Where did the “rectangle analogy” come from and how compelling is it?
The nature-nurture dichotomy is often illustrated as a false dichotomy by comparing attempts to determine the relative importance of genes and environments to development of a phenotype to attempts to determine the relative importance of length and width to the area of a rectangle. IOW, both are portrayed as futile and meaningless topics to study.
But where did this analogy come from? It is often attributed to Donald Hebb: according to one article, Hebb was once asked “Which, nature or nurture, contributes more to personality?”, and replied by asking (rhetorically of course), “Which contributes more to the area of a rectangle, its length or its width?” This article (Serpell 2013) cited a book chapter by Meaney (2004) to support the attribution of this quote. Yet Meaney acknowledged that many details about this story and accompanying quote are uncertain and inconsistent: “Like all good urban myths, there are multiple versions of this story. The context changes somewhat, but Hebb’s reply remains intact in its piercing brilliance” (Meaney 2004, p. 2). There are other sources attributing this quote, or at least a general version of it, to Hebb as well (e.g. Francis & Kaufer 2011, Coon & Mitterer 2008, p. 79, Silver 2018). But it has also been attributed to William Greenough (Herbert 1997), and other authors will sometimes cite it without attribution (making it seem like they came up with the analogy) (Ehrlich 2000, p. 6, Endler 1973, p. 289). Other authors have also cited it without explicit attribution in order to criticize the argument (e.g. Barnes et al. 2014, p. 28, Sesardic 2005, pp. 52–3). Sesardic (2005, pp. 52–3), however, cites Hebb’s 1980 book Essay on Mind as one of the sources for the rectangle analogy, and the earliest of all the sources Sesardic cites. But the waters are muddy enough here for one article to refer to the story of Hebb saying this as “perhaps apocryphal” (Barth & Kuhlman 2013).
Actually, it looks like the first use of this analogy was by Leonard Darwin in 1913 (Darwin 1913, p. 153).
Anyway, of course, this argument has been criticized already. Mostly the responses (“refutations” depending on who you ask) focus on the distinction between causes of individual differences in a trait and causes of the trait itself. So supposedly while it is BS to separate genetic/environmental causes of a trait (much like separating length/width causes of rectangle area), it is not BS to separate these causes of variation in that trait in a population. One of the critics who make this argument (among others) is philosopher Neven Sesardic. As Gavan Tredoux recently summarized, “Like most well-informed commenters, Sesardic deals with the rectangle argument from the point of view of populations. Given a population or collection of rectangles, we can readily establish which side contributes more to the areas, or whether there is little difference.” Similarly, Plomin et al. (2013), as quoted by Barnes et al. (2014), noted that “if we ask not about a single rectangle but about a population of rectangles, the variance in areas could be due entirely to length, entirely to width, or both.”
But there is also the fundamental fact that the relationship between length, width, and area is multiplicative rather than additive, so area = length*width. So you can’t figure out which is “more important” than the other — unless you take the logarithm of both sides, which yields the equation log(area) = log(length) + log(width) (Sesardic 2005, p. 53). So if we have length = 4 and width = 3, then which is more “important”? Here, log(area) = log(12) = about 1.08, log(4) = about 0.60, and log(3) = about 0.48. Thus, 1.08 = 0.6 + 0.48, so clearly length is more important than width.
Wahlsten (1990) notes that this practice, which is focused on removing non-additive relationships from data before it is analyzed, can distort the actual relationship between variables, rather than actually solving the non-additivity problem:
“The log transform alters the relations among the variables; consequently, transforming the scale of measurement may conceal the relations among heredity and environment, as it might conceal the essence of gravitation.”(Wahlsten 1990) (p. 118)
And on the very next page of this paper:
“If H and E really are multiplicative in a particular situation, a calculated “heritability” is nonsensical and taking the log of the observations may compound this.”(Wahlsten 1990) (p. 119)
