Tuesday, August 29, 2006

The Zen of Zeno

The Greeks were ace weren't they? The olden days ones, not today's chaps obviously, rotters the lot of them. Forever gabbling away, can't understand a word of it.

Plato says that Zeno was 'tall and fair to look upon' which, I think you'll agree, is backed up by this statueOne member of this rather spiffing club was a bloke called Zeno who came up with a number of irritating Paradoxes that are both obviously wrong and yet more tricky to actually disprove.

My favourite of many years is that of Achilles and the tortoise where Zeno shows that despite being many times faster than the tortoise and with only a short head start to make up it is still impossible for Achilles to overtake our lumbering quadruped.

As Aristotle puts it "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead."

I'm not sure that's a clear as it could be though. Allow me to demonstrate.

Let's say Achilles is ten times faster and the tortoise has ten meters head start. In the time it takes Achilles to run to the tortoise's starting point the tortoise has only progressed a meter - the clever money goes on Achilles at this point, surely? No, think of the odds you'll get on the tortoise for a start!

Death of Achilles; it appears he became rather effete in his last momentsSo Achilles runs the next meter but by this time the Tortoise has made it another ten centimeters. Achilles covers this distance but is now short a centimeter - then short ten millimeters - then one millimeter. In fact every time Achilles reaches the point where the Tortoise was the Tortoise has moved on. Forever. In ever decreasing increments.

Now I've raced Tortoises many, many times and this almost never happens in reality, despite not being as fast a runner as Achilles - but where's the flaw in Zeno's logic? Bertrand Russell couldn't work it out and he was a clever bastard.

One blogger makes an ultimately unsatisfactory, but valiant, attempt to solve the quandary here at Spunkyy thoughts

Incidently, I collect philosophers' deaths - everyone has to have a hobby don't they? My sources say Zeno was killed by the "tyrant of Elea" but it's all a touch too vague for me. I'll probably let you in on some of the more exotic ones at some future time - if it's possible to ever reach that point.

Read more about Zeno here


Mich said...

Since no one ever comments on your philosophy - *philosopher in training*. I would say the flaw is in the idea of the infinite which is a *****y messy thing. It would come up as an exponential wouldn't it... I'm sure phycisits at some point have cheated their way around this problem. It is a classic paradox... so the logic itself would be hard to criticise.

Jim Jay said...

Woop! Five months after posting I gotr a comment - cool.

Well I think the big flaw is the assumption that space and time are infinitely divisable (which is what you're saying I think)

I also think if you take a paradigm shift - stepping outside of the parametres of the question you can make a nonsense of it - but in its own terms Zeno's paradox is a bloody pain.

Incidently, I only thought afterwards but some of my other "philosophy" posts are probably more interesting...

on the relationship between subjective and objective reality, on free will, on tradition, and lastly on death

If you're interested

kyy said...

g'day jim jay,

i've posted a response (see comment no. 2) to some concerns raised about my analysis of Zeno's Paradoxes by 'philosphers_are_boring_fucks' (is that you?), and updated my resolution of Zeno's First Paradox.

Spunkyy, from Myriaden.

kyy 2007-04-02 1716 z+10

Jim Jay said...

Cheers spunkyy, very interesting stuff - I'll need to have a think about it - but 'philosphers_are_boring_fucks' is not me (how disappointing) I could never be so gauche :)