Butterfly Effect, The

The case where small causes lead to big consequences. This applies to a system with an energy source which enables events to ripple through it, improving, impairing, or simply changing its behaviour or its fitness for the environment it is in. It applies most obviously in the field of weather forecasting, and was discovered by the mathematical meteorologist Edward Lorenz in 1959.

While experimenting with a computer programme designed to supply forecasts for months ahead, Lorenz set out to verify a simulation that he had already run, and to extend it further into the future. For the new run, he fed back into the computer a set of numbers which he assumed to be identical to the set he was already using, since he copied them off a printout. Then off he went for a (now famous) coffee, leaving the computer to chunter away to itself with this re-entered data set. But when he got back, he found something surprising. The first couple of days of modelled weather were reasonably similar to the original, but then they departed from it and eventually became completely different. The reason was that whereas the computer was working with numbers to six decimal places, the printout just showed the first three decimal places. Although the difference between the numbers was extremely small, it radically altered the result. Evidently, in a chaotic system such as the weather, small differences can have big consequences. Lorenz had demonstrated sensitive dependence on initial conditions.^B20

He published his results at a scientific meeting in Tokyo in 1962, and then went on to develop the idea. Ten years later, at a meeting in Washington DC in 1972, he presented a paper, “Does the Flap of a Butterfly’s Wings in Brazil Set off a Tornado in Texas?” and the image has stuck.^B21

The weather is a good way of demonstrating the butterfly effect because it is chaotic. It can produce almost any result within a certain range and still be weather. Complex systems—antelopes, for instance—do not have this quality. On the contrary, they sustain a high degree of homeostasis: they must maintain a more-or-less unchanging temperature, metabolism and form under all circumstances short of catastrophe (being eaten by a lion). But even antelopes can fail to prevent chaos entering their systems. Grazing in the wrong place, near where some lions are hiding, or being pricked by a thorn which causes an infection, will probably not prove fatal, owing to the antelope’s powers of prevention and recovery—its resilience—but it might.

Little events can ripple through an orderly complex system and change it completely. Chaos can break into even the most orderly system, giving the butterfly’s wing its slim, but significant, chance.

Here is an example of a small event with big consequences. No complex system is without its weaknesses, but in the early years of the twentieth century, the complex system called Europe had achieved, to an extraordinary degree, qualities which might be seen as ideal in a civilisation, with a strong culture and a strong—though still far from completed—trend of improvement in measures of social justice such as education, social security and political participation.

The future Kaiser Wilhelm II, Emperor of Germany, was born on 27 January 1859. It was a breech (feet-first) birth. At the time, only some 2 percent of babies born in the breech position survived. The greatest risk in a breech birth is that the baby’s head squeezes the umbilical cord running up alongside it, causing it to suffocate. To avoid offence to royal decency, Dr. Eduard Martin, who was in attendance, did not like to raise the Empress’ long skirts, and had to do everything by feel.^B22

When the child was in the birth canal with its head still in the uterus, and with both arms raised above its head, Dr. Martin manoeuvred its left arm down out of the canal, using (as he explained in his report) “considerable force”—that is, enough to tear the brachial plexus in the complex of nerves in the baby’s neck. He then, as was required, rotated the child’s trunk in the birth canal. The only way to achieve this rotation without injury is to use both hands to grip the upper trunk firmly before turning it. Dr. Martin did it by pulling on the now protruding left arm.^B23

The baby was thought to be dead for several minutes following the birth, and modern medical judgment estimates that he would have been hypoxic (lacking oxygen) for at least eight minutes, sufficient to produce “minimal brain damage”, a condition whose symptoms are now well-recognised. It is not associated with loss of intelligence, but with psychopathic disturbances, hyperactivity, loss of attention span and inability to develop social sense or empathy, with the person having little or no understanding of the impact of his behaviour on others.^B24

The young prince’s left arm was paralysed and six inches shorter than his right arm, and the effects of the injury were soon also revealed in his twisted neck. His mother, Vicky, Queen Victoria’s eldest daughter, referring to his “deformity” and “disfigurement”, never came to terms with his injury; she felt revulsion towards him, and lavished affection, instead, on her other children. Prince Wilhelm developed a hatred towards his mother and towards the English in general.^B25

