Math Spectrometer

Memorial Day

The rabbi said, and he was right, that for many of those present in the synagogue today, Memorial Day will never be the same again.  The former student at my school (I never taught her, but I did teach siblings) was killed in the line of duty.

The details were so sad.  The line of well-wishers stretching out of the sanctuary, snaking around the hallway, with more and more arriving the whole time.  The classmates, some of whom I barely recognized, teary-eyed and stunned.  The dozens of uniformed military personnel, some of whom probably didn't know her.  The teachers, most of whom were long-time colleagues (you had to be at least a little bit long-time to have known her), who were were proud of their influence on her, but saddened to have to be reminded of it today.

The old veterans 2 rows in front of me who surely never met her, but who tearily saluted as her casket was carried by.  The revving of the motorcycles carrying more vets who showed up to become part of her funeral procession.  The difference in their eyes and in the eyes of the rest of us who haven't been to a hundred of these.

The pathetic wastes of carbon atoms who came (a few blocks away) to cheer the deaths of servicemen and servicewomen because it fits their (so-called) religious beliefs.

Half of my brain wants to say that her death was so senseless.  But the other half keeps reminding me that the word 'senseless' is disrespectful and not quite accurate here.  Adjectives fail me.

Requiscat in Pace

Dear Andrea

I have a few students this year (and every year) whose main impediment to learning happily and calmly is the pressure they feel from their parents.  One had been getting low C's and D's for a while, but worked really hard and got a respectable B- on a tough test.  But he was unhappy—his parents have conditioned him to feel like all hard work will always earn A's, and anything less represents some sort of failure.  I have another student (I'll call her Andrea) who is a perfectly fine math student.  She earned a B- for the term, and will probably stay in the B or B- range.  Getting an A in this class at my school probably puts a student in the top 10-15% of all the math students in our entire major metropolitan area.  Andrea is not quite of that caliber, and she easily accepts that.  But she's no slouch, either, and she works pretty hard, and she does fine.  But she came to me worried about her grade, because she thought that if she got some form of C for the term, her parents would "literally kill [her]".  "Literally" is obviously an exaggeration here—I don't think they'll even hit her or anything like that.  But I do know they put an extraordinary amount of pressure on her.  The only reason, I suspect, that they were okay with her second place finish in the state competition in her sport was that she lost the in final round to her older sister.

So.  An open letter:

Dear Andrea,

You are a good math student.  In fact, at some point, you're going to have to face the fact that you're probably even a better math student than you think you are.  I know you've been conditioned to believe that getting an A is the only acceptable evidence of being a good student, but I've been doing this teaching thing for a long time (about as long as you've been alive), and I want you know that getting an A isn't everything.  You work hard, pay attention in class, and you're intellectually curious.  If you weren't worried about your grade, I suspect you might actually enjoy math more than you let on.  I would rather have a room full of students like you than a room full of A students who are apathetic and jaded.

I know that with some encouragement, you can probably come to accept your grades and even be as satisfied with them as I am.  But I also know that your parents are a different story.  They control most aspects of your life, and you have to make them happy.  I will be glad to tell them everything I'm telling you, but from what you've said, that might not convince them (at least right now) to cut you some slack.  Objectively, it seems silly for anyone to think that you're going to be one of the top students in every one of your classes for your entire life.  That's just not possible for normal people like you and me.  Your parents will understand that eventually.

But yes, that doesn't solve your problem, does it?  You have to deal with them now.  And you might have to deal with them until you leave home for college, or maybe even longer than that.  So my best advice is this:  you have to see your parents' pressure on you for what it is.  They love you.  They want the best for you.  They have some very specific ideas about what 'success' means, and those ideas involve doing everything right all the time.

They're wrong.

They're human beings, and so they're flawed.  And you love them, so you have to accept those flaws.  They might make your life miserable in a lot of ways, but it will not be forever.  Believe your teachers.  Believe that voice inside yourself that tells you that you really, really have done your best, even if you didn't get an A.  Find ways to gently bring your parents to understand that you can't be the best at everything all the time.  No one can.  Don't yell at them about it—that will just make them dig in to their beliefs more strongly.  Playing the angry teenager just reinforces their idea that you're not mature enough to understand their position that you could be working harder and getting A's.  Your teachers will back you up on this if you really do continue to make a genuine, sincere effort.

It's hard for any teenager to see his or her parents as just regular people.  And you won't be able to do that completely for a long time.  But sometimes, regular people are just...wrong.  And that's what your parents are now.  Their pressure comes from their love for you, but that doesn't make it right.  Keep making good decisions in your life like you are now.  This will help them trust you more.  You will eventually earn the credibility to say "Mom, Dad, sorry, but...I really did the best I could, and this is how it turned out.  And if it means I don't get into MIT, then, well...that's okay with me.  I'm satisfied with my effort and with the result, and I hope you can be, too."

