Difference between revisions of "Racing tortoises"
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=Synonyms= | =Synonyms= | ||
=Definition= | =Definition= | ||
| + | Welcome to the Great Athenian Man–Tortoise Run-off. My name’s Zeno and I’ll be your commentator for the big race. I have to say, however, that the result is a foregone conclusion. Achilles has made the terrible mistake of giving Tarquin the tortoise a 100-yard head start. Let me explain. | ||
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| + | Tarquin’s tactic is to keep constantly moving, however slowly. If Achilles is to overtake Tarquin, first he must get to where Tarquin is when the race starts. That will take him several seconds. In that time, Tarquin will have moved on a little and will then be a short distance ahead of Achilles. Now if Achilles is to overtake Tarquin, he must again get to where Tarquin is first. But in the time it takes Achilles to do that, Tarquin will again have moved forward slightly. So, Achilles once more needs to get to where Tarquin is now, in order to overtake him, in which time, Tarquin would have moved forward. And so on. You get the picture. It’s just logically and mathematically impossible for Achilles to overtake the beast. | ||
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| + | Still, it’s too late to place your bets on the tortoise now, because they’re under starter’s orders, and … they’re off! Achilles is closing … closing … closing … Achilles has overtaken the tortoise! I can’t believe it! It’s impossible! | ||
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==Source== | ==Source== | ||
| + | The ancient paradox of Achilles and the Tortoise, attributed to Zeno (born c. 488 BCE) | ||
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=Motivation & Background= | =Motivation & Background= | ||
=Cross-References= | =Cross-References= | ||
=Recommended Reading= | =Recommended Reading= | ||
Revision as of 00:19, 25 October 2016
Contents
Synonyms
Definition
Welcome to the Great Athenian Man–Tortoise Run-off. My name’s Zeno and I’ll be your commentator for the big race. I have to say, however, that the result is a foregone conclusion. Achilles has made the terrible mistake of giving Tarquin the tortoise a 100-yard head start. Let me explain.
Tarquin’s tactic is to keep constantly moving, however slowly. If Achilles is to overtake Tarquin, first he must get to where Tarquin is when the race starts. That will take him several seconds. In that time, Tarquin will have moved on a little and will then be a short distance ahead of Achilles. Now if Achilles is to overtake Tarquin, he must again get to where Tarquin is first. But in the time it takes Achilles to do that, Tarquin will again have moved forward slightly. So, Achilles once more needs to get to where Tarquin is now, in order to overtake him, in which time, Tarquin would have moved forward. And so on. You get the picture. It’s just logically and mathematically impossible for Achilles to overtake the beast.
Still, it’s too late to place your bets on the tortoise now, because they’re under starter’s orders, and … they’re off! Achilles is closing … closing … closing … Achilles has overtaken the tortoise! I can’t believe it! It’s impossible!
Source
The ancient paradox of Achilles and the Tortoise, attributed to Zeno (born c. 488 BCE)
