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All right, hi class,

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we're back at modeling complex systems.

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In this video, what I'd really like to do

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is go over the three
key words of our title.

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So models, complex systems,
what did these words even mean?

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I'm sure some of you
signed up for this course

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because you have to, it's
a mandatory or core course

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for our complex systems program.

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I'm sure some of you maybe just joined

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because the description was interesting,

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but that doesn't mean
that you have an idea

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of what we're gonna do here.

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So I want to clear up
some common misconceptions

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about the course, and also just talk

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about what models and
complex systems mean here.

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So there's a classic quote
from Albert Einstein,

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and I'm sure a lot of
you have already heard,

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things should be made
as simple as possible,

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but not simpler.

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And this is really one of the key insight

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behind what we mean here by models,

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is that we try to simplify the the world,

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be it through just thinking
about what's important,

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or mathematical equations
or computational programs.

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The idea is just to simplify something

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in order to better understand it, right?

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So if I ask you at some
point in this semester

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to model an ant colony,

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you could go and dig one in your backyard

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and then bring, you know,
one of these end colonies

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in a glass box to class or you know,

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for show and tell on video.

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But that doesn't really help us

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understand how ant colonies work.

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Similarly, you know,
you could take one ant

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and look at it very closely,

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but that wouldn't really
help you understand

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how colonies like come to
be these complex structures?

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How can ant colonies grow mushroom?

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How can they discover
things, and search for food?

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It's really about their
behavior as a whole.

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So there has to be a sweet spot somewhere

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between considering more than one ant,

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and also not embracing like the complexity

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and craziness of the real world.

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So we're gonna try and use computational

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and mathematical model as parables

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or cartoons for what the world is

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to help us understand the key ingredient.

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There's another quote that
I think better captures

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what I mean by this,

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and I'm stealing this juxtaposition

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of two quotes from a book called

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"The Computational Beauty of
Nature" by Gary William Flake.

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So the second quote is
from Bertrand Russell,

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the philosopher, and he says,

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"The point of philosophy
is to start with something

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"so simple as not to seem worth stating,

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"and to end with something so paradoxical

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"that no one will believe it."

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And we'll see more of that later,

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but that's really here what we mean

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by models and complex systems,

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is to try and build something

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that's simple in its construction,

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and yet help us understand
the richness of the world.

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I'm not sure what I mean
here by this definition,

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rule-based phenomenological mechanisms.

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But really here what I
want to stress is that

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this course is about mechanistic models,

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mental representation,

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mathematical computational representation,

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but not necessarily like curve fitting.

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So there's a whole world
of statistical models

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and how to deal with that.

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Here we're more concerned
about the models themselves,

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and we're gonna do a little
bit of model fitting,

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model selection way later in the class.

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But here it's more about the construction,

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and the key word here is mechanisms,

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are models that try to help us

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understand what drives a system
is gonna be the key part,

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it's about qualitative
behavior and outcomes,

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which is what I mean by Phenomenology

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in this way of definition.

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And one thing we like to say

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at the complex systems center here

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is that data science and modeling

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are sort of the microscope
and the lab benches

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for this growing field of
complexity science, right?

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So to drive biology, for example,

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you need to be able to
observe biology in the wild

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maybe with a microscope in all its glory,

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cells fighting each other,

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but you also need to be
able to do experiments

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in a controlled setting on lab benches.

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And data science is

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how we observe the world
in complexity science,

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and modeling is sort of
how we do experiments.

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So the models becomes in
silico or silicone laboratories

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where we can run our own control settings

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and try to figure out under what condition

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something interesting happens.

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If you're more of a physicist,

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maybe you instead of a microscope,

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you can think of a telescope,

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data science is how we observe deep space.

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And then modeling would be

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something like our particle
accelerator, right?

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But still something more controlled

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where we can run experiments in our head,

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or on our computer, or with pen and paper.

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But that's the role of
modeling is to allow us

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to do these experiments.

