Re: JSH: Without a trace

From: William Hughes (wpihughes_at_hotmail.com)
Date: 12/04/04 

Date: 4 Dec 2004 13:13:34 -0800

jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0412040702.1058c65a@posting.google.com>...
> 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.

"Without a trace" has no precise meaning, (and not much meaning
in any sense). You are retreating into not even wrong territory.

However, something that has disappeared without a trace is any
mention of the constant term. This makes perfect sense. Each
time you brought up the constant term, everyone would ask:
"isn't the constant term of (a(x)/w(x) + 7/w(x)) equal to 7?"
Unfortunately for you, you could not answer this question without
aknowleging that your entire argument was fallacious.
And too many people were asking the question for you to comfortably
ignore it. So you could either admit you were wrong or retreat
into not even wrong territory. No one is surprised by your choice.

                          - "William Hughes"

                      

>
> 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

  • 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: 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)
  • 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: 64-bits is not necessarily faster ?
    ... Add and subtract are twice as fast, multiple and divide tens of times. ... Memory pointers, file index/pointers, nano-sec timers, more ... Great for algorithmic functions and function calls. ...
    (borland.public.delphi.non-technical)
  • Re: A Possible (or not) Proof for the Eudoxius Theorem - Number Theory - Help
    ... a is a multiple of b or is between two consecutive multiples of b, ... done is by invoking well-ordering. ... divide a, we know that a is not a multiple of b. ...
    (sci.math)