My Work--Objective Review - alt.math.undergrad

Message from discussion My Work--Objective Review

W. Dale Hall

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More options Jun 22 2003, 1:21 am

Newsgroups: sci.math, sci.skeptic, alt.writing, alt.math.undergrad

From: "W. Dale Hall" <wd_h...@pacbell.net>

Date: Sun, 22 Jun 2003 05:20:51 GMT

Local: Sun, Jun 22 2003 1:20 am

Subject: Re: My Work--Objective Review

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James Harris wrote:
> noraba...@hotmail.com (Nora Baron) wrote in message <news:36024859.0306191512.51c012d3@posting.google.com>...

... stuff deleted ...

> As requested in my second reply, you need to give more detail here.

> Also as noted repeatedly, proofs don't duel.

> If I'm wrong then there's an error in my proof.

> Trying to attack one proof by claiming it contradicts with another is
> useless.

> You can cast doubt that way, but to prove a "proof" false, you have to
> deal with the actual argument within it.

>>>>Let r' = F12(r) and s' = F12(s). Note that
>>>>both r' and s' are algebraic integers. Thus eqn (1)
>>>>reduces to

>>>> r'*a2 + s'*5 = 1.

>>>>That is, a2 is also coprime to 5.

>>>>Similarly one shows that a3 is coprime to 5.

>>>Which looks like a good example to show those who wondered how what
>>>I've shown highlights an error in *taught* mathematics.

>>>It's basically an abuse of Galois Theory.

>> What's the abuse?

> My belief has been that posters like yourself have been abusing Galois
> Theory as I don't believe it's wrong. I think you're cheating, which
> is why you wish to go to some other argument rather than deal with the
> one I've presented.

> So I see it as an abuse.

> Alternatively, Galois Theory IS wrong.

> Or you may *believe* I'm wrong, but if I'm wrong there would be a way
> to show it using my work.

> That is, if mathematicians are experts, which by definition they are,
> and I'm not a mathematician, but claim to have a proof, it hardly
> makes sense for mathematicians to use an alternative argument, as I'll
> point out the potential for abuse.

> It'd seem more rational for mathematicians to save their energy and
> attack my work itself.

>>>>Therefore if one of a1, a2, or a3 is coprime
>>>>to 5, they all are.

>>>>But a1*a2*a3 = 65. Thus at least one of a1,
>>>>a2, and a3 is NOT coprime to 5. Thus a contradiction.

>>>>The claim in the Advanced Polynomial Factorization
>>>>paper is therefore wrong.

>>><deleted>

>>>Now I've explained more than once that I prove that x has y as a
>>>factor, but x/y is not an algebraic integer, which is a

>> contradiction.

>>>So *obviously* there's a problem somewhere with what mathematicians
>>>are doing if they think they can prove something that's false.

>>I would say obviously there is a problem somewhere,
>>yes.

> Then it hardly makes sense for you to spend time and effort not
> addressing my central claim which is that I have a proof.

> After all, if you found an error in that proof, you could make a VERY
> short post, and it'd be over instantly--no more discussion needed.

> CERTAINLY if I refused to acknowledge the truth, then I might continue
> arguing, but at least other posters would know there was a discovered
> error which they could view themselves to make their own decision.

How about this:

Let z be any root of the polynomial:

p(x) = x^3 - 12 x^2 + 65,

and define these polynomials:

q(x) = 8 x^2 - 76 x -185
r(x) = 8 x^2 - 4 x - 45
s(x) = 4 x^2 - 37 x - 104

Then the following are trivial, if tedious, to show:

5 = q(z)*r(z).
z = r(z)*s(z).

Finally, r(z) has minimal polynomial

MinPoly(r(z)) = x^3 - 969 x^2 + 315 x + 5

This shows that

1. 5 and z [remember z is *any* root of p(x)] have a mutual
factor, r(z).

2. r(z) is an algebraic integer.

3. The remaining factor of 5 is another algebraic integer q(z).

4. The remaining factor of z is another algebraic integer s(z).

5. r(z) is NOT a unit.

