What the Tortoise Said to Laurie - Lauren Ipsum: A Story About Computer Science and Other Improbable Things - page 17

“I doubt that!” said Achilles. Laurie wasn't sure what Tortoise was getting at, but she
doubted it, too.
“Achilles, would you please keep count of our hypothetical string? I want to add a third piece
one-quarter of an inch long,” said Tortoise. “Is our string now one and three-quarters inches
long?”
Achilles retrieved a much-used notebook from under his helmet and scribbled some figures.
“It seems so,” he said.
“With one-quarter inch to spare?” asked Tortoise.
“Yes,” replied Achilles. “Only one-quarter inch! You are a finger's width away from defeat!”
“Add an eighth -inch piece,” Tortoise said. “Do I still have some space left over?”
“Yes, but I'll have beaten you soon!” the Greek Logician crowed. “Your string is an eighth of
an inch away from the limit, and you've done only four pieces!”
“Your arithmetic is correct as always, Achilles. But in the interest of science, let us continue
until the bitter end,” Tortoise said.
“It won't be long,” said Achilles. “What is your next move?”
“I would like to add another piece of string, this time one-sixteenth inch long.”
“Done!” Achilles scribbled away. “Only one-sixteenth inch left, old friend!”
“Only that much?” said Tortoise. “Then for the next one, I would like to add a piece of string
one thirty-second inch long.”
“As you wish, poor Tortoise. One thirty-second of an inch added. There is only one thirty-
second inch remaining, and an infinity of strings to go! There will be plenty of rope left to
trip yourself with!” said Achilles.
“Please add a sixty-fourth-inch piece of string,” said Tortoise, “then a one-hundred-twenty-
eighth-inch piece, and a two-hundred-and-fifty-sixth-inch piece, and then a five-hundred-
twelfth-inch piece, and then—”
“Slow down, Tortoise! You are going too fast,” Achilles said. “And those are very big—no,
very small numbers.” He figured and scribbled for a minute. “There is only a five-hundred-
and-twelfth inch remaining. It's too bad we're not splitting hairs , or you could have gotten a
little farther! Do you give up now?”
“ Oh. I see!” exclaimed Laurie. “Achilles, Tortoise is right.”
“What? Don't change your mind now when we are so close to victory!” Achilles cried.