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jst...@gmail.com

unread,
May 19, 2007, 11:31:03 AM5/19/07
to
I'm not a professional mathematician, so my efforts can be called
recreational.

Years ago I got a paper published, and sci.math'ers went after it, and
got it retracted by the journal editors with some emails. The journal
later died, shutting down after one more edition.

The sci.math'ers of course have maintained that my paper was wrong,
and that they were right.

Over the years I've worked at explanations of my research that take
away the objections they relied upon so that I can convince that my
original work was valid, and they were wrong.

I finally have that paper which I've tested in posts to this newsgroup
and alt.math and alt.math.undergrad as understandably I do not like
the sci.math newsgroup, but was not surprised that sci.math'ers came
over to attack my paper.

And I have been gratified that their tactics have failed this time as
the paper does cover everything as I need against their kind of
opposition.

They use tactics that I've learned over the years are not about
getting to the truth, but about convincing people that I am wrong, so
I have directly answered those tactics with proof presented in such a
way as to shut them down.

But what now?

Journals are wary of me now. After all, one journal keeled over and
died!!!

The paper is available to the world on a Google group of mine, but
that seems like a crap shoot--waiting and hoping that someone will
notice this result.

And what a result!!!

I managed to use identities to get some incredible number theory
analysis done.

And that's so simple of a thing, like people use identities all the
time in mathematics.

e.g.

x^2 + 2xy = z^2

add y^2 to both sides to get

x^2 + 2xy + y^2 = y^2 + z^2

and you can solve for x:

x = sqrt(y^2 + z^2) - y

So I have a remarkable technique that relies on subtracting from
identities, extending mathematics. Growing knowledge.

A spectacular story that even includes an entire mathematical journal
imploding, and the will of a newsgroup against the foundations of
mathematics itself where Usenet posters managed to trump the formal
peer review process--and I'm stuck.

The real world is often about comfort, and just like inconvenient
truths can get fought in other areas, so can they in mathematics.

As long as people like you allow mathematicians to not do their jobs
for their own comfort against knowledge, there will not be change.

No matter what they say, mathematicians are highly political people.
I think they claim to be otherwise to protect themselves.

But remember, those mathematicians at that journal that originally
published my research caved with just a few emails from some
sci.math'ers and consider that my research is bold, innovative, and
correct, relying at its base on using identities in a very powerful
way for analysis.

If you were a mathematician at a major university considering having
your life significantly changed by accepting the truth, or sitting
back like you just didn't know so that things could go as before,
might you not be tempted if you thought you could get away with it?

Mathematicians are human beings too.

So then, what do I do? If mathematicians work to close all the doors
against an inconvenient truth, what options do I have?


James Harris

José Carlos Santos

unread,
May 19, 2007, 1:50:37 PM5/19/07
to
On 19-05-2007 16:31, jst...@gmail.com wrote:

> I'm not a professional mathematician, so my efforts can be called
> recreational.

By the same argument, since Fermat was not a professional mathematician
(he was a judge), his efforts can be called recreational. Is that what
you think?

> Years ago I got a paper published, and sci.math'ers went after it, and
> got it retracted by the journal editors with some emails. The journal
> later died, shutting down after one more edition.

Are you under the delusion that there is some connection between those
two facts?

> Over the years I've worked at explanations of my research that take
> away the objections they relied upon so that I can convince that my
> original work was valid, and they were wrong.

Convince? Who, besides you?

> I finally have that paper which I've tested in posts to this newsgroup
> and alt.math and alt.math.undergrad as understandably I do not like
> the sci.math newsgroup, but was not surprised that sci.math'ers came
> over to attack my paper.
>
> And I have been gratified that their tactics have failed this time as
> the paper does cover everything as I need against their kind of
> opposition.

Isn't that what you said about the previous paper?

> But what now?
>
> Journals are wary of me now. After all, one journal keeled over and
> died!!!

What has that to do with you?

> The paper is available to the world on a Google group of mine, but
> that seems like a crap shoot--waiting and hoping that someone will
> notice this result.
>
> And what a result!!!
>
> I managed to use identities to get some incredible number theory
> analysis done.
>
> And that's so simple of a thing, like people use identities all the
> time in mathematics.
>
> e.g.
>
> x^2 + 2xy = z^2
>
> add y^2 to both sides to get
>
> x^2 + 2xy + y^2 = y^2 + z^2
>
> and you can solve for x:
>
> x = sqrt(y^2 + z^2) - y

What do you mean by "sqrt", James?

> So I have a remarkable technique that relies on subtracting from
> identities, extending mathematics. Growing knowledge.

How much mathematics have you extended so far?

> So then, what do I do? If mathematicians work to close all the doors
> against an inconvenient truth, what options do I have?

Keep sucking your thumb.

Best regards,

Jose Carlos Santos

Larry Hammick

unread,
May 19, 2007, 2:41:00 PM5/19/07
to
"José Carlos Santos"

> On 19-05-2007 16:31, jst...@gmail.com wrote:
>
>> I'm not a professional mathematician, so my efforts can be called
>> recreational.
>
> By the same argument, since Fermat was not a professional mathematician
> (he was a judge), his efforts can be called recreational. Is that what
> you think?
>
>> Years ago I got a paper published, and sci.math'ers went after it, and
>> got it retracted by the journal editors with some emails. The journal
>> later died, shutting down after one more edition.
>
> Are you under the delusion that there is some connection between those
> two facts?
Well, we really should give JSH credit for finding a journal that was
willing to publish some of his shit, probably without even reading it. I
would have it thought it quite unlikely. And I'm sure he misses the outfit!
LH


Peter Percival

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May 19, 2007, 2:58:25 PM5/19/07
to
jst...@gmail.com wrote:
>
>..

>
> So I have a remarkable technique that relies on subtracting from
> identities, extending mathematics.

Um... have mathematicians never subtracted from identities before? You
seem to be referring to this triviality:

if X = Y then X - Z = Y - Z.

Not exactly earth-shattering is it?

--
Remove "antispam" and ".invalid" for e-mail address.

jst...@gmail.com

unread,
May 19, 2007, 9:00:39 PM5/19/07
to
On May 19, 11:58 am, Peter Percival

<Peter_Perci...@antispamhotmail.co.uk.invalid> wrote:
> jst...@gmail.com wrote:
>
> >..
>
> > So I have a remarkable technique that relies on subtracting from
> > identities, extending mathematics.
>
> Um... have mathematicians never subtracted from identities before? You
> seem to be referring to this triviality:
>
> if X = Y then X - Z = Y - Z.
>
> Not exactly earth-shattering is it?

Nope! The technique relies on that but that is not all of it.

