After a swimming lesson we’re walking back past Naughton’s, the pub on the corner of our street. Just then a man opens up the metal trapdoors on the footpath, exposing steps leading down into the cellar which is full of barrels. Lillian is fascinated. She bends over to peer down into the cellar.
“What’s that!?” she asks.
“That’s where they store the beer,” I say.
“I didn’t know that. How did you know that?”
“Well… I’ve lived around here long time…”
“But nobody else knows that.”
“Well, I guess quite a few people do know about the beer cellar” I respond.
“But babies don’t know that when they’re just born,” she objects.
“I guess that’s right,” I concede, noting to myself that even a 6 year old can come up with the theory of the mind as starting out as a tabula rasa waiting to be impressed by knowledge through experience.
Following instructions she brought home from school, Lillian did her first mathematical induction this evening.
If you put two different pairs of socks in a bag, she figured out that you have to pull out three to be sure that you’ve got a pair – because once you’ve pulled out two, you either have a pair already, or you’ve got one from both pairs, so the next one must match one you’ve already got…
If you put three different pairs of socks in a bag, she figured out that you have to pull out four to be sure that you’ve got a pair… 4 pairs and you need to pull out five…
So you always need to pull out one more than the number of pairs in the bag…
Lillian is just back from two weeks in Taiwan and Japan with her grandparents.
This evening she wanted to do some coloring in. We download pictures-for-coloring-in from the internet – easily findable via Google.
“What sort of pictures do you want?” I asked.
“Um… what about something a bit different… something like…”
She thought hard for a moment. Then –
(Eventually we settled for sea shells. )