JSH: But it just amazes me
JSH
that there were these people in the mathematical field who didn't give
a damn. They didn't care about the truth, so what were they doing
there?
Working it out over the years I've determined that for some people the
dream of royalty did not die with the transition to democratic
societies around the world, so they've simply worked to set up shop
where they can chase that dream.
And academia is a place that lets them play at their dreams of being
royalty.
In a class society the king does not have to be the best at anything.
He is simply the king.
So for these people in setting themselves up as wannabe royalty, merit
does not matter.
They don't care if you're right or wrong if you're someone they've de-
classed in their minds!
And you can see how far they can go with what is increasingly looking
like a solution to the factoring problem.
How hard to check?
For major researchers, oh, minutes, maybe a few hours to program it
and watch it go, and then there should be calls to colleagues and
excited discussion, and oh yeah, notifying of security experts and
intelligence services around the world.
But instead there is a dragging of the feet by people who don't want
to let go.
I mentioned on sci.physics that the world may decide to 0 fund
academia and I'm increasingly thinking that will happen as the modern
academic world seems to attract medieval thinking, and in the medieval
world it was not about truth or merit, but about class.
There has to be some way to break that out of academia so that people
within academic walls do not feel free to dismiss results that they
don't like.
My suggestion is 0 funding. If the money is taken away then only the
best people will still remain as like me, they will find a way.
The BEST people do not need handouts or what I call white collar
welfare.
So 0 funding academia is increasingly looking like the way to go, as
this latest incredible example shows: you people are fighting powerful
mathematics as if you can win!
But why would you even want to win?
James Harris
Bruce Stephens
[...]
> And you can see how far they can go with what is increasingly looking
> like a solution to the factoring problem.
>
> How hard to check?
>
> For major researchers, oh, minutes, maybe a few hours to program it
> and watch it go, and then there should be calls to colleagues and
> excited discussion, and oh yeah, notifying of security experts and
> intelligence services around the world.
Anybody attempting to "program it and watch it go" will need to post
their attempt, wait for you to insult their deliberate attempts at
misunderstanding you, then add in whatever corrections you suggest and
try again. People over the years have tried and so far nobody's found a
working factoring solution (none have been fast enough, and many failed
to find factors (and did so slowly)). That process tends to take a
couple of weeks, not minutes or hours.
[...]
JSH
wrote:
You're describing basic research. In getting to the latest results I
had LOTS of missteps and failures.
But you have to think people are complete idiots to believe you don't
get a technique that involves solving for k, with
k^2 = q mod N
by factoring
2q + jN
with j a nonzero integer, into f_1 and f_2, and finding k from: k = 3^
{-1}(f_1 + f_2)
with about a 50% probability of success, and certainty if 2q - f_1^2
is a quadratic residue modulo N.
That is a HIGHLY specific result and looks like something that might
come from years of basic research, with lots of failures and missteps.
If your post is your defense before say, a senate committee? They
will shred you apart.
ANY ethical researcher in the field given indication that the above
works would have no choice about what he or she should do next, but
should not have to be prodded anyway!
They should leap to do the right thing which is inform.
You have a duty to inform.
Think carefully. You may think there's no way you'd be in front of
the U.S. Senate testifying on this issue but I assure you that your
imagination simply needs to be bigger if you so think.
In fact, replying to me, you may guarantee that happens as I put you
on a list of people who SHOULD testify.
James Harris
JSH
That should be k = 3^{-1)(f_1 + f_2) mod N. Forgot the "mod N" part.
Don't want to give people any excuses.
> with about a 50% probability of success, and certainty if 2q - f_1^2
> is a quadratic residue modulo N.
It IS wonderful mathematics and I give one relation where the algebra
offers an infinity of them.
Maybe part of what distresses me is this refusal to be interested in
wonderful mathematical results that show these surprisingly simple yet
powerful relations between numbers.
I cannot imagine real researchers behaving in such a way, so I
conclude you are fakes.
I mean, to live through history being made! To not just be in a
position to read about great discoveries from the "shoulders of
giants" like Archimedes or Newton or Riemann, but to be LIVING it, and
to drag your feet and dawdle and whine means to me you are not
researchers at all.
You're pretenders. Wannabe's. Fakes.
