WEBVTT

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SEAN ROBINSON:
There's an exercise

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we do very early in the
semester, where we hand out

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to the students a bunch
of small aluminum cuboids.

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They're long rectangles, a
few centimeters on each side.

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And then we hand them a
very cheap plastic ruler,

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a $0.16 ruler from an
office supply store.

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The cubes are machined
to very high precision

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to be identical to each other.

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The rulers are very inexpensive.

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And we have them--
we say, go measure

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the length, width, and
height of this cuboid.

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Don't tell anybody
what you measured.

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But just write down
your best measurement,

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and your best estimate
of the uncertainty

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on that measurement,
and along with that,

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come up with a
measure of the volume.

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Maybe, you measure
the volume, say,

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by multiplying x times y
times z, and an estimate

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of the uncertainty on that.

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And everybody thinks this
is a very silly exercise.

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It's so easy.

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This is something you would
do in elementary school.

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Here we are in our third year
as physics majors at MIT.

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Why are we wasting
our time on this?

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But if it's so easy, then when
we flip around the white board

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and show everybody all
each other's answers,

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if it's so easy, why
are the answers all so

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different from each other?

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That is a big moment
of cognitive dissonance

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for the students.

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And then we spend the next,
say, 15 to 45 minutes,

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really, just having a very
active discussion about, what

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did these error bars
that you reported

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to us as your uncertainty
on the volume,

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what does that really mean?

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Why is this person's
error bar so small?

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Why is this person's so large?

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Let's look at the spread between
all of the different people's

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numbers and compare it to what
you reported as uncertainty.

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Are these things consistent?

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Are these inconsistent?

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For the instructor who's
leading that discussion,

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that's somewhat of a
challenge because he's

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about to see some numbers,
and lead a discussion on it,

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which he's never seen before.

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Inevitably, all of our
instructors get up to the plate

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and do a good job at that.

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But it's remarkable, how much
comes from this very simple

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little exercise.

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The students learn a lot
about random errors, which

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are statistical
errors, which are

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something you can learn from a
mathematics book on statistics.

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You learn a lot about
systematic errors, which

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are very, very difficult,
and no one really

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has a good understanding of.

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But it all comes up in
this very simple exercise

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that everybody
learns a lot from.

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In general, it's
always a challenge

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for a teacher to run
a group discussion

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and get the students to actually
participate in that discussion,

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right?

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In general, that's
always something

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that's tricky as a teacher.

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People want to sit back,
and be quiet, and just hear

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what other people have to say.

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It's always a challenge.

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For this exercise,
which is usually

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done at the end of
a three hour session

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where they've been
measuring other things,

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and then you flip
around the board

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and show them the list of
numbers, people are surprised.

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This is something-- this is
numbers they just measured.

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And they're surprised what they
see that everybody else did.

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It is not hard at all
to get people talking

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and really get them
all participating

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in that conversation.