of the Don't Ask Don't Tell. Aaron argues that the story of Esther, in which she hides her Jewish identity from the king until she is forced to reveal it to save her people, bears a similarity to the military’s current policy regarding gays. In particular, Esther hid her ethnic/religious identity and the king did not inquire about that identity until events required Esther to disclose the truth. Aaron argues that this ancient tale reflects a basic truth about policies like Don't Ask Don't Tell: they are inherently unstable.

I am not impressed by the piece. The claim that DADT is inherently unstable is not novel: I don't think that anyone, whether they are for or against gays in the military, thought that DADT had any long-term stability. Policies in which an identity is acceptable only as long as it is not blatant are by nature unstable since such policies generally arise when certain groups are discriminated against, but the discrimination is not universally accepted and therefore must be discreet. To continue to use Jews as an example, the quotas on Jewish student admissions to Ivy League schools prior to the 1960s worked in a fashion similar to DADT. Applicants who were obviously Jewish were covered by the quotas. But little effort was made to actively determine the identity of general applicants. (This is to some extent an oversimplification. Dan Oren's excellent book "Joining the Club" discusses this in more detail). This ambivalence was in part due to the fact that Jews were accepted enough that a serious backlash was feared from excessive enforcement of the anti-Jewish quotas. Similarly, DADT in the military came as a compromise when both gay rights groups and anti-gay groups had political power. Such a compromise is inherently unstable.

Aaron also does not address the fact it is not clear from the text why Esther kept her Jewish identity secret from the king. Aaron cites the traditional commentaries which weave elaborate stories of Esther keeping the various classical prohibitions of Judaism such as kashrut and Sabbath observance. Some of the classical commentaries say that Esther kept her Jewish identity hidden because of Persian attitudes towards the Jews. Others invoke other explanations. For example, according to some commentators, Esther kept her identity hidden because of her relation to the line of Saul, the first king of Israel. If it became known that she was of royal blood, her political position would have become much more complicated. Given the ahistorical nature of the story of Esther, it seems to me that the likely reason for her keeping her Jewish identity hidden is primarily to make an interesting story.

My twin correctly notes that there are good reasons to abolish DADT and allow gays to serve openly in the military. However, those reasons exist without any analogies to Biblical texts. We can make the correct decisions without recourse to ancient texts whether we see those texts as religious or literary in nature. DADT is bad policy. We don’t need the story of Esther and Mordechai to tell us that.

Two Quick Notes on Civil Rights

Unfortunately, I'm very busy this week and so haven't had much time to blog. Therefore I would like to quickly bring up two civil rights issues. First, Texas, the state known for executing people who were almost certainly innocent like Cameron Todd Willingham , is now set to execute another innocent man. Hank Skinner is set to be executed. The evidence against Skinner was based primarily on eye-witness testimony from a single witness who has since recanted. There are many other details about the case (such as the government's refusal to let Skinner have a DNA test) that make the situation appalling. Texas is going to execute an innocent man.

In the other news of appalling civil rights issues, we have an amazing act of censorship by Italy. An Italian judge has convicted three Google executives for violating Italian privacy laws. The crime apparently was running Youtube. in 2006, a group of youths uploaded to Youtube a video of them harassing and assaulting an autistic child. That's pretty despicable. And when Youtube received a legal complaint, they took the video down and cooperated with the Italian police in locating the children who made the video. Apparently, that is not enough. Any video which violates Italian privacy laws is now the fault of Google and Google employees can suffer both civil and criminal fines. Google has correctly outlined that this is a serious threat to free speech around the globe. This is all the more a problem because many civilized countries have extradition treaties with Italy. Considering the Italy is the same country which tried to require anyone in Italy uploading videos or writing blogs to register with the government, it seems pretty apparent that this is another example of Berlusconi and his corrupt media cronies trying to do their hardest to screw over media not under their control. Hopefully, either higher-level Italian courts will overrule this decision or the EU will step in.

