Update on Game-Based High School

I wrote a while back on a high school that uses games as its primary pedagogical tool. NPR's All Things Considered has a new report on the school. Excerpt:

"In math, we're traveling around the world," says sixth-grader Rocco Rose, a student at Quest to Learn and a citizen of Creepytown — an imaginary city where his class learns math and English. The students play travel agents, convert currencies, keep blogs about their travel experiences and budget trips.

Creepytown is structured like a video game that has jumped out of the computer. During their 10-week "missions," students learn to adapt and improvise.

"The second trimester, Creepytown went broke," Salen says. "They had ... an economic crisis. So the kids worked to figure out ... what had gone wrong. And then they proposed the design of a theme park to bring revenue in."

Systems Thinking

Salen says playing with complex dynamic systems gives kids opportunities to learn.

Students "learn how to solve problems, how to communicate, how to use data, how to begin to predict things that might be coming down the line," she says.

They also learn something called systems thinking, which Salen says is one of the cornerstones of 21st century literacy. It helps you understand how the behavior of a derivatives trader in Hong Kong affects housing prices in Florida. When a system becomes sufficiently complex, Salen says, you start to get outcomes that are hard to foresee.

"Suddenly you begin to get what's called emergent behavior, and in emergent behavior, that system, the elements in it, begin to relate to one another in ways that can be unpredictable," she says.

Hell yeah! If we can give the next generation early experience with complex systems and unintended consequences, there may be hope for the future yet.

Too Important to Fail?

The federal government is set to take over mortgage companies Fannie Mae and Freddie Mac. Earlier this summer, the government rescued the investment bank Bear Stearns. In each case it was decided that, even though the companies were in trouble of their own making, the damage caused by their failure would be too great for the economy to bear.

Strictly speaking, this isn't how our economy is supposed to work. It's supposed to be survival of the fittest: the companies that make the best decisions survive, and others fail. In this way good practices are rewarded, better business models evolve, and society progresses.

The problem is that, as part of this evolutionary process, the US economy has become increasingly interdependent. Companies need each other to survive, so that if a big one goes down it could take others with it. In the cases of Fannie Mae, Freddie Mac, and Bear Stearns, it was deemed that the failure of these companies would take out entire sectors of the economy, and as a country we couldn't let that happen.

I won't argue the merits of these decisions, but I'm interested in what they say about our economy. We're accustomed to thinking of our economy in terms of a system of competing animals. If one dies, others arise to take its place. But it may turn out our economy is more like another system: the human body, wherein if one part fails, the system suffers as a whole.

If this is true, then the whole of economic theory is based on an incorrect assumption. We may have some fundamental rethinking to do about how our economy works and why.

The paradox of order and randomness

Consider the following two images:




First view each image as is, and then click on them to see larger versions. Ignore for a moment the different sizes, and the copyright notice in the second picture (hope I'm not breaking any laws!) What's going on in these pictures?

The first is a randomly generated image, in which a computer essentially flipped a coin to decide the color (black or white) of each pixel. The second is composed of alternating black and white pixels in a checkered pattern (click on the image to see this clearly.)

At this resolution, the first picture still has some texture to it. But zoom out a bit more and it would reduce to a uniform grey, just like the second.

This highlights something of a paradox in complex systems theory: complete randomness is actually pretty boring. Sure, it's unpredictable, but because it has no structure, there's not much else you can say about it. And if you squint at it, it all averages out to grey. Contrast this to the following fractal image:



Now this picture has a lot of interesting structure to describe, like most complex systems.

Why is this a paradox? Because according to the defintions of complexity we discussed some months ago, a completely random system is more complex than anything else! Any order or structure in a system makes it easier to describe, thereby reducing complexity according to conventional definitions. So the fractal is actually less complex than the random image.

Complex systems researchers have recognized this problem for a long time, but there's no consensus on how to resolve it. Some have suggested adopting a different definition of complexity that behaves something like this:



That is, complexity is greatest somewhere between total order and complete randomness. But this is unsatisfying; complexity is not a mere mixture between order and randomness, but a delicate balance combining features of the two.

