Kipli's Cage

As I commented before, the distinction between what goes on in public (in the public arena) and what is done by public officials as agents of the people is lost on some people. Including, apparently, Bill O'Reilly.

From an item at Media Matters:

From the June 27 edition of Fox News' The O'Reilly Factor, which also featured guest Tony Perkins, president of the Family Research Council:

O'REILLY: But if there are other things around it, then they should be able to have it, just like the Supreme Court. Right? There's a copy of the Ten Commandments right over the justice's head -- chief justice's head. But there are other, Magna Carta, things like that. So I mean, what's the rub?

MURRAY: Well, I don't think they should have it in any circumstances.

O'REILLY: You'd ban the Ten Commandments from any public exposition?

MURRAY: I think religious symbols are inappropriate for --

O'REILLY: All religious symbols?

MURRAY: Yes.

O'REILLY: OK, nothing. So secular society, religious symbols should be banned, kind of like in the Soviet Union and Red China?

MURRAY: Well, no, I think that people have a right to practice their religion. And I don't think public --

O'REILLY: You can't have it in a public arena?

MURRAY: In a public institution --

O'REILLY: Can't have it, ban it?

MURRAY: Yes. And I also --

O'REILLY: You know what you sound like? You sound like a fascist.

MURRAY: No, I --

O'REILLY: Yes, you do. Ban it.

MURRAY: No, I think public institutions should be neutral, should not have religious displays. I think people are free to practice their religion on private property in the way that they want to, but I think public institutions should not play a role in presenting religious --

O'REILLY: All right. What are you saying, Mr. Perkins? Did you figure out this ruling?

A common O'Reilly "debate" tactic is to interrupt his guest with short questions that seem to demand immediate answers: "All religious symbols?", "You can't have it in a public arena?", "Can't have it, ban it?" When he does that, the guest is thrown off: does he continue with his answer to a previous question or try to quickly 'clarify' the point and then continue? In the first case, O'Reilly simply repeats his question, leaving the impression that the guest is avoiding the issue, while in the second O'Reilly asks another question and spins the talk away to another point. In either case, the guest never gets a chance to completely state his position and comes out of the segment sounding like a dolt.

O'Reilly also likes to use tangential comments to get his guest off track. Here he does it with his comment "So secular society, religious symbols should be banned, kind of like in the Soviet Union and Red China?" Now the guest is left looking like he supported the Soviet Union totalitarian regime unless he tries to specifically address that issue. And zing! The guest is off message!

But here O'Reilly also demonstrates either his ignorance of the issues or his willful disregard for them. Notice how he goes from discussing religious symbols in a "public exposition" (which is vague, but the guest seemed to take it to mean an exposition by the government) to a "secular society" which in his mind means banning all religous symbols from any display in public whatsoever, thus banning them from the "public arena". The guest is left appearing to support not the removal of religous displays put in place by governmental bodies or officials but the banning of all religious symbols---cover up those crosses on church buildings! When the guest tries to clarify, O'Reilly cuts him off and moves on to the next person.

But who is advocating that all religious symbols be banned from any display in public (meaning: a private individual or group displaying religious symbols where they may be viewed in public)? I have not read of any such call by the ACLU or the Americans United for Separation of Church and State, the primary actors in these cases (which does not mean that there aren't any -- but I have tried to keep abreast of events).

O'Reilly's guest simply wants government to stop displaying religious symbols. O'Reilly turns him into a "fascist" who wants to ban all public displays of religious symbols (which is not his position) by conflating public displays with displays by public officials.

This note on Reason's Hit and Run, coupled with this opinion piece by Anne Applebaum of the Washington Post prompts me to urge all people going through airport security:

Stop taking off your shoes.

Despite what you may think, you are not required to remove your shoes and pass them through the x-ray machine. Here's a travel tip from the TSA itself:

Am I wearing the right shoes?

You are NOT REQUIRED to remove your shoes before you enter the walk-through metal detector. However, TSA screeners may encourage you to remove them before entering the metal detector as many types of footwear will require additional screening even if the metal detector DOES NOT alarm.

Footwear that screeners will encourage you to remove because they are likely to require additional screening:

• Boots

• Platform shoes (including platform flip-flops)

• Footwear with a thick sole or heel (including athletic shoes)

• Footwear containing metal (including many dress shoes)

Footwear that screeners are less likely to suggest you remove includes:

• "Beach" flip-flops

• Thin-soled sandals (without metal)

TIP: Since a thorough screening includes x-ray inspection of footwear, wearing footwear that is easily removable helps to speed you through the screening process.

