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.

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 the conflict was not simply one dimensional.

And that's where I work. I create mathematical objects, symmetrical objects, using Galois' language, in very high dimensional spaces.

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.

One learns grammar from language, not language from grammar.

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.

One language is never enough.

One language is never enough.

Many people only speaks one language.

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.

The whole earth was of one language and of one speech.

The whole earth was of one language and of one speech.

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 the whole earth was of one language, and of one speech.

And the whole earth was of one language, and of one speech.

Language is one of man's most important inventions.

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.

One of the obstacles is women's foreign language skills.

No, uh no, I wait one that was really bad body language the worst body language I've ever seen.

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.

What one has to learn is more than the language.

Language is one of the most important inventions of mankind.

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.

And let's pretend the other one is good at language skills.

It would be able to translate from one language to another.