James Harris
Gordon Burditt
>> > like a solution to the factoring problem.
It's not a solution to the factoring problem if it's not fast.
Where's your complexity analysis? What moderate-sized numbers
(numbers you cannot factor in your head) have you factored with it?
>> > How hard to check?
>>
>> > For major researchers, oh, minutes, maybe a few hours to program it
>> > and watch it go, and then there should be calls to colleagues and
>> > excited discussion, and oh yeah, notifying of security experts and
>> > intelligence services around the world.
Isn't that the responsibility of the person claiming to make the
discovery?
>> Anybody attempting to "program it and watch it go" will need to post
>> their attempt, wait for you to insult their deliberate attempts at
>> misunderstanding you, then add in whatever corrections you suggest and
>> try again. =A0People over the years have tried and so far nobody's found =
>a
>> working factoring solution (none have been fast enough, and many failed
>> to find factors (and did so slowly)). =A0That process tends to take a
>> couple of weeks, not minutes or hours.
>
>You're describing basic research. In getting to the latest results I
>had LOTS of missteps and failures.
Perhaps you should STOP publishing your missteps and failures (even
on USENET). Reduce your method to an algorithm. Include a complexity
analysis. Check it. Check it again. Test it on all numbers it
is advertised to work on (all odd composites except 15?) up to
2**32. Find 3 people who are not out to get you and/or suppress
your discovery (if that's possible) and have them check it. If you
find a mistake, fix it, then start over with the checking.
One important quality of researchers that you lack is the desire to
avoid publishing error-ridden crap. Real researchers check their
results.
If they find a mistake, do *NOT* accuse them of deliberately
misunderstanding you, and if in fact they did misunderstand you,
re-write your description so it's easier to understand.
When you've gotten through that, *THEN* publish. And you should be
trying to get published somewhere besides USENET and your blog.
One thing you never manage to do on any of your proofs: state
(clearly!) the theorem you are attempting to prove before starting
to prove it. Forget that, and in the math classes I took, you'd
get an F.
Do the math. Stop making whining excuses for not doing the math like:
- The NSA is out to get me.
- The FBI is out to get me.
- The mathematical community is out to get me.
- Math academics are out to get me.
- Math academics are out to ignore me.
- The world economy will crash if I reveal this.
You've had this stuff on your blog for a year. They didn't get you yet.
They aren't going to bother getting you. You've done a much better job
of discrediting yourself than a CIA disinformation campaign could.
>But you have to think people are complete idiots to believe you don't
>get a technique that involves solving for k, with
People are not idiots for ignoring a technique that changes very
often and has been extremely error-ridden in the past and can only
be expected to be error-ridden in the future. Worse, the author
isn't even willing to check his own work!
>If your post is your defense before say, a senate committee? They
>will shred you apart.
>
>ANY ethical researcher in the field given indication that the above
>works would have no choice about what he or she should do next, but
>should not have to be prodded anyway!
Please stop calling readers of "sci.crypt" math researchers. You
sully the entire subject of mathematics with your looniness.
>They should leap to do the right thing which is inform.
You are posting on sci.crypt. Stop accusing people of being math
researchers unless they are willing to admit it or you have proof.
At best, you might end up with some math students and amateur
cryptographers.
>You have a duty to inform.
No, I do not have a duty to inform about anything mathematical, as
I'm *NOT* a math researcher.
>Think carefully. You may think there's no way you'd be in front of
>the U.S. Senate testifying on this issue but I assure you that your
>imagination simply needs to be bigger if you so think.
You need to be testifying about the sad state of health care for
people with Narcissistic Personality Disorder.
JSH
> >> > And you can see how far they can go with what is increasingly looking
> >> > like a solution to the factoring problem.
>
> It's not a solution to the factoring problem if it's not fast.
> Where's your complexity analysis? What moderate-sized numbers
> (numbers you cannot factor in your head) have you factored with it?
>
> >> > How hard to check?
>
> >> > For major researchers, oh, minutes, maybe a few hours to program it
> >> > and watch it go, and then there should be calls to colleagues and
> >> > excited discussion, and oh yeah, notifying of security experts and
> >> > intelligence services around the world.
>
> Isn't that the responsibility of the person claiming to make the
> discovery?