Sincerely,
Your teacher, who has seen more students in your position than your parents have.

It Really Happened?

I still sort of can't believe that Barack was elected.  After 2000 and 2004, I really had to see it to believe it, and I only barely do believe it.  Watching the crows erupt in cheers and tears when the news programs called it for Obama was one of the most moving experiences I can remember outside personal, family events.

The fact that crowds full of people of every race were celebrating the election of a Black man a mere 43 years after the Voting Rights Act is a bewilderingly fast reversal of attitude for this country.  Sure, there are still plenty of people who think Obama is going to destroy the country by...I don't know...agreeing to surrender to bin Laden when he calls and asks, turning us into a socialist country by allowing the government to buy a stake in financial institutions (oh, right, the Republicans already did that), taxing us into oblivion (an excellent way to ensure long-term control of government by the Democrats, I'm sure), or flat-out killing babies (an actual belief documented by a relative, who was told this directly at work).  But for the most part, it was a flat-out, fairly fought, and significant win.  For the Black guy.  Wow.

But having said that, I'd like to add that I'm equally happy just for the knowledge that we're finally getting a serious, thoughtful, dedicated public servant back in the White House.  Someone who I'm pretty sure is a decent, smart, compassionate, humane person.  Someone who will think about the less fortunate as much as the middle and upper classes.  Someone who wants our country to win the respect of the world via our actions, not our military.  Someone who can turn that respect into greater national security.  Someone who wants to hold on to power by doing the right thing and earning popularity and votes, not by manipulating the political system so that opponents lose elections due to disenfranchised voters and unsympathetic, partisan judges.

So, sure, the accomplishment of a majority white country putting a person of color in charge (unprecedented, as far as I can tell, though I'd welcome comments correcting that claim if I'm wrong) is an amazing one.  But mostly?  I'm just glad the long national nightmare of George W. Bush is just about finally over.

Starting Over

Well, we're about to start a new school year.  I've been on massive child-care duty this past week because my daughter's daycare center is on vacation, and my wife has already started her school year.  My daughter is cute, adorable, funny, and growing up to be a great kid (she's almost 2-and-a-half), and I have great respect for people who stay home and take care of kids all day;  but having said that, being a stay-at-home parent certainly isn't the job for me.  I'm actually kind of excited to start a new school year.

Some teaching goals:

1. My long-term project (proofs of theorems involving triangle centers) in my geometry class was quite successful;  so much so that I want it to become the focus of the whole year this year, and not just the last half.  So I'll be identifying relevant theorems from early on in the year, and supplementing as necessary starting as early as October.  I'm glad to take a little extra time in the beginning if it means a more successful large view for the kids.  I just hope they buy into it as well as last year's students did.
2. I have to be sure that I don't let a few students infect the attitude of a whole class.  Last year, the students with good attitudes barely spoke up in a couple of my classes, and it really hurt the everyday banter with them when I had to get on some of the other kids' cases.  I'm not sure what better strategy I can use this year (if I have to), but I'm going to have to think of something because I just didn't feel like I was serving some of my most deserving students very well.
3. I gotta be better organized.  I cleaned out all my files over the summer, and I'm starting over with more space allotted to organization;  this is my chance.  Now or never.  I need to write down more of what I teach and plan ahead better, especially in my algebra class, where the long term is complicated by the fact that I'm not crazy about the book's organization, and I stray from it regularly.  Someday I'll have to either find a better book or just...y'know...write my own.  (Anyone have any algebra books for fairly fast-paced algebra classes they especially like?)

My classes are a little smaller this year, so that should help with the amount of grading.  Also, I'm not starting the year having to spend quite as much time with my daughter—she's much better about going to sleep.  On the other hand...I'll be following the election pretty closely, so the early part of the year will have plenty of distractions.

I know...boring post...I'm sure I'll have more to say about teaching once the year starts.  For now my wife and I are eagerly awaiting Barack Obama's vice presidential pick.  We'll know in, oh, 15 hours (probably) but the suspense is killing us.

