Hi. The previous sections we talked about how. When solving problems, people have perspectives, representations of the problem. And then they have heuristics, which are techniques they use to find solutions, given their representation. We've been focusing on individual problems, individual solutions. In this lecture, what I wanna do is I wanna talk about recombination. So once I've got a solution, or even once I got a heuristic, how I can recombine those to come up with even more solutions or more heuristics. And we're gonna see the awesome power of recombination. Now remember, stepping way back for a second, we've been trying to think about innovation in the previous lecture. Where does innovation come from? What we're gonna is, recombination is incredibly powerful and if we have a few solutions. Or futuristic. We can combine those to create evermore and that may be the real driving force behind innovation in the economy, is that when we come up with a solution we can then recombine it with all sorts of other solutions and that leads to ever and ever more innovation. Let me give an example to show how this works. Think about those. You know math test or IQ test you might take online and they might give you a question like this: one two three five blank thirteen; you've got to ask what number goes in there, right? And the answer here is just eight. You can get this either one of two ways. You can one plus two equals three, two plus three equals five, you know five plus eight equals thirteen and so on, or you can subtract thirteen minus eight equals five, eight minus five equals three and so on. Here's another one, one four blank fifteen or sixteen, 25, 36, right? The answer here is nine and this is just squares. They can also have very hard ones 126 blank 1806. Now I don't put this on here to make us not feel intelligent. I just want to show you that these can be hard and I want to show the power of recombination. The first one, which was very easy, required subtraction. The second one, which was harder, involved squares. This one, which seems almost impossible, just requires combining those two techniques. Let's think about it, what's two minus one? That's one, but that's also one squared. What's six minus two? That's four, but that's also two squared. What's. 42 minus six, that's 36, which is six squared. And, what's 1806 minus 42. That's 1764, which is 42 squared. So the answer to this one, 42, could be gotten by realizing. Just combine the first two tricks, squaring and subtracting and that gives us the answer. With this idea that you can recombine is really a driver of economic growth generally, and also a driver of science. Cuz when you come with a new solution we can combine that solution. With other solutions, and we get this geometric explosion in the number of possibilities. To show you how the geometric explosion works, we want to use, at least economics, just do a little bit of math. So let's start off with something simple and then we'll do something more complicated. So we're gonna get ten possible, you know, solutions or techniques I can use and I wanna just pick three of them. Well, we can think of this as defining mathematical problem. We're gonna box the ten objects and I just wanna pick three objects from those ten. How many ways to do it? Well there's ten things I could pick first, nine things I could pick second and eight things I could pick third. This actually, though, overstates the total number, because if I pick object A, and then object B, and then, object C, that's the same thing as picking C, and then B, and then A, or C and then A, and then B. So, if I think about those three objects, there's three things I could pick first. Two things I could have picked second, and one thing I could pick third. So these are the different ways of arranging those three options. So I get ten times nine times eight, divided by three times two times one, which is 120. So if I have ten solutions, or, you know, ten technologies or ten heuristics or ten ideas, that gives me 120 combinations of three. A 120 doesn't sound very big. It's not, but the point is we got way more than ten solutions and way more than ten juristics and way more than ten scientific theories. You've gotta ton of them. So, let's blow up the numbers a little bit. Let's suppose we have a deck of cards. Suppose I have 52 cards in a deck and I wanna just combine twenty of them. How big of a number do I get then? Well, there's 52 cards I could pick first, 51 second and so on all the way down to 33 cards I could pick for the twentieth. But now I've got those twenty cards. I could have picked those same twenty cards in lots of different orders. So there's any one of twenty could have been picked first, any one of nineteen could have been picked second and so on. So my answer is going to be 52 times 51 times 50, all the way down to times 33 divided by twenty times nineteen, times eighteen, times so on. That's gonna be the number of ways to pick twenty cards from 52. Well how big is that? Huge. It's a 100 and 25 trillion. So the thing about combining technologies, combining heuristics, combining ideas, we get this huge explosion. And every time anybody has an idea it can be combined with every other idea and every other combination of ideas. And this may be a big reason why we see so much growth. Why we've been able to sustain growth. So think back to our economic growth model, right? Remember we had that like A times capital to the beta, times labor to the one minus beta thing? And A was the technology parameter? Both, and for sustained growth, we needed that A to get bigger, and bigger, and bigger? Well, one thing that makes that a bigger, and bigger, and bigger, is when people have ideas. >> They can be recombined with every other idea, which leads to more and more growth. This