Polymathematics

Details, Details.

The number of details to take care of during this, my supposed spring break, is astounding.  But I can see the light at the end of the tunnel, and I just found a remarkable simple proof of the existence of the 9-point circle (or Feuerbach's circle) that I will truly try to post before school starts again.  I've been looking for a proof of that for some time now, and I found one involving complex numbers, but the one I'm going to post (here it is!) is quite surprisingly basic, using relatively simple theorems.

I have, however, been keeping up with the blog by reading comments.  Amazing, I'm still getting comments on my .999...=1 post after 2 years.  Most of the comments are just the same old arguments that I address in the follow-up posts.  I owe a tip of the hat, though, to Monimonika...a commenter who has staunchly defended the truth of that fact against every inane commenter.  I don't have that kind of patience.  Way to go, and thanks, Monika.

Okay...pay some bills...clean up a little...then maybe I can start on that proof.  I can't understand why I haven't found any other proofs of this online that are as simple.

Why I Support Barack Obama

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

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.

Nothing To Say

When I started this blog, I had plenty to say.  I had observations on teaching, political semi-rants, cool mathematical content.  Now and then I still have some of these.  And I'm doing some interesting things at work, but telling all the details might compromise my anonymity.  But the tidbits to relate to you all just aren't coming as fast as they used to.  Not that I plan to give up the blog;  I still want to expand my Advanced High School Math Project.  And I'm sure I'll have more to say as the next presidential election approaches.

But this whole child-rearing proposition is...well...very tiring.  The baby is great:  healthy, smart, cute, determined (adjectives that have been independently confirmed, so it's not just Dad talking here).  And for the most part, I'm enjoying my time with her, even if now and then I'm totally exhausted.  By which I mean "now";  my wife and I have made a pact that we will be in bed by 9pm tonight, and we're giddy at the thought of a full night's sleep.

And this tiredness just doesn't leave much room for clever observation or for a whole lot of professional introspection or for finding obscure proofs online and rewriting them in high-school-student-accessible form or for political outrage.  So, forgive me for the lapse in new material.  Look for Ceva's Theorem next in the AHSMP so that my co-writer and I can start talking about lesser-taught triangle centers.

And now...a (hopefully) blissful, long night's sleep for a 1.3 drooplid math teacher.

Initial 1's

A friend of mine has been thinking about the well-known fact that many lists of seemingly random numbers (addresses, physical constants, populations) contain far disproportionately many initial 1's (compared to other initial digits, which decrease in frequency up to 9).

He noted that many physical constants are ratios—constants of proportionality, for example.  So he calculated the probability that any two random numbers x and y between 0 and 1 (random with a flat distribution) have a ratio y/x that starts with a 1 (meaning its first non-zero digit:  .00013 counts as an initial 1).

Cool answer:  1/3

The proof is left as an exercise (unless there's an outcry for it).  Just a little tidbit to tide you over, since I haven't been posting much.

Have I mentioned?

...that regular blogging with a baby during the school year is almost impossible.

Today I watched 58 tests getting spit out of the copy machine.  The first are being written right now as I'm typing.  I will have to examine every page (5 or 6) of every test in the next week or so.  Wish me luck.

(P.S.  I'm now regularly getting significant numbers hits on some of my pages in the Advanced High School Math Project (see sidebar), and I'm convinced it's a worthwhile undertaking.  I'm still looking for submissions, especially during this time that my posts can't be as frequent.)

"Alleged"

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.

How Many Administration Officials Does It Take...

...that step down amid allegations of scandal or abuse of power before the president's praise about Alberto Gonzales' honorable name being dragged through the mud just rings completely hollow?  At some point (Oh, I don't know, when the top law-and-order official in a law-and-order administration puts loyalty to his boss above the law?  Maybe?  Or when actual apparently honorable people resign because they don't think they can do their jobs anymore in an ethical manner?  Maybe?) George Bush is going to have to come to terms with the idea that what he considers honor might only be misplaced adherence to a good-ole-boy-network ethic to hold on to power no matter what.  That's not honor;  that's arrogance and greed.

And my vote for Gonzales' replacement?  Realistically speaking, of course, it will have to be a Republican.  I would trust John Danforth.  He seems moderate, sensible, and beyond ethical reproach.  And as a former senator, he would likely be confirmed easily.

Exponential Sunday Night Blues (with drooplids)

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.

The Last Thing...

that I ever thought I'd post here would be household cleaning advice.  But this really works, and it's so much environmentally friendlier than standard detergents.  This works well (no, I'm serious, it does) to clean countertops, stainless steel sinks, bathtubs, laminate tables, etc.  I wouldn't use it on wood, because of the abrasive nature of baking soda.

It says on the baking soda box that it can be used for cleaning, but I never quite figured out how until now.  Here's some very specific instructions—I'm still refining the process, but this is working pretty well.

Pour a large box of baking soda into a watertight plastic container, and include a small spoon in there, too.  It's much easier to sprinkle the baking soda that way than from the box.  Fill an empty spray bottle (I got mine at Target) with cheap vinegar (4 parts) bottled lemon juice (1 part), and a tablespoon or two of orange oil or peppermint oil (for scent).

Sprinkle a small amount of baking soda (less than you might think) on the surface to prepare it.  Spray a small section with the vinegar solution (watch the fizzing from the chemical reaction—and if someone knows the exact chemistry of that reaction, please post it in the comments;  I'm very curious and I don't remember enough basic Chem to get that right), and scrub with a sponge.  Rinse the sponge (you can scrub the sink while you're at it) and repeat the spray and scrub.  The hardest part is getting rid of the residue of baking soda when you're done.  Remember that the vinegar works better than water to get rid of it, so I've taking to spraying some on a paper towel right at the end of the process to clean it up.  Of course, if there is a small residue left over, it's just baking soda...no big deal.

Just be sure to keep water out of your baking soda container so it doesn't clump.

We've been trying to keep our household greener, and this is a very easy way.  Cheaper than most cleaners, too!

Okay, there.  I've done it.  I've given cleaning advice.  I am now officially, thoroughly domesticated.

UPDATE:  First of all, thanks to the commenter for explaining the chemical reaction.  Second, ummmm, don't use this on a stove.  If you get all the residual baking soda off, it's probably okay, but I thought I had, and then when I used the stove, the stuff I missed turned all yellow and crusty.  So, good for counters, bad for stoves.