Another example showing use of identities is with

x^2 + 2xy = z^2

as you can add y^2 to both sides and then solve to find

x = sqrt(y^2 + z^2) - y

so saying that my technique relies on subtracting from identities does
not tell you what the technique is, nor does it mean it's not
remarkable.

I think you show part of the problem I face though as I'm a very
logical person, whereas I get confronted with quite a few people from
the mathematical community who just don't follow basic rules or seem
to get confused on very basic details, but they are the gatekeepers.

So I get a paper published and these people just proclaim that
publication in a peer reviewed mathematical journal is meaningless!
Unless you mention some other result that they like then they explain
why publication matters!

The mathematical journal dies after succumbing to group pressure and
they say that's not a big deal, like it happens every day.

So I work for years on an approach that takes away the ability to find
easy ways to confuse people in rejecting, and you can see your
newsgroup cluttered with nonsense stuff from these people fighting
mathematical proof.

I say that the situation is really a case of some pretend people who
wish they could be real mathematicians who can't, so they play it,
like actors. And when challenged they just make up anything to say to
defend what they do.

But what they do is not mathematics, no matter how much they sell it
as such.

And if you spend time learning crap stuff--GIGO--then what makes any
of you think you gain a real advantage?

You get taught junk, and your mind is being fueled by junk, from
people who will never accept a proof--if it doesn't suit them.

They just are not smart enough to do real mathematics.


James Harris

jshs...@yahoo.com

unread,
May 20, 2007, 12:13:12 AM5/20/07
to

You have stated many times that the people who post to the math
newsgroups are nothing. They are not real mathematicians. Then how
did they put any pressure on a math journal? What was there leverage
James? What did they threaten to do to them if they did not retract
your paper? How about some details instead of just empty baseless
accusations.

Peter Percival

unread,
May 20, 2007, 9:14:19 AM5/20/07
to
jst...@gmail.com wrote:
>
> On May 19, 11:58 am, Peter Percival
> <Peter_Perci...@antispamhotmail.co.uk.invalid> wrote:
> > jst...@gmail.com wrote:
> >
> > >..
> >
> > > So I have a remarkable technique that relies on subtracting from
> > > identities, extending mathematics.
> >
> > Um... have mathematicians never subtracted from identities before? You
> > seem to be referring to this triviality:
> >
> > if X = Y then X - Z = Y - Z.
> >
> > Not exactly earth-shattering is it?
>
> Nope! The technique relies on that but that is not all of it.
>
> Another example showing use of identities is with
>
> x^2 + 2xy = z^2
>
> as you can add y^2 to both sides and then solve to find
>
> x = sqrt(y^2 + z^2) - y
>
> so saying that my technique relies on subtracting from identities does
> not tell you what the technique is, nor does it mean it's not
> remarkable.

I don't wish to sound impolite but inferring that

x = sqrt(y^2 + z^2) - y

from

x^2 + 2xy = z^2

is still trivial. It follows from the quadratic formula which children
learn in secondary school. Adding y^2 is called "completing the
square."

Note: what I call secondary school, you probably know as high school.

jst...@gmail.com

unread,
May 20, 2007, 11:16:56 AM5/20/07
to
On May 20, 6:14 am, Peter Percival

Yes!

I have another technique that is not what you showed, and it is not
completing the square. It is a remarkable technique.

If you wish you can simply post it and explain why you think it's not
remarkable.

But posting examples of use of identities that ARE trivial do not make
it trivial as well, understand?

Does that make sense to you?


James Harris


Frank J. Lhota

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May 20, 2007, 7:21:31 PM5/20/07
to
You want suggestions? You've probably read everything that I suggest here,
but since you asked, here is my advice for how you can be more effective.

1. Please be clearer and more precise about your claims and assumptions.
Numerous times you have presented algebraic arguments dealing with
divisibily and primeness without specifying *which* ring you're dealing
with, or the domain / range of your functions, or whether these functions
are polynomials, etc. No respectable mathematician is going to accept a
theory if she / he is unclear about what that theory is; doing so would be
the scholarly equivalent of writing a stranger a blank check.

2. Even when the clearest of explainations is given, there will be
posters who will have questions about this work. To win over these posters,
you need to directly answer these questions. For years now, posters have
asked you to clarify what this "flaw" in the ring of algebraic integers is,
but in spite of the repeated requests, you have never identified a commonly
used theorm about algebraic integers that turns out to be false. Many of
your replies to other poster's questions have been exceedingly rude. If you
really don't want to convince other posters of the correctness of your work,
that's fine. But with your uncooperative behavior, you forfeit any right to
complain about not being accepted by these groups.

3. If you want to be taken seriously, cut the social critique of
mathematicians. Did Alfred Einstein advance the theory of relativity by
writing screeds about how classical physicists don't really care about
physics? Did Max Planck win converts to his quantum theory by contending
that those professor who did not immediately accept his work work would soon
be lead out of their universities in handcuffs? No, because such statements
would alienate the very people that they needed to win over. Rants like this
come across as paranoid and narcissistic. I'm a little reluctant to advise
you to cut out the social stuff, for you do have a sizable readership who
follow your posts to get a laugh from your over-the-top rants. Maybe, at
some level, you relish your role as the Howard Beale (see
http://www.imdb.com/title/tt0074958) of the math groups. If so, please feel
free to continue with the rants. But as long as you write about the great
math conspiracy, you will be viewed as a crank.

4. Aim for less lofty goals. When I play on a local softball team, I
harbor no illusions about playing well enough to become a professional
baseball player. I simply am not good enough at the sport to compete
professionally, especially at my age. But nothing prevents me from having
fun with the sport! I take the same approach to mathematics. Since we are
amatures, it is highly unlikely that either you or I will make a major
discovery missed by the professional mathematicians. That does not mean that
we cannot enjoy exploring the topic. Show a little humility in your posts.
Don't take it so hard if you discover something that does *not* completely
revise math as we know it; almost nobody in these groups expects to do it.
Instead, take pleasures in the less earth-shattering but still entertaining
discoveries that we can realistically accomplish.

5. Learn more math! You have blown off book recommendations in the past,
and frankly you have left some of us with the impression that you understand
little more than high school math. Do you really know what an elliptic curve
is, and why elliptic curves are so important to modern number theory?
Elliptic curves are pivotal to Wiles's proof of FLT. To have any credibility
as a critic of this work, you need to demonstrate some expertise on elliptic
curves. If you want to convince us that Galois theory is all wet, you first
need to convince us that you know what a ring is. If you don't know the
answers to these questions, read a book. You'll be a better mathematician,
and besides, it's fun.

So these are my suggestions. You've read them before, and if you don't
follow them, you're bound to read them again.

