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“An infinite string? Infinite means it's really, really, really, really, really,
really
long. Really,”
said Laurie. Really.
“Ah! So you agree with
me
,” Achilles said. “That means the burden of proof must be borne
by the other side.”
“The burden of Achilles on my
back
is more than enough!” Tortoise grumbled.
“Friend Tortoise is wise about many things,” said Achilles. “But he is clearly wrong this
time. He says that an infinite string can be exactly
two inches
long!”
“But how can an infinite string be two inches long?” Laurie asked.
“His claim is preposterous and indiscrete,” said Achilles. “We are in continuous disagree-
ment about it.”
“I never disagree,” said Tortoise. “I only discuss, especially with an intellect such as yours,
Achilles. Your understanding has no limit.”
“You are too kind, dear Tortoise.”
“I mean every word,” said Tortoise. “Allow me to suggest a way to settle the question by Ex-
periment.”
“Please, suggest away,” said Achilles.
“Let us build—hypothetically, of course!—an infinitely long piece of string and then meas-
ure it. Miss Ipsum can be our impartial judge.”
“I accept. Experiment is always better than mere Theory,” Achilles said. “And an impartial
judge sounds wonderful, especially when she already agrees with me!”
“Excellent,” said Tortoise. “Miss Ipsum, imagine you have an infinite number of pieces of
string. If you laid them all end-to-end, would that be infinitely long? Hypothetically?”
“Yes, it must be,” said Laurie.
“Infinity is infinity,” said Achilles. “It's only logical.”
“I wonder. Suppose we start with a piece of string
one
inch long,” Tortoise said. “Then add a
second piece of string that is
one-half
inch long. How long are they together?”
“One and a half inches,” Laurie said.
“And that is shorter than two inches?” Tortoise asked.
“One-half inch shorter. Unmistakably,” Achilles said.
“We all agree thus far,” said Tortoise. “Perhaps we shall converge upon the same conclu-
sion.”
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