Of course, I have my own opinion as to how this paradox should be resolved. But that's a tale for another time.

The Wire

I've been working my way through The Wire for the past semester or so. For those who don't know, the Wire is a TV drama exploring the drug trade in Baltimore and its intersection with all the different systems that function in the city. The first season centers on a drug organization and the police unit investigating them, and the series telescopes outward from there, adding the docks, city hall, the education system, and the print media to its focus in subsequent seasons. The creator, a former cop and public school teacher in Baltimore, has a deep understanding of how all these systems interact with each other, and in particular, how the organizational dynamics of a system can impede that system's objectives. Watching the series should be worth graduate credit in both sociology and complex systems theory. (In fact, one academic journal has issued a call for papers on the series. Deadline is September!)

There are many different jumping-off points I could use from the series, but I'll focus today on a recurring pattern: Drug sellers run a highly complex organization. They switch stash-houses frequently, speak in code, and never let the top guys get anywhere near the actual drugs. Some within the police department realize this, and set up sophisticated surveillance operations to gather information about the drug sellers. But every now and then one of the "top brass" in the police department gets wind of this operation, and wonders why so much time and money are being spent to investigate a bunch of "thugs." They send down a command to send a boatload of units down to the drug area and start locking people up.

Needless to say, this works about as well as attacking a swarm of gnats with a sledgehammer. They catch a couple low-level dealers, but ruin all the intelligence they had on anyone higher up. So the investigation must start all over again.

In theoretical terms, the mistake here is attempting a blunt, simple solution to a nimble, complex problem. When you look for it, you can see this mistake in many places, from our pre-Petraeus anti-insurgency strategy in Iraq, to our federal education policy that mandates standardized tests. To truly solve a complex problem requires an approach as subtle and multifaceted as the problem itself.

Sub-Prime Mortgage Crisis Part II: Lessons for Complex Systems

Last time, we talked about what went wrong in the US mortgage market, based on the explanation given by NPR and This American Life. What does this debacle tell us in general about how complex systems can go wrong?

The main problem, in a theoretical sense, is that a feedback loop got too long and complex.

A feedback loop is the process by which an action leads to a consequence for the actor. Let's look at the old mortgage system:



Under this system, if the bank made a bad loan, they'd lose their money. So there was a very direct link between action and consequence. Banks have been dealing with this feedback loop for centuries and have gotten pretty good at making only loans that will get repaid.

But in the early 2000's, the system was replaced by this:



There's still a feedback loop here, but it's longer and more complex. Long, complex feedback loops are dangerous because they can fool people into thinking they're making good decisions, when really their bad decisions haven't caught up with them yet. The investors were pouring yet more money into the broken system, because their actions hadn't caught up with them yet, and they were too far removed from the homeowners to see what terrible shape they were in.

We moved essentially from

bad action ---> bad consequence

to

REALLY bad action --- (long time delay) ---> REALLY bad consequence

It's unlikely that investors will make this same mistake again, because they understand much better now how the mortgage market works. But the general mistake of stretching out a feedback loop, and assuming that you're doing well just because nothing's gone wrong so far, will probably be repeated many, many times.

Life's Universal Scaling Law

It ain't easy being green. Biology has long suffered under the label "soft science," a term used (often disparagingly) to draw a contrast with the "hard sciences" of physics and chemistry, whose laws are guaranteed with the certainty of mathematics. But this picture is not altogether true. While biological processes are more complex than physical ones, making simple mathematical formulas harder to come by, there are yet some mathematical rules that hold with a remarkable degree of consistency.

One famous example is the relationship of a animal's mass to its metabolism (the rate at which it expends energy). This relationship is expressed in the simple formula

R = R₀M^3/4,

where R is the metabolic rate, R₀ is a constant, and M is the mass of the organism.

Separate laws exist for mammals, birds, unicellular organisms, and even living structures like mitochondria within cells. The values of R₀ are
different for each law, but the mysterious 3/4 exponent stays the same.

