was geeking out looking at imaginary numbers (is there anything they can't do?). ran across this anecdote. it would ring less made-up if was all over the web, but it isn't. searching the web for *asimov chalk imaginary* fails to yield stuff. so i'll just reproduce it here for posterity's sake. you know, for the children.

Apparently Asimov was studying science and mathematics; but he

had a friend who was studying philosophy, and they often had lunch

together immediately following a lecture that formed a part of his

friend's course.

One day, Asimov happened to arrive early, decided to drop in on the

philosophy lecture, and slipped into the room, to find himself faced

with two lists on the blackboard. One was headed "Realists" and the

other "Mystics", but Asimov was astounded to see the word

"Mathematicians" under the heading "Mystics". So much so, that he

walked forward, put up his hand and asked for an explanation from the

philosophy professor.

"Ah, so we have a mathematical guest who thinks he's a realist!" said

the professor, with a condescending smile. "Mathematicians, my young

friend, are mystics, because they believe in the existence of unreal

objects; for example they believe in the existence of such a thing as

the square root of minus one."

"I know we *call* the square root of minus one imaginary, but it's just

as real as other numbers," said Asimov indignantly. "And we're

certainly not mystics!"

"Very well," said the professor, smirking a little, "if you say that

the square root of minus one is as real as other numbers, come down here

and show us all. Give me the square root of minus one pieces of chalk!"

And all the philosophy students started to laugh.

For a moment Asimov didn't know what to say, and went a bit red, while

the students' laughter grew louder, and the professor's smirk grew

bigger. But then he suddenly shouted out, "OK! I'll do it!" and there

was an immediate silence.

"I'll do it," Asimov went on, "on one condition. And the condition is

that you give me a half piece of chalk to do it with."

"All right," said the professor, a little puzzled. What was going on?

He broke a fresh stick of chalk in two. "Here's your half piece of

chalk. Now what are you going to do?"

"Ah, but wait a minute," said Asimov. "You haven't kept your side of

the bargain yet. This isn't a half piece of chalk. This is *one* piece

of chalk!"

And the students gradually began to laugh again.

"It's a half piece of chalk!" said the professor, getting a bit

flustered. "A new piece of chalk has a regulation length, and this is

half that regulation length, so this is a half piece of chalk."

"Well, now you're springing a *very* arbitrary definition on me," said

Asimov, beginning to enjoy himself. "The *regulation length of a piece

of chalk* enters philosophical debate about reality. Really??? But

even if I were to accept your definition, how can you be sure that this

piece of chalk is *exactly* half the regulation length? You just broke

it casually in two. You'd have to go to a very great deal of trouble to

divide it in half–in fact, you couldn't possibly do what you said

you'd do *exactly*, so I say you don't know what "one half" really

means, in the real world. But either way, if you think you can use a

number like one half to count pieces of chalk, you're wrong."

The professor was speechless.

"But I'm sure you'll agree that doesn't mean that one half isn't a real

number, just because you can't use it to count pieces of chalk with,"

said Asimov. "I'll tell you what: when you have a better idea of what

you mean by one half, or even what you mean by reality for that matter,

we can discuss the square root of minus one."

And he left, and waited for his friend outside in future.

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