Mathematical Blog

2003-06-24T00:51:00.000-07:00

The Michigan Case

The facts of the UM affirmative action case are surely familiar to readers (scroll down, if not). Today the Supreme Court ruled two things: (1) the UM point system violates the 14th amendment, and (2) the individualized racial preference system used by UM's law school is constitutional. For 1, the arguments were fairly standard--that the rules gave blanket advantage to people of one race, thereby violating the equal protection clause of the 14th amendment. For 2, the supreme court ruled that because the law school admissions policy looked at individual circumstances in analyzing race, it did not violate the equal protection clause. Justice O'Connor noted that the admission percentages of minorities varied from year to year in the law school, showing that race was not a decisive factor in their admission.

It was heralded by affirmative action advocates as a huge victory, even though it severely limited the scope of affirmative action (heretofore limited only by the unconstitutionality of quotas). It was also heralded by affirmative action opponents as a victory because it would severely limit the ability to use race as a factor in deciding admissions. I think that the supreme court made the right decision on both counts.

In the undergraduate admissions policy, students were awarded extra points simply for being of an under-represented minority. Skin color could influence 1/5th of the admission profile. This plainly puts fully-represented races (like whites and asians) at a disadvantage which denies them the equal protection of the law, and is thus unconstitutional.

However, as has been pointed out ad nauseum, we do not live in a color-blind society. Thus if someone is discriminated against for being black or hispanic, comes from a poor school, and still does well, it seems wrong not to take that into account over a white in good circumstances who does equally well. Thus looking at an individualized profile of each student will allow admission officers to get a good picture of which students deserve admission. Perseverance in the face of harsh circumstances is something which should be rewarded, and doing so denies no one equal protection under the law. It is when points are awarded solely on the basis of race that equal protection is denied, since arbitrary blacks and hispanics get a boost based solely on their skin color. A black student with rich, well-educated parents, who goes to a good private schools has not had significant educational hurdles to jump over. She is not at a disadvantage against a white student, and would probably be at a significant advantage relative to one in poor circumstances. Perhaps these cases are rare, but perhaps not that rare. In any case, the rareness of the blacks in good circumstances does not speak either way for the constitutionality of the requirement.

The supreme court decision today will force selective schools to look more carefully at each application on a case-by-case basis. This is a good policy generally, and will result in a more fair application process for students of all colors. It will force a more careful analysis of the specific abilities of students and their worthiness for admission. I strongly support such an admissions policy for reasons independent of race. This case illustrates that when policies are geared to equality of opportunity based on merit, everyone benefits. Think about how many black students will receive a more thorough examination of their worthiness for admission to UM; with such a policy in place, every student admitted to UM will be truly have earned their admission. That seems like a good thing for everyone.

2003-06-08T22:30:00.000-07:00

Affirmative Action

On Friday, I saw a Dateline Special Report on NBC about affirmative action at the university of Michigan. The issues are well known: prior to a few years ago, UM had a system which gave admission percentages for under-represented minorities and everyone else, depending on their academic credentials. In a certain bracket, whites and Asians got in at a rate of 30%, while African Americans, Hispanics and Native Americans got in at a rate of 100%. Now UM has moved to a point system where a number of factors give people points, and a certain number of points gets you into the university. Being from a poor family gets you 20 points, so does being an under-represented minority. Something like 100 points are needed to get into the university.

These policies are such clear violations of the 14th amendment that everyone feels the need to cloud the issue with irrelevant details (like whether the policy is a good policy or not). These details are irrelevant for the same reasons that the morality of racism is irrelevant for the free speech of racists: we believe in certain values which transcend the prudence of a particular policy. Freedom of speech and religion. Things enshrined in the 1964 Civil Rights act and the 14th amendment, which reads (in part):

"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."

It is plainly discriminatory to give someone extra points for being of a certain race, and hence is both illegal for private industry and the government (Civil Rights Act), and unconstitutional for the government. Note that this is true whether or not diversity is a good thing.

And so in 1998, a college student who was denied admission the UM-Ann Arbor filed civil suit against UM, saying exactly that. In general, I have an intuitive respect for people who champion the constitution. Not so, this time. This woman is a loser, plain and simple.

On the program, she said that the first words out of her mouth after receiving the rejection letter were "Can we sue them?" This is the reaction of someone with no ability to take responsibility for her life. She didn't even know why she could sue them, and she already wanted to do it. Later in the program, it was revealed that she had dreamed of going to medical school and becoming a doctor. But, because of the crushing blow she received when she didn't get accepted to her first pick for college, she didn't go to medical school. She "lost a lot of confidence" in herself. If that's not the mark of a loser, I don't know what is.