idea of ideas building on ideas is the foundation of the theory of economic growth due to Marvin [inaudible], used at Harvard, called recombinant growth. And the idea is, ideas get generated all the time. You know, the steam engine gets enveloped, developed. The gasoline engine gets developed. The microprocessor gets developed. And all these things get recombined into interesting combinations. And those combinations, in turn, get recombined; right, to create ever more growth. So that's the basic idea behind recombinant growth. So if you take something like the steam engine, right, here's a picture of the early Newcomen atmosphere engine, which is really just a steam engine, right? It's got all these things. It's got pumps, right? It's got a steam piston. It's got a boiler, right? It's got a water reservoir. It's got this little, like, Level thing like a teeter totter. These are solutions to previous problems. The gasoline engine, right. So it's also got pistons and fuel injectors on and all sorts of stuff. It consist of recombinations of all sorts of different problems. So what we get are is this big machines, even here the computer on your desk, right, it consist of solutions to all sorts of other problems. So, a lot of our inventions. A recombinations of old solutions. Take your car. Your car consist of an engine, wheels, steering mechanisms, now it consist of all sorts of electronic stuff. So a car - even though it's a solution to a problem - is comprised of a whole bunch of solutions to other problems combined in interesting ways. So it's these recombinations that can drive a lot of growth. When you think about all those parts into the kind of steam engine, they weren't developed with a kind of steam engine in mind. They were developed for other purposes. And this is an idea from biology called exactation. Now the classic example of exactation, is the feather. Birds developed feathers primarily to keep them warm. But eventually those same feathers allowed them to fly. So expectation simply means this, you come up with some innovation, some solution for one reason, but then it gets exacted, it gets used in another context. So, Emily Dickinson famously said, hope is the thing with feathers. It's a good thing to keep in mind. Right? Cause feathers are this classic example of expectation. Hope, innovation, change is the thing with feathers as well. It is our ability to take a solution for one problem and apply it to something new. What do I mean? Take the laser. The laser was not [inaudible]. The kid with the laser, they didn't think, wow! We can now have laser printers, we can have laser pointers. No, that wasn't what they were thinking at all. They just came up with a laser. So once something's developed, it gets used for all sorts of things that were never expected, through this power of recombination. Even perspectives do. So, remember my sort of silly perspective on the candy bar, domesticity perspective? Well, you might think, you know, that. Doesn't really make a lot of sense. Domesticity doesn't make a lot of sense, as a perspective. It's a use, it's sort of a useless perspective. But in fact, masticity might be a really useful perspective for other problems. For example, if I'm coming up with pasta or breakfast cereal, or something like that, there may be that sort of a sweet spot in terms of masticity, so that could be a really good way of looking at those problems. So even failed solutions. For one problem may work really well for solutions to other problems. So, famous example here, right, is the post it note, that the glue that's used in post it notes was originally sort of a failure. It was a glue that didn't stick very well. But it turned out to be useful for other sorts of problems, mainly making sticky notes. Now there's more to it than this though. So it's not just the recombination of ideas cause for hundreds and thousands of year?s people had ideas. And here's where we've got to sort of reach just one level deeper. If you think about why we've had such sustained growth, how is it these ideas have been able to be combined, we have to recognize there had to be some way to communicate those ideas. So Joel Mokyr wrote a wonderful book called the Gifts of Athena. In the Gifts of Athena he talks about how. The rise of things like modern universities, printing press, and scientific communication allowed ideas to be transferred from one location and one person to another. And so what really led to this, you know, huge burst of activity, you know, sometimes called the technological revolution, was the fact that we could now share those ideas and then recombine them. Because, you know, like a tree, if an idea falls in a forest, nobody hears it, and nothing happens to it. So where are we? Here's where we are. Think about. Innovation. You think about problem solving, several things going on. First is, you have to represent that problem some way. Second thing is you gotta have someone looking for solutions to that problem. Different people represent problems in different ways, different people look for different solutions to problems, that means different people can help one another out through that diversity. Second thing. Once somebody finds the solution to a problem, once somebody comes up with some sort of product, or even comes up with a representation, like a perspective or a heuristic, that can be recombined with all the other ways of thinking and all the other solutions we have and lead to ever more growth. So you wanna ask, where does innovation come from? It comes from diversity, of perspectives and heuristics. And it comes from recombination of those new ideas. And that's what allows for, you know, ever improving solutions to problems. And ever improving new ideas, new products, new technologies, and new policies. Thank you. [sound].
