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The Tortoise boldly claimed that if Achilles gave him a small head start, he would win the race.
Achilles laughed at this, for of course he was a mighty Greek warrior and swift of foot, whereas the Tortoise was heavy and slow.
"How big a head start do you need?" Achilles asked the Tortoise with a smile.
"Ten meters," the Tortoise replied.
Achilles laughed louder than ever. "You will surely lose, my friend, in that case," he told the Tortoise, "but let us race, if you wish it."
"On the contrary," said the Tortoise, "I will win, and I can prove it to you by a simple argument."
"Go on, then," Achilles replied, with less confidence than he felt before. Achilles knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this.
The Tortoise began his argument. "Suppose that you give me a 10-meter head start. Would you say that you could cover that 10 meters between us very quickly?"
"Very quickly," Achilles affirmed.
"And in that time, how far should I have gone, do you think?"
"Perhaps a meter – no more," said Achilles after a moment's thought.
"Very well," replied the Tortoise, "so now there is a meter between us. And you would catch up that distance very quickly?"
"“Very quickly, indeed."
"Granted. And yet, in that time I shall have gone a little way farther, so that now you must catch that distance up, yes?"
"True," Achilles said slowly.
"And while you are doing so, I shall have gone a little way farther, so that you must then catch up the new distance," the Tortoise continued smoothly.
Achilles said nothing.
"And so you see, in each moment you must be catching up the distance between us, and yet I – at the same time – will be adding a new distance, however small, for you to catch up again."
"Indeed, it must be so," said Achilles wearily.
"And so you can never catch up," the Tortoise concluded sympathetically.
"You are right, as always," said Achilles sadly.
But then a flash of inspiration suddenly came upon Achilles, and he looked at the Tortoise with renewed confidence.
"Unless..."
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There is a lesson to be learned in this parable. It took humankind almost two millenia to find a mathematical answer to the Tortoise's argument, but if applied to the political world, what is the counter to the Tortoise's argument?
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