Metric Time

Aside from you chronically late people, we all know how time works:

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This system is okay. But also, it’s kind of crazy.

Why 60 minutes per hour? Why 60 seconds per minute? It goes back to Babylon, with their base 60 number system—the same heritage that gives us 360 degrees in a circle. Now, that’s all well and good for Babylon 5 fans, but our society isn’t base-60. It’s base-10. Shouldn’t our system of measuring time reflect that?

So ring the bells, beat the drums, and summon the presidential candidates to “weigh in,” because I hereby give you… metric time.

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Now, this represents a bit of a change. The new seconds are a bit shorter. The new minutes are a bit longer. And the new hours are quite different—nearly two and a half times as long.

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So why do this? Because it’d be so much easier to talk about time!

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The Math Ceiling: Where’s your cognitive breaking point?

One afternoon, the head of my department caught me in the staff room and posed a musing question.

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(He later confessed that he was just curious if he could play puppet-master with this blog. The answer is a resounding yes: I dance like the puppet I am.)

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So, do we have ceilings?

The traditional orthodoxy says, “Absolutely yes.” There’s high IQ and low IQ. There are “math people” and “not math people.” Some kids just “get it”; others don’t.

Try asking adults about their math education: They refer to it like some sort of NCAA tournament. Everybody gets eliminated, and it’s only a question of how long you can stay in the game. “I couldn’t handle algebra” signifies a first-round knockout. “I stopped at multivariable calculus” means “Hey, I didn’t win, but I’m proud of making it to the final four.”

But there’s a new orthodoxy among teachers, an accepted wisdom which says, “Absolutely not.” Continue reading

The Newcomb Paradox

Or, Humility in the Face of Weirdness 

You’re on an alien spaceship orbiting the planet Newcomb. Don’t worry—the air is perfectly breathable. They’ve even got magazines in the waiting room.

As part of their research into human behavior, the aliens have placed two boxes in front of you: a transparent box containing $1000, and an opaque box, whose contents remain a mystery.

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You’re allowed two options: take both boxes, or take just the opaque box.

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It seems obvious. You’d be crazy to leave the guaranteed $1000 behind, right?

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She Wants Us to Study for Math

Our teacher’s gone utterly crazy.
No one can fathom her wrath.
She wants us to do the impossible:
She wants us to study for math.

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How can you study for something
where talent is so black-and-white?
You get it, or don’t.
You’ll pass, or you won’t.
It’s pointless to put up a fight.

Her mind must have leaked out, like water,
and slipped down the drain of the bath.
I might as well “read up on breathing”
as study for something like math.

Math’s an implacable tyrant,
a game that I never can win.
And even if I stood a prayer of success,
how would I even begin?

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My teacher, the madwoman, told me:
First, list the things that you know.
Her mind’s gone to rot.
Still, I’ll give it a shot,
though I’m sure that there’s nothing to—

oh!

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The Math Major Who Never Reads Math

In college, I was one of those compulsive read-everything kids. I even felt pangs of guilt when I skipped optional reading. But there was one gaping hole in this policy of mine, large enough to squeeze a whole degree through.

I never did the reading for math. You know, my major.

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I’m not proud of it, but I know I’m not alone. As students from primary school to PhD have discovered, mathematical writing is a different beast. It’s not just a matter of jargon, equations, or obscure Greek letters. It’s something more basic about the way mathematical texts are structured and paced.

The trick is this: In mathematics, you say things precisely once.

(And no, I’m not going to repeat that.)

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The Secret to All Areas

(Except Area 51, which I Am Not Authorized to Divulge)

or, The World Through Rectangular Glasses

Now that I’m teaching middle school, I find myself wrestling with the sheer number of area formulas that my students need to know (or at least be passingly familiar with). Rectangles, triangles, parallelograms, trapezia…

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The logic is this: A handful of geometric figures keep recurring throughout our world. Once you know how to spot them, they’re everywhere, like the Wilhelm Scream. It’s useful to determine the sizes of these shapes effortlessly, via formulas.

That’s all true, so far as it goes. But reducing geometry to formulas alone can lead to tragic misunderstandings, like when a student asked a friend of mine: “Is there a simple way to remember the difference between volume and surface area?” That’s like asking for a simple way to remember the difference between oceans and deserts: You can only confuse them if you have deep misconceptions about each.

So when I teach these formulas, I try to remind myself of an elegant truth: when it comes to area, everything is rectangles.

And yes, I mean everything.

So let’s begin. With rectangles, finding area is a simple matter of multiplication. In each rectangle, you’ve got a little array of squares:

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