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From: dkingsle@umn-d-ub.D.UMN.EDU (david kingsley)
Newsgroups: comp.edu,sci.math,sci.physics
Subject: Re: Student preparedness
Summary: Isaac Asimov
Message-ID: <686@umn-d-ub.D.UMN.EDU>
Date: 18 Jan 89 22:39:52 GMT
References: <605@ucrmath.EDU> <6578@killer.DALLAS.TX.US> <19252@shemp.CS.UCLA.EDU> <331@sunset.MATH.UCLA.EDU>
Organization: U. of Minnesota-Duluth, Computer Center
Lines: 54

In article <331@sunset.MATH.UCLA.EDU>, troly@redwood.math.ucla.edu (Bret Jolly) writes:
> In article <85191@sun.uucp> landman@sun.UUCP (Howard A. Landman) writes:
> >My first grade teacher taught that there was no such thing as a negative
> >number.  It took me three years to figure out she was wrong, but when I
> >did, I was furious for a month.
> 
>   My 3rd grade teacher said the same thing, but I didn't believe her.
> I tried to explain them, but that only served to enrage her. She
> pulled me up in front of the class and said, "All right smarty, show
> the class numbers less than zero on your fingers. See, you can't, so
> there aren't any! Nyaah!" I had just come to this country and the
> encounter left me wondering if Americans were just intellectually
> inferior.

This reminds me of something I read in Isaac Asimov's book, "Asimov
on Numbers"

In college, Asimov was waiting for a friend's class to finish and sat
in the back of the room.  The instructor had lists of scientists and
mystics on the board and included mathematicians in the list of mystics.
Asimov asked why, and the instructor said, "Because they believe in
numbers that don't exist.  The square root of minus one doesn't exist,   
but they believe that it has an existence of some sort."

Asimov said, "What do you mean?  It's just as real as any other number." 

The instructor said, "My friends, we have here a budding mathematician who
believes that the square root of minus one exists.  If so, would you care to
hand me the square root of minus one pieces of chalk?"

Asimov hesitated, then said, "Okay, I'll do it, if you hand me half a
piece of chalk."

The instructor took a piece of chalk, broke it into two pieces, and
handed one of the pieces to Asimov.  He then said, "Okay.  Now fulfill
your end of the bargain."

Asimov said, "That isn't half a piece of chalk.  It's one piece.  It
certainly doesn't look like two or three."

The instructor replied, "A one half piece of chalk is half a regulation
piece."
 
Asimov said, "Now let's assume that I accept your defintion of half a
piece of chalk.  How can you be sure that isn't a .52 or a .48 piece?
Furthermore, how can you feel qualified to talk about the square root
of minus one when you're a bit fuzzy on the concept of one half?"

The instructor then became infuriated and ordered Asimov, laughing,
out of the room.

David Kingsley
Department of Mathematics and Statistics
University of Minnesota, Duluth