All right, hi class,
we're back at modeling complex systems.
In this video, what I'd really like to do
is go over the three key words of our title.
So models, complex systems, what did these words even mean?
I'm sure some of you signed up for this course
because you have to, it's a mandatory or core course
for our complex systems program.
I'm sure some of you maybe just joined
because the description was interesting,
but that doesn't mean that you have an idea
of what we're gonna do here.
So I want to clear up some common misconceptions
about the course, and also just talk
about what models and complex systems mean here.
So there's a classic quote from Albert Einstein,
and I'm sure a lot of you have already heard,
things should be made as simple as possible,
but not simpler.
And this is really one of the key insight
behind what we mean here by models,
is that we try to simplify the the world,
be it through just thinking about what's important,
or mathematical equations or computational programs.
The idea is just to simplify something
in order to better understand it, right?
So if I ask you at some point in this semester
to model an ant colony,
you could go and dig one in your backyard
and then bring, you know, one of these end colonies
in a glass box to class or you know,
for show and tell on video.
But that doesn't really help us
understand how ant colonies work.
Similarly, you know, you could take one ant
and look at it very closely,
but that wouldn't really help you understand
how colonies like come to be these complex structures?
How can ant colonies grow mushroom?
How can they discover things, and search for food?
It's really about their behavior as a whole.
So there has to be a sweet spot somewhere
between considering more than one ant,
and also not embracing like the complexity
and craziness of the real world.
So we're gonna try and use computational
and mathematical model as parables
or cartoons for what the world is
to help us understand the key ingredient.
There's another quote that I think better captures
what I mean by this,
and I'm stealing this juxtaposition
of two quotes from a book called
"The Computational Beauty of Nature" by Gary William Flake.
So the second quote is from Bertrand Russell,
the philosopher, and he says,
"The point of philosophy is to start with something
"so simple as not to seem worth stating,
"and to end with something so paradoxical
"that no one will believe it."
And we'll see more of that later,
but that's really here what we mean
by models and complex systems,
is to try and build something
that's simple in its construction,
and yet help us understand the richness of the world.
I'm not sure what I mean here by this definition,
rule-based phenomenological mechanisms.
But really here what I want to stress is that
this course is about mechanistic models,
mental representation,
mathematical computational representation,
but not necessarily like curve fitting.
So there's a whole world of statistical models
and how to deal with that.
Here we're more concerned about the models themselves,
and we're gonna do a little bit of model fitting,
model selection way later in the class.
But here it's more about the construction,
and the key word here is mechanisms,
are models that try to help us
understand what drives a system is gonna be the key part,
it's about qualitative behavior and outcomes,
which is what I mean by Phenomenology
in this way of definition.
And one thing we like to say
at the complex systems center here
is that data science and modeling
are sort of the microscope and the lab benches
for this growing field of complexity science, right?
So to drive biology, for example,
you need to be able to observe biology in the wild
maybe with a microscope in all its glory,
cells fighting each other,
but you also need to be able to do experiments
in a controlled setting on lab benches.
And data science is
how we observe the world in complexity science,
and modeling is sort of how we do experiments.
So the models becomes in silico or silicone laboratories
where we can run our own control settings
and try to figure out under what condition
something interesting happens.
If you're more of a physicist,
maybe you instead of a microscope,
you can think of a telescope,
data science is how we observe deep space.
And then modeling would be
something like our particle accelerator, right?
But still something more controlled
where we can run experiments in our head,
or on our computer, or with pen and paper.
But that's the role of modeling is to allow us
to do these experiments.
And before I move on to complex systems,
I just wanna say that modeling in general for me
was sort of a real revelation
because it's this deeply romantic tool
because it allows you to do science wherever you want it.
You can be by a fire on the beach of Lake Champlain,
or you can be walking down a railroad track at night.
An idea comes into your head,
you're curious about the system.
You can start thinking
once you've trained yourself with modeling
about what are the key parts of that system,
what are the key mechanisms,
and start running experiment in your head.
And one of the reason I say that this is a romantic tool
is because once you master it,
it allows you to follow your heart
and follow your curiosity,
and tackle any questions that you think is deep,
and important, and follow your curiosity
throughout different fields.
So it really brings scientists together
and gives us a common language.
And the idea of common language is also at the core
of what we call complex systems.
So the classic definition goes as follows.
Complex systems can sometimes behave in ways
that are entirely unpredictable.
The human brain, for example, might be described
in terms of cellular functions
and neurochemical interactions,
but that description does not explain human consciousness,
a capacity that far exceeds simple neural functions.
Consciousness is an emergent property.
In other words, something that's more than just
-the sum of its parts. -Exac.
The whole is more than the sum of its parts.
If you're in this class, chances are
you've heard this sentence already,
that's the classic definition of a complex systems.
I really like the way this is illustrated by Peter Dodds,
in this website or online textbook
almost called "Complexity Explained."
So there's the address in the bottom left of the screen,
and I invite you all to go check it out.
Peter, the director of our center,
has this great quote on there,
"There's no love in a carbon atom,
"no hurricane in a water molecule,
"no financial collapse in a dollar bill."
And really, basically in all of these sentence,
love, hurricane, and financial collapse
would be what Jordi described as emergent property,
and it's this idea that you can't study the whole
by only studying individual parts of the system.
Murray Gell-Mann, one of the founders
of the Santa Fe Institute
and of complexity science as we know it today
originally proposed that this area of research
should be called PLECTICS.
and PLECTICS meaning woven, interwoven, or interconnected,
or more like unseparable.
And I really like this original proposal,
the word itself is a little pretentious, maybe.
But what I do like about it, it's not about the systems,
it's about the philosophy with which we tackle the systems.
So when you start calling yourself
a complex system scientist,
you might get some pushback from other scientists
because it sounds like everyone else
is studying simple systems,
and that's just not the case, right?
Political scientists, evolutionary biologists,
immunologists, ecologist, most fields of science
are studying complex systems.
So what do we mean when we use that word?
Is that we embrace the fact that all of these fields,
all of these systems that we care about
actually interconnected, and you can't separate them,
they're Plectics, interwoven.
So then it's more about the philosophy
with which you tackle these systems,
and then it's about signaling
that you're looking for a common language.
And modeling is one of these common languages,
and using complex systems is a common language to do that.
So that's what we're gonna be trying to do
through modeling here,
but often through data science as well,
is how different fields can come together
to do transdisciplinary research.
So just to like sum that up very briefly, right?
When I say modeling here, I just mean representing,
it's not about fitting a line or forecast,
doesn't have to be mathematical,
sometimes it's just gonna be a cartoon putting,
you know, things in boxes,
sometimes it's just gonna be a mental representation,
it's about representing.
By complex we mean inseparable,
things that are interwoven, interconnected.
And by systems we just mean wholes, right?
We just mean that, we have a big picture perspective
of whatever it is that we care about.
And that's broad, but that's what this course is about.
So it is a complex business
that we're trying to tackle here.
It is one of our other courses,
I invite you to look at, you know,
principles of complex systems, our data science courses
if you want to get a better picture
of the different set of tools
that define this common language of complexity science.