I am reminded of George Washington Carver, a brilliant botanist and food chemist. He was born a few years prior to the civil war, and was raised by the family who had owned his parents (both died). They educated him and treated him well, sending him to a good high school (for the day). He was accepted to go to Highland University in Kansas. When he arrived for an interview, the interviewer said something like "I’m sorry. There's been a mistake. We don't take Negroes here."

Did Carver let this shake his confidence in himself? No. He found a university that would take him, and proceeded to save large portions of the southern economy from ruins. He advised rotating peanuts through cotton fields to nitrogenate the soil, and then proceeded to come up with hundreds of uses for peanuts and sweet potatoes, practically founding modern food chemistry. Here was a man of great brilliance who faced up against discrimination much more blatant and severe than what the Michigan woman who brought the suit against UM faced. Yet he did not let it bring him down, he triumphed in spite of it.

Now of course not everyone can be like George Washington Carver, but it does seem interesting to contrast the two cases for what it's worth: a big loser versus a great American innovator…

2003-05-20T01:06:00.000-07:00

Very Long Rant

I saw The Matrix Reloaded today, and it was everything I expected. That is, it was an extremely well-made piece of brilliant filmmaking which lacked much.

The original Matrix was considered a revolutionary movie, both in terms of bringing philosophy to the masses, and creating a number of new editing and special effects styles which were parodied ad nauseum. In this latter respect, it might be compared to Jaws or Star Wars: not particularly good movies, though highly entertaining and influential. The matrix introduced viewers to the skeptical philosophy of Descartes' First Meditation, and also gave some vague elements of eastern philosophy which rested on what appeared to be fundamental misunderstandings of Buddhism. The interest of the skeptical tract was muddied by the extremely improbable "human battery" premise, and also by the odd bits of Christian allegory.

Most viewers were wowed; I was disappointed, though I walked away with a "what might have been" feeling about the movie. Its fundamental theme was fatalism: something rather bizarre for such a wannnabe humanistic movie. The "oracle" was a mysterious (though eminently likable) African-American women who spewed sophisms from every corner, ruling peoples lives with her words. Not surprisingly, her predictions came true, causing Neo (Reeves) to question the very nature of his existence. Morpheus (Fishburn) was happy to accept this brand of fatalism, knowing all along that Neo was really "the one."

These sorts of themes were continued into the second movie, which is unfortunate, as the Wachowski brothers are "much greater visual stylist[s] than a philosopher[s]," as the Onion put it (referring to a different, equally gifted filmmaker.)

In this movie, Fishburn reprises his role as a religious fanatic, though this time he is correctly labeled as such by the supporting characters. In order to pursue his odd religion (based upon the oracle's predictions), he risks the future of humanity on his faith in Neo. Unfounded faith, as it turns out. Essentially, Neo, though "the one," was designed to be the one. He was planned by "The Architect" (the version of Descartes' malicious demon) from the very inception of the matrix. There have been five versions of him before, and (one might infer), there would be many more to come. But Neo makes a different choice from his predecessors, choosing to rescue his love (unconvincingly played by Carrie-Anne Moss) instead of saving humanity. Much of the dialogue in the architect scene is painful or nonsensical, but the message is clear: even if you choose to rebel, that was designed into the system.

This fatalism is repeated so explicitly throughout the movie that it begins to sound like the pathetic explanations of a C- philosophy student. "You've already made the choice," the Oracle tells Neo, "you're just waiting to understand it." This is some kind of essentially nonsensical dualist fatalism. How can one understand something without intentionality? How can one be predetermined to choose something with intentionality present? These questions are partially addressed when Neo meets the Merovingian, a power-brokering computer program which informs Neo that since he does not understand why he is acting as he does, he has no power. For the Merovingian, causality is the province of the weak, and those with power can manipulate it. Thus intentionality is identified with power in an odd way. This seems to suggest that one cannot separate knowledge, power and intentionality. And a relationship is causal only to the extent it can be controlled.

Thus causality is fundamentally an intentional concept, and since Neo has no understanding of the causal relations which caused him to act as he did, he was at the mercy of others with genuine intentionality. This is played out later when Neo finds out that he has never been free, that he was always just the pawn in a large chess game created by the matrix's god.

