Zeno's Paradoxes

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Introduction and Rationale

“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.” - Aristotle1

Zeno of Elea was a Greek mathematician and philosopher who was known for

his stimulating paradoxes that tried to prove what some might believe impossible.

Zeno’s paradoxes, in some form, have been the base for almost all of the theories

generated about space and time and infinity since his time to our current one, such as

Tomson’s Lamp. His ideas and principles influenced Greek philosophers such as

Aristotle to observe the world in a different, more mathematical way. One of his most

famous paradoxes was
…show more content…
This is a clear example

of a day to day paradox that we encounter and do not stop to think about it. Its

principles are the same as Zeno’s.

In this paradox, consider a lamp with a switch. The switch enables to turn the

lamp on and off. Thomson started at a time 0 by switching the light on and at the end

of one minute turned it off. Now he took halve a minute to turn the light on again and

a quarter of a minute to turn it off. This continuous motion creates an infinite

sequence. The graph below illustrates this idea;

Whereas, the sum of the infinite series is two minutes.

Thomson aim with this experiment is to answer the following question: after

two minutes is the lamp switched on or off? On and Off are represented in binary

form as 1s and 0s, respectively.

JuliaPaes Barreto Sampaio Modiano

Candidate Number: 000461-0071

Time (mins) 0 1 1,5 1,75 1,875 1,9375 2,125 2,26875 2,4125

On or OFF (1 or 0) 0 1 0 1 0 1 0 1 0

Thomson 's Lamp

011.51.751.8751.93752.1252.268752.4125

Time (mins)

By looking at the graph we are able to see that at time 2 we are not able to see if

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