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Solving Zeno's Paradox: Achilles vs. Tortoise Algebra

Dive into Zeno's argument flaws, explore theory of types, and solve Achilles vs. Tortoise dilemma using algebra. Find out time for Achilles to catch the Tortoise!

rebekah-mullins
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Solving Zeno's Paradox: Achilles vs. Tortoise Algebra

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  1. Your Concerns (from quiz) • What (if anything) is wrong with Zeno's argument? • What about the theory of types? Later (minutes) • Is Zeno the sixth patriarch or is he not? • Significance in positioning the Tortoise upwind of Achilles? Later (weeks) • Use ordinary algebra to find how long it will take for Achilles to catch the Tortoise. Right now

  2. Achilles vs Tortoise (algebra) Assume that Achilles runs with a speed of 1 rod per second, so that his position is given by: A(t) = position of Achilles over time = 0 rods from start + (1 rod/sec)· (t sec) position position position 0 1 2 A(t) 1 rod/sec 1 rod/sec 1 rod/sec Units?

  3. 1/2 rod/sec 1/2 rod/sec 1 rod/sec Achilles vs Tortoise (algebra) Assume also that the Tortoise runs with a speed of 1/2 rod per second and has a head start of 10 rods, so that his position is given by: T(t) = position of Tortoise over time = 10 rods from start + (1/2 rod/sec)· (t sec) 0 1 2 11 10 A(t)T(t) A(t) 1 rod/sec 1 rod/sec 1 rod/sec 1/2 rod/sec What is t when A(t) = T(t)? What is the time when the position of Achilles is the same as the position of the Tortoise? A(t) = 0 rods + (1 rod/sec)· (t sec) = T(t) = 10 rods + (1/2 rod/sec)· (t sec) (1 rod/sec)· (t sec) - (1/2 rod/sec)· (t sec) = 10 rods (1/2 rod/sec)·(t sec) = 10 rods (1 rod/sec - 1/2 rod/sec)· (t sec) = = 20 sec (t sec) = 10 rods / (1/2 rod/sec)

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