What the Tortoise Said to Laurie - Lauren Ipsum: A Story About Computer Science and Other Improbable Things - page 18

“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 notebook:
+ 1/512 inch
+ 1/1,024 inch
+ 1/2,048 inch
+ 1/4,096 inch
+ 1/8,192 inch
+ 1/16,384 inch
+ 1/32,768 inch
+ 1/65,536 inch
+ 1/131,072 inch
+ 1/262,144 inch . . .
“ That should keep him busy. If anyone has the patience to actually count to infinity, it's
Achilles. Thank you for your assistance, Miss Ipsum.”
“You're welcome, Mister Tortoise,” said Laurie. “I didn't know something so big could be so
small.”
“That's the Power of Two,” said Tortoise. “If you cut a number into two halves, then cut it in
two again, and so on, very soon it will be too small to see. But there will always be
something left over.”
“Mister Tortoise, do you know how long this road is? It feels like it goes on forever. I'm try-
ing to get to Symbol.”
“This road is quite long,” he replied. “In fact, it is infinite.”
“Oh, no! How do I get to the end?”
“You can do it in two simple steps.”
“How?”
“How do you think? A step with your right foot, then a step with your left foot,” said Tor-
toise. “Your point of view is what's important. It's integral.”
Of course! If an infinite string could be less than two inches long, then an infinite road could
certainly be less than two steps, if you looked at it in the right way. Laurie closed her eyes