by David Kordahl

I’ll start this column with an over-generalization. Speaking roughly, scientific models can be classed into two categories: mechanical models, and actuarial models. Engineers and physical scientists tend to favor mechanical models, where the root causes of various effects are specified by their formalism. Predictable inputs, in such models, lead to predictable outputs. Biologists and social scientists, on the other hand, tend to favor actuarial models, which can move from measurements to inferences without positing secret causes along the way. By calling these latter models “actuarial,” I’m encouraging readers to think of the tabulations of insurance analysts, who have learned to appreciate that individuals may be unpredictable, even as they follow predictable patterns in the aggregate.
Operationally, these categories refer to different scientific practices. What I’ve called a difference between mechanical vs. actuarial models could just as well be sketched as a difference between theory-driven vs. data-driven models. Both strains have coexisted in science for the past few centuries.
Just for fun, we might attempt to caricature the history of modern science in the mechanical vs. actuarial terms introduced above. In the seventeenth century, Isaac Newton proposed a law of universal gravitation, applicable everywhere throughout the universe, which allowed naturalists to imagine that all physical effects, everywhere and for all time, were caused by physical laws, just waiting to be discovered. This view was developed to its philosophical extreme in the eighteenth century by the French mathematician, Pierre Laplace, who imagined that the universe at any particular moment implicitly contained the specifications for its entire past and future.
But in the nineteenth century, Charles Darwin introduced his theory of natural selection, which allowed naturalists to take actuarial models more seriously. Just as hidden order could cause the appearance of randomness, hidden randomness could cause the appearance of order. Read more »



Considered the epitome of genius, Albert Einstein appears like a wellspring of intellect gushing forth fully formed from the ground, without precedents or process. There was little in his lineage to suggest genius; his parents Hermann and Pauline, while having a pronounced aptitude for mathematics and music, gave no inkling of the off-scale progeny they would bring forth. His career itself is now the stuff of legend. In 1905, while working on physics almost as a side-project while sustaining a day job as technical patent clerk, third class, at the patent office in Bern, he published five papers that revolutionized physics and can only be compared to Isaac Newton’s burst of high creativity as he sought refuge from the plague. Among these were papers heralding his famous equation, E=mc^2, along with ones describing special relativity, Brownian motion and the basis of the photoelectric effect that cemented the particle nature of light. In one of history’s ironic episodes, it was the photoelectric effect paper rather than the one on special relativity that Einstein himself called revolutionary and that won him the 1922 Nobel Prize in physics.

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In November 1918, a 17-year-student from Rome sat for the entrance examination of the Scuola Normale Superiore in Pisa, Italy’s most prestigious science institution. Students applying to the institute had to write an essay on a topic that the examiners picked. The topics were usually quite general, so the students had considerable leeway. Most students wrote about well-known subjects that they had already learnt about in high school. But this student was different. The title of the topic he had been given was “Characteristics of Sound”, and instead of stating basic facts about sound, he “set forth the partial differential equation of a vibrating rod and solved it using Fourier analysis, finding the eigenvalues and eigenfrequencies. The entire essay continued on this level which would have been creditable for a doctoral examination.” The man writing these words was the 17-year-old’s future student, friend and Nobel laureate, Emilio Segre. The student was Enrico Fermi. The examiner was so startled by the originality and sophistication of Fermi’s analysis that he broke precedent and invited the boy to meet him in his office, partly to make sure that the essay had not been plagiarized. After convincing himself that Enrico had done the work himself, the examiner congratulated him and predicted that he would become an important scientist.
For me, a highlight of an otherwise ill-spent youth was reading mathematician John Casti’s fantastic book “