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Does Zeno's paradox make sense?
in A Level Maths by Diamond (51,000 points) | 17 views

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Zeno's paradoxes are a fight between motion the lack the lack of it, in other words, motion vs immobility. They postulate that there is motion concealed in immobility and motion is but an illusion as a result of our senses playing tricks on us.

The most famous of Zeno's arguments is the Achilles:

'The slower when running will never be overtaken by the quicker; for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower must necessarily always be some distance ahead.'

This is usually put in the context of a race between Achilles (the legendary Greek warrior) and the Tortoise. Achilles gives the Tortoise a head start of, say $10 m$, since he runs at $10 ms^{-1}$ and the Tortoise moves at only $1 ms^{-1}$. Then by the time Achilles has reached the point where the Tortoise started $(T_{0} = 10 m)$, the slow but steady individual will have moved on $1 m $ to $T_1 = 11 m$. When Achilles reaches $T_1$, the labouring Tortoise will have moved on $0.1 m$ (to $T_2 = 11.1 m$). When Achilles reaches $T_2$, the Tortoise will still be ahead by $0.01 m$, and so on. Each time Achilles reaches the point where the Tortoise was, the cunning reptile will always have moved a little way ahead.

 

by Wooden (715 points)

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