Reprinted from Lewis Carroll, “What the Tortoise Said to Achilles,” Mind 4, No. 14 (April 1895): 278-280.
Achilles had overtaken the Tortoise, and had seated himself comfortably on its back.
“So you’ve got to the end of our race-course?” said the Tortoise. “Even though it does consist of an infinite series of distances? I thought some wiseacre or other had proved that the thing couldn’t be done?”
“It can be done,” said Achilles. “It has been done! Solvitur ambulando. You see the distances were constantly diminishing; and so –“
“But if they had been constantly increasing?” the Tortoise interrupted “How then?”
“Then I shouldn’t be here,” Achilles modestly replied; “and you would have got several times round the world, by this time!”
“You flatter me — flatten, I mean” said the Tortoise; “for you are a heavy weight, and no mistake! Well now, would you like to hear of a race-course, that most people fancy they can get to the end of in two or three steps, while it really consists of an infinite number of distances, each one longer than the previous one?”继续阅读