T: 1m/s
A: 2m/s
T: 1m
1.75
1.875
1.9375
1.5
0
1
T: 0.5m
A: 1m
1.75
1.875
1.9375
1.5
0
1
A: 0.5m
T: 0.25m
1.75
1.875
1.9375
1.5
0
1
I could continue this but I would never reach 2 metres, the point where Achilles is set to overtake the tortoise, since if you continue adding fractions with the next power of two as the denominator and 1 as the numerator to the number one, (e.g. 1 + 1 2 + 1 4 + 1 8 … ) you will never reach two. What would happen, however, if the tortoise travelled at 0.01m/s? Achilles would still never catch up! What if the tortoise travelled at 0.001m/s? Achilles could not catch up. What if the tortoise travelled at 0.0…01m/s? The tortoise is travelling so slowly it is not moving, yet Achilles still cannot catch up, therefore, taken to an extreme, this paradox states moving isn’t possible. As movement is one of the seven life processes making a being living, in the limit, this paradox states that nothing is alive! Therefore, Zeno is correct in a sense, however, as demonstrated by my example, the proof of his paradox has a limit. In my example, the limit is 2m. So, what he paradox is stating is that, given the starting speeds, it is impossible for Achilles to overtake the tortoise in 2 metres. However, if you extend the race beyond this limit, it becomes untrue and it has been proven many times that races can be over the limit, for example in the Olympics. Zeno only considers a part of reality by considering only the section of the race before the limit, so Zeno’s paradox is true within the limit, but, as I have illustrated, untrue if the limit is breached. Despite this, this paradox did lead us to realise that finite things can be split infinite times. The concept of an infinite series is used today in finance to work out mortgage payments, which is why they take an infinite amount of time to pay off! So, thanks to Zeno, I apparently must live to an age of 167 just to afford a garden shed! This is a valid way to structure the problem, but it means that Achilles will never reach the point where he overtakes the tortoise, and a conclusion is that we are all actually dead, oh dear.
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