And here's the point of that.

Let's go run it and see.

Now we've handled two of the three cases. One case, it's completely solved.

Well, the old state was zero and now we have a 1 over N plus 1 so let's say 1 3.

The harder question is How often will an object come out of the pipeline being fed with objects?

You could pick 2 and 7. You could pick whatever you want

So this we rewrite as (let me use that same green color) 373 plus... we want to write the ones under the ones place, and the tens place under the tens place, so that we're adding the appropriate values.

Or I guess you could start with 1 0 and that would work, too.

And it continues on the same way as starting with 1 1.

And I was shivering.

10 plus 5 is 15.

We talked earlier about the Arab Spring, and the power of all this.

And the answer is 0.25, which is 1 0.75 using the law down here.

We go 1, 2, 3, 4.

V so this gives me one over one, one over two and one over three.

Let me do it one more time.

So to avoid that, I want to put all of these I want to rewrite all of these as fractions.

And over here, we have nine things with a mass of one kilogram, which we could write as 1 1 1 1 1 1 1 1 1.

I mean Oh Ha Ni.

We introduced this in Chart State 0.

It's also like saying thirty three goes into four hundred thirty two point three, thirteen point one times.

Different model, right?

Let's see the difference here.

Let's get started.

Those are simply proportions that can be compared to each other as we've done for many things.

The big difference was that the bar chart is defined over 2D data.

Well, this is another big piece right here.

In the example I've chosen here are the measurements of 5., 6., 7., 9., and 10.

Columns go down, rows go across.

Normal touch sensors that you see,

So six divided by two is three.

So we could subtract that ten hundredths minus nine hundredths is one hundredth.

In fact, when I started teaching this course, in Unit 1 I was trying to think of a website that was 100 static, and I can't think of one.

And this is about shifting baseline.

And I use that seashell again to buy more fish.

Get your ass up there. Do you mean to tell me that you cannot do one single pullup?

Well, we can write the 5 in the ones place, and carry the one. But what did we just do? What does this 1 represent?

What the rest of the number is after I've subtracted 128 from it if it was 1 or nothing.

So it's four hundred forty.

Let's get 1 more view into how this relationship between grammars and parsing states plays out.

The other way we could have thought about this is you could have looked at the length of each of these sides.

And I'll just give you a few examples.

This was kind of the defining slogan.

So once again, I can graph it on the number line. x is greater than 1 right there.

It's pretty straightforward to see the chains have a maximum possible path length of n 1 and this n 1 is an upper bound on the path link of any graph with n nodes and so we are checking to see if we can make B into a chain.