BTW you still haven't answered questions about the object ring raised in
this thread:

http://groups.google.com/group/alt.math.recreational/browse_frm/thread/70e2dc5e664d8f18/5207ddf63834f55d

In fact, in your most recent paper, you are even /less/ specific about this
ring. How do you expect the world to base math on a ring whose very
definition is unclear? Please clarify what you mean by the object ring.

--
"All things extant in this world,
Gods of Heaven, gods of Earth,
Let everything be as it should be;
Thus shall it be!"
- Magical chant from "Magical Shopping Arcade Abenobashi"

"Drizzle, Drazzle, Drozzle, Drome,
Time for this one to come home!"
- Mr. Wizard from "Tooter Turtle"


jst...@gmail.com

unread,
May 20, 2007, 9:15:21 PM5/20/07
to
On May 20, 3:21 pm, "Frank J. Lhota" <FrankLho.NOS...@rcn.com> wrote:
> You want suggestions? You've probably read everything that I suggest here,
> but since you asked, here is my advice for how you can be more effective.
>
> 1. Please be clearer and more precise about your claims and assumptions.
> Numerous times you have presented algebraic arguments dealing with
> divisibily and primeness without specifying *which* ring you're dealing
> with, or the domain / range of your functions, or whether these functions
> are polynomials, etc. No respectable mathematician is going to accept a
> theory if she / he is unclear about what that theory is; doing so would be
> the scholarly equivalent of writing a stranger a blank check.

That objection does not apply to the current paper. I talk about what
ring is being considered at each point as needed.


> 2. Even when the clearest of explainations is given, there will be
> posters who will have questions about this work. To win over these posters,
> you need to directly answer these questions. For years now, posters have
> asked you to clarify what this "flaw" in the ring of algebraic integers is,
> but in spite of the repeated requests, you have never identified a commonly
> used theorm about algebraic integers that turns out to be false. Many of
> your replies to other poster's questions have been exceedingly rude. If you
> really don't want to convince other posters of the correctness of your work,
> that's fine. But with your uncooperative behavior, you forfeit any right to
> complain about not being accepted by these groups.

I don't work to win over, but to present a correct argument. Correct
arguments should do all the work for you.

As for the ring of algebraic integers it is quite a bit much to ask me
to go beyond proving that it must have some flaw to also showing
exactly what arguments believed to be theorem fail since I can prove
that it must be flawed.

Yes, it'd be nice for me to go the extra step but how can you still
use a ring that is provably flawed relying on the excuse that I
haven't shown a particular argument thought to be a theorem to be
false?

Yet I can point out that I can start in the ring of algebraic
integers, subtract a key expression valid in that ring, from an
identity--which of course can't change the ring--and proceed to find
that with a few more steps I'm forced out of the ring of algebraic
integers, but how is that possible?

It is only possible because the ring of algebraic integers is flawed,
as for instance, it's NOT possible to do that in the ring of
integers.


> 3. If you want to be taken seriously, cut the social critique of
> mathematicians. Did Alfred Einstein advance the theory of relativity by
> writing screeds about how classical physicists don't really care about
> physics? Did Max Planck win converts to his quantum theory by contending
> that those professor who did not immediately accept his work work would soon
> be lead out of their universities in handcuffs? No, because such statements
> would alienate the very people that they needed to win over. Rants like this
> come across as paranoid and narcissistic. I'm a little reluctant to advise
> you to cut out the social stuff, for you do have a sizable readership who
> follow your posts to get a laugh from your over-the-top rants. Maybe, at

> some level, you relish your role as the Howard Beale (seehttp://www.imdb.com/title/tt0074958) of the math groups. If so, please feel


> free to continue with the rants. But as long as you write about the great
> math conspiracy, you will be viewed as a crank.
>

I had a paper published. A few sci.math'ers with some emails making
false claims got it yanked. A little later the freaking journal died.

You people just suck.

That story could not have taken place in physics.

It just couldn't.

It could take place in the mathematical world because of its
weaknesses.

You people cannot be convinced by mathematical proof alone.

You have to be won over.

> 4. Aim for less lofty goals. When I play on a local softball team, ...

I've achieved my lofty goals.

And I am aiming now for rather mean ones--convincing people I have no
respect for to follow their own damn rules, while repeatedly dealing
with pedantic blow hards who find it easy to dismiss even the most
basic of facts, like that dead math journal and the prior publication.

Many of you cannot be convinced by mathematical proof alone, so I'm
going for that extra.


James Harris

jshs...@yahoo.com

unread,
May 20, 2007, 9:37:13 PM5/20/07
to

Yet again James, the journal folded because it published flawed papers
like yours. Simple. Not earth shattering. I am sure others have closed
there doors before and will in the future. Publications go under all
the time. You really need to pay attention to things beyond your own
rantings.

If taken another way, how well could the journal have been trusted in
reviewing your paper if a few e-mails would cause them to retract it.
If that was the case they weren't very reputable and temporary
publication by them wouldn't be something to brag about.

Rupert

unread,
May 20, 2007, 10:07:40 PM5/20/07
to

Not at all. If you are claiming to have overturned accepted
mathematics then we are quite entitled to ask you which parts of
accepted mathematics, and to point out the flaws in the proofs.

Frank J. Lhota

unread,
May 20, 2007, 11:54:14 PM5/20/07
to
<jst...@gmail.com> wrote in message
news:1179710120....@z24g2000prd.googlegroups.com...

> On May 20, 3:21 pm, "Frank J. Lhota" <FrankLho.NOS...@rcn.com> wrote:
>> You want suggestions? You've probably read everything that I suggest
>> here,
>> but since you asked, here is my advice for how you can be more effective.
>>
>> 1. Please be clearer and more precise about your claims and
>> assumptions.
>> Numerous times you have presented algebraic arguments dealing with
>> divisibily and primeness without specifying *which* ring you're dealing
>> with, or the domain / range of your functions, or whether these functions
>> are polynomials, etc. No respectable mathematician is going to accept a
>> theory if she / he is unclear about what that theory is; doing so would
>> be
>> the scholarly equivalent of writing a stranger a blank check.
>
> That objection does not apply to the current paper. I talk about what
> ring is being considered at each point as needed.

... but you still haven't given us a decent definition of your dear object
ring. In this matter, we've been extrorndinarily patient with you. If you
persist in stonewalling any clarification of your work, you will soon find
that everyone will blow you off as a crank.

>> 2. Even when the clearest of explainations is given, there will be
>> posters who will have questions about this work. To win over these
>> posters,
>> you need to directly answer these questions. For years now, posters have
>> asked you to clarify what this "flaw" in the ring of algebraic integers
>> is,
>> but in spite of the repeated requests, you have never identified a
>> commonly
>> used theorm about algebraic integers that turns out to be false. Many of
>> your replies to other poster's questions have been exceedingly rude. If
>> you
>> really don't want to convince other posters of the correctness of your
>> work,
>> that's fine. But with your uncooperative behavior, you forfeit any right
>> to
>> complain about not being accepted by these groups.
>
> I don't work to win over, but to present a correct argument. Correct
> arguments should do all the work for you.

