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From: JSH on 3 Jul 2010 19:57
It's almost a relief now to have the results around residues as so
much of my research seemed to just kind of go over old ground--in
simpler ways, yeah, but still areas where other research was
available--or in the case of Fermat's Last Theorem, supposedly just
proved a negative. And I say supposedly as YEARS ago I long tired of
arguing over FLT, but even if you think you've proven the thing, so
what? It's a negative. It's like, ok, so you can't get certain
solutions, and that's it! Nothing else! It's like a big downer.

Of course to try and prove FLT--not saying I did prove it but that I
believe I did--I invented or discovered (take your pick), tautological
spaces. There it's also kind of funny as over a decade ago, back in
early 2000 when I was arguing about them, I'm not sure if I'd named
them yet, on this newsgroup posters were RIPPING on me about them.
Insults flew!!! Just like now. But ok, so posters were ripping on
them, saying it was such a stupid idea, and nothing important could be
done with identities--and recently when I brought them up again, some
posters claimed, yup, that they were already a part of established
mathematics!!!

Of course by then I'd gone beyond trying to prove a negative and
unleashed them against binary quadratic Diophantine equations. THAT
was also one of my more satisfying results, as it was kind of a
surprise that all these modular equations could pop out this explicit
result which just so happened to allow you to generally simplify all
binary quadratic Diophantine equations to the form u^2 + Dv^2 = F. It
was sort of a weird feeling. I'd argued about tautological spaces for
years. Felt they were solid and powerful, but besides FLT had only
used them with no (or limited?) success against the factoring problem.

So it was like I BELIEVED I'd proven FLT with these things, and
thought tautological spaces were incredibly powerful, so if they were
so damn great they should be able to solve the factoring problem, and
I couldn't figure out a way (um, yeah, solving binary quadratic
Diophantine equations would be a way, which just didn't occur to me
before). And what happened was one day I was just kind of thinking to
myself like usual, hey, tautological spaces, they're really cool.
What can I do with them? And I started down the path which lead to
binary quadratic Diophantine equations. So it was kind of a random
thing.

And the problem there was I simplified an already well-worked area.
So with computers programmed with the more complex stuff, there's no
necessity for human beings to switch to something simpler. So I ended
up in arguments on Usenet--people trashing the result as worthless--
and that was about it! Except for Google search results. One of the
big movers that caught my attention was that I took over top spots on
searches related to that result. But that's been true for a couple of
years now as I think that result is about two years old now. Which
goes to that weird thing I get where I don't get excited much any more
as I'll do something like generally solve binary quadratic Diophantine
equations with my tautological spaces and take over Google search
results related to the research--and nothing else happens!!!

Nothing. It's like taking over the definition of mathematical proof
in Google. I was shocked and amazed when I had the #1 spot for the
definition of mathematical proof, and even more impressed when define
mathematical proof brought up my math blog, and that was YEARS AGO.
The next interesting thing that happened there was when the Wikipedia
managed to reclaim the #1 and #2 spot at least for define mathematical
proof. Pushing my definition down to #3. But recently my definition
returned to #2, and probably long-term the Wikipedia can't win that
battle. It's just a matter of time...

Oh, so I had finally a positive result with binary quadratic
Diophantine equations, but math people already had techniques! Worse
techniques, yes. Easily proven to be more complicated ways to do what
I'd simplified, yes. But they weren't budging on improving and how do
you make them? Can lead a horse to water but can't make him or her--
think.

And still I've skipped over my first clear as a bell positive result
which came back in 2002 along with what I have long believed to be a
proof of FLT--not arguing that it is but I BELIEVE it is--which was my
prime counting function.

I argued ON AND ON about my prime counting function as I COULD NOT
BELIEVE that showing a P(x,y) function that lead to a partial
difference equation, which lead to a partial differential equation and
thus explained the connection of the distribution of prime numbers to
complex numbers like x/ln x and Li(x) could be ignored or denied. And
it was. It still is.

About 8 years now with the best path to proving or disproving the
Riemann Hypothesis clearly out there and math people have succeeded in
ignoring it for all that time. One of the most profound intellectual
mysteries of them all.

How did they? How could they?

Ok, truth is, no one really gives a damn about the freaking Riemann
Hypothesis!!! I know I don't. I don't know why anyone else should
care about it either. It's more or less a muddled idea of a guy
trying to find something I did find, which mathematicians have
succeeded in ignoring for over eight years....

NO one appears to give a flying frack at a rolling donut about RH. AT
least not in actuality, what they SAY may be different, but as for
using whatever path is available? Clearly, no. They don't give a
damn in action, so who cares about words.

Which brings us back to k^m = q mod N.

Ok, so I'd tried to use tautological spaces against the factoring
problem for YEARS--failing to see the path that would later be a
general solution to binary quadratic Diophantine equations--without
success, so I branched out and went to something I called surrogate
factoring.

Surrogate factoring was a concept that factoring one number T, might
be accomplished by instead factoring another number S, the surrogate,
which would lead to the factorization of T. I worked on that concept
for YEARS, trying to mathematicize it.