As he grew up he showed symptoms typically associated with minimal brain damage, such as requiring his advisers and generals to participate in a court life that was to a significant extent based on practical jokes. The head of the German Military Cabinet, Dietrich von Hülsen-Haeseler, died of a heart attack while dancing for the Kaiser in a large feather hat and a tutu. He required his advisers to take part in morning gymnastics, which he spiced with pranks such as cutting General Scholl’s braces with a penknife. The British foreign secretary Sir Edward Grey found the Kaiser “not quite sane, and very superficial”. He reminded him, he wrote, of “a battleship with steam up and screws going, but with no rudder”; he could well “cause a catastrophe some day”.^B26

His politics were largely shaped by an appetite for revenge, which his ministers were usually able to ignore. When the German envoy was killed by the Boxer rebels in China in 1900 he ordered that Peking should be razed to the ground. During a tram drivers’ strike in Berlin in the same year, he ordered that troops should move in and gun down at least 500 people. In 1919 (after his abdication) he wrote that no German should rest until all Jews on German soil had been exterminated.^B27

His one consistent pleasure was the company of tall young men in the army. He explained that it was in his regiment that he found his family, his friends, his interests, everything which he had previously missed. In their daily company he was able to reduce each complex issue to a “purely military question”.^B28

In retrospect we can always see the big-brained reasons for big events: the rivalries between the empires of that time, the excessive confidence that comes when small nations join up into an empire, the knowledge learned from industry about how to organise large numbers of men, the implications of German dominance of Europe’s North Sea ports and trading routes, the trouble with the ailing rivals—the Austro-Hungarian and Russian empires—dangerously played-out in the Balkans. Realpolitik can explain everything backwards.

On the other hand, these were states which had achieved an astonishing degree of accomplishment, along with links of family, friendship and passport-free travel in a diverse European culture described and celebrated by critics such as Stefan Zweig. There is no reason to believe that the First World War would have taken place without the lifelong and anachronistic commitment of the Kaiser to that end. And there is no reason to believe that this commitment would have occurred if it had not been a breech birth, or if the doctor has been sufficiently skilled to deliver the baby without injury, or insufficiently skilled to achieve a live birth. Or if he had felt it was all right to raise the Empress’ skirts.^B29

The series of events set in train by that failure is arguably the most catastrophic in human history, decisively shaping the modern world, and giving its problems a rootedness; even a sense of being under a curse. The war of two halves that followed—and the revolutions and genocides that came with it—traumatised our civilisation. Some butterfly . . .

Evidently, a high degree of sensitivity to initial conditions is a quality that can shape history. But there are two points to note about it before finally abandoning all confidence in the idea that there is any point in planning ahead. The first is that a resilient system—a complex system as distinct from a merely chaotic one—is usually capable of dealing with disturbances and maintaining its stability, its homeostasis, for a long time. That is what resilience means.

The second point is that even a resilient system can indeed be destroyed or transformed by an event which hits the spot—which happens to have the right leverage. That maximum result from a minimum cause may be exactly what we want when working with a system: it is the ideal aim of effective systems-thinking. But, if it hits the wrong spot, it can travel like a tsunami, and destroy comprehensively. Maybe if the system in question were perfectly resilient, that would not happen. But perfection is at risk from outside events which, on arrival, disrupt it. Behaviour which had previously been good—a polite reluctance to lift a lady’s skirt even in an emergency, for instance—can, if luck is bad enough, leave even resilience overwhelmed.

Resilience is the stability which confers life and form in a living world which otherwise, as the victim of chaos, predation and bad luck, would never have got anywhere. Most little random disturbances—like most little random mutations—don’t get anywhere. But sometimes they do, with good or bad consequences, however well the system may be defended against them. It is the weak point in resilience: it has a gambling addiction—the Butterfly Defect.

Related entries:

Gaia, Connectedness, Emergence, Entropy, Unintended Consequences.