Friday, July 24. 2009
Kenny commented yesterday:
I'm not sure I agree with you that useful and beautiful are inseparable. I like Ken Wilber's division into the "good" (by which he means "morally good"), the "true," and the "beautiful." When I think about it, it seems to me that these three are all goals that we strive for, and they are all pretty independent of each other, and that everything else we strive for can be fit into one of these three buckets.
When I first read about Wilber's good/true/beautiful model, I really liked it. I had always thought that aesthetics – the philosophy of beauty – had gotten short shrift in metaphysical discussions. Beauty is a lot like Consciousness, in that it is a powerful subjective experience that everyone is familiar with, and yet is impossible to rationally pin down or define. The experience of beauty went a long way to justify existence for me – it was something impersonal and transcendent, and yet experienced in a direct, unmediated, and personal way.
Unfortunately, there is a fly in the beauty ointment, and its name is Stephen Pinker. How the Mind Works did a thorough job of deconstructing various human standards of beauty into biologically useful adaptations. Our standards for human physical beauty maps very closely to physical health, youth, and fecundity – that is, a woman looks hot to the degree that she looks like a biologically successful mate. Most people's notion of a beautiful landscape – with trees, grass, water, and open spaces and views – is almost exactly the preferred environment of our ancestors living in African savannas. While our subjective experience of these things has nothing to do with utility, it is almost impossible not to recognize that they came about because of evolutionary usefulness.
The same thing applies to the mathematical arts that Lockhart praised so highly for being valuable "for their own sake." He is perfectly correct – people solve puzzles because it's fun, and it's in our human nature to do so. But ask yourself – why is it fun? Why is it in our nature to want to solve puzzles? Because generalized curiosity had survival value to our ancestors.
The pattern is so consistent that after a few dozen examples, you stop regarding beauty as some platonic ideal, and instead see it as a complex heuristic for detecting things that are useful to survival and procreation. The important point here is that utility and beauty are essentially correlated. Beauty is a heuristic for recognizing usefulness.
Now, because beauty is a heuristic, it can be wrong, or even irrelevant. Not everything that is beautiful is useful - sometimes the heuristic yields false positives. It is still a mystery to us why music should be considered beautiful, when we can ascribe no survival function to it. Likewise, not everything that is useful is beautiful -- our minds have other mechanisms for recognizing usefulness besides beauty. Because beauty is a heuristic that evolved millions of years ago in an environment very different from our current environment, it can especially go wrong.
To the extent that beauty is meaningful and significant, is the degree to which it maps onto some kind of utility. To the extent that it does not map onto utility, is the extent to which it is arbitrary.
None of this changes our actual human relationship to beauty. We will still love beautiful things, simply because they are beautiful. And Lockhart is correct that an ability to recognize and appreciate the beauty and fun of mathematics is ultimately superior to rote skill at manipulating symbols. I just don't think you'll be able to separate the beautiful from the good . . . or, if you can, it won't really matter anyway.
Monday, July 20. 2009
Paul Lockhart's "Lament" repeatedly questions the purpose of education as well as its methods. He doesn't just grieve that true mathematics isn't being taught, but rather that it is not recognized as an art, something that ennobles the spirit and gives joy, something loved for its own sake and not any sort of utility that it brings. He wants math to be lumped in with the liberal arts – literature, music, painting, etc. – things that the education establishment teaches without regard to vocational preparation. This sort of thinking runs counter to the "3 R" crowd just who want their kids to get jobs and balance their checkbooks.
Anyone who would divide education into "the useful" and "the beautiful" is bound to run into trouble, because they are not separate. The useful is beautiful – ask any engineer, businessman, homemaker or child who set about to solve a practical problem and found an elegant solution. The beautiful is also useful – if nothing else, by giving pleasure to its consumers and creators. Any attempt to divide them invariably leads to people running to unhealthy extremes in either direction. On the one hand, you get college professors determined to magnify their greatness by emphasizing their uselessness. On the other hand, you get No Child Left Behind, in which anything that's not part of a pathetically low standard of usefulness is jettisoned. Either way, both utility and joy get destroyed.
