Hi... Remember we were talking about problem solving. We talked about, when you

first solve a problem, what you do is come up with a perspective, a way of

representing the set of solutions. Then we talked about how you use heuristics to

search among those possible solutions, given your representation. And we've seen

how having lots of heuristics and diverse heuristics can help you find, look at more

points, and find, possibly find better solutions. What we wanna do in this

lecture, is combine those two ideas, perspectives plus heuristics, to show why

teams of people. Can often find solutions to problems that individuals can't. That

why teams are better. Now I say teams, I'm gonna use this in a very loose sense. I

don't necessarily mean, a team of people sitting in a room and brainstorming. That

sort of stuff. What I mean is, a collection of people, possibly you know,

working even over time. So even if it's something like your toaster on your

counter, you can think of that as being something that's been really consistently

and constantly improved upon by a team of people. So there's the person who first

invented the toaster. Then somebody improved it. Then somebody come up with

the crumb tray. Then somebody came up with the automatic shut off. And all sorts of

things, right? So a toaster consists of a whole bunch of improvements. And you can

think of that as being. That current solution we have is being something that

the team has come up with. So again, by team I don't necessarily mean a group all

working together and in some unit. You just need a collection of people. So how

does it work? Why are teams and why are groups of people better than individuals?

Well, let's go back and let's think about the, the candy bar example. Remember I had

one landscape, one perspective based on calories, and that had three local peaks,

right? And, well, let's represent those by A, B and C. And then I had another

landscape that was represented by masticity, and that had five peaks. And we

can call these, let's call these A, B, D, E and F. So, these are different than the

peaks for the caloric landscape. With the one exception. Notice for sure that A,

which is the best possible point, that has to be a point in the caloric landscape and

it's also gotta be a peak in the masticity landscape. And that's because it's the

best possible point. So it's the best possible point, it's gotta be a point in

every landscape. Now we can characterize these problem solvers. By their local

peaks, by their local optimum. So, the local optimum of the caloric landscape are

A, B, and C. The local optimum for the domesticity landscape are A, B, D, and F.

And we remember we said that the caloric landscape was a better landscape than the

masticity landscape. Because of the fact that it had fewer local optima. So one way

to figure out how good you are at solving a problem is how many local optima you

have given your perspective and your heuristic. Now here was something the

heuristic, right? Is just hill climbing. Let's go deeper. Cuz that's just a, that's

a fairly crude way of thinking about how good a problem solver is. We can actually

take into account, the average value of those peaks. So the piece where people get

stuck are A, B, C, D, E, and F. And we can assign a value to each of those. So

suppose the value of A is ten, B is eight, and so on. So A is the out local op, the A

is the global optimum, and some of these other peaks aren't so good. Well we can

usually can ask, what's the average value of a peak for the caloric problem solver?

So the problem solver who thinks in terms of the caloric perspective, then gets

stuck at A, B, and C. What's the average value? Well, A has a value of ten. B has a

value of eight. C has a value of six. And so, we're gonna give the abilities as the

average of those three peaks, which is eight. But if I look at the masticity

problem solver, they get stuck at, at A, B, D, E, and F. And those have values ten,

eight, six, two, and four. And the average of those is six. So when you think about

the ability of the masticity problem solver as being six. So not only did it

correct problems of our local optima. They had higher average values. This is another

reason why that person's a better problem solver. Let's think of them now, though,

as working as a team. I think, in the working as a team, the caloric problem

solver gets stuck at A, B, and C, the domesticity problem solver gets stuck at

A, B, D, E, and F. Let's suppose, first, [inaudible] problem solver works on the

problem first, and she gets stuck at B. She then passes the problem to the

[inaudible] problem solver. And the [inaudible] person says, well, you know

what? I can't help you, because B looks pretty good to me. Because B is also a

peak for him. Suppose instead, though, that the caloric problem solver gets stuck

at C. And she passes C on to the masticity problem solver. And now this masticity

person, C, if you notice, isn't anywhere in this list. C is [inaudible] optima.

That means that the masticity person can get from C to some other local optima. And

it's gotta be one that's better. Why does it have to be better? Because she's, this

person's hill climbing, if he's hill climbing, then he's got to be able to find

something that's better than C and that's going to be either A or B. So the

intersection of these local optima A and B are the only places where they can get

stuck. If, for example, the [inaudible] person went first and got stuck at E, then

the [inaudible] person could take E and get to someplace else, either A, B or C.