Besides this, the fact that the SAME polynomials q,r,s suffice to
produce the common factor between z and 5 is in accord with what one
expects from Galois theory; the common minimal polynomial for the
(varying) factor of 5 is similarly in accord with what one would
expect from Galois theory.

Since the a's in the factorization of

65 x^3 - 12 x + 1 = (a1 x + 1)(a2 x + 1)(a3 x + 1)

are precisely equal to (-1) times the roots of

p(x) = x^3 - 12 x^2 + 65 = (x - r1)(x - r2)(x - r3),

this result about the roots of p(x) directly shows that JSH is wrong.

> Now then are you a mathematician?

> If so, then you are a math expert by definition. Then if there is an
> error in my paper you should be able to point it out, and quit wasting
> so much time trying to fight my proof with claims of other proofs of
> your own.

The above shows that the so-called "Primary argument" in your paper is
in error. I may spend the time and effort to isolate the first error in
that section, but I will make no promises at this time.

>>>Finally, notice the attempt to disprove a proof with *another*
>>>argument, which is claimed to be a proof.

>> You claimed something was true. I gave an argument
>> to show it wasn't.

> You fought a conclusion of one argument, which I claim is a proof,
> with another argument which you claim is a proof.

> I challenge you to find an error in my argument; you challenge me to
> find an error in yours.

> It's a waste of time.

> I'm not a mathematician. My argument is simpler.

I have shown *directly* that your conclusion is in error. I may look
closer to find the initial error. It is not my responsibility to wipe
your rumpus every time you make poopy, though, so I may just leave you
all stinky.

> So now there are dueling claims. You claim you gave an argument--I
> presume you'd claim it is correct--proving me wrong, I say you're
> wrong.

But I've shown *directly* that your conclusion is incorrect. Is that any
sort of thing you should pay attention to?

> Isn't anyone else bothered by the implication that mathematics is a
> mess?

Doesn't it bother you to be just plain wrong?

AGAIN????

> What's with all the debate?

> Are all mathematicians such losers that they can't handle a claim from
> an admitted non-mathematician, about a paper that's on display 24
> hours a day?

Are you such a loser that you need to harangue, taunt, cast aspersions,
and make a nuisance of yourself? All for reasons that wouldn't be
acceptable if you were in fact correct, yet you are apparently NEVER
correct.

> ARE YOU ALL LOSERS??!!!

> Yup, I'm frustrated.

>> Four possibilities:

>> 1. I have an error in my argument. You however did
>> not point out any error.

> I'm not a mathematician. Why in the hell should I necessarily be able
> to find an error in your argument?

> Dueling claims continue.

I have shown you to be wrong. Irrefutably. Do the arithmetic.
The above numbers are r(z) are common factors of 5 and z (where z
ranges over the roots of the polynomial p(x)), so they are also
common factors between 5 and your ai's . Each ai has a factor in
common with 5. Theses factor are (1) integral over Q, (2) not units.

>> 2. You have an error in your argument. I did not
>> point it out in my post, but it has been pointed
>> out many times previously. Your argument depends
>> on the form that a factorization has in a degenerate,
>> singular case (when m = 0). You argue implicitly
>> that that same form of factorization must hold in the
>> nonsingular case in which you are actually interested.
>> It does not. This has been pointed out innumerable times.
>> Arturo and others have tried many times to get
>> you to understand it, but they have failed. I will
>> probably fail as well.

> If that's true then you can reference actual statements in the paper.

The actual statement is this:

Therefore, with the factorization

65 x^3 - 12 x + 1 = (a1 x + 1)(a2 x + 1)(a3 x + 1)

one fo the a'2 is coprime to 5.

> What I see is an unsupported statement, and worse, you have an appeal
> to authority by mentioning Arturo Magidin.

What I see is a pattern of obsession with the evil Arturo Magidin, and
an inability of JSH to distinguish between poo and poonola.

