How come the plural of "simplex", in standard mathematical usage, is "simplices", but the plural of "complex" isn't "complices"?

My first thought is that it's because "complex" is also a noun in standard English, so it pluralizes like the English noun, while "simplex" isn't.

(As you may have guessed, I'm reading something that mentioned simplicial complexes.)

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That's probably it. More specifically, it's that mathematicians coining the terms didn't really pay attention to linguistics, and used the simple English plural for "complex" they already knew, but looked up the proper plural for "simplex".

Hey, at least they didn't come up with something completely New and Stupid™ like "octopi".

I have often wished that the distinction between "complex" and "complicated" was echoed in "simple". Wouldn't it be nice, for example, if one could describe something that was (possibly) complex but not complicated, as "simplicated"?

When we say that a set is partially ordered, we mean that it has a partial ordering, no? And likewise, totally ordered sets have total orderings. Shouldn't it be the case, then, that a well-ordered set has a "good ordering"?

Interesting thought, Mark. But you could go the other way and describe something as "comple".

And then, as I think about it... I think the most appropriate choice has been made all along.

Exactly right, Jonah. And if you're dealing with a countable set, it should be "fewer than or equal to."

I turned in an algebraic topology homework set with "complices" all over it once.

I also put in entirely gratuitous references to the Hairy Ball Theorem.

The grader actually drew eyebrows on that one.

...thus making it into the Hairy Eyeball theorem.

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