Now, I've flown about 6 times in the last few months. Each time I have refused to remove my shoes. The conversation goes something like this:

(I put my carry-on bag onto the x-ray conveyer belt, including any keys, change or other metal items. I then approach the metal detector and am stopped by a TSA employee.)

TSA: Sir, I recommend that you remove your shoes and run them through the x-ray machine.

ME: No thanks.

TSA: We do recommend it. Otherwise you may be selected for secondary screening.

ME: I understand. No thanks.

TSA: Okay then. Step on through.

(I walk through the metal detector.)

TSA: Sir, you've been selected for secondary screening. Please step over there and wait for a security agent.

The secondary screening consists of running a wand over my shoes, then over my body, followed by a light pat down and checking behind by belt buckle. Finally, they check for explosive residue on my shoes. Once that clears, I'm on my way. The entire time I am able to watch my bag after it comes off the x-ray machine.

I know that many people object to a pat down -- and I agree that some stories I've heard worry me. But I've found that the simple act of refusing to take off my shoes has actually decreased my stress.

For one, I no longer have to walk around in my sock feet. It seemed that I was always the one who took off his shoes first, then waited around while the people in front of me fumbled with their laces or straps, then (inevitably) had some kind of issue with the metal detector. So they go back and forth until the thing doesn't beep at them and all the while my toes are getting cold. Then there's the hassle of gathering my things, looking for a seat so that I can put on my shoes comfortably, or having to balance against a wall to get them on. I know, I could wear shoes that are easy-on-easy-off, but I like to travel in the shoes I have.

But more importantly, I don't feel like I'm one of the sheep. I realize that Hitler and Nazi comparisons are not appropriate nowadays (are they ever?) and am not trying to invoke Godwin's Law on myself, but when I look around and see all those people dutifully removing their shoes, I can't help but see images from the mini-series Holocaust. In that film, I vividly recall seeing a long line of naked people all waiting to enter what they thought was a delousing shower. The feelings of helplessness that I'm sure they felt must have been overwhelming. I can't imagine what it would be like to be in that position.

Again, I'm not trying to say that the TSA practices are akin to Nazi death camps. Of course that's ridiculous. But I can't help the feelings that I get when I see otherwise reasonable people blindly subject themselves to what I believe is degrading and humiliating. Even more so when people agree with clinical psychologist Steven Strosnider, who said in this article:

"Some people feel a sense of degradation," Strosnider continued, "like 'How dare you ask me to take my shoes off.' Some people think, 'It's come this this? I have to go through this to fly?' They don't realize this is procedure."

"This is procedure." Yeesh. I'd like to know if this procedure actually has made us safer. I suspect not.

Others may find the pat down degrading -- so far I've not experienced that -- and feel more comfortable in their sock feet. If so, go ahead and take 'em off.

But as for me, I'll keep mine on, thank you.

There are lots of comments at various places on today's Supreme Court decisions, including SCOTUSblog and Volokh Conspiracy. One of the best posts that I've seen so far is at Balkanization.

A couple of my own comments (from a decidedly non-lawyer):

The dissent by Scalia (analyzed by Balkan) bothers me very much. At the start, Scalia lists many instances of either Congress, the President, or the Supreme Court invoking, acknowledging or otherwise incorporating references to God or a Supreme Being. In doing so, Scalia is furthering a fundamental confusion that many Ten Commandment supporters seem to have: acts committed in public are being confused with acts committed on behalf of the public. Scalia later writes:

If religion in the public forum had to be entirely nondenominational, there could be no religion in the public forum at all. One cannot say the word "God," or "the Almighty," one cannot offer public supplication or thanksgiving, without contradicting the beliefs of some people that there are many gods, or that God or the gods pay no attention to human affairs. With respect to public acknowledgment of religious belief, it is entirely clear from our Nation's historical practices that the Establishment Clause permits this disregard of polytheists and believers in unconcerned deities, just as it permits the disregard of devout atheists.