You don't work to win over? That's very telling. It indicates that the real
problem is that deep down, you *don't* want us to accept you and your work.
The role of the maverick mathematical pioneer, the sole holder of the truth
against a sea of cruel and foolish opposition, feeds a strong emotional need
of yours. And so you present your ideas in a way that virtually guarantees
their rejection. Our rejection is your vindication!

That is my diagnosis as an amature therapist. With therapy, as with
mathematics, you're better off seeking the advice of a professional.

> As for the ring of algebraic integers it is quite a bit much to ask me
> to go beyond proving that it must have some flaw to also showing
> exactly what arguments believed to be theorem fail since I can prove
> that it must be flawed.

OK, for the hundreth time, you tell us that this ring is flawed while
refusing to be specific about what that flaw is. You say this rocks the
pillars of modern algebra, but consider it unreasonable to expect you to say
*which* pillar of modern algebra is problematic. Does this sound like the
approach you would use if you were really trying to convince us?

Again, you're looking for rejection. And you're (outwardly) complaining when
you get it.

> That story could not have taken place in physics.
>
> It just couldn't.

Of course it could: a crappy little Physics journal about to go under could
accept a paper out of sheer despiration. Once it was accepted, they could
discover it was so unsound as to be unpublishable.

> It could take place in the mathematical world because of its
> weaknesses.
>
> You people cannot be convinced by mathematical proof alone.
>
> You have to be won over.
>
>> 4. Aim for less lofty goals. When I play on a local softball team, ...
>
> I've achieved my lofty goals.
>
> And I am aiming now for rather mean ones--convincing people I have no
> respect for to follow their own damn rules, while repeatedly dealing
> with pedantic blow hards who find it easy to dismiss even the most
> basic of facts, like that dead math journal and the prior publication.
>
> Many of you cannot be convinced by mathematical proof alone, so I'm
> going for that extra.

This is about as pure Narcissism as it gets. It is not quite as bad as your
fantasy about billions of people worldwide recognising your fame for this
work, but it's close enough. James, get help!

Glen Wheeler

unread,
May 21, 2007, 6:57:34 AM5/21/07
to
"Frank J. Lhota" <FrankLh...@rcn.com> wrote in message
news:MuGdnbHJLdl7iszb...@rcn.net...

> <jst...@gmail.com> wrote in message
> news:1179710120....@z24g2000prd.googlegroups.com...
>> I don't work to win over, but to present a correct argument. Correct
>> arguments should do all the work for you.
>
> You don't work to win over? That's very telling. It indicates that the
> real problem is that deep down, you *don't* want us to accept you and your
> work. The role of the maverick mathematical pioneer, the sole holder of
> the truth against a sea of cruel and foolish opposition, feeds a strong
> emotional need of yours. And so you present your ideas in a way that
> virtually guarantees their rejection. Our rejection is your vindication!
>
> That is my diagnosis as an amature therapist. With therapy, as with
> mathematics, you're better off seeking the advice of a professional.
>
> [...]
>
>> [...]

>> You people just suck.
>
> Again, you're looking for rejection. And you're (outwardly) complaining
> when you get it.
>
>>
>> I've achieved my lofty goals.
>>
>> And I am aiming now for rather mean ones--convincing people I have no
>> respect for to follow their own damn rules, while repeatedly dealing
>> with pedantic blow hards who find it easy to dismiss even the most
>> basic of facts, like that dead math journal and the prior publication.
>>
>> Many of you cannot be convinced by mathematical proof alone, so I'm
>> going for that extra.
>
> This is about as pure Narcissism as it gets. It is not quite as bad as
> your fantasy about billions of people worldwide recognising your fame for
> this work, but it's close enough. James, get help!
>

Frank, have you read (any of) James' blog? This is neither new nor
helpful; he is a deeply troubled individual, and I don't really know how
much psychological help a newsgroup has ever managed to impart. It is
probably going to exacerbate the problem.

I don't really know what to do about his work either. It's broken,
everyone can see that. Unless he alters it in a fundamental way, and builds
something of real value out of it, there won't be anyone to publish it
either. He has been given absolutely outstanding assistance by several
people over time, as well as his fair share of abuse; but it doesn't change
anything.

I pose a question to the group, seriously: why are there large discussions
about this here? Boredom?

--
Glen


Christopher J. Henrich

unread,
May 21, 2007, 9:32:37 AM5/21/07
to
In article <4651...@dnews.tpgi.com.au>, Glen Wheeler <sp...@gew75.com>
wrote:

> > This is about as pure Narcissism as it gets. It is not quite as bad as
> > your fantasy about billions of people worldwide recognising your fame for
> > this work, but it's close enough. James, get help!
> >
>
> Frank, have you read (any of) James' blog? This is neither new nor
> helpful; he is a deeply troubled individual, and I don't really know how
> much psychological help a newsgroup has ever managed to impart. It is
> probably going to exacerbate the problem.
>
> I don't really know what to do about his work either. It's broken,
> everyone can see that. Unless he alters it in a fundamental way, and builds
> something of real value out of it, there won't be anyone to publish it
> either. He has been given absolutely outstanding assistance by several
> people over time, as well as his fair share of abuse; but it doesn't change
> anything.
>
> I pose a question to the group, seriously: why are there large discussions
> about this here? Boredom?

I guess even the most austere of mathematicians have a sneaking
appetite for soap opera.

--
Chris Henrich
http://www.mathinteract.com
God just doesn't fit inside a single religion.

sg...@hotmail.co.uk

unread,
May 21, 2007, 10:02:23 AM5/21/07
to
James Harris wrote:

> As for the ring of algebraic integers it is quite a bit much to ask me
> to go beyond proving that it must have some flaw to also showing
> exactly what arguments believed to be theorem fail since I can prove
> that it must be flawed.

Let's borrow one of your own analogies. Suppose that at the end of the
nineteenth century an amateur physicist claimed that classical
mechanics was flawed. However, whenever anybody asked him to give an
example of an actual prediction of classical mechanics that he thought
was incorrect, he refused to do so, saying that it was "a bit much to
ask", seemingly under the impression that a physical theory could be
shown to be flawed without providing a single incorrect prediction of
said theory.

