## Zeno’s Paradox – ‘Tortoise and the Hare’

25 Feb

#### THIS STOPS ME FROM COMITTING SUICIDE BECAUSE…….Maths is wrong

Generally believed to have been thought of by Zeno of Elea, these are a set of problems to support Parmenides’ ‘all in one’ doctrine especially the notion that motion is nothing but an illusion.

“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.”

Aristotle, Physics VI:9, 239b15

One famous example is ‘Achilles and the Tortoise’. I have changed it to a ‘Tortoise and the Hare’.

‘Tortoise and the Hare’

Imagine straight-line race between a tortoise and a hare.

Assumptions:

• Assume that the tortoise was given a 100m head start
• Assume both the hare and the tortoise are travelling at constant speed and the hare is travelling faster.

[After time period x0] The hare has travelled 100m and reached the tortoise’s starting point. During this x0 time period, the tortoise has moved a certain distance, let’s say 20m.

[After time period x1] In another period of time, the hare has moved 20m and reached the tortoise’s starting position after time period x0. Meanwhile the tortoise has moved a further 4m ahead

[After time period x2] In another period of time, the hare has moved 4m and reached the tortoise’s starting position after time period x1. Meanwhile the tortoise has moved a further 0.8m ahead

[After time period x3] In another period of time, the hare has moved 0.8m and reached the tortoise’s starting position after time period x2. Meanwhile the tortoise has moved 0.16m ahead

Thus, after infinite time periods, the hare reaches an infinitely small distance from the tortoise but never passes it. We know that in real life this is not how it works and the hare would overtake the tortoise. Thus this is a paradox. Listverse.com explains this well (http://listverse.com/2010/05/28/11-brain-twisting-paradoxes/):

JFrater: I will point out the problem with this paradox to give you all an idea of how the others might be wrong: in physical reality it is impossible to transverse the infinite – how can you get from one point in infinity to another without crossing an infinity of points? You can’t – thus it is impossible. But in mathematics it is not. This paradox shows us how mathematics may appear to prove something – but in reality, it fails. So the problem with this paradox is that it is applying mathematical rules to a non-mathematical situation. This makes it invalid.

An interesting paradox that just makes you think about certain things in a little more detail.

Posted by on February 25, 2011 in Random

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### 4 responses to “Zeno’s Paradox – ‘Tortoise and the Hare’”

1. February 25, 2011 at 6:48 PM

Dude this is deep stuff…classic mensa!

2. February 26, 2011 at 7:52 PM

After reading the joke,i needed a poo… x

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