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Hi. The previous lecture we talked about perspectives. How we represent problems.

Â In this lecture we're gonna talk about heuristics; how you go about finding

Â solutions to problems once you've represented in your perspective. So a

Â heuristic is, it's a technique, a tool, it's a way in which you look for new

Â solutions. So in a sense we've already talked about this. We've talked about

Â those landscapes. What we're really talking about is heel climbing on those

Â landscapes. They sort of assumed you're at some point and what you do is climb hills.

Â So when I'd find things like a local optima, right? So here's a picture of this

Â local optima. What I was implicitly assuming is that if I'm at some point

Â here, that I can climb a hill and get to here. So the reason these are local optima

Â is because if I. Tried to climb hills, I'd be stuck at any one of those points. Cuz

Â any direction would be down. But hill climbing, [inaudible] just sort of

Â climbing up a hill, is just one of many possible heuristics you could use. Now,

Â heuristics are gonna be defined relative to the problem you're trying to solve. So,

Â for example, one famous heuristic that's in a lot of books on how to innovate is

Â called, do the opposite. What does do the opposite mean? It means, think of

Â [inaudible] the existing solution is and do the exact opposite. So for example,

Â think about how to set, when you go buy something. When you go buy something,

Â somebody else tells you the price. What the opposite be? Do the opposite would be

Â that you actually tell them the price. Well, a lot of companies have been

Â starting to do exactly this. So a company like Priceline, you go to the hotels and

Â you say to the airlines, here's how much I'd like to pay to stay at your hotel or

Â to use your airline. It's the exact opposite. Or alternatively, you can think

Â about firms producing products. We normally think that they want to beat,

Â lower costs, they want their costs below that of the firm. Or you could do the

Â opposite and say, I want my price to be higher, because I want to signal quality.

Â So doing the opposite is a strategy that sometimes leads to really interesting

Â innovations. That's a heuristic. And you can think of this in the context of

Â problem solving generally. By this, there's some sort of solution that, that

Â exists. I'm going to do the exact opposite. So if everybody makes, else

Â makes grilled cheese sandwiches by putting the cheese in between the bread, then I'm

Â going to do the opposite and actually put the cheese outside the bread. If you

Â haven't tried that, it's actually pretty good. Here's another one. Big rocks first.

Â Now Stephen Covey has written a bunch of books on what makes people successful,

Â what rules do you follow to be successful. When you think of these books, like The

Â seven Signs of Successful People, or, you know, almost any one of these self-help

Â books. They're filled with heuristics. And one of those heuristics often is, big

Â rocks first. What is big rocks first? It says, suppose that you have to do the

Â following task. You've got a bucket here, and you've got a bunch of rocks that you

Â got to put in that bucket, of various sizes. With the little rocks in first,

Â what happens is that the buckets fills up the little rocks. But then when you pick

Â the big rocks in, they don't all fit. They spill out the side. But if you put the big

Â rocks in first, alright? So let's erase these, all these rocks. And let's start

Â over. Three GAR bucket. I put the big rocks first, then I put the little ones

Â in, oh, fill in the gaps here, and everything will work fine. So big rocks

Â first, little rocks second, if you're filling a bucket. And Covey argues that

Â this is something that something successful people know how to do. They put

Â the big rocks in first. Now rocks, you know, it's not, it's not like most

Â successful people spend a lot of time filling buckets with rocks. The idea here

Â is. Big rocks represent the important things. So Cubby is saying if you want to

Â be successful, deal with important things first. That's the sign of success. That's

Â a rule, that's a heuristic, that successful people use. So what he's saying

Â is, there's a lot of problems out there. If you follow this heuristic, you'll find

Â better solutions, if you deal with big rocks first. Here's the rub though there's

Â a famous theorem in computer science called the no free lunch theory, theorem

Â proved by Wolfred and McCready. And in this theorem what they show is the

Â following. If you take two heuristics that each tell you to search the same number of

Â solutions, so by that I mean if we, if you had do the opposite versus random search,

Â or do the opposite versus check the thing that's one bigger than your

Â representation. So if they each tell you to search the same number of points, then

Â if you look across all possible problems. Now again, all possible problems is going

Â to mean that some of these problems are incredibly hard, and some are really easy.

