Tag Archives: science

When Systems Are Like Sand


From pragprog.com

From pragprog.com

We live in a very complex world; a world made up of a vast network of interconnected systems. Each large macro-system such as our economy, or the environment is made up of numerous smaller complex systems that are all connected and independent on each other.  How it is that large and complex system such as an economy or eco-system fail, and is it possible to predict when these systems will failure before it happens?

Large systems such as the economy or environment are so complex that they are almost impossible to compute (in other words predict) the exact future of the system. For this reason, we build models of systems (abstractions) so that we can better understand how the various parts of these systems interact and affect one another. One very successful model has been designed to do just that, and it involves building piles of sand.

In 1987, three physicists working on complexity theory tried an experiment by piling up grains of sand one at a time[i]. The sand pile would grow until at some point a landslide would occur. Sometimes the landslide would be very small, but at other times, the whole side of the pile might collapse in a catastrophic failure. The purpose of their experiment was to determine why they would sometimes get a catastrophic failure, and if by learning that they could apply their findings to other complex systems that sometime fail. That experiment has famously become known as the bak-tang-wiesenfeld sandpile model, has been tested and found applicable for many complex systems from financial markets to weather forecasting to predicting solar flares.

Why System Fail

When you pile sand up one grain at a time, each grain falls at random rolling down the sand pile until it finds a stable perch along the side. What looks stable however, may actually be a grain of sand just barely hanging on from falling farther own the side. When a new grain of sand drops, it may touch and jostle another grain that is just barely hanging on and knock that grain loose. Now two grains are tumbling down the side. At this point, both grains might find a place to rest and the slide will stop, or if they encounter more grains that are barely hanging on, they too may be added to the landslide. Two grains become four, tumbling down the side increasing the odds that they will encounter more loose grains and increase the size of the slide. The result of all of this is that a single grain of sand (like the last straw that broke the camel’s back), can cascade into a failure where a large part of the pile joins in a catastrophic landslide and the whole pile of sand collapses.

How does this apply to systems like our economy or the environment? When all the subsystems within a large system are healthy we say that the system is robust, because a few small failures (like grains of sand rolling down the side) will not encounter other weaknesses and stability can easily return to the system. The weaker those underlying subsystems become though, the more that that each part is pushed to the very edge and is just barely holding on,  the more likely that a small disturbance will push it over the edge with the increased potential of a cascading system failure.

In fact, we have seen exactly that, over and over again, throughout history. Take for example the great Mayan Civilization that collapsed around 950 A.D. It is estimated that the Mayan population at one point exceeded 10 million people living on the Yucatan Peninsula, in an area about the size of Southern California.  When the Spanish arrived centuries later, they found no cities, and a total population in the 10’s of thousands. What happened? Did millions of people just walk off into the jungle and give up a life of luxury in the city? Until recently we could only guess about what happened. Several recent studies[ii] however, have shed light on what really caused the Mayan Civilization to collapse.

First of all, as you can guess, is takes a lot of farm land to feed 10 million people without the use of tractors, water pumps for irrigation and fertilizer to replenish the soil. The Mayan developed a habit of farming an area to exhaustion, then picking up and moving down the road to a new area. As a result the soils on the peninsula were very shallow, poor in minerals and nutrients, and could not hold much water. When land is over used as was the case with the Mayans, it may take decades or longer for nature to reclaim the land and replenish the nutrients. The Mayans were squeezing everything they could out of the land, pushing crop yields to the limit at all times. The soils became weaker and thinner over time. Agriculture on the Yucatan Peninsula was becoming like a very unstable pile of sand with farms just barely hanging on trying to meet demand.

Building great cities also requires a lot of timbre used in construction and to build cook fires. Archeological records show that vast areas of forest were stripped down to bare land in the centuries leading up to collapse. Unknown to the Mayans at the time was the fact that the jungle trees plays a vital role in controlling the climate. Trees provide shade and help prevent rain water from evaporating rapidly from the soil. Dry soil is easily blown by the wind, and gets taken away as dust. Trees also cool the surrounding air as they transpire (evaporate) water from the surface of their leaves, and exhaling Oxygen while pulling in CO2 from the atmosphere.

Over time, with thinning top soil from wind erosion, and without the trees to help hold moisture in the ground, the entire regional climate was slowly being changed. Beginning in the eighth century A.D. the climate started to get warmer, and dryer. At first, the occasional summer drought started to occur more often, and then eventually became a prolonged drought that spanned a century. Collapse did not happen overnight; it actually took about 150 years of worsening conditions before the cities were completely abandoned. It began as an increase in malnourishment and starvation in the poorest parts of the population. This was followed by increased violence as people began fighting and giving human sacrifice over what few crops remained. Eventually, exasperation in a failed system led the remaining survivors to return to a simpler life in small villages.

Could a situation similar to what happened to the Mayans take place in our modern society, full of wondrous technologies? Our current world is much more complex and interconnected that the Mayan civilization. Could our hyper-complex civilization suddenly collapse like a giant pile of sand, as the Mayan’s did? The answer is YES, it is possible. The likelihood and timing of that possibility however, requires more research.

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