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