Re: JSH: Fool all of the people, all of the time?
From: Nora Baron (norabaron_at_hotmail.com)
Date: 12/07/04
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Date: 6 Dec 2004 16:17:52 -0800
James Harris wrote:
> imaginatorium@despammed.com (Brian Chandler) wrote in message
news:<f2c35871.0412051119.5b676b91@posting.google.com>...
> > jstevh@msn.com (James Harris) wrote in message
news:<3c65f87.0412050552.40525729@posting.google.com>...
> > > imaginatorium@despammed.com (Brian Chandler) wrote in message
news:<f2c35871.0412042036.542cbcd6@posting.google.com>...
> > > > jstevh@msn.com (James Harris) wrote in message
news:<3c65f87.0412040746.3ff61803@posting.google.com>...
> > > >
>> > > [snip]
>> > >
>> > > > Good question. But to believe that my results haven't
traveled
>> > > > through mathematical society at this point you have to believe
that a
>> > > > very basic argument, which I know I can explain in about an
hour as I
>> > > > did it in-person at my alma mater Vanderbilt University, which
shoots
>> > > > down one of the underpinnings of algebraic number theory could
just
>> > > > float out there, be argued about by me on Usenet for years,
and never
>> > > > get heard of by leading mathematicians.
>> > >
>> > > Impressive bit of sentence construction. Incidentally, though:
"argued
>> > > about by me on Usenet for years" - which bit _is_ this? I know
you
>> > > seem to have been claiming to have found errors in 'core' for
years,
>> > > but I thought they were different arguments. Since as you say
>> > > yourself, you've been wrong a lot in the past, and the important
bit
>> > > is the current argument, which alone of course is Correct, how
long
>> > > has this bit been going? I'd have thought less than "years"...?
>> > >
>> > > [snip]
>> >
>> >
>> > The full timeline is that back in December 1999 I first discovered
an
>> > approach which would lead to the analysis tool of non-polynomial
>> > factorization.
>>
>> <snip>
>>
>> > The earliest arguments in this area go back to December 1999.
>>
>> OK - I'll give you your "arguing for years".
>>
>
>So you will accept what is true. How wonderful for you.
>
>> > > Newsflash!! People are asking questions!! Here's the commonest
one:
>> > >
>> > > "What does 'properly a unit' mean?"
>> > >
>> > > Only you can answer.
>> > >
>> >
>> > That's an old game of trying to cause major arguments over the use
of
>> > some term or other, as I now simply shift from usage that
sci.math'ers
>> > find easily works to provoke confusion.
>>
>> Sorry, I'm a bit lost here. You're accusing me of "playing a game",
>> just because I asked what a bit of your argument means? I don't
>> understand what you mean when you claim that while
something-or-other
>> is not a unit in the ring of algebraic integers, it _is_ "properly a
>> unit". I guess it means something to you, but I surmise it means
>> nothing to anyone else. (That means you are speaking a private
>> language, and the closest to fame you can hope for is the status of
a
>> Voynich manuscript in a half-millennium or two.)
>
>You take a phrase out of context, and make a big deal out of it,
>asking for some explanation, when in context when used the explanation
>was in what I said.
>
When real mathematicians use a new term, they
define it. Period. No dependency on 'context'.
>It's an old tactic that sci.math'ers have used for years.
>
The tactic here is evasion.
>Pick a phrase, take it out of context, make a big deal out of it.
>
>And, you know? Lots of times I HAVE used certain phrase differently
>from standard usage, and misused terms I didn't understand or simply
>just didn't care a lot to get exactly right in informal discussions.
>
Mathematics, unlike sociology, has to be precise.
>Time after time, posters have reacted as if these posts are such
>important communications that perfection is a requirement.
>
There is no reason in mathematical discourse not to be
explicit and precise.
>I reserve the right to at times just babble. It's not a big deal.
>
Then in return don't expect anyone to believe you.
>This is Usenet.
>
So? Are you trying to do math or not? It doesn't matter
where you do it.
>> I find all this stuff about peering into polynomials looking for
>> 'factors' a bit confusing, too. I mean, of course in (a) below,
>> there's a factor of 4 that can be divided off:
>>
>> (a): 4x^2 + 4x - 4
>>
>> So if n is an integer - any integer - I know that 4n^2 + 4n -4 is a
>> multiple of 4. However:
>>
>> (b): (x+1)(x+2)
>>
>> Does this polynomial have a factor of 2 in it? I can see a '2', but
it
>> doesn't look like a factor. And again I know that any integer n
means
>> that (n+1)(n+2) is a multiple of 2. So what's going on? Is there any
>> difference from the case of (a). You seem to reject the idea that
>> there's really any difference between talking about polynomials *as*
>> polynomials and evaluations of polynomials, because that's "voodoo
>> math" - have I got that right?
>
>Well here's a good chance to show how sci.math'ers routinely try to
>mislead.
>
>With integer you have the any integer either is even or has a residue
>of 1.
>
>That is, given an integer x, either x = 0 mod 2, or x = 1 mod 2.
>
>So trivially you can put up something like (x+1)(x+2) and know it must
>be even.
>
>However, in the ring of algebraic integers, no such relations exist.