Here Scalia is saying directly that the Establishment Clause "permits the disregard" of (essentially) non-Christian, non-Jewish, non-Muslim believers or atheists. He makes this even more blatant later:

Finally, I must respond to Justice Stevens' assertion that I would "marginaliz[e] the belief systems of more than 7 million Americans" who adhere to religions that are not monotheistic. Van Orden, ante, at 13-14, n. 18 (dissenting opinion). Surely that is a gross exaggeration. The beliefs of those citizens are entirely protected by the Free Exercise Clause, and by those aspects of the Establishment Clause that do not relate to government acknowledgment of the Creator. Invocation of God despite their beliefs is permitted not because nonmonotheistic religions cease to be religions recognized by the religion clauses of the First Amendment, but because governmental invocation of God is not an establishment. Justice Stevens fails to recognize that in the context of public acknowledgments of God there are legitimate competing interests: On the one hand, the interest of that minority in not feeling "excluded"; but on the other, the interest of the overwhelming majority of religious believers in being able to give God thanks and supplication as a people, and with respect to our national endeavors. Our national tradition has resolved that conflict in favor of the majority.

But the Establishment Clause does not demand that anything said or done in the public forum be nondenominational. Scalia does not distinguish between acts committed in public or by public officials (qua private citizens) with acts committed in the name of the public and with the full force of an official's office behind it.

If I stand on a street corner and proclaim my belief in God or rent airtime on the local television station to encourage people to accept Jesus Christ, I am speaking in the public forum. It would be ludicrous to think that somehow I, as a private individual, am violating the Establishment Clause. Yet that is the implication that Scalia wants us to draw: any discussion of religion or religious act carried out in public would be banned.

And when the President ends a speech with "God bless America" or ends his oath of office with "so help me God", I can allow that those words are said by an individual and do not carry with it the force of his office. And obviously if a senator were to speak at a religious meeting, I can see it as something that he does as an individual. Those acts, public though they may be, are not violations of the Establishment Clause. These are not "governmental invocations of God."

But why should the majority (or any group) have the right to give God thanks "as a people", meaning with the aid of government? Isn't that what churches are for, to gather with others of similar religious beliefs to give thanks to God or ask for his beneficence? And can't churches get together with other churches to offer their collective prayers? Why is it that believers feel the need to get government to do their worshipping for them?

The early Baptists understood the problem well: when you allow religion to bend government to its will, even with the noble intention of offering thanks to God, you run the risk of government bending religion. Perhaps Scalia believes that "our national tradition" has said that the majority may employ government to its own religious ends, but I am not convinced, neither that it does nor that it should.

Jay Richards of the ID the Future website, tries to answer an objection against Intelligent Design: Who designed the designer?

But he misstates the objection. According to Richards:

Suppose someone says: “X is designed,” or “Intelligent design is the best explanation for X.” Make X any event or structure you like. Think, for instance, of Mt. Rushmore. It clearly gives evidence that it was designed—sculpted, to be exact. Would it make any sense for someone to protest, “Well then who sculpted the sculptor? Who designed the designer? Ha! Q.E.D.”

That objection is ludicrous. We know Mount Rushmore was designed regardless of the identity or causal history of the sculptors, and we know it based on what we observe.

This is true even in those cases where the designer is (probably) not human. (I’ll speak of a designer in the singular because, all things being equal, Ockham’s Razor reminds us not to multiply entities unnecessarily). In principle, SETI researchers could discern intelligent signals if any such signals are ever detected by their equipment. Presumably these would come from an extraterrestrial source.

But that's not the objection that Richards should be responding to. The objection "What about the designer?" is aimed at Dembski's use of his "explanatory filter" to explain some event:

1. Stage One: Natural law. Is there a natural law that would explain the event? I.e., is there some sequence of events, governed soley by natural laws and not randomness or human intervention, that would leave from some previous event to this one? If not then we need to pass the event to the next stage of the filter.

2. Stage Two: Chance. Maybe there is no natural law that would explain the event, but the event is still highly likely to have occurred by 'chance'. Is there a probability distribution that we can put on the space of all possible events that would make this particular event likely to have occurred? If not, then we say that the event exhibits "complexity," tentatively rule out chance as the reason for the event, and pass it on to the next stage.

3. Stage Three: Specification. At this point, we need to examine the event for "specification". Dembski's definition is not precise, but often specification is taken to mean that we can describe the event without referring to the event itself, and that it is conceivable to have such a description before having seen the event.

   If we cannot specify the event then the filter drops us into the 'Chance' category as an explanation for the event: it may be highly improbable, yet it did indeed happen. Hey, that's life.

   But if the event is specified then Dembski claims that the only explanation is that it was designed. Probably by some intelligent thing.

We can now see the core of the ID argument: life (or certain elements of biological life forms) exhibit specified complexity therefore (by the explanatory filter) life (or elements of it) must have been designed. Therefore there must exist (or have existed) an intelligent designer.

Note that this isn't a scientific theory: it is a claim (or an argument based on claims). But we'll let that go for now.

