If that angle becomes 0 we end up with a degenerate triangle

So now I'm going to show you a number of projects that we've built, from one dimensional, two dimensional, three dimensional and even four dimensional systems.

Beyond it is another dimension a dimension of sound... a dimension of sight... a dimension of mind.

Let's say in the very first time the difference between position and landmark is 10.

We match their dimensions.

In this example, picture a robot that starts at initial position 5.

It's a single row of numbers of a position 1 dimensional.

Everywhere would be in 2D the entire image.

Let's say that a hypersphere is the 4D equivalent of a 3D sphere.

The new area we added are these rows over here.

Now, to explain this, let me first tell you what parameters characterizes a Gaussian.

Galaxies seem to fit all over this particular family of profiles.

So the only difference, class, is that our object now moves in a 2 dimensional space, where as in class, it moved in a 1 dimensional space.

Let's say I have Point 2.

It's amazing, this entire program over here implements a one dimensional common feature.

This is our first programming assignment.

So we remap the data onto the space over here, with x1 over here and x2 over here.

In linear regression, the function has a particular form which is W1 times X plus W0.

cubes game

3D Rubik's cube game

The answer is obviously 1.

Okay. This kind of gives us some intuition for how this works in 2 dimensions.

It's of index signed from zero.

And notice I'm going from a space that has two dimensions to a space it has three dimensions, or three components.

My codomain by definition is R3.

sort of... a portal between this reality and the next.

All the other values should be zero.

If you take a pin hole camera you can position the pin hole itself anywhere.

You don't have to have a parametric equation.

It doesn't work in a universe with four dimensions of space, nor five, nor six.

With this notation X2 is a four dimensional vector.

We have to understand that we are interacting with the forth dimensional reality when we are just activating our third eyes.

It gets us the value function, and it gets us the policy action.

For our direction to be a dimension, it has to be at right angles to all other dimensions.

You understand how to incorporate motion, and you really implement something that's actually really cool, which is a full Kalman filter for the 1D case.

The orthogonal dimension in this direction carries alomst information, so it suffices, in most cases, to project the data onto this 1 dimensional space.

Even though moving one over here and one over there would give a better solution.

When you study the mathematics of string theory, you find that it doesn't work in a universe that just has three dimensions of space.

Now when we talk about a three dimensional surface it's a three dimensional surface of a four dimensional sphere that means that any of the three dimensions that are over here on the surface, I can only draw two but that means, if this is true, if the Universe is a three dimensional surface of a four dimensional sphere, that means if you go up and if you just keep going up, you'll eventually come back from the bottom.

Right here, I defined x and v as vectors in R2.

If you take the intersection of that plane and that cone and in future videos, and you don't do this in your algebra two class.

And this is the inner product of these 2 vectors over here.

Where this one is the orthogonal vector shown over here.

My next question pertains to the tracking problem that we talked about in class.

So for example the point 2, 3, which might be right there, will be mapped to the three dimensional point, it's kind of just drawn as a two dimensional blurb right there, but I think you get the idea, would be mapped to the three dimensional point 5, 1, 6.