Now that we've seen several examples of complex systems,

let's try to abstract some of the properties of the ones that we've seen.

The first property is one that I've mentioned several times.

Complex systems are composed of simple components,

often called agents.

That is, they're simple, relative to the system as a whole.

Another common property is that the components of the system

interact in nonlinear ways.

We'll talk about what the term "nonlinear" means in the next unit.

But very informally, it means that the components interact in such a way

that you can't just sum up all their activities

and thereby derive what the whole system is doing.

Colloquially, we might say that the whole

is more than the sum of the parts.

That's really what nonlinear means. We'll come back to that.

We've also seen that, in the systems we looked at,

the components were not controlled by any central executive.

There was no central controller for the ants, or the immune system,

or in our economy, or in any of the other samples I showed.

Instead, what we saw is that the system was able to organize itself

in a decentralized way. Finally,

a key notion that's important across all complex systems

is the concept of so-called emergent behavior.

The term "emergent" here refers to properties of the system

that can't be easily understood from individual components,

or small groups of individual components;

but rather are collective outcomes of the whole system,

and have to be understood at the system level

rather than at the individual level.

Let's give some examples of the kinds of emergent behaviors

I'm talking about.

The first one might be called hierarchical organization.

This refers to things like biological organisms,

which have hierarchical structure

ranging from cells to organs to body-wide systems,

to the whole body and even on to colonies and society.

How such hierarchies emerge in the first place,

and how the different levels interact,

are important questions for the field of complex systems.

In this course we'll see some examples of different kinds of hierarchies.

A different kind of emergent behavior is information processing;

that is, the system as a whole gaining information from the environment

and about its own state as well;

and using this information to make decisions, as a whole,

about what actions to take.

The components don't gain the information,

or make the decisions, individually.

This kind of information processing can only be done

on the level of the system as a whole.

We'll see how complex systems such as ant colonies,

the immune system, and so on

are able to collectively perceive and use information

for the fitness of the whole system.

Another example of emergent behavior

is what I'll call the complex dynamics of the system.

The word "dynamics" refers to how the system changes in its patterns

in space and in time.

For instance, we might see ants building up foraging trails.

So the whole colony takes on a kind of pattern

that changes in complex ways over time.

You might also think of stock prices,

which change in a complicated and unpredictable way.

Having complex dynamics is a property of

all the complex systems we're going to see.

Finally, in all of these systems we see evolution and learning.

All these systems, whether they be biological, social, or technological,

exhibit some kind of evolution in the Darwinian sense,

and this evolution often results in adaptation, or learning.

That is, systems improve themselves to survive

or do better in some environment.

This is something we'll focus on a lot in this course.