0:00

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â these things get recombined into interesting combinations. And those

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â different people look for different solutions to problems, that means

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

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

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

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

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

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

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

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

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

Â