Of course it isn't "a bit much to ask". What the hell do you think
that established mathematics is, if not a collection of theorems and
proofs? If you want to show a problem with established mathematics,
you have to show a problem with either a theorem or a proof. Simply
claiming that a certain ring is "flawed" is completely meaningless
until you can actually give a precise definition of what it means for
a ring to be flawed. And even if you inexplicably break the habit of a
life time and *provide* such a definition, together with a proof that
it applies to the algebraic integers, you will not have shown any
problem in number theory until you present an example of a proof or
theorem which claims that the algebraic integers do not satisfy your
definition of "flawed".

-Rotwang

Frank J. Lhota

unread,
May 21, 2007, 11:02:38 AM5/21/07
to
First of all, my apologies to the group for messing up the subject
line. I put the "JSH:" back in. Sorry for the inconvenience.

On May 21, 6:57 am, "Glen Wheeler" <s...@gew75.com> wrote:

> Frank, have you read (any of) James' blog? This is neither new nor
> helpful; he is a deeply troubled individual, and I don't really know how
> much psychological help a newsgroup has ever managed to impart. It is
> probably going to exacerbate the problem.

I've read a little of his blog, back when it was called "Math for
Profit" or something like it. It seems to be a rehash of his newsgroup
screeds. His posts were enough to convince me that he is a rather
extreme example of an NPD sufferer.

In the past, however, he has done posts where he has expressed
recognition of the problem. Given that he was asking for suggestions,
I thought there might be a small chance that he might be open to good
advice. As his reply indicates, he is still in heavy denial mode, but
I still thought it was worth a try. By the time I sent this advice,
James had already threatened to call Berkeley in order to raise an
ethics charge against Arturo Magidin, so it is hard to see how
anything in this thread could have made the problem any worse.

> I don't really know what to do about his work either. It's broken,
> everyone can see that. Unless he alters it in a fundamental way, and builds
> something of real value out of it, there won't be anyone to publish it
> either. He has been given absolutely outstanding assistance by several
> people over time, as well as his fair share of abuse; but it doesn't change
> anything.
>
> I pose a question to the group, seriously: why are there large discussions
> about this here? Boredom?

Boredom is part of it; the volume on alt.math.recreational group has
been a little low. The other reason for the large discussions is that
Harris has a sizable fan base of readers who find his fantastic,
unrestrained style of ranting to be amusing. I've always been a
little uneasy with the idea of finding entertainment value in the
byproduct of someone's mental disorder. To be fair to the fan of James
Harris, however, James bears some responsibility for his condition. He
has demonstrated an awareness of his problem, and yet he does not seek
the help necessary to deal with it.


sg...@hotmail.co.uk

unread,
May 21, 2007, 11:45:53 AM5/21/07
to
Frank J. Lhota wrote:

> I've read a little of his blog, back when it was called "Math for
> Profit" or something like it. It seems to be a rehash of his newsgroup
> screeds. His posts were enough to convince me that he is a rather
> extreme example of an NPD sufferer.
>
> In the past, however, he has done posts where he has expressed
> recognition of the problem. Given that he was asking for suggestions,
> I thought there might be a small chance that he might be open to good
> advice. As his reply indicates, he is still in heavy denial mode, but
> I still thought it was worth a try.

I am inclined to believe that James became beyond redemption a few
years back, when he changed from believing that he was destined for
greatness to believing that he had already achieved greatness. He used
to quickly abandon flawed arguments and then return the following day
with new flawed arguments, whereas now he has been holding on to the
same flawed arguments for years. That he maintains that the paper he
sent to SWJPAM was correct is a case in point.

> Boredom is part of it; the volume on alt.math.recreational group has
> been a little low. The other reason for the large discussions is that
> Harris has a sizable fan base of readers who find his fantastic,
> unrestrained style of ranting to be amusing. I've always been a
> little uneasy with the idea of finding entertainment value in the
> byproduct of someone's mental disorder. To be fair to the fan of James
> Harris, however, James bears some responsibility for his condition. He
> has demonstrated an awareness of his problem, and yet he does not seek
> the help necessary to deal with it.

Indeed. As somebody who has mental health problems myself I don't feel
particularly guilty deriving low-brow entertainment from JSH threads,
since unlike me James is completely unwilling to take any steps to
improve his situation, despite some excellent opportunities to do so.
A man with two broken legs is not funny, but a man with two broken
legs who would rather try to run a marathon than see a doctor *is*
funny.

-Rotwang

Tim Peters

unread,
May 21, 2007, 2:39:42 PM5/21/07
to
...

[sg...@hotmail.co.uk]
> ...


> Indeed. As somebody who has mental health problems myself

You do a remarkably good imitation of sanity to my eyes :-)

> I don't feel particularly guilty deriving low-brow entertainment
> from JSH threads, since unlike me James is completely unwilling to
> take any steps to improve his situation, despite some excellent
> opportunities to do so. A man with two broken legs is not funny,
> but a man with two broken legs who would rather try to run a
> marathon than see a doctor *is* funny.

Especially when he insists he wins his marathons despite never taking a
step (doing any real work), and that the bones sticking through his skin at
a dozen different angles are evidence of superhuman abilities. Besides, he
won a 50-yard dash once in high school, so why should he even both running
now ;-)

Watching a JSH argument often reminds me of the infamous Black Knight scene
in Monty Python's "Holy Grail" movie ... here:

http://www.mwscomp.com/movies/grail/grail-04.htm

The Black Knight keeps taunting King Arthur during a sword fight, all the
while losing limb after limb. In the end, with both arms and a leg hacked
off, the Black Knight still refuses to concede.

BLACK KNIGHT:
Come here!
ARTHUR:
What are you going to do, bleed on me?
BLACK KNIGHT:
I'm invincible!
ARTHUR:
You're a looney.
BLACK KNIGHT:
The Black Knight always triumphs! Have at you! Come on, then.
[whop]
[ARTHUR chops the BLACK KNIGHT's last leg off]
BLACK KNIGHT:
Oh? All right, we'll call it a draw.
ARTHUR:
Come, Patsy.
BLACK KNIGHT:
Oh. Oh, I see. Running away, eh? You yellow bastards! Come back
here and take what's coming to you. I'll bite your legs off!

Believe it or not, some people don't think that scene is funny either ;-)

jst...@gmail.com

unread,
May 21, 2007, 8:16:15 PM5/21/07
to
On May 21, 3:57 am, "Glen Wheeler" <s...@gew75.com> wrote:
> "Frank J. Lhota" <FrankLho.NOS...@rcn.com> wrote in messagenews:MuGdnbHJLdl7iszb...@rcn.net...

Hardly. I write papers, and I use the newsgroups to help me critique
my arguments and this time I also needed to give certain people an
opportunity to accept a rebuttal to their prior claims.

It was the decent thing to do.

