trochee

Stories from one of my advisors regarding her very bright 2 year old, from her, but with pointers updated to LJ identities, where relevant and semi-anonymized elsewhere.

advisor E is grading my homework. She is chatting with bright 2-going-on-3-year-old T while she is working.

"Ah, T, see,", she says, to T and to her husband, "I've finally found someone who's more of an overachiever than me: [

trochee]. Where I was looking for:'yes, it's infinite', he writes 'yes, it's infinite: proof by contradiction' and then includes two pages of unassailable logic."
"Is

trochee one of [

trochee-and-

exterra]?" asks T., who doesn't miss a trick, but treats the two of us as an undifferentiated older-than-him mass of human-who-likes-him.
"Yes," said E, "[

trochee] is someone where I work too."
But T isn't done. "What's a contradiction?" he asks.
"That's when I say two things that can't both be true," responds E. She gives him a few examples: "T is upstairs and T is downstairs."
T catches on fast: "Like when I say 'I have pasta on my plate and I don't have pasta on my plate'?".

Somehow, at two and seven-eighths, T has already grasped prop logic by the handle end. He's even got the culture: examples should use p's. p∧¬p is ...well, yes. A contradiction.

If I could tell him how many undergrads I've met who can't grasp this, I'd ... be upstairs and downstairs at the same time, or something.