22. Emergence and Complexity

Stanford University.

OK, so we will pick up on the one topic that was not

covered from two days ago because you guys needed

to go play around with these cellular automata first.

So I will work with the assumption

that everybody here has now spent

48 hours playing with those.

But presumably because of the sleep deprivation,

you've forgotten much of it by now.

So we will cover some of it.

OK, back to that issue of fractals and butterfly

effects and that whole business that, by the time

you look at chaotic systems that are

determinist but aperiodical, that, when

they seem to be lines crossing, getting back

into the same spot, look closely enough

and they're not going to actually be touching.

And the centerpiece of why that matters

was that whole business of, these

both appear to be the same.

And take them out a decimal place

and they're actually different.

And a gazillion decimal places out.

And the entire sort of rationale for thinking in that way

is the notion that a very small difference here

can make a difference one step to the left.

And a million decimal places out there, a small difference,

will make a difference one before that.

In a scale-free way, a fractal, this here, a difference here,

a million decimal places out is just as likely

to have consequences for one over as this one for one

over fractal, scale free, all of that.

But the critical thing that is encompassed in this

is the notion that tiny little differences

can have consequences that magnify and magnify

and amplify into a butterfly effect.

So cellular automata are a great way

of seeing this principle along with a number of others that

are relevant to all of this.