What is your definition of “complex systems”?
So my one sentence definition is
systems that don’t yield to
compact forms of representation
or description, and I should explain that.
In the systems that physicists study,
you can often write down on one page
a few very beautiful, elegant equations, like Newton’s
laws for the conservation of momentum, or the Maxwell field
equations for electromagnetism, and so forth.
And you can explain a huge amount of empirical data
when it comes to the genome, or the brain, or properties
of society or literary history, as far as we know,
there are no such beautiful, elegant, compact descriptions.
And that, for me, is evidence
that we’re dealing with a complex system.
Now, why is that? So, the reason why I think it’s difficult
to do is because those are systems that encode long histories.
One of the characteristics, for me,
of a complex system, is that it has found a means,
or a mechanism, for extracting from its environment
some information, in order to use it to behave
adaptively. To predict and control.
And consequently, it needs to be described using models
that have a slightly different flavor to the ones that
we have been traditionally familiar with in the mathematical natural sciences.
And typically, those models will be computation.
So, I’m going to ask you
the same question that I’m asking everybody, which is
what is your definition of a complex system. Oh no!
That’s what everybody says.
In theoretical computer science, we don’t say that
systems are complex or simple, per se,
we more typically say that questions are
complex if those questions require a lot of computational
resources to solve. A lot of time, a lot of memory,
a lot of communication between people.
Some limited resource.
Different questions might have different levels of computational complexity. So for instance,
if what you want to know is what will the system
look like t time steps from now,
you can answer that question with about t time
by simulating it forward, but an interesting
question might be, well, maybe there is no algorithm that works much
faster than that. Maybe there’s no way to leapfrog over
the history. Maybe like a chaotic dynamical system that
has no closed-form solution, maybe there is no shortcut to doing
that laborious step-by-step simulation.
So, for me, I find it helpful to, rather than
saying, is this system simple or complex? I mean, I don’t deny
that we often have clear ideas about that, but I find it helpful
to change the question a little bit to, give me
a yes or a no question you want to answer about this sytem,
or a quantity you want to compute about this system, and then let’s talk
about how hard it is computationally to answer that question
or compute that quantity.
Well, it’s a complicated
concept. I didn’t say complex, just kind of
complicated.
So, this actually ties in with a discussion I’m sure we’ll
have on information, so I have a rather precise notion
of what I mean when I refer to a natural or artificial
system as complex, and what I mean in particular is that it has a very sophisticated
internal causal architecture that stores and processes information.
So, the technical things that we’ll talk about shortly have to do
with how we measure stored information and the amount of structure.
So, information in many ways stands in for trying to describe
how complex a complex system is, and various
kinds of information processing and storage can be associated with how a system is organized.
So it’s a key concept, certainly
Shannon’s original notion of information as degree of surprise,
degree of unpredictability in a system, or how random a system is
needs to be augmented. So that’s certainly the focus of a lot
of my work is trying to delineate that there are many different kinds of information,
not just Shannonian information.
So, my definition of complex systems
is a system that has
interactions. It has nonlinear elements in it.
I tend to work on high dimensional systems not low dimensional systems.
And I like to use the methods of statistical mechanics
from physics to understand problems in these systems.
Most of the time, the interesting features in these systems have
scaling properties, that is to say they have power laws
or fractal objects in them, embedded in them someplace,
either in the actual physical arrangement of them
or in terms of the statistics that you see.
So my basic definition is that a complex system consists of a bunch of entities
that may not start out diverse, but end up being diverse. They are connected
in some way, usually through some sort of network structure or some spatial
structure, and they get information and signals through that network
or local structure, but they also sometimes get some global signals or global information,
which could be prices in a market, or temperature in a system, so that
in addition to be sort of diverse and interconnected, they are also interdependent, so the
actions of one agent in the system will sort of
influence or have implications for another agent. So in the context
of a social system, like in economics, I’ll say that if I go in and buy bread in the grocery store
whether I buy whole wheat bread or white bread, you really don’t
care. It’s not interdependent. There’s no real strong interdependence, other than to
the prices. But if I decide to drive my car on the road
or drive my car really fast down the road, those sort of things, then that actually can affect you
in a big way. So they’re interdependent. And the last thing
is in addition to having these
interdependent behaviors and networks and diverse agents, that the agents adapt
and respond to the environment which that they’re in. So it’s not just a case of them following
simple rules, but that they sort of adapt. Now this last part
gets a little bit tricky philosophically, because adaptation is really just a higher-order
rule, so you can have a first-level rule and then a meta rule
and so, you could say that they are rule based, but they are sort of meta rule based,
that they allow for behavior that
can respond to the signals that they are getting both globally and locally. Now the last thing
will mention is another sort of paradox in the definition of complex adaptive systems
is that a system like that can be complex, but it need not be.
