Will he ever get past?
I'm back! And I'm still blogging about Julian Baggini's 100 thought experiments to see how well my evolutionary philosophy can cope with these historically difficult problems. Let's ease back in at a nice slow pace...
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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 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!
Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 46.
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So what do think about this paradox? Can you overtake my thoughts on it? I'll be back on Friday to see where you've gotten to.
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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 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!
Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 46.
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So what do think about this paradox? Can you overtake my thoughts on it? I'll be back on Friday to see where you've gotten to.
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