As an undergraduate, I once went to a talk in psychology that was also attended by a prominent professor of psychology. The speaker flashed up a slide with some math, and almost immediately, while I was still trying to make heads or tails of it, the professor said: “Now that’s clever.”
The compliment was directed at the speaker, of course, but I was impressed by the professor who’d managed to parse, understand, and evaluate the dense math within seconds. “He must be terribly smart,” I thought to myself.
A new study by Kimmo Eriksson, published last month in the journal Judgment and Decision Making, suggests that I’m not alone when it comes to a certain awe for math and the mathematically sophisticated. The problem is that the mathematically unsophisticated can’t necessarily differentiate clever math from “nonsense” math.
Erikkson asked 200 participants with postgraduate degrees in a variety of disciplines to evaluate the abstracts of two scientific papers, one from evolutionary biology and the other from sociology. For each participant, one of the two abstracts was selected at random and appended with an extra sentence of totally unrelated math:
Neither abstract referred to sequential effects or had factors that corresponded to the variables in the equation. “The manipulation,” wrote Erikkson, “amounted to inclusion of meaningless mathematics.”
Nonetheless, participants rated the abstract with added math significantly higher than the abstract without math when it came to the quality of the reported research. (Remember that the math was randomly assigned to either abstract, so this effect reflects an advantage for the added math, not for either abstract on its own merits.) The author calls this the “nonsense math effect.”
But not all participants were equally susceptible to the allure of nonsense math. Participants whose postgraduate degrees were in mathematics, science, or technology actually trended in the opposite direction, with lower ratings for the abstract containing nonsense math. Those with degrees in the humanities, social sciences, or education, however, were suckers for the math, with those whose degrees were in medicine falling somewhere in between.
Were those participants duped by the math stupid or merely gullible? I suspect they were neither. When it comes to science, non-experts often have the experience of not understanding something and of deferring to those with greater expertise. So it’s not so surprising that participants who didn’t understand the math or its connection to the content of the abstract might have attributed this to their own ignorance and not to the researchers’ incompetence. “If I knew more math or evolutionary theory or sociology,” they might have thought to themselves, “this last mathematical bit would make perfect sense.”
But my guess is that many participants didn’t even bother to make sense of the variables or puzzle over what “sequential effects” could refer to – they simply glossed over the equation as “fancy math that I’m unlikely to understand." I’d call this lazy rather than stupid: an unfortunate symptom of a broader cultural attitude towards math as something arduous and reserved for those with special, innate talent.
I still have a certain awe for math and the mathematically sophisticated (in fact, I’m happily married to the speaker of that psychology talk I attended all those years ago), but I’m less inclined to make an automatic inference from “mathematical” to “smart,” or to think of mathematical ability as fixed and innate. Like any claim, a mathematical statement can be useful or irrelevant, insightful or dull. Sometimes it just takes a little thought and expertise to figure out which.
Tania Lombrozo is an Assistant Professor of Psychology at the University of California, Berkeley. You can follow more of what she's thinking at Twitter (@TaniaLombrozo) and at NPR's 13.7: Cosmos and Culture, where she typically blogs on Mondays.