"Finally got it" aka "what it really is" is always an arbitrary interpretation. Why not view it as a finite cousin of 2-adic numbers? The article doesn't even mention modular arithmetic.
Here, "finally getting it" means going from "the way computers represent negative numbers, chosen to make the math work out" to "the way computers represent negative numbers, chosen to make the math work out, but I poked around with a few examples."
Also, a monad is just a monoid in the category of endofunctors, so I’m not sure why when people are trying to learn about them they need any more than that. ;)
When you advertise your article as helping your readers "finally get" a concept, then giving them "more than that" is precisely what you should wanna do, but also giving them more than the obvious examples that are available to anyone.
Haha! I actually made the connection when viewing the recent Veritasium video on p-adic numbers. They were walking through an proof of how ...9999 = -1, because if you add one to it, it yield zero. I was like, that's just like two's complement, and how you represent -1 by filling the places with the largest representable digit!
Here, "finally getting it" means going from "the way computers represent negative numbers, chosen to make the math work out" to "the way computers represent negative numbers, chosen to make the math work out, but I poked around with a few examples."