The Professor’s Beloved Equation

This was so beautiful! It couldn’t have been done anywhere else but Japan. The premise is that this math professor has Alzheimer’s, or at least a special form of it, such that his memory is only 80 minutes long. In the movie his memory was shown to have reset every day at the least, so every morning when his housekeeper arrives, the following conversation takes place:

“Konichiwa!”
“What’s your shoe size?”
“24 centimetres.”
“My, what a noble number… It’s the factorial of 4.”
“What is a factorial?”
“If you multiply all the whole numbers from 1 to 4, you get 24.”
“What’s your telephone number?”
“576-1455”
“Did you say 5,761,445? Why, that’s wonderful. That’s equivalent to the prime numbers up to one billion. In any event, come in.”

And then every day she came in after that, the same thing would repeat.

“What’s your shoe size?”
“24. The factorial of 4!”
“That’s wonderful. What a noble number…”

He meets her afresh every day, and while she goes about her daily chores he disrupts infuses her housekeeping experience with a good dose of math.

On the day one of the professor’s papers got accepted for publication in a journal:

“Do you often submit your papers to magazines?”
“Right.. I sent my proof to the Journal of Mathematics, Vol. 37 today. That’s good. ”
“Oh, no! I should’ve sent it express. Only first place takes a cash prize.”
“No, there’s no need to send it express. It’s important to arrive at the truth before anyone else, but it’s more important that the proof be beautiful. ”
“Are there such things as beautiful or ugly proofs?”
“Of course. In a truly correct proof, air-tight and compelling reasoning coexists without contradiction, with supple logic. Just as no one can prove why stars are beautiful, it’s difficult to express the beauty of mathematics.” He paused for a beat.
“What’s your birthday?”
“February 20th.”
“What a charming number!” The professor takes off his watch.
“220… Take a look at this. Back in college, I won the President’s award for my paper on Transcendental Number Theory.”
“Ah.. what a great honor..” the housekeeper tried to be relevant.
“No, that doesn’t matter. Can you read the number?”
“President’s Award No. 284. Does that mean you’re the 284th person to receive the honor?”
“I suppose. The question is 284 and 220. This is no time to be washing dishes. Come with me, quick!”

They walk over to the blackboard. The professor writes 220 and 284 on two ends.
“What do you think?”
“Well, I.. Both have 3 digits… How can I phrase this? At the meat counter at the supermarket, if there are two packets of ground beef, one 220g and one 284g, they seem the same to me. One quick glance, and they look similar. They’re both in the 200 range, and all the digits are even…”

“That’s a keen insight. Intuition is important. Grasp the numbers intuitively from your heart. Do you know what a divisor is?”
“Yes, I think so, I remember studying them.”
“Let’s write out all the divisors for 220 and 284, excepting themselves.”
220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
284: 1, 2, 4, 71, 142,
“You can calculate all those divisors in your head?”
“I’m just using the same intuition you did. Onto the next step.”
1 + 2 + 4 + 5 + 10 + 11 + 22 + 44 + 55 + 110 = 284
1 + 2 + 4 + 71 + 142 = 220
“Will you behold, this beautiful chain of numbers. Add all the divisors for 284, and you get 220. Add all the divisors for 220, and you get 284. They’re amicable numbers.”
“Amicable numbers?”
“Mm. Such pairs are very rare. Even Fermat and Descartes only discovered one pair each. They’re numbers bound to each other by God’s design.”
“God’s design…”
“Mm. Isn’t it beautiful? Your birthday and the number engraved on my wristwatch are so perfectly intertwined.”

He gave everyone in his acquaintance names, mathematical names that represented their characteristics. To the housekeeper’s son, he gave the name “Root” (of course, pronounced “Root-oh” in Japanese)

“I can tell you’ve a wise heart in here. All right, you’re a Root. You accept any number that comes your way, rejecting none. A truly generous symbol, Root.”

Root starts coming by the house everyday since the Professor cannot stand the idea of Root waiting at home alone for his mother while his mother prepares dinner for a complete stranger. After being thoroughly schooled in the beauty of numbers by the professor, Root goes on to become a math teacher, and teaches his students about the professor’s lifelong equation:

“Pi is the circle ratio, right? “i” is the square root of -1 and an imaginary number. Here we have pi, a number that continues to the ends of the universe, and the imaginary number “i” which never shows itself. What’s tricky, is “e”. “e” is also called the “Napier number,” after John Napier, the British mathematician. The Napier number is one of the constants so critical to math. For now, I’ll just tell you the conclusion. If you calculate this “e”, its value is 2.7182818284…. This is just like pi. It goes on and on and on forever. It’s an irrational number. From an infinite universe, pi drifts down to “e”, and shakes hands with the bashful “i”. They come together, and hold their breaths… none of them are connected. But, if a single human adds just one thing… the world is transformed.
root
The contradiction is resolved. Zero. In other words, the realm of nothingness embraces them.

Today, we celebrate this equation. When a single human added just one thing to my contradictory and irrational life.

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