The movie also hinges around the question of whether technology is enslaving us or not. In one scene, Neo says that the reason that the machines which maintain Zion are not enslaving them is that they can be destroyed or shut off. In other words, they have no choice in the matter, unlike humans. The machines in the matrix are different inasmuch as they can choose their own destiny to a greater extent even than humans can.

This sort of anti-humanistic philosophy bothers me. I'm sure the Wachowski brothers believed themselves fundamentally humanists, due to their strong opposition to technology. Machines are always portrayed as having malevolent purposes, wanting only to control or to destroy. But machines are nothing like that. Technology is the strongest power that humans have. In the past few hundred years, it has liberated humanity from the greatest of suffering, while from Thoreau on, anti-technology zealots have been dragged along, kicking and screaming. These have not been the people who moved the world forward, but they held it back either from their hatred of the "dehumanizing" effects of technology or their ideological disagreements with science about the nature of reality (opposition to evolution, the dangers of genetically modified crops, etc, etc.) Thus I'm forced to disagree with the matrix from its very starting assumptions.

Nature has been the enslaving force to humanity. The more we are able to free ourselves from the arbitrary influence of environment, the more free we will really become; not the other way around.

There are other ways that the matrix movies are lacking, most notably in acting and scriptwriting. Reeves and Moss present terrible performances devoid of any emotion or convincing role-playing. One gets the feeling that they just learned their lines a few minutes prior to walking on the set. The bad scriptwriting doesn't help either. The philosophy presented is frequently presented in a bland, textbook manner. Rather than trying to subtly incorporate it into the story (which might yield a good film), the writers decided to hit the viewers over the head with it. They may as well have labeled the scenes with subtitles saying "A deep philosophical point is being presented." This is not how to make good cinema.

None of the above is to say that I didn't enjoy the movie. I enjoyed it very much. It was a fun action movie, with truly spectacular special effects, and often breathtaking cinematography. The Wachowski brothers are plainly geniuses of the highest order when it comes to visual expression. Their use of lighting and color paint beautiful pictures of unimagined worlds of splendor and pain. These visuals are all really fantastic. The problems come mainly in their attempts to express themselves in other ways. One of their main strengths as cinematographers (the bluntness of their visual style) comes back to haunt them in what should be subtle discussions of subtle issues. Rather, they hit the reader over the head, seeming to say "look how profound I'm being." Oh what might have been...

2003-05-13T10:42:00.000-07:00

Mail Time

I just got something lovely in the mail. That's right, I am now a card-carrying member of the ACLU. John Ashcroft, eat your heart out...

2003-05-13T10:30:00.000-07:00

Going down south

Tomorrow, I head to Atlanta for the Cumberland Graph Theory Conference. Should be a nice good time: good invited speakers, interesting talks, etc. I'm not giving a talk myself, but then again I was invited at the last minute by someone who is substituting for someone who was supposed to give a talk. That's about four levels from talk-giving territory. I'll try to post from Atlanta if I get a chance.

I'm currently writing two papers with a professor who is a good friend of mine. The process is weird. I'm writing one based on research I've mainly been interested in, and he's writing a similar sort of paper himself. We then put both our names on each paper in the same order. Of course I don't object to his name going on the paper I'm writing (he's been there guiding all the research I've been doing, and has done some of it himself), but it does seem odd to put my name on the paper he's writing. He's opposed to the idea of not having my name on it, so I guess that's the way the cookie crumbles.

When I get either one published, this will massively reduce my Erdos number from infinity to 2. Unfortunately, I can't ever reach 1. I definitely wish that I could have known Erdos before he died. Every description I've heard of him makes him sound like he's about the nicest person imaginable, and I know that he was a brilliant and enthusiastic mathematician. Apparently he also liked talking to bright undergraduates interested in doing mathematical research. Unfortunately, he died when I was in the 8th grade at the age of 83. He lived a long and fulfilling life, but it's so sad that he couldn't have done more of what he loved.

2003-05-07T15:27:00.000-07:00

Patriotism

There was a letter in the Pantagraph today about how people who "support the troops," but who were opposed to the war were inconsistent. Their views make no sense. The letter-writer also said that there are two possible views on your country: you either support its interests, or you're unpatriotic. I agree, but I disagree with the writer's implicit assumption that the war is in the interests of the country. Even if true, this simply means that people who were opposed to the war might simply have been wrong and patriotic. I also include in my country's interests that it should genuinely represent the people and act in a moral fashion. One might agree that the war was in the country's narrowly defined interests, but not more broadly defined and still be patriotic.

