NSF Project: A Pompous Parade of Arithmetic

March 28, 2019 by Charlespermalink

After a much-too-long period without anything new here (I’ll spare you the moving-related excuses), I’m overdue to write a few summaries here of the lab’s newest projects! First up is our NSF grant, which is currently around two-thirds complete, having funded me entirely for the first half of the academic year, and concluding at the end of May. The goal is to produce a book – now around half-finished (the discrepancy between these two fractions is a touch disconcerting) – that details the introduction of statistical methods and, more importantly, the philosophical understandings of chance that were taken to license their use, into biology, from the publication of Darwin’s Origin to the early days of the Modern Synthesis.

It’s important to start out by saying what the book isn’t. The goal is absolutely not to write another history of statistics, even one focused narrowly on statistics in the life sciences. I could do no better than reproducing some kind of poor version of Stigler’s History of Statistics, which wouldn’t be worth anybody’s time. But the story that hasn’t yet been told is a different one, and while it is connected to the technical tools – it certainly couldn’t have happened without them – it moves beyond being an introduction to when various methodologies were developed and how they were first applied to biological problems.

Fundamentally, I started thinking about this project when I became deeply confused by the following contradiction. Evolutionary theory, as it looks in 1859 with the publication of Darwin’s Origin, is a fundamentally non-mathematical, non-statistical theory about the unfolding of the history of life. More or less, when a modern reader comes to Darwin’s book, she finds a fairly comfortable theory, one which doesn’t sound particularly “dated” or dramatically different from the ways in which a contemporary biologist would understand evolution.1 And yet, there is a difference – and a particularly dramatic one – between the evolutionary theory of Darwin’s day and that of our own. For evolution now could hardly be considered without the tools of statistics and probability. Descriptions of populations in mathematical biology are expressed in terms of distributions of traits, and evolutionary forces are described as those causes which change those distributions over time.2

How did this change happen? And how can we square the two apparent facts that today’s biology and Darwin’s are both broadly resonant with one another and yet evidently contradictory in a very important respect? This is, of course, a paradigmatic philosophy of biology question, and I and many others have approached it in a variety of ways, analyzing the use and nature of statistical inferences and concepts of chance across the evolutionary sciences.

What has yet to be done, however, is the subject of this work. The introduction of these methods into biology was accomplished by a dedicated and relatively narrow group of biologists: figures like Francis Galton, Karl Pearson, W. F. R. Weldon (whose bust in the Oxford Museum of Natural History is pictured here), George Udny Yule, R. A. Fisher, Sewall Wright, and J. B. S. Haldane. And this introduction was not performed haphazardly. On the contrary, these biologists had deep and profound reasons – often philosophical reasons, in fact – for altering the theory that they had inherited (pun fully intended) from Darwin.

Such implementation did not happen quietly. The title of the book (or, at least, what I hope will be the title of the book – let’s see if my editors agree) is A Pompous Parade of Arithmetic, so named after a criticism that Weldon mentions having received from an anonymous critic during the often quite virulent debates that unfolded over the last few years of the 19th and first few years of the 20th centuries.3 This debate itself has been the subject of an active cottage industry in the history of biology, a resource to which I will turn extensively in the central portion of the book.

Yet another portion of the story has also yet to be told, and this forms the last few chapters – or at least, I think it will, as I’m only about halfway through writing it at the moment. [Cue the obligatory “you should be writing” meme from academic Twitter.] There’s a general understanding that there were a number of rich, interesting perspectives at work in the biometrical school – the first group to integrate statistics into biology, consisting broadly of Weldon, Pearson, and colleagues – but there is a broad sense that these perspectives were abandoned as the biometricians “lost” the debate over variation and inheritance to the “Mendelian” camp, led primarily by William Bateson, in the first decade of the 20th century. Statistics remained banished until the development of the Modern Synthesis (roughly independently, or so the story goes) re-integrated genetics and statistics over the middle decades of the 20th century. I have a hunch, however, that the extent of continuity from the biometrical school into the early days of the Synthesis is broadly undersold, and I hope to investigate those links in greater detail soon.

Lastly, I should make sure to note that there’s also a portion of the project that’s targeted at providing history of biology materials for secondary and early college students. After having worked with teacher-preparatory programs at LSU and attended the NSTA conference in New Orleans last year (with great thanks to my colleagues Erik Peterson and Greg Macklem), I’m hoping to fill a need that prevents such teachers from easily incorporating history of biology materials into their teaching – namely, the hard work of curating a variety of primary-source excerpts from the authors across this period, and the connection of their issues to contemporary questions in the understanding of evolutionary theory. Thanks to a grant from UCLouvain’s Université numérique (“Digital University”) program, I’ll also be translating these materials into French! UCLouvain will also take charge of hosting the materials on their digital-pedagogy platform.


  1. There are a few places where I think this is false – for instance, in Darwin’s linked discussion of the principle of divergence and the economy of nature. See more in my paper with Daniel Swaim on this topic! ↩︎

  2. Those of you who know the recent history of the philosophy of biology will know that I’m being (intentionally) provocative here. There is a healthy debate over just how to understand these distributions, forces, and causes; more about that in future posts. But suffice it to say for now that I believe that the historical story and the contemporary story are, in fact, deeply linked with one another. ↩︎

  3. I suspect that the critic was William Bateson, but I have no documentary evidence to prove the point. ↩︎
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