The Libertarian Case for Affirmative Action

I know, I know, that seems like a contradiction in terms.  I'm not a libertarian, although I do have a natural aversion to government interference in my personal life (I mean, who doesn't?), and I think that the market is a better option for regulation of some portions of society than many of my fellow liberals probably think it is.  But affirmative action (giving some preferences in hiring or college admissions based on race or gender in order to redress the inequalities created by past outright discrimination) is a libertarian's worst nightmare.  It doesn't treat all people equally, and it involves government interference in business and education.  Many libertarians are now seeing Barack Obama's success and popularity as evidence that affirmative action is no longer necessary.  If white people are willing to elect a black man to be their president, this argument goes, surely there can't be all that much day-to-day discrimination anymore, and thus the reasons for affirmative action no longer exist.

The libertarian solution to the problem of blatant discrimination in the workplace or in college admissions is simply to make a minimal law that says "it is illegal to discriminate based on race or gender", and then enforce that law vigorously.  The anti-affirmative action stance is voiced in this article on this very subject.

But I have to disagree.  Not on principle, but as a practical matter.  I simply don't see how that law is enforceable in any practical way.  Let's imagine a typical situation in which such a law might be invoked:

A trucking company is located in an urban area that is racially diverse—say, 40% black and 60% white just to simplify.  This trucking company has 150 employees, and 6 of them are black (that's 4%).  This has been the approximate percentage for a few years when a group of 5 black local residents who were denied jobs there files a suit under this theoretical anti-discrimination law.  How should the government handle this?

1. Approach the owners directly and ask about the disproportionately low hiring rate for black people?  The obvious response is simply "They were denied jobs because of their employment history, not because they were black."
2. Confront the owners with resumés showing that the 5 candidates appear to be well-qualified?  Response:  "They were not as well-qualified as the other applicants for those jobs."
3. Demand all records pertaining to all hires over the period of time covered by those applicants' applications, and try to determine whether any racial preference to white people shows up?  Response:  "I was personally more familiar with the references (previous employers) given by the people we actually hired."
4. Research all previous employers of all applicants to determine whether the current employer only does business with other racist companies, thus making reliance on references a measure that is  inherently biased against black applicants?  Response:  "I was unaware of any bias in those companies."
5. Point out how an inability to find more than 4% qualified black employees in a 40% black neighborhood (with 5 qualified applicants already present as parties to the lawsuit) simply strains credulity?  Response:  "I remember those applicants—I just simply don't think they would have fit in with our work force."

What can the government do here?  Second-guess every hiring decision made by this company?  What if the company is huge, with decades worth of hiring records?  Are we going to tell businesses exactly what kinds of qualifications do and don't matter for the purposes of hiring?  Is "not fitting in" an unacceptable reason to deny someone a job?  Isn't enforcing such a broad anti-discrimination law simply too intrusive?  I would certainly think so if I were in charge of hiring for any company.  I'd rather simply be told:  "If you want to satisfy us that you're not a racist, you'd better have X% of your workforce be non-white as evidence that you're not an outright racist company."  Then I could do my own balancing of "fitting in" with overall workforce composition.  That seems a less intrusive way to enforce equal opportunity.  We can discuss and argue the validity of any specific formula for X, but a cold statistical analysis has to be a more libertarian solution than case-by-case meddling in every business's hiring process.

Now...will it happen that some qualified white applicant will be denied a job in favor of an arguably less-qualified black person? Unfortunately, probably yes.  Although I would bet (without any real way to know for sure) that this would happen less often than a qualified black person losing out to racism.

Note that #5 above seems like a pretty good argument by the time a possibly racist employer has responded to the evidence in such a slippery manner.  Yet it is essentially an argument from quotas.  We should see quotas not as a way to force a company to hire and promote X% black people, but rather as the least intrusive and most flexible way to obtain evidence of racist or non-racist hiring practices.

Furthermore, note that a white person who is denied a job (supposedly) due to affirmative action will probably consider legal action, and fully expect that their complaint be taken seriously and that the situation will be rectified.  I would argue that affirmative action is simply the only practical, large-scale solution to meet that same expectation by black people, who have, in fact, been demonstrably discriminated against historically.

And finally, if it's indeed true that affirmative action is no longer necessary because white people don't typically discriminate based on race anymore, then...well...achieving that X% level of black employees simply won't be difficult, will it?  That means that any such law will never again be invoked to challenge a non-racist company, so what's the problem?

Hi, and Welcome

Hi.  And welcome.

Some of you already know me.  I'm Polymath from the Polymathematics blog.  I've decided to separate my blogging of my personal life, teaching experiences, and political views from my math writing.  My math writing gets much more traffic, and I'm hoping to do more of it, and I don't want my more personal blogging to distract from that.  At some point soon, I will be adding a third blog containing explanations of basic high school math concepts.  Most of the explanations I've seen online strike me as being neither very clear nor very helpful to a confused student.  I may be kidding myself, but I think I can do better.  Disclosure:  I also hope to write high school math texts (in publish-on-demand format) that I can make some money from.  I will provide those links when they become available.  The original blog, linked above, will remain alive as a place to write about more advanced math.  In particular, I plan to continue expanding the Advanced High School Math Project.