Patriotism is fundamentally about intentionality. What your intentions for your country? Do you think that bad things should happen to it or good things? The academic who wished "a thousand Mogadishus" in the Iraq war was not patriotic. Someone who thinks that the government is acting immorally and against the interests of the people it was created to represent is quite patriotic, especially if that person speaks up and tries to change the government's actions. In short the government is different from the people, and pro-war policies are not necessarily good for the country.

Earlier today, I had one of McDonald's new Grilled Chicken Caesar salads, with a diet coke. I sat and read a paper on predicative systems of analysis while eating my tasty and inexpensive salad. When I was done, I reflected on how good life is. I'm a free individual: free to make my own choices on what to say, write, buy, eat, wear, etc. I go to a school which is mediocre by my country's standards, but is better than most (perhaps all) schools on the entire continent of Africa. The government is stable, life is good. This is America, and I truly believe that it is the greatest country in the world to live in. I don't disagree with our country's foreign policy or domestic security policy in spite off this love for country but because of it.

2003-04-25T22:05:00.000-07:00

The Ethical Duty of Scientists

Lawrence Krausse writes: "in spite of the implicit hierarchy associated with education, students should get a sense of the 'anti-authoritarianism' of science: that there are, or should be, no scientific authorities whose views are not subject to question." Is this true? No serious scientist would question certain kinds of extremely fundamental methods and facts. No physicists, for example, question whether the Compton effect actually happens. Is this because of the existence of genuine evidence, or rather simply because such things are not allowed. Some relativists have argued that it's solely because such things were never allowed. I think there's merit to both sides.

Let's take an example that's close to my heart. I have never checked the proof that the Taylor series of sin(x) actually is what calculus textbooks say it is. I've seen a handwavy argument which tells what the dervatives of sine and cosine must be, and everything else follows from that (in a way I totally understand). I don't trust the handwaving argument, but I do know that I could go find a book which gives a proof. I think this is possible because I know people whom I trust who have told me that such a proof is possible. It makes no sense that they would give me such an easily disprovable lie, and it likewise makes no sense to assume that such mathematicians can't identify good proofs. Does this mean that my knowledge of harmonic analysis is somehow "radically underdetermined"? No, not at all. It is underdetermined, but in a quite rational way. I don't particularly care about the proof, and I have every reason to believe that it exists. In other words, 10,000,000 analysts can't be wrong. Thus my knowledge of analysis is necessarily a social construct which is incomplete by its very nature. That, it seems to me, is a good thing too. Total logical understanding isn’t the point of mathematics. Mathematical understanding is.

Krausse continues:

Nevertheless, confronting misconceptions, deliberate or not, our own or others', is probably the single most important factor driving progress in science, and in a broader sense society. Scientists must not allow nonsense to remain unconfronted, regardless of whose sensibilities we offend. Once we allow empirical truth to be blurred with impunity in one important area of human activity, we jeopardize the very basis of a healthy democracy.

Only when we are willing to accept the universe for what it is, without myth or fear or prejudice, can we hope to build a truly just society.

So I found myself in Chicago in early April proposing a possibly unpopular thesis: scientists have a special ethical responsibility at this particular time to question our government's actions. It appears that this administration is marginalizing the recommendations of major scientific organizations on the one hand, while defending artificial "research" to support political goals, or, worse still, manufacturing it.

Empirical constraints that may otherwise guide sensible policy making seem to be evaporating.

This raises a good point. Perhaps scientists do indeed have a moral responsibility to expose nonsense wherever they find it. Thus when the adminstration speaks of the deep ethical issues surrounding cloning, scientists must force them to separate reproductive cloning from creation of cloned stem cells. There are no serious ethical issues about the latter. Scientists have failed on this one. Scientists have also failed to express how small the ethical debate on research in embrionic stem cells is. We aren’t talking about some kind of horrible evil here. We’re talking about cells that were already being manufactured in fertility clinics, and were just being thrown away. This was not properly impressed upon the public. Perhaps there’s some evil in manufacturing these cells in the first place (that thesis would require some serious arguments in its favor--it has none), but if so, the evil of researching them is no greater. Certainly it would be wasteful to simply throw them away.

A year ago, the American Physical Society passed a resolution calling on the government to delay deployment of a missile defense system until it was demonstrated to be workable against realistic threats.