Dick Cheney Undefeated

My twin has a piece up at the Huffington Post arguing that Dick Cheney's recent outspokenness is due in part to Cheney's unique political position as an undefeated Vice-President. Cheney is the first VP in a long time who did not end his political path in an electoral defeat. Aaron argues that this, combined with other historical factors, puts Cheney in a unique position where it is socially acceptable for him to be loudly critical of the current President. The piece is interesting although I think he doesn't address one reason why there is attention given to Cheney: The Republicans have no natural leader at this point and Cheney is one of the few people who potentially could fit in that position. In any event, the piece is worth reading and provides some interesting historic tidbits about prior VPs.

Orthodox Jews, Vaccination, and Mumps

I've discussed anti-science attitudes among Orthodox Jews in previous blog posts. I've also discussed how this has resulted in low vaccination rates among Orthodox, especially charedi, Jews. Now we are seeing the consequences. Over the last three weeks, a mini-epidemic of mumps has broken out in New York among the Orthodox population. The first cases started appearing this summer in Williamsburg, but there are now over 1500 cases and the epidemic has made inroads into the general non-Orthodox population. Apparently while a majority of the Orthodox Jews are vaccinated, the level of vaccination was reduced enough that herd immunity no longer applied. Quoting from the LA Times:

Mumps is marked by a swelling of the salivary glands, giving the victim a characteristic chipmunk-like appearance. Most victims have fever and headache, and a few suffer from hearing loss, meningitis and swollen testicles that can lead to infertility. It was once a common disease in the U.S., with an average of 186,000 cases per year before the mumps vaccine, now included in the mumps-measles-rubella, or MMR, vaccine was introduced in 1967. The mumps part of MMR is thought to be the least effective of the three vaccines, with 73% to 91% of those vaccinated obtaining proteciton after one dose and 79% to 95% after two doses.

Patient zero in the current outbreak was an 11-year-old boy who returned from England on June 17. Mumps has become more common in that country recently because of the substantial number of parents who refuse to let their children receive the MMR under the misguided belief that the vaccine can cause autism. About 7,400 cases of mumps were reported in Britain last year.

Orthodox Jews have accounted for more than 97% of cases, and the majority -- 61% - -are among 7- to 18-years-old. More than three-quarters of the patients are male. Among those for whom vaccination status is known, 88% had received one dose of MMR and 75% had received two doses.

The threat of sterility needs to be especially emphasized. In Orthodox Judaism, there are few things more important than having children. Mumps can induce infertility in both males and females. It is not at all unlikely that children who have gone through this epidemic will have trouble finding marriage prospects. Thus, the failure to vaccinate has produced what may become terrible, long-term problems for many children for the rest of their lives. The Orthodox unwillingness to vaccinate has become a self-inflicted wound. In this case, anti-science attitudes were far from harmless and the results may yet grow to more seriously threaten both the Orthodox population and other people as well. Failure to vaccinate children creates serious risk to your children and the people around your children. Vaccinate. For some of these children, it is already too late. They will bear the physical and social scars of their parents' decisions.

Math Anxiety, Math Education and Gender Expectations

A recent study has shown that young girls in the United States who are taught by teachers with math anxiety are more likely themselves to develop anxiety of about math. The study is by psychologist Sian Beilock et al. at the University of Chicago. Her research looked at second graders’ anxiety levels in mathematics. She found that, with her sample, there was no correlation between gender and attitude towards math at the beginning of the school year. However, by the end of the school year, girls were much more likely to develop math anxiety. Moreover, girls were much more likely to develop such anxiety if their female teachers had math anxiety. Rather than summarize all of the more interesting details in the study, what follows first is a large quote from the study followed by my comments:

If it is simply the case that highly math-anxious teachers are worse math teachers, one would expect to see a relation between teacher anxiety and the math achievement of both boys and girls. Instead, teachers with high math anxiety seem to be specifically affecting girls’ math achievement—and doing so by influencing girls’ gender-related beliefs about who is good at math.