> I don't really know what to do about his work either. It's broken,
> everyone can see that. Unless he alters it in a fundamental way, and builds
> something of real value out of it, there won't be anyone to publish it
> either. He has been given absolutely outstanding assistance by several
> people over time, as well as his fair share of abuse; but it doesn't change
> anything.
>

Yeah, and before I got published posters would repeatedly claim that
no one believed me and no mathematician would ever accept my work.

They actually use language that would indicate that every
mathematician on the planet was in agreement with them, and disagreed
or would disagree with me.

And when I DID get published the fury on the newsgroups was palpable
in the posts, and in the conspiracy to email the journal, which
succeeded in getting my published paper yanked.

Yet am I not STILL listed as a published author in Mathematical
Reviews?

(I am curious can someone with access please check?)

> I pose a question to the group, seriously: why are there large discussions
> about this here? Boredom?
>

I think it's fear. For some reason certain posters I think believe if
they don't keep up a steady stream of negatives in reply to my
research that I might gain acceptance, but hey, I like to send these
paper to mathematicians.

I've emailed this latest to number theorists from Australia to
Washington state here in the US.

Oh yeah, I also submitted it to the Bulletin of the AMS.

I am ready for a steady effort over time focusing on individual number
theorists around the world, so the newsgroups are still the place
where mostly I talk out ideas.

The emphasis this weekend was first on testing for errors, as I do
consider replies claiming mistakes carefully.

Secondary I offered posters who disputed my research an opportunity to
recant.

The failure of posters to find errors meant that with that offer I
began emailing mathematicians around the planet, and also submitted to
my first journal.

This process can take YEARS.

Post what you will here, as if it matters. I did want suggestions
before, but finding little decided that I should go where success did
occur before.

I did, after all, get published once. I can do it again.


James Harris

Rupert

unread,
May 21, 2007, 8:38:28 PM5/21/07
to

Errors were found. You refused to listen.

> meant that with that offer I
> began emailing mathematicians around the planet, and also submitted to
> my first journal.
>
> This process can take YEARS.
>
> Post what you will here, as if it matters. I did want suggestions
> before, but finding little decided that I should go where success did
> occur before.
>
> I did, after all, get published once. I can do it again.
>

Only by accident. It will be a miracle if you ever write a paper that
can actually pass peer review.


> James Harris- Hide quoted text -
>
> - Show quoted text -


Patrick Hamlyn

unread,
May 21, 2007, 8:54:33 PM5/21/07
to
jst...@gmail.com wrote:

<...>


>I've emailed this latest to number theorists from Australia to
>Washington state here in the US.
>
>Oh yeah, I also submitted it to the Bulletin of the AMS.
>
>I am ready for a steady effort over time focusing on individual number
>theorists around the world, so the newsgroups are still the place
>where mostly I talk out ideas.

Well I suppose you're performing a service of sorts here.

You're providing a 'first line' of defence against criminally negligent,
incompetent and lazy people who manage to sneak into esteemed positions in
academia and lurk there going through the motions.

You've already exposed one group of such people, perhaps somewhere there's
another waiting to be 'found out'.

I know your real aim is to join their ranks, but you may have to be satisfied
with exposing one or two of them instead...
--
Patrick Hamlyn posting from Perth, Western Australia
Windsurfing capital of the Southern Hemisphere
Moderator: polyforms group (polyforms...@egroups.com)

jst...@gmail.com

unread,
May 21, 2007, 9:06:18 PM5/21/07
to

I know of no errors found. That is of interest to me.

I have been listening, but possibly I missed something?

In your case there were corrections you had to make to various claims
you made, but I don't remember you finding any errors.

For instance you claimed that a function I call Q(x) did NOT provide a
handle by which all factorizations of

175x^2 − 15x + 2 = 2(f(x) + 1)* (g(x) + 1)

are covered, which is a claim you later retracted acknowledging that I
am correct.

You also claimed that for the expression

r^2 + rs − (2 + 2xt + tQ(x))st + s^2 = (2x + Q(x))t^2

it was not true that when Q(x) = -2x +/- u, where u is a unit in the
ring of algebraic integers that the expression is valid in the ring of
algebraic integers.

It took my noting that in that case the expression is monic for you to
then agree.

I think though I was chided for supposedly not being clear.

Other than that I know of no claims of error on your part, so please
elaborate.


James Harris

Rupert

unread,
May 21, 2007, 9:38:40 PM5/21/07
to

Oh, you're talking about the new paper? I thought we were talking
about the old paper. Well, I did find a couple of mistakes - see the
other thread - but they weren't that important to the main argument, I
don't think. However, when we get to the main argument, I can't find
an interpretation of what you say that isn't trivially false. It may
be that you have some interpretation in mind that I haven't thought
of, or it may be that what you say isn't coherent at all, so I don't
definitively say that I've found a mistake, but certainly as it stands
the exposition is appalling.

You write "And now the prior question can be answered as if Q(x)=-2x-1
or Q(x)=-2x+1, the conditional expression is true across the ring of
algebraic integers, as in general if Q(x)=-2x +/- u, where u is a unit
in the ring of algebraic integers the conditional is in that ring, but
otherwise you are forced outside the ring of algebraic integers."

That's appallingly expressed. It turned out part of what you meant is

"Suppose that Q is a function from the algebraic integers to the
algebraic integers, and Q(x)=2x+u for all algebraic integers x, where
u is some unit in the ring of algebraic integers. Suppose further
that
s=7 and t=5 and that x is an algebraic integer. Then, the following
expression, considered as a polynomial in r,


r^2+rs-(2+2xt+tQ(x))st+s^2-(2x+Q(x))t^2,


is a monic polynomial with algebraic integer coefficients."

Which is trivial.

But then you write "but otherwise you are forced outside the ring of
algebraic integers." What does this mean? Does it mean that if Q is
any other function, then the polynomial is not a monic polynomial with
algebraic integer coefficients? That's very obviously false. So if you
don't mean that, then what do you mean?


> For instance you claimed that a function I call Q(x) did NOT provide a
> handle by which all factorizations of
>
> 175x^2 − 15x + 2 = 2(f(x) + 1)* (g(x) + 1)
>
> are covered, which is a claim you later retracted acknowledging that I
> am correct.
>
> You also claimed that for the expression
>
> r^2 + rs − (2 + 2xt + tQ(x))st + s^2 = (2x + Q(x))t^2
>
> it was not true that when Q(x) = -2x +/- u, where u is a unit in the
> ring of algebraic integers that the expression is valid in the ring of
> algebraic integers.
>
> It took my noting that in that case the expression is monic for you to
> then agree.
>
> I think though I was chided for supposedly not being clear.
>
> Other than that I know of no claims of error on your part, so please
> elaborate.
>

Rupert

unread,
May 21, 2007, 9:54:21 PM5/21/07
to

What I claimed is that the expression is not equal to zero for *all*
algebraic integers, which is the natural interpretation of what you
were saying. It was certainly very clear what *I* was saying, but
nevertheless you went into a rant about how I didn't know any
mathematics, and apparently still don't understand what my claim was,
despite all the very clear explanations and despite the fact that it
should have been perfectly clear the first time.