Â That no heuristic is any better than any other. So if you take a heuristic like big

Â rocks first, that means that it's no better than the other heuristic across all

Â problems. So does that mean that Covey's wrong? No, it doesn't mean that Covey's

Â wrong cause [inaudible] theorem says, again, if you look, and here, they use the

Â word algorithms that [inaudible] heuristics. But if you look across all

Â problems. No heuristic is better than the other. What Covey's saying is, he spent a

Â lot of time in management. And what he thinks is, the types of problems you see

Â in management lend themselves to the big rock search first heuristic. The types of

Â problems you face as a person are big rocks first kinda problems. And so

Â therefore, big rocks first is a good algorithm to use, a good heuristic to use

Â to find solutions to problems. Here's another way to think about the no free

Â lunch thing. If you don't know anything about the problem. If you know something

Â about the type of the problem, then no heuristic is really that much better than

Â any other one. Or if you don't know if your perspective on the problem is

Â [inaudible], you might as well just hill climb. Once, though, you've learned

Â something about the problem, you might realize that, you know, this is a big

Â rocks first kinda problem. But it could be the case that it's not a big rocks first

Â kinda problem. So, for example, there are some things that are little rocks first

Â kinda problems. Let me give you an example from my own life. I put in a fence around

Â my yard, and a had to dig a whole bunch of holes. So if you're digging a hole in the

Â ground like this. Alright, so here's the hole you're gonna dig, and there's big

Â rocks in here, and little rocks in here. You actually wanna take the little rocks

Â out first.'Cause if you don't take the little rocks out first, you can't get the

Â big rocks out. So if you're filling a bucket with big rock first. If you're

Â digging a hole with the little rocks first. So if you don't know anything about

Â the problem, what the no free lunch theorem says is, that no heuristic is

Â better than any other. If you know a lot about the problem, you can figure out,

Â should I do big rocks? Or should I do little rocks? Now, we talk a lot in terms

Â of metaphor. Let's actually take this to real problems. So let's see how these

Â heuristics [inaudible] diverse heuristics is really useful in terms of finding

Â solutions to problems. So let's suppose I got a representation of probably

Â consistent two dimensions. So I've laid down all my possible solutions in this big

Â grid. And these could be anything you want, so let's say, on this side you've

Â got types of ice cream and on this side you got the number. Of chunks, many

Â chocolate chips in it. And this is, let's say, the size of those chocolate chips.

Â This is my representation of that problem. Now what I could do is I could think,

Â what's my heuristic? Well my heuristic might be that I look to the north, south,

Â east and west. So that's one heuristic. And these are actually forming nodes in

Â about nine of my neighborhoods. And that would be one way that I could look for

Â possible solutions. But that's not the only way. I could take these same pints of

Â ice cream and you could have somebody else who says, well you know, that's sort of

Â inside the box thinking, I'm gonna look to the north-east, north-west, south-east and

Â south-west. And this is a different way, different heuristic, different way to look

Â for solutions. If I have one person who looks like this. And another person who

Â looks like that. And I combine them. Right? What do I get? I get that I look at

Â more points. So diverse heuristics are really useful. If we have different ways

Â of searching this base of possibilities because of the fact that we're actually

Â gonna search more points. Let's combine all this for a second. What were

Â perspectives? Perspectives were ways of representing the problem. Right? So, one

Â perspective that looks like this. Another person may have a perspective that makes

Â those same you know, problems, or the same set of solutions look like that. What is a

Â heuristic? A heuristic is how we search. So one person might hill-climb. And so

Â that person would get stuck. At these points, right? Of these two landscapes.

Â Another person might not have [inaudible]. They might have some do the opposite role.

Â Which means they sort of jump all the way to the opposite side of the space. Well,

Â that might mean that they don't get stuck at this point because they jump all the

Â way to here. And it might mean they don't get stuck at this point, because they jump

Â all the way to there. So what we're going to see in the next lecture is how diverse

Â perspectives plus diverse heuristics enable teams of people, groups of people

Â to find better solutions to problems. So let's wrap this up. The previous lecture,

Â we talked about perspectives. Now, perspectives are representations of

Â problems. In this lecture, we talked about heuristics, which is how we search within

Â our perspectives. And we learned this important theorem called the no free lunch

Â theorem. That, unless we know something about the problem, no heuristic is better

Â than any other. But if we do know something about the problem, then we might

Â be able to come to a better heuristic. We've also seen how diverse heuristics. If

Â given a problem, if I look in different directions than you look, that means we

Â search for more points. What we're going to see next is how if we've got lots of

Â people working on a problem, and we have lots of different perspectives and lots of

Â different heuristics, then collectively we'll be able to do better than any one of

Â us could do individually. Okay. Thanks.

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