This study explores the relation between female teachers’ math anxieties and their students’ math achievement. Thus, it is an open question as to whether there would be a relation between teacher math anxiety and student math achievement if we had focused on male instead of female teachers. In one sense, the lack of male elementary school teachers in the United States makes this a hard question to answer. Yet, it is an important question, given research suggesting that girls are more socially sensitive than boys in early elementary school (16). Thus, it is possible that even with male teachers, a relation between teacher anxiety and female student achievement might occur. Nevertheless, the literature on math anxiety, gender modeling, and the impact of negative stereotypes on achievement lead us to speculate that any relation between male teacher anxiety and girls’ math achievement would be obtained through a different route than the one proposed here. Moreover, in the current work, the relation between female teachers’ math anxieties and girls’ math achievement was mediated (or accounted for) by girls’ beliefs that boys are better at math. Hence, it seems unlikely that a male teacher’s math anxiety would affect girls’ math achievement by pushing girls to confirm that boys are good at math.

In addition, children do not blindly imitate adults of the same gender. Instead, they model behaviors they believe to be gendertypical and appropriate (9). Thus, it may be that first- and secondgrade girls are more likely to be influenced by their teachers’ anxieties than their male classmates, because most early elementary school teachers are female and the high levels of math anxiety in this teacher population confirm a societal stereotype about girls’ math ability (2). This match between teacher math anxiety and societal norms would not hold for male teachers exhibiting math anxiety. However, if such a correspondence is important in influencing student achievement, we would expect that for school subjects for which girls are stereotyped to excel (e.g., language arts), male teachers’ anxieties would have an impact on male more than female students’ achievement.

It is important to note that the effects reported in the current work, although significant, are small. There are likely many influences on girls’ math achievement and gender ability beliefs overand above their current teachers’ anxieties. For instance, previous teachers, parents, peers, and siblings who either do or do notmodel traditional academic gender roles may play an important part in shaping girls’ gender ability beliefs and their math achievement more generally. Exploring these relationships—in addition to the influence of both male and female teachers—will help to elucidate the full range of social influences on student achievement.

In conclusion, we show that female teachers’ math anxiety has consequences for the math achievement of girls in early elementary school grades. Given that this relation is mediated by girls’ gender ability beliefs, we speculate that female teachers model commonly held gender stereotypes to their female students through their math anxieties. These findings open a window into gender differences in math achievement and attitudes that emerge over the course of schooling.

Interestingly, math anxiety can be reduced through math training and education (17 –19). This suggests that the minimal mathematics requirements for obtaining an elementary education degree at most US universities need to be rethought. If the next generation of teachers—especially elementary school teachers—is going to teach their students effectively, more care needs to be taken to develop both strong math skills and positive math attitudes in these educators.

How should we respond to this study? As with all initial scientific studies, the data is by its nature tentative, but in this case it looks very robust.Consequently I will for the remainder of this post assume that the phenomenon as described in Beilock et al. is accurate.

We currently focus most of our resources aimed at getting young women to be confident in math at the middle school and high school level. Moreover, prominent celebrities who have tried to deal with this problem have focused almost exclusively on this older age cohort. Danica McKellar for example has focused on encouraging mathematical confidence and learning in middle school girls. This new study suggests that much of the damage done to girls’ mathematical confidence occurs at a very young age. Thus, we may need to rethink where resources are being allocated. Unfortunately, this study does not as of yet include any long-term follow-up. So how much of this early math anxiety is correctable later is not clear. Aside from this sort of vague generality about resource allocation, here are four concrete proposals that need discussion.

