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Hi. The previous sections we talked about
how. When solving problems, people have

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perspectives, representations of the
problem. And then they have heuristics,

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which are techniques they use to find
solutions, given their representation.

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We've been focusing on individual
problems, individual solutions. In this

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lecture, what I wanna do is I wanna talk
about recombination. So once I've got a

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solution, or even once I got a heuristic,
how I can recombine those to come up with

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even more solutions or more heuristics.
And we're gonna see the awesome power of

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recombination. Now remember, stepping way
back for a second, we've been trying to

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think about innovation in the previous
lecture. Where does innovation come from?

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What we're gonna is, recombination is
incredibly powerful and if we have a few

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solutions. Or futuristic. We can combine
those to create evermore and that may be

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the real driving force behind innovation
in the economy, is that when we come up

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with a solution we can then recombine it
with all sorts of other solutions and that

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leads to ever and ever more innovation.
Let me give an example to show how this

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works. Think about those. You know math
test or IQ test you might take online and

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they might give you a question like this:
one two three five blank thirteen; you've

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got to ask what number goes in there,
right? And the answer here is just eight.

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You can get this either one of two ways.
You can one plus two equals three, two

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plus three equals five, you know five plus
eight equals thirteen and so on, or you

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can subtract thirteen minus eight equals
five, eight minus five equals three and so

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on. Here's another one, one four blank
fifteen or sixteen, 25, 36, right? The

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answer here is nine and this is just
squares. They can also have very hard ones

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126 blank 1806. Now I don't put this on
here to make us not feel intelligent. I

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just want to show you that these can be
hard and I want to show the power of

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recombination. The first one, which was
very easy, required subtraction. The

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second one, which was harder, involved
squares. This one, which seems almost

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impossible, just requires combining those
two techniques. Let's think about it,

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what's two minus one? That's one, but
that's also one squared. What's six minus

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two? That's four, but that's also two
squared. What's. 42 minus six, that's 36,

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which is six squared. And, what's 1806
minus 42. That's 1764, which is 42

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squared. So the answer to this one, 42,
could be gotten by realizing. Just combine

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the first two tricks, squaring and
subtracting and that gives us the answer.

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With this idea that you can recombine is
really a driver of economic growth

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generally, and also a driver of science.
Cuz when you come with a new solution we

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can combine that solution. With other
solutions, and we get this geometric

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explosion in the number of possibilities.
To show you how the geometric explosion

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works, we want to use, at least economics,
just do a little bit of math. So let's

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start off with something simple and then
we'll do something more complicated. So

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we're gonna get ten possible, you know,
solutions or techniques I can use and I

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wanna just pick three of them. Well, we
can think of this as defining mathematical

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problem. We're gonna box the ten objects
and I just wanna pick three objects from

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those ten. How many ways to do it? Well
there's ten things I could pick first,

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nine things I could pick second and eight
things I could pick third. This actually,

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though, overstates the total number,
because if I pick object A, and then

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object B, and then, object C, that's the
same thing as picking C, and then B, and

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then A, or C and then A, and then B. So,
if I think about those three objects,

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there's three things I could pick first.
Two things I could have picked second, and

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one thing I could pick third. So these are
the different ways of arranging those

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three options. So I get ten times nine
times eight, divided by three times two

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times one, which is 120. So if I have ten
solutions, or, you know, ten technologies

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or ten heuristics or ten ideas, that gives
me 120 combinations of three. A 120

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doesn't sound very big. It's not, but the
point is we got way more than ten

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solutions and way more than ten juristics
and way more than ten scientific theories.

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You've gotta ton of them. So, let's blow
up the numbers a little bit. Let's suppose

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we have a deck of cards. Suppose I have 52
cards in a deck and I wanna just combine

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twenty of them. How big of a number do I
get then? Well, there's 52 cards I could

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pick first, 51 second and so on all the
way down to 33 cards I could pick for the

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twentieth. But now I've got those twenty
cards. I could have picked those same

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twenty cards in lots of different orders.
So there's any one of twenty could have

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been picked first, any one of nineteen
could have been picked second and so on.

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So my answer is going to be 52 times 51
times 50, all the way down to times 33

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divided by twenty times nineteen, times
eighteen, times so on. That's gonna be the

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number of ways to pick twenty cards from
52. Well how big is that? Huge. It's a 100

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and 25 trillion. So the thing about
combining technologies, combining

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heuristics, combining ideas, we get this
huge explosion. And every time anybody has

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an idea it can be combined with every
other idea and every other combination of

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ideas. And this may be a big reason why we
see so much growth. Why we've been able to

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sustain growth. So think back to our
economic growth model, right? Remember we

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had that like A times capital to the beta,
times labor to the one minus beta thing?

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And A was the technology parameter? Both,
and for sustained growth, we needed that A

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to get bigger, and bigger, and bigger?
Well, one thing that makes that a bigger,

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and bigger, and bigger, is when people
have ideas. >> They can be recombined with

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every other idea, which leads to more and
more growth. This idea of ideas building

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on ideas is the foundation of the theory
of economic growth due to Marvin

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[inaudible], used at Harvard, called
recombinant growth. And the idea is, ideas

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get generated all the time. You know, the
steam engine gets enveloped, developed.

