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.