No. I think academics may think that but most people believe that if
you see something really important then YOU have a duty to inform if
you are an expert in that field, while I see this weird attitude from
academics that it is the duty of someone else to convince you.
But if you are an expert and get shown a simple way to find quadratic
residues modulo N the simple HUMAN CURIOSITY should move you, if there
is any way it is correct as that is a novel thing.
Like say the discussion was over birdwatching, and I noted a beautiful
rare bird, and you ranted back at me that I needed photos in
triplicate, with a paper, and signed affidavits from several other
people who saw the bird, oh, and I needed to get published and only
THEN might you, a supposed bird watching pro, even care to CONSIDER
that MAYBE I might have something interesting.
People won't buy that, and they won't buy that experts couldn't see a
simple and important mathematical result from an amateur, and claims
that I should fight this huge fight by writing papers and trying to
convince journals is just academic insanity and more reason to reform
the current system.
After all, what did people do before journals and papers? Or do you
labor under the assumption these always existed?
Here is the result again. Beautiful simple mathematics--a rare bird:
To solve a quadratic residue q modulo N, where N is an odd composite,
that is, find k, where k^2 = q mod N, remarkably you can use factors
f_1 and f_2 of
2q + jN
where j is a non-zero integer, and f_1*f_2 = 2q + jN, in the relation:
k = 3^{-1}(f_1 + f_2) mod N
which will work roughly 50% of the time, and it will always work if 2q
- f_1^2 is a quadratic residue modulo N.
That is an incredible result from elementary number theory showing an
impressively easy way to solve for quadratic residues modulo N.
So if a real bird aficionado sees a beautiful rare bird does he need
the person who provides a photo to write a paper, submit to a journal
and CONVINCE a large academic audience?
No.
James Harris
Gordon Burditt
>> >> > and watch it go, and then there should be calls to colleagues and
>> >> > excited discussion, and oh yeah, notifying of security experts and
>> >> > intelligence services around the world.
>>
>> Isn't that the responsibility of the person claiming to make the
>> discovery?
>
>No. I think academics may think that but most people believe that if
>you see something really important then YOU have a duty to inform if
>you are an expert in that field, while I see this weird attitude from
What makes you think that by posting to sci.crypt, you are reaching
experts in mathematics? Or even people who *know* experts in
mathematics enough to even pick up the phone and talk to them about
math?
>academics that it is the duty of someone else to convince you.
If you're accusing me of being an academic, you're very, very wrong.
If I am an expert on something, I'm going to have to be convinced
that a supposed new discovery is real before making a fool of myself
in front of other experts by passing it on.
>But if you are an expert and get shown a simple way to find quadratic
>residues modulo N the simple HUMAN CURIOSITY should move you, if there
>is any way it is correct as that is a novel thing.
>Like say the discussion was over birdwatching, and I noted a beautiful
>rare bird, and you ranted back at me that I needed photos in
>triplicate, with a paper, and signed affidavits from several other
>people who saw the bird, oh, and I needed to get published and only
>THEN might you, a supposed bird watching pro, even care to CONSIDER
>that MAYBE I might have something interesting.
Considering that the last 5 times you claimed you spotted a
pterodactyl, it turned out to be (1) a chicken sandwich, (2) the
Windows logo, (3) the shadow of your hand, (4) the sun, and (5) a
stuffed toy on a TV screen that looks like the Linux penguin, I'm
not going to take you seriously the next time you claim to have
spotted a pterodactyl, or, for that matter, a bird. And I'm not
going to believe an 8-month-old bird spotter can reliably identify
birds either, especially not after they mis-identify several of
them in a row.
If any known competent birdwatcher claims to have spotted a bird
long believed to be extinct, like a pterodactyl, I'm still going
to ask for photographs.
>People won't buy that, and they won't buy that experts couldn't see a
>simple and important mathematical result from an amateur, and claims
But it's not just from an amateur, it's from a mathematical infant.
>that I should fight this huge fight by writing papers and trying to
>convince journals is just academic insanity and more reason to reform
>the current system.
>
>After all, what did people do before journals and papers? Or do you
>labor under the assumption these always existed?
Hopefully they did not waste time reading papers from infants claiming
mathematical knowledge written in their diapers. And if a supposed expert
sent me bullshit to read the last 10 times, I'm not going to be in any
hurry to read his next message. There are other people who might actually
know some math who are more worth my time.
