Blog 3. Complex Systems—including you, me, and weather

A social fix = new regulation (nonlinear rule) = new problem?

In our society, we create new laws (e.g. Medicare) by legislation as done by congress, state legislatures, county supervisors, or town councils. We create new regulations (speed limits and plumbers’ license requirements) through agencies who get their authority from higher legislation. Each law or regulation is intended to fix a previous problem, and sure enough, each law or regulation generates at least one new problem.

Symptoms and causes.

Often, this new problem occurs because legislative and regulatory solutions address symptoms rather than the underlying causes. President Johnson’s war on poverty did not end poverty, but urban renewal moved some poor people out of their own neighborhoods.  Federal flood insurance did not stop destruction of beach houses by storms. Instead, it encouraged the construction of more beach houses.  To uncover the causes, we have to understand a few things about the behavior of complex systems, because society itself is a complex system.  Parts of society down to a large church or corporation are complex systems nested within each other and within the bigger complex system.

For an expanded definition of nonlinear things and complex systems, see Blog 2, or see an illustrated on-line short course offered by the Santa Fe Institute.  In short, a complex system is composed of many independent actors who interact by nonlinear rules.  I’m a nested set of complex systems.  At least, my body is.  It has tens of trillions of cells, and even more bacteria than cells, and it has various solids and fluids, all of which interact and change themselves and each other nonlinearly through chemical and electrical signals.  Just thinking about it changes the signals. Well, I generate the largest internal signal when thinking about chocolate, but you get the idea.

There are about 20,000 bodies (citizens, that is) in my small town. As towns go, that isn’t big.  But each citizen has different desires, different driving speeds despite the speed limits, different responses to the price of gas or the names on the ballot, and each puts different pressures on everyone else. Right now, we citizens can’t even agree on the name for a new town hall, and if you think our responses are linear (result proportional to the cause), just read the vociferous letters to the editor in our newspaper.  Have I convinced you that my town is a complex system?  Well, how about my state? A political party? The nation?  The geopolitics of the world?

The powerful butterfly?

A complex system might sometimes amplify a small perturbation, depending on conditions within the system (that is, the status of all the actors and all the rules of interaction at the time).  You’ve heard of the butterfly effect.  A butterfly flaps its wings and later there’s a thunderstorm somewhere else.  That’s amplification.  (Yes, the weather is another complex system.)

A nonlinear rule of interaction can have so-called bifurcation points, points from which two different futures may develop.  Suppose the rule is this: If the accused man weighs more than 150 pounds, he is to be hanged. If he weighs less, he goes free.  Note that the future of the accused may be switched by a random speck of dust on his head.

Likewise, if the situation is just right (or just wrong, depending on your view), a small cause in a complex system can amplify into a big effect.  Archduke Ferdinand of Austria was murdered on 28 June 1914, with the result that millions of innocent people were subsequently killed in World War I. The future of a complex system is sometimes influenced by the tiniest difference.  That’s why you should always strive for good things in the world. Your actions may amplify.  And you’ll never know it, so forget about taking the credit.

Few big, many small.

There’s a characteristic of complex systems that isn’t fully understood yet.  Big events happen rarely, small events happen more frequently.  If you plot the sizes of the events versus the frequency of occurrence on a logarithmic scale, you get a straight line, which indicates that mathematically the size varies with the frequency to some negative power. Consider what happens when you dribble sand grains slowly onto a growing conical pile of sand.  Little landslides occur frequently, big avalanches occur rarely. Sometimes this characteristic is referred to as “one-over-f-noise.”  Big wars happen rarely, small military actions happen frequently.  That’s true for earthquakes, too.

Why should wars and flowing sand display a similar characteristic?  Good question. What’s our point in this? You and I are establishing that society is a complex system, and most of its parts are complex systems, right down to motor vehicle laws and the unwritten rules by which different drivers (the actors) adjust their speeds and spacings from other drivers. We’re back to that traffic jam mentioned in Blog 2.  If your job is to reduce the traffic jams, you had better know something about the rules by which drivers act or react, and something about the behavior of a system of interacting drivers.  You might be tempted to hire more highway policemen , but remember that  a car parked by the side of the road can cause a so-called “gapers’ block”.  Likewise, the mere sight of a police car in dense traffic, like any other unusual or threatening circumstance, could trigger yet another traffic jam.

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