These laws have been observed since 1930, but the reason for the 3/4 exponent has been a mystery until recently. The discovery by Geoff West et al of a mechanism underlying this law was a major triumph for the complex systems movement: a universal law of life explained by complex systems principles.

Specifically, West showed that the 3/4 exponent comes from the way a living thing distributes its resources. If the cells in an animal acted like independent beings, each gathering and consuming its own food, the metabolic rate would be a simple multiple of the mass, that is

R = R₀M

with no exponent. But the cells of an animal aren't independent. They work together to collect, process, and consume energy. To do this they need networks (such as blood vessels) to move resources around. West and his collaborators showed that the 3/4 exponent is determined by the requirements that the network a) reach every part of the animal's body, and b) waste as little energy as possible.

Extending this approach, they were able to explain other scaling laws like the relationship between heart rate and mass. Currently, West is investigating scaling laws in large-scale living communities, such as forests and cities.

I haven't talked much about network theory (a topic for another time perhaps) but West's work suggests the great potential of this complex systems subfield to explain some of life's mysteries.

Is Life Fractal?

I'm sure you all know what fractals look like, but a few pretty pictures never hurt anyone:



Isn't that cool? The key thing about fractals is that if you look at just a small part of it, it resembles the whole thing. For instance, the following picture was obtained by zooming in on the upper left tail of the previous one:



One of the original "big ideas" of complex systems is that fractal patterns seem to appear spontaneously in nature and in human society. Let's look at some examples:

Physical Systems: Pop quiz: is this picture a close-up of a rock you could hold in your hand, or wide shot of a giant cliff face?



I don't know what the answer is. Without some point of reference it's very hard to determine the scale because rocks are fractal: small parts of them look like the whole.

Other examples in physical systems include turbulence (small patches of bumpy air look like large patches) and coastlines (think Norway). These two examples in particular inspired Benoit Mandelbrot to give fractals their name and begin their mathematical exploration.

Biological Systems: Here's an example you're probably familiar with:



And one you probably aren't:



The first was a fern, the second was a vegetable called a chou Romanesco, which has to be the coolest vegetable I've ever seen.

In the case of these living systems, there's a simple reason why you see fractals: they are grown from cells following simple rules. The fern, for example, first grows a single stalk with leaves branching out. These leaves follow the same rule and grow their own leaves, and so on.

Of course, the pattern doesn't exist forever. If you zoom in far enough, eventually you see leaves with no branches. This is an important feature of all real-world fractals: there is some minimum scale (e.g. the atomic scale or the cellular scale) at which the fractal pattern breaks down.

Social Systems: Some people like to extend this reasoning to the social realm, arguing that individuals form families, which form communities and corporations, which form cities, nations and so on. You can try to draw parallels between behavior at the nation level or the corporation level to behavior at the human level.

Personally, I'm a little dubious on this argument. My doubts stem partly from my personal observation that humans seem to act morally on an individual scale, but that corporations on the whole behave far worse than individuals. I think there's something fundamentally different about the centralized decision-making process of a human, and the more decentralized process of a corporation. But this is all my personal opinion. Feel free to debate me on it.

Is Global Complexity Worth It?

I had a wide-ranging lunch conversation with my friend Seth
a week ago. We touched on many things, but kept circling back to the above question. More specifically, I was wondering if our current level of global complexity could ever be sustainable, even with the best international governance and planning.

Let's define what we're talking about. In today's world, actions you take have consequences around the globe. For example, if you buy a computer, it likely was not made in a workshop down the road. The parts that go into your computer come from many different countries. These parts had to cross vast distances to come together, burning oil from other countries in the process. These parts were assembled in yet other countries, shipped several more times, and finally delivered to you. The money that you paid for the computer feeds back into all these various countries and processes, strengthening and perhaps changing them.

The effects of this global entanglement have been amazing. Without it, we wouldn't have computers, cellphones, airplanes, plastics, television, cars, or curry powder in the supermarket. None of these products can be made in any one local community; they all require cooperation on a continental, if not global, scale.

But I'm worried by globalization, on both a theoretical and practical level. It's clear that as humans, we aren't living within our means--I won't go into the details of that argument here. What concerns now is whether the very structure of our global society may be preventing us from ever living within our means.

