Complex systems won this year’s Nobel. Here’s what it means.
With the Nobel prize going to two major figures in climate science as well as a giant in statistical physics, it is certainly a win for…
With the Nobel prize going to two major figures in climate science as well as a giant in statistical physics, it is certainly a win for complex systems.
Complex systems has had a long lull in the popular culture since its heyday in the 1990s where it was dubbed a New Kind of Science. We knew then that it was just old kind of science with new clothes.
Computers are finally advanced enough to keep up with simulations of trillions of galaxies and millions of universes. Flocks of birds that used to amuse us early Linux users are now child’s play compared to what we can now do.
With all this power at are figure tips to predict and understand, we may want to ask whether this will help us in the end. So far, it seems as if the model predictions for global warming that Sukyuro Manabe produced in the 1970s were spot on, yet attempts to mitigate such warming have failed.
Many systems are complicated but not complex, for example, an internal combustion engine or a rocket are complicate, but they are not complex. Far from it, they rely on having very predictable and regular behavior. A complex system is a system that has many interacting parts that produce some phenomenon that is emergent, such as the amazing patterns in flocks of birds or phase transitions in molecules.
The US military has long recognized that the fog of war is the result of a complex system. Hence, it invests in large simulation environments that can probe thousands or millions of interacting parts. Yet, the real world is always that much more complex and unpredictable.
In 2002, 2021 Nobel laureate Giorgio Parisi wrote an article about what complex systems look like from his physicist’s perspective. He points out that, for example, classical physics tended to restrict itself to simple problems out of necessity. Newton, Laplace, and Hamilton to name a few had no means for really understanding complex systems. Newton struggled with the three body problem, cranking out a few perturbations but ultimately failing. Complex systems tend to be inherently intractable mathematically.
Statistical mechanics in the 19th century and quantum in the 20th forced physicists to confront complex systems as it turned out that basic constituents of matter: fluids, heat, gases, crystals, atoms, and light are all complex systems.
There is an argument between physicists and complexity scientists about whether one can get “simple” behavior from a complex system, as the general rule of thumb is that a complex system has complex behavior from simple rules. A lot of matter doesn’t work that way. You can, after all, get crystals which are pretty simple, but the way in which they form is quite complex.
Parisi defines a complex system as a system where “its behavior dependence crucially on its details.” I think this is an important point because it relates to concepts in chaos like sensitive dependence on initial conditions. Complex systems have sensitive dependence on many of their conditions. That is why they can have so much variation from simple rules and different conditions. Yet, complex systems are also not necessarily chaotic. Nor are they ordered. They exist somewhere on the margins in between, neither purely random nor perfectly periodic, but swinging back and forth between the two.
Parisi uses the example of protein folding as a complex system. Long strands of RNA, for example, which can fold in many different ways because there are many different foldings that have close to minimal energy. Yet, if we see these as complex systems, then we need not understand them in their full complexity but only understand them probabilistically. And because they are complex and sensitive to their conditions, this might be more useful, since the RNA can fold in so many unpredictable ways.
This approach can help us in many complex systems where we don’t understand all the rules. Rather than understand the rules, we can generate probabilistic rules and understand the sort of distribution of different possibilities.
Consider an example like a pandemic spreading around the world. This is a complex system where a funeral can lead to a sudden outbreak. (This happened in Albany [pronounced Al-benny], Georgia.) We can’t predict those occurrences, but we can try to understand and model the probable outcomes. Like proteins and lightning and other natural phenomena, the virus is going to follow some path of least resistance. Because it is a complex system, we cannot understand exactly what that path is but we can understand the probable paths.
One final critical point about this that Parisi makes that we need to consider carefully is that the word “prediction” no longer means what is used to mean in classical physics. We cannot provide precise predictions of complex or chaotic phenomena. All we can do is provide probabilities. That includes the fate of our planet. In any predictive model, we have to make assumptions about how all the parts are going to play together, including us. Yet, certain things are clear: when humans do not do the right things, good things rarely happen.
Parisi, Giorgio. “Complex systems: a physicist’s viewpoint.” arXiv preprint cond-mat/0205297 (2002).