From any cube, these are our three operations or our three movements we can do.

Betty arrive at point A?

To the forward command centre take me.

You're in good hands.

I'm kind of learning along with you guys what works and what doesn't.

Well, you have this force right here.

We still have much more to do.

We looked at the curbs. The curbs were throwing shadows south, so we could tell the bridge was running east west across the river.

This car now has its state an x, a y, and an orientation, theta.

When you multiply it by a scalar, or you're not changing its direction.

Unarching their course, somewhere heading to New York and Philadelphia.

Watch the animal.

So, an officer on horseback starts at the back of a column of marching soldiers and rides to the front of the column.

We're moving towards, you know, a lack of privacy, really.

For our purposes, a dimension is a direction, which we can picture as a line.

I would just go 1 to the horizontal and then 2 to the vertical.

We go two to the left.

Are you driven by significance or love?

Now, what's our trick of finding gradients?

Here's an example of a right handed coordinate system. Say, I want to build a building.

So there's the tenth guy.

Frictions between Japan and the U.S. are easing up for a change.

Listen carefully.

Yes! My power pose. (Applause) (Laughs)

We want to rotate 2 12ths of the way around the circle. So that's 60 degrees.

As you move the line around watch how it will snap to a red direction, a green direction and a blue direction.

There are three principle actions.

See, look, it does a little dance, and then it carries on in exactly the same direction that it took in the first place.

So let me try my best attempt at drawing this.

You can just keep going below 40.

And now in the x direction, this is the x term, my x radius is 3.

But in this cell over here I have to turn to the left side.

Now, within that there is some interesting things happening.

Don't worry about it. You look fine. Turn around and back up.

We just take the square root of this, so it's 2.

And they use them in the same way we use our binocular vision.

Check the document's spelling from the cursor and forward

Though I joke about it,

The state space is augmented correspondingly.

So, now the robot is heading in the direction of pi 2, and it moved forward 10 meters in the Y direction, instead of the X direction.

She is getting better day by day.

So all the red sides, for example, face one direction south.

Copy that. Moving to intercept.

And we're allowed to either go forward.

Again, there is an entire literature.