Achilles and the Tortoise were just finishing a picnic. The food had been simple, bread with olive oil and wine to drink. They lounged in the shade of a tree, happy to be hidden from the hot summer sun.
“Have you ever noticed that shadows move throughout the day?” asked the Tortoise.
“I haven’t given it much thought.” said Achilles. “I suppose it could be true. I know that in the morning there is a shadow on the west side of my house and in the evening the shadow is in the east, but I’ve never payed any attention to how the shadow gets from one place to the other. I don’t even know for certain that it is the same shadow. For all I know during the day one shadow leaves and another one comes.”
“That’s the problem with you Heroes, you are always rushing places. Isn’t it nice to take some time off and just watch the world, rather than try to change it?”
“Well I’m watching the shadow of this tree right now, and I see that the shadow is moving slightly since the leaves are being pushed by the breeze. Is that the motion of which you speak?”
“No, trust me, even if the tree were perfectly still its shadow would still move.”
“It must not be moving very fast then,” observed Achilles.
Just then an old man with a grizzled beard approached them wearing a placard. On the placard was written the words “Say NO to Change.”
“Oh no,” whispered the Tortoise to Achilles, “I hate politics.”
“I rather enjoy a good debate,” Achilles said confidently. “Hello there stranger! Tell me, what new policy are you protesting with that sign?”
“Oh no sir, you misunderstand,” said the stranger. “This sign has nothing to do with politics. It is instead to protest everyone going about doing impossible things.”
The Tortoise thought this a rather odd thing to say, and told the stranger. “I will grant you that doing impossible things all the time is a rather rude way to live, however, I’m not sure I understand… Which impossible things do you accuse everyone of doing?”
“Well, moving at all of course! My name is Zeno of Elea, and I have proof that any movement is absolutely impossible. Now if only people would listen to me and stop!”
This seemed strange indeed to our two picnickers. Achilles said, “Now see hear sir. My name is Achilles, famed throughout the world for my acts of bravery and athleticism. I consider myself something of an expert on motion. I have moved many times. Indeed just this morning the Tortoise and I walked out here for a picnic under this tree.”
“No you didn’t,” said Zeno.
Achilles sat in a shocked silence.
“I beg your pardon,” said the Tortoise, “but I was with him. We put the basket on my back and walked out here.”
“Not possible. Let me demonstrate. In order to get to this tree you first must have walked half way to the tree. Do you agree?”
“We agree that we must have walked halfway first, but I don’t see how that prevents us from moving,” said Achilles.
“Let me explain. So you first went half way, but in order to do that you must have travelled one half of the half way. And in order to do that you must have travelled half of this new distance. And so on, for forever. In other words in order to move here you must have done as infinite number of things. Clearly that is impossible, there is not enough time for you to do an infinite number of things.”
Achilles replied, “While your argument is convincing, I have moved so many times with absolute ease. Moving is far from impossible. In fact I’ll prove it. I’m going to run home.”
“Care to make this interesting?” said Zeno, who was not shaken by Achilles words. “How much faster are you than your friend the Tortoise?”
“Why, I must be twice as fast,” said Achilles proudly.
“Is that so? In that case I would like to propose a wager. I bet that you, the great Achilles, cannot get home any faster than Mr. Tortoise here.”
“I’ll gladly take that bet,” said Achilles.
“Wait a moment!” spoke the Tortoise who had become rather worried. “There is no possible way that a normal race between Achilles and I could be fair.”
“If that is how you feel,” said Zeno, “then how about we give Mr. Tortoise a head start. Let him begin the race from half the way home, while you Achilles begin at this tree.”
“That seems fair. After all I am Achilles, the fastest person I know.”
They waited for the Tortoise to move into position, and then Zeno shouted “Ready! Set! Go!”
What was the result of the race?