What neither side seems to realize is that they are arguing about ethics – in the classic Greek sense of answering the question: "What is a worthwhile life?" Education is just the practical implementation of a notion of ethics. Once you've decided what a good life looks like, you try to prepare your citizens to have that sort of life. Everyone educator and politician starts by saying, "We all agree that we want what's best for the child" – without acknowledging that we have vastly different notions of what "best" really is. You can't say what's a good curriculum until you decide what kind of life you want your children to have . . . and you can't decide that without determining what life is, ultimately, all about. Is life about Work? Is life about Experience? Is life about Happiness?
Last year I went to a workshop for directors of independent schools, a crash-course for new board members. One of the duties of a board of directors is to define the mission statement of the school and to make sure all policies are serving the mission. In talking about mission statements, the facilitator explicitly made the connection to ethics: "Your mission is really about what you want your kids to be. In general, every parent and every school has the same three goals for their kids. We want them to be Successful. We want them to be Happy. And we want them to be Good. The priority you assign to each of those goals will determine the character of your school."
I thought that was a pretty good analysis. Most public schools emphasize Success as the primary goal, with Happiness a distant second and Goodness not even on the radar. Many parochial schools put their notion of Goodness at the top, and then Success, and then Happiness. Waldorf schools explicitly put Goodness (i.e. spiritual capacity) at the top of the list. Happiness probably comes next; Waldorf schools are the few I've ever seen that took Happiness seriously as an important part of human development. No one wants to say that Success comes last – it's hard to be happy without some measure of success – but it is correctly recognized as a means, and not an end in itself.
Friday, July 17. 2009
In his essay on teaching mathematics, Kenny referenced an essay, "A Mathematician's Lament," by Paul Lockhart. The first two pages of Lockhart's "Lament" capture exactly what is wrong with math education today. I described it to my wife (who studied music and studio art in college) and her eyes got big with realization. "So it's not my fault I hated math," she said.
Lockhart's essay sparked several different ideas for me, but here's the most obvious:
Lockhart's critique can be mapped almost exactly onto science education, as well. Ask most people what they remember about their primary school science education, and you get a flash of vocabulary lists and diagrams: solid-liquid-gas, kingdom-phylum-class-order, proton-neutron-electron, nucleus-membrane. Everyone remembers endlessly drilling vocabulary lists, labeling the parts of an insect or an atom . . . for no particular reason. All of these facts are presented as timeless truths, with absolutely no context as to why people cared, how they figured these things out, or what they used to think. The history of science, if it is ever mentioned at all, is just like other history classes (another discipline murdered by schooling): names, dates, and events. "In 1953 Watson and Crick discovered the structure of the DNA molecule." The story, the drama, the passion, the arguments and counter-arguments . . . that's all completely lost.
Sometimes the curriculum attempts to have students do science, in exercises called "labs" – but those are just a bad parody of science, going through the motions of someone else's experiment to prove something the student already knows. "Plants need sunlight to grow. Nooooo shit, Sherlock."
Students come away from science class with all the wrong impressions. If they like science class, they might think that scientists know most everything. If they hate science class, they think scientist know everything about nothing worth caring about.
Sometimes science classes do talk about the process of science . . . a three-page introductory chapter that defines "hypothesis", "experiment", and "conclusion." And maybe "test" and "control." Those concepts are explained and then never, ever used again. Students never get to ask their own questions, identify significant parameters, design their own experiments, draw their own conclusions, or share their findings with their peers. They never get to critique someone else's experiment, question their conclusions, or propose better experiments. They never suffer through counter-intuitive results, or worse yet inconclusive results. In the course of teaching them all about what we know, they are never told what we don't know – the fascinating mysteries that remain to be solved.
Worst of all – you can complete an entire undergraduate college science curriculum and still never do a genuine experiment. Most people don't get to really do science until they get to graduate school. And then they mostly do the experiments their professors tell them to do.
The only thing that saves science from the educational system is the fact that science is one of the most natural activities known to man. Science is just curiosity. "I wonder what angle of ramp will make me jump the highest on my skateboard." "I wonder what happens if I mix blue paint with yellow paint." Humans will always be trying things, sharing what they know, and trying more things.
