The Nonsense Math Effect
Please insert the phrases “money manager,” “hedge fund,” “large pension plan,” and “underperformance” at will throughout this piece.
Mathematics is a fundamental tool of research. Although potentially applicable in every discipline, the amount of training in mathematics that students typically receive varies greatly between different disciplines. In those disciplines where most researchers do not master mathematics, the use of mathematics may be held in too much awe. To demonstrate this I conducted an online experiment with 200 participants, all of which had experience of reading research reports and a postgraduate degree (in any subject). Participants were presented with the abstracts from two published papers (one in evolutionary anthropology and one in sociology). Based on these abstracts, participants were asked to judge the quality of the research. Either one or the other of the two abstracts was manipulated through the inclusion of an extra sentence taken from a completely unrelated paper and presenting an equation that made no sense in the context. The abstract that included the meaningless mathematics tended to be judged of higher quality. However, this “nonsense math effect” was not found among participants with degrees in mathematics, science, technology or medicine.
Within the field of pure mathematics, academic writing is expected to be completely transparent to anyone knowledgeable about the mathematical concepts involved. A typical reviewer of a pure mathematics paper will not tolerate a sentence or paragraph for which the meaning is obscure. The same cannot be said about some other academic disciplines. The mathematical physicist Alan Sokal famously composed a paper that was deliberately obscure and nonsensical; he submitted it to the journal Social Text where the editors accepted it for publication (Sokal 1996a, 1996b). This so called “Sokal hoax” demonstrated that there are experienced readers of research publications who will not necessarily react adversely to the fact that a text cannot really be made sense of. Indeed, as Sokal and Bricmont (1998) documented in a book following up on the hoax, obscurity is a hallmark of certain academic traditions associated with terms like postmodernism and relativism. However, these science-bashing genres were not responsible for the abuse of mathematics I referred to above; on the contrary, I found mathematics to be poorly used in fields where the tools of science are held in uncritically high regard. The acceptance and admiration of writing that actually does not make much sense may be found in both camps.