FINDING YOUR ROOTS: The Life of pi and i
By Neil McKinnon
Quentin Quo Vadis was an elderly squirrel. He wasn’t just an ordinary elderly squirrel. He was an elderly squirrel who was very good at math. At least he used to be good at math.
Nowadays, he could barely remember his own name. Usually, he knew that it started with Q but that was as far as he could go. Forgetting didn’t bother him, though, for often his neighbor Melissa, a large sea cucumber who loved to shop, would hail him from her kitchen window as he left his house, “Quo Vadis,” Melissa would call in her tubular voice, “Where are you going?”
Then she would laugh at some private joke and slam her window without waiting for an answer. Occasionally, she would test his math skills and ask a second question, “What’s pi to two decimal places?”
Quentin knew that Melissa was trying to embarrass him because his memory was failing… and he knew just how to answer without having to remember.
“Is that hair-deprived husband of yours around?” he asked.
“Why yes. Lester’s taking a bath.”
Quentin smiled. Lester was always taking a bath. He was a large, round, bald jellyfish who stayed in the bathtub and liked to croon Croatian Bricklaying Ballads. His voice was not that good so his main talent was making himself larger or smaller by ingesting or expelling water—an activity that Quentin felt was mildly gross.
“Tell him to adjust himself until he’s exactly one metre in diameter,” Quentin said. “Then put a tape around him. The distance around Lester will be pi.”
“But I want decimal points,” Melissa said.
“May I have a small container of donkey sweat?” Quentin replied.
Melissa looked puzzled. “What’s that got to do with pi?”
“Just count the letters in each word,” Quentin said mysteriously and walked away.
Melissa and her questions were the least of his problems. Some days he couldn’t even remember if the square root of 1 was 1 or -1. Occasionally, he couldn’t remember that √1 meant the square root of 1.
One day he confided all this to his best friend, Henry, a confused giraffe. On even days Henry wondered if he was actually a tall tree who just thought he was a giraffe. On odd days he wondered if he was really a giraffe who sometimes thought he was a tall tree. On top of this, Henry worried that maybe he was just a thought in another mind—someone else’s idea of a tall tree or a giraffe. Then he wondered in whose mind he might be a thought. All this wondering made Henry even more confused, so he sometimes relaxed by humming Hungarian Birdwatching Ballads. But Henry did know about square roots.
“You don’t have to remember,” he told Quentin in a lofty voice. “Just multiply them out. 1 x 1 = 1 and -1 x -1 = 1. Therefore they are both the √1. The same is true for the square root of any number—like 2 x 2 = 4 and -2 x -2 = 4, so the √4 = 2 or -2. You don’t have to remember anything. Just be careful with fake numbers.”
Quentin flicked his tail—more of a slow wave really—and gave a sigh. He knew there was no such thing as fake numbers. Henry probably meant imaginary numbers. Well, he certainly knew the difference between real and imaginary numbers. A real number is any number that can be found on a number line like 2 or zero or -6. An imaginary number is . . . uh-oh, he couldn’t remember.
Now he was in a quandary. (Note to reader: a quandary is not a foundry built in a quarry). What should he do? Then he had an idea. He’d go and talk to his former student Heidi. She never forgot anything.
Heidi was a middle-aged mosquito who spent all her spare time playing tennis. She was often disqualified for riding across court on the ball and puncturing her opponent just as he was about to return her serve… or for leaving the tennis court and sucking all the blood out of some spectator who had made the mistake of cheering for her rival. When not playing tennis she liked to go to karaoke bars where she sometimes yodeled a medley of Moroccan Bartending Ballads.
Heidi was only too glad to take time out. “Thank God you came,” she said bitingly. “I can’t ride the ball anywhere near him or I’ll die from the smell.”
Quentin recognized her opponent, a very fat rabbit with stinky feet known around town as T. Rex. No one knew what the T stood for but the rumor was that it was short for Toxic. T. Rex often supplemented his foot odor and punctuated his on court hops with loud gaseous explosions. He was known as the town’s most odoriferous citizen. To disguise his explosions he sometimes sang Samoan Barrel Racing Ballads.
T. Rex threw down his racket. “If you stop, I win by default,” he said flatulently.
“Do you remember what an imaginary number is?” Quentin asked Heidi.
“Sure do. An imaginary number is small i.”
“I know you’re small,” said Quentin. “And I also know that you’re not an imaginary number.”
“No, no, not me,” said Heidi. “You know how a normal square root works, right? Like the √9 = 3. Well, you can take the square root of any positive number or zero, but what happens when you try to take the square root of a negative number? A bunch of alarms will go off in your head, and you say, ‘Hey, I can’t take the square root of a negative number! That doesn’t make sense!’ Well, you’d be sort of right… because when you square any positive or negative number, you get a positive number, so thinking backwards you can’t take the square root of a negative.
“But some weird math guys decided they wanted to take the square roots of negative numbers anyway. They made up a new number and called it i. Then they said that √-1 = i. Therefore, i x i = -1. Now, with this new number, you can take the square root of a negative number. For instance, the √-4 is √4 times the √-1, or 2 times i.”
“Thank you,” said Quentin. “You’re just about the smartest mosquito I know. Your smelly friend has hopped off, but I think I see trouble coming.”
Heidi looked up to see a tiny rat heading straight for them. But this wasn’t any tiny rat. This was a tiny rat named Bernie who used to think and act like a police officer. Now he was a police officer who acted like a rat. Between arrests he liked to belt out Bolivian Butt Scratching Ballads.
“I could run you in for practicing bad math,” he told Quentin in a wharfish voice. “Everybody knows you can’t take the square root of -1.
“And you,” he turned to Heidi, “I’ve got a desk full of complaints from tennis players with itchy bites.”
Quentin explained that small i was the square root of -1.
“You just made that up,” Bernie said.
“No, I didn’t. It was invented by a bunch of weird math guys.”
“Then they made it up.”
Quentin nodded. “Maybe they didn’t invent the square root of -1, maybe it was there and they discovered it—but that’s another question.”
Quentin walked away, feeling very good, knowing that small i would exist whether he remembered it or not… OR WOULD IT?
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