So a Quaker Gets in a Fight…
Big Whirls have little whirls that feed on their velocity
and little whirls have lesser whirls and so on to viscosity — Lewis F. Richardson
This articles target mathematician is Lewis F Richardson, one of my favorite mathematicians because he emulates the thesis that I presented in the last one: Mathematics is a human activity and is affected by economics, philosophy, politics, history, etc.
Richardson said the above quote when he was doing meteorology research and noticed the fractal nature of storms (click the link below if you need a reminder about fractals from the first article).
But he stopped his work when he discovered that the British Air Force was using his research to develop chemical weapons, but he took it a step further and destroyed the rest of his research on weather patterns. Why did he do this?
Richardson, born in 1881 in the UK, was a Quaker. His pacifist upbringing affected his scientific work and mathematics, influencing him to not only destroy all of his weather research, but it also impacted his mathematical theory of war.
Being born in 1881, by the start of WWI Richardson would have been 34 giving him years of work in the sciences after he received his Ph.D. in Mathematical Psychology (which uses mathematical modeling in psychological research) from the University of London. His mathematical theory of war developed the scientific study of conflict after Karl Marx introduced Conflict Theory- (claims the conflict comes from power differentials) to the world in 1848 in The Communist Manifesto.
The Theory:
The propensity for war between two nations is a function of the length of their common border.
He used statistics to study the causes of these wars and considered economics, language, and religion. The data led him to develop a hypothesis, that there are many more small fights, in which only a few people die than larger ones that kill many. Given that it was impossible to give an upper limit on the size of the conflict, the propensity for two countries to go to war developed a Poisson Distribution- (a distribution that describes the probability of events happening in a fixed time frame if they occur and a constant rate and are independent of each other). This same relation was also found in gang violence in Chicago and Shanghai. In his research his variable was the number of deaths, so all sorts of conflicts, with the necessity of it being deliberately aggressive, got bundled up together into what he called “Deadly Quarrels”. A death would get categorized into a quarrel based on the time and place, not on how the death occurred, which could potentially skew the data. However, Richardson scaled the data to a magnitude, similar to how earthquakes are measured, so an error of 10% only meant an error of one magnitude.
The one obvious potential issue with the conclusion of the theory is the type of distribution that is developed, it assumes that each event is independent of the others. But what about those events that are retaliation to previous events, like how WWII was in part a retaliation to the aftermath of WWI? But this conclusion is impactful and important today.
A subtly of this theory is the belief that human behavior can be properly quantified in a deterministic way. The specific sort of determinism is the statistical kind, that if you have enough data then it points toward the nature or tendency of the thing being studied. If this is possible, then the guesswork of studying human behavior is removed.
There is in the world a great deal of brilliant, witty political discussions which leads to no settled convictions. My aim has been different: namely to examine a few notions by quantitative techniques in the hopes of reaching a reliable answer”-L.F.Richardson
Back to Fractals
In his pursuit to find a relation between the probability of two countries going to war and the length of their common border, Richardson ran into inconsistencies in the data of countries borders. This conflicting data was due to the Coastline Paradox- The coast/border of a country increases the smaller the tool use to measure it. Simply put a country has a near infinite perimeter, if you continue to half the size the “ruler” you will begin measuring infinitesimal distances. This is essentially Zenos’ paradox. However, in reality, you get to an infinitesimal distance that it doesn’t add anything to the overall distance. But the discrepancies in the data that Richardson had were not at that level of accuracy.
So what is one possible interpretation of this? If there seem to be more small wars than large ones, and the border between countries is nearing to infinity then war, or just conflict, is inevitable.
Beyond the Math:
Why does a scientific study of conflict matter? Because there is a generation, anyone born after 1990, that has never lived in the US without war. We are currently in 9 wars and have been in 13 since the US began the War on Terror in 2001. There has been a 17% increase in hate crimes in 2017 alone and on average a 23% increase in gang homicide since the five years prior to 2012. Those of born post-1990 have been raised in conflict and war as the norm. We consume more violent media now than people used to consume in their entire life and we wonder why there have been record-breaking increases in mental illness among the youth. Gaining an understanding of how conflict, war, and ultimately violence propagates is a step in the direction toward making anti-war sentiments a reality. Going about this in a scientific and statistical way removes the emotion that is often associated with violence. Emotion and connection should be used in studying violence, these are human lives that were taken away from families and friends — often taken away wrongfully — but a decision that is made while emotional is not the best decision.
In the next article, I will be diving into Richardson’s ideas on what can pacify war, and what causes war. However, it should be noted that since all of his work is statistical it is only correlations and not causations.