What is important is that if the explanatory filter is applied to the event "an intelligent designer existed", then we're put in an interesting situation. Could the designer be explained by natural law? Not by any we know. Could the intelligent designer be a product of chance? Seems very unlikely. Is the intelligent designer specified? Well, it seems so.

So who/what designed the designer?

That's the objection Richards should be responding to -- an objection (among others) to Dembski's explanatory filter. Instead he pulls in some gobbledygook about the objection claiming that some thing was not the product of design if we can't say anything about the designer. He misses (or aimed away from) the real objection.

A similar point was made by rossum at talkreason.org.

Keith Devlin thinks math is hard but possible:

Any mathematician who says she or he finds math easy isn't tackling sufficiently challenging problems. The fact is, what most of our students don't realize is that mathematicians are not people who find math easy. We don't. We find it hard. The key factor is that we recognize that, given enough effort, and enough time, it is nevertheless possible.

But for some reason, American students don't seem to get that. Rather than sticking with a problem over a period of days (or weeks, or months, etc.), they tend to give up when faced with a difficulty or false start. They lack the "spark" that Devlin claims to have seen in the past:

In contrast to most of the students I dealt with at home [the U.K.], many of my American students were highly motivated, hard working, fiercely competitive, and determined to show they were the best in the world. They would go to heroic lengths to avoid being defeated by a problem. Two decades later, living in the US now, I still encounter such students from time to time. But they no longer seem to be in the majority. For most of the young people I meet, the spark I used to see in their predecessors seems to be absent.

Devlin asks how this came about, and what can be done about it (if anything).

I think there are several factors that help explain why students have lost the ability (or interest) to persist in mathematics.

• More options. There are so many more things for students to do with their time that they don't have time for thinking about mathematics. It would be easier to say that thinking is hard and it's easier to watch t.v. or surf the internet, but I don't think that gives students enough credit. The kinds of activities that they engage in, from sports to cultural, simply provide them with more interesting and stimulating experiences.

  Gone are the days that someone discovers a predilection for mathematics because they were cooped up inside on a rainy afternoon and came across a collection of math problems in the family library. Students have more things to do than hard problems in mathematics.

• Denigration of hand calculations. Many educators argue that the calculator should be incorporated early on in mathematics education. In doing so, students are supposedly freed from having to perform tedious, "mindless" calculations and instead can focus on "the big picture".

  But there is something to be said for carefully carrying out a long sequence of calculations, especially in calculus. Students learn to think carefully, pay attention to detail, and develop an attention span that allows them to follow more than three algebraic steps without taking a t.v. break. They also start to see patterns and forms that can encourage mathematical thinking. And it only takes a few instances of reaching the end of a calculation and finding out you've made a mistake to make you more careful, and thus better, in the future.

  That's not to say that students can't be careful thinkers without doing lots of calculations by hand. It's just that it may be tougher to develop good habits/skills without them. Students who rely primarily on calculators tend to limit themselves — they can't imagine doing mathematics without a calculator and so are never quite able to go beyond the numeric and experience mathematics at a higher level.

• Lack of instant gratification and external acclaim. As Devlin points out, "large numbers of [American youth] bring a feverish intensity to sporting endeavors, putting in endless hours of dedicated training to become the best in their school, their district, their country, or even the world, yet only a few will put in the same kind of effort to mastering mathematics."

  But in mathematics, there are no cheering fans ready to lift you on your shoulders when you finish off that proof. There is very little external recognition of mathematical accomplishments — or really any academic pursuit. Why work hard at an assignment when no one, except possibly the instructor, is going to pat you on the back and say "good job"? Unfortunately, many students don't receive positive comments from their peers for doing well or having solved a difficult problem.

• No prior experience with challenges. It is not in vogue, pedagogically, to challenge students with problems that they cannot solve (at least not immediately). That might damage their fragile psyches and discourage them from pursuing mathematics. There is some wisdom in that, but overall I think students are intrigued by puzzles and problems — they want to solve things. The challenge for the curriculum is to find the right mixture of accesibility and difficulty. It's not easy to do, I'll grant, but I think more students should come to college with the experience of having tackled open-ended problems on a regular basis.

  More colleges/universities should be working with local public schools to develop "Math circles". These would expose students at all levels to the world of mathematics as a method of problem-solving, not as simply a set of rules to be exercised.