So a system can have those components to it, but it can end up producing
an equilibrium. Especially if I look at an economic system
some parts of economic systems really equilibriate quite well, but then others
end up being really complex. So if you look at oil consumption
over time at the global level, that’s pretty predictable, it’s a pretty stable pattern
but if I look at oil prices over time, that’s complex, because
there’s much more interdependencies and all those things come into play.
So John Holland and I sometimes joke that we should call them systems capable of producing
complexity. That doesn’t sound as remarkable.
Okay, well, that is a question that people have debated a lot.
I guess
most people would agree that a complex system is a system of many interacting parts
where the
system is more than just the sum of its parts.
It shows emergent behaviors which are not just the sum of the individual behaviors
of the parts. Other people add
extra elements to that, but that’s probably what my definition is
pretty much. It’s a system of interacting parts which shows emergent behaviors.
Okay, that’s pretty simple. Sort of unpacking that
takes a little more time.
So I’m going to give you a definition of complex systems, but
I will remind you that many important concepts
like virtue and life are very hard to define
and I think complex systems are somewhat in that category.
Nonetheless, the kinds of systems that I call complex
have many interacting active components
and the interactions between the components have
nontrivial or nonlinear interactions
and that leads to the system having unpredictable behavior. You may have
heard those things before. But importantly,
all of the components are either learning or
modifying their behavior in some way while the system
is behaving.
And so that leads to all kinds of interesting dynamics.
So that’s roughly what I think of when I think
of a complex system. So do you think that adaptation is
essential for complex behavior?
Well, it’s essential for the kind of complex behavior that I’m most interested in
Okay, fair enough.
I think my definition is probably like a lot of other people’s
definition in that a complex system is something
with a lot of interacting parts where something
about the way those parts behave when they interact is qualitatively different
than the way they behave if you look at them individually. So
it’s something with emergent phenomena. And I think we can then quibble
about what exactly all those words really mean
so for example I might mean something a little bit different than some other people, but I
don’t think I have anything particularly unique in my definition.
Complex systems tend to be things that
are different from simpler, usually
physical, systems in that they tend to be heterogenous, they tend to
be made up of parts that are the not the same kind of parts. For example,
people and firms in a city are all different. They are not all the same.
They tend to be, many of them are open ended, although not all of them.
So a city or an ecosystem can keep on evolving
Often the thing that makes them hardest to study in terms of making predictions
about them is that they also typically have chains of causation
mechanisms that make things happen that are circular, so there are feedbacks
both positive and negative that make their evolution
at least more difficult to study than in simpler physical
systems or engineered systems, where we can deal with them in regimes where they’re simpler
and linear, and they can respond in ways that we can at least hope to characterize.
So those things are still an operating definition of what a complex system
might be. But they go a long way to say what a complex system typically
is, from ecosystems to organisms to cities to brains.
A complex system is one
that contains enormous numbers of actors or agents
that are interacting in usually in a nonlinear kind of fashion
form which all kinds of
multi-level behavior evolves from
So there are these emergent phenomena, but also
I think a critical part of a complex system that distinguishes it
from what we might call a simple system, like the motion of the planets around the sun,
is that on the one hand, you can't
encapsulate the dynamics in just a few
simple equations and that is intimately related
to the fact that these systems are evolving
and are adaptable. And I think that this is one of the most
crucial differences between that and traditional systems that I
have dealt with in most of my career under the guise of physics.