Tuesday, 14 January 2014


Most nights I end the day with a lesson, but on some I quiz The Girl on what we’ve learned lately. Either way, though, the conversation usually ends up far from where we started.

Do you remember what a paradox is? I asked her.

“It’s like … that drawing of a hand,” she said. “That’s drawing the other hand, that’s drawing the hand.”

You mean the Escher drawing? I asked, thinking of one I had shown her.

“I don’t know what kind of drawing it was,” she said.

I know the one you’re talking about, I said, and I see what you mean – that drawing was impossible, so it was a kind of paradox. The artist’s name was M.C. Escher.

 “He was Scottish?” The Girl asked seriously. “McEscher?”

I laughed. No, I said – those are initials. And many of his drawings are impossible, so those count as paradoxes. Can you think of anything like riddles, or thought experiments?

“Ooh!” The Girl said. “Like if Pinocchio said that his nose would grow longer. If his nose didn’t grow, he’d be lying, so his nose would have to grow, so he’d be telling the truth, so … you know.”

Perfect, I said. 

“Or like the paper that said that the thing on the other side of this card is false, and the one on the other side of this paper is true,” she said.

Perfect again, I said – I’m proud of you.

“There was somebody you said in Ancient Greece that was really into paradoxes,” The Girl said. “Was it Hero?”

A number of Greek philosophers played around with paradoxes, I said – I think Zeno is the one you’re thinking of. Hero lived much later in Alexandria -- where the greatest library ever was? – and he invented the steam engine, 1,700 years before anyone else.

“That was actually kind of stupid,” The Girl said.

Why? I asked. I thought it was quite clever.

“But they couldn’t do anything with a steam engine!” she said. “They didn’t have … um .. the right fuel?”

Right, I said – unless you have fossil fuels, steam engines aren’t really worth it. But he didn’t know that – inventions are never obvious right off the bat. You remember those record players you saw someone play on television? Thomas Edison invented those, but he pictured people using them to teach or take dictation; he didn’t even think of using them to play music. A lot of things were just invented before people knew what to do with them.

“He invented the light bulb too,” The Girl said.

I know, I said. I wonder if, when he got the idea, a light bulb appeared over his head, and he looked up and said, ‘Hey! That’s my idea!’

“Do you think that before him, when people had an idea, a candle appeared over their head?” The Girl said.


Anubis Bard said...

I've always loved paradoxes. If nothing else, a good paradox is an important reminder that reason and language can lead us into traps if we don't remember that they are imperfect instruments. I think in the long run an insight like that makes for a humbler, but more powerful intellect. So kudos for giving the girl that gift.

Brian Michael said...

I love your conversations with your daughter! What a great Father you are to care so much in sharing the wonders of this world with her! What a quick intellect she has for one so young. Blessings, Fr Brian

Brian Kaller said...


Thanks -- they can be great fun for kids. I also tried to talk a bit about the limits of pure reason, but her nine-year-old eyes were glazing over at that point, and we went to read Harry Potter.

Thank you so much -- glad you're reading. My secret is that I only write about the good nights. :-)