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And before I move on to complex systems,

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I just wanna say that
modeling in general for me

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was sort of a real revelation

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because it's this deeply romantic tool

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because it allows you to do
science wherever you want it.

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You can be by a fire on the
beach of Lake Champlain,

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or you can be walking down
a railroad track at night.

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An idea comes into your head,

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you're curious about the system.

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You can start thinking

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once you've trained yourself with modeling

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about what are the key
parts of that system,

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what are the key mechanisms,

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and start running experiment in your head.

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And one of the reason I say
that this is a romantic tool

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is because once you master it,

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it allows you to follow your heart

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and follow your curiosity,

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and tackle any questions
that you think is deep,

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and important, and follow your curiosity

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throughout different fields.

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So it really brings scientists together

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and gives us a common language.

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And the idea of common
language is also at the core

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of what we call complex systems.

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So the classic definition goes as follows.

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Complex systems can
sometimes behave in ways

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that are entirely unpredictable.

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The human brain, for
example, might be described

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in terms of cellular functions

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and neurochemical interactions,

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but that description does not
explain human consciousness,

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a capacity that far exceeds
simple neural functions.

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Consciousness is an emergent property.

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In other words, something
that's more than just

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-the sum of its parts.
-Exac.

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The whole is more than
the sum of its parts.

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If you're in this class, chances are

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you've heard this sentence already,

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that's the classic definition
of a complex systems.

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I really like the way this is
illustrated by Peter Dodds,

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in this website or online textbook

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almost called "Complexity Explained."

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So there's the address in the
bottom left of the screen,

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and I invite you all to go check it out.

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Peter, the director of our center,

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has this great quote on there,

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"There's no love in a carbon atom,

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"no hurricane in a water molecule,

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"no financial collapse in a dollar bill."

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And really, basically in
all of these sentence,

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love, hurricane, and financial collapse

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would be what Jordi described
as emergent property,

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and it's this idea that
you can't study the whole

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by only studying individual
parts of the system.

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Murray Gell-Mann, one of the founders

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of the Santa Fe Institute

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and of complexity science
as we know it today

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originally proposed that
this area of research

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should be called PLECTICS.

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and PLECTICS meaning woven,
interwoven, or interconnected,

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or more like unseparable.

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And I really like this original proposal,

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the word itself is a
little pretentious, maybe.

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But what I do like about it,
it's not about the systems,

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it's about the philosophy with
which we tackle the systems.

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So when you start calling yourself

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a complex system scientist,

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you might get some pushback
from other scientists

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because it sounds like everyone else

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is studying simple systems,

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and that's just not the case, right?

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Political scientists,
evolutionary biologists,

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immunologists, ecologist,
most fields of science

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are studying complex systems.

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So what do we mean when we use that word?

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Is that we embrace the fact
that all of these fields,

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all of these systems that we care about

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actually interconnected,
and you can't separate them,

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they're Plectics, interwoven.

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So then it's more about the philosophy

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with which you tackle these systems,

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and then it's about signaling

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that you're looking for a common language.

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And modeling is one of
these common languages,

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and using complex systems is
a common language to do that.

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So that's what we're gonna be trying to do

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through modeling here,

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but often through data science as well,

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is how different fields can come together

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to do transdisciplinary research.

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So just to like sum that
up very briefly, right?

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When I say modeling here,
I just mean representing,

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it's not about fitting a line or forecast,

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doesn't have to be mathematical,

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sometimes it's just gonna
be a cartoon putting,

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you know, things in boxes,

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sometimes it's just gonna
be a mental representation,

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it's about representing.

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By complex we mean inseparable,

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things that are
interwoven, interconnected.

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And by systems we just mean wholes, right?

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We just mean that, we have
a big picture perspective

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of whatever it is that we care about.

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And that's broad, but that's
what this course is about.

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So it is a complex business

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that we're trying to tackle here.

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It is one of our other courses,

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I invite you to look at, you know,

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principles of complex systems,
our data science courses

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if you want to get a better picture

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of the different set of tools

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that define this common
language of complexity science.