Constructing a unit normal vector to a surface

WEBVTT
Kind: captions
Language: en

00:00:00.385 --> 00:00:02.515
Now that we hopefully have a conceptual understanding...

00:00:02.515 --> 00:00:05.350
...of what a surface integral like this COULD represent,

00:00:05.350 --> 00:00:08.073
...I want to think about how we can actually construct...

00:00:08.073 --> 00:00:10.009
...a unit vector...

00:00:10.009 --> 00:00:13.669
...a unit normal vector, at any point on the surface.

00:00:13.669 --> 00:00:15.483
And to do that, I will assume...

00:00:15.483 --> 00:00:18.221
...that our surface can be parametrized...

00:00:18.221 --> 00:00:21.282
...by the position vector function, r...

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...and r is a function of two parameters.

00:00:23.432 --> 00:00:27.569
It's a function of u, and it is a function of v.

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You give me a u and a v and...

00:00:29.529 --> 00:00:31.489
...that will essentially specify...

00:00:31.489 --> 00:00:35.002
...a point on this two-dimensional surface right over here.

00:00:35.002 --> 00:00:37.931
It could be bent, so it kind of exists in three-dimensional space...

00:00:37.931 --> 00:00:42.738
But a u and a v will specify a given point on this surface.

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Now, let's think about what the directions of r...

00:00:46.865 --> 00:00:48.983
...the partial of r with respect to...

00:00:49.399 --> 00:00:52.188
...the partial of r with respect to u looks like...

00:00:52.188 --> 00:00:54.524
...and what the direction of the partial of r...

00:00:54.524 --> 00:00:57.692
...the partial of r with respect to v looks like.

00:00:57.953 --> 00:00:59.989
So let's say that we're at some...

00:00:59.989 --> 00:01:01.289
...we're at some point.

00:01:01.828 --> 00:01:03.729
We're at some point, (u,v).

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So for some (u,v), if you'd find the position vector...

00:01:06.635 --> 00:01:09.457
...it takes us to that point on the surface right over there.

00:01:09.457 --> 00:01:12.651
Now let's say that we increment u just a little bit.

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And as we increment u just a little bit,

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...we're going to get to another point on our surface,

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...and let's say that other point on the surface...

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...is right over there.

00:01:19.630 --> 00:01:20.826
So what would r...

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What would this r_u vector look like?

00:01:23.121 --> 00:01:24.881
Well its magnitude is essentially going to be..

00:01:24.881 --> 00:01:26.598
...dependent on how fast it's happening,

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...how fast we're moving towards that point,

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...but its direction is going to be in that direction.

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It's going to be towards that point.

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It's going be along the surface.

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We're going from one point on the surface to another.

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It's essentially going to be tangent to the surface at that point.

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And I could draw a little bit bigger.

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It would look something like that.

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r... r_u.

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So I just zoomed in right over here.

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Now let's go back to this point.

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And now let's make v a little bit bigger.

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And let's say if we make v a little bit bigger,

00:01:53.448 --> 00:01:55.101
...we go to this point right over here.

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So then our position vector, r, would point to this point.

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And so what would r_v look like?

00:02:00.970 --> 00:02:02.817
Well its magnitude, once again, would be dependent on...

00:02:02.817 --> 00:02:05.634
...how fast we're going there, but the direction is what's interesting.

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The direction would also be tangential to the surface.

00:02:09.078 --> 00:02:11.090
We're going from one point on the surface to another...

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...as we change v.

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So r_v might look something like that.

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And they're not necessarily...

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These two aren't necessarily perpendicular to each other.

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In fact, the way I drew them, they're not perpendicular.

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So r_v is like this, but they're both tangential to the plane.

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They're both essentially telling us, right at that point,

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...what is the tangent? What is the slope in that...

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...in the u direction, or in the v direction?

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Now, this is...

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When you have two...

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When you have two vectors that are...

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...that are tangential to the plane,

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...and they're not the same vector, these are actually...

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...already specifying...

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...these are already kind of determining a plane.

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And so you can imagine a plane that looks something like this.

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If you took linear combinations of these two things,

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...you would get a plane that both of these would lie on.

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Now, we've done this before, but I'll re-visit it.

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What happens when I take the cross product...

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...of r_u and r_v?

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What happens when I take the cross product?

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Well first, this is going to give us another vector.

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It's going to give us a vector...

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...a vector that is perpendicular to both...

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...to r_u AND r_v.

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Or another way to think about it is...

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...this plane, that these...

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...when you take the cross product...

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...this plane is essentially a tangential plane...

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...to the surface.

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And if something is going to be perpendicular...

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...to both of these characters,

00:03:30.452 --> 00:03:32.555
...it's going to have to be normal to them...

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...or, it's definitely going to be perpendicular...

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...to both of them, but it's going to be normal...

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...to this plane.

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Which is essentially going to be...

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...perpendicular to the surface itself.

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So this right over here...

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...is going to be A normal vector.

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This is... I'll write it...

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Well, let me just write it this way.

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This is A normal vector.

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I'm not saying THE unit normal...

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I'm not saying THE normal vector, 'cause you have...

00:03:52.906 --> 00:03:54.442
...you could have different normal vectors of...

00:03:54.442 --> 00:03:55.691
...different magnitudes.

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This is A normal vector, when you take the cross product.

00:03:58.861 --> 00:04:01.641
And we can even think about what direction it's pointing in.

00:04:01.641 --> 00:04:04.477
And so when you have "something" cross "something else"...

00:04:04.477 --> 00:04:06.417
...the easiest way I remember how to do it is...

00:04:06.417 --> 00:04:07.995
...you point your left thumb...

00:04:07.995 --> 00:04:09.724
Oh, sorry. You point your RIGHT thumb...

00:04:09.724 --> 00:04:11.439
...in the direction of the first vector...

00:04:11.439 --> 00:04:13.870
So, in this case, r_u.

00:04:13.870 --> 00:04:14.839
So let me see if I can...

00:04:14.839 --> 00:04:15.709
...if I can draw this.

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I'm literally looking at my hand and trying to draw it.

00:04:18.402 --> 00:04:20.443
So you put your right thumb...

00:04:20.443 --> 00:04:22.303
-- so this is a right-hand rule, essentially --

00:04:22.303 --> 00:04:24.339
...in the direction of the first vector...

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...and then you put your index finger in the direction of...

00:04:28.200 --> 00:04:29.634
...the second vector...

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...right over here.

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So this is the second vector.

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So that's the direction of my index finger.

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So my index finger is going to look something like...

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...that.

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And then you bend...

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...you bend your middle finger inward...

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...and that will tell you the direction of the cross product.

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So if I bend my middle finger inward,

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...it will look something...

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...it will look something like this.

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And then of course, my other two fingers are just going to be...

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...folded in like that, and they're not really relevant.

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But my other two fingers and my hand looks like that.

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And so that tells us the direction.

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The direction is going to be like that.

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It's going to be upward-facing.

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That's important, because you have normal vectors.

00:05:05.635 --> 00:05:06.672
One could...

00:05:06.672 --> 00:05:09.208
Or there's two directions of "normalcy," I guess you could say.

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One is going out like that...

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...outwards...

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...or I guess...

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...in the upward direction...

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...one would be going downwards,

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...or going -- I guess you could say -- into the surface.

00:05:17.886 --> 00:05:19.524
But the way I have set it up right now,

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...this would be going outwards.

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It would be A...

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It would be A normal vector...

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...to the surface.

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Now, in order to go from A normal vector...

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...to the UNIT normal vector,

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...we just have to normalize it.

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We just have to divide this...

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...by its magnitude.

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So now we have our drumroll.

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The unit vector...

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And it's going to essentially be...

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It's going to be a function of u...

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It's going to be...

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...a function of u and v.

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You give me a u or a v...

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...and I'll give you a...

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...that unit normal vector.

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It is going to be equal to...

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...the partial of r...

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...the partial of r with respect to u...

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...crossed with...

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...the partial of r with respect to v...

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That just...

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Now that gives us A normal vector,

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but it hasn't been normalized.

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So we want to divide...

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...by the magnitude...

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We want to divide by the magnitude...

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...of the exact same thing.

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r_u crossed with r_v.

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And we're done!

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We have constructed a unit normal vector.

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And in future videos, we'll actually do this with concrete examples.


Conceptual understanding of flux in three dimensions

WEBVTT
Kind: captions
Language: en

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Let's say we are operating...

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...in three dimensions.

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And I have a function, rho,

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...which is a function of (x,y,z)...

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...and it gives us the mass density...

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...at any point in three dimensions,

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...of some fluid.

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Some particular fluid.

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Maybe it's a gas, or a fluid,

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...water. Who knows what it is?

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Some type of substance.

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It gives us the mass density...

00:00:19.486 --> 00:00:21.385
...at any point in three dimensions.

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And let's say we have another...

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...function. This is a scalar function.

00:00:24.559 --> 00:00:25.776
It just gives us a number...

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...for any point in 3D.

00:00:27.282 --> 00:00:29.213
And then, let's say we have another function, v,

00:00:29.213 --> 00:00:30.676
...which is a vector function.

00:00:30.676 --> 00:00:32.069
It gives us a vector...

00:00:32.069 --> 00:00:33.831
...for any point in three dimensions.

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And this right over here tells us...

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...the velocity of that same...

00:00:37.322 --> 00:00:40.370
...the velocity of that same fluid or gas...

00:00:40.370 --> 00:00:42.128
...or whatever we're talking about.

00:00:42.128 --> 00:00:43.726
Now let's imagine another function.

00:00:43.726 --> 00:00:45.544
And this might all look a little bit familiar, because we did it...

00:00:45.544 --> 00:00:47.013
We went through a very similar exercise...

00:00:47.013 --> 00:00:49.226
...in two dimensions when we talked about line integrals.

00:00:49.226 --> 00:00:51.705
Now we're just extending it to three dimensions.

00:00:51.705 --> 00:00:53.411
Let's say we have a function, f.

00:00:54.119 --> 00:00:55.361
Let's say we have a function, f,

00:00:55.361 --> 00:00:57.181
...and it is equal to...

00:00:57.181 --> 00:00:58.292
...the product...

00:00:58.292 --> 00:01:00.739
...the product of rho and v.

00:01:00.739 --> 00:01:02.627
So for any point in (x,y,z)...

00:01:02.627 --> 00:01:04.167
...this will give us a vector, and then...

00:01:04.167 --> 00:01:06.666
...we'll multiply it times this scalar right over here...

00:01:06.666 --> 00:01:08.910
...for that same point in three dimensions.

00:01:08.910 --> 00:01:10.445
So it's equal to...

00:01:10.445 --> 00:01:13.055
...rho times v.

00:01:16.163 --> 00:01:17.494
Let me use the same color...

