knzhou.github.io
When I was a kid, I thought this minutia was incredibly boring. It turned me off science, which
seemed to boil down to the drawing of arbitrary distinctions and the memorization of arbitrary
rules.
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Thankfully, none of this trivia matters for the Olympiad, or physics in general. It’s cargo
cult learning, which vaguely looks like science, but in reality just keeps you busy.
But if it’s really that bad, why are millions of kids subjected to it every year? And why do
hundreds of thousands of teachers repeat it endlessly, exactly as they themselves were taught?
Well, the underlying problem for the teacher is that solving real, interesting problems takes a fair
amount of dedication and background on the part of the student. Covering minutia is a convenient
alternative, because most students can be trained to do it, and an infinite number of quiz problems
on it can be easily generated and graded. That’s why, when the physics education researcher
Edward Redish once asked his students what the most important equation in mechanics was, the
most common response was
d
=
at
2
/
2. These days, teachers can use programs to automatically
generate hundreds of uniform acceleration problems, so that their classes can stay busy for decades.
In math-heavy subjects, such as physics, there often isn’t enough genuine minutia to fill a whole
course. So curriculum designers compensate by making up fake minutia that no professional actually
uses, such as the ten different mechanical advantage formulas, or the amazingly complex rules for
rounding. Often, the rules you’re supposed to memorize don’t even agree from school to school,
and the reason is that they truly don’t matter. No puzzle in physics has ever hinged on whether
the One True Order of Operations was PEMDAS or PEDMAS, even though people never seem to
tire of debating it on social media. If you’re like I was as a kid, you’ll want to ignore this noise
altogether, but unfortunately grades
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are still quite important at this stage in your life. My advice
is to grit your teeth, learn it just well enough to maintain decent grades, and immediately forget it.
Treat schoolwork as a day job and save your energy for deeper things.
Of course, some of the arbitrary-looking stuff you learn in school actually does turn out to be
important. For example, you’ll probably spend a lot of time manipulating matrices, in what seems
to just be a complicated way to rewrite basic algebra. Most school teachers can’t tell you why this
is worthwhile, but matrices turn out to be extremely important in more advanced physics. So how
can you tell what you need to know? In general, you can avoid this problem by sticking to good
books. They’ll contain exactly what actually matters.
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And learning these questionable rules is the good part; most of the time you just work on cutesy crafts. If
you didn’t go to an average American public school, examples include drawing hand turkeys, decorating cupcakes,
sculpting mitochondria, and making collages. In a typical week, I would make a burger-shaped book report, a Lego
model of Lithium, and a mosaic of Manitoba. I’d also have to bug my Chinese-educated parents to buy construction
paper, not regular paper, leaving them wondering why I needed scissors, glue, posterboard, and 5 colors of paper just
to learn long division. Indeed, most non-Americans are surprised by our emphasis of crafts over actual information,
which ultimately stems from certain modern educational philosophies. These philosophies say that it’s a sin for a
teacher to simply tell students what’s true; they should construct it from themselves. In practice, what this meant is
that we’d receive about two sentences of information, then get assigned some random topic, like quokkas or quasars.
Then we would spend hours copy-pasting from Wikipedia, with the teacher occasionally swinging by to remind us to
“use critical thinking”, which was kind of hard when nobody knew what the hell was going on.
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Grades can be a decent indicator of learning if you have good teachers. But if you have bad teachers, they just
indicate obedience: whether you were able to parrot back dubious information, quickly and reliably, with a smile.
And we all know that the most expensive private schools give out the most A’s. So given the well-known problems of
grades, one might think it would be better to measure students in a way that has been carefully developed, refined,
and standardized by a competent outside party, such as an exam of some sort... but in the United States, such exams
are drastically watered down and deeply out of fashion. That’s why competitions are so important. They are even
more controversial among educators than standardized tests, since many educators view any kind of competition as
immoral, but the truth is that the competitive aspect is irrelevant. The real point of competitions is that they’re one
of the few places left you can put your skills to work on nontrivial problems, to see if you truly understand something.
And they’re definitely the only place you can do that with no budget or outside help.
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