A Nontrivial Manifesto

Abstract

D got strange looks on his first visit to a bar in Minneapolis. My English friend, on his maiden voyage to the States, had stumbled upon one of those little linguistic divergences between the colonies and the mother country. What Americans refer to euphemistically as a “bathroom,” Britons unabashedly describe by the direct “toilet,” and Dan had asked some Yanks for directions to the latter. A first encounter with this difference of dialect can be startling to our naive American ears. Words that seem natural to one person can have an unintended effect on the uninitiated. One instance of this same problem among physicists is far less benign than Dan’s mishap; it causes unnecessary frustration and impels bright students to leave our field: our flippant description of just about anything as “easy,” “simple,” or “obvious.” And then, there is the T-word. Flip through an average textbook or article, and you are likely to come across one of these insinuating taunts: “Obviously . . .,” “After some simple algebra . . .,” “An easy derivation shows . . .,” “It should be clear that . . . .” A student reading the book for the first time may not find the derivation in question nearly so clear as the subtext: “If you don’t understand this immediately, your ineptitude for physics must surely exceed that of a rutabaga.” However, no word in the physicist’s vocabulary exudes more contempt and scorn than the obnoxious “trivial.” We use this word with reckless abandon: “The proof is trivial.” “Trivial algebra yields . . .” “I assigned just a few trivial problems this week.” No other word better exemplifies how the jargon of our trade can be so condescending. I will grant that unlike the other terms I have just indicted, “trivial” can have a technical mathematical meaning: the uninteresting solution to a differential, matrix, or other equation. However, most of the times we invoke this word, we have no such excuse, and even in those technical contexts we can come across as pompous. Others before me have pointed out the pitfalls of this parlance. Richard Feynman wryly observed, “Mathematicians can prove only trivial theorems, because every theorem that is proved is trivial.” The offending words have even inspired a tired genre of conversation among us students, as when a friend in my research group recently observed, “If you are a professor and you don’t know how to work out the algebra, you just say ‘it’s trivial’ and the class won’t ask you about it.” There is an irony, though, in our adoption and usage of the word. My predecessors here at Oxford, from the university’s beginnings until around 1550, spent their first year among these dreaming spires studying the “trivium.” That course consisted of the easiest three subjects (in their minds) of the liberal arts—rhetoric, logic, and grammar—and our present word “trivial” was derived from its name. After completion of the trivium, medieval pupils graduated to the more challenging “quadrivium” of music, astronomy, geometry, and arithmetic. How funny that it is this last discipline that we now love to mock with the T-word. In 1500, arithmetic was the very definition of nontrivial.