My baby, the finite state machine (2006)
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It amused me (I know, easily amused) that for a while I could end a pointless argument with my daughter by using a non sequitor. You know "But why can't I play for another 15 minutes!?", "There are zeppelins in the sky." "... huh? really? Where?"
Then it amused my wife, after my daughter had identified this edge in her particular state machine, when we had battling non sequitor arguments, "Oh yeah? Zebras are monochromatic!" "So? Water ice subliminates below 5% relative humidity!"
At 19 months (the original article stated this as an age) the evolution of how kids interact and choose to interact changes almost daily. With my kids there was a peak around 3 years of age before things normalized out. Always interesting raising kids.
Sounds like a job for Hidden Markov Models. They model a system in which you can see a state-dependent output (e.g. "I want to play for 15 more minutes!") and there are clever algorithms for guessing, based on a sequence of observed outputs, what the hell just happened internally. Very handy stuff:
Still neat though.
That's not my point. I've raised two. The youngest is 11. There are problems with your suggested approach- it teaches the child that all it takes is a cry and poof mom gives in (we call parents that are suckered in by the crying "well-trained" by their children); it doesn't solve the problem. In this case The Problem is "OMG THIS HAS NEVER HAPPENED BEFORE AND IT HURT AND NOW I'M FREAKED OUT" - at this point it's not about the pain, it's about being freaked out. Mom appears to have tried treating and comforting and it just didn't work. Mom figuring out that a state reset was necessary is brilliant. It's not like she put the kid in the crib and walked away for an hour (which, btw, is perfectly acceptable when the child Just Won't Quit.)
This is parenting genius. It's really not much different than the approach my friend took: kid gets hurt (bump, bruise, scrape, cut, etc), cries ... so dad gives a hug, does his Magical Wave over the injury, blathers some incomprehensible Magic Words and poof kid stops crying. Psychology, plain and simple.