Towards the end of a long train journey from Edinburgh to Leeds yesterday, my 10-year old daughter asked repeatedly “what time is it?, “how long have we got left?” and (of course) “are we nearly there yet?”
Our perception of time inevitably started to drag!
I told her of an ancient philosopher called Zeno, who believed that it was impossible to arrive at any destination because every journey is endless and that I was beginning to think he was right!
Reasonably enough, she rejected this because the app on my phone said we were due to arrive in Leeds at 8.39pm.
“But” I replied “we could go halfway from here to Leeds and have a break. Then we could go halfway from there to Leeds and have another break. We could keep doing that forever and, although we would get closer and closer to Leeds, we would never actually get there because we could always divide the remaining distance by two.”
“That ancient guy doesn’t know what he’s talking about!” she said.
I opened the calculator on my phone and told her to do 2 ÷ 2.
“I don’t need a calculator; it’s easy. The answer is one.”
“Yes but keep doing it. You’ll never get to zero.”
“Of course I will” she said, taking the phone and doing 1÷2 and 0.5 ÷ 2.”See! It’s already getting smaller!”
“Yes but it never gets to zero. Keep going.”
Determined to prove me wrong, she carried on until the train pulled into Leeds with the calculator showing a number with lots of noughts but which wasn’t actually zero.
“I’m right and you’re wrong!” she beamed. “We’re here!”
“No” I said. “That’s the whole point: we’re both right. It’s called a paradox.”
“Yeah, whatever! Now where’s Grandad picking us up from?”