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.