Yet the administration scrapped a longstanding international treaty, committing billions of dollars to the deployment of a missile defense system that even under the most liberal interpretation of the data has a success rate of 40 percent.

We would not accept such innumerate policies in the private sector. What if Detroit put on the assembly line a new breed of S.U.V.'s that toppled over when executing curves at greater than 30 miles an hour 60 percent of the time, or if the makers of nuclear power reactors demonstrated that prototypes catastrophically failed 40 percent of the time?

Right. If that happened, government regulation would clamp down on the automobile industry. More importantly, people would stop buying the the SUV’s. In this case, the taxpayers are the people who are buying the system, and our best scientists tell us that it’s fairly implausible to work. Our best political theorists tell us that it’s potentially destabilizing. The message isn’t being put across well enough.

Krausse’s fairly weak thesis is as follows: “A democracy, like science, functions best only when all actions are open to question, and when we require the highest levels of accountability. If there is a risk that politics is being placed above empirical truth on issues of vital national importance, inaction by scientists may be unethical.”

I agree, but it seems to me like there is no real difficulty in this regard. Scientists are acting. They just aren’t being effective at getting their point across. The question of the extent to which ethics is required in science is a good one, but there is no evidence to suggest that it’s not already there. While I hate to sound like an intuitionistic ethicist, we do intuitively understand that these sorts of things are necessary. The system works. No real need for a change, other than perhaps an increase in effectiveness.

2003-04-25T20:40:00.000-07:00

Double Take

I went to the ATM today, and I looked at the balance on the receipt. It was $700 less than I expected. "What?!!", I said to myself, "$700? Where did that go? I don't remember making any $700 purchases." Of course, when one makes a purchase (tuition, books, computer, food, or even the gas bill), one associates the amount with the thing purchased. There is a rational minimax calculation which goes on where the person looks at the benefit and the cost, and says "Ah yes, that's a good purchase." Yet when money is paid out with no tangible benefit, it can be easily forgotten. There is simply no benefit to associate it with. Such was the case with the $700. I did indeed pay out that much money, yet I received no tangible benefit from it. "Ah yes," I recalled, "the fucking government! That's where the money went." My check to the IRS had cleared. I paid my taxes, and all I got was this lousy war.

An interesting side note: the first thing that occurred to me was that my check card had been stolen. Theft seemed like the most rational explanation for where the money went. My opinion on where the money went has yet to change.

2003-04-24T21:45:00.000-07:00

Why Statistics is not Mathematics

I'm taking a statistics course. I fucking hate it. I know, I know, I'm one of those math guys; I should love statistics. No! Liar! Statistics isn't math; it's engineering. In this statistics course, we've had one distribution after another stuffed down our throats. Poisson, chi-squared, normal, hypergeometic, lognormal, gamma, etc. Some things are mathematically interesting (the central limit theorem, for example), but it's just not mathematics. Sure, it has all the trappings of math, esoteric equations, etc. But we never prove anything. The matherial is not guided by the structure of mathematical interest, but rather by "this is on an actuarial exam" or "this one comes up a lot in casualty insurance." Certainly there are mathemtically rigorous accounts of statistics, and I would guess that there are interesting theorems & proofs there. I understand that Brownian motion has spawned some new and interesting advances in analysis. That's mathematics, but having one proof in a one semester course at the college level is not math. The teachers and the students care about it solely because of its practical applications to insurance. That's a kind of engineering, not mathematics.

2003-04-24T15:50:00.000-07:00

Those who don't know their history are doomed to repeat it

A bit of history: I started a blog last July. It was mainly about politics. Then, assuming that whatever readership I had was sure to be uninterested in mathematical ramblings, I started another. Well, I got bored with the whole blogging business. I never posted long things because I was afraid it would bore readers. I mainly posted links with pithy comments. What a waste of time, right! Right. That's why I'm starting a new blog. Why a new blog, and not just revamp one of the two old ones? Well, that's blogger's business--they're no longer mine. I set to delete them both, and I no longer have access to them, even though they're still there. Sitting on Blogger's servers, taking up space and domain names. Is there a point to this? No, but again, that's blogger's business.

So what will this blog be about? Whatever I fucking feel like. I'll swear, I'll talk half-baked politics, I'll talk about Kantian metaphysics, I'll talk graph theory and logic, I'll talk education, I'll talk pointless crap, and I'll talk about the Simpsons and Monty Python. No limits, no restrictions. I have a lot of thoughts. Most of them are ill informed, most of them are crap. You don't like it, don't read.