00:01:17.494 --> 00:01:19.189
...that I used for v before.

00:01:25.051 --> 00:01:27.369
And there's a couple of ways you could conceptualize this,

00:01:27.369 --> 00:01:28.441
...so you could view this as...

00:01:28.441 --> 00:01:30.845
Obviously it maintains the direction of the velocity,

00:01:30.845 --> 00:01:32.746
...but now its magnitude...

00:01:32.746 --> 00:01:33.759
One way to think about it is...

00:01:33.759 --> 00:01:35.360
...kind of the momentum density.

00:01:35.360 --> 00:01:36.514
And if that doesn't make too much sense,

00:01:36.514 --> 00:01:38.176
...you don't have to worry too much about it.

00:01:38.176 --> 00:01:40.189
Hopefully, as we use these two functions,

00:01:40.189 --> 00:01:41.662
...and we talk-- think a little bit more...

00:01:41.662 --> 00:01:42.829
...about them relative to a surface,

00:01:42.829 --> 00:01:45.522
...it'll make a little bit more conceptual sense.

00:01:45.522 --> 00:01:47.040
Now, what I want to do...

00:01:47.040 --> 00:01:48.907
...is think about what it means...

00:01:48.907 --> 00:01:50.007
...what it means...

00:01:50.007 --> 00:01:51.242
...given this function, f,

00:01:51.242 --> 00:01:54.191
...to evaluate the surface integral...

00:01:54.191 --> 00:01:56.104
...over some surface...

00:01:56.104 --> 00:01:57.823
So we're going to evaluate over some surface.

00:01:57.823 --> 00:02:00.129
We're going to evaluate f...

00:02:00.129 --> 00:02:04.403
We're going to evaluate f dot n,

00:02:04.403 --> 00:02:07.194
...where n is the unit normal vector at every--

00:02:07.194 --> 00:02:08.561
...at each point on that surface,

00:02:08.561 --> 00:02:11.786
...dS.

00:02:11.786 --> 00:02:12.829
d-surface.

00:02:12.829 --> 00:02:14.981
So let's think about what this is saying.

00:02:15.381 --> 00:02:18.216
So first, let me draw my axes.

00:02:18.216 --> 00:02:21.621
So I have my z-axis.

00:02:21.621 --> 00:02:23.085
z-axis...

00:02:23.085 --> 00:02:24.409
This could be my...

00:02:24.409 --> 00:02:25.650
Let's make that...

00:02:25.650 --> 00:02:27.707
Let's make that my x-axis.

00:02:27.707 --> 00:02:29.637
And let's say that this right over here...

00:02:29.637 --> 00:02:31.654
...is my y-axis.

00:02:31.654 --> 00:02:33.124
And let's say my surface...

00:02:33.124 --> 00:02:34.047
...I'll use that same color...

00:02:34.047 --> 00:02:36.422
My surface looks something like that.

00:02:36.422 --> 00:02:39.135
So that is my surface.

00:02:39.135 --> 00:02:41.904
That is the surface in question.

00:02:41.904 --> 00:02:43.526
That is S.

00:02:43.526 --> 00:02:44.838
Now let's think about the units,

00:02:44.838 --> 00:02:46.551
...and hopefully that'll give us conceptual understanding...

00:02:46.551 --> 00:02:48.869
...of what this thing right over here is measuring.

00:02:48.869 --> 00:02:50.094
It's completely analogous to...

00:02:50.094 --> 00:02:51.590
...what we did in the two-dimensional case...

00:02:51.590 --> 00:02:52.712
...with the line integrals.

00:02:52.712 --> 00:02:54.595
So we have a dS.

00:02:54.595 --> 00:02:56.244
A dS is a little chunk of area...

00:02:56.244 --> 00:02:57.569
...of that surface.

00:02:57.569 --> 00:02:59.524
So that is dS.

00:02:59.524 --> 00:03:01.456
So this is going to be area.

00:03:01.456 --> 00:03:02.304
And if we want to break...

00:03:02.304 --> 00:03:03.077
This is...

00:03:03.077 --> 00:03:04.404
We want to pick particular units...

00:03:04.404 --> 00:03:06.053
This could be square...

00:03:06.053 --> 00:03:07.460
This could be square meters.

00:03:07.460 --> 00:03:08.344
And I think when we do...

00:03:08.344 --> 00:03:10.137
...particular units, it starts to make...

00:03:10.137 --> 00:03:11.971
...a little bit more concrete sense.

00:03:11.971 --> 00:03:13.310
Now, the normal vector...

00:03:13.310 --> 00:03:14.546
...at that dS...

00:03:14.546 --> 00:03:15.661
The normal vector is going to...

00:03:15.661 --> 00:03:16.535
...point right out of it.

00:03:16.535 --> 00:03:18.604
It's literally normal to that plane.

00:03:18.604 --> 00:03:20.818
It's literally normal to that plane.

00:03:20.818 --> 00:03:22.374
It has a magnitude 1.

00:03:22.374 --> 00:03:24.409
So that is our unit normal vector.

00:03:24.409 --> 00:03:27.568
And f is defined throughout this three-dimensional space.

00:03:27.568 --> 00:03:28.855
You give me any (x,y,z),

00:03:28.855 --> 00:03:30.089
...I'll know its mass density,

00:03:30.089 --> 00:03:30.873
...I'll know its velocity,

00:03:30.873 --> 00:03:32.059
...and I'll get some f.

00:03:32.059 --> 00:03:34.009
I'll get some f at any point...

00:03:34.009 --> 00:03:36.723
...at any point in three-dimensional space,

00:03:36.723 --> 00:03:38.458
...including on the surface.

00:03:38.458 --> 00:03:39.908
Including right over here.

00:03:39.908 --> 00:03:41.925
So right over here, f might look...

00:03:41.925 --> 00:03:44.376
...f might look something like this.

00:03:44.376 --> 00:03:47.169
So that is f right at that point.

00:03:47.169 --> 00:03:48.161
Right at that point.

00:03:48.161 --> 00:03:49.142
So what does all of this mean?

00:03:49.142 --> 00:03:50.408
Well when you take the dot product...

00:03:50.408 --> 00:03:51.992
...of two vectors, this is essentially saying,

00:03:51.992 --> 00:03:53.694
"How much do they go together?"

00:03:53.694 --> 00:03:55.276
And since n is a unit vector,

00:03:55.276 --> 00:03:56.776
...since it has a magnitude 1,

00:03:56.776 --> 00:03:58.111
...it's-- this is essentially saying..

00:03:58.111 --> 00:03:58.895
"What is..."

00:03:58.895 --> 00:04:00.421
"What is the magnitude...

00:04:00.421 --> 00:04:01.522
...of the component of f...

00:04:01.522 --> 00:04:03.191
...that's going in the direction of n?"

00:04:03.191 --> 00:04:04.338
Or the component-- Or...

00:04:04.338 --> 00:04:05.941
"What is the magnitude of the...

00:04:05.941 --> 00:04:06.759
...component of f that is...

00:04:06.759 --> 00:04:08.740
...normal to the surface?"

00:04:08.740 --> 00:04:10.595
Or "How much of f is normal...

00:04:10.595 --> 00:04:11.311
...to the surface?"

00:04:11.311 --> 00:04:12.820
So the component of f that is...

00:04:12.820 --> 00:04:13.921
...normal to the surface...

00:04:13.921 --> 00:04:16.053
...might look something like...

00:04:16.053 --> 00:04:17.653
...might look something...

00:04:17.653 --> 00:04:19.777
...like that.

00:04:19.777 --> 00:04:21.395
Might look something like that.

00:04:21.395 --> 00:04:22.875
And this right over here...

00:04:22.875 --> 00:04:24.212
...will essentially just give...

00:04:24.212 --> 00:04:25.777
...the magnitude of that.

00:04:25.777 --> 00:04:26.730
And it's just going to...

00:04:26.730 --> 00:04:29.007
It's just going to keep the units of f.

00:04:29.007 --> 00:04:30.476
n, right over here, just specifies...

00:04:30.476 --> 00:04:32.864
...a direction. It has no units associated with it.

00:04:32.864 --> 00:04:33.944
It's dimensionless.

00:04:33.944 --> 00:04:36.093
f's units are going to be...

00:04:36.093 --> 00:04:37.875
...units of mass density,

00:04:37.875 --> 00:04:38.827
So it could be...

00:04:38.827 --> 00:04:39.928
It's going to be...

00:04:39.928 --> 00:04:41.008
Let's say it could be...

00:04:41.008 --> 00:04:44.496
...kilogram per meter-cubed.

00:04:44.496 --> 00:04:45.195
That's...

00:04:45.195 --> 00:04:46.924
Well that's actually just the rho part.

00:04:46.924 --> 00:04:48.878
So it's mass density times velocity.

00:04:48.878 --> 00:04:51.216
Times meters per second.

00:04:51.216 --> 00:04:52.271
Let me write it in those colors...

00:04:52.271 --> 00:04:52.911
...so we have...

00:04:52.911 --> 00:04:54.437
...clear what's happening here.

00:04:54.437 --> 00:04:55.604
So the units of f...

00:04:55.604 --> 00:04:57.878
...are going to be the units of rho...

00:04:57.878 --> 00:04:59.204
...which are going to be...

00:04:59.204 --> 00:05:02.372
...kilogram per cubic meter...

00:05:02.372 --> 00:05:03.579
That's mass density.

00:05:03.579 --> 00:05:05.838
...times the units of v...

00:05:05.838 --> 00:05:07.646
...which is meters per second.

00:05:07.646 --> 00:05:09.124
Meters per second.

00:05:09.124 --> 00:05:11.776
And we're going to multiply that times meters squared.

00:05:11.776 --> 00:05:12.837
So what you have is...

00:05:12.837 --> 00:05:13.557
You have a meter and then...

00:05:13.557 --> 00:05:14.894
...a meter squared in the numerator...

00:05:14.894 --> 00:05:16.512
That's meters cubed in the numerator.

00:05:16.512 --> 00:05:17.946
And meters cubed in the denominator.

00:05:17.946 --> 00:05:20.142
That, that, that cancels out.

00:05:20.142 --> 00:05:22.846
And so the units that we get for this...

00:05:22.846 --> 00:05:24.043
The units that we get for this...

00:05:24.043 --> 00:05:26.474
...are kilogram per second.

00:05:26.474 --> 00:05:27.971
And so the way to conceptualize it...

00:05:27.971 --> 00:05:29.833
Given how we've defined f...

00:05:29.833 --> 00:05:32.041
...when we say what we say f represents...

00:05:32.041 --> 00:05:33.361
The way to conceptualize this...

00:05:33.361 --> 00:05:35.576
This is saying, "How much mass..."