Tuesday, July 14. 2009
I read Kenny's essay about teaching mathematics so that it becomes obvious: not just how to arrive at the correct answer, but how to genuinely recognize the answer as obviously true. He wants his students to know why communitivity of multiplication is true. I like what Kenny's doing. But it also got me thinking about a different why question . . .
I had a fantastic math teacher at the NC School of Science and Mathematics, Dr. Steve Davis. People warned me before my first class -- "Oh, he has all these stories he tells that have nothing whatsoever to do with math. Especially golf." But then I got to his class, and listened to his stories, and realized all those people were wrong. All his stories were about life, and in his world, math was all about life.
The class he taught was called "Introduction to College Mathematics" or "ICM". (I take credit for coining the popular pronunciation of the acronym: "Ick-um".) The structure of the class was something experimental and new; in fact, the school was being given grant money by Digital Equipment to develop the class, to find a genuinely useful way to incorporate computers into teaching math. The class was replacing pre-calculus, so it had to cover the same sorts of pre-calculus material but also cover a lot of other ground, too.
The first day of class, the very first thing Dr. Davis said was: "Why have you been studying math all these years?" His question was met with stunned silence. Of all the questions we ever had encountered in a math class, this was not one of them. Nobody had the least idea of what to say. After thirty seconds of silence he got impatient and slammed his fist on his lectern. "C'mon, people, WHY? Why have you been studying math? You've been doing it for the past ten years, at least. Why? And don't tell me, 'Because it's good for you.' You are not five-year-olds being told to eat their vegetables."
This, also, was new. We weren't used to teachers yelling at us to answer questions -- at least, not on the first day, and questions we had never been taught the answer to. We were smart kids -- we were not used to not knowing the right answer, and perhaps too embarrassed to admit that we didn't.
"You mean, you actually let someone force you to do something for ten years, and you never asked why you were doing it? You actually let someone waste that much of your time?" His tone was mocking.
Another thirty seconds of silence. "I'm sorry," he said, tossing his chalk into blackboard tray, "But I can't go on. I can't teach this class until you answer that question for me."
"Well, it's useful," one girl timidly offered.
"Yes. WHY is it useful? Useful for what?"
"Well, there's money."
"You mean, making money? I can tell you from personal experience, mathematicians don't make much money." (smile)
"No, doing calculations on money."
"Good. Money's important. But we could have stopped at third grade if all you needed to do was add up your loose change. Why did you keep studying math?"
"Well . . . You have to know math to do engineering and physics."
"Are you going to be an engineer?"
"Ummm . . . no."
"I suspect that most of you will not become engineers or physicists. Most of you will never use calculus in your professional lives. Why do you study mathematics?"
And so it went, in a Socratic dialog, for the whole 45 minute class. I don't remember everything that was said, but I remember where we wound up: mathematics was a tool for modeling the world. It was "the queen and servant of the sciences" (quoting E.T. Bell), the most generalized way we understand the universe, and also the most universally applicable way of making predictions about how something will behave. That set us up for the material we would cover for the rest of the year: geometric probability, the graphing of functions, an understanding of limits, interpolation and fitting of functions to data . . . all of which naturally led us into calculus. More importantly, though, was the way that lecture made me feel about mathematics. What previously had seemed abstract, cold and useless now felt immediate, powerful, and alive. I felt like someone was showing me the secrets of the universe.
I also must confess: he was correct. I became a molecular biologist, but I never used calculus again. What I did do was a lot of algebra and a lot of fitting curves to data . . . the very skills we developed in that class.
I think of all this, after reading Kenny's essay, because Dr. D was trying to give us the other "why". We had spent years learning how to manipulate symbols, and never fully appreciated the value of the tool that we had. Every "word problem" that had been given to us was bizarrely arbitrary: we never knew, exactly, why it was important to know how many apples Johnny had. It was just more symbols, pushed around for no reason. Dr. Davis gave us the reason. No, better yet: he made us find the reason.
