Wikipedia "occasional" word of the day: involution

At an all-day meeting today, one of my colleagues used the word "involution", which made many a brow furl. What was that? What does that mean? How's that?

Three of us headed to Wikipedia for the translation and had a good time. The definitions led to many more raised brows and chuckles:

• An involution is a function that is its own inverse, so that f(f(x)) = x for all x in the domain of f
• Any involution is a bijection.
• Examples of involutions include: identity map, circle inversion, the ROT13 transformation, and the Beaufort polyalphabetic cipher.

We know so little...