Who's the Philosopher?

"So how did your philosophy class go last night? "

Brilliant! I was on a roll. They laughed, they learned, and they all intend to turn up next week too.

"And your energy held out? You didn’t slump halfway through?"

I didn’t! The first half was run on adrenalin and the second on a really strong cup of coffee.

"This was about the ancient Greek philosophers wasn’t it?"

Aye, Thades, Heraclitus, Parmenides, Dirtinees…

"There wasn’t one called Dirty knees."

Sorry, got carried away there.

"But they enjoyed it?"

Oh yes, especially my drawings on the whiteboard illustrating Xeno’s Paradox.

"What’s that?"

You don’t know the tale of Achilles and the Tortoise?

"Can’t say it sounds familiar."

Ah, right then, imagine this mug is Achilles and this spoon is…

"Not that spoon, I’m using it."

Oh, OK, then let’s say this mobile phone is the tortoise and my bowl of muesli is the finishing post.

"Finishing post?"

Sorry, didn’t I say? Achilles and the tortoise are having a race.

"A man and a tortoise?"

Yes, and Achilles is twice as fast as the tortoise.

"That’s not very fast is it?"

That doesn’t matter. For the purposes of this tale it just makes it easier if we say Achilles is twice as fast as the tortoise.

"If you say so."

Good. Now Achilles, being a generous chap, decides to give the tortoise a head start of nearly half the track…

"Very generous."

…because he figure’s he’ll still beat him.

"Just don’t tell me Achilles is going to have a nap just before he gets to the finishing post because he’s over confident."

No, that’s The Tortoise and the Hare. Different story.

"Oh, OK."

Where was I?

"Achilles is twice as fast as the tortoise and has given him nearly half the track head start."

That’s right. So you would expect Achilles to overtake the tortoise just before the finishing line wouldn’t you?

"As long as he isn’t caught napping, I guess so."

But the fact is he never overtakes the tortoise.

"Why not?"

I’m so glad you asked that. This is what the paradox is all about. You see when Achilles reaches the point where the tortoise was, the tortoise will have moved half as far again. Look – if this mug of coffee has moved a foot across the table, then the phone will have moved 6 inches right?

"Right…"

Now, what happens when Achilles reaches the phone… er, the tortoise… now?

"The tortoise has moved half as far again."

That’s right, and when Achilles reaches where the tortoise was, it’s moved again. And so on, and so on. So logically, Achilles never actually reaches the tortoise, because every time he reaches the point it was, it’s moved on. Brilliant, eh?

"There’s an easier solution than that."

What do you mean?

"If the tortoise doesn’t want to be overtaken by Achilles he just needs to kick him hard in the heel at the point he’s about to pass."

His heel?

"Yes, that’s Achilles' weak point isn’t it?"

Hrmph. Just as well you’re not a philosophy tutor then isn’t it…
_