Well, I had no idea what the answer was.

But I did know that *evolution* in Greek is εξέλιξη, as an element-for-element calque: both mean “out-twisting”.

And ενέλιξη means “in-twisting”, which should correspond to Latin(-derived) *involution*.

And I looked up the definition of ενέλιξη, and it gave me a bunch of geometrical stuff: ενέλιξη (from the Papyros dictionary):

Στην προβολική γεωμετρία ε. ονομάζεται κάθε μη ταυτοτική προβολικότητα μεταξύ σχηματισμών α’ βαθμίδας και με τον ίδιο φορέα, που συμπίπτει με την αντίστροφή της. Αν μία προβολικότητα έχει ένα ενελικτικό ζεύγος, τότε είναι μία ε.

In projective geometry, an i. is every non-identity projection between first-grade formations with the same bearer, which coincides with its inverse. If a projectivity has an involutionary pair, it is an i.

(Approximate translation, since I don’t know any Greek geometric terminology.)

I then looked up the definition of involution, and it gave me a bunch of geometrical stuff: Involution (mathematics) – Wikipedia

In mathematics, an (

anti-)involution, or aninvolutory function, is a function f that is its own inverse,f(f(x)) =xfor all x in the domain of f.…

2.3 Projective geometryAn involution is a projectivity of period 2, that is, a projectivity that interchanges pairs of points. Coxeter relates three theorems on involutions:

- Any projectivity that interchanges two points is an involution.

I don’t understand geometric terminology in English either, but I hereby decree that they are same difference.