First, let’s get the most controversial possibility out of the way: We may want to consider more direct encouragement of males to engage in elementary school teaching. Put less politely, we should consider affirmative action and other incentives to encourage males to go into elementary school teaching, at least for math. While this study showed that young girls picked up on the math anxiety of their female teachers, it is clear that young males did not gain math anxiety from female teachers. Moreover, math anxiety is simply less common among males. Thus, male students will be unlikely to pick up math anxiety, and female students will not pick it up from male teachers until they are older. This proposal has a number of problems. Foremost among them is that it assumes that male teachers will not act in an overly sexist fashion, either explicitly or implicitly denigrating female mathematical ability. Unfortunately, it is clear from anecdotal evidence that many teachers of both genders do explicitly disparage young girls’ mathematical ability. See for example this thread at SkepChick . Moreover, the exact impact of male teachers is far from clear: The study looked only at female teachers. Without more data about how students of both genders interact with male teachers both with and without math anxiety, this proposal must by nature be extremely tentative. The argument can be made that this will send a bad message to young children, i.e., that only males can teach or do math. However, that’s erroneous. Currently, around 90% of elementary school teachers are female. If we replace the females with math anxiety with males without math anxiety or even males with mild math anxiety, the fraction of teachers who are male will still be well below half. So this step also helps correct for a pre-existing gender disparity in elementary sc hool teaching.

Second, and almost as controversial as the first proposal, we can encourage teachers, especially females, to not go into elementary school teaching if they have math anxiety or simply aren’t very good at math. Unfortunately, we already suffer serious problems in the United States getting qualified people to teach elementary school. So directly altering who we encourage to become teachers is non-optimal. Similarly, increasing the required level of math background for elementary school teachers is not a good response. Moreover, as Beilock discusses, proper education can remove or reduce math anxiety. This leads directly to the third possible response.

Third, we must take more steps to directly reduce math anxiety in teachers and people planning on becoming teachers. This should likely focus on female teachers or teacher-candidates who have shown to have serious math anxiety issues. We can introduce them to additional areas of math, where the math is easy to understand and fun. Very elementary number theory and graph theory may be relevant areas. More broadly, we can also have them play mathematical games that get them more comfortable with the idea that math can be fun. Zendo for example would be an excellent potential confidence builder.

Fourth, we can take direct steps to expose young females to mathematically confident females. One method of doing so is to have the math sections of elementary education taught by separate teachers who are more mathematically confident. Even in schools with high percentages of teachers with math anxiety, some teachers will still likely be mathematically confident. Having those teachers handle the math teaching for other teachers (or possibly specializing to only teach math) is an option. Also, we can encourage young girls by having them directly interact with female mathematicians. Part of the problem is that mathematically confident females generally go into industry, sciences or upper tiers of academia, not elementary school teaching. So, mathematicians and scientists should visit local elementary schools. If schools can regularly sponsor visits by firefighters, police officers and members of other vocations and professions, there’s no reason that mathematicians and scientists can’t do the same thing. It doesn’t take much to show up and say “Hey! Look! I’m a lady who does math. And I enjoy it!”

Fortunately, resources which are spent encouraging the general public and children of all ages to be more mathematically confident can potentially work in general to help the situation with female students. Thus, work like Steven Strogatz’s new regular column in the New York Times to help make math more accessible to the general audience can be helpful.
No matter what happens we need to look at this data dispassionately at the same time as we try to gather more information about the transmittable nature of math anxiety. As a society we are short-changing many bright young females. Because those students then do not go into math-intensive areas of study,the society suffers. These problems need to be addressed. We are not doing enough now to address them.

Barack Obama, The US Senate, LBJ, and Gratuitous Promotion of Family Members

My twin has a piece up at the Huffington Post arguing that Obama should take a lessons from Lyndon Johnson in how to work with the Senate. The central thesis is that Obama needs to take four lessons from Johnson. I'm not convinced that Aaron is completely correct here. I found his earlier piece arguing that the Democrats should force the Republicans to engage in genuine filibusters to be more persuasive. Both pieces are worth reading. At this point, it seems apparent that many Republican senators have zero interest in actually running a government and are genuinely trying to just be as obstructionist as possible. Richard Shelby's attempt to put a hold on every single Obama nominee seems to be the logical conclusion of the current Republican behavior. Both of Aaron's pieces are worth reading, but at this point, I suspect that Obama's best course of action at this point may be to try to get the public to understand how little cooperation he is getting from both House and Senate Republicans.