Mark Murray
>> After all, what did people do before journals and papers? Or do you
>> labor under the assumption these always existed?
>
> Hopefully they did not waste time reading papers from infants claiming
> mathematical knowledge written in their diapers. And if a supposed expert
> sent me bullshit to read the last 10 times, I'm not going to be in any
> hurry to read his next message. There are other people who might actually
> know some math who are more worth my time.
In they days before journals people self-published.
Newton published his Pricipia, to critical acclaim. Much Alchemy was
dicarded along the way as unrepeatable rubbish. Refereed journals
evolved later (I know not when, but suspect the late 1800's/early
1900's) as a measure to separate rubbish from the good stuff.
As this is all done be humans, they don't always get it right,
but with many eyes on the problem, an evolution to correctness
can be achieved.
M
--
Mark Murray
David Malone
>Newton published his Pricipia, to critical acclaim. Much Alchemy was
>dicarded along the way as unrepeatable rubbish. Refereed journals
>evolved later (I know not when, but suspect the late 1800's/early
>1900's) as a measure to separate rubbish from the good stuff.
According to Wikipedia, Philosophical Transactions of the Royal
Society started in 1665 and included papers by Newton. It says it
is the second oldest (European) journal after Journal des scavans,
which started in the same year. I would guess the review process
has changed quite a bit over the years though.
David.
Noob
> You're pretenders. Wannabe's. Fakes.
Nasty hobbitses?
Gordon Burditt
>> mathematical knowledge written in their diapers. And if a supposed expert
>> sent me bullshit to read the last 10 times, I'm not going to be in any
>> hurry to read his next message. There are other people who might actually
>> know some math who are more worth my time.
>
>In they days before journals people self-published.
And when people self-published, they took the effort to *CHECK*
their work before publishing, so other people in the field would
bother to read it.
JSH, do you regularly read the math papers created by the local
kindergarten class, just in case they might have a proof for Fermat's
Last Theorem in there? Or do you figure that this stuff is not
worth reading and skip it? How about reading the stains on newspapers
at the bottom of bird cages, in case the bird is a mathematical
genius?
>Newton published his Pricipia, to critical acclaim.
I doubt he would have gotten people to read it if he had published 43
different error-ridden versions of it in the previous year, and he
finally got it right. If you want people to take your work seriously,
*CHECK IT FIRST*. Don't publish garbage.
>Much Alchemy was
>dicarded along the way as unrepeatable rubbish.
Carelessly-written stuff by an author with a history of lots of
math mistakes will also be discarded as rubbish, whether there's a
little truth behind it or not. CHECK YOUR WORK before publishing.
>Refereed journals
>evolved later (I know not when, but suspect the late 1800's/early
>1900's) as a measure to separate rubbish from the good stuff.
Elementary math mistakes are a sign that something is rubbish.
That's your stuff, JSH. If you finally get it right, why are
you surprised that nobody takes it seriously?
Lits O'Hate
> Think carefully. You may think there's no way you'd be in front of
> the U.S. Senate testifying on this issue but I assure you that your
> imagination simply needs to be bigger if you so think.
>
> In fact, replying to me, you may guarantee that happens as I put you
> on a list of people who SHOULD testify.
Please add me to your list.
--
"so i let her go...a dream dies, just thoughts left, maybe
i'm just not meant for that wife and kids thing, but for her
i would have..." -- James Harris
Dann Corbit
@f1g2000prf.googlegroups.com>, jst...@gmail.com says...
Your FLT solution was trounced as piddle, each and every time you tried
to revive it.
You "Solution to factoring" is not more efficient than the Sieve of
Eratosthenes to form an exhaustive list or trial division of possible
factors up to the square root of N. Since these are literally two of
the very oldest known algorithms (and worst, in terms of complexity),
your "solution" was scooped by well over 2000 years. Modern solutions
to this puzzle are far more efficient, but still have an exponential
complexity component of some kind.
If you understood complexity analysis you would realize that what you
propose as a solution is truly laughable. But there is little chance of
you cracking open a book to discover what all of that "big-O" stuff
means.
