Yesterday I posted to facebook the following dinner conversation that I had with Katie:
Me: Why are you not eating your fish?
Katie: The pieces are too big.
I cut the pieces, but Katie is still only picking at them.
Me: What’s wrong now?
Katie: There are too many pieces!
Within the hour, my mathematical friends commented with a number of associations they made while reading this, as well as suggestions for what to study next with Katie. Someone suggested I turn this into an optimization problem and teach her about Lagrange multipliers to help her solve it. A more abstractly minded person suggested Banach-Tarski. Other mentioned topics included measure theory, set theory, and even thermodynamics! Reading these comments was just as amusing as having the original conversation with Katie. Kids can say deep things without realizing it and adults can then make great connections. I love both!
Can you think of examples where a kid said something without second thoughts and then adults had a deep discussion based on it?