Tuesday, April 7, 2009

From Among the Great Ones of Our Dispensation

Again I find myself reading a book in some of my spare time. Mainly I read it on my lunch hour at work and it's the second time I've studied its pages and I've never failed to be disappointed in how much I walk away with. The book is called Isaac Asimov on Numbers. It's a book about mathematics. Now to the singleminded and those whose blinders allow them interest only in one chosen field, a book about mathmatics may not seem too enticing, but I am one who revels in any new learning or knowledge. As a result I rejoice in a writer who can help me understand binary code in the course of a few pages, or make imaginary numbers less imaginary for me. In any case I'd recommend this book to anyone with a thirst for knowledge. My reason for posting this here, however, is more specific.
Now, I am not one to condone the behavior widespread in society today of trying to be better than someone else, but I am a fan of moments of pure intelligence flowing into an individual, espcially in the midst of an intellectual and idealogical debate. Such a story was to be found within the pages of this book and I just thought I'd post the debate here for any with interest to read. Bear in mind that this is about Isaac Asimov when he was a young student facing off against an already established professor:

When I was a mere slip of a lad and attended college, I had a friend with whom I ate lunch every day. His 11 a.m. class was in sociology, which I absolutely refused to take, and my 11 a.m. class was calculus, which he as steadfastly refused to take--so we had to separate at eleven and meet at twelve.
As it happened, his sociology professor was a scholar who did things in the grand manner, holding court after class was over. The more eager students gathered close and listened to him pontificate for an additional fifteen minutes, while they threw in an occasional log in the form of a question to feed the flame of the oracle.
Consequently, when my calculus lecture was over, I had to enter the sociology room and wait patiently for court to conclude.
Once I walked in when the professor was listing on the board his classification of mankind into the two groups of mystics and realists, and under mystics he had included the mathematicians along with the poets and theologians. One student wanted to know why.
"Mathematicians," said the professor, "are mystics because they believed in numbers that have no reality."
Now ordinarily, as a nonmember of the class, I sat in the corner and suffered in silent boredom, but now I rose convulsively, and said, "What numbers?"
The professor looked in my direction and said, "The square root of minus one. It has no existence. Mathematicians call it imaginary. But they believe it has some kind of existence in a mystical way."
"There's nothing mystical about it," I said, angrily. "The square root of minus one is just as real as any other number."
The professor smiled, feeling he had a live on on whom he could now proceed to display his superiority of intellect (I have since had classes of my own and I know exactly how he felt). He said, silkily, "We have a young mathematician here who wants to prove the reality of the square root of minus one. Come, young man, hand me the square root of minus one pieces of chalk!"
I reddened, "Well, now, wait--"
"That's all," he said, waving his hand. Mission, he imagined, accomplisshed, both neatly and sweetly.
But I raised my voice. "I'll do it. I'll do it. I'll hand you the square root of minus one pieces of chalk, if you hand me a one-half piece of chalk."
The professor smiled again, and said, "Very well," broke a fresh piece of chalk in half, and handed me one of the halves. "Now for your end of the bargain."
"Ah, but wait," I said, "you haven't fulfilled your end. This is one piece of chalk you've handed me, not a one-half piece." I held it up for the others to see. "Wouldn't you all say this was one piece of chalk? It certainly isn't two or three."
Now the professor wasn't smiling. "Hold it. One piece of chalk is a piece of regulation length. You have one that's half the regulation length."
I said, "Now you're springing an arbitrary definition on me. But even if I accept it, are you willing to maintain that this is a one-half piece of chalk and not a 0.48 piece or a 0.52 piece? And can you really consider yourself qualified to discuss the square root of minus one, when you're a little hazy on the meaning of one half?"
But by now the professor had lost his equanimity altogether and his final argument was unanswerable. He said, "Get the hell out of here!" I left (laughing) and thereafter waited for my friend in the corridor.

So there you have it ladies and gentlemen. From that little discourse I think it was evident that the development of Asimov's mind and interests was already beyond the norm and well on it's way to placing him to where he now rests among the great ones of our dispensation's thinkers. If you want any more from him or if you want a quick easy way to understand imaginary numbers or other mathematical concepts that are really neat, just pick up the book and away you go.

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