A portal! A pathway to another dimension!

Have you always been able to multitask like this?

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.

You unlock this door with the key of imagination.

In time you will learn to see what is extra dimensional with as much clarity as you learn to see the physical dimension.

I prefer to think of them as battling evil in another dimension.

WOMAN It's me. I'm the guilty one.

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

So if you think about the distinction between copies and remix, and the distinction between the professional and the amateur, of course, we get this matrix lawyers deal in two dimensions, you guys in hundred dimensions but here is my two dimensions

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

You're traveling through another dimension a dimension not only of sight and sound, but of mind.

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

A gaussian with a small amount of uncertainty might look like this.

All the other values should be zero.

And the reason is shown in the following graph

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

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.

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.

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

We live in one of these worlds, and I can only show it as a sheet, but it's really three dimensional.

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

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

Let's say I have Point 2.

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.

How many ways are there to get to this cell?

cubes game

3D Rubik's cube game

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

They don't fall over. They don't fall.

In fact, more generally, this is an in dimensional feature back there.

My codomain by definition is R3.

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.

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

An online multi player platform 2D shooter

Max. viewport dimensions

So, a one dimensional space is just a line.

So, what about four dimensions?

And five?

Let me draw them for you just so you can visualize it.

It might be possible to have a fairly small uncertainty in 1 dimension, but a huge uncertainty in the other.

You don't have to have a parametric equation.

And you could now place 0.1 instead of the delta T to get this specific F matrix.

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

We match their dimensions.