Hello and Welcome to Unit 4.

This is the first of several units on power laws.

In this unit I’ll say what power laws are,

will explore some of their mathematical properties.

And see how they’re the related

to fractals and self-similarity.

In the next unit we’ll look at

some examples of power laws.

And talk about how to work with power law data.

In Unit 6, we’ll look at some of many

different mechanisms that can generate power laws.

So we’ve actually already encountered power laws

in the previous unit that equation

we work with again and again and again

for the box counting dimension

Well, that’s a power law.

And we saw that when that equation is true,

when that equation is obeyed over a range of scales s

that we are dealing with a fractal

for some sort of self similarity

and so what we are gonna see

in this unit and the next several

is that there are other situations

that are described by similar equation,

not necessarily box counting,

it might be something else.

But when we see an equation like that

that is an indication

that there’s some sort of scale-free behavior

so we begin this unit by looking at

an initial example of a power law.

So we have something concrete to talk about

and then in the rest of this unit

I’ll talk about a number of the mathematical properties,

and interesting and important features of power laws,

and also talk about something that aren’t power laws

and contrast power law behaviors

with normal or Gaussian behavior.

And so we’ll talk about the central limit theorem.

So let’s get started

in the next video with an initial example