Any situation can be made humorous (or more so, if it's already funny) by the addition or subtraction of pants or monkeys. At least, so said a dear friend of mine several years ago. I'm inclined to believe him.
As far as I know, there is no mathematical object known as a monkey; until last night, I thought the same was true of pants. As this nomenclature is due to W. Thurston, it has been suggested that they should be called Thurstonian pant-pairs.
A colleague of mine has written a paper on the subject.
Heegaard Splittings and the Pants Complex