nonlinearities

Physical systems are nonlinear. Global climate is one good example. In general, nonlinear problems are hard to solve and they are not as easy to understand as linear systems. Furthermore, linear systems are quite predictable whereas nonlinear ones are inherently not. While this may sound like a lot of techno-babble, rest assured that it is something all of us are familiar with.

Most of the time we assume things will behave linearly. What that means is that we believe things are additive. Something like, if you eat twice as much you will gain twice as much weight. This sort of thinking is extremely common in popular medicine. People think that if some vitamin is good for them, then twice as much vitamin must be twice as good. Or if a lot of alcohol is bad for them then some alcohol must be somewhat bad. But this is not always true.

A common nonlinearity that interferes with this type of prediction is a threshold. We are all familiar with thresholds. For example it takes some energy to get something moving. Once it moves however, things return to "normal." And by normal we mean it behaves more or less linearly. If you push twice as hard, it will move twice as fast. And everyday experience is usually in that realm. When you ride a bike as a kid, you are really moving too slowly for air resistance to become much of a problem. Within your normal operating conditions all you worry about is rolling resistance, which is pretty much linear. You pedal harder and you go faster. And the harder you pedal the faster you go.

Many physical systems have these "linear regimes," and it therefore becomes really tempting to think that things are always linear. Until something weird happens. All living systems eventually cross another threshold called death. And nothing is weirder than having someone die in a freak accident. Such an unpredictable event leaves us wondering and shaking our heads. That is the problem with thresholds and nonlinearities. There is often no going back.

But most of us would rather not think about that ultimate nonlinearity called death. Although death is certain, predicting when it will strike is impossible. And although we have grown accustomed to not expecting it during everyday normal activities, occasionally it does strike out of the blue. And when it does we look for a reason. Something of higher purpose that is more predictable. We yearn for linearity because it gives us some measure of control.

And the same is true for our ecosystem. We would like to think it is under control. We would like to think it will always return to normal. And although there are freak incidents such as storms, earthquakes, and other turmoil, at the end of the day we think it will all blow over. There is always another day. But nonlinear systems do not behave that way. Sometimes they cross a threshold and take another course altogether. They go on a new path that is radically different from the one traveled before. And the change may be irreversible.

Nature is very intricate and complex. There are many checks and balances, and things tend to settle in a solid and stable equilibrium. Look at our bodies. They can take a fair beating and survive large parameter swings. They are extremely adaptable. They are robust and have many built-in mechanisms to restore equilibrium. But occasionally a very small disturbance in one key parameter will take them across a lethal threshold. Suddenly a radically different path is taken. One that is irreversible and undesirable. And the same body that held together so well and weathered so many storms is now quickly taken apart.

As any parent knows, it is dangerous to play with fire- or greenhouse gases for that matter.