For these specific patients, we actually just suture these materials.

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.

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

The new area we added are these rows over here.

And you didn't have to go through that exercise.

All the other values should be zero.

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.

Are there any shifts we could do oh we could totally shift over that (b).

Nearest neighbor works really well for small input spaces like three or four dimensions.

A factor, again, is one of these tables.

I went on to freeflying.

And the result of this product is going to be an n dimensional vector y.

Prepare your minds for a new scale... . ..of physical scientific values, gentlemen.

And, on the right is open five, ten and two.

Here, this is a three by four dimensional matrix.

And the other piece of knowledge that we need is that the dimension of the matrix is going to be written as the number of row times the number of columns in the matrix.

They are usually easy to implement.

And that's where I work.

And so here's the challenge

We also memorize the action name as before.

With this notation X2 is a four dimensional vector.

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

It's A transpose times B times A that you subtract from the remaining omega prime, and the same for C over here.

cubes game

3D Rubik's cube game

We implemented both of them.

And you notice, again, this is a 3 by 2 matrix and the result is a matrix of the same dimension.

N by N, kind of like we have up here.

I want you to plug in the f matrix.

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.

Fly your ship in a 4d environment

I still haven't heard any charges. Attempted assault.

So the matrix A is a m by n dimensional matrix, so m rows and n columns and we are going to multiply that by a n by 1 matrix, in other words an n dimensional vector.

But in the end, she'll carry out her mission.

Obviously, moving a robot in any direction is easier than being constrained by the filters or the car.

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

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

We, we assume it has certain characteristics.

And now the deed is done.

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

Well, we can do the same thing in the third dimension with a four dimensional object.

But combined in a certain way, they can create something that still looks three dimensional,

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