It's all very one dimensional.

We have progressed from a zero dimensional point, to a one dimensional line segment, to a two dimensional triangle.

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

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.

And that's why my training examples are now N dimensional rather N plus one dimensional vectors.

So, a one dimensional space is just a line.

Let's for now just consider the one dimensional case.

like a 4 dimensional or 5 dimensional figure.

Left field, center field, to get an idea of where the target is. but there was one dimensional, straight down an alley.

Essentially it becomes one dimensional, we lose our 2 dimensionality

And now Mu2 is going to be an n dimensional vector.

In this case X is one dimensional which is N 1.

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

Now we extend it out one inch and we have a one dimensional line segment.

Sorting multi dimensional array

Insert 2 dimensional vector

Toward the Dimensional Gate.

Let's look at one more way of representing a four dimensional object.

Remember that now this state space is 3 dimensional, not 2 dimensional.

What I am saying though is that human beings are not one dimensional.

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

It's amazing, this entire program over here implements a one dimensional common feature.

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

And one can, in fact, reconstruct the 3 dimensional shape of this object.

However, I printed out a 2 dimensional table, not a 3 dimensional table.

create scientific 2 dimensional graphs

It's a 3 dimensional state.

Here's a 2 dimensional space.

So next, we will talk about two dimensional and three dimensional shapes of ellipticals.

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

When I reduce, I will do this for the one dimensional case on paper.

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

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.

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

They're two dimensional vectors, but we can extend it to an arbitrary number of dimensions.

So, it works really well for low dimensional problems like 3 dimensional robot localization problems.

An extraordinary one.

A two dimensional vector is needed

This is a 47 dimensional vector.

So it becomes slightly three dimensional.

It's truly a three dimensional space.

This is a three dimensional machine.

Often they are 3 dimensional vectors.

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

Finally, I copy the 3 dimensional symbol for my policy straight into the 2 dimensional array.