Hi. The previous lecture we talked about perspectives. How we represent problems. In this lecture we're gonna talk about heuristics; how you go about finding solutions to problems once you've represented in your perspective. So a heuristic is, it's a technique, a tool, it's a way in which you look for new solutions. So in a sense we've already talked about this. We've talked about those landscapes. What we're really talking about is heel climbing on those landscapes. They sort of assumed you're at some point and what you do is climb hills. So when I'd find things like a local optima, right? So here's a picture of this local optima. What I was implicitly assuming is that if I'm at some point here, that I can climb a hill and get to here. So the reason these are local optima is because if I. Tried to climb hills, I'd be stuck at any one of those points. Cuz any direction would be down. But hill climbing, [inaudible] just sort of climbing up a hill, is just one of many possible heuristics you could use. Now, heuristics are gonna be defined relative to the problem you're trying to solve. So, for example, one famous heuristic that's in a lot of books on how to innovate is called, do the opposite. What does do the opposite mean? It means, think of [inaudible] the existing solution is and do the exact opposite. So for example, think about how to set, when you go buy something. When you go buy something, somebody else tells you the price. What the opposite be? Do the opposite would be that you actually tell them the price. Well, a lot of companies have been starting to do exactly this. So a company like Priceline, you go to the hotels and you say to the airlines, here's how much I'd like to pay to stay at your hotel or to use your airline. It's the exact opposite. Or alternatively, you can think about firms producing products. We normally think that they want to beat, lower costs, they want their costs below that of the firm. Or you could do the opposite and say, I want my price to be higher, because I want to signal quality. So doing the opposite is a strategy that sometimes leads to really interesting innovations. That's a heuristic. And you can think of this in the context of problem solving generally. By this, there's some sort of solution that, that exists. I'm going to do the exact opposite. So if everybody makes, else makes grilled cheese sandwiches by putting the cheese in between the bread, then I'm going to do the opposite and actually put the cheese outside the bread. If you haven't tried that, it's actually pretty good. Here's another one. Big rocks first. Now Stephen Covey has written a bunch of books on what makes people successful, what rules do you follow to be successful. When you think of these books, like The seven Signs of Successful People, or, you know, almost any one of these self-help books. They're filled with heuristics. And one of those heuristics often is, big rocks first. What is big rocks first? It says, suppose that you have to do the following task. You've got a bucket here, and you've got a bunch of rocks that you got to put in that bucket, of various sizes. With the little rocks in first, what happens is that the buckets fills up the little rocks. But then when you pick the big rocks in, they don't all fit. They spill out the side. But if you put the big rocks in first, alright? So let's erase these, all these rocks. And let's start over. Three GAR bucket. I put the big rocks first, then I put the little ones in, oh, fill in the gaps here, and everything will work fine. So big rocks first, little rocks second, if you're filling a bucket. And Covey argues that this is something that something successful people know how to do. They put the big rocks in first. Now rocks, you know, it's not, it's not like most successful people spend a lot of time filling buckets with rocks. The idea here is. Big rocks represent the important things. So Cubby is saying if you want to be successful, deal with important things first. That's the sign of success. That's a rule, that's a heuristic, that successful people use. So what he's saying is, there's a lot of problems out there. If you follow this heuristic, you'll find better solutions, if you deal with big rocks first. Here's the rub though there's a famous theorem in computer science called the no free lunch theory, theorem proved by Wolfred and McCready. And in this theorem what they show is the following. If you take two heuristics that each tell you to search the same number of solutions, so by that I mean if we, if you had do the opposite versus random search, or do the opposite versus check the thing that's one bigger than your representation. So if they each tell you to search the same number of points, then if you look across all possible problems. Now again, all possible problems is going to mean that some of these problems are incredibly hard, and some are really easy. That no heuristic is any better than any other. So if you take a heuristic like big rocks first, that means that it's no better than the other heuristic across all problems. So does that mean that Covey's wrong? No, it doesn't mean that Covey's wrong cause [inaudible] theorem says, again, if you look, and here, they use the word algorithms that [inaudible] heuristics. But