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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â being recombined. Okay, thanks.

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