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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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we talked about perspectives. Now,
perspectives are representations of

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

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

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

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

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

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

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

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

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

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us could do individually. Okay. Thanks.