> It took my noting that in that case the expression is monic for you to
> then agree.
>

When you made that argument, another interpretation of what you were
saying which was trivially correct suggested itself, so I went with
that interpretation instead. It would be nice if you weren't so
incompetent at expressing yourself, and if, when people say things
which are very clear and trivially correct, you didn't go into a
foolish rant about how they don't understand mathematics.

> I think though I was chided for supposedly not being clear.
>

Which you certainly weren't.

> Other than that I know of no claims of error on your part, so please
> elaborate.
>

Rupert

unread,
May 21, 2007, 10:04:20 PM5/21/07
to

This certainly does not imply that the expression is "valid in the
ring of algebraic integers". It implies that there are two solutions
for r in the ring of algebraic integers for each algebraic integer x.
This is the point I was making all along.

> I think though I was chided for supposedly not being clear.
>
> Other than that I know of no claims of error on your part, so please
> elaborate.
>

jst...@gmail.com

unread,
May 21, 2007, 11:36:54 PM5/21/07
to

Understanding that point is crucial to understanding the paper.

r^2+rs-(2+2xt+tQ(x))st+s^2-(2x+Q(x))t^2

is not generally valid in the ring of algebraic integers, unless

Q(x) = -2x +/- u

where u is a unit in the ring of algebraic integers as otherwise it is
not monic.

Now to me that is trivial but you seem to have some problems with it
so I'm forced to give an example, like consider

x + 3y = z

as an example of an expression not generally valid in the ring of
integers because it requires that y = (z-x)/3, and I can pick integers
x and z such that it is false in that ring, for instance z=2, x=1,
would require y=1/3, and that is not an integer.

New mathematical approaches can force you to think in a different way.

My research forces you to consider what expressions are generally
valid in a particular ring.

Because in every major ring EXCEPT the ring of algebraic integers, if
you only use expressions valid in that ring, and ring operations, you
remain in the ring.

That is true for the ring of integers, and also the ring of gaussian
integers, and it also applies to fields as well, as for instance,
using expressions valid in the field of reals, you cannot be forced
into the complex numbers.

Unique among all the major rings is the ring of algebraic integers
where provably, as shown in my paper, only using expressions valid in
the ring of algebraic integers, you can be forced out of that ring, as
even with

r^2+rs-(2+2xt+tQ(x))st+s^2-(2x+Q(x))t^2

monic with an appropriate choice of Q(x), it can be shown that f(x) is
not an algebraic integer for a given integer x, and in my paper I use
x=2, while it WORKS for x=1, as then you get integer solutions.

So for x=1 you remain in the ring of algebraic integers, while for
x=2, you are forced out!

It is not a complicated argument, and it is not refutable.

The only major ring that has this odd property that you can be forced
out using only expressions valid in the ring and ring operations is


the ring of algebraic integers.


James Harris

Rupert

unread,
May 22, 2007, 12:30:07 AM5/22/07
to

Er, could you elaborate? It's obviously still monic in r.

Rupert

unread,
May 22, 2007, 12:38:31 AM5/22/07
to

Okay, I've got a version of your claim which is correct.

Suppose that Q is a polynomial in one variable x with algebraic
integer coefficients. Then, considering the above expression as a
multinominal in r, s, t, and x, its leading coefficient in t will be a
unit if and only if Q(x)=-2x+u for some unit u.

You really need to work on expressing yourself properly.

So, back to the paper...

> > - Show quoted text -- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -

Rupert

unread,
May 22, 2007, 12:47:59 AM5/22/07
to
> ...
>
> read more »- Hide quoted text -

>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -

So, now it appears you think there's something strange about this fact
that you just observed, you think there's some sort of question about
how it can happen. So I suppose the question is, why is this
observation at all remarkable or interesting? What do you think the
puzzle is?

jst...@gmail.com

unread,
May 22, 2007, 1:00:08 AM5/22/07
to

And it may seem strange that the mathematics requires an expression
that is valid in the ring of algebraic integers for ALL the variables
r, s, t and x, since in the paper I pick s=7, and t=5, but those are
just my arbitrary choices.

Someone else could pick something else, including values that would
make them non-monic, like if you wished to try and put

x + 3y = z

in the ring of integers, noting that if z=7, and x=1, it works,
because that is just one special case with one set of choices.

> You really need to work on expressing yourself properly.

The language is carefully chosen, it's just not what you are used to
seeing.

That kind of rigidity of thinking is a problem of the modern math
world.

You claim it's about precision in language, when I see it as being
about only looking at the mathematics one way.

> So, back to the paper...
>

You have conceded all the major points, since it is true that the
expression subtracted from the identity is valid in the ring of
algebraic integers in general only for certain values of Q(x).
Intriguingly in the paper with x=1, the value of Q(x) I choose to test
validity in the ring of algebraic integers does give a result valid in
that ring, clearly showing how you can actually stay in the ring.

But it is only valid because you get integer solutions.

The next value, with x=2, bumps you out of the ring, because you get
non-rational solutions, showing the problem I mentioned where the ring
of algebraic integers is unique in comparison to the other major
rings, like the ring of integers, the ring of gaussian integers, and
even rings that are fields like reals or the field of complex numbers.

It is a quirky ring, unique in this way.


James Harris

Rupert

unread,
May 22, 2007, 1:14:02 AM5/22/07
to

No, it's incoherent babble. You are incapable of stating your claims
properly.

> That kind of rigidity of thinking is a problem of the modern math
> world.
>
> You claim it's about precision in language, when I see it as being
> about only looking at the mathematics one way.
>

You're wrong.

> > So, back to the paper...
>
> You have conceded all the major points, since it is true that the
> expression subtracted from the identity is valid in the ring of
> algebraic integers in general only for certain values of Q(x).

What I have conceded is that the expression given, considered as a
polynomial in r, s, t, and x, will have a unit coefficient in t^2 (and
no terms in t^2 times any polynomial in r, s, and x) if and only if
Q(x)=-2x+u for some unit u. That is utterly trivial.

