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  • What is your definition ofcomplex 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