Re: U2-darn few bugs...

[David Auerbach auerbach@xxxxxxxx]

On Mar 1, at 11:31 AM, Patricia M. Godfrey wrote:
> My brother, a retired physicist who once taught practical math, and
> my niece, a high school teacher who teaches math inter alia, both
> agree with Carl. Surely there are many things in higher math that
> have little or no relation to corporeal realities? IIRC, negative
> numbers are called "imaginary."
> --
Depends what you mean by corporeal realities. For the supermarket
you probably need at most the rationals (numbers which ratios of
integers). Add in the irrationals (which means not-ratios) and
you've got enough for everyday newtonian physics (bridge building). 
For more sophisticated physics you're going to need things like
solutions to equations where roots of negative numbers (called
imaginary for no good reason; just as real as 17). come in.
 But it is possible to ask very very simple questions about the
integers the answers to which need the "higher" math machinery. Some
of these simple questions took centuries to get answers-- like
Fermat's theorem or the 4-color map theorem. Some (like how many
primes whose difference is 2 there are; or the conjecture that every
even number larger than 2 is the sum of two primes) remain
unanswered at the present time. Solve one of those and your odds of
getting an obit with a picture in the New York Times goes from nil to
certainty.
And, of course, it is mildly arcane facts about prime factorization
that leads to useful encryption algorithms that are used all the time
on the internet.




David Auerbach
Department of Philosophy & Religion
Box 8103
NCSU
Raleigh, NC 27695-8103