So what can be done? Of course I wouldn't want to limit options of students — except in the classroom where I would put strong limitations on calculator use. In the past, I have gone so far as to ban them on tests altogether; some students were okay with that, others struggled because they never really learned how to solve an equation (just type it in and press 'Solve', right?), what the graphs of fundamental functions look like (so they can't look at the definition of a function and know how that function will behave), or how to approximate quickly the value of a given expression. They simply don't have an intuitive feel for mathematical concepts.

I would also encourage teachers in high school to give students a wide variety of problems, some easy, some challenging and some hard. Encourage the students to work on them over a period of days or weeks by not asking for the solution right off. Instead, just ask for "progress reports" on the problems — which ones were they able to solve? How did they solve them? Which ones are still open, and what have they tried? Not every assignment should be like this, of course, but it would be a good start to have a few of these types of problems going at any one time.

And professors could do a better job of exposing students to math/problem solving outside of the classroom. In the past I have written puzzle columns for the school newspaper; I plan to do that again in the future. The response was not overwhelming (in fact, it was rather disappointing), but I think some students enjoyed the chance to flex their analytic muscles. And perhaps a few did some extended thinking on a non-course related mental exercise that they would not have otherwise.

But another, bigger, change will have to come from academia itself. The more that the university is run like a business, where the "product" is the student, or the students (or their parents) are the "customers", the more difficult it will be to get students away from their instant gratification desires. After all, they aren't paying X dollars a year just to be challenged — they expect a degree that leads to a good job. That, however, is another issue.

Happy Birthday Alan Turing!

He was a pioneer in mathematical logic and computability theory. At the tender age of 24 he published On Computable Numbers, with an Application to the Entscheidungsproblem, a groundbreaking work that provides the foundation for computer science. In that article, Turing introduces what is now called a Turing machine as an abstract model of computation: a problem can be solved algorithmically if and only if some Turing machine can be programmed to solve it (this is known as the Church-Turing thesis).

On Computable Numbers also completed the destruction of Hilbert's program. David Hilbert proposed to formalize mathematics so that it could be determined whether any particular mathematical statement was true or false, and that this determination be done in an algorithmic (systematic) way. It was his hope to eliminate ignorance from mathematics once and for all. He once said, 'in mathematics there is no ignorabimus' (there is no we shall not know).

Kurt Godel struck down part of Hilbert's program in 1931 when he showed that any mathematical system sophisticated enough to handle arithmetic would either be inconsistent (a statement and its negation could both be proved — not a good thing) or incomplete (some statement in the system could not be proved, nor could its negation — some statement would be true without being provable).

Turing finished off the Hilbert program by showing that the system would also not be decidable — there is no algorithm for determining, for every statement, whether or not it is provable. Godel showed that there were some strange animals in the mathematical universe; Turing showed that we have no way of telling which animal is strange.

During World War II, Turing worked for British GCHQ to break German cryptographic ciphers, most notable the Enigma cipher. After the war he turned to the development of a 'computer brain'; his philosophical take on artificial intelligence was given in the article Computing Machinery and Intelligence. His 'test' for discriminating between a human and a computer (based on responses gathered via questions and responses given a computer terminal) has become famous as the Turing test (also see here).

See the Alan Turing Home page for more on Turing.

A hearing was held Monday by a subcommittee of the Pennsylvania state legislature, on teaching intelligent design in public schools. HB 1007 reads in part:

The General Assembly of the Commonwealth of Pennsylvania hereby enacts as follows:

Section 1. The act of act of March 10, 1949 (P.L.30, No.14), known as the Public School Code of 1949, is amended by adding a section to read:

Section 1516.2. Teaching Theories on the Origin of Man and Earth.--(a) In any public school instruction concerning the theories of the origin of man and the earth which includes the theory commonly known as evolution, a board of school directors may include, as a portion of such instruction, the theory of intelligent design. Upon approval of the board of school directors, any teacher may use supporting evidence deemed necessary for instruction on the theory of intelligent design.

(b) When providing supporting evidence on the theory of intelligent design, no teacher in a public school may stress any particular denominational, sectarian or religious belief.

As has been pointed out many times elsewhere, there is no "theory" behind intelligent design. It is not a scientific theory to be taught as an alternative to evolution and is not supported by biological scientists. Some ID proponents such as Paul Nelson of the Discovery Institute are honest enough to admit that they do not have a 'full-fledged' theory, or at least not one that is ready to teach in schools.

Also, intelligent design proponents go to great lengths to avoid talking about religious matters, in particular about the nature of the designer or any purported means by whicn a design was put into effect. Consider this exchange between Behe and a Pennsylvania legislator from the AP report:

Michael J. Behe, a biological sciences professor at Lehigh University, told the subcommittee that intelligent design has no religious underpinnings. Critics argue that it is a secular variation of creationism, the biblical-based view that regards God as the creator of life.