A Quick Note on a Silly, Pseudo-recursive Class of Functions

Let f(n) be a function from the natural numbers from the natural numbers. Suppose further that f(1)=1, and assume that f(n) is equal to the number of positive integers k that are less than equal to n and satisfy f(k) | k. Then it is not hard to show that in fact f(n)=n. Now suppose we instead look at the exact same thing, but insist that f(n) count the number of k that are at most n and satisfy f(k)|P(k) where P is some fixed polynomial with integer coefficients.

For some choices of P, we do not have any function f which would satisfy the desired recursion. For example, if P(x)=x+1 we don't have any function f satisfying the recursion. To see this, note that we have either f(2)=1 or f(2)=2. If f(2)=1, then f(1)|1, and f(2)|2, so in fact f(2)=2. Consider the other case where f(2)=2. If so, since 2 does not divide 3, we must have f(2)=1. Contradiction and nd of p.

Here's my question which I have not been able to make substantial progress on: Are there any valid choices of P and f that satisfy the recursion and don't have f(n)=n for all n?

Thoughts and links after the recent Massachusetts election

First, I have to say that a lot of liberals seem upset over Coakley's loss to Brown. Frankly, given Coakley's poor record on civil liberties (including her despicable behavior handling the Amirault situation) I can't find myself getting worked out over the matter. Two pieces I recommend on the matter: My twin has a piece at the Huffington Post talking about lessons the Democrats should take away from this election. Ed Brayton has a piece up talking about what this says about Coakley and the Democrats chances for their legislative agenda. Brayton makes the point that the Democrats still have strong majorities in both the House and Senate. So if they can't push through their agenda then it is hard to explain it as anything other than general incompetence.

A Different Take on Ireland's New Blasphemy Law

Readers are likely aware that Ireland has a new anti-blasphemy law. The response to the law has been understandably negative. It is hard to reconcile outlawing of blasphemy and modern notions of free speech. The law has been met with mockery and derision. See for example here and here. However, Whiskey Fire has an interesting piece up arguing that the law makes much more sense in context. In particular, an anti-blasphemy law is required by the Irish Constitution. The new blasphemy law helps actually minimize the chance that blasphemy prosecutions will occur since the large fines mandated by the law force any blasphemy prosecutions have to occur under the Irish High Court rather than the circuit courts. This effectively prevents local yahoos from filing blasphemy charges. Whiskey Fire's entire piece is very worth reading and is a good example of how political situations can often be more complicated than they first appear.

Hat tip to Almost Diamonds.

Jack Chick, Native Americans and Henotheism

Everyone's favorite Christian fundamentalist tract writer, Jack Chick, has a new tract, Crazy Wolf. This tract is apparently aimed at Native Americans and attempts to show how their traditional religious beliefs are really demon worship.

The tract starts with two stereotypical Native Americans talking about how one of their own, Mary, has accepted the "White God" and how they are unhappy with her. One of them, Margaret, is particularly unhappy because Mary tried to evangelize to Margaret's young daughter Sarah. I guess Jack Chick can't quite understand why someone might be justifiably upset if someone tried to interfere with one's kids’ religious upbringings.

Margaret then discusses how they tried to get a medicine man to put a curse on Mary, but "some strange power" prevented the medicine man's curse from working. So, they decided to ask the assistance of a powerful witch named Crazy Wolf.

Notice that every individual so far in this tract has an English name except for the old, evil witch. I guess it's just a sign of how baddass he is that he as stereotypic name, or something like that. At least his name isn't "Injun Joe."

Of course, Crazy Wolf tries to use his Devil-granted powers to shapechange into a massive wolf to eat Mary. He fails because of Mary and her pastor's prayers. An angel materializes which beats up Crazy Wolf. Mary then further prays that Crazy Wolf will accept Jesus as his personal lord and savior.

We all know this part of the routine: Injun Joe, sorry, Crazy Wolf, talks to Mary and accepts Jesus as his personal lord and savior. Crazy Wolf declares that "my real name is Billie Wolf." Apparently, he has a good name, but it only gets used once he's saved. Then, as happens in so many Jack Chick tracts, he dies a violent death, as Margaret shoots him with a shotgun in revenge for failing to kill Mary.

