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SPEAKER: And so we can do this just for
fun with these little cardboard bricks

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here.

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For instance, if I want to build a
pyramid of height 4, how do I do it?

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Well, I can build a pyramid of height 3.

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Let me go ahead and build
a pyramid of height 3.

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How do I build a pyramid of height 3?

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Well, I build a pyramid of height 2.

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And then I add to it.

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Well, OK, how do I build
a pyramid of height 2?

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Well, you build a pyramid of height 1.

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How do I do that?

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Well, you just put the brick down.

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And so here's where
things kind of bottom out.

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And it's no longer a cyclical argument.

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You eventually just do some actual work.

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But in my mind, I have to remember all
of the instructions you just gave me,

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or I gave myself--

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I had to build a pyramid of
height 4, no; 3, no; 2, no; 1--

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now I'm actually doing that.

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So here's the pyramid of height 1.

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How do I now build the
pyramid of height 2?

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Well, rewind in the story.

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To build a pyramid of height 2,
you build a pyramid of height 1.

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And then you add one more layer.

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So I think to add one more layer,
I essentially need to do this.

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Now, I have a pyramid of height 2.

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But wait a minute, the story began with,
how do I build a pyramid of height 3?

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Well, you take a pyramid of
height 2, which I have here,

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and you add an additional layer.

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So I've got to build
this additional layer.

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I'm going to go ahead and give myself
the layer, the layer, the layer.

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And then I'm going to put the original
pyramid of height 2 on top of it.

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And voila, it's a
pyramid of height 3 now.

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Well, how did I get here?

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Well, let me keep
rewinding in the story.

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The very first question
I asked myself was,

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how do you build a pyramid of height 4?

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Well, the answer was build
a pyramid of height 3.

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Great.

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That's done.

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Then add one additional layer.

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And if I had more hands, I could
do this a little more elegantly.

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But let me go ahead
and just lay this out.

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Here's the new level of height 3.

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And now I'm going to go of a width 4.

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Now I'm going to go and put the pyramid
of height 3 on top of it until, voila,

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I have this form here
of Mario's pyramid.

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So it's a bit cyclical, in
that every time I asked myself

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to build a pyramid of a
certain height, I kind of

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punted and said, no, build
a pyramid of this height.

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No, build a pyramid of this height.

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No, build a pyramid of this height.

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But the magic of that algorithm
was that there was constantly this,

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do a little more, work build a layer,
do a little more work, build a layer.

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And it's in that implicit building
of layer after layer after layer

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that the pyramid itself, the
end goal, actually emerges.

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