If she gets to A or B the masticity person is also stuck. If she gets to C, then the

masticity person can then in turn take it up to A or B so the only places that the

team can get stuck is A or B. If you make this form up called the intersection

property that the local optima for the team is the intersection of the local

optima for the individuals. So, if we look at the team, there's only two places the

team can get stuck, ten and A, and the average value there is nine. So, the

ability of the team is higher than the ability. Of either person. And the reason

why is because the team's local optima is the intersection of the local optima for

the individuals. So the reason why, then, we see over time products get better, the

reason why we see teams being really innovative, the reason why we see a lot of

science being done by teams of people is because the only place a team can get

stuck is where everybody on the team can get stuck. So this very simple model,

having perspectives and heuristics, can explain, why is it the case that teams are

so much better than individuals? And why, over time, we keep finding better and

better solutions to problems. It's not necessarily that we're getting smarter.

Now, it's true, we are coming up with new ways to represent problems. And we also

are coming up with all sorts of new heuristics all the time. We're developing

new ways to solve problems all the time. But another thing that's going on, is,

just because of the accumulation of so many different ways of looking at

problems, and so many different ways of trying to solve them, that we get the

intersection. Of all those peaks and that gives us better solutions. So here's the

big claim. The team can only get stuck at a solution that's a local optima for

everyone on the team. That means the team has to be better than the people in it. So

what we want, right, you want people with different local optima. You want people to

get stuck in different places. Well how do we get it? We don't. We've already looked

at this twice, right? We looked at it first perspective perspectives. So if you

coat it this way and I coat it this way, then we're going to get stuck in different

places. We also want people with different heuristics. If I look in this direction

and this direction, and you look in this direction and this direction, and we add

us together, we look in all four of those directions. So what we want, is we want

diverse perspectives, and we want diverse heuristics. And that diversity will give

us different local optima, and those different local optima will mean that we

take the intersections, and we end up with better points. That's sort of the big

idea. So if we take, again, let's play this out in more deals. And imagine we've

got these, just, here's this set of solutions. If one of us looks like this.

And one of us looks maybe two to the left. And one looks two down. And one looks to

the north, south, east and west. If we have all of these different, you know,

maybe one person looks two over this way, all these different heuristics looking at

the problem that means we're less likely to get stuck at the same point. Which

means the team is going to do better. Or, over time, society is going to do better

finding solutions to problems. This all seems really smooth and nice and great and

we've seen, teams are better, we see the value of diverse perspective, we see the

value of diverse heuristics. But what's missing? Cuz this seems highly stylized.

There's two things that I've left out. First one is [sound] right, we can write

this down as communication. I've assumed that when you've got a team solving a

problem that they can communicate their solutions to one another right away. Now

that's not always the case. There's a lot of misunderstandings going on and we might

not listen. I might just say, no I'm not listening. I'm not listening, right? And

no matter what you say we don't find a better solution. And think of something

like the toaster though, it's weird, we can communicate through the toaster. If I

come up with a better toaster and I make it, then you can look at my solution and

know what I've done and then you can add the crumb tray. So think about making an

artifact, the artifact itself, the artifact is the solution. That gets

communicated right away, but generally speaking communication can be a problem.

The other thing I've assumed is that. There is the possibilities that an error.

In interpreting the value of a solution. So, I'm assuming if somebody proposes a

solution and its better, we instantly know it. It's as if there's some sort of oracle

we can go to and say, oh yip, that's a better solution. That may not always be

the case. So it could be that I could do something really interesting and people

just think no, it's a bad idea. They make an error in terms of whether or not its

interesting thing or it could be that I propose something that's worse, and people

think oh that's a great idea and then we actually look and it's not a good idea. So

I've assumed there no errors in determining the value of the solution, and

when somebody proposes this solution, you know exactly what it's worth. That's not

always going to be the case. So it's won't always be true that there's perfect

communication in this perfect evaluation. So, in a Ricksher model, we could include

communication error. And that's going to hurt teams. And we can also include just

errant evaluation. That's also going to hurt teams. Even so, right, this power,

this model has shown us something fairly powerful, which is that diverse

representations of problems in diverse ways of coming up with solutions can make

teams of people better able at coming up with solutions than individuals. And it

also sort of told us where innovation is coming from, right? Innovation is coming

from different ways of seeing problems, and different ways of finding solutions.

There's a lot going on, right? And now, I've got this model of problem solving,

and when you think about people finding solutions to particular problems. Now we

want to step back a bit in the next lecture when I think about, what about

bigger things like designing a house, designing a car, designing a railway

system, designing a city, the bigger problems. Well, often times those bigger

problems, the solutions, you would think of a, like making a computer. The computer

may consist of the solutions to a whole bunch of sub-problems. So where we want to

go next is you want to talk about how we combine solutions to come up with new

solutions. And we'll see how that can even be used as an argument to where economic,

where economic growth comes from. It actually comes from individual solutions

being recombined. Okay, thanks.