Friday, September 28, 2007

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…
_

17 comments:

Mary Witzl said...

I first encountered this tale in Japanese, at work. Two of my Japanese colleagues did their damndest to explain it to me using all sorts of clever words and strategies and I finally got it -- sort of -- but my poor colleagues' teaching ability had been truly challenged. My inability to readily grasp this wasn't due to a language failing on my part; it was a logic problem. To this day I blush to remember.

Kim Ayres said...

Give me a bunch of kitchen utensils, or if in a bar, a few glasses and a packet of peanuts and I can explain just about anything...

Andreas said...

Kim,

thanks for the warm welcome and the comment on my blog. As you may have noticed (or not, as my site is in German language only ;-)), my son is also a bearer of the famous 47th chromosome. Of course that's why I stumbled upon your blog.

But it is not the main reason for me regularly returning to your pages (though your post "Losing my religion" really struck a chord, and I had to put a quote from it on my "About this blog" page: http://einsmehr.kilu.de/?page_id=5 Yes, even in English ;-)).

It's the way you think, the way you write, and your humour that I really appreciate. Keep on going your way, whatever you like to call it, normal or not so normal.

Andreas

P.S.: Thanks for the comment regarding usability of my pages with IE - I had not realised this before,but you were right, I'll have to check this out.

Eryl Shields said...

So glad to hear your first class went well.

Perhaps one evening we can spend some time in a bar - with peanusts and vodka - and you can explain the whole notion of paradoxes to me. They seem to be constructed for no other reason than for people to discuss how to solve them. I definitely did overtake several car shaped tortoises on the way to uni the other day. I was crap at logic.

Mary Witzl said...

Some day, Kim, I'll buy you a few beers and a bag of peanuts and we'll see how well you do explaining this to me. I suspect my brain's logic components are still stuck on the brain assembly line somewhere, along with my directional skills, going around and around in an endless circle, sadly unclaimed.

Jeff said...

Kim

Glad to hear class went so well as I knew it would.

In regards to the rest of this post and your explaining with glass's at the bar.......it would take a whole lota pints my friend.

Peace

Sam, Problem-Child-Bride said...

There was too a Dirty Knees!! He's famous for saying "Look then upon the state of a man's sandals to learn what kind of a man he is. Ignore his knees completely."

Glad the class went so well, Kim.

Tom said...

An oldie but goody:

In the high school gym, all the girls in the class were lined up against one wall, and all the boys against the opposite wall. Then, every ten seconds, they walked toward each other until they were half the previous distance apart. A mathematician, a physicist, and an engineer were asked, "When will the girls and boys meet?"

The mathematician said: "Never."

The physicist said: "In an infinite amount of time."

The engineer said: "Well... in about two minutes, they'll be close enough for all practical purposes."

Here's future classes and bigger questions.

Carole said...

I have never heard of Zeno's paradox before and now that I have, ackkk... Racing has nothing to do with distance, it has to do with speed and endurance. Are philosophers just magicians in disguise. Because I think you just used sleight of mind on us.

Kim Ayres said...

Andreas - thank you for your warm words, they are really appreciated. I suspected there might be a DS connection from some of the links on your blog. I've added you to my links :)

Eryl - Paradoxes are a bit of fun when you fancy a vertigo-inducing mental exercise, but Xeno's paradox actually has quite profound implications for philosophy.

If you can start off with sound premises, and go through completely logical steps, and still end up with a patently false answer, what does that actually say about the use of Reason, the cornerstone of philosophy?

Mary - I notice that both you and Eryl mention the pub option rather than a coffee in a kitchen...

Jeff - or coffee - I'm particularly difficult to shut up when I've had a double espresso

Sam - I stand corrected :)

Tom - that reminds me a bit of another joke:

An engineer, a scientist, a mathematician, and a philosopher are hiking through the hills of Scotland, when they see a lone black sheep in a field.

The engineer says, "What do you know, it looks like the sheep around here are black."

The scientist looks at him skeptically and replies, "Well, at least some of them are."

The mathematician considers this for a moment and replies, "Well, at least one of them is."

Then the philosopher turns to them and says, "Well, at least on one side."

Carole - here's another to make your brain spin:

"The sentence below is false."
"The sentence above is true."

Eryl Shields said...

Perhaps it says that reason, being just another human construct, must be used with caution.

I'm really trying not to quote Nietzsche here!

Amy said...

Glad your class went well. I know you must be a great prof. I wish I could sit in the class.

SafeTinspector said...

I thought they were bombarding the tortoises with arrows that logically could never hit the buggers?

Kim Ayres said...

Eryl - it's true - it's very difficult not to start quoting Nietzsche once you've read him.

Amy - "prof" is a bit of an over description for an adult evening class tutor, especially coming from a real "prof". I'm sure you'd love the class though.

SafeT - it was clearly a dangerous place being a tortoise in close proximity to a philosopher in Ancient Greece

PI said...

Glad it was good. I wondered about the heel too. I can't really grasp it at the moment as I'm trying to work out why I'm unavailable from some comment boxes.

Colonel Aureliano Buendía said...

Either the turtle is getting faster or Achilles is getting slower, but I bet Achilles passes the turtle at the 90 yrd line.

Kim Ayres said...

Pat - that's probably just Maroon's - he uses Haloscan for his comments and sometimes it jsut wanders away for a bit. Usually comes back though.

Justin - I like the new title - very Latin American Dictatorish. Bueno.