00:05:35.576 --> 00:05:37.399
"How much mass, given this mass density,

00:05:37.399 --> 00:05:39.704
...this velocity, is going directly...

00:05:39.704 --> 00:05:41.822
...out of this little dS,

00:05:41.822 --> 00:05:42.359
...this little...

00:05:42.359 --> 00:05:44.138
...'infinitesimally' chunk of surface...

00:05:44.138 --> 00:05:46.156
...in a given amount of time?"

00:05:46.156 --> 00:05:46.880
And then if we were to add up...

00:05:46.880 --> 00:05:48.130
...all of the dS-es,

00:05:48.130 --> 00:05:50.055
...and this is what essentially that surface integral is,

00:05:50.055 --> 00:05:52.033
...we're essentially saying,

00:05:52.033 --> 00:05:53.270
"How much mass,

00:05:53.270 --> 00:05:54.606
...in kilograms per second,

00:05:54.606 --> 00:05:55.324
...that's what we picked...

00:05:55.324 --> 00:05:56.510
How much mass...

00:05:56.510 --> 00:05:59.091
...is traveling across this surface...

00:05:59.091 --> 00:06:01.721
...at any given moment in time?"

00:06:01.721 --> 00:06:03.351
And this is really the same idea we do with...

00:06:03.351 --> 00:06:04.287
...the line integrals.

00:06:04.287 --> 00:06:07.908
This is essentially the flux through a two-dimensional surface.

00:06:07.908 --> 00:06:09.352
So this is...

00:06:09.352 --> 00:06:12.605
...the flux through a 2D surface.

00:06:18.559 --> 00:06:19.164
And this isn't like...

00:06:19.164 --> 00:06:21.582
...some crazy, abstract thing.

00:06:21.582 --> 00:06:22.762
I mean, you could imagine...

00:06:22.762 --> 00:06:24.023
You know, you could imagine...

00:06:24.023 --> 00:06:26.717
...something like water vapor in your bathroom.

00:06:26.717 --> 00:06:27.876
Water vapor in your bathroom.

00:06:27.876 --> 00:06:28.722
And I like to imagine that,

00:06:28.722 --> 00:06:29.910
...because that's actually visible,

00:06:29.910 --> 00:06:32.107
...especially when sunlight is shining through it.

00:06:32.107 --> 00:06:33.908
And we've all seen water vapor...

00:06:33.908 --> 00:06:34.579
...through a...

00:06:34.579 --> 00:06:35.725
...water vapor in our bathroom when...

00:06:35.725 --> 00:06:37.241
...you have a ray of sunlight, and you can see...

00:06:37.241 --> 00:06:38.240
...how the particles...

00:06:38.240 --> 00:06:39.791
...how the particles are traveling.

00:06:39.791 --> 00:06:41.321
And you see they have a certain density...

00:06:41.321 --> 00:06:42.228
...at different points.

00:06:42.228 --> 00:06:43.441
And so you could imagine...

00:06:43.441 --> 00:06:44.526
You could imagine...

00:06:44.526 --> 00:06:46.493
You care about the surface...

00:06:46.493 --> 00:06:48.493
...the surface of your...

00:06:48.493 --> 00:06:50.394
Maybe you have a window.

00:06:50.394 --> 00:06:52.509
Maybe you have a window in the bathroom.

00:06:52.509 --> 00:06:53.885
So you have a window.

00:06:53.885 --> 00:06:55.021
And so, if you were...

00:06:55.021 --> 00:06:57.058
If the surface was the window,

00:06:57.058 --> 00:06:57.704
...and the window...

00:06:57.704 --> 00:06:58.777
And let's say the window's open,

00:06:58.777 --> 00:06:59.639
...so it's kind of a...

00:06:59.639 --> 00:07:01.072
There's nothing physical there.

00:07:01.072 --> 00:07:02.031
It's just kind of a...

00:07:02.031 --> 00:07:03.899
...a rectangular surface that...

00:07:03.899 --> 00:07:06.331
...things can pass freely through,

00:07:06.331 --> 00:07:08.014
...if-- and f was essentially...

00:07:08.014 --> 00:07:10.128
...the mass density of the water vapor times...

00:07:10.128 --> 00:07:11.670
...the velocity of the water vapor,

00:07:11.670 --> 00:07:13.677
...then this thing right over here will essentially tell you...

00:07:13.677 --> 00:07:15.687
...the mass of water vapor that is traveling...

00:07:15.687 --> 00:07:18.341
...through that window at any given moment of time.

00:07:18.341 --> 00:07:19.774
Another way to think about it is...

00:07:19.774 --> 00:07:20.804
Imagine a...

00:07:20.804 --> 00:07:21.862
Imagine a river.

00:07:21.862 --> 00:07:23.695
And I'm going to conceptualize this river...

00:07:23.695 --> 00:07:24.606
...as kind of a...

00:07:24.606 --> 00:07:26.644
...just a section of the river.

00:07:26.644 --> 00:07:27.894
And I'm conceptualizing it...

00:07:27.894 --> 00:07:28.718
This is kind of...

00:07:28.718 --> 00:07:29.218
...a river.

00:07:29.218 --> 00:07:30.449
Obviously this would be the surface...

00:07:30.449 --> 00:07:31.573
...that we normally see.

00:07:31.573 --> 00:07:32.960
But obviously it has some depth.

00:07:32.960 --> 00:07:34.585
It's three-dimensional in nature.

00:07:34.585 --> 00:07:36.838
And so we would know the density.

00:07:36.838 --> 00:07:37.686
Maybe it's constant.

00:07:37.686 --> 00:07:40.060
You know the density, and you know the velocity...

00:07:40.060 --> 00:07:41.105
...at any point.

00:07:41.105 --> 00:07:42.786
That's what f gives us.

00:07:42.786 --> 00:07:44.558
So that tells us...

00:07:44.558 --> 00:07:46.789
As we said, we could view that as the...

00:07:46.789 --> 00:07:49.358
...momentum density at any given point in time.

00:07:49.358 --> 00:07:51.939
And maybe our surface is some type of a net.

00:07:51.939 --> 00:07:53.434
Our surface is some type of a net.

00:07:53.434 --> 00:07:55.010
And the net doesn't even have to be rectangular.

00:07:55.010 --> 00:07:56.521
It could be some weird-shaped net.

00:07:56.521 --> 00:07:57.830
But I'll do it in rectangular, just because it's...

00:07:57.830 --> 00:07:58.978
...easier to draw.

00:07:58.978 --> 00:08:02.041
It's some type of net that in no way impedes the flow...

00:08:02.041 --> 00:08:02.975
...of the fluid.

00:08:02.975 --> 00:08:04.124
Then once again,

00:08:04.124 --> 00:08:05.658
...when you evaluate this integral,

00:08:05.658 --> 00:08:08.045
...it would tell you the mass of fluid that is flowing...

00:08:08.045 --> 00:08:09.069
...through that net...

00:08:09.069 --> 00:08:11.040
...at any given moment of time.

00:08:11.040 --> 00:08:12.057
So hopefully this makes...

00:08:12.057 --> 00:08:14.194
...a little bit of conceptual sense now.

00:08:14.194 --> 00:08:15.044
In the next few videos,

00:08:15.044 --> 00:08:16.088
...we'll actually think about...

00:08:16.088 --> 00:08:16.804
...how to...

00:08:16.804 --> 00:08:18.304
...how to calculate this,

00:08:18.304 --> 00:08:20.008
...and how we can actually represent it...

00:08:20.008 --> 00:08:21.745
...in different ways.


Microsoft CEO Summit  Innovation in Education

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:02.490
KEVIN: Next, I've got
Walter Isaacson is

00:00:02.490 --> 00:00:05.400
going to moderate a really
great session on innovation

00:00:05.400 --> 00:00:06.400
in education.

00:00:06.400 --> 00:00:09.340
And certainly Walter doesn't
need much introduction, either.

00:00:09.340 --> 00:00:12.470
He's the chairman, and
president, and CEO,

00:00:12.470 --> 00:00:13.620
of the Aspen Institute.

00:00:13.620 --> 00:00:16.850
He's been the CEO of CNN, and
the editor of Time Magazine.

00:00:16.850 --> 00:00:19.310
He's also a
bestselling biographer.

00:00:19.310 --> 00:00:20.800
So please help me
welcome Walter.

00:00:23.090 --> 00:00:23.840
WALTER: Thank you.

00:00:23.840 --> 00:00:26.070
Thank you, Kevin.

00:00:26.070 --> 00:00:28.400
Well, our session right
now is on something

00:00:28.400 --> 00:00:31.340
that keeps coming up in
our conversation, which

00:00:31.340 --> 00:00:34.500
is education and how
innovation in technology

00:00:34.500 --> 00:00:36.374
are going to transform it.

00:00:36.374 --> 00:00:37.540
I think it's a useful topic.

00:00:37.540 --> 00:00:41.435
If Ben Franklin came back today
and walked into a classroom,

00:00:41.435 --> 00:00:42.550
he'd say, "Oh, yeah.

00:00:42.550 --> 00:00:43.994
That's exactly how we did it.

00:00:43.994 --> 00:00:45.160
That's exactly what we made.

00:00:45.160 --> 00:00:47.620
The teacher stands there
and gives a little lecture,

00:00:47.620 --> 00:00:49.780
and 24 kids are sitting around."

00:00:49.780 --> 00:00:53.170
It's the one major
sector of our lives

00:00:53.170 --> 00:00:54.830
that has not been
totally transformed

00:00:54.830 --> 00:00:56.320
by the digital revolution.

00:00:56.320 --> 00:00:58.200
And I think we're at
an inflection point.

00:00:58.200 --> 00:01:03.070
It's about to happen, whether
it's MIT and Harvard joining up

00:01:03.070 --> 00:01:07.000
for edX the way Stanford has
already been doing for higher

00:01:07.000 --> 00:01:10.610
education, or what's happening
in the K through 12 classroom.

00:01:10.610 --> 00:01:12.687
Starting with you,
Bill, you've written

00:01:12.687 --> 00:01:15.270
about four or five things that
are going to be transformative,

00:01:15.270 --> 00:01:17.680
but let me start with the
first one you talk about,

00:01:17.680 --> 00:01:19.277
which is re-imagining textbooks.

00:01:19.277 --> 00:01:21.860
How do you think that's going
to change, and make personalized

00:01:21.860 --> 00:01:23.390
education?

00:01:23.390 --> 00:01:27.520
BILL: Well, if you get pervasive
digital devices, very cheap

00:01:27.520 --> 00:01:30.660
tablets, and pervasive
internet connection,

00:01:30.660 --> 00:01:34.850
then one can imagine eliminating
the paper-based textbook.

00:01:34.850 --> 00:01:38.240
And an interactive textbook
is a very different thing.

