Lauren Ipsum: A Story About Computer Science and Other Improbable Things Read Online Free

the
question by Experiment.”
    “Please, suggest away,” said Achilles.
    “Let us build—hypothetically, of course!—an infinitely long piece of string
and then measure 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 conclusion.”
    “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.
    “No, I’m sure Tortoise is right,” said Laurie. “Don’t you see?
Every piece he adds is half as long as the one before. That leaves just enough
room left over. Even if he adds an infinite number of pieces, the string will never reach two inches.”
    “Well, hardly ever,” said Tortoise.
    Achilles grimaced. “It appears you’ve proven the impossible again, Tortoise. But
just to make sure, I will check the arithmetic myself .” He continued to
scribble in his