For everyone who blanches at binomials, cringes at coefficients or detests derivatives: you’re not alone! Even scientists may avoid math if they can, according to a study on the effect of equation density on the likelihood a scientific publication will be cited by other scientists. (Original paper here) The effect is small; for every additional equation per page, a paper is 5% less likely to be referenced. Still, the result is notable because it was observed in the physics literature, a discipline generally associated with mathematical sophistication. A similar finding has been observed for biology papers, but for some reason there was less surprise that biologists avoided mathematics.
We equate math with universal truths like 1+1=2, but math is often expressed in a strongly context-dependent way via ad hoc notation. Research publications often introduce novel notation precisely because their originality. Authors have to invent names and symbols for what they are representing with their equations, or else overload existing symbols with yet another possible meaning. Consequently, there’s a limit to how much understanding can transfer from the math in one paper to the next. It’s like reading a foreign language without ever acquiring a significant vocabulary; you never stop needing to look up terms in the dictionary. Or like reading English and having to remember whether the author is from the US or the UK to know what ‘biscuit’ means.
If our own scientists have trouble reading each others’ math, how will beings from another planet fare? That question is implied by the movie Arrival. It’s an excellent bit of filmmaking I would strongly recommend experiencing for yourself. The challenge of communicating across language barriers with minimal common experience is central to the plot of the film. The task is posed to linguists but also physicists on the assumption that math and science are the universal language. While the movie doesn’t really unpack the cultural context of math specifically, it does explore the ways that culture and experience generally shape our communication and perhaps more importantly what we don’t communicate because we just assume it. Suffice to say, it feels very relevant at a time when those of us in the US are reconsidering just how much ground we actually have in common.
Whether it’s for math, politics, or first contact with aliens, communication requires clarity. That includes a clarity in your reasoning as well as how you express your conclusions. There’s a brief scene in Arrival where the head linguist tells a story about the origin of the word ‘kangaroo’ to persuade an army commander to let her operate a certain way. After he agrees and leaves, she admits that the story is false but it ‘proves her point.’ From a film with plenty of engrossing visuals and gripping dramatic developments, that moment has stuck with me most strongly. It’s a familiar tradeoff between simplicity and accuracy. Yet it might also be a tradeoff between short term communication success and long term distrust. It’s left me wondering what convenient ‘truths’ I rely on and what the cost may be down the road.
Do you encounter this sort of rhetorical shorthand in your discipline? How do you handle it?