The Prefix Dia-

A good teacher is always aware that there are things they can learn.

One of the ways in which I encourage students to connect mathematics to other topics is by showing how words and morphemes used in mathematics are used elsewhere. For instance, “median” in mathematics refers to a number in the middle of a list, while the median of a divided road refers to the strip of land in the middle.

In one such case, I asked the students in my Freshman Orientation Seminar this summer to come up with some words that started with “dia-“. The mathematical terms “diameter” and “diagonal” came to mind, naturally; non-mathematical terms included “diaphragm”, “diabetes”, and “diarrhea”, the last of which caused more than a few chuckles from the Freshmen.

I’ll confess: Probably based on its similarity to “bi-” and the fact that Romance words for “two” start with <d> (French “deux”, Spanish “dos”, English “duo”), I came into this conversation thinking that “dia-” meant “two”. This also makes sense with the mathematical terms, since the diameter joins two sides of a circle and the diagonal connects two corners.

So when I asked the class, based on this word list, what “dia-” meant, I was surprised when one of them said “through”. Looking back on the list now, I’m even more surprised: There’s nothing about the medical terms they came up with that superficially suggest “through”, either. I recall having had teachers who would have shook their head condescendingly at “through” because,¬†darnit, they know the answer is “two”. Instead, I paused, mulled it over, and entertained the possibility that I was wrong.

Which I was, sort of.

I think the students were also expecting me to chide them for coming up with “diarrhea”. To an extent, I should have seen that one coming; when I do this sort of exercise, I avoid using “circum-” because of the giggling that comes with “circumcise” or “circumcision”. Instead, I was more curious about “diabetes”, so I took a few moments to look it up. The word means “to come through”, and refers to frequent urination as a common symptom (“diarrhea”, meanwhile, means “to flow through”). “Diaphragm”, meanwhile, means “a barricade across”.

Pretty much every word that starts dia- in English started with this sense of “through” or “across” (“dialog”, “diaphanous”, “diaspora”), although some (such as “diabolical” and “diagnostic”) have lost the obvious connection. The only apparent exceptions I can find are “diary” (which comes from the Latin for “day”, and is related to “diurnal”) and “diamond” (which originally lacked the “i”).

By the way, the Online Etymology Dictionary¬†says I was not entirely wrong: While “dia-” in Greek meant “through” or “across”, it was most likely because of the sense of joining two sides or points.

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