'Achilles and the Tortoise' Paradox

This is an ancient paradox thought up by this wierd guy called Zeno, who lived circa 450 B.C., in Elea, Greek. Here it goes:

Achilles is to race the tortoise over 100m. Since Achilles can run 10 times faster than the tortoise, the tortoise is given a 10m head start. The race starts and Achilles set of in pursuit of the tortoise. In the time Achilles takes to cover the 10m to reach the point where the tortoise started, the tortoise covered 1m, and so is 1m ahead. By the time Achilles covered the extra 1m, the tortoise is 1/10 m ahead. And when Achilles reached that point, the tortoise is 1/100 m ahead, and so on, ad infinitum. Thus, the tortoise will be in the lead forever, albiet by smaller and smaller margins; and the great Achilles can never overtakes his opponent to win the race.

********

Real life application of the above argument:

Suppose your mouse pointer is on the 'Back' button of your Internet Explorer and you wish to click on it get out of this irritating, mind-boggling page. You'll 1st of all need to half click the button. And to do that, you'll need to quarter click the page. And so on. In fact, before you can click on the button, you must make an infinite number of ever decreasing fraction clicks on the button.

And if you are sick of this button clicking business and wish close the Internet Explorer, you can't. Because in order to close the Internet Explorer, you've to move your mouse pointer to the 'X' button on the top right hand corner, and before you do that, you'll need to move your mouse pointer half way to the top right hand corner and so on. (Not to mention you still have to click on it. =P)

As Zeno pointed out all that time ago, you simply can't go through an infinity series of stages in a sadly all too finite amount of time. It's in fact, impossible to do anything - logically speaking.

Now try and click the back button. 

 

What's wrong with this argument?

 

From 101 Philosophy Problems by Martin Cohen