

Guessing the Teacher's Password - t0pj
http://www.overcomingbias.com/2007/08/guessing-the-te.html

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Alex3917
Someone should write a book like the little schemer but for physics. One of
the best classes I took in college was somewhat like this. We measured the
period of the pendulum using our heartbeats, and we also measured how long it
took things to roll down differently sloped ramps. From this we derived the
period of the pendulum and the relationship between slope and speed.
Eventually we used this to derive the universal law of gravitation using the
period of the moon's orbit as the only given. It was pretty cool because there
was no math involved. Instead of using calculus to derive the equations, we
instead found them inductively by iterating over a couple thousand lines in
excel and then looking for the pattern. The idea of the class was to
understand physics by deriving all the equations the same way the people who
discovered them did. It was pretty cool.

~~~
pchristensen
What school/teacher? I'd be interested in finding a curriculum or any
references about that. I have daughters and I'm dying to find a good way to
present science to them.

~~~
Alex3917
Prof. Peter Stein at Cornell. The class is Physics 202. I can email you the
class notes and problem sets if you'd like. I'll also email him and ask if
he's thought about publishing the course materials online.

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ph0rque
Can you just put them online somewhere?

~~~
Alex3917
<http://www.alexkrupp.com/Phys202.zip>

If you glance at my answers to problem sets 4, 5, and 8 then you'll get the
general idea of what the course involves. The problem sets are really fun
because you're forced to play with the numbers and really understand the
material. It might not be as hard as a traditional physics course, but it's
every bit as rigorous in the real sense of the word. It's brilliance is that
it really stresses the fundamentals, probably more so than any other physics
material in existence. This is important because, as one professional Go
player said after observing a Japanese baseball game,

"In every confrontation with a real American professional team it seems that
what we need to learn from them, besides their technique of course, is how
uniformly faithful their players are to the fundamentals. Faithfulness to the
fundamentals seems to be a common thread linking professionalism in all
areas." (T. Kageyama)

~~~
rms
Sounds like a great course. How exactly did that course fit into the Cornell
curriculum? Was it an elective for most people or could it substitute for
algebra/calc based physics?

~~~
Alex3917
Cornell has two sets of requirements. The requirements for your college within
the university, and the requirements for your major. This course fulfilled the
distribution requirements for the college I was in. However, it wouldn't
necessarily count as one of the required science classes for your major. So,
for example, if you were a physics student then it wouldn't count toward your
major, so therefor it would make more sense to take another class that you
could count toward both your major and your college distribution requirement.
Sorry if this is unclear, it's kind of complicated.

~~~
rms
Thanks, that made sense.

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boredguy8
I spend some of my time teaching at a private university. During a discussion
with one student he said, "All I really know about Plato is that he thought
the forms were transcendent whereas Aristotle thought the forms were
immanent."

"Oh," said I, "that's interesting. What does it mean for a form to be
transcendent or immanent?"

"I don't know, I just know that's what they thought."

We then had a discussion about whether or not he really knew that, and whether
or not he was OK with paying over $25k a year to learn how to be a parrot.

The sad thing: he was OK with it, and probably rightly so. He realized that
mostly what people want are parrots and you can get paid quite a decent amount
of money for being a good parrot. Not a bad gig if you're fine being a cog.
There are certain comforts it provides.

------
aneesh
This sadly is how the world works. In school, even in high school and college,
the students who guess the teacher's password are rewarded. The (few) students
who make an effort to discover and think through something on their own are
criticized for wandering from the beaten path, even on the occasions when
they're actually right.

High school science competitions (school science fairs, all the way upto
Siemens-Westinghouse and Intel STS) particularly guilty of this.

~~~
boredguy8
"The (few) students who make an effort to discover and think through something
on their own are criticized for wandering from the beaten path, even on the
occasions when they're actually right."

I remember I just -couldn't- accept that we can't take square roots of
negative numbers. I mean, sure, two negatives multiplied together is a
positive, but...there HAS to be a way! Numbers, to my 6th grade mind, weren't
arbitrarily going to deny your ability to manipulate them.

Fortunately for me, I happened to be reading a book on Mandlebrot and in the
course of discussing his work the author introduces the concept of imaginary
numbers. So the next day in class I asked: "Are you suuuure?"

"Yes, I'm sure."

"Well, I was reading in this book and so-and-so says you can take the square
root of negative numbers, you get 'i' for the root of -1 and..."

"Why don't you go wait outside."

Where I got told that although I move to the beat of a different drummer, when
I'm in her class, I really just need to be quiet. That's when public education
and I had a falling out from which our relationship has never recovered.

All of that to say: I think part of the 'problem' is that kids who do try to
think on their own are often in a situation where they're challenging accepted
rules without the social grace to do so constructively. But rather than being
taught the social skills, they're just shut down. Very sad, actually. They
could be taught how to 'wander well'.

~~~
Prrometheus
Isn't sqrt(-1) = i an axiom though, and not a theorem? In other words, if you
just started with the integers and the basic rules of arithmetic, you will
never run into the need for imaginary numbers. It's only after you posit their
existence that a lot of cool results flow from it.

Am I wrong there?

~~~
boredguy8
I don't really know how to interpret your sentence. Complex numbers are a
field in which you do 'basic rules of arithmetic'. You can't do the 'basic
rules of arithmetic' on integers.

i is defined as sqrt(-1), if that answers your question.

~~~
Prrometheus
I should have said "Real Numbers" instead of "Integers", sorry.

My point is that sqrt(-1) = i is an extra assumption that you don't need to
make in order to derive the math you do in school. If you don't make that
assumption, you can still derive a lot of math. If you do make that
assumption, then you can also derive the theorems of complex analysis.

I think that's true, anyway. I could be wrong.

It just seems strange to me that someone would be bothered by the lack of
negative square roots, since their existence is never derived, only assumed.
But then again, people's minds work very differently, especially in
Mathematics.

I was the opposite in Math class. I fought accepting "i" when they tried to
teach it to us since it seemed so arbitrary and contrived to me. This was
before I discovered that all Math is arbitrary and that there is no "real
math", anyway.

~~~
ashu
As the "Road to Reality" explains, if you study Quantum mechanics, complex
numbers become every bit as "real" as the integers or real numbers. You just
can't explain some of the quantum mechanical phenomena or concepts without
using complex numbers at all.

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nsrivast
overcomingbias is one of those websites you should read every article in, like
paul graham's essays

~~~
jsomers
yeah, although you'd have a lot more work to do. Not only are there multiple
posts a day but some of Elizer's have dependency trees reaching months back!

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noonespecial
I remember the first time I got an F on an assignment even though I'd gotten
the correct answer to every problem.

I hadn't reached my correct answers the "right" way.

~~~
cdr
If the teacher was teaching a process, and looking for evidence that you
understood that process, it seems entirely reasonable to not count your work.

~~~
noonespecial
I had simply taken shortcuts I'd seen later in the book for factoring
quadratics. They wanted to see it written exactly as it appeared in the
current examples.

I realized that math in school was more like one of those simon games where
you just mindlessly press the arbitrary sequence of lights you just saw, than
actual mathematics. This analogy helped me suffer through "school math" while
I perused real math on my own.

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cdr
I've been thinking along similar lines since I've been interviewing; far too
many interviewers are only looking for the password.

------
DaniFong
Only tangentially related, but years ago, in elementary school, I decided to
guess the password after the school restricted access to SimCity. I got it
right on the first try, it was just the school name, but I told everyone 'I
hacked it', for major props.

