We live in a complex world with diverse people, firms, and governments whose behaviors aggregate to produce novel, unexpected phenomena. We see political uprisings, market crashes, and a never ending array of social trends. How do we make sense of it? Models. Evidence shows that people who think with models consistently outperform those who don't. And, moreover people who think with lots of models outperform people who use only one. Why do models make us better thinkers? Models help us to better organize information - to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures. In this class, I present a starter kit of models: I start with models of tipping points. I move on to cover models explain the wisdom of crowds, models that show why some countries are rich and some are poor, and models that help unpack the strategic decisions of firm and politicians. The models covered in this class provide a foundation for future social science classes, whether they be in economics, political science, business, or sociology. Mastering this material will give you a huge leg up in advanced courses. They also help you in life. Here's how the course will work. For each model, I present a short, easily digestible overview lecture. Then, I'll dig deeper. I'll go into the technical details of the model. Those technical lectures won't require calculus but be prepared for some algebra. For all the lectures, I'll offer some questions and we'll have quizzes and even a final exam. If you decide to do the deep dive, and take all the quizzes and the exam, you'll receive a Course Certificate. If you just decide to follow along for the introductory lectures to gain some exposure that's fine too. It's all free. And it's all here to help make you a better thinker!
Recombination
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En provenance du cours de University of Michigan
Model Thinking
1145 notes
À partir de la leçon
Diversity and Innovation & Markov Processes
In this section, we cover some models of problem solving to show the role that diversity plays in innovation. We see how diverse perspectives (problem representations) and heuristics enable groups of problem solvers to outperform individuals. We also introduce some new concepts like "rugged landscapes" and "local optima". In the last lecture, we'll see the awesome power of recombination and how it contributes to growth. The readings for this chapters consist on an excerpt from my book The Difference courtesy of Princeton University Press.
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Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
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].
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