Tuesday, July 7. 2009
I got some comments off-line on yesterday's post regarding Sandra Tsing-Loh's affair and subsequent divorce, which have prodded me into clarifying my position on sex within marriage. Discussions of sexual morality always seem to get people worked up – yet another clue that it's something important, and worth discussing.
I thought I was pretty safe, in terms of political correctness, because nine-tenths of my arguments were just citations of things women had written about sexuality within marriage. However, I because I said something directly about marriage partners being obligated to "put out on a regular basis," I crossed some mysterious line that men are not allowed to cross. If a woman like Sandra Tsing-Loh writes about a man who refuses to have sex with his wife for two years, she's allowed to say "that's a raw deal." If a man says it's unreasonable for a spouse to refuse to have sex for two years, then suddenly everyone thinks I'm talking about the sexual enslavement of women, the subjugation and humiliation of half the human race. In other words, I'm the Taliban.
There were multiple levels of rights and responsibilities that are involved in all sexual activity, and it's easy to get them confused:
When I spoke about "putting out on a regular basis," I'm definitely not talking about #1. All human beings have a right to the sanctity and integrity of their own bodies. Everybody has a right to freely choose when and with whom to have sex. Using physical force to coerce sex from another is rape, even in marriage, and is a crime in all civilized nations. Nobody's forcin' nobody to do nothin', ok? And, to be 100% clear, everything I'm writing here applies equally to woman and men, so there's no double standard going on.
So, that being said . . . I do think a married person has a moral obligation to have sex with their spouses. There are very few conditions in the typical, traditional marriage contract that are spelled out in detail. All that "love, honor, cherish" stuff is pretty vague on the details and open to lots of interpretation. There are a couple things that are extremely explicit, though:
If an arrangement between two people lacked these principles, I don't think we would call it "marriage." (We could argue about that, but let's not. I think we can agree that this is the traditional understanding of the meaning of marriage.) Because sexual exclusivity is explicitly stipulated as a core principle of the arrangement, I think it deserves very special consideration. It wouldn't be spelled out that way unless it was important. I think it's also clear that this is something going against the grain of human nature: if it were perfectly natural and normal and expected to be monogamous for our entire lives, we wouldn't have to make solemn promises about it.
If you make a commitment to lifelong sexual exclusivity, it seems to me that the conscious, prolonged attempt to withhold sex from a spouse, contrary to their desires, is clearly breaking faith with that commitment. People don't get married to become celibate. They have a reasonable expectation to reasonable access to sex.
Ahh, but what's "reasonable"? That's where all the marriage counselors and sex therapists get involved. I'm sure the answer is dependent on lots of personal factors of health, opportunity, and desire. I've already said that "never" is not reasonable. Usually, "reasonable" is whatever the couple can mutually agree upon as reasonable, or at least acceptable.
This is the point at which I move from "moral obligation" to "strongly recommended advice." And that advice is just a rehash from a dozen pop psychologists, which is this: you should have sex whenever either spouse wants it.
Mostly, this comes out of my functional extension of the Golden Rule, strongly recommended for good working relationships of all kinds, which states: All reasonable requests made in good faith should be met in good faith. If your spouse asks you to do something, and it's reasonable, then you should do it. Or, to put it another way, the default answer to spousal requests should be Yes. If your wife asks you to move the junk off the porch because company is coming over, you should do it. Maybe you have a perfectly good reason not to move the junk right this moment, because you're busy or tired or whatever – that also is a reasonable request. Of course, this principle would be quickly subverted if it wasn't coupled with another principle, which is: Don't make unreasonable requests. Ask for what you need, with the understanding that everyone will work in good faith to meet everyone's needs.
Usually, when I spell out this philosophy, people think it's silly – either because they agree with me and think it's so obvious that it isn't worth saying, or because they totally disagree and think such an rule would result in someone, at some point, being totally taken advantage of. For my money, it is an essential part to any good working relationship. All kinds of interpersonal friction are minimized if you trust that the other person has a good reason for their requests. It restricts arguments to things that are worth arguing about. It communicates trust and respect.
