Hi. Welcome back. In the previous lecture, we used replicator dynamics to develop

something called Fisher's Fundamental Theorem. And Fischer's Fundamental Theorem

says the more variation, the faster you can adapt. So that makes sense. It makes

sense to, to encourage variation, because you can adapt more quickly. But notice

this runs counter to something we learned early in the class, which was six sigma.

Remember the idea behind six sigma was, as you've got some landscape here, if you've

got a whole bunch of variation. Then these ones that are highly variant, like here

and here, are gonna be low fitness, low payoff, low value. So you'd like to reduce

variation. And if you can get rid of those and only have the ones at the top of the

peak then you're gonna do a lot better. So six sigma says reduce variation,

replicated IMX is increasing. And six sigma works. By the way, there's a

wonderful book recently written by Atul Gawande called The Checklist which showed

how in the medical profession by reducing variation, you can do a lot better. So it

got a lot of evidence, where it used just one graph in preventing central line

infections in intensive care. How when they introduced six sigma techniques, what

you saw is this massive reduction In the number of infections. So I am not

disputing in any way that sick signal works, nor am I disputing in any way that

fisher's fundamental theorem works. It's a fundamental theorem, and there's lots of

evidence from ecology and biology that in fact that does happen, more variation,

more adaptation. So both are true, yet we have this problem in that they're opposite

proverbs, right? You're never too old to learn, you can't teach an old dog new

tricks. Don't change forces in midstream. Variety is the spice of life, opposite

proverbs. The pen is mightier than the sword; actions speak louder, louder than

words, right? [laugh]. How do we make sense of these things when they

contradict? Well here is when models are useful and proverbs aren't. Our models

have assumptions. So what's going on in case of Fishers fundamental theorem and

what's going on in the case of the six signal. The way to think of this is to go

back to another thing we've learned - the no free lunch theorem, the no theorem, no

algorithm, no [inaudible], reduce creation, increase creation is going to

work in all settings. You want to understand. What settings one's gonna work

in, and what settings the other's gonna work in. So let's think about it for a

minute. You've got this landscape. And if you've got this landscape you gotta think

when would you wanna use six sigma, and when would you wanna use Fisher's

Fundamental Theorem. Well let's suppose this landscape is fixed. And you've spent

a lot of time and you've figured out here's the peak. Well if you've figured

out here's the peak, then what you'd like to do is you'd just like to hang out on

that peak. You'd like to go six sigma If the landscape stays fixed. Then you want

to use sig sigma. But suppose the landscape suddenly moves. Well if the

landscape moves and you're using sig sigma then you have no possibility of moving

them. There's nothing to select, there's no new ideas to choose from. So the

distinction between when you use Sig Sigma and when you use Fisher's Fundamental

Theorem comes down to the nature of the environment. Fisher's Fundamental Theorem

is about an issue like ecological environments, about dynamic learning

environments. Basically saying if the world is churning, if things are changing,

then you want more variation, If things are fixed, if they are in equilibrium then

you want to go full Sig Sigma. So let's think remember we talked about different

processes we could have. We could have ordered processes, we could have fixed

equilibrium processes, we could have random processes, we could have complex

processes. But another way to think of that is that you could sort of think of

equilibrium processes being a process that's stable; it's got a fixed landscape.

You can think of a complex, or periodic or a random process as being. More like an

adaptive landsca pe, like a dancing landscape, and what you get in those sorts

of worlds, you want more variation. In equilibrium world, you want to go six

signal. So what we learn is. If it's a fixed landscape problem, then you what

would like to reduce variation [laugh] and stay on top of that peak. So let?s think

about Atul Gawande's book The Checklist, what is he talking about. He's talking

about things like getting a plane off the ground. He's talking about things like

cleaning tubes that go into people's bodies. We've probably figured out how to

do that. Those problems are fixed and so you wanna reduce variation. You wanna

create checklist so nobody makes mistakes. What about, what are dancing landscapes

problems? Well, dancing landscapes problems are things in ecologies, species

are constantly evolving, ecosystems are constantly changing and it's in a way

adapt or die. The same is true in a lot of the business world. I think with your

marketing strategy. That's not a checklist because the thing is your marketing

strategies gotta change as consumer preferences change. The landscape is

advancing Or if you're thinking about product innovation. You can't have a

checklist. You've gotta constantly be changing your product. So some of what you

do is straight fixed landscape. Its job shops sort of work, And in those cases,

you wanna go six sigma. Some of what you do is part of a complex adaptive system:

things are constantly changing. In those cases you want to heed the advice of

Fisher's fundamental theorem which is that the rate at which you can adapt is

probably going to be somewhat proportional to the amount of variation you have so you

want to encourage new ideas so you can possibly learn from them. So what we've

learned is by having multiple models, we can then adjudicate which models can work

in which setting by looking at the assumptions of those models. If we just

have opposite proverbs, we're stuck with two contradictory statements. So one of

the huge advantages of becoming a many model thinker is that you can then look at

the assumptions of the model, What's the assumptions in Fischer's fundamental

theorem is that, that landscape that you're not at a peak. Cuz, you?re not at a

peak you want to move towards it. In the Sixth Sigma setting, they presumption is

that you?re at the peak and therefore you want to reduce variation. So this is, I

think a really nice example, Fishers Fundamental Theorem, and the contrast with

Sixth Sigma of seeing how thinking with models helps us make sense of the world.

All right, Thank you.