Hi. It's Mr. Andersen and this is thinking and causation level seven, scale mechanisms
and complex systems. If you haven't watched the video on mechanisms you should definitely do
that. But what we're going to be dealing with are not simple systems but complex systems,
systems like climate or the human brain or a cell. Complex systems, we're starting to discover,
are actually explained a lot of the time by real simple mechanisms or scale mechanisms. And so
this video is about how do we get complexity out of these scale mechanisms. What is a mechanism?
Remember it's the series of events or actions that lead from a cause to an effect. So we'll put this
up here to represent that idea of mechanism. But I've also included the idea of a scale. So these
big massive complex things can oftentimes be described by simple, very simple, mechanisms or
rules that govern that complex system. So we're going to kind of work between these two. By the
time you've watched this video you should be able to identify the simple rules or scale mechanisms
in something like a fractal, so Sierpinski's triangle is an example of that or even water
as a universal solvent. But I'm going to start with one of the first complex systems that was
modeled and this is called Conway's Game of Life. So let me put it out and we'll take a look at it.
So Conway's Game of Life has been described as a zero player game. What you do is you fill in
these cells either as alive or not. So we could say this one's alive and then you just hit play.
Nothing happens. So that's not very exciting. I could put two cells alive
and nothing happens. But if I put three cells alive
then we get what's called an oscillator. So we get start to get some complexity. It's being run by
just these simple rules. But now let me just add one more thing. So if I add one more thing then we
get massive complexity coming out of that. So let me clear this off and let's describe the system.
So the system we're trying to figure out is just this simple shape. So it's got these four squares
that are on in Conway's Game of Life. We could take a lot a lot of time to just watch this and
see what happens and try to figure out what's going on, but that would take too long. So I'm
going to give you Conway's Game of Life. These are the rules and then I'm going to write over here
what is the scale mechanism, what are the basic rules and then we'll play it.
So the rules are very simple. I'll include them below. But it's essentially if you have less
than two neighbors, so like if you have less than two neighbors around you that are alive,
then you're going to die. If you've got greater than three neighbors
then you would die. So it's almost overcrowding. And then if you have exactly three neighbors,
so if you have three neighbors like this, then this one would come alive. And that's
where we start to get that oscillation. But let me work through how these simple
simple rules are manifested in the complex system that we're studying.
So if this is generation one, just like I have up here, then what is generation two gonna look like?
Well we almost have to think through each of these cells. So if you think of this cell right here,
so this cell right here, since it has three exact neighbors then it's going to be born.
So we could say there's going to be a new one here. If we look at this one right here,
that cell is going to have three neighbors. So we would say it's going to have three neighbors
exactly. And so I don't see any rules that's going to kill that so that one would be alive.
This one would be alive. If we look at the next one, so this cell right here has two neighbors and
so it's going to stay alive. And so what we get is a pattern that looks like this. So this would
be generation two. We could start to think about what's the next generation going to have. Since
this one right here has three neighbors then we could say that's going to be alive. So let me set
the next generation. So that would be alive. And let me work out all the rest of the generations.
So each of these generations is just following the rules, in the scale mechanism, the simple rules.
And so if we go forward we could go forward and we could kind of check each of our generations.
Or we could just let it play and you could see that more generations would show up.
Now this is a very simple example. We could load one of the ones that are on here. So this is the
example. It's called the acorn. So we could just start with this configuration in Conway's Game of
Life. And if we let it go what you get is, this is not a live, this is just a little game that's
following the simple rules over here, but you're getting a massive amount of complexity coming
out of that. And so what do we have? We have a complex system like we have in the game of life,
but it's being created by this little simple scale mechanism over on the right side.
So what we're going to do next is I'm going to set up another complex system and then
we're going to try to figure out what are the rules. Okay for the next example of a complex
system we're going to look at how a social network forms. So this is an app that shows
how simple social networks would form as new people make connections with other people.
This is just a simulation. So we could do the same thing over with increasing the number of
links between people. And you see we get a huge amount of complexity. If we look at
the internet it has a very similar pattern. And it's formed in a complex system in a similar way.
So what i'm going to do is set up a different system that's a little bit more manageable.
So what I'm going to do is I have these eight people. They're going to join this social
network over here. So we could put Alex here. We'll put Bria here and then Caleb here. And
what I want you to do is just watch me build this social network and figure out if you can figure
out what's the scale mechanism or what are the rules that are allowing me to build this network.
All right. Now let me write down how many connections each of these people have.
So we find that Bria has seven connections. Caleb only has one
connection. Diana has six connections. And everybody else has two connections.
So did you figure out what the scale mechanism was? Let me try it again.
So if we look at the numbers again, so Bria has seven connections. That sounds familiar.
Alex has one. Caleb has six and everybody else has two.
So you can see that we're starting to get a similar kind of a network forming,
but what are the scale mechanisms? If you would pause the video and try to figure out, based on
cause and effect, what are the scale mechanisms. You can either use a piece of paper or the
thinking slides that are below. But then unpause the video and let's see how our ideas compare.
So the rules that I got is if what you do when you join is you find the most popular person,
in this case it would be Bria and then you just form a connection with them. Then you form your
next connection with the second most popular and you form a connection. Now this is how social
networks form. You're more likely to connect to somebody who has more connections. There is a tie
breaker. If there was a tie between who is second most popular then you would use the spinner.
And so what we've got is just a scale mechanism, a simple set of cause and effect rules that lead to
this more complex system. So now that we've done that what I would encourage you to do is find one
of the thinking slides below. So you could start with something like a fractal and Sierpinski's
Triangle or even do a little chemistry and look for the simple rules that govern water
as a universal solvent. The key thing is to define the complex system. What are we trying to study?
And then identify the simple rules, the scale mechanism that leads to that complexity. So that's
scale mechanisms and complex systems, causation level seven. And I hope that was helpful.