Two or three weeks ago I wrote a piece about the complications of Hispanic surnames.

Despite the complications, there is definitely something appealing about taking your surname from both parents, not just from the father. The problem, of course, comes up in the next generation: what do you do then? Do the names have to get longer and longer? You can end up with names like Pablo Diego José Francisco de Paula Juan Nepomuceno María de los Remedios Cipriano de la Santísima Trinidad Ruiz y Picasso, whom you probably know better as just Pablo Picasso — but that shortening misses the stateliness of his entire name.

It turns out that there is a fascinating connection here with mathematical theorems! By a great serendipity there happened to be a paper in last month’s issue of the Journal of Humanistic Mathematics titled “The Surname Impossibility Theorem,” which not only ties into the multiple surname question but also relates very explicitly to Kenneth Arrow’s Impossibility Theorem, which I would normally be teaching this week. I did so every summer but not in 2020 because of… well, you know why. No sophomore cohort this summer at CSA, alas. Anyhow, the basic concept here is that we develop a set of criteria that a perfect X has to have — where X is a voting system, a surname system, a grading system, whatever — and then end up showing that it is mathematically impossible to satisfy all those criteria. Remind you of Heisenberg? Or Gödel, perhaps? Part of the astonishing power of mathematical reasoning is that one can prove that a certain proposal is actually impossible — not just difficult, not just unlikely, but absolutely, incontrovertibly impossible. (OK, in each case it does depend on accepting certain pre-existing conditions — postulates or axioms — and if you can convincingly reject one of those the proof is called into question. The most famous example is non-Euclidean geometry.) I wrote a bit about Arrow’s Theorem last year; Arrow proved that no voting system, not even Ranked Choice Voting, can satisfy all of the small number of requirements that we impose on fair voting; Adam Graham-Squire’s paper on surnames uses Arrow’s approach to draw a similar conclusion about surnames. (It’s no coincidence, by the way, that Graham-Squire has a hyphenated surname.) I’ll summarize his criteria below, but go read the paper yourself; it’s short, informative, and not particularly difficult.

Graham-Squire proposes five criteria for a surname system:

• It should be traditional (consistent with your culture).
• It should be esthetically pleasing and practical (admittedly hard to quantify).
• It should be ancestor-respecting (indicating your heritage).
• It should be sibling-matching (siblings should have the same surname).
• It should be egalitarian (non-sexist, gender-neutral, non-heterosexist).

Naturally we could disagree with one or more of these. The important thing is that we cannot satisfy all of them, so something has to give. Now go read the article.

Categories: Linguistics, Math