Now, what I want to know is, why is that so exciting, or in the least
interesting?

hagman

unread,
May 22, 2007, 6:44:17 AM5/22/07
to
On 22 Mai, 05:36, jst...@gmail.com wrote:
> On May 21, 6:38 pm, Rupert <rupertmccal...@yahoo.com> wrote:
[snipped a lot so that we can see the point that is crucial to
understanding the paper]

>
> Understanding that point is crucial to understanding the paper.
>
> r^2+rs-(2+2xt+tQ(x))st+s^2-(2x+Q(x))t^2

This is an algebraic expression, i.e. something that takes a numerical
value
if one feeds numerical values into r,s,t,x and specifies a suitable
function for Q.

>
> is not generally valid in the ring of algebraic integers, unless

Please define the notion of being generally valid for an *expression*.

>
> Q(x) = -2x +/- u
>
> where u is a unit in the ring of algebraic integers as otherwise it is
> not monic.
>
> Now to me that is trivial but you seem to have some problems with it
> so I'm forced to give an example, like consider
>
> x + 3y = z

This is not a numeric expression but an equality.
What does it mean for an *equation* to be generally valid?

>
> as an example of an expression not generally valid in the ring of
> integers because it requires that y = (z-x)/3, and I can pick integers
> x and z such that it is false in that ring, for instance z=2, x=1,
> would require y=1/3, and that is not an integer.

Is there any relation between the notions of general validity for
a) expressions and
b) equations?
(My guess: An equation A=B is valid iff the expression A-B is valid.
An expression A is valid iff the equation A=0 is valid. - But this
would
still require at least one of the two uses of "generally valid" to be
defined.)
Once you have given a nice definition of "generally valid", you have
succeeded in providing common grounds for talking about your theory.
The obvious next question then is: Are there any interesting theorems
about general validity that can be formulated? And proven?
For example, if A and B are generally valid, can anything be said
about
the general validity of other expressions (e.g. A+B)?

I think it was Rupert who suggested in some post something like the
following
(but you did not expressly acknolegde that interpretation):

Assume A is a ring and P is a polynomial in n variables, i.e. an
element of A[X_1,X_2,...,X_n].
Let B be a ring containing A and let V={(b_1,..,b_n) in B^n |
P(b_1,...,b_n)=0} be the
set of zeroes of P in B^n.
Then P is said to be "generally valid in B" if all projections of V to
B^(n-1) obtained by simply
dropping a variable are surjective.
(In other words, setting all but one variable to specific values from
B, the resulting polynomial
in one variable has a root in B.)

Confirmation of this interpretation would be greatly welcome.

>
> New mathematical approaches can force you to think in a different way.
>
> My research forces you to consider what expressions are generally
> valid in a particular ring.

First, it forces *you* to specify what "generally valid" (expression/
equation) means.

>
> Because in every major ring EXCEPT the ring of algebraic integers, if
> you only use expressions valid in that ring, and ring operations, you
> remain in the ring.
>
> That is true for the ring of integers, and also the ring of gaussian
> integers, and it also applies to fields as well, as for instance,
> using expressions valid in the field of reals, you cannot be forced
> into the complex numbers.
>
> Unique among all the major rings is the ring of algebraic integers
> where provably, as shown in my paper, only using expressions valid in
> the ring of algebraic integers, you can be forced out of that ring, as
> even with
>
> r^2+rs-(2+2xt+tQ(x))st+s^2-(2x+Q(x))t^2
>
> monic with an appropriate choice of Q(x), it can be shown that f(x) is
> not an algebraic integer for a given integer x, and in my paper I use
> x=2, while it WORKS for x=1, as then you get integer solutions.
>
> So for x=1 you remain in the ring of algebraic integers, while for
> x=2, you are forced out!
>
> It is not a complicated argument, and it is not refutable.

Indeed, hardly refutable, if nobody knows what general validity means.

hagman

W. Dale Hall

unread,
May 22, 2007, 2:20:51 PM5/22/07
to
jst...@gmail.com wrote:
> On May 21, 5:38 pm, Rupert <rupertmccal...@yahoo.com> wrote:
>> On May 22, 10:16 am, jst...@gmail.com wrote:

... stuff deleted ...

>>> I am ready for a steady effort over time focusing on individual number
>>> theorists around the world, so the newsgroups are still the place
>>> where mostly I talk out ideas.
>>> The emphasis this weekend was first on testing for errors, as I do
>>> consider replies claiming mistakes carefully.
>>> Secondary I offered posters who disputed my research an opportunity to
>>> recant.
>>> The failure of posters to find errors
>> Errors were found. You refused to listen.
>>
>
> I know of no errors found. That is of interest to me.
>
> I have been listening, but possibly I missed something?
>

In your paper, you appear to assert the following
factorization:

P(x) = 175 x^2 - 15 x + 2 = 2(f(x)+1)(g(x)+1)

for algebraic integer functions f(x),g(x), by which I
understand you to mean functions that take algebraic
integer values for algebraic integer values of x.

There is no such factorization. The reason is that P(x)
takes some values for algebraic integers x, that are not
divisible by 2 in the ring of algebraic integers. One
such value of x is sqrt(3). P(sqrt(3)), which is

P(sqrt(3)) = 527 - 15 sqrt(3)

is not a multiple of 2 in the ring of algebraic integers,
because P(sqrt(3))/2 is a root of the quadratic equation

2 x^2 - 1054 x + 138527 = 0

where you'll note that the polynomial is (a) irreducible,
(b) primitive, and (c) NOT monic.

However, your factorization of P(x) has a factor equal to 2.
Therefore, the remaining factors cannot all consist of
algebraic integers.

If you insist on a factorization of P(x) with one factor
equal to the constant 2, then the factorization cannot
involve only functions taking algebraic integer values
for algebraic integer values of x, by the above argument.

It is this place where you depart from the ring of algebraic
integers, not via any fancy dancing with "subtracting from
identities".

... more stuff deleted ...

>
> Other than that I know of no claims of error on your part, so please
> elaborate.
>

Have a look at what I wrote above.

>
> James Harris
>

Dale

sg...@hotmail.co.uk

unread,
May 22, 2007, 8:17:47 PM5/22/07
to
Tim Peters wrote:

> [s...@hotmail.co.uk]


> > Indeed. As somebody who has mental health problems myself
> You do a remarkably good imitation of sanity to my eyes :-)

Thanks. It's nothing terribly serious.

> Watching a JSH argument often reminds me of the infamous Black Knight scene
> in Monty Python's "Holy Grail" movie ... here:
>
> http://www.mwscomp.com/movies/grail/grail-04.htm

I know it well. It seems that quite a few of the regular posters to
JSH's threads are avid Monty Python fans (I sure am); I think that
this fact may shed some light on Glen Wheeler's question about why
James gets the attention he does.

-Rotwang

mensa...@aol.com

unread,
May 23, 2007, 12:09:26 AM5/23/07
to

"An argument is a collected series of statements
intended to establish a proposition."

"No, it isn't."

>
> -Rotwang


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