00:01:38.240 --> 00:01:40.770
In fact, the boundary
between quiz,

00:01:40.770 --> 00:01:44.490
lecture, textbook, is
basically eviscerated.

00:01:44.490 --> 00:01:48.050
You can track the
student, bring in a video,

00:01:48.050 --> 00:01:51.170
ask him a few questions
to keep them engaged.

00:01:51.170 --> 00:01:55.220
And the invention of
what that multimedia

00:01:55.220 --> 00:01:58.670
educational thing called
the future textbook,

00:01:58.670 --> 00:02:01.350
but it's really all those
things brought together.

00:02:01.350 --> 00:02:06.350
We're in the process of figuring
out what that is right now.

00:02:06.350 --> 00:02:09.415
And there's a lot of
innovators-- for profit,

00:02:09.415 --> 00:02:13.010
and nonprofit innovators--
who are participating in that.

00:02:13.010 --> 00:02:15.040
WALTER: I was at
Sci and Math Academy

00:02:15.040 --> 00:02:18.870
in our hometown of New Orleans,
which Sal and I come from, run

00:02:18.870 --> 00:02:20.880
by some Teacher
America Corps members.

00:02:20.880 --> 00:02:22.060
And there are no textbooks.

00:02:22.060 --> 00:02:23.981
They just have curriculum.

00:02:23.981 --> 00:02:25.980
And the teachers up there
on a dashboard saying,

00:02:25.980 --> 00:02:28.110
oh, these two students
don't understand

00:02:28.110 --> 00:02:29.630
that x and y are different.

00:02:29.630 --> 00:02:33.510
And these two--
how do you-- do you

00:02:33.510 --> 00:02:37.050
think there'll be just a totally
disruptive transformation

00:02:37.050 --> 00:02:38.360
of how we do curricula?

00:02:38.360 --> 00:02:40.200
Or do you think
textbooks will then just

00:02:40.200 --> 00:02:41.792
be put in digital form?

00:02:41.792 --> 00:02:44.250
BILL: Well, we want to be a
little conservative about this,

00:02:44.250 --> 00:02:51.000
because in a sense, every time
something new comes along,

00:02:51.000 --> 00:02:54.280
they say education will change.

00:02:54.280 --> 00:02:58.100
Textbooks came along and
anybody could read them.

00:02:58.100 --> 00:02:59.930
We got TV sets.

00:02:59.930 --> 00:03:01.870
We got videotape.

00:03:01.870 --> 00:03:05.000
We got computer-aided
instruction.

00:03:05.000 --> 00:03:09.680
And so far technology-- at
least in the classroom--

00:03:09.680 --> 00:03:11.030
has had absolutely no effect.

00:03:11.030 --> 00:03:16.300
So the issues of motivation--
why should I learn this?

00:03:16.300 --> 00:03:18.280
Am I the person
who's good at this?

00:03:18.280 --> 00:03:23.470
There's so much complex human
motivation in the learning

00:03:23.470 --> 00:03:27.760
process that to say
that just to mechanize

00:03:27.760 --> 00:03:30.330
the pieces-- like, OK,
just click on the lecture,

00:03:30.330 --> 00:03:35.180
we don't need the lecturer-- the
actual usage of things like MIT

00:03:35.180 --> 00:03:40.300
OpenCourseWare is mind-blowing
for one reason-- basically

00:03:40.300 --> 00:03:41.760
nobody uses it.

00:03:41.760 --> 00:03:45.680
I mean, take the very best
Walter Lewin physics course,

00:03:45.680 --> 00:03:48.040
which is the third one up there.

00:03:48.040 --> 00:03:50.890
About 3,000 people have
gone through the thing.

00:03:50.890 --> 00:03:52.050
And it's free.

00:03:52.050 --> 00:03:53.360
It's fantastic.

00:03:53.360 --> 00:03:55.730
I love the guy.

00:03:55.730 --> 00:04:00.250
But there's no market for
people at home at night

00:04:00.250 --> 00:04:03.580
saying "Oh, yeah, how do
those wave equations work?"

00:04:03.580 --> 00:04:10.260
Without a job or a degree,
so far this whole hey,

00:04:10.260 --> 00:04:13.140
it's online, therefore it will
be utterly different-- there's

00:04:13.140 --> 00:04:17.250
been as many failures
as successes.

00:04:17.250 --> 00:04:22.420
Now I think some of the stuff
that Sal and Bror are involved

00:04:22.420 --> 00:04:25.900
in are going to be
amazingly successful.

00:04:25.900 --> 00:04:28.210
So I do think this
time, this is different.

00:04:28.210 --> 00:04:32.700
WALTER: So everybody talked
about flipping the classroom,

00:04:32.700 --> 00:04:35.780
and you are the ones who've
been successful at that so far.

00:04:35.780 --> 00:04:38.199
Explain how you think
that's going to work.

00:04:38.199 --> 00:04:40.240
SAL: Yeah, you know, when
you go to this reality,

00:04:40.240 --> 00:04:41.704
and it's been happening already.

00:04:41.704 --> 00:04:44.120
I mean, for us it's been kind
of an inadvertent adventure,

00:04:44.120 --> 00:04:47.700
but you have this reality where
students are going to a place,

00:04:47.700 --> 00:04:49.700
and they're learning from
videos and exercises,

00:04:49.700 --> 00:04:52.100
and getting feedback-- you
start to realize, well, OK.

00:04:52.100 --> 00:04:54.290
They can all learn at
their own pace now.

00:04:54.290 --> 00:04:56.420
And as soon as you make
that one assumption--

00:04:56.420 --> 00:04:58.670
that every student can learn
at their own pace, master

00:04:58.670 --> 00:05:01.105
concepts, and move on, and
kind of build a scaffold--

00:05:01.105 --> 00:05:02.480
it actually allows
you to rethink

00:05:02.480 --> 00:05:04.370
every aspect of the
education system.

00:05:04.370 --> 00:05:07.820
You no longer have to group
kids by age-based cohorts.

00:05:07.820 --> 00:05:09.930
You no longer have
to have a teacher

00:05:09.930 --> 00:05:11.680
the front of the room
giving a lecture.

00:05:11.680 --> 00:05:16.350
You no longer have to
have all the desks pointed

00:05:16.350 --> 00:05:17.577
in the same direction.

00:05:17.577 --> 00:05:19.410
You no longer have to
have teachers separate

00:05:19.410 --> 00:05:20.510
from each other.

00:05:20.510 --> 00:05:21.980
You know, I have 20 students.

00:05:21.980 --> 00:05:22.960
You have 20 students.

00:05:22.960 --> 00:05:24.480
And we have no peer interaction.

00:05:24.480 --> 00:05:27.540
And so what we're seeing is--
and we started off as kind

00:05:27.540 --> 00:05:29.860
of a virtual thing for
anybody out there to learn--

00:05:29.860 --> 00:05:30.710
WALTER: Actually,
will you explain

00:05:30.710 --> 00:05:32.085
the story of how
you got started?

00:05:32.085 --> 00:05:33.085
That's near to my heart.

00:05:33.085 --> 00:05:35.085
AL: Oh, yeah, New Orleans
connection-- you know,

00:05:35.085 --> 00:05:37.270
right after I got married,
family from New Orleans

00:05:37.270 --> 00:05:38.353
was visiting me in Boston.

00:05:38.353 --> 00:05:39.860
I'm now in northern California.

00:05:39.860 --> 00:05:43.220
And 12-year-old cousin Nadia
having trouble with math.

00:05:43.220 --> 00:05:44.940
And I offered to tutor her.

00:05:44.940 --> 00:05:48.090
And a little-- about
two years into it,

00:05:48.090 --> 00:05:49.340
word got around in the family.

00:05:49.340 --> 00:05:51.440
And I was tutoring
about 15 cousins.

00:05:51.440 --> 00:05:55.490
And then famously, a
friend said-- well,

00:05:55.490 --> 00:05:56.990
I was having trouble
scaling myself.

00:05:56.990 --> 00:05:57.720
I had a day job.

00:05:57.720 --> 00:06:01.260
And he said why don't you
stick some lessons on YouTube?

00:06:01.260 --> 00:06:05.570
I said, "No, that's for cats
playing piano, not real math."

00:06:05.570 --> 00:06:08.420
But then I gave it a shot,
and famously, my cousins

00:06:08.420 --> 00:06:10.670
told me they like me better
on YouTube than in person.

00:06:10.670 --> 00:06:14.220
And so I kept going.

00:06:14.220 --> 00:06:17.420
And so the YouTube videos,
there's a ton of them now.

00:06:17.420 --> 00:06:19.880
There are six million kids
using it every month now.

00:06:19.880 --> 00:06:22.611
We're a team of 30 people now.

00:06:22.611 --> 00:06:23.110
But yeah.

00:06:23.110 --> 00:06:25.602
So when we launched
kind of in a big way,

00:06:25.602 --> 00:06:27.310
and we started building
our organization,

00:06:27.310 --> 00:06:29.750
we assumed this is just a
supplemental thing out for kids

00:06:29.750 --> 00:06:32.607
anywhere to learn, or
adult learners, too.

00:06:32.607 --> 00:06:34.065
But then some school
districts said

00:06:34.065 --> 00:06:35.351
no, this is interesting to us.

00:06:35.351 --> 00:06:37.850
This is kind of different--
true differentiated instruction.

00:06:37.850 --> 00:06:39.100
This could be a game changer.

00:06:39.100 --> 00:06:41.400
WALTER: And tell us what school
districts have adopted it.

00:06:41.400 --> 00:06:43.000
And give me an example
of how that's worked

00:06:43.000 --> 00:06:43.500
AL: Yeah.

00:06:43.500 --> 00:06:45.780
So the most famous is Los
Altos in Silicon Valley.

00:06:45.780 --> 00:06:49.300
They're now district wide,
but it's been a KIPP prep,

00:06:49.300 --> 00:06:52.250
Summit prep, a couple of other
charter schools in Oakland.

00:06:52.250 --> 00:06:55.080
I think the one that's actually
pushed the envelope the most is

00:06:55.080 --> 00:06:57.163
Marlborough School in Los
Angeles, which is really

00:06:57.163 --> 00:06:58.150
an elite girl's school.

00:06:58.150 --> 00:07:01.146
And what they did is they
said, yeah, no reason for it--

00:07:01.146 --> 00:07:02.520
we have to do this
Prussian model

00:07:02.520 --> 00:07:05.010
where all students
learn at the same pace.

00:07:05.010 --> 00:07:08.210
And we're going to have a
seventh through 12th grade

00:07:08.210 --> 00:07:12.600
girls all in the same classroom,
all learning at their own pace.

00:07:12.600 --> 00:07:14.640
And if you visit one
of these classrooms,

00:07:14.640 --> 00:07:16.390
there's a ton of peer
to peer interaction.

