JSH: Without a trace

From: James Harris (jstevh_at_msn.com)
Date: 12/04/04 

Date: 4 Dec 2004 07:02:46 -0800

Some of you may have noticed that I'm talking about abstractions now
at higher and higher levels, which I think should help.

For instance, given a multiple of a polynomial it has been well
accepted that you can divide that multiple off without leaving a
trace.

Consider

P(x) = 5(x+1)(x+2) = 5x^2 + 15x + 10

and it is true that you can divide 5 from that factorizaton giving

(x+1)(x+2) = x^2 + 3x + 2

without leaving a trace. That is, there is no indication left that
the polynomial was ever multiplied by 5, as how could there be?

Rationally there are an *infinity* of potential multiples that you
could use, so why mathematically should a factorization of x^2 + 3x +
2, have traces of one particular multiple, like traces of 5.

Now that's obvious with polynomial factors but some sci.math'ers
clearly have many of you convinced that things change if you have

P(x) = (a_1(x) + b_1)(a_2(x) + b_2) = 5x^2 + 15x + 10

and NOW divide the 5 off, as many of you seem convinced that NOW if
the a's and b's are somehow complex, or weird, or otherwise different
from what you get with polynomial then maybe, hmmm, possibly, you
know? Maybe there IS a trace, right?

But how?

If I divide the 5 off, then I have a factorization of

x^2 + 3x + 2

just as before, and there is no rational reason to suppose that a
trace of 5 is left, as why 5? Why not 7? Or 293874983?

Logically, it doesn't matter how complicated that a's and b's are in
that example, when the 5 is divided off, it goes--without a trace.

The situation now where posters argue with me, with arguments that
have to boil down to some trace being left by a multiple, so that they
can argue that the multiple divides through dependent on some
variable, is not unlike an argument between a scientist and people who
don't believe in evolution, but worse.

In my case I have precedent from thousands of years of mathematics
that a multiple can be divided off, absolute logic, and just the plain
oddity of the notion that a multiple has to leave a trace when it's
divided off, but STILL people have argued with me quite successfully,
and I figure many of you, despite what I say here, remain unconvinced
that I'm right.

And you are no different than Creationists arguing with scientists
against evolution. Or people who don't believe man landed on the
moon.

You are no different, and in fact worse, as here it's mathematics,
with absolute proof.

You people who can't accept mathematics are no different from those
other people who can't accept science. You may think you like or even
love mathematics, but you cannot when you refuse to accept even the
most basic concepts in mathematics, with a result that clearly you
don't like.

I understand the *desire* to have certain things be true, but in
mathematics that doesn't matter. At the end of the day, you put away
your emotions, and go with what's true--if you truly value
mathematics.

James Harris
http://mathforprofit.blogspot.com/

Relevant Pages

  • Re: JSH: Without a trace
    ... given a multiple of a polynomial it has been well ... > and it is true that you can divide 5 from that factorizaton giving ... > without leaving a trace. ... > In my case I have precedent from thousands of years of mathematics ...
    (sci.math)
  • Re: return in void functions
    ... >> easier to use and works with multiple returns and exceptions. ... the ones you want to trace. ... but I don't see what the problem with multiple exit points ...
    (comp.lang.cpp)
  • Re: [patch 4/5] x86, ftrace, hw-branch-tracer: reset trace on close
    ... the trace, the trace is not contiguous, anyway. ... So you want multiple reads of /debug/tracing/trace to return different ... If you use quilt, you can add: ... VAT Registration No.: DE129385895 ...
    (Linux-Kernel)
  • Contacts dissapearing
    ... multiple versions of Outlook. ... patialy dissapearing without a trace. ... party software being used to share certain folders ... but the problem effects any contact list including the ...
    (microsoft.public.outlook.contacts)
  • Re: Periodicity of a^n mod c
    ... divisor of 2^. ... and then take the least common multiple of these orders. ... possible exponent m = m, ... and the exponent of a will divide the resulting quotient ...
    (sci.math)