So, I am Simon DeDeo.

I am an external faculty here 
at the Santa Fe Institute,

and I am also a professor 
at Indiana University,

where I work in Computer Science
and also in the Cognitive Sciences.

We'll be talking in this 
unit about "Renormalization".

So, I actually did my PhD 
in physics years and years ago,

and it's fair enough to say 
that since 1950

the most interesting thing, in fact, 
perhaps the only thing that has driven

theoretical physics has been the 
problem of Renormalization.

And in pursuit of understanding 
what on Earth that was,

we developed an enormous amount of 
extremely complicated mathematics.

When I came to work in the Cognitive 
Sciences, when I came to study

social systems, and social behavior, 
what I realized is that the tools

that we had developed in physics for 
Renormalization, and, in fact,

no just the tools for the underlying 
concepts,

became incredibly useful for 
trying to understand

a very different kind of problem.

And that's because Renormalization 
is a general set of tools

for how theory simplifies; 
it is a set of tools to tell you

how to throw out information about 
the world; how to throw out things

you may not know, you may not be 
able to know, and how to throw out

things in fact you may 
not even care about;

to throw out the stuff that
you think is irrelevant.

And Renormalization is the story about 
what happens when you do that;

what happens not just to the observations
you make about the world,

but also to the theories that you 
use to explain those observations.

So, an example, certainly not
from the physical sciences,

would be the problem
of macroeconomics.

So, every few months or every six 
months or every year, every ten years,

macroeconomists take a snapshot
of the state of the economy.

They try to figure out who's employed,
who's unemployed, where are the pockets

where people are developing 
new businesses,

where are the pockets that are contracting
where people are losing their jobs

where people are living.

So, the macoreconomists take 
a snapshot of the economy

at different points in time.

So, there is a 2008 snapshot,

a 2009 snapshot,

a 2010 snapshot,

all the way up to 2016 and beyond.

And if you study macoreconomics, your 
basic job is to look at a snapshot here

and to look at the unemployment 
numbers, right?

The number of people who are employed, 
let's say, you might look at the GDP,

you might look at the Gini coefficient 
that measures inequality...

Depending upon the kind of 
macroeconomist you are,

you have a small set of variables here, 
and if you have good macroeconomics,

theory is gonna tell you 
what happens next year,

And if your theory is really good, 
it might even tell you

what happens the year after that.

So, that's macroeconomics, but we
know of course that something

like the number of people who're 
unemployed is not what you'd think of

as a fundamental variable in 
the same way

that we say the electric field is a 
fundamental variable

or that the pH of a solution in your 
blood is a fundamental variable.

This, in fact, is a summary of 
an incredibly complicated

and messy world that 
people inhabit

And moment to moment,

certainly not year to year,

every second, people in the 
actual economy are making deals,

they are trading money, ok?

They are hiring each other,...
they are hiring,

sure they are getting jobs,
they are losing jobs, right?

They may even hire people who 
have skirts, like tihs, ok?

And so, in fact, the actual story 
of how the economy works

is a series of second by second

accounts of everything 
that happens within,

let's say, the United States

or indeed everything that happens
wtihin the global economy,

within the aspects of human behavior 
we think of as economic.

And so, what macroeconomics 
does is, in fact,

an attemtpt is to summarize everything
that's going on in the economy

at one point in time and build a theory 
about what's going to happen next,

operating only with these 
variables here, ok?

But the actual reality of the 
situation is far more complicated,

and at the end of 2009, let's say 
when the indicators come out,

that's the product, in fact, of many, 
many evolutionary steps.

Just second-by-second moments in 
the history of actually what happened.

So, if we had Godlike powers, right?

If we had machines that could 
know everything and predict everything,

we have no need for this up here.

All we do is to look at 
the world as it is.

And then we'd evolve it 
forward in time

through some sort of massive eight
billion person strong agent-based model.

And, occasionally, if somebody, 
for some reasons, says

"oh, what's the unemployment
is going to be in 2011?",

we just take a snapshot of the 
system much later,

summarize it,

ok?

and get a new set of statistics here.

The problem is,...

is not only ...

"is operating at this level impossible?"

It's also perhaps not even 
useful because even if our

computer could simulate setp-by-step 
what happens in the world,

it may not focus our attention on
what actually matters, right?

So, one person, let's say, gets a
job in one part of the country,

how important is that?

If we're a policy maker, 
for example,

should we intervene here?

or should we intervene here?

One thing macroeconomics has 
been going for is not just simplicity.

The number of equations a good 
macroeconomic theory might need

to go from here to here, is much 
smaller than the massive number

of equations you need to go 
from here to here to here

every step along the way.

Not only is the macroeconomist
more efficient,

but it may be the case 
that these higher level

variables are somehow more 
useful, more explanatory.

And, of course, we 
do this all the time.

So, if you're a cognitive scientist, 
if you say somebody's interested

in the psychology of human 
decision-making, you know, in fact,

that the account you built has pretty 
much the same relationship

to the firing of neurons 
in somebody's brain

that macroeconomics has to 
all of the complexity to everything

that actually is going on in 
the economy itself.

And so, in fact, many 
scientific subjects are

fundamentally doing 
this kind of science.

They're constantly projecting or,

this is the word that we'll 
come up over and over in this

set of modules, or 
their "coarse-graining".

This underlying complicated reality to 
produce a set of good descriptions,

And not just to produce a set of 
good descriptions, but, in fact,

to produce a theory that relates those 
description as they evolve over time.

The relationship 
between this level

and this level is the 
story of Renormalization,

and what we'll do here is give
you a series of examples

that will slowly build up in 
complexity for how that works.