If (by some miracle) you were to produce a method to factor two huge
integers, the world would not fall apart. People would just switch
crypto techniques away from methods that rely on factoring being
difficult towards other methods that do not use factoring. It would
actually be beneficial rather than detrimental in the long run, since
solutions to difficult problems often lead to interesting advances.
If you ever want to make an actual contribution it really will be
necessary for you to read the existing literature. For instanace, if
you knew (and understood!) about things like GNFS you would never have
made your silly claim.
Don Quixote, tilting at windmills, at least had a particular charm.
Your responses to honest attempts to help you are vile and vulgar.
I expect more of the same in the future.
JSH
Actually I isolated out a key part of the argument, wrote a paper and
submitted it to a mathematical journal which published it until some
sci.math posters mounted an email campaign against my paper which
spooked the editors who withdrew it against my wishes:
http://www.emis.de/journals/SWJPAM/vol2-03.html
So BY THE RULES that part of the argument was formally peer reviewed
and published, though I'd guess you dismiss publication in those
circumstances?
The journal later keeled over and died, but EMIS keeps its archives
up:
http://www.emis.de/journals/SWJPAM/
They also resurrected my paper though I don't bother linking to it, as
I've simplified and advanced the argument. You can simply do a search
in Google on: algebraic integer entanglement
> You "Solution to factoring" is not more efficient than the Sieve of
> Eratosthenes to form an exhaustive list or trial division of possible
> factors up to the square root of N. Since these are literally two of
<deleted>
Then no worries!!!
It just AMAZES me how Usenet posters can take the most dramatic things
and act like they're nothing.
The actual story which you didn't bother to tell is so much more
interesting, as, like, an ENTIRE mathematical journal blew up, went up
in flames!!! Died. Went six feet under.
ENDED ITS EXISTENCE.
Isn't that a lot more interesting than what you claimed?
Math people are just blocking, and they destroyed one of their own
journals as part of that blocking.
So I went to the factoring problem.
I wonder if there are mathematicians around the world waiting, hoping,
wondering if they can still get away with the blocking, even with a
way to factor with quadratic residues modulo N.
I'm wondering as well. Maybe they can.
If so, then in a year I'll just celebrate another belated anniversary
of this result.
There isn't much hope. If these bastards could destroy a math journal
like NOTHING, and it not matter, then what can't they do?
James Harris
Enrico
>
> - Show quoted text -
=================================================
Getting back to your claim of a very simple way to solve quadratic
residues modulo an odd number N, coprime to 3.
Can you show how your method works to solve X^2 = 2 mod 161
using the factors of 161 (which are 7 and 23) ?
I tried your method and had to use j = 2 and f1 (or f2 ) = 2 to
get anything to work - I could find the answers, but they were
not linked to both factors of the modulus in the way your
blog example shows.
Cheat sheet:
X = 18
X = 74
X = 87
X = 143
Side note:
18 + 143 = 161
74 + 87 = 161
Enrico
JSH
Good one! Yuck I'm having problems with it myself. Well THAT is why
I put these things out on Usenet, just in case someone can find a
problem before I call in the cavalry.
I'll keep working at this one to see if I can get it to work.
James Harris
Chris McDonald
<hundreds-of-lines-snipped-because-James-is-unable-to-do-so>
>On Nov 9, 5:48=A0pm, Enrico <ungerne...@aol.com> wrote:
>>
>> I tried your method and had to use j =3D 2 and f1 (or f2 ) =3D 2 to
>> get anything to work - I could find the answers, but they were
>> not linked to both factors of the modulus in the way your
>> blog example shows.
>Good one! Yuck I'm having problems with it myself. Well THAT is why
>I put these things out on Usenet, just in case someone can find a
>problem before I call in the cavalry.
>I'll keep working at this one to see if I can get it to work.
But didn't you previously *prove* that you method would work?
Hadn't you already *solved* this problem for the world?
I cannot possibly fathom how it could now be flawed?
--
Chris.
JSH
> JSH <jst...@gmail.com> writes:
>
> <hundreds-of-lines-snipped-because-James-is-unable-to-do-so>
>
> >On Nov 9, 5:48=A0pm, Enrico <ungerne...@aol.com> wrote:
>
> >> I tried your method and had to use j =3D 2 and f1 (or f2 ) =3D 2 to
> >> get anything to work - I could find the answers, but they were
> >> not linked to both factors of the modulus in the way your
> >> blog example shows.