00:07:16.390 --> 00:07:18.820
And what the teacher's doing--
they're no longer the lecturer.

00:07:18.820 --> 00:07:20.540
They're doing one
on one interactions.

00:07:20.540 --> 00:07:23.440
It's made the classroom more
of an interactive, or human

00:07:23.440 --> 00:07:24.360
experience.

00:07:24.360 --> 00:07:27.950
WALTER: Bror, what have you
learned about how people learn,

00:07:27.950 --> 00:07:29.602
and how does that get applied?

00:07:29.602 --> 00:07:31.060
And maybe even do
it, if you would,

00:07:31.060 --> 00:07:32.344
in an international context.

00:07:32.344 --> 00:07:34.260
So many people here are
from around the world.

00:07:34.260 --> 00:07:36.051
What have you learned
from around the world

00:07:36.051 --> 00:07:38.220
of how different
people learn things?

00:07:38.220 --> 00:07:42.110
And especially in your higher
education and career training

00:07:42.110 --> 00:07:45.000
things at Kaplan--
tell us how that works.

00:07:45.000 --> 00:07:46.670
BROR: What's great
about working now

00:07:46.670 --> 00:07:50.240
at this intersection between
education, technology,

00:07:50.240 --> 00:07:52.750
and actually learning science
is that all of these things

00:07:52.750 --> 00:07:56.453
are now ready to go, ready
to get something really done.

00:07:56.453 --> 00:07:59.850
And on the learning science
side, a lot of the things Sal

00:07:59.850 --> 00:08:03.300
is describing actually
back up exactly what's

00:08:03.300 --> 00:08:05.580
being found when you
look experimentally

00:08:05.580 --> 00:08:06.917
at how people actually learn.

00:08:06.917 --> 00:08:09.250
And there's been a lot of
that work over the last 20, 30

00:08:09.250 --> 00:08:14.780
years-- things like giving
people control over their pace.

00:08:14.780 --> 00:08:17.350
And that turns out to
help all learners, novices

00:08:17.350 --> 00:08:19.410
and expert learners.

00:08:19.410 --> 00:08:22.844
Things about using media
together with a voice over,

00:08:22.844 --> 00:08:24.760
and that's exactly how
Sal Khan's videos work.

00:08:24.760 --> 00:08:25.920
He doesn't show his face.

00:08:25.920 --> 00:08:29.420
He's actually showing a key--
write it as he's doing it.

00:08:29.420 --> 00:08:32.234
So your eye is tracking what
he's actually talking about.

00:08:32.234 --> 00:08:34.900
That turns out to line up with a
bunch of the research about how

00:08:34.900 --> 00:08:36.710
you should use media--
things about using

00:08:36.710 --> 00:08:41.020
simple, informal language,
things about technology-- that

00:08:41.020 --> 00:08:43.330
allow you to take a really
good learning solution.

00:08:43.330 --> 00:08:45.952
Because the best tutors do
these kinds of things, too.

00:08:45.952 --> 00:08:47.410
What technology
lets you do is take

00:08:47.410 --> 00:08:50.970
a good solution-- or
actually a bad solution--

00:08:50.970 --> 00:08:55.430
and make it affordable,
reliable, available, and data

00:08:55.430 --> 00:08:56.510
rich.

00:08:56.510 --> 00:08:59.520
So all of those things now
become possible for us to do.

00:08:59.520 --> 00:09:02.350
And it's possible for us
to do around the globe.

00:09:02.350 --> 00:09:05.990
The materials that you create
that are introductory materials

00:09:05.990 --> 00:09:07.840
and demonstration
materials can suddenly

00:09:07.840 --> 00:09:10.560
become available to
everyone around the globe.

00:09:10.560 --> 00:09:13.130
And then you have local
folks who get together

00:09:13.130 --> 00:09:15.790
to provide that next
stage of feedback,

00:09:15.790 --> 00:09:17.910
and counseling, and
answering questions

00:09:17.910 --> 00:09:20.990
that the online materials
don't actually describe.

00:09:20.990 --> 00:09:22.840
And that local
work can also then

00:09:22.840 --> 00:09:26.250
become culturally more connected
to where you are, and give

00:09:26.250 --> 00:09:28.780
examples where that
is happening as well.

00:09:28.780 --> 00:09:32.710
It gives a terrific opportunity
to make the whole process much

00:09:32.710 --> 00:09:35.504
more efficient around
time and effort.

00:09:35.504 --> 00:09:37.920
And what it actually does--
and this is a little bit odd--

00:09:37.920 --> 00:09:42.180
but it begins to drag education
into the modern economy,

00:09:42.180 --> 00:09:43.970
where to do all
this, you actually

00:09:43.970 --> 00:09:46.380
have to spend a lot
more effort up front.

00:09:46.380 --> 00:09:49.300
This is not typically somebody
sitting down the night before

00:09:49.300 --> 00:09:51.020
and doing a whole course.

00:09:51.020 --> 00:09:53.255
It becomes well, let's look
at the learning science.

00:09:53.255 --> 00:09:54.630
Let's think about
our objectives.

00:09:54.630 --> 00:09:56.000
Let's structure this thing.

00:09:56.000 --> 00:09:58.120
Let's figure out where
do the interactives go.

00:09:58.120 --> 00:10:00.410
When do we need a
person to engage?

00:10:00.410 --> 00:10:02.920
When do we use the
automated systems?

00:10:02.920 --> 00:10:04.230
That can be a lot.

00:10:04.230 --> 00:10:05.790
You build all that.

00:10:05.790 --> 00:10:08.790
But now your variable costs
come down, potentially,

00:10:08.790 --> 00:10:12.840
because you're using teachers,
well-trained human beings,

00:10:12.840 --> 00:10:16.010
in a system for what
they're really good at.

00:10:16.010 --> 00:10:18.140
And allow the machines,
and the tools,

00:10:18.140 --> 00:10:21.300
and the media to be designed
to do the rest really well.

00:10:21.300 --> 00:10:24.330
So at kaplan, as a business
doing this kind of work,

00:10:24.330 --> 00:10:26.864
we're trying very hard
now to actually use

00:10:26.864 --> 00:10:29.030
large scale-- we have more
than a million learners--

00:10:29.030 --> 00:10:32.930
to begin to generate data, to do
experiments along these lines,

00:10:32.930 --> 00:10:36.330
just as Sal is doing-- to
see if we apply this learning

00:10:36.330 --> 00:10:40.600
science now at scale, as a
learning engineering exercise,

00:10:40.600 --> 00:10:41.820
can we get those benefits?

00:10:41.820 --> 00:10:43.520
And then can we keep
going, and scale,

00:10:43.520 --> 00:10:45.317
and transform how we
do all our education?

00:10:45.317 --> 00:10:46.900
It's a very exciting
time to be doing.

00:10:46.900 --> 00:10:49.320
WALTER: Sal, what
Bror just described

00:10:49.320 --> 00:10:52.340
is really how a for-profit
model can work well,

00:10:52.340 --> 00:10:55.440
because it can do the
upfront cost, do it to scale.

00:10:55.440 --> 00:10:57.150
Yours is a non-profit model.

00:10:57.150 --> 00:11:00.250
Then we have the model,
the Harvard-MIT doing edX,

00:11:00.250 --> 00:11:03.670
and Stanford doing two different
things, whatever it may be.

00:11:03.670 --> 00:11:06.530
How do you see the mix of
profits and non-profits,

00:11:06.530 --> 00:11:08.534
and what's the advantages
of each in this?

00:11:08.534 --> 00:11:09.950
SAL: Yeah, I think
it's all great.

00:11:09.950 --> 00:11:11.908
I think we really are in
kind of a Renaissance.

00:11:11.908 --> 00:11:14.520
I mean, every week we're hearing
a new-- I mean, Harvard, MIT,

00:11:14.520 --> 00:11:15.850
these are not
small institutions.

00:11:15.850 --> 00:11:17.450
This is, I think it was
the biggest announcement--

00:11:17.450 --> 00:11:19.550
WALTER: You have four degrees
from amongst them, right?

00:11:19.550 --> 00:11:19.760
SAL: Yes.

00:11:19.760 --> 00:11:21.480
So I'm making sure
that they'll never--

00:11:21.480 --> 00:11:23.500
WALTER: And Bill never got
one, as far as I can remember.

00:11:23.500 --> 00:11:24.530
[INAUDIBLE] got an honorary--

00:11:24.530 --> 00:11:26.530
SAL: He's is getting a
higher return on his.

00:11:26.530 --> 00:11:32.332
[LAUGHTER]

00:11:32.332 --> 00:11:33.290
I think it's all great.

00:11:33.290 --> 00:11:34.150
It's all innovation.

00:11:34.150 --> 00:11:36.500
I think everyone is seeing
what works in certain contexts.

00:11:36.500 --> 00:11:37.440
And saying that we
should do that, too.

00:11:37.440 --> 00:11:38.690
We should do that.

00:11:38.690 --> 00:11:41.292
Our thought, or my
thought process-- and it

00:11:41.292 --> 00:11:43.250
was really kind of
delusional, when I literally

00:11:43.250 --> 00:11:47.000
was operating out of a
closet for several years--

00:11:47.000 --> 00:11:49.430
it was that we are kind
of at this inflection

00:11:49.430 --> 00:11:50.390
point in history.

00:11:50.390 --> 00:11:52.910
We've been talking about
it this whole session.

00:11:52.910 --> 00:11:57.010
And I felt that any
inflection point in history

00:11:57.010 --> 00:11:58.440
needs new institutions.

00:11:58.440 --> 00:12:02.950
And it wasn't obvious that
new institutions to this point

00:12:02.950 --> 00:12:04.890
had actually percolated up.

00:12:04.890 --> 00:12:06.945
New companies had, but
not new institutions.

00:12:06.945 --> 00:12:09.320
And so in my delusional-- I
read a lot of science fiction

00:12:09.320 --> 00:12:11.510
books-- I was,
like, maybe I could

00:12:11.510 --> 00:12:13.380
be like Hari Seldon
in the Foundation.

00:12:13.380 --> 00:12:18.250
This could-- we read the
same books, obviously.

00:12:18.250 --> 00:12:18.885
But they're--

00:12:18.885 --> 00:12:21.260
BILL: People who read The
Foundation are in the vanguard.

00:12:21.260 --> 00:12:23.440
SAL: Yes, Isaac Asimov.

00:12:23.440 --> 00:12:27.710
But I mean, it was crazy,
and kind of idealistic

00:12:27.710 --> 00:12:28.322
on one aspect.

00:12:28.322 --> 00:12:30.530
But on another aspect, it's
completely practical now.

