Monday, June 13, 2022

"Why Complex Systems Collapse Faster"

Professor (physical chemistry, U. of Florence) Ugo Bardi writing at Tablet Magazine

All civilizations collapse. The challenge is how to slow it down enough to prolong our happiness.

During the first century of our era, the Roman philosopher Lucius Annaeus Seneca wrote to his friend Lucilius that life would be much happier if things would only decline as slowly as they grow. Unfortunately, as Seneca noted, “increases are of sluggish growth but the way to ruin is rapid.” We may call this universal rule the Seneca effect.

Seneca’s idea that “ruin is rapid” touches something deep in our minds. Ruin, which we may also call “collapse,” is a feature of our world. We experience it with our health, our job, our family, our investments. We know that when ruin comes, it is unpredictable, rapid, destructive, and spectacular. And it seems to be impossible to stop until everything that can be destroyed is destroyed.

The same is true of civilizations. Not one in history has lasted forever: Why should ours be an exception? Surely you’ve heard of the climatic “tipping points,” which mark, for example, the start of the collapse of Earth’s climate system. The result in this case might be to propel us to a different planet where it is not clear that humankind could survive. It is hard to imagine a more complete kind of ruin.

So, can we avoid collapse, or at least reduce its damage? That generates another question: What causes collapse in the first place? At the time of Seneca, people were happy just to note that collapses do, in fact, occur. But today we have robust scientific models called “complex systems.” Here is a picture showing the typical behavior of a collapsing system, calculated using a simple mathematical model (see Figure 1).

https://tablet-mag-images.b-cdn.net/production/84bec9ba6f30b08183700dddf8a953a4b6f78117-627x402.png?w=1200&q=70&auto=format&dpr=1

Figure 1: The Seneca curve, from Bardi’s ‘The Seneca Effect’ (2017). The intensity of something as a function of time (going left to right). For intensity, imagine it is the value of a financial stock. It grows slowly, then it declines rapidly when the company generating it goes bankrupt.

But we can also make simple, nonmathematical models of collapse. Look up the term “stick bomb,” and you’ll find many examples of geometric structures made from popsicle sticks that appear stable—until you shift one of the sticks away from the others. Then the whole thing suddenly disappears in a small explosion of flying sticks. A harmless kind of Seneca effect.

A stick structure is a very simple thing, but it embodies the essence of the mechanism of collapse because it is a network. A network is composed of many elements, or “nodes,” connected to one another by “links.” In a stick bomb, the nodes are the points where the sticks touch each other, while the sticks themselves are the links. When you remove one of the links, you weaken the nearby nodes. When one node lets go of a link, the collapse moves to other nodes. This is sometimes called a “cascading failure,” another name for the Seneca effect.

It is a curious feature of cascading failures that all the elements in the system collaborate to bring the system down entirely. But it is a characteristic of networks that small perturbations are rapidly transmitted to the entire structure. Recall the proverbial straw that broke the camel’s back. A straw is a very small thing, it weighs almost nothing, but it can bring down a thousand-pound camel. Or consider how small cracks can grow until they eventually destroy the largest structures. That’s how failures occur....