If it works for putting the cap on the tube of toothpaste or taking out the trash, it also works for sex. Make your best effort to meet the needs of your spouse, and you will maximize everyone's peace and contentment. If you ignore their needs and desires, you will pay a price for it.
Monday, July 6. 2009
Word of infidelity travels fast. Sandra Tsing-Loh, a writer I have long followed and enjoyed, confessed to an affair and impending divorce in her latest essay in The Atlantic ("Let's Call the Whole Thing Off," July/August 2009), but I didn't even get the magazine in the mail before I was reading reactions to it in the Wall Street Journal ("Losing Confidence in Marriage," July 3-5, 2009). How sad.
I don't want to bust Sandra's chops just yet, because the tone of her essay captures enough pain and regret to engender my sympathy, if not my understanding. She uses words like "horror", "emotional pain", and "humiliation" to describe the experience. She consistently expresses her concern for the well-being of her children as her primary and overriding goal – good. I feel almost exactly the same sadness for her that I feel when a personal friend goes to splitsville. And yet, bust her chops I must. If she decides to write a think-piece in a national magazine questioning the sensibility of lifelong monogamy, then she is quite literally asking for it.
Sandra is well aware that a recently-divorced adulterer is not exactly a credible witness when it comes to questioning the value of marriage. I credit her with a writer's courage to put it out there, anyway. Still, what comes out is neither a tell-all confession nor a robust argument for why marriage is a failed institution; underneath her mea culpa is a stubborn attempt to find justification for her actions. Rather than divulge the raw details of her own situation, she lays out her critiques in the confessions of her girlfriends, who tell a consistent tale of career women marooned in sexless marriages. For instance, Rachel, a successful environmental lawyer, is married to Ian, a work-at-home freelancer, who is to all appearances a model husband: he remodels kitchens, cooks gourmet food, takes the kids to soccer practice. Yet he allegedly refuses to have sex with his wife, because she is too fat, sloppy, and undisciplined. Evidently internet porn is a sufficient outlet for him.
As far as I can tell, this doesn't prove that marriage is broken – just that Ian is an asshole. I think anyone who enters into a contract of sexual exclusivity can rightfully be expected to put out on a regular basis. That's part of the deal. It used to be that everyone knew that, too. Withholding sex is about as destructive and hurtful as infidelity.
Sandra seems to be slyly implying that she, also, was stuck in a sexless marriage, presumably due to an unreasonable and/or unlovable husband. Yet, based on her essay from two years earlier, "She's Just Not That Into You," in which she confessed to preferring food to sex with her husband, it seems she was the one refusing sex. At that time she was arguing for the normalness and acceptability of low libido -- hey, c'mon, it's not that important anyway. Now that she's found a man who can make her engine race again, sex is suddenly too important to override her concern for her family. Either way, she implies she is powerless to resist her biological urgings or non-urgings, and in fact morally obliged to accept them as they are. If he doesn't thrill me anymore, and someone else does . . . well, what do you expect me to do?
Interestingly, very similar observations are made in other Atlantic essays that she references . . . but which come to the exact opposite conclusions. In "The Wifely Duty" (January/February, 2003), Caitlin Flanagan also explores the phenomena of undersexed marriages, and finds, not the irreversible wilting of desire due to age or familiarity, but rather overworked career women too tired to feel amorous and too resentful of their clueless husbands, who once again failed to notice the house is out of toilet paper. Flanagan's advice, echoed by lots of therapists, is that regular sex, whether you feel like it or not, is the cure to lots of marital ills, and that (gasp) it's actually fun for everyone once you get going.
Another essay, "Of Sex and Marriage," by Cristina Nehring, points out that all the things that create good marriages – communication, equality, monogamy, honesty, security, harmony – are also often the things that kill libido. We are attracted to the unattainable, the wild, the uncontrolled, interloper – everything marriage isn't. And yet again, the conclusion is not that something is wrong with marriage – rather, something is wrong with our understanding of sexuality. Her prescription is not to bemoan the loss of sexuality – after all, there are more important things in life – but to take responsibility for it and "remystify" it. In other words, to work at it. She advises a more subtle and artistic approach, rather than the tedious regularity of the "wifely duty," but still, the direction is the same: happy marriages can and do find ways to have sex.
