Exponential growth, that's the key here.

Layered, like nachos. Exponential growth.

First they don't grow.

This is the problem that we face, due to the doubling caused by Exponential Growth.

So sort of, if you continue down here, you're gonna see vacuum tubes show up.

This is at an early stage, but you can show with the exponential growth of the amount of information about the brain and the exponential improvement in the resolution of brain scanning, we will succeed in reverse engineering the human brain by the 2020s.

They do not scale quadratically, in fact, normally they scale exponetially with the dimensionality of the state space because you need exponentially many particles to fill up the state space.

So the idea here is just to show you that exponential functions are really, really dramatic.

Uh,in your case,I'm guessing the progressionis exponential.

Our population and our use of the finite resources of planet Earth are growing exponentially, along with our technical ability to change the environment for good or ill.

So, if you look at this, this plot, you'll see that, well this roughly looks like a straight line, and a straight line on a

HAPPY ENDlNG

Well, you say, what's the exponential function?

And now I'm going to take the most extreme of all steps.

And every time they turn themselves over there is some damage.

That's been recognized because the number of particles you need to fill a high dimensional space tends to grow exponentially with the dimensionality of the space.

Exponential function

You add the exponents.

What do you think you have in a month? We're at a billion.

But that's just but some number.

Let's calculate how much money we have earned.

range( start, stop, step ) so you can also, if you want, tell it, how much to int

Add Function

So we know the basic trig functions.

In fact, those of you who are still conscious and mathematically competent, will note that this is a semi log plot.

In other words, the rate of increase is exponential.

But our brains are wired for a linear world.

If I have the same base 10 right over here, so I can add the exponents.

We're almost there.

So, you see, it works just as easily with negative numbers.

Plus 80 .

Think about the theory of evolution.

To illustrate this idea with a picture imagine we have some function f(n).

Well, I have to raise it to the second power.

The histogram filter's biggest disadvantage is it scales exponentially, and the reason is any grid that is defined over arcade dimensions will end up having exponentially many grid cells in the number of dimensions, which is really unfortunate because we can't really represent high dimensional grids really well.

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So what do we want to make our v prime?

And we're all concerned about energy and the environment.

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You don't have to have exponents, it's just that these exponents are probably where the motivation for calling these even functions and odd functions came from.

You know, you all have smartphones, we're all connected to the web.

So a to the first times a to the seventh,

And let's understand this is not an incremental sort of change.

So I end up with s squared times the Laplace Transform of y, minus s times y of 0 minus 1 times y prime of 0.

And in a trillionth of a second it expanded exponentially into what became the universe we know.