Crazy Wolf goes to heaven and is told that "You just made it by the skin of your teeth! You believed on(sic) Me and that saved you. Billie Wolf, enter thou into the joy of thy Lord." Margaret of course goes to hell to burn for eternity.

This tract raises some interesting issues about Chick's theology. For example, as with some prior tracts, demonic forces are not only real, but very powerful. There's an almost henotheistic aspect to the story. Henotheism is the belief that many deities exist while only worshipping one. Chick’s Jesus becomes relevant primarily after death or during the apocalypse. In Chick’s pantheon, there are many deities but Jesus, the deity of death and destruction, reigns supreme.

Implied in this narrative is the teaching that prayer for a soul can actively lead to salvation. This is confusing. The entire point of Chick’s theology is that all that matters is whether an individual has accepted Jesus or not. If God and prayer can alter that decision, then the even minimal theological explanation of why everyone is not saved breaks down. It becomes within God’s power to alter whether or not individuals are saved. This renders the primary evangelical apologetic of such a deity non-feasible. In particular, damnation is usually defended by arguing that God cannot force people to accept Jesus as their savior. Yet here we see God apparently doing exactly that.

The importance of names is also worth noting. Aside from the not so subtle racism associated with Chick’s name choices, this is part of a general pattern in Chick's theology. What one calls something matters. Thus, for example, in previous tracts aimed at Islam, Chick argues that Allah is not just another word for God. This brings up an issue: Consider the following hypothetical: Someone is explained the entire evangelical belief system but with the words "Satan" and "Jesus Christ" swapped throughout. Then that person accepts Satan as personal lord and savior, does Chick think that that person is saved or not? If names matter then presumably Chick would believe that such an individual is not saved.

The tract of course ends with the usual warning that only Jesus saves. But the wording is worth noting: "Trusting religion, idols, ceremonies, nature gods or the Virgin Mary to save you is only chasing the wind!" That last phrase is not normally in these tracts. I suspect that to Chick "chasing the wind" sounded like an Injun phrase. This fits Chick's Jesus using the phrase "skin of your teeth" which is much less formal than how Chick's faceless, glowing Jesus normally talks.

So what is the overall lesson of this tract? The take away message seems to be that Native Americans are primitive savages but they get cool magical powers. And as long as you accept Jesus eventually, you get to play with the powers for a long time.


Note: Between drafting and posting this review I ran across another review that is worth reading.

Unscientific America and Pluto: The problem isn't the scientists

I recently read Chris Mooney and Sheril Kirshenbaum's Unscientific America. Their thesis is that anti-science attitudes and the general lack of scientific knowledge in the United States are not the fault of the public or the media, but largely of scientists failing to communicate effectively. My response to this thesis is not positive. This book has been extensively discussed elsewhere. (Of these discussions, I recommend PZ Myers take, Joshua Rosenua's, this balanced analysis by Scicurious, this positive review by Chad Orzel, and this review by Mike at Real Climate)

A major theme of the book is that scientists are out of touch with the general public and spend too much time mocking the public or denouncing journalists rather than trying to engage the public and journalists to understand science. This argument may have some merit. However, the authors offer little evidence for their claim. Simply put, Mooney and Kirshenbaum are wrong: bad science journalism is far more the fault of bad science journalists than it is the fault of disengaged scientists.

Mooney and Kirshenbaum’s primary example of scientists being out of touch with the general public is the 2006 decision to recharacterize Pluto. After the discovery of Eris in 2005 and discovery of other similar objects, it became apparent to astronomers that consistent classification standards required that either Pluto be classified as a non-planet or that many more objects would need to be labeled as planets. Thus, in 2006, the International Astronomical Union constructed a new definition of planets which reclassified Pluto to the status of “dwarf planet.” Readers will likely recall the media outcry that erupted in response to this “downgrading” which included internet petitions and resolutions by various state governments supporting Pluto’s right to continue to be a planet. Mooney and Kirshenbaum point to the popular reaction and astronomers’ failure to anticipate or understand the reaction as an example of how scientists are out of touch with the general public. (There has been some discussion over the validity of Mooney and Kirshenbaum’s point and see for example these two remarks).