Behe said intelligent design merely contends that evidence of complex physical structures shows that design, rather than evolution, is responsible for an organism or cell.

Some lawmakers struggled to understand the concept.

"I've always viewed evolution as sort of the ultimate design. It would change and adapt and accommodate to whatever the situation was," said Rep. P. Michael Sturla, D-Lancaster. "When did the intelligent design occur, in your theory?"

Behe had no answer.

"Questions like, 'When did the designing take place?' ... are all good questions. We'd love to have answers for them, but they are separate questions from the question, 'Was this designed in the first place?'" Behe said.

In other words, attempting to engage in scientific inquiry with respect to ID will get you nowhere. Sturla's question is a good example of a scientist's mindset; Behe's answer (none) was an indication of an contentless 'theory'.

And if ID is not religious in nature, why did the writers of the bill feel the need to specifically require that "[w]hen providing supporting evidence on the theory of intelligent design, no teacher in a public school may stress any particular denominational, sectarian or religious belief"?

There may come a time that ID is a respectable scientific theory. At that point, and only at that point, should it be included in the curriculum. Until then, ID proponents need to stop pushing their wedge and get down to the hard job of actually doing science.

Happy birthday to Siméon Denis Poisson.

Interestingly, today I plan to introduce the Poisson distribution in class. Now what's the probability that the two events should coincide?

Happy Birthday John Forbes Nash, Jr!

One of the most likely mathematicians to have a decent Q score, primarily because of the movie A Beautiful Mind.

Nash is most famous for his work in game theory, developing what is now called the Nash equilibrium. His work in game theory earned him a Nobel Prize in Economics.

Dan Eggen and Julie Tate of the Washington Post today provide the first of two articles on how terrorism cases are being counted by the Bush administration.

An analysis of the Justice Department's own list of terrorism prosecutions by The Washington Post shows that 39 people — not 200, as officials have implied — were convicted of crimes related to terrorism or national security.

...

Just one in nine individuals on the list had an alleged connection to the al Qaeda terrorist network and only 14 people convicted of terrorism-related crimes — including Faris and convicted Sept. 11 plotter Zacarias Moussaoui — have clear links to the group. Many more cases involve Colombian drug cartels, supporters of the Palestinian cause, Rwandan war criminals or others with no apparent ties to al Qaeda or its leader, Osama bin Laden.

People got on the Justice Department's list in many cases because they were suspected of having terrorist links or being involved in terrorist activities. Even if those suspicions could not be borne out, they still remained on the list.

The Post looked at 361 cases and tried to determine what kind of connection each individual had with terrorist groups/activities. For 180 cases, they could not find any such connection.

In many cases, people on the list were charged (and convicted) of crimes having nothing directly to do with terrorism. It may be that these people were actually involved in bad stuff, but the government couldn't muster quite enough evidence to prove it; they were at least convicted of something so they're either in jail or deported and the country is safer for it.

And to be sure, there were individuals who had clear connections with terrorist groups, and in some cases were actively involved in terrorist activities, including Richard Reid (the Shoe Bomber) and Iyman Faris who admitted being a member of Al Qaeda and planned to blow up the Brooklyn Bridge. And it is reasonable to believe this:

Barry M. Sabin, chief of the department's counterterrorism section, said prosecutors frequently turn to lesser charges when they are not confident they can prove crimes such as committing or supporting terrorism. Many defendants also have been prosecuted for relatively minor crimes in exchange for information that is not public but has proved valuable in other terrorism probes, he said.

Mr. Sabin goes on to say that someone could only have gotten on the list if there was, at least initially, some concern about a possible threat to national security. That may be, but what happens when they are found to not be a threat?

"What we're seeing over time is the equivalent of mission creep: Cases that would not be terrorism cases before Sept. 11 are swept onto the terrorism docket," said Juliette Kayyem, a former Clinton administration Justice official who heads the national security program at Harvard University's John F. Kennedy School of Government. "The problem is that it's not good to cook the numbers. . . . We have no accurate assessment of whether the war on terrorism is actually working."

That's exactly the issue: is the "war on terror" actually working? How do you even measure that kind of thing? Maybe a simple measure would be to count how many terrorist cells were active in the U.S. before the "war", and count how many are active now. Unfortunately, that kind of knowledge is very hard to acquire. Especially if, as Eggen and Tate say: "In the end, most cases on the Justice Department list turned out to have no connection to terrorism at all."

