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.

It's all very one dimensional.

But the conflict was not simply one dimensional.

One idea is that our three dimensional universe may be embedded in a high dimensional space, just as you can imagine on these sheets of paper.

The other point that's worth noticing is how one dimensional this projection is.

There might be somebody on one right now, participating in multi dimensional engagement.

So in one dimensional systems this is a project called the self folding proteins.

The strange one looks likes this that we live in a three dimensional world.

And one thing that's very important is to combine traditional tabular data with three dimensional and geospatial information.

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

Stereochemistry is the study of three dimensional chemistry, as essentially understanding the actual three dimensional structure of things.

create scientific 2 dimensional graphs

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

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

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

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

It s truly a three dimensional space.

This is a three dimensional machine.

So it becomes slightly three dimensional.

Freeflying is more the three dimensional skydiving.

It s a thin film, two dimensional existence.

One thing that three dimensional interactions and the general idea of imbuing computation with space affords you is a final destruction of that unfortunate one to one pairing between human beings and computers.

Now to put some neurobiological meat on this abstract model, we constructed a simple one dimensional world for our favorite subject, fruit flies.

And the power of Galois' mathematical language is it also allows us to create symmetrical objects in the unseen world, beyond the two dimensional, three dimensional, all the way through to the four or five or infinite dimensional space.

But their three dimensional orientation is still different.

Or you could go into three dimensional art.

So it's actually a multi dimensional user interface.

So imagine a grid, like the one I'm showing you right now, and now imagine, within that grid, that two dimensional sheet, imagine neurons.

You can imagine ants on one of them thinking it's a two dimensional universe, not being aware of another population of ants on the other.

In fact, they live in a 12 dimensional space.

And she was talking about seven dimensional, inverted universes.

And basically, the concept is, how do you represent the three dimensional image of the night sky that surrounds us onto a flat, portable, two dimensional surface.

The problem with it is and the reason I will never build another one like it is that this is a product of two dimensional thinking.

This way you can make recursive and multi dimensional arrays.

And it randomly generates points within a three dimensional matrix.

They can be planar formations, they can be three dimensional formations.

I think I understood you to say that you could reconcile that with a world that doesn't become one dimensional, where we all have to think the same.

Middle board of this three dimensional chess game economic power among states.

Cars are three dimensional objects that have a fixed position and velocity.

Poverty is a multi dimensional phenomenon associated with economic and structural problems.

Because a DNA sequence is a one dimensional entity, it lends itself much better to single number comparisons than a four dimensional body does. The genes that lead to the production of the human and chimpanzee femur may be 98 99 identical, but it is impossible to say whether the bones themselves are more or less similar than that.

The musicians played off a three dimensional graph of weather data like this.

And that life enjoys a three dimensional existence, which is alien to us.

The musicians played off a three dimensional graph of weather data like this.