However, while reading Unscientific America, serendipity struck and I had occasion to read an article in the December 26, Puerto Rico Daily Sun, from Scripps Howard News Service. This article discussed extrasolar planets and how astronomers have recently discovered smaller extrasolar planets which are closer to what life-sustaining planets would look like. From the article:

"The first extrasolar planets were discovered 15 years ago, and now more than 400 have been found and at an accelerating pace. The early discoveries were gas giants on the order of Jupiter and Pluto and they have orbited far too close to their stars. But as techniques have improved, astronomers are able to identify smaller, occasionally rocky, planets, orbiting far enough from their stars to be close to what is considered a habitable zone."

The author is apparently trying to talk about astronomy while discussing "gas giants on the order of Jupiter and Pluto." Of course, Pluto is not a gas giant. Pluto is a tiny ball of rock, so small it isn't able to keep orbital debris out of its path. That's the entire reason it got downgraded from being a planet. It is small and rocky, not a gas giant. Anyone paying any attention to the faux controversy over Pluto should remember this. Indeed, anyone who remembers anything from grade school would know that Pluto is small and rocky.

This foolish statement about Pluto shows what is really wrong. While scientists may not be the best communicators, putting a majority of the blame for the status quo on scientists is wrong. The problem isn't the scientists. The problem is not that the scientists mistreat journalists and the media. The problem is that the media is full of people so ignorant that we get an article from a major news service claiming that Pluto is a gas giant. Not all journalists are this clueless. But cloning Carl Zimmer simply isn't a viable option. If we're going to deal with this problem, we need to focus on the actual causes. And poor journalism is far more the fault of ignorant journalists than it is of unengaged scientists.

Orthodox Judaism, Science, and Natan Slifkin

Both Orthodox and Ultra-Orthodox/Charedi Jews commonly reject many basic parts of the scientific understanding of the world. For example, many Orthodox Jews believe in a global Nocahian deluge some five thousand years ago and reject evolution. In the charedi world, this rejection of science is even broader. The charedi rejection of science is substantially different from that of other branches of Orthodoxy. Rather than simply reject specific theories based on their own theological predilections, charedim, including charedi leaders (called by their followers "Gedolim" which is Hebrew for "great ones") take an actively hostile view of science.

I was unaware of the depth of charedi fear of and disdain for science until I recently began examining the controversy surrounding Natan Slifkin. Slifkin is a charedi Rabbi who wrote a series of books looking at the interplay between Judaism and biology. Slifkin made three primary of arguments: First, he argued that the evidence for evolution was overwhelmimg. Second, he argued that belief in evolution was not incompatible with Judaism. Third, he argued that the Rabbis of the Talmud could be wrong about science. For the charedim, the second two points apparently caused far more concern than the first. In 2005, many of the Gedolim joined to issue a ruling in which Slifkin was labeled a heretic. Possession and reading of his books was banned.

The charedi rejection of science goes far beyond simple opposition to evolution. For example, I was recently disturbed to learn from a conversation with Slifkin that some major charedi Rabbis believe in spontaneous generation of small rodents. I had been aware that such beliefs had survived until the early 1900s, but I was shocked to find out that many prominent charedi rabbis still believe spontaneous generation of small creatures. The charedi attitude towards science is in many ways connected to a deep worry of persecution. Moshe Sternbuch, the current chief Rabbi of the Edah Charedis, a prominent organization of Israeli charedim, stated that scientists say the world is old because "they want to refute the words of our Sages and undermine the faith that exists amongst the Jewish people. Their main concern is to try to shake the faith in G-d — which has been accepted by us generation after generation."

