Teaching Calculus

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  • Nikolay Brodskiy
  • Alexander Brodsky

Part 03 (Transcript)

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So shortest path ...

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... is made by straight line.

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Does it agree with everybody's understanding?

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Of what shortest and straight ...

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Student: I think [...] about 2-dimensional space and no other constraints. Sure.

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Two-dimensional space, no other constraints, yes, yes.

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Sure? All right. So ...

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Let's try to bring that abstraction to reality.

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Can we? Can you?

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Well, this is not straight for sure, right?

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It's obviously not straight.

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So what would be straight?

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Can you find in reality this straight path?

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Student: No. [...].

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Student: Sometimes.

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Sometimes?

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Can you tell me an example of when you can find a straight path?

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Student: Like [...] straight path [...].

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Student: [...] straight path.

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Student: But from [...] it's not straight.

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Yes, er ...

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OK, well, you see ...

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What I want now is to bring that abstraction which is exact, right?

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... to reality.

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So that it is well maybe sort of exact.

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In a sense that I can ...

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... find this straight path with any precision I want.

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Because sometimes you have to be nano-skill precise, right?

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Well if you build a computer don't you want to be very very precise?

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Right? So, how can you be that precise?

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Student: You kind of [...].

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Yes, approximations. So ...

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Student: We have to make approximations of point [...] is not significant enough to consider.

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OK. So, building anything ...

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... you make approximations?

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And this is the first thing you understand that ...

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... anything you want to do or to build ...

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... it is only going to be an approximation ...

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... of whatever your thoughts are, right?

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And then you decide what the precision that you want to follow, right?

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And then if that precision is ...

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... ten to the power negative ...

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... ten ... meters ...

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So, what would you use?

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Is there any ruler that is ... um?

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Student: [...].

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Well, yes, sure, I'll have to make the points smaller.

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Student: [...], right?

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Yes, yes.

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Er ... What I'm saying is that what would be technical implementation of the device making the straight line.

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Student: [...] can be absolutely straight.

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Yes. What is it that can be almost absolutely straight?

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Student: A laser.
NB: A laser?

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No?

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Well, you see ...

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And two people in the same room ...

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NB: Question ...
Student: [...].

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Student: [...].

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NB: So that ...
Student: [...].

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NB: Are you there?
Student: Yes.

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NB: Are you there?
Student: Yes.

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Well ...

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We are here.

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So, yes we can assume all kind of things, right?

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And we can assume that line goes straight.

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Right? From one point to the other point.

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But over here we know it doesn't.

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Well, do you know that line doesn't go along straight line?

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No, you don't know?

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NB: All it ...
Student: [...].

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Straight enough. Now, well, what is enough, right?

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NB: Er ... I just ...
Student: [...].

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Student: So, [...].

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On Earth, yes, yes.

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