So, in the end, I can't make any sense of Sandra's arguments. Men unwilling to have sex with their wives? I confess, I have never heard of such a thing, outside of a few closeted gay men. Women might complain about men's promiscuous and seemingly undiscriminating sexual nature, but it has one advantage: men are ready to have sex anytime, anywhere, and with anyone – even their less-than-svelte wives. If women find themselves unable to sexually enjoy their husbands, the condition is not incurable. It certainly doesn't have to prevent sex. It definitely doesn't signal the end of a marriage. Why did Sandra do it? All I can say is: no good reason.
Saturday, July 4. 2009
In response to my rant about government-run health insurance being positioned as a "competitor" to private health plans, Kenny writes:
I suppose I should be comforted by the fact that Obama's rhetoric is rigorously moderate. But actually the opposite is happening; it is only making me more cynical. Obama made some very moderate statements about the auto industry, as well. Here was his position on March 30:
Ah, good. Sounds very moderate and responsible. But, a few months later, the government winds up acquiring a 60% stake in General Motors. I guess the United States government was interested in running GM.
When Obama was running for president, he was widely lauded as the sign of a "post-racial America." His "more perfect union" speech on race was an eloquent statement of how we can move past identity politics and embrace a common good. But then his first Supreme Court nominee is Sonya Sotomayor, who, no matter what you think of her relative merits, is not winning any prizes for being a "post-racial" icon. Were she not a Latina woman, would she have gotten that nomination? The best that people can say of her is that she is merely competent.
Then there's the banking bailout. On February 20 White House press secretary Robert Gibbs, when asked if the Obama administration would seek to nationalize CitiGroup and Bank of America, he responded that the administration continues to "strongly believe that a privately held banking system is the correct way to go." But in the following months, the administration proceeded to put the banks in a headlock, forcing them to take aid that is worth more than double the banks' own capitalization, whether they want it or not, regulating their compensation, secretly pressuring executives to make certain acquisitions and not complain about it, either. Now most pundits seem to agree that CitiGroup and BofA are essentially nationalized in effect if not in name.
Do you see the pattern here? Moderate rhetoric, followed by extremely liberal action. Some people on the left see this as merely masterful politics -- after all, the winning strategy has always been to make your own position appear to be the middle of the road. But how much longer can you say one thing, and do another, before it stops being politics and starts being hypocrisy?
Wednesday, July 1. 2009
On the big call-out quotes page in Newsweek this week, I saw the following quote :
Normally, I can stay calm about politics. But this sort of flagrant attack on common sense makes me angry. The president is insulting my intelligence.
Here's an analogy for you:
Let's say all the umpires in Major League Baseball got together and decided that they would form their own baseball team, and compete against the other Major League teams. They are going to play -- AND officiate -- all the games. Who do you think is going to win in a match-up between the Yankees and the Umpires? The Umpires can't hit 90 mph fastballs . . . but they don't have to. They just call them balls, and every single player up gets a walk to first. The Umpires can't pitch a ball over the plate to save their life . . . but that won't stop them from calling them strikes anyway. Every game is no-hitter, and the Umpires cruise to a World Series victory.
Does anyone have the audacity to call this a "competition?" If the Yankees give up in disgust, does that mean the Umpires are a better baseball team?
The federal "public option" for health care does not have to worry about making a profit . . . unlike every other insurance provider. It's easy to win market share on price, when you can give the product away. The government does not have to persuade people to pay for its products -- they compel payment, through taxes. Or just print more money. The government does not have to persuade doctors to participate in their insurance plan -- they can mandate that they do, or not practice medicine at all. The government does not have to negotiate with pharmaceutical companies -- they mandate drug prices, regardless of market value. Oh, yeah, and they can't get sued.
Let's get this straight. The Obama administration does not intend to fix healthcare by "competing" with private companies, in any meaningful sense of the world. They are doing just the opposite: using monopolist power to kill all competition. If they want to nationalize the healthcare industry, fine, I can understand why they might want to do that. But don't try to dress it up as a "competitor" in a free marketplace.
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