First, feedback loops are getting too complex. Suppose we lived in a simple, hundred person community, and someone was stealing from his neighbors, dumping trash in the public square, or doing other undesirable actions. These actions would become apparent to everyone in short order, and the community could punish the perpetrator in various ways; economically, socially, even physically.

In theory, we have a legal system now to provide these kinds of punishments. But the more complex our society becomes, the harder it is to identify those who are screwing things up. Furthermore, laws and enforcement vary wildly across countries. Multinational corporations can get away with dumping trash in the ocean, toppling Central American democracies, intentionally creating blackouts in California, or supporting sweatshops in China because a) the actions might be legal in whatever location they're operating out of, b) they can obscure their practices behind a wall of complexity that regulators can't penetrate, and c) the consumers usually have no idea what the company is doing and therefore can't exercise moral judgment in their purchases. It could be decades before any consequences (legal, economic, or environmental) catch up with the perpetrator. And decades is too long to be an effective deterrent.

Second, we are increasingly interdependent. Witness how the mortgage crisis spread throughout American economic sectors and is now spreading through the world. Infectious diseases like avian flu have the potential to go global due to the volume of international travel. Even our environmental problems have globalized--we worry about global warming now, whereas the environmental agenda in the past was more about local pollution issues.

I see this as a problem because it means we have only one chance to screw up. The inhabitants of Easter Island destroyed their ecosystem and suffered for it, but the damage was contained to the island. In our current connected world, one disaster could ruin things for all humanity.

Can we do anything about global complexity and interdependence? I've been thinking about ways we can promote some simplicity in our economy, like buying local food or supporting local independent retailers over mega-chains. I'm not advocating we go back to preindustrial tribal society, but a little extra simplicity seems like a good thing.

Phase Transitions

One of the biggest projects of complex systems research is to find "universal" phenomena: patterns that manifest themselves in similar ways across physical, social, and biological systems. One phenonenon that appears regularly throughout complex systems is phase transitions: those instances when a slight change in the rules causes a massive change in a system's behavior. These changes only seem to happen when the system is at certain "critical" points. Understanding when these phase changes occur, and what happens when they do, will go a long way toward increasing our understanding of systems behavior in general.

To illustrate the many manifestations of this idea, let's look at some examples:

• Physics: Water boils at 212 degrees Fahrenheit. This fact is so commonplace that it's easy to forget how fundamentally surprising it is. Temperature is basically a measure of how "jittery" the molecules in a substance are. Most of the time, if you increase water's temperature by a degree or two, you make the individual molecules buzz around faster but the liquid itself ("the system") retains all of its basic properties. But at the magical point of 212 degrees, a slight change in jitteriness radically changes the system's behavior. At the critical point, the slight change is just enough to overcome certain forces holding the molecules together, and off they go.



• Computer Science: Say you give a computer a randomly selected problem from a certain class of problems (like finding the shortest route between two points on a road map), and see how long the computer takes to solve it. Of course, there are many ways of "randomly" choosing a problem, so let's say you have some parameters which tell you how likely some problems are versus others. For the most part, a small change in the parameters won't change the complexity of the problem much, but at some critical values, a small change can make the problem much simpler or much more difficult. (For a technical exposition see here.) Papadimitriou claimed that, in some mathematical sense, these are the same kind of phase transitions as in solids and liquids, but I don't know the details on that claim.



• Mathematics: There are several mathematical phenomena that behave like phase transitions, but I'll focus on bifurcations. A dynamical system in mathematics is a system that evolves from one state to another via some rule. Change the rule a little and you'll change the system's behavior, usually not by much, but sometimes by a whole lot. For instance, the system might shift from being in equilibrium to alternating between two states. Change the rules a bit more and it could start cycling though four states, then eight. Another small change could land you in chaos, in which predicting the future behavior of the system is next to impossible.