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The gasoline engine gets developed. The
microprocessor gets developed. And all

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these things get recombined into
interesting combinations. And those

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combinations, in turn, get recombined;
right, to create ever more growth. So

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that's the basic idea behind recombinant
growth. So if you take something like the

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steam engine, right, here's a picture of
the early Newcomen atmosphere engine,

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which is really just a steam engine,
right? It's got all these things. It's got

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pumps, right? It's got a steam piston.
It's got a boiler, right? It's got a water

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reservoir. It's got this little, like,
Level thing like a teeter totter. These

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are solutions to previous problems. The
gasoline engine, right. So it's also got

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pistons and fuel injectors on and all
sorts of stuff. It consist of

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recombinations of all sorts of different
problems. So what we get are is this big

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machines, even here the computer on your
desk, right, it consist of solutions to

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all sorts of other problems. So, a lot of
our inventions. A recombinations of old

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solutions. Take your car. Your car consist
of an engine, wheels, steering mechanisms,

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now it consist of all sorts of electronic
stuff. So a car - even though it's a

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solution to a problem - is comprised of a
whole bunch of solutions to other problems

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combined in interesting ways. So it's
these recombinations that can drive a lot

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of growth. When you think about all those
parts into the kind of steam engine, they

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weren't developed with a kind of steam
engine in mind. They were developed for

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other purposes. And this is an idea from
biology called exactation. Now the classic

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example of exactation, is the feather.
Birds developed feathers primarily to keep

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them warm. But eventually those same
feathers allowed them to fly. So

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expectation simply means this, you come up
with some innovation, some solution for

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one reason, but then it gets exacted, it
gets used in another context. So, Emily

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Dickinson famously said, hope is the thing
with feathers. It's a good thing to keep

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in mind. Right? Cause feathers are this
classic example of expectation. Hope,

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innovation, change is the thing with
feathers as well. It is our ability to

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take a solution for one problem and apply
it to something new. What do I mean? Take

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the laser. The laser was not [inaudible].
The kid with the laser, they didn't think,

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wow! We can now have laser printers, we
can have laser pointers. No, that wasn't

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what they were thinking at all. They just
came up with a laser. So once something's

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developed, it gets used for all sorts of
things that were never expected, through

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this power of recombination. Even
perspectives do. So, remember my sort of

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silly perspective on the candy bar,
domesticity perspective? Well, you might

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think, you know, that. Doesn't really make
a lot of sense. Domesticity doesn't make a

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lot of sense, as a perspective. It's a
use, it's sort of a useless perspective.

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But in fact, masticity might be a really
useful perspective for other problems. For

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example, if I'm coming up with pasta or
breakfast cereal, or something like that,

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there may be that sort of a sweet spot in
terms of masticity, so that could be a

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really good way of looking at those
problems. So even failed solutions. For

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one problem may work really well for
solutions to other problems. So, famous

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example here, right, is the post it note,
that the glue that's used in post it notes

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was originally sort of a failure. It was a
glue that didn't stick very well. But it

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turned out to be useful for other sorts of
problems, mainly making sticky notes. Now

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there's more to it than this though. So
it's not just the recombination of ideas

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cause for hundreds and thousands of year?s
people had ideas. And here's where we've

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got to sort of reach just one level
deeper. If you think about why we've had

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such sustained growth, how is it these
ideas have been able to be combined, we

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have to recognize there had to be some way
to communicate those ideas. So Joel Mokyr

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wrote a wonderful book called the Gifts of
Athena. In the Gifts of Athena he talks

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about how. The rise of things like modern
universities, printing press, and

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scientific communication allowed ideas to
be transferred from one location and one

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person to another. And so what really led
to this, you know, huge burst of activity,

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you know, sometimes called the
technological revolution, was the fact

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that we could now share those ideas and
then recombine them. Because, you know,

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like a tree, if an idea falls in a forest,
nobody hears it, and nothing happens to

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it. So where are we? Here's where we are.
Think about. Innovation. You think about

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problem solving, several things going on.
First is, you have to represent that

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problem some way. Second thing is you
gotta have someone looking for solutions

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to that problem. Different people
represent problems in different ways,

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different people look for different
solutions to problems, that means

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different people can help one another out
through that diversity. Second thing. Once

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somebody finds the solution to a problem,
once somebody comes up with some sort of

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product, or even comes up with a
representation, like a perspective or a

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heuristic, that can be recombined with all
the other ways of thinking and all the

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other solutions we have and lead to ever
more growth. So you wanna ask, where does

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innovation come from? It comes from
diversity, of perspectives and heuristics.

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And it comes from recombination of those
new ideas. And that's what allows for, you

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know, ever improving solutions to
problems. And ever improving new ideas,

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new products, new technologies, and new
policies. Thank you. [sound].