Measuring the transition to disaster

-May 17, 2013

Disasters occur when disease spreads so far that it can’t be contained, when the electromagnetic fields of the brain lose order and cause a seizure, when clouds convert from fantastic puffy shapes to towering thunderheads that emit tornados across the plains, and when economies switch from boom to bust.

Figure 1: Tornado emerging from a thunderhead (photo courtesy of NOAA).

The transition from tranquility to disaster is also like water turning to steam.

Have you ever put a cup of water in a microwave for a few minutes? Plenty of time that it should have boiled, but didn’t? Then you reach in to remove the cup and, at the slightest jostle, the water bursts into a boil. What has happened is that the water reached a temperature above the boiling point without making the transition to steam: it superheated to a meta-stable fluid state and the tiniest perturbation to the system caused a dramatic change.

The same thing happens in economic meltdowns, but since economists study them rather than physicists and engineers, boom-to-bust transitions aren’t well understood. (I’m kidding. Kidding! Economics is impossible because if anyone ever solved that puzzle, the whole system would change by virtue of that person’s buy/sell actions.)

It is possible to see disaster coming.

Certain warning signals  indicate lack of stability even when a system appears calm.

The earliest warning sign is human obliviousness in the form of over-approximation.

In analyzing complicated systems, like weather, fisheries, spread of disease, and economies, people have to make approximations to make progress. Some approximations are better than others. Assuming that a system is in equilibrium when it’s not can be devastating.

Some systems are never quite in equilibrium. The equilibrium state of a bicycle is lying on its side. The equilibrium state of something that is alive, is dead. The equilibrium state of an economy is… unknown, but probably most resembles the various forms of feudalism that people endured for the vast majority of the last 10,000 years.

To make progress in analyzing complex systems, we think of local, rather than global, equilibrium; temporary steady states. Hopefully, we do so with eyes wide open because when we assume that systems on the precipice of transition are in equilibrium, we make big mistakes.

Critical Slowing Down
The first indicator of impending doom (I mean, transition) is that a system seemingly in equilibrium takes longer to recover from small changes. A certain stock climbs in value and after an adjustment caused by stocks in a separate sector, its price doesn’t recover. You feel perfectly healthy, but you can’t kick that cough. You bump a cup of water in a microwave oven…

Mathematically, critical slowing down is expressed as an increase in the system’s autocorrelation. Autocorrelation is the average of the product of the current state of the system and its past states. As the time delay between states decreases, autocorrelation increases in systems about to go bonkers.

Figure 2: Critical slowing down is indicated by delayed recovery from small system changes (Copyright Ransom Stephens).

Temporal resonance and flicker
Flicker is another indicator of instability, a prelude to disaster: rather than two states coexisting, the system flickers between separate states. The calm before the storm.

Spatial resonance
The next indicator is spatial resonance. Severe thunderstorms are presaged by dense clouds forming in separate regions of a plain at the same time.

Economic bubbles occur shortly after separate financial markets react to a given stimulus in the same way at the same time.

Spatial and temporal resonance are usually evidence of correlation. Two effects of the same cause. Stock market crashes are increasingly caused by separate groups of traders using similar algorithms. It’s no big deal if one investment firm dumps a bunch of stock, but if they make that decision based on an algorithm with properties shared by other firms, then they all dump the stock at once and generate a crash.

Loading comments...

Write a Comment

To comment please Log In