It makes a two dimensional image look more three dimensional.

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.

So you can basically program any three dimensional shape or one dimensional, two dimensional up into this chain completely passively.

Toward the Dimensional Gate.

It's called dimensional analysis.

And three dimensional shapes

Do a little dimensional analysis.

It's all very one dimensional.

We take this curved 12 dimensional space and transform it into a flat four dimensional space.

We take this curved 12 dimensional space, and transform it into a flat, four dimensional space.

Often curves in two dimensional (plane curves) or three dimensional (space curves) Euclidean space are of interest.

It s truly a three dimensional space.

But reality is not one dimensional.

So it becomes slightly three dimensional.

I couldn't imagine three dimensional space.

We could've had n dimensional vectors.

It's truly a three dimensional space.

This is a three dimensional machine.

I'm also looking to take my work from the two dimensional form to a more three dimensional form.

It's still a mapping from a three dimensional, I guess we could call it a three dimensional matrix vector to a three dimensional vector. Each of these are members of R3.

Now, take into account the fact that we live in a three dimensional universe, OK, a three dimensional space.

Well, we take this three dimensional stack of images and treat it as a gigantic three dimensional coloring book.

Let's say that I have a one dimensional subspace. Let's call that V1, for it's a one dimensional subspace.

Higher and higher and higher and higher

It s a thin film, two dimensional existence.

An amaryllis flower looking really three dimensional.

We could have had three dimensional vectors.

It's a thin film, two dimensional existence.

This is still a two dimensional space.

So this is my three dimensional plane.

But these aren't necessarily two dimensional beasts.

Freeflying is more the three dimensional skydiving.

In 1746, d Alembert discovered the one dimensional wave equation, and within ten years Euler discovered the three dimensional wave equation.

And we're also translating that into two dimensional systems so flat sheets that can self fold into three dimensional structures.

Kind of like how each page of a newspaper is its own two dimensional surface embedded within our three dimensional world.

To be able to make predictions about the fundamental particles we might see there, it seems that they are all facets of some strange symmetrical shape in a higher dimensional space.

To be able to make predictions about the fundamental particles we might see there, it seems that they are all facets of some strange symmetrical shape in a higher dimensional space.

Higher, higher

Higher, higher!

Higher! Higher!

But the conflict was not simply one dimensional.

United Nations reform is all dimensional and multifaceted.

But what if our world were two dimensional?

These are all four dimensional, we're dealing in

Now, let's do it the dimensional analysis way.