ESHS/HSS Annual Meeting

Measuring Coastlines from Anti-War Research to Fractal Geometry

• In Event: Mathematics in Motion: Equations as Mediators for the Circulation of Knowledge

English Abstract

In the 1940s, Lewis Fry Richardson (1881-1953) faced a complication in his research on the lengths of borders and coastlines. Richardson, a British mathematician and meteorologist, was studying the relationship between border length and propensity for war. This was part of a larger project, driven by his Quaker upbringing and pacifist values, to mathematically model the causes of war with the hopes of preventing future wars. However, Richardson could not get consistent results for the lengths of the frontiers that he studied, a variation of measurements that is now referred to as the “coastline paradox.” Richardson wrote about his challenges in an article that was posthumously published as “The Problem of Contiguity” in 1961. This article was taken up by Benoit Mandelbrot (1924-2010), the “father of fractal geometry.” In particular, Mandelbrot’s 1967 paper “How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension” directly borrowed Richardson’s charts and equations. In this talk, I examine the path of Richardson’s equation from his own research to Mandelbrot’s, taking note of what contexts and considerations moved with the equation and what did not. Richardson developed his coastline research as one aspect of his anti-war research, which stemmed from a lifelong commitment to pacifism, and he researched both borders and coastlines. While Mandelbrot frequently credited Richardson for influencing him (somewhat of a rarity for Mandelbrot), he did not carry the same political commitments that Richardson had, nor did he discuss Richardson’s broader project of pacifist mathematics. How does the movement of this equation accurately represent, or fail to encompass, the ways in which Mandelbrot was influenced by Richardson and the legacy of his pacifist project?

Author

• Abigail Alling Taylor-Roth, University of Chicago