>
>That is, there is no non-unit in the ring of algebraic integers such
>that EVERY algebraic integer is either divisible by that number or has
>the same residue.
>
So do you think, given (x + 1)(x + 2), where x is an algebraic
integer, that its divisibility or coprimeness to 2 does not
depend on x ? If it *is* divisible by 2, does 2 always factor
out of it in the same way?
>You don't even have the even case with algebraic integers as in the
>ring of algebraic integers it is NOT true that (x+1)(x+2) must have 2
>as a factor.
>
I would like to see you prove that. Can you?
But in any case you are missing the point. (x + 1)*(x + 2)
may be coprime or noncoprime to 2 for various values of x. But
there can be no doubt that its coprimeness or noncoprimeness
is a FUNCTION of x.
And that is really the point that is relevant to your
factorization of P(x) and P(x)/49, isn't it? How factors of
49 might divide out of a product of functions of x ? Does it
necessarily always happen in the same way, or is it dependent
on x ?
>Now the example (x+1)(x+2) in the ring of integers is childish
>mathematics at the most basic level, but posters have routinely used
>that example for years to try and claim that it shows how my research
>can be wrong.
>
It's meant as an analogy, since you do not seem to be able
to understand the real thing.
>You people don't even try hard.
>
>> And what ever should I think about (c) - absolutely no trace of a
'3'
>> anywhere:
>>
>> (c): x(x+1)(x+2)
>>
>
>Yet another childish example based on any *integer* x, either being
>divisible by 3 or having a residue of 1 or 2.
>
>That childish game can be played on and on with integers, but it has
>no meaning outside of the ring of integers, and it doesn't invalidate
>my research findings.
>
>> Another thing I wonder about: OK, suppose the dam bursts. Suppose
>> suddenly you are on tv shows and whatnot. The mathematicians are all
>> disgraced, flung into debtors jails. Are you going to rewrite all
the
>> text books? Who will do it?
>
>Mathematicians will NOT all be disgraced and flung into jail.
>
>If there are some who end up prosecuted it'd most likely be a choice
>few.
>
>And hey, not all mathematicians work in the area of algebraic number
>theory. Number theorists are the ones who are really going to take
>the hit.
>
>How might a prosecution work?
>
>Well, consider a federal prosecution that considers whether or not
>some number theorist knowingly continued both to teach what I'd shown
>to be false, and to receive federal funds for their research.
>
Are people jailed now for teaching false things? You are
aware probably that some people still teach Bohr's model of
the hydrogen atom. Are they being prosecuted?
>So they'd have tax dollars for two things: teaching and research
>
>The charge would be fraud. Evidence might include emails of that
>mathematician and conversations had with colleagues who would be
>pulled into grand juries and later into court to testify under oath.
>
>Likely punishment? A fine. Blockage from receipt of any more federal
>funds. Censure from their university, and probably removal from
>teaching position.
>
Might the blade cut both ways? You have tried very hard to
convince large numbers of people that your "proof" is right,
even in the face of counterexamples which you have not
refuted. Prosecuting you for fraud would be trivial. There
would be literally thousands of expert witnesses, and none of
them for the defense. You have repeatedly accused people here
of lying simply because they post arguments saying your
proof is wrong. You have accused people of committing fraud.
If you are wrong (AND YOU ARE!), YOU could be sued for libel.
In fact you have previously accused people of lying about
many of your former arguments, and then later you were forced
to admit they were right. RIGHT NOW, your own postings which
include (1) the accusations of lying and (2) the later
admission that those you were accusing were correct, could be
used against you in a lawsuit for libel. Who do you think
would win?
>> FWIW, I have a copy of Herstein's "Topics in [pre-Harrisian]
Algebra"
>> here, and it only mentions algebraic integers very briefly, in the
>> problems. There's the usual definition, then the first problem
reads:
>>
>> 10. If _a_ is any algebraic number, prove that there is a positive
>> integer _n_ such that _na_ is an algebraic number.
>>
Error there: last phrase should be 'algebraic integer'.
>> (I can type more if required.) Well, is Herstein's solution to this
>> problem wrong?
>>
>
>Amazingly enough, most people actually care about what's TRUE.
>
Which in this very case you overlooked entirely with your
self-serving non-answer.
>More than likely there will be a flood of mathematicians into
>algebraic number theory, as it will be an opened up field with major
>opportunities for advancement.
>
Delusion.
>Think about it. In many areas a young mathematician can work for
>years and get nowhere. In algebraic number theory, they will have the
>opportunity to be a significant figure in the remaking of an entire
>discipline.
>
>When that finally gets out, it will be the hottest field in
>mathematics.
>
Hey, my offer of a bet of $100 that the Annals of Mathematics
will reject your paper "Advanced Polynomial Factorization"
still stands. If they publish it, I send you a one hundred
dollar bill. If they reject it, you send $100 to the charity
of my choice, and post a cancelled check on a website to prove
you did it. If you are confident enough to threaten lawsuits
and prosecution for fraud, surely you must be confident that
the world's most prestigious math journal will get it right.
How about it? Do you believe your own "proof", or not ?
.
Nora B.
>
>James Harris
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