> It seems to me that you are unsure of your own statement, and possibly
> wish to convince others without presenting actual evidence.

It seems to me that you should go back and find out where you are wrong,
and perhaps learn to verify a proof *before* calling people names.

>> 3. Both of us have errors in our arguments.

>> 4. Neither of us has an error in our arguments. There
>> is a fundamental contradiction in mathematics. I
>> think we should just put this idea aside. It
>> is the least likely of the possibilities and it
>> does not obviously lead anywhere.

> There is no fundamental contradiction in mathematics.

> I have presented the most logical possibility before which is that
> mathematicians are lying.

Oops, in the presence of evidence, the most logical possibility is the
one that's in agreement with the evidence. To date, all the evidence
we have is your track record, as compared to the track record of the
contributors of sci.math in demolishing your false claims.

These track records suggest something quite different from what you're
suggesting as being most likely. Could it be that you're blinded by
your obsessive need to show up those fargin iceholes?

>> It's also possible that the fact I used about automorphisms,
>>which comes from Galois theory, is wrong. That too seems
>>unlikely since Galois theory has been around for over 160
>>years and looked at by many very smart people, and this
>>fact is encountered at the most basic level. I think that
>>too should be put aside.

> I don't care how long it's "been around", if it's false it's false.

> If it's true it's true.

Galois theory has been tested FAR more than

(1) Relativity,
(2) Quantum mechanics,
(3) Object math [snrk]

> And that condition is independent of time.

> However, I should point out that Galois Theory is a field theory.

Again, you betray abysmal ignorance. You must imagine that results
derived from field considerations cannot be used to make statements
about subrings of that field. That's pretty much an indictment of
the level at which you operate, and that level will place a strict
limit on how far you can proceed, except by sheer accident.

> My work is not over fields.

> Still either you screwed up that F12 bit above, or Galois Theory is
> wrong.

Or, as I have just shown *directly*, you are just plain wrong.

Couldn't get your brain wrapped around that concept, now, could you?

> I'm interested in other replies that address whether you screwed up
> Nora.

Nora is correct. JSH is incorrect.

>>>It's like trying to fight a proof with a proof, but proofs can't

>> fight

>>>each other.

>> We both present arguments. You say yours is a proof.
>>I say mine is. We are not both right. In the end
>>we have to try to convince other people and each other.

> <deleted>

> That's stupid.

> A proof begins with a truth and proceeds by logical steps to a
> conclusion which then must be true.

Oh, but, er, didn't I just show you how wrong you were?

Your conclusion IS WRONG!

> So all that's necessary is to start at the beginning and trace out
> each step.

Too bad you screwed up, isn't it?

> That IS possible with my paper, and I've done it which is why I get to
> have fun calling people like you out, and also calling you a jackass.

But your arguments lead you to incorrect conclusions. Why on earth would
you continue with such poor results? Doesn't it embarass you to make a
fool of yourself with such amazing regularity?

> You'll have a harder time tracing out your argument, but it might help
> you out to try, if you have the ability Nora.

No, standard mathematics is well-enough constructed, and comes with
sufficient infrastructure (by means of an array of lemmas & theorems,
standard examples and techniques) that allow one not only to produce
proofs but also to isolate errors.

> Yup, are you smart enough Nora?

It's all about how *smart* someone is, isn't it? The world
isn't always just about how *smart* people are, but sometimes
it's about producing correct results. No matter how *smart*
you think you are, as long as you continue to be wrong while
insisting you're right, as long as you continue to insult those
who *are* right, you're going to be chasing your own tail.

How long do you intend to keep this stupid game going? Lots of us
use this as a form of perverse entertainment; my guess is that you
are also using it in that way, believing somehow that you're fooling
someone. If you truly believe you're correct, you'll do something to
make that manifest, such as getting yourself some education in the
fields where you pretend to have ability.

> Screw convincing people. People are often stupid enough to be
> convinced of just about anything.

It's clear you can be convinced of anything you scribble down.

> James Harris

Dale

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