For another example, see these videos of Rabbi Aharon Schechter in which Schechter gets actively angry at the thought of people trying to investigate evolution, the age of the earth and related questions:






This attitude, one of perceived persecution and anger, seems to stem from two sources: First the charedi worldview is very wrapped up in the history of persecution against Jews. Thus, the charedim see any modern event in that light. Second, the charedi worldview is profoundly self-centered. They assume that essentially everyone cares about what they are doing. Thus, if scientists come to a conclusion that clashes with standard charedi beliefs, the charedi infer that the scientists are trying to target them. In this regard, comparison between the charedi leaders and the leaders of fundamentalist Christianity today is not favorable to the charedim. While many evangelical Christians and fundamentalist Christians reject much science, it is rare for their leaders to claim that scientists are trying specifically to destroy their religion.

However, the anti-science beliefs discussed here are not held by just the charedim. The modern Orthodox also have serious problems with much of science. Alexander Nussbaum has examined modern Orthodox attitudes towards science (see his article in Skeptic as well as Nussbaum's article "Creationism and Geocentrism Among Orthodox Jewish Scientists." in the January-April set of Reports of the National Center for Science Education). Nussbaum found that even among orthodox Jews attending secular colleges, a large fraction reject much of biology, astronomy, geology and other branches of science. About three quarters of the respondents when asked about the age of the Earth, said that it was less than 7000 years old. The vast majority (around 90%) believed that all land animals descend from animals on Noah's ark. Possibly most disturbingly, around a quarter of the students believed that evolution was not only false, but that scientists were deliberately concealing this fact.

Nussbaum also found that undergraduates majoring in scientific areas were less likely to accept many aspects of basic science. Nussbaum proposed that:

It seems that the science majors and degree holders — precisely because they were more likely to be exposed to evolution — were subject to additional community influences not to be “taken in” by the “heresy” they would hear, and were even less accepting of evolution. And individuals with a science background from that community have the added responsibility to use their knowledge and standing to promote religious doctrine in scientific matters.

Presumably the science majors would respond that they are more involved in science and so are more able to see the terrible problems with vast swaths of modern science.

While I had seen Nussbaum's work many years ago, I had generally assumed that something was wrong with his work. While these anti-science viewpoints were not unknown among the Orthodox students when I was an undergraduate at Yale, these views were not as popular as they appeared to be in Nussbaum's study. However, I'm now a graduate student interacting with students at Boston University. Here it seems that the profile of the Orthodox beliefs fits Nussbaum's data much better. Indeed, I recently found myself in a situation with six Orthodox students in the room and five out of the six believed in a literal global flood. When a conversation ensued, one student was unwilling to say whether he believed or not some of the more interesting claims in the Talmud such as the aforementioned spontaneous generation or the existence of the phoenix. That may have been in part due to the student not wanting to discuss the matter, but the overall reaction still agrees strongly with Nussbaum.

Why are otherwise moderate theists so willing to disregard large sections of modern understanding of the world? There are a variety of factors at play. However, one factor that is worth considering is the Orthodox attitude towards Talmudic rabbis, Talmud, and associated midrashic texts. While in some respects Jewish willingness to look at associated commentary or to interpret verses using Oral Law allows for moderation and incorporation of new knowledge. That willingness can also backfire. In particular, for many Orthodox Jews, statements made by Talmudic rabbis are by nature intrinsically infallible. Thus, instead of using the Oral Law as a way of reconciling science and religion, it is used to add additional statements that must be taken as literally true. whether they are about mice arising from mud, or birds burning themselves to regenerate for another life.

So far, this anti-scientific attitude does have some limits. I'm not aware of any Orthodox Jews (regardless of type) who believe in a flat earth. But geocentrism does certainly exist among Orthodox Jews. Most disturbingly, however, is that these anti-science views seem to be becoming more common rather than less in the Orthodox world, especially in the charedi world. The charedi world is not disconnected from the rest of the Orthodox world. If the charedi world becomes more extreme, it will likely pull the rest of the Orthodox world in the same direction.

If Modern Orthodox Judaism is to be taken seriously as a reasonable religion, able to survive in the modern world, then these trends need to be countered by responsible Orthodox leadership.