if you look across all problems. No heuristic is better than the other. What Covey's saying is, he spent a lot of time in management. And what he thinks is, the types of problems you see in management lend themselves to the big rock search first heuristic. The types of problems you face as a person are big rocks first kinda problems. And so therefore, big rocks first is a good algorithm to use, a good heuristic to use to find solutions to problems. Here's another way to think about the no free lunch thing. If you don't know anything about the problem. If you know something about the type of the problem, then no heuristic is really that much better than any other one. Or if you don't know if your perspective on the problem is [inaudible], you might as well just hill climb. Once, though, you've learned something about the problem, you might realize that, you know, this is a big rocks first kinda problem. But it could be the case that it's not a big rocks first kinda problem. So, for example, there are some things that are little rocks first kinda problems. Let me give you an example from my own life. I put in a fence around my yard, and a had to dig a whole bunch of holes. So if you're digging a hole in the ground like this. Alright, so here's the hole you're gonna dig, and there's big rocks in here, and little rocks in here. You actually wanna take the little rocks out first.'Cause if you don't take the little rocks out first, you can't get the big rocks out. So if you're filling a bucket with big rock first. If you're digging a hole with the little rocks first. So if you don't know anything about the problem, what the no free lunch theorem says is, that no heuristic is better than any other. If you know a lot about the problem, you can figure out, should I do big rocks? Or should I do little rocks? Now, we talk a lot in terms of metaphor. Let's actually take this to real problems. So let's see how these heuristics [inaudible] diverse heuristics is really useful in terms of finding solutions to problems. So let's suppose I got a representation of probably consistent two dimensions. So I've laid down all my possible solutions in this big grid. And these could be anything you want, so let's say, on this side you've got types of ice cream and on this side you got the number. Of chunks, many chocolate chips in it. And this is, let's say, the size of those chocolate chips. This is my representation of that problem. Now what I could do is I could think, what's my heuristic? Well my heuristic might be that I look to the north, south, east and west. So that's one heuristic. And these are actually forming nodes in about nine of my neighborhoods. And that would be one way that I could look for possible solutions. But that's not the only way. I could take these same pints of ice cream and you could have somebody else who says, well you know, that's sort of inside the box thinking, I'm gonna look to the north-east, north-west, south-east and south-west. And this is a different way, different heuristic, different way to look for solutions. If I have one person who looks like this. And another person who looks like that. And I combine them. Right? What do I get? I get that I look at more points. So diverse heuristics are really useful. If we have different ways of searching this base of possibilities because of the fact that we're actually gonna search more points. Let's combine all this for a second. What were perspectives? Perspectives were ways of representing the problem. Right? So, one perspective that looks like this. Another person may have a perspective that makes those same you know, problems, or the same set of solutions look like that. What is a heuristic? A heuristic is how we search. So one person might hill-climb. And so that person would get stuck. At these points, right? Of these two landscapes. Another person might not have [inaudible]. They might have some do the opposite role. Which means they sort of jump all the way to the opposite side of the space. Well, that might mean that they don't get stuck at this point because they jump all the way to here. And it might mean they don't get stuck at this point, because they jump all the way to there. So what we're going to see in the next lecture is how diverse perspectives plus diverse heuristics enable teams of people, groups of people to find better solutions to problems. So let's wrap this up. The previous lecture, we talked about perspectives. Now, perspectives are representations of problems. In this lecture, we talked about heuristics, which is how we search within our perspectives. And we learned this important theorem called the no free lunch theorem. That, unless we know something about the problem, no heuristic is better than any other. But if we do know something about the problem, then we might be able to come to a better heuristic. We've also seen how diverse heuristics. If given a problem, if I look in different directions than you look, that means we search for more points. What we're going to see next is how if we've got lots of people working on a problem, and we have lots of different perspectives and lots of different heuristics, then collectively we'll be able to do better than any one of us could do individually. Okay. Thanks.