This blog will contain all of my new personal posts on teaching, family, and politics, and it contains some of my "greatest hits" from the original blog.  In the past, I have tried to keep my identity hidden so I could blog more freely about my teaching experiences.  I will no longer try to remain anonymous;  I don't think that's feasible if I plan to sell my texts in the future.  I'm not going out of my way to reveal my identity, but my observations might occasionally have to be censored because of this new policy.

Welcome (or maybe welcome back) to my life.

Why I Support Barack Obama

(original post and comments here)

I know, I know.  I've promised more math posts and failed to deliver.  The truth is, it takes quite a while to write a math blog post because I have to design all the diagrams and equations and convert them to the right format to upload.  So more math posts, I promise, I promise.  Eventually.

But as much as I like math, a much more weighty issue is rising to prominence:  We will elect a new president in about 9.5 months, and that person will take office in less than a year.  I've made no secret about my disdain for the current administration, and for George W. Bush, in particular.  I've also mentioned my admiration for Obama before.  But now I'm more convinced than ever that he is the right choice by far to be our next president.  I know my readership is not very high, and most people land here for my math pages.  But I think my reasons are good, and I would feel uneasy if I didn't do something here to tell you what those reasons are, especially with only a week to go before "superduper" Tuesday.  Please feel free to link to this post if you agree with me (or if you disagree, for that matter).  If you must steal my words without attribution, at least they might help elect the man.

1. This is the reason that I hear the least, but it's among the most important to me.  The president, in addition to being our leader, is our representative—the public face we show the world.  Our modern world is no longer one which appreciates a superpower throwing its rich, white, establishment weight around.  Europeans, South Americans, Middle Eastern countries, and sworn terrorist enemies resent that to varying degrees about us.  Electing a young, multi-ethnic president will present a much different face:  one that says, "We've come to realize that our strength comes from our diversity.  Our economic strength resides in the hard work of our immigrants (both willing and unwilling) in our present and our past, and we all have a stake in our success.  There's more to this country than you are accustomed to seeing."
2. Let's face it, the resentment I feel towards George Bush and the resentment a lot of Republicans feel towards Clinton (both of them, actually, but Hillary, in particular) are not helpful emotions in unifying this country to face the world's threats (terrorism, genocide, environmental degradation, shortages of natural resources like oil and water).  Obama is probably the least divisive candidate on either side.  He attracts very liberal Democrats (Like most of the Kennedys!  C'mon, that's gotta count for something!  They're saying:  "If you voted for John, or if you planned to vote for Robert, please vote for Obama.") and even conservative Republicans who are attracted to his integrity and his willingness to seek common ground.  He isn't perfect, of course, no candidate is.  But he offers the best hope of emerging from the D./R., RedState/BlueState, Fundamentalist/Secularist stalemate corner that our politics of division (thank you, Karl Rove and Lee Atwater) has painted us into.  Clinton is the opposite.  She's so divisive that Republicans will come out of the woodworks to vote against her in the general election.  And even if (somehow) she really were elected, it would just perpetuate the antagonism, and that has just got to stop.
3. It's a little clichéd, but true:  a president of color will surely send a strong signal that people of color (and, frankly, all people not born into White, male, Christian privilege) need no longer assume that this country won't let them succeed.  It won't be an end to racism, of course, far from it.  And I'm even a bit worried that conservatives will use an Obama presidency to claim that "Racism is over! We don't need affirmative action or any of that anymore, see!"  But despite that possibility, the benefits outweigh the risks.  At the very least, an Obama candidacy will emphasize the political importance of people of color, even if loses.
4. He's smart (extraordinarily so, I think) and confident about it.  This means that he won't, out of insecurity, appoint cronies and yesmen to important positions around him.  Bush didn't pick grown-ups (Gates, Petraeus) for important posts until late in his presidency, and Clinton has too many favors from her husband's administration to return to make wise, considered appointments.  I have confidence that Obama wouldn't hesitate even to name people he disagrees with to cabinet positions if he respects their accomplishments and thinks they'll do a good job.
5. He clearly inspires young people to be involved in politics.  The supposed apathy of genX and genY has worried older and "wiser" generations for a long time now.  But Obama is inspiring record numbers of young people to be involved and vote.  While the Baby Boomer generation might not be happy about losing power to a younger generation, the change has to happen sometime, and it should happen by inspiration, not by default.
6. I believe he has real integrity.  For one thing, he has tried to run a decent campaign.  Some tactics that could be considered underhanded are probably impossible to avoid, but I really believe he is committed to changing how political campaigns are designed.  For another, he talks about sacrifice and the need to for everyone to change—his speeches are inspiring without being all warmfuzzyfeelgood all the time.  For a third, he has real experience in the trenches of community organizing, which he undertook because he believed in it, not because he thought it would bring him the presidency (kindergarten aspirations, notwithstanding).