Possibly had as many faux results with it as I'd had trying to prove
FLT years earlier--and not saying I DID prove FLT, just that I BELIEVE
I proved FLT. And worse, I'd declare doom and gloom every time I
thought I had something. As I predicted the collapse of world
civilization if I'd broken RSA encryption by solving the factoring
problem.

--Ah the passion of youth. Being years older now and having watched
the world weather any number of crises, I'm not as worried any more.
But it's hard not to still worry, some.--

Ok, so I worked on surrogate factoring for years with little success,
but thought I was doing great. But one day realized I wasn't and
reversed equations, or reversed equations and later realized I wasn't,
and found that I could solve quadratic residues mod p.

To see the dominance of that idea, search in Google (yup, has to be
Google): solving quadratic residues

If you DO that search you'll get a page on my math blog showing how to
solve quadratic residues mod p, even though I've generalized the
method to mod N, and now gone beyond quadratic residues to mth
residues. But that freaking page still comes up #1. What gives? I
puzzle over these things. Why does the world like mod p so much?
Why? Why??!!!

Ok, so I pondered this fascination of the world with that result as
revealed by Google searches and fiddled with it for a while, until I
got my mth residue result which has a historical oddity in that it has
T, instead of S, though it IS it would seem surrogate factoring. I'd
reversed the equations of surrogate factoring. So now it's T. BEFORE
T stood for--Target. It was to be the target number to be factored by
the surrogate, which was S, until the reversal.

And finally I had a positive result, which was not in an area as well-
worked, and bigger bonus came later, as I found I could solve discrete
logs, and it was then a very much positive result, and it just made me
feel better. It gives you kind of a golden feeling of warmth...

I look at that result, and say, hey, that's not just proving a
negative! And hey, that's not just finding a simpler or different way
to handle something people already think is solved!! THAT is a brand
new baby. All shiny and new and squealing with a healthy cry.

Which is a result that is a LOT more fun.


James Harris
From: Owen Jacobson on 3 Jul 2010 23:49
On 2010-07-03 19:57:16 -0400, JSH said:

<snip>

Don't drink and post, folks.

-o

From: Mark Murray on 4 Jul 2010 04:12
On 04/07/2010 00:57, JSH wrote:

<Rambling, whiny essay snipped>

> Possibly had as many faux results with it as I'd had trying to prove
> FLT years earlier--and not saying I DID prove FLT, just that I BELIEVE
> I proved FLT. And worse, I'd declare doom and gloom every time I
> thought I had something. As I predicted the collapse of world
> civilization if I'd broken RSA encryption by solving the factoring
> problem.
>
> --Ah the passion of youth. Being years older now and having watched
> the world weather any number of crises, I'm not as worried any more.
> But it's hard not to still worry, some.--

And he starts to get a handle on his error-prone hubris!

> Ok, so I worked on surrogate factoring for years with little success,
> but thought I was doing great. But one day realized I wasn't and
> reversed equations, or reversed equations and later realized I wasn't,
> and found that I could solve quadratic residues mod p.

Solve? Maybe. Efficiently/uniquely? Naah.

> To see the dominance of that idea, search in Google (yup, has to be
> Google): solving quadratic residues
>
> If you DO that search you'll get a page on my math blog showing how to
> solve quadratic residues mod p, even though I've generalized the
> method to mod N, and now gone beyond quadratic residues to mth
> residues. But that freaking page still comes up #1. What gives? I
> puzzle over these things. Why does the world like mod p so much?
> Why? Why??!!!

Drunken proof-by-google.

> Ok, so I pondered this fascination of the world with that result as
> revealed by Google searches and fiddled with it for a while, until I
> got my mth residue result which has a historical oddity in that it has
> T, instead of S, though it IS it would seem surrogate factoring. I'd
> reversed the equations of surrogate factoring. So now it's T. BEFORE
> T stood for--Target. It was to be the target number to be factored by
> the surrogate, which was S, until the reversal.
>
> And finally I had a positive result, which was not in an area as well-
> worked, and bigger bonus came later, as I found I could solve discrete
> logs, and it was then a very much positive result, and it just made me
> feel better. It gives you kind of a golden feeling of warmth...
>
> I look at that result, and say, hey, that's not just proving a
> negative! And hey, that's not just finding a simpler or different way
> to handle something people already think is solved!! THAT is a brand
> new baby. All shiny and new and squealing with a healthy cry.
>
> Which is a result that is a LOT more fun.

And with all that self-praise and amazement over your own
pronouncements, how many significant factorisations/discrete
logarithms have you solved?

NONE.

Baby numbers used to illustrate a process don't count.

M
--
Mark "No Nickname" Murray
Notable nebbish, extreme generalist.
From: MichaelW on 4 Jul 2010 05:39
On Jul 4, 9:57 am, JSH <jst...(a)gmail.com> wrote:

> Which goes to that weird thing I get where I don't get excited much any more
> as I'll do something like generally solve binary quadratic Diophantine
> equations with my tautological spaces and take over Google search
> results related to the research--and nothing else happens!!!
>

This claim is not true. You have not solved BQDE's, only given a
simplification that is not very good.

Easy to claim to be world class if you reinvent your own history.

Regards, Michael W.
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