• Ecology: Okay enough with theory, let's look at some situations where phase transitions matter in a huge way. Ecosystems are adaptive, meaning that they can absorb a certain amount of change while maintaing their basic state. However, Folke et. al. have extensively documented what they call "regime shifts" in ecosystems--changes in ecosystems from one stable state to anoher, very different stable state (think rainforest to desert.) Often these shifts appear triggered by human behavior. Folke et. al. also review ways to increase ecosystem resilience (i.e. make them less susceptible to regime shifts) by, for example, promoting and maintaining biodiversity.



• Economics: Well for starters, there was the Great Phase Transition of 1929, or the current phase transition triggered by sub-prime lending. In both events, small crashes cascaded into much larger ones because of underlying problems in the market: in the first case people buying stocks with borrowed money; in the second case investment in risky mortgages that only make sense when interest rates are low. These underlying problems created a situation where a single "spark" could bring the whole market down.



• Social Sciences: The idea of a "tipping point" actually belonged to sociological theory before Malcolm Gladwell popularized it. It refers to any process that, upon gaining critical momentum, cascades dramatically. The term was first coined to describe white flight: once a critical number of nonwhites moved into a neighborhood, all the whites would head for the 'burbs. It has since been used to describe all manner of trends and fads, as well as contagious diseases. Trends that never catch enough initial supporters will die out quickly, but beyond a certain point, they're unstoppable. "Facebook" ustoppable.

Given their importance and ubiquity, understanding the how, why, and when of phase transitions is a crucial project. The good news is that they're not totally unpredictable--there are certain signs that tell you when a phase transition may be approaching. However, this discussion must wait for another time.

The What and the Why

So what are complex systems, and why are they worth studying? These two questions could fill books, and I will be returning often to both of them, but it only makes sense to start this blog off with a preliminary stab at some answers.

What are complex systems? They are systems which have so many parts and variables that traditional scientific models fail to describe them. They are found across the physical, biological, and social sciences. The salient features that distinguish complex systems are:

• Many small parts that interact to create large-scale behavior. These "parts" may be molecules, cells, people, animals, air particles, or grains of sand.
• A sufficient number of parts so that even if the individual interactions between them were perfectly understod (as they are in some physics situations), it would still be computationally impossible to precisely predict the large-scale behavior.
• Despite the impossibility of exact predictions, these systems still exhibit characteristic behaviors which make them amenable to mathematical analysis. These behaviors may include self-similarity (intermediate-scale behavior mimics large-scale behavior, e.g. local governments resemble national governments) and tradeoffs or fluctuations between large-scale cooperation and individual or small-scale action.

So why study these systems? First of all, we study them because they shape our world. I think it's no exaggeration to say that the future of humanity depends on our understanding of how complex systems work (for example, responding to global warming will require a deep understanding of the many systems that interact to create greenhouse gases, and how these systems can be changed.)

The second reason we study these systems is that it has not already been done. Broadly speaking, the problems of simple systems in science have already been solved. Given two particles, molecules, or cells; a physicist, chemist, or biologist could pretty much tell you how they will interact. Small-scale interactions are well-understood in all areas of the physical sciences (the social sciences are a different matter, but we can discuss this later.) On the other hand, complex systems are not only poorly understood, they have historically been ignored in many areas of science. The reason for this is that exact predictions are the stock and trade of physical science. To scientifically tackle problems where exact prediction is impossible requires a paradigm shift. Scientists must learn to ask different kinds of questions and expect different kinds of answers. This paradigm shift started sometime in the 80's (more on complex systems history in further posts) and it is still occuring today. Because the field is so young, many fundamental questions are still open. This makes it a great field for the scientifically adventurous.

The third argument for complex systems study is that it is fascinating. Inherently interdisciplinary, complex systems research brings together scholars from across the hard and soft sciences. Because the focus is on big-picture questions, an open mind can be just as valuable an asset as libraries of technical knowledge. The culture of complex systems research is such that no questions are off limits, and investigating problems outside of your field of expertise is encouraged rather than shunned. So you get to work on fascinating problems, and no one tells you not to!

That's my summary of what I do and why. Future posts will focus more on specific systems or conceptual issues. In the meantime, please comment!