There.  Those are my reasons.  I hope someone is listening.

Not In Our Country

(original post and comments here)

When I get back from vacation, I promise I will post some more math posts in the AHSMP.  But for now, you should take a look at this link.  We tend to think that that violence against women is decreasing in our country.  That law enforcement organizations have learned to take rape and domestic violence more seriously.  And perhaps they have.  But not everywhere.  Of course, this situation is a legacy of our awful treatment of American Indians, and part of the problem is that, according to the law, it's not entirely clear if this really is taking place in our country.  But for the sake of the women of South Dakota (on or off of a reservation), let's hope the law enforcement and funds are provided to help that shelter.

Please consider a donation of goods or money—for the women's sake and to send a message that this is unacceptable in our country.

"Alleged"

(original post and comments here)

Yet another public figure is involved in a possible "sex scandal".  Senator Craig from Idaho was arrested for lewd conduct for allegedly engaging in behaviors that indicated to an undercover police officer that he was interested in a homosexual liaison.  I stress the word allegedly not out of sarcasm because I believe he really did it (I don't really have an opinion about that), but because of how that word is used in some of the reports about it.  This article, in particular, bothers me.  It talks about his "alleged homosexuality" and about a blogger who had "accused Craig of homosexual sex".  Using words like alleged and accused is especially harmful here.  It perpetuates the myth that the crime he stands accused of is being gay or bisexual.  That is not his alleged crime.  His alleged crime is engaging in lewd behavior that would have been a crime whether he was soliciting homosexual or heterosexual sex.

The brain science is pretty clear that sexual preference is a biological drive, not a moral choice.  If Craig made any poor moral choice, it was (allegedly) to break the law by propositioning for sex in a bathroom.  Also, if it turns out he is in fact gay, then choosing to oppose equal rights for gay people is at best sad and self-loathing and at worst hypocritical.

Our language often implies more than we think.  Let's use words like alleged and accused for crimes, not for being gay.

Exponential Sunday Night Blues (with drooplids)

(original post and comments here)

Sunday nights are never very fun for my wife and me.  We've named it the Sunday Night Blues.  You can't really start on any project because you'll have to put off the end when the week hits.  Everything you do just feels like biding time before the week starts.  You should be going to sleep, but you're not sleepy because you slept in or took a lazy Sunday nap.  But every minute you stay awake is another unit of grogginess you'll have to deal with the next day.  (By the way, what is the unit for grogginess?  I propose the drooplid.  You are 1 drooplid groggy if you do that head-jerking drift-into-dream-for-3-seconds thing we're all familiar with.  If you're still mostly able to function, but you're still kind of tired, you're probably around 60 centidrooplids groggy.  If you really can't keep your eyes open, you're probably 2 or 3 drooplids groggy.  Any takers on that unit?  Other suggestions?) So all you can do is watch lame TV or cruise the internet or play a game and think about work.  That's the Sunday Night Blues.

My school starts up again in four days.  Sure, I'm ready.  Day One will probably go fine.  I'm eager to meet my classes, and the constant daycare I'm providing to my daughter (while wonderful for bonding) is getting tiresome.  There's only so much intellectual interest you can get from an 18-month-old.  But...I can't start any big projects, etc., etc.  It's Exponential Sunday Night Blues.  And since the baby woke up before I wanted to, I have the Blues and I'm 75 centidrooplids groggy.  Good thing this kid is so darned cute.

UPDATE:  I realized that I need to calibrate my scale of drooplids.  You know what 1 drooplid is, but we need a reference for 0 drooplids.  0 drooplids is the amount of grogginess after the following series of events:  you got 8 hours of sleep on Saturday night, and you're at home alone all day on Sunday, and you take a nap at 12:30pm without setting an alarm, and wake up briefly at 1:30, but you still feel a little tired so you drift back to sleep until 2:45, when you wake up on your own and you realize you still have half a free day with nothing to do but read and work out and watch a movie.  I don't expect that to happen to me again before I retire, but that's 0 drooplids.  Insomnia due to caffeine is measured in negative drooplids.