SPEAKER: And so we can do this just for fun with these little cardboard bricks
here.
For instance, if I want to build a pyramid of height 4, how do I do it?
Well, I can build a pyramid of height 3.
Let me go ahead and build a pyramid of height 3.
How do I build a pyramid of height 3?
Well, I build a pyramid of height 2.
And then I add to it.
Well, OK, how do I build a pyramid of height 2?
Well, you build a pyramid of height 1.
How do I do that?
Well, you just put the brick down.
And so here's where things kind of bottom out.
And it's no longer a cyclical argument.
You eventually just do some actual work.
But in my mind, I have to remember all of the instructions you just gave me,
or I gave myself--
I had to build a pyramid of height 4, no; 3, no; 2, no; 1--
now I'm actually doing that.
So here's the pyramid of height 1.
How do I now build the pyramid of height 2?
Well, rewind in the story.
To build a pyramid of height 2, you build a pyramid of height 1.
And then you add one more layer.
So I think to add one more layer, I essentially need to do this.
Now, I have a pyramid of height 2.
But wait a minute, the story began with, how do I build a pyramid of height 3?
Well, you take a pyramid of height 2, which I have here,
and you add an additional layer.
So I've got to build this additional layer.
I'm going to go ahead and give myself the layer, the layer, the layer.
And then I'm going to put the original pyramid of height 2 on top of it.
And voila, it's a pyramid of height 3 now.
Well, how did I get here?
Well, let me keep rewinding in the story.
The very first question I asked myself was,
how do you build a pyramid of height 4?
Well, the answer was build a pyramid of height 3.
Great.
That's done.
Then add one additional layer.
And if I had more hands, I could do this a little more elegantly.
But let me go ahead and just lay this out.
Here's the new level of height 3.
And now I'm going to go of a width 4.
Now I'm going to go and put the pyramid of height 3 on top of it until, voila,
I have this form here of Mario's pyramid.
So it's a bit cyclical, in that every time I asked myself
to build a pyramid of a certain height, I kind of
punted and said, no, build a pyramid of this height.
No, build a pyramid of this height.
But the magic of that algorithm was that there was constantly this,
do a little more, work build a layer, do a little more work, build a layer.
And it's in that implicit building of layer after layer after layer
that the pyramid itself, the end goal, actually emerges.