00:12:30.530 --> 00:12:33.180
Maybe we could do
civilization-scale education.

00:12:33.180 --> 00:12:34.170
We can make it free.

00:12:34.170 --> 00:12:35.700
We can make it an institution.

00:12:35.700 --> 00:12:37.408
I mean, this content
I was talking about,

00:12:37.408 --> 00:12:40.520
if Newton had made videos on
calculus, I wouldn't have to.

00:12:40.520 --> 00:12:41.990
This stuff is evergreen.

00:12:41.990 --> 00:12:42.916
It's not changing.

00:12:42.916 --> 00:12:44.290
BILL: His notation
was a little--

00:12:44.290 --> 00:12:45.170
SAL: Yeah, he was
a little eccentric.

00:12:45.170 --> 00:12:46.300
BILL: Leibniz will do.

00:12:46.300 --> 00:12:49.529
SAL: Yeah, Leibniz
might have been, yeah.

00:12:49.529 --> 00:12:50.820
But so this stuff is evergreen.

00:12:50.820 --> 00:12:52.340
This stuff is going
to-- these videos

00:12:52.340 --> 00:12:54.423
could be teaching-- not
just videos, interactions,

00:12:54.423 --> 00:12:56.920
questions, simulations,
they could teach kids

00:12:56.920 --> 00:12:58.380
500 years from now.

00:12:58.380 --> 00:13:01.329
And so it just seemed like
too crazy of an opportunity

00:13:01.329 --> 00:13:03.370
to try to-- I mean, there's
nothing wrong with it

00:13:03.370 --> 00:13:05.860
as a business, but maybe
it could be an institution.

00:13:05.860 --> 00:13:07.820
That was the thinking for us.

00:13:07.820 --> 00:13:09.750
WALTER: Bill, how
does that change

00:13:09.750 --> 00:13:14.182
the role of the teachers, and
help you scale good teachers?

00:13:14.182 --> 00:13:15.890
BILL: Well, what we'd
really like to know

00:13:15.890 --> 00:13:21.920
is why is it so hard to get kids
motivated around these things?

00:13:21.920 --> 00:13:24.290
I mean, after all, it's
really in the kids' interest

00:13:24.290 --> 00:13:27.330
to get a high school degree
and get a college degree.

00:13:27.330 --> 00:13:29.120
It's not just that
you make more money.

00:13:29.120 --> 00:13:31.010
You meet more
interesting people.

00:13:31.010 --> 00:13:34.430
Everything is better
about that path in life.

00:13:34.430 --> 00:13:39.459
And so our failure to convince
them to help themselves

00:13:39.459 --> 00:13:41.000
in that way, it's
very disappointing.

00:13:41.000 --> 00:13:43.860
And the US statistics
are horrific.

00:13:43.860 --> 00:13:46.680
We doubled what we put into
education over the last 20

00:13:46.680 --> 00:13:47.690
years.

00:13:47.690 --> 00:13:50.660
And our output did
not improve at all.

00:13:50.660 --> 00:13:53.340
And other countries,
on the other hand,

00:13:53.340 --> 00:13:56.200
have done very, very well.

00:13:56.200 --> 00:13:59.930
So as for younger
students, there's

00:13:59.930 --> 00:14:04.360
going to be a structured
environment where a teacher is

00:14:04.360 --> 00:14:07.260
there supervising
them quite a bit.

00:14:07.260 --> 00:14:09.490
One of the most interesting
things-- at a conference

00:14:09.490 --> 00:14:11.215
Sal and I went to, we
heard about a thing

00:14:11.215 --> 00:14:13.090
called an alliance
school, which is a charter

00:14:13.090 --> 00:14:14.940
school in California,
which in the US

00:14:14.940 --> 00:14:17.600
is where most of the good
experimentation takes place.

00:14:17.600 --> 00:14:20.690
They have a class
of 48, but when

00:14:20.690 --> 00:14:22.990
they ask the kids what
they liked about the class,

00:14:22.990 --> 00:14:25.460
they said, oh, it's
so small and personal.

00:14:25.460 --> 00:14:29.380
Well, it's because they have
16 with the teacher, 16 doing

00:14:29.380 --> 00:14:33.970
peer education-- and peer
education, where you have kids

00:14:33.970 --> 00:14:36.720
help other kids, that
is a coming thing.

00:14:36.720 --> 00:14:41.300
And figuring out how to
technologically help those kids

00:14:41.300 --> 00:14:43.775
group together, make that
work, that is super powerful.

00:14:43.775 --> 00:14:46.020
It's also very cheap.

00:14:46.020 --> 00:14:47.870
And then they have
a final group of 16,

00:14:47.870 --> 00:14:52.310
where they're just looking
at Khan Academy type content,

00:14:52.310 --> 00:14:54.600
playing some of the
math game things.

00:14:54.600 --> 00:14:58.000
And so you do math by
rotating through the three

00:14:58.000 --> 00:14:59.480
different experiences.

00:14:59.480 --> 00:15:04.580
And their results are way
better than a class of 25

00:15:04.580 --> 00:15:06.429
done the normal way.

00:15:06.429 --> 00:15:08.720
WALTER: You just said that
most of the experimentation,

00:15:08.720 --> 00:15:11.500
innovation being done is from
some of the innovative charter

00:15:11.500 --> 00:15:13.260
schools in the country.

00:15:13.260 --> 00:15:16.420
In New Orleans now, almost every
kid goes to a charter school.

00:15:16.420 --> 00:15:17.640
And the parents have choice.

00:15:17.640 --> 00:15:19.056
It's almost a
voucher system where

00:15:19.056 --> 00:15:21.170
the money follows the student.

00:15:21.170 --> 00:15:25.010
So you have competition, where
a KIPP and a YES and whatever

00:15:25.010 --> 00:15:28.278
do it-- why shouldn't
that be the model, as it

00:15:28.278 --> 00:15:30.402
is with higher education,
where there's competition

00:15:30.402 --> 00:15:31.890
and people have choice.

00:15:31.890 --> 00:15:34.670
Why should that be the model
to drive innovation in K

00:15:34.670 --> 00:15:35.740
through 12?

00:15:35.740 --> 00:15:39.170
BILL: Well, it's not like
higher ed is fantastic.

00:15:39.170 --> 00:15:42.290
The dropout rates
in US universities

00:15:42.290 --> 00:15:45.160
are higher than
any other country.

00:15:45.160 --> 00:15:48.040
Their costs have also
gone up, actually

00:15:48.040 --> 00:15:50.220
more than a factor of
two in the last 20 years.

00:15:50.220 --> 00:15:53.020
And the output has not
improved all that much.

00:15:53.020 --> 00:15:55.390
So there's pathologies
there as well.

00:15:55.390 --> 00:16:01.020
The uniform, sort of monolithic,
state by state approach

00:16:01.020 --> 00:16:04.440
that we have-- yes, that
probably holds things back.

00:16:04.440 --> 00:16:08.260
But politically to get that
to change is very hard.

00:16:08.260 --> 00:16:11.400
I mean, charter schools--
California shorts their charter

00:16:11.400 --> 00:16:13.100
schools in a way
that most of them

00:16:13.100 --> 00:16:17.220
are financially
unstable right now.

00:16:17.220 --> 00:16:22.180
And the union often are
used for the status quo,

00:16:22.180 --> 00:16:26.280
whether it's against charters
or against personnel systems.

00:16:26.280 --> 00:16:28.670
So it's very, very
tough, because everybody

00:16:28.670 --> 00:16:30.730
wants a minimum standard.

00:16:30.730 --> 00:16:32.550
And using a
market-based approach,

00:16:32.550 --> 00:16:34.740
you worry that you
won't hit that minimum.

00:16:34.740 --> 00:16:38.250
And so you get this
kind of rigid approach

00:16:38.250 --> 00:16:39.630
as the acceptable.

00:16:39.630 --> 00:16:41.280
WALTER: But is that good or bad?

00:16:41.280 --> 00:16:46.850
BILL: Well, I don't know how
to-- it's very hard to change.

00:16:46.850 --> 00:16:50.160
There are countries that
do this better than we do.

00:16:50.160 --> 00:16:52.340
And you hope that we
could learn from them.

00:16:52.340 --> 00:16:55.229
So you have-- can we learn
how to do personnel systems?

00:16:55.229 --> 00:16:56.770
And then can you
bring technology in?

00:16:56.770 --> 00:16:58.730
Those are the two
things that should

00:16:58.730 --> 00:17:03.320
make you optimistic
about education--

00:17:03.320 --> 00:17:09.720
that people like Kaplan
are on a for-profit basis,

00:17:09.720 --> 00:17:14.500
and things like Khan Academy
really are going to catch on.

00:17:14.500 --> 00:17:19.020
But the institutions will be
slow to recognize these things.

00:17:19.020 --> 00:17:21.510
Thank goodness for charters
and some young teachers

00:17:21.510 --> 00:17:26.069
who are willing to
essentially break the rules.

00:17:26.069 --> 00:17:32.070
WALTER: Bror, why do you think
the profit model will succeed

00:17:32.070 --> 00:17:35.360
in a world where so many people
are now doing this for free?

00:17:35.360 --> 00:17:36.690
BROR: It's a great question.

00:17:36.690 --> 00:17:39.180
Part of it is because,
as we just talked about,

00:17:39.180 --> 00:17:41.390
technology is not
the only answer.

00:17:41.390 --> 00:17:44.750
It doesn't actually solve all
of the human training needs.

00:17:44.750 --> 00:17:48.950
The human mind is built
to take a lot of feedback,

00:17:48.950 --> 00:17:51.617
a lot of customized feedback,
and to use that very well.

00:17:51.617 --> 00:17:53.450
There are some things
that you can automate.

00:17:53.450 --> 00:17:55.375
And over time, there will
be more and more things.

00:17:55.375 --> 00:17:57.000
But at the end of
the day, if you're

00:17:57.000 --> 00:17:58.980
trying to write a
persuasive essay,

00:17:58.980 --> 00:18:00.830
you need somebody
to give you feedback

00:18:00.830 --> 00:18:03.620
on why it's not persuasive,
and how to do it again.

00:18:03.620 --> 00:18:07.870
And then to look and see did you
get it right this time or not?

00:18:07.870 --> 00:18:10.070
Another aspect of
this, why I think

00:18:10.070 --> 00:18:13.540
there's real value that
people will pay for,

00:18:13.540 --> 00:18:17.050
is connecting the
outcomes of education

00:18:17.050 --> 00:18:19.460
itself to the outcomes
that are needed,

00:18:19.460 --> 00:18:20.600
let's say in the workplace.

00:18:20.600 --> 00:18:22.850
So a lot of our work is in
the higher education space,

00:18:22.850 --> 00:18:24.740
so folks go from
us to the workplace

00:18:24.740 --> 00:18:26.940
to many of your
businesses, perhaps.