Good for the Post for starting to look into how the claimed numbers square with the facts.

CJR Daily notes the lack of critical analysis (or even good old-fashioned fact checking) surrounding President Bush's recent stump for the Patriot Act:

When the president says that we have convicted more than 200 terrorist suspects on various charges, he may well be correct under the new broad definition of "terrorism." But it would be nice if reporters explained that widening of the net to readers. Their audience may also be interested in reading about all we don't know -- like if the president's numbers are correct. As readers ourselves, we know we're sure curious.

CJR points to this article by Bert Dalmer of the Des Moines Register as an example of good investigative reporting. Apparently the definition of "terrorism" has broadened over the last few years, including what counts as anti-terrorism. Incidental arrests, not germane to the original investigation, are still counted as anti-terrorism activities (and thus successes of the Patriot Act).

The Patriot Act did do some streamlining and did clarify some powers/procedures available to law enforcement. But it also broadened the scope of secret courts and lowered the threshold for justifying some information-gathering activities (into what we might normally consider private). To the extent that those activities are directed at very specific threats to national security, I find it difficult to argue strongly against them. However, soon after the passage of the Patriot Act, it became clear that not all of the new powers available the government would be limited to terrorists. And when the Justice Department is reluctant to tell Congress how often various provisions have been used or starts some fancy accounting to up the numbers, I would hope that Congress would grow a pair and start demanding some accountability.

See this series of articles by Dahlia Lithwick of Slate for a careful examination of some of the provisions of the Patriot Act.

Filed under 'Entertainment' on cnn.com: CNN announces programming changes

I think this story illustrates the problems that I have with CNN (and news programs on other networks). Look folks: as long as you continue to present news as 'entertainment' you continue to lower the thinking ability of the average American.

As Jon Stewart said: Stop, stop, stop, stop hurting America.

How did I miss this one?

Happy birthday Aleksandr Mikhailovich Lyapunov!

Lyapunov, a studeny of Chebyshev, did work in what might today be considered applied mathematics (mainly in hydrostatics) but also did work in probability. He influenced dynamical systems theory, including differential equations and nonlinear analysis. Researchers in chaos theory have made significant use of his work.

Of particular note is the Lyapunov exponent (or exponents). These measure, in some sense, how sensitive a system is to initial conditions. In a very sensitive system, any small change in the initial conditions may lead to large changes over a short period of time; less sensitive systems are more robust with respect to small perturbations. Lyapunov exponents help provide a quantitative measure to describe a qualitative phenomenon: if the largest one is positive, we have chaos.

Happy Birthday Max Zorn!

Zorn is best known for his maximum principle, called Zorn's Lemma by Tukey. The Lemma is equivalent to the Axiom of Choice and the Well Ordering Principle (in Zermelo-Fraenkel set theory).

To state Zorn's Lemma, we need to start with the notion of a partially ordered set. Given a set `X`, a partial order on `X` is a relation `\leq` defined on `X` such that `\leq` is:

1. Reflexive: `a \leq a` for all `a` in `X`

2. Antisymmetric: `a \leq b` and `b \leq a` implies that `a = b` for all `a,b` in `X`

3. Transitive: if `a \leq b` and `b \leq c` then `a \leq c` for all `a,b,c` in `X`

We say that `(X,\leq)` is a partially ordered set, or poset.

Note that we do not require that for any `a` and `b` in `X` we have `a \leq b` or `b \leq a`, i.e., there may be elements in `X` that are not comparable. (For example, let `X` be the power set of `\{1,2\}` with the relation of `\subseteq`; the elements `\{1\}` and `\{2\}` are not comparable.)

A subset `A` of `X` has an upper bound if there is some `u` in `X` such that `a \leq u` for all `a` in `A`. A maximal element of `A` is some `u` in `A` such that for no `a \neq u` in `A` is it the case that `u \leq a`. Given any poset `(X,\leq)`, a chain is a set `C` of (pairwise) comparable elements: for any `a,b` in `C`, either `a \leq b` or `b \leq a`.

Finally, we have Zorn's Lemma: If `X` is a (nonempty) poset such that every chain has an upper bound then `X` has a maximal element.

For example, let `X` be the set `\{1,2,...,100\}` with the relation of `a \leq b` if and only if `a` divides `b`. In this case, it is easy to see that every chain (e.g., `\{3,12,24,72\}`) has an upper bound (simply take the largest number in the chain) and that `X` has several maximal elements (e.g., 100, 99, 90, and 53).