> >Good one! Yuck I'm having problems with it myself. Well THAT is why
> >I put these things out on Usenet, just in case someone can find a
> >problem before I call in the cavalry.
> >I'll keep working at this one to see if I can get it to work.
>
> But didn't you previously *prove* that you method would work?
The method DOES work. The question is, how well?
> Hadn't you already *solved* this problem for the world?
Well doubt is why I post on Usenet.
> I cannot possibly fathom how it could now be flawed?
That's where it's fun.
James Harris
JSH
Yeah, I worked backwards knowing that 7 and 23 are factors, and it
works at:
j = 111, f_1 = 143, and f_2 = 125
T = 17875
And that is HORRIBLE, as it's at 55 iterations.
At lesser values it is giving you the answer for 7 but not 23, and 23
but not 7, until you reach that threshold.
Nasty example. Cool!!! The solving quadratic residues mod p works
like always but here the probabilities are clearly not about 50% with
the mod N. Maybe I tried to jump from prime to composites plus primes
too hastily, eh?
Of course I could toss the alternate equations at it, and see what
happens:
T = 10q mod N
and
k = 19^{-1}(3(f_1 + f_2)) mod N
There are an infinity of these relations. I've just talked first
about the first one, and that is the second one. There are an
infinity more.
I wonder if it shifts the probabilities with composites. With N a
prime I don't think it matters.
The prime case is so pretty and simple, but the composite case is the
"sexy" one, so here I am, pushing it.
Beautiful mathematics made to dance for the crowd so that maybe
they'll toss their pennies.
James Harris
JSH
Correction, not the second one, the third one. I skipped the second
one but don't remember why as I did it about a year ago.
Works with T = 1147, f_1 = 31, f_2 = 37, gives k = 87.
87^2 = 2 mod 161
> I wonder if it shifts the probabilities with composites. With N a
> prime I don't think it matters.
Well that's one thing with my research--usually lots of variables
available.
Here the variable I'm shifting is one I call alpha, or 'a' in posts.
Initial relation is with a=1, which had fits with N = 161, and q = 2.
Here a=3, handles it with the second T, but still took a while because
the probability is per factorization, and the first T had 4 non-
trivial factorizations.
Ok. That was for curiosity. I'm back to pondering why a=1, did so
horribly. Seems I don't have the probabilities right here, except for
the prime case. Composites have proven to be trickier than just
assuming the same numbers as for primes, which yes, is expected, but I
was hoping...
Interesting.
James Harris
Noob
> Actually I isolated out a key part of the argument, wrote a paper and
> submitted it to a mathematical journal which published it until some
> sci.math posters mounted an email campaign against my paper which
> spooked the editors who withdrew it against my wishes:
> http://www.emis.de/journals/SWJPAM/vol2-03.html
cf. http://dl.free.fr/gMojEGqSw/jsh.pdf
> So BY THE RULES that part of the argument was formally peer reviewed
You can't be sure your paper actually was formally peer reviewed.
Is the review process completely anonymous, or are the reviewers' names
disclosed at some point?
> The journal later keeled over and died, but EMIS keeps its archives
> up:
> http://www.emis.de/journals/SWJPAM/
>
> They also resurrected my paper though I don't bother linking to it, as
> I've simplified and advanced the argument. You can simply do a search
> in Google on: algebraic integer entanglement
You should write a new paper, and submit it to SWJPAM.
> It just AMAZES me how Usenet posters can take the most dramatic things
> and act like they're nothing.
As always, you are ever so easily amazed.
Bruce Stephens
[...]
> Good one! Yuck I'm having problems with it myself. Well THAT is why
> I put these things out on Usenet, just in case someone can find a
> problem before I call in the cavalry.
It feels like just a couple of days since you said
<http://groups.google.com/group/sci.crypt/msg/0d8cfe4849ffb4ba>:
>> You're describing basic research. In getting to the latest results I
>> had LOTS of missteps and failures.
>>
>> [...]
>>
>> That is a HIGHLY specific result and looks like something that might
>> come from years of basic research, with lots of failures and
>> missteps.
Of course