JSH: Resolution now possible

From: James Harris (jstevh_at_msn.com)
Date: 10/17/04 

Date: 17 Oct 2004 07:13:23 -0700

After over two years of arguing on the specifics of my techniques of
polynomial factorization which adds to even more years of arguing
before about factorizations I think it's finally clear how to move to
resolve all the issues:

1. My position is that the definition of the ring of algebraic
integers requiring roots of monic polynomials with integer
coefficients is arbitrary and misleading in that you can have numbers
properly units that are excluded on the technicality that they are not
roots of monic polynomials with integer coefficients.

2. In support of my position I have given the full algebraic argument
showing a contradiction between numbers shown to have a specific
factor, versus exclusion of that factor in the ring of algebraic
integers based on a technicality.

My work in this area has faced several formal peer reviews and not
shown to be flawed, though some sci.math'ers have diligently argued
otherwise and even actively interfered in the journal process by
sending emails to a journal that had a paper of mine, and succeeded in
cowing the chief editor Ioannis Argyros so that he withdrew my paper
without proper cause and without even allowing me to defend against
the charges the sci.math'ers made.

They broke him completely.

3. I have outlined a complete ring I call the object ring based on
two primary requirements:

  a. No rational unit other than 1 or -1 is in the ring.

  b. No non-unit member of the ring is a factor of any two integers
that are coprime in the ring of integers.

Using that definition you can look back at numbers not units in the
ring of integers and find that they are units in the ring of objects
which shows how misleading the ring of algebraic integers can be.

Basically you can have u_1 u_2 = 1, where u_1 is a unit, but while it
is in the object ring it's not an algebraic integer because of the
technicality that it's not the root of a monic polynomial with integer
coefficients, and that means that u_2 is not a unit.

Then you might assume that u_2 because it's not a unit in the ring of
algebraic integers is properly a factor of some other algebraic
integer, when it's actually a unit factor.

>From there you can continue to build a huge edifice of error, and
unfortunately that is what occurred as an entire branch of mathematics
was built up from this simple error.

My mathematical position is absolutely solid, which leaves posters
arguing about the details trying to convince that constants are not
constants, though I can show they are relying on unit factors to make
their arguments.

However, despite repeated explanations these posters continue with
their assertions, and they have shown a willingness to step far out of
bounds like with their coordinated email assault on my paper that went
to the Southwest Journal of Pure and Applied Mathematics:

http://www.emis.de/journals/SWJPAM/vol2-03.html

My take on the issue is that since it's readily explainable by using
analogies like

x^2 + 4x + 3 = (x + 3)(x + 1)

and talking about how a corollary doesn't exist in the ring of
algebraic integers that I can get some people to think about the
silliness of fighting over arbitrary convention, as if just because
some people over a hundred years ago put up a definition you can throw
out algebra!

Over time some people should understand the argument, and see through
the tactics used against me to gain an ever more negative opinion of
the math community.

Over time that negative opinion, especially given that math professors
continue to teach erroneous ideas--now possibly deliberately giving
young minds false information--will likely move to specific actions
against the math community, well within most of your lifetimes.

Given societies propensity for harsh penalties, some of you may face
jailtime or significant loss of personal fortune, along with a great
deal of shame.

My suggestion at this point is objectivity.

If I'm right you have nothing to gain and everything to lose by
fighting correct mathematical results. While you may feel that you
can win, that is the typical criminal thinking that helps to keep our
world so interesting.

Criminals usually think they'll get away with it, so if you wish the
adjective "criminal" added to you, properly, and face a very angry
society down the road, as people take education kind of seriously,
then continue as you have been doing.

Huge universities like Princeton or Harvard can be brought to their
knees on this issue, and your academic colleagues probably won't be
appreciative of the massive black eye that academia can get.

Alternatively, you can simply start playing fair, and I say start
since sci.math'ers have repeatedly stepped over bounds, from nasty
webpages including copyright violations, to coordinated email
assaults, to just plain meanness in lots of little ways.

You have presented a story of hostility toward the world and against
the truth, and even if you feel that was other sci.math'ers, don't
make the mistake of thinking life is fair.

If a few years from now, you're sitting in a jail cell, wondering how
you got there, or wandering the streets, unable to get a job, then the
door will have been closed as you will not be able to come back to
now.

James Harris

Relevant Pages

  • Re: JSH: Resolution now possible
    ... My position is that the definition of the ring of algebraic ... >properly units that are excluded on the technicality that they are not ... >roots of monic polynomials with integer coefficients. ... >out algebra! ...
    (sci.math)
  • Re: -- explorer le fourier --
    ... In algebra there is a ... semi-group and a commutative ring R and consider ... if one wants to generalise certain famous properties of polynomials ... was a generalisation of serre's question: ...
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  • Re: Possible flaw in the polynomial ring A[X] construction
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  • Re: JSH: Simple proof
    ... >polynomials with integer coefficients. ... of a unit is defined only with respect to some ring. ... >> commutative algebra) this should be possible in a few lines instead ... No>>sides<< in that discussion just mathematics! ...
    (sci.math)
  • Re: Possible flaw in the polynomial ring A[X] construction
    ... distinguish it from the product of polynomial functions. ... for rings of finite characteristic, so let us consider the base ring to ... the ring of polynomials over this field is ... with the base ring being the field of two elements. ...
    (sci.math)