Of course Zorn's Lemma can apply in a wide variety of situations. It can be used, for example, to show that every ring `R` has a maximal ideal.

I received this flyer while purchasing some items from the local home supply store:

Now, isn't the parking lot an odd place to install ceramic tile?

Marlene Zuk, a biology professor at UC Riverside, has this to say about her perception of students' attitudes in college:

They readily confess to me that they have not consulted the text and do not remember my lecture. They have nothing to say about the concepts we've covered. Yet somehow, a kernel of faith stays resolutely sheltered in each undergraduate bosom — they believe honestly and with conviction that they get it, and therefore deserve a high grade.

Don't get me wrong. I hardly expect all students to understand the material immediately, or even ever, and I also realize that my teaching could be confusing or badly organized. Wrong answers are part of the game. What I find troubling is the lack of concern about their ignorance or poor performance, the epidemic of what a colleague of mine calls unwarranted selfregard.

Many students (at least the ones I've encountered in the last few years) do seem to lack a certain amount of self-criticism. Especially in lower-level mathematics classes, they feel that if they have done the assigned problems (meaning: written something down and turned it in) then they understand the material. "What's that? Do more than the assigned problems? But why? I know understand it. Study examples in the text or notes? But why? I did the assigned problems."

Then when it comes test time and they are asked to demonstrate more than an ability to mimic homework problems (after all, a trained chinchilla can do that), they falter. In many cases, I believe, it is because they have failed to ask themselves if they truly understand what they are doing, or have failed to honestly answer that question.

It can be tough to be self-critical. After all, how do you know that you don't understand something if you already think you do? One thing students could do (aside from more homework problems) is to explain their work to someone who is willing to give them honest feedback. Sometimes things that make sense to you don't make sense to someone else, and it's because you don't really get it (or even have it wrong).

Another tactic students could use is to come to office hours and present a couple of solutions to the professor. When I have a student in my office, I prefer that they show me what they did on a problem (or tried to do) and then we talk about why that didn't work and what else to try. Often I will have the student present their work at the board and ask them questions as we go. It is often possible to pinpoint some key areas of confusion or weakness with just a few questions. Students who are able to present good solutions and answer my questions are usually in good command of the material.

But there's another element in the mix, at least at the school I had been teaching at: the desire of students to appear smart without having to work at it. I've seen this over and over: a student who did well in high school without really trying becomes used to being told how smart he is (and it's usually a male), and enjoys the respect he gets from his peers who think of him as a genius. When he hits college he isn't prepared for putting in long hours of study and, what's more, doesn't want to let people see him doing the studying. After all, if he has to study, doesn't it mean that he isn't really that smart?

Caught by their lack of preparation and their pride, many of these students perform poorly on college-level tests and become discouraged (or resentful of the professors). Unless they are able to adopt the perspective of Socrates and admit what they do not know, their college experience will be less than fulfilling.

And I don't think my experiences are unique.

Media Matters has a good summary of the differences between Whitewater (and other Clinton-era investigations) and Watergate. The summary was prompted by a comparison in a Wall Street Journal editorial between the press coverage of Watergate versus the press coverage in the Clinton era:

That [the press coverage] was all very different from the Clinton era, when many good reporters did similarly important digging. (Susan Schmidt at the Washington Post and Jeff Gerth of the New York Times come to mind.) But far from being praised for their enterprise, they often became pariahs at their own newspapers and the targets of White House attacks. Much of the media took political sides, rather than stick to their higher obligation of ensuring that a President doesn't misuse his Constitutional authority. This was the motive for our own extended coverage of Whitewater and the other ethical corner-cutting of the Clinton years.

It is nice to know that the WSJ wants to make sure a president doesn't "misuse his Constitutional authority". But it would be nicer to know that they are honest enough to admit that 1) despite multiple investigations, no abuse by the Clintons has ever been proven, and 2) we might benefit from an investigation or two of the current administration. I won't be holding my breath that the WSJ will lead the way.

Gregory Lamb of the Christian Science Monitor previews a report by the National Institute of Standards and Technology (NIST), due to come out later this month, on the state of machine-translation systems:

The agency is expected to give top honors, not to the linguistic-savvy programs at universities and elsewhere, but to a newcomer: Internet search company Google. Google's apparent success suggests that a new approach to translation - fancy math rather than linguistic know-how - may be the way forward in a field that has struggled with the nuance and ambiguity of human language.

"Observers speculate" that a beta version of the software may be available in a few months.