In her eminently fascinating book, Carolyn Weber writes about the questions she hurled at a fellow student.  She then observes:

I now understand why the words conversation and conversion are evocative of each other, turning toward each other, yet separated merely by where you are “at.”

(From Surprised by Oxford: a Memoir, p. 82)

https://www.amazon.com/Surprised-Oxford-Memoir-Carolyn-Weber/dp/084992183X