00:18:26.940 --> 00:18:30.230
And one of the missing
things in higher education

00:18:30.230 --> 00:18:33.895
is a very clear link
between how people

00:18:33.895 --> 00:18:36.450
are doing in their first
six months of work.

00:18:36.450 --> 00:18:39.150
And shouldn't that
be a feedback loop

00:18:39.150 --> 00:18:42.210
that comes back to the training
environments, or the learning

00:18:42.210 --> 00:18:44.290
environments, to modify those?

00:18:44.290 --> 00:18:47.210
And from Doctor Kahneman's
work last night, discussion

00:18:47.210 --> 00:18:49.170
last night, one of the
fundamental barriers

00:18:49.170 --> 00:18:51.020
is the system one,
system two problem,

00:18:51.020 --> 00:18:54.970
which is that experts--
more than half of what

00:18:54.970 --> 00:18:59.200
is human expertise in an
expert's mind is subconscious.

00:18:59.200 --> 00:19:01.960
That is, when they
teach a novice,

00:19:01.960 --> 00:19:03.750
as you do, you stick
an expert up in front

00:19:03.750 --> 00:19:04.950
and have them teach.

00:19:04.950 --> 00:19:09.250
They will tell a
novice less than 30%

00:19:09.250 --> 00:19:11.380
of what the novice needs
to know to execute.

00:19:11.380 --> 00:19:13.520
It's why your first year
in any job is an agony.

00:19:13.520 --> 00:19:15.937
It's because all of the
experts before you ended up not

00:19:15.937 --> 00:19:17.770
telling you more than
30% of what you needed

00:19:17.770 --> 00:19:19.504
to know the first
day on your job.

00:19:19.504 --> 00:19:21.420
There are techniques--
and we're experimenting

00:19:21.420 --> 00:19:24.145
with those at Kaplan-- that
come out of cognitive science.

00:19:24.145 --> 00:19:26.550
And I've talked with some
of you about those things.

00:19:26.550 --> 00:19:28.340
It's called cognitive
task analysis,

00:19:28.340 --> 00:19:31.455
where you identify with
objective measures-- out

00:19:31.455 --> 00:19:34.170
of 1,000 people
in your workforce,

00:19:34.170 --> 00:19:36.940
who are the three that
you want to clone?

00:19:36.940 --> 00:19:39.080
Who are the three who
are making decisions

00:19:39.080 --> 00:19:43.220
that are amazing for your
business in their role?

00:19:43.220 --> 00:19:47.170
And then you can do an interview
process to get more like 70%

00:19:47.170 --> 00:19:48.390
of that.

00:19:48.390 --> 00:19:50.790
And then create training
materials, and methods,

00:19:50.790 --> 00:19:55.640
and practice that targets those
skills, put those in place,

00:19:55.640 --> 00:19:57.380
and begin the
feedback loop on it.

00:19:57.380 --> 00:20:00.900
With an objective reason, you
can make it clear, transparent,

00:20:00.900 --> 00:20:03.030
what you're trying
to do and why.

00:20:03.030 --> 00:20:05.390
And that allows you to
change it over time, too.

00:20:05.390 --> 00:20:08.890
As the job role changes, you
keep interviewing new experts

00:20:08.890 --> 00:20:10.380
and you make adjustments.

00:20:10.380 --> 00:20:14.390
Well, now, that takes real
work, and repeated work.

00:20:14.390 --> 00:20:18.500
It's also enormously valuable
for both you as employers

00:20:18.500 --> 00:20:21.970
and for the employees,
to now sign on and know

00:20:21.970 --> 00:20:24.150
that the training
track is leading

00:20:24.150 --> 00:20:26.340
to high-quality
expertise that's been

00:20:26.340 --> 00:20:27.920
validated in the workplace.

00:20:27.920 --> 00:20:30.870
So to me what's happening
now-- and it's terrific--

00:20:30.870 --> 00:20:35.390
is the free solutions are
providing an increasing

00:20:35.390 --> 00:20:38.740
baseline of learning
materials, right?

00:20:38.740 --> 00:20:42.840
You can't get away with
poorly designed lectures,

00:20:42.840 --> 00:20:44.180
and then ignore the students.

00:20:44.180 --> 00:20:46.180
It's just no, that's not
going to work any more.

00:20:46.180 --> 00:20:48.310
There's all these
great free materials

00:20:48.310 --> 00:20:50.350
to provide a baseline.

00:20:50.350 --> 00:20:53.240
And then above that, that's
where it gets exciting.

00:20:53.240 --> 00:20:54.520
What comes after that?

00:20:54.520 --> 00:20:56.110
What feedback do you do?

00:20:56.110 --> 00:20:57.935
How do you design
outcomes to improve

00:20:57.935 --> 00:20:59.862
on what's available that's free?

00:20:59.862 --> 00:21:02.070
And I think it'll be, just
like always in technology,

00:21:02.070 --> 00:21:04.445
an ever increasing
race that way.

00:21:04.445 --> 00:21:06.820
And so I think that's part of
what's exciting about that.

00:21:06.820 --> 00:21:08.444
WALTER: Sal, you can
remember your days

00:21:08.444 --> 00:21:10.760
at MIT and at Harvard.

00:21:10.760 --> 00:21:13.220
Khan Academy has
no such campuses.

00:21:13.220 --> 00:21:15.470
Kaplan has places
where people go,

00:21:15.470 --> 00:21:17.940
but they aren't quite
campuses like that.

00:21:17.940 --> 00:21:22.130
What is the role, if any,
that actual, physical campuses

00:21:22.130 --> 00:21:24.671
with human interaction
should and will play?

00:21:24.671 --> 00:21:26.170
SAL: I think it's
a huge role, and I

00:21:26.170 --> 00:21:27.878
think the important
part is what you just

00:21:27.878 --> 00:21:29.870
said-- the human interaction.

00:21:29.870 --> 00:21:32.215
And the problem is if you go
to most campuses right now,

00:21:32.215 --> 00:21:33.590
yeah, we're all
in the same room,

00:21:33.590 --> 00:21:35.440
but there's actually very
little human interaction.

00:21:35.440 --> 00:21:37.695
I mean, I used to sit in
300-person lecture halls

00:21:37.695 --> 00:21:38.900
the whole semester.

00:21:38.900 --> 00:21:40.430
I didn't know the professor.

00:21:40.430 --> 00:21:42.340
I might have known two people in
the classroom-- no interaction.

00:21:42.340 --> 00:21:44.000
WALTER: By the way, every
professor who taught you

00:21:44.000 --> 00:21:45.291
claims that they know you well.

00:21:45.291 --> 00:21:46.960
SAL: Yeah, they saw potential.

00:21:46.960 --> 00:21:47.590
Yeah.

00:21:47.590 --> 00:21:48.770
I don't know.

00:21:48.770 --> 00:21:49.060
Yeah, I met a couple of them.

00:21:49.060 --> 00:21:51.518
WALTER: More people taught Bill
Computer Science at Harvard

00:21:51.518 --> 00:21:53.007
than even ever taught there.

00:21:53.007 --> 00:21:54.260
Yeah.

00:21:54.260 --> 00:21:56.980
SAL: But so what
I say, I imagine

00:21:56.980 --> 00:21:58.480
school for my own children.

00:21:58.480 --> 00:22:01.090
I imagine a highly
interactive environment.

00:22:01.090 --> 00:22:04.490
And so what we think is--
education's a spectrum.

00:22:04.490 --> 00:22:06.320
At this end is your
multiplication,

00:22:06.320 --> 00:22:07.930
facts, and vocabulary.

00:22:07.930 --> 00:22:10.389
And then out here is building
a robot, starting a business,

00:22:10.389 --> 00:22:11.846
painting a picture--
I mean, really

00:22:11.846 --> 00:22:13.287
open-ended, creative things.

00:22:13.287 --> 00:22:15.370
And what we see as the
role of technology is-- OK,

00:22:15.370 --> 00:22:16.635
we're already doing this part.

00:22:16.635 --> 00:22:18.510
And we're going to keep
pushing the envelope.

00:22:18.510 --> 00:22:19.270
We'll use data
and we'll, make it

00:22:19.270 --> 00:22:20.210
better and better and better.

00:22:20.210 --> 00:22:21.210
And we'll iterate on it.

00:22:21.210 --> 00:22:25.039
And we'll connect it to real,
economic, valuable things.

00:22:25.039 --> 00:22:27.080
And then as we do this,
there's kind of some fear

00:22:27.080 --> 00:22:29.370
that I-- is this is going
to-- because right now, this

00:22:29.370 --> 00:22:30.690
is where school is focused.

00:22:30.690 --> 00:22:32.040
Is this going to replace
the teachers there?

00:22:32.040 --> 00:22:34.206
Is it going to turn them
into monitors of some kind?

00:22:34.206 --> 00:22:38.110
No, no, this is an opportunity
to move the humans over here,

00:22:38.110 --> 00:22:39.517
where the humans are good.

00:22:39.517 --> 00:22:41.600
WALTER: Bill, what do you
think the role of things

00:22:41.600 --> 00:22:46.460
like social networks and gaming
are in transforming education?

00:22:46.460 --> 00:22:48.575
BILL: Well, it's
fascinating that one

00:22:48.575 --> 00:22:50.860
of the educational
start-ups, this one Grockit,

00:22:50.860 --> 00:22:56.010
has the ability to do SAT
testing, all these things.

00:22:56.010 --> 00:22:58.690
And you can do the
quizzes on your own,

00:22:58.690 --> 00:23:01.550
or you can do them
with a group of people.

00:23:01.550 --> 00:23:06.110
And overwhelmingly-- over 90%--
people choose to do it almost

00:23:06.110 --> 00:23:09.450
as a contest, where if somebody
is slow, then you can say,

00:23:09.450 --> 00:23:11.047
wow--

00:23:11.047 --> 00:23:12.630
WALTER: On a social
network, you mean?

00:23:12.630 --> 00:23:15.440
BILL: Well, it's online,
multiple people interacting.

00:23:15.440 --> 00:23:16.660
The word social network--

00:23:16.660 --> 00:23:18.405
WALTER: But I mean
it's not place based.

00:23:18.405 --> 00:23:19.280
BILL: No, its online.

00:23:19.280 --> 00:23:21.210
Exactly.

00:23:21.210 --> 00:23:23.760
No, it's a $10 a month
thing, where you sign up

00:23:23.760 --> 00:23:24.710
and you have access.

00:23:24.710 --> 00:23:28.390
And you can do
solo tests, or you

00:23:28.390 --> 00:23:31.066
could go into this sort
of gaming-like thing.

00:23:31.066 --> 00:23:32.440
Now the gaming
thing, some people

00:23:32.440 --> 00:23:36.950
really take it where they design
a very rich, interactive game.

00:23:36.950 --> 00:23:39.880
Manga High's a
for-profit that's done

00:23:39.880 --> 00:23:43.330
a pretty strong set
of games for math.

00:23:43.330 --> 00:23:46.060
Our foundation is funding a lot
of people, like Zoran Popovic

00:23:46.060 --> 00:23:49.590
over at UW and others, to
do some rich games that

00:23:49.590 --> 00:23:55.920
have a way of engaging you
in some mathematical things

00:23:55.920 --> 00:23:59.100
that you may not even
realize that you're learning.

00:23:59.100 --> 00:24:02.210
So there's a lot
of promise there.

00:24:02.210 --> 00:24:04.540
Gaming and
simulation, hopefully,

00:24:04.540 --> 00:24:08.320
can make the subject more
approachable, more interesting,

00:24:08.320 --> 00:24:09.840
more hands on.

00:24:09.840 --> 00:24:11.450
WALTER: Kaya
Henderson was walking

00:24:11.450 --> 00:24:14.270
the hall-- the chancellor of
the Washington, DC schools--

00:24:14.270 --> 00:24:17.270
and was explaining that
with gaming, there's

00:24:17.270 --> 00:24:20.650
something odd, which is that the
boys take to it, because it's

00:24:20.650 --> 00:24:21.920
a real competition.

00:24:21.920 --> 00:24:24.240
And they will stay up all
night to beat their friends

00:24:24.240 --> 00:24:27.890
and get more points, and
suddenly be 50 points ahead.

00:24:27.890 --> 00:24:30.530
But-- and I don't want to just
make it a gender-based thing,

00:24:30.530 --> 00:24:32.730
but different people
learn differently.

00:24:32.730 --> 00:24:35.840
And that gaming, in some ways,
turns some other people off.

00:24:35.840 --> 00:24:38.037
Do you see that?

00:24:38.037 --> 00:24:38.870
SAL: We do see that.

00:24:38.870 --> 00:24:40.559
Actually, I mean,
the first complaint

00:24:40.559 --> 00:24:42.350
when the Los Altos
pilot started, was there

00:24:42.350 --> 00:24:44.670
was a subset of boys who got
addicted to it, literally.

00:24:44.670 --> 00:24:46.920
Like they couldn't-- it was
a good addiction, I guess.

00:24:46.920 --> 00:24:49.060
But they were learning math,
but they were-- just couldn't

00:24:49.060 --> 00:24:50.435
get them-- their
parents couldn't

00:24:50.435 --> 00:24:51.914
get them to focus
on anything else.

00:24:51.914 --> 00:24:53.080
WALTER: Gee, what a problem.

00:24:53.080 --> 00:24:53.710
SAL: Yeah, no.

00:24:53.710 --> 00:24:56.320
There are worse things.

00:24:56.320 --> 00:24:58.340
But what we did see
is there are also

00:24:58.340 --> 00:25:00.340
ways to motivate girls
with game mechanics.

00:25:00.340 --> 00:25:02.260
And it's not-- obviously,
it's a distribution.

00:25:02.260 --> 00:25:05.780
And we have seen that girls are
more focused on achievement,

00:25:05.780 --> 00:25:07.610
more focused on what
they've done, more

00:25:07.610 --> 00:25:10.010
focused on their
portfolio of actions,

00:25:10.010 --> 00:25:12.520
while boys are more
focused on points.

00:25:12.520 --> 00:25:14.675
And maybe we don't outgrow
it, for some of us.

00:25:14.675 --> 00:25:16.800
WALTER: Speaking of people
who haven't outgrown it,

00:25:16.800 --> 00:25:19.120
let me open it up for questions.

00:25:19.120 --> 00:25:20.160
Please.

00:25:20.160 --> 00:25:23.980
If we can turn up the lights,
and raise some hands, and get

00:25:23.980 --> 00:25:25.037
started.

00:25:25.037 --> 00:25:27.370
BROR: One thing I might say
about the gaming side, which

00:25:27.370 --> 00:25:30.010
is it is actually very
interesting, because the risk

00:25:30.010 --> 00:25:31.870
is some of the gaming
elements can wind up

00:25:31.870 --> 00:25:34.090
being more distracting
than helpful.

00:25:34.090 --> 00:25:36.270
But once you get
an initial mastery,

00:25:36.270 --> 00:25:38.590
then the gaming elements
provide that encouragement

00:25:38.590 --> 00:25:40.870
for repeated practice,
which is what's

00:25:40.870 --> 00:25:43.190
needed to build a lot of
fluency and familiarity,

00:25:43.190 --> 00:25:45.420
so that the skills
begin to be embedded.

00:25:45.420 --> 00:25:46.900
So there's this
careful trade-off

00:25:46.900 --> 00:25:49.340
between when you're initially
instructing, and trying

00:25:49.340 --> 00:25:52.457
to get ideas across, the
very first examples you show,

00:25:52.457 --> 00:25:55.040
and then practice environments
that are exciting and engaging.

00:25:55.040 --> 00:25:57.850
WALTER: And you've written
about that mastering that

00:25:57.850 --> 00:26:00.119
comes from-- it's something
we sometimes miss.

00:26:00.119 --> 00:26:00.910
BROR: Yes, exactly.

00:26:00.910 --> 00:26:02.868
WALTER: In the traditional
education structure,

00:26:02.868 --> 00:26:04.240
we lecture and then we test.

00:26:04.240 --> 00:26:05.657
But we don't give
that-- and games

00:26:05.657 --> 00:26:06.781
can do that, you're saying.

00:26:06.781 --> 00:26:08.230
BROR: Yes, games can do that.

00:26:08.230 --> 00:26:11.090
But so can simple things
like worked examples,

00:26:11.090 --> 00:26:15.120
where you go from talking
about what you need to do.

00:26:15.120 --> 00:26:16.602
Then you give a demonstration.

00:26:16.602 --> 00:26:18.810
It turns out demonstrations
are enormously important.

00:26:18.810 --> 00:26:21.820
Show somebody doing
what you said.

00:26:21.820 --> 00:26:24.180
And then you do what's
called a work example, where

00:26:24.180 --> 00:26:26.870
you give people partially
filled out work.

00:26:26.870 --> 00:26:29.380
And so you do a piece, they
do a piece, you do a piece,

00:26:29.380 --> 00:26:30.360
they do a piece.

00:26:30.360 --> 00:26:33.530
It's exactly what the
best tutors actually do.

00:26:33.530 --> 00:26:34.920
But the technology
now allows you

00:26:34.920 --> 00:26:36.690
to take what is
a very effective,

00:26:36.690 --> 00:26:39.210
an expensive learning
technique, and turn it

00:26:39.210 --> 00:26:41.720
into something that can
be distributed en masse.

00:26:41.720 --> 00:26:43.840
And that gives you
then that experience,

00:26:43.840 --> 00:26:45.850
and builds the mastery
and confidence.

00:26:45.850 --> 00:26:47.600
And it turns out it
shrinks learning time,

00:26:47.600 --> 00:26:49.320
and increases the
amount of mastery.

00:26:49.320 --> 00:26:50.028
It's fascinating.

00:26:50.028 --> 00:26:53.010
WALTER: And you should read his
blog, by the way, Number One.


Surface integral ex3 part 4: Home stretch

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Kind: captions
Language: en

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So I stopped abruptly 12
minutes into the last video

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because 12 minutes was too long.

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I needed a break.

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But where we left off, we
were in the home stretch.

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We were evaluating the
third surface integral.

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And we were setting it up as
a double integral with respect

00:00:12.618 --> 00:00:14.350
to r and theta.

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And we just had to
set up the bounds.

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And we know that r takes
on values between 0 and 1.

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And theta takes on values
between 0 and 2 pi.

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So r, we're going to integrate
with respect to r first.

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r takes on values
between 0 and 1.

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And theta takes on values
between 0 and 2 pi.

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And so now we are
ready to integrate.

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So let's do the first part.

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Let's do this inside
part right over here.

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And I'm just going to
rewrite the outside part.

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So this is going
to be equal to-- we

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have our square root of 2
times the integral from 0

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to 2 pi of-- and we have
d theta right over here.

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So that's the outside.

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This inside part
right over here,

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we can rewrite it as
if we distribute the r.

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It's r minus r squared
cosine of theta.

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Now we're going to
integrate with respect to r.

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So when we integrate with
respect to r, cosine of theta

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is just a constant.

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So if you integrate
this with respect to r,

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you get-- and I'll do
it in that pink color--

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if you integrate with respect
to r, the antiderivative of r

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is r squared over 2.

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And the antiderivative
of r squared

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is r cubed over 3 minus r
cubed over 3 cosine theta.

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This is just a constant.

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And we're going to
evaluate that from 0 to 1.

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So when you would
evaluate it at 1,

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you get 1/2 minus
1/3 cosine theta.

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So you get 1/2-- I'll just
do it right over here--

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1/2 minus 1/3 cosine theta.

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And then minus both of
these evaluated at 0,

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well those are
just going to be 0.

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0 squared minus 0
squared times whatever.

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It's all going to be 0.

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So this business
right over here just

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evaluates to 1/2 minus
1/3 cosine of theta.

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And so we get the integral.

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This is all going
to be equal now

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to the square root of 2 times
the integral from theta 0

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to 2 pi of 1/2 minus 1/3
cosine of theta d theta.

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And this is equal to
square root of 2 times

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the antiderivative
of 1/2 is 1/2 theta.

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And the antiderivative of
cosine theta is sine theta.

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So minus 1/3 sine theta.

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And we're evaluating
it from 0 to 2 pi.

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When you evaluate
these at 2 pi, you

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have-- let me just write it all
out-- this is the home stretch.

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I don't want to make
a careless mistake.

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We have square root of 2 times--
let's evaluate it at 2 pi--

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1/2 times 2 pi is pi minus
1/3 times sine of 2 pi-- well

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that's just going to be 0.

00:03:09.890 --> 00:03:14.480
And when you evaluate it
at 0, 1/2 times 0 is 0.

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Sine of 0 is 0.

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So that all comes out to 0.

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So all of this business
simplifies to pi.

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And we are done.

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We've evaluated surface three.

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It is square root of 2, or
the third surface integral,

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or the surface integral
over surface three.

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It is square root of 2 pi.

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And we are done.

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So this part right over
here is square root 2,

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or root 2, times pi.

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So this entire surface
integral that we started

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like 80 videos ago, evaluates
to-- the orange part

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evaluates to 0.

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The blue part, 3 pi over 2.

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And then the magenta part
is square root of 2 pi.

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So we're left with 3 pi over
2 plus the square root of 2

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pi is the value of our
original surface integral.