Some time back, I had a bad habit. I would open a cupboard to get something, then forget to close it. My wife was somewhat miffed by this – understandably, because our kitchen had an infestation of moths at the time. So, she found herself having to tell me, again and again – close the cupboard doors!
Okay, I admit it – my previous blog post was published on April 1. The foundations of mathematics are not really under attack, not now. But they were once!
Here’s a famous puzzle: imagine a village barber, who cuts the hair of everyone who doesn’t cut their own hair. Sounds simple enough, but who cuts the barber’s hair?
Infinite numbers are weird. They gnash their teeth against our intuition. They don’t behave how, deep down, we think numbers ought to behave.
That should not be surprising, since our intuition was formed around tiny little numbers like 3.1, 4000 or seven billion and two.
My son asked me a riddle this afternoon – “What goes up but never down?”
I said “An elevator!”
He seemed surprised by my answer, so I said “Voyager I!”
Then he complained that the riddle was so generic, there were millions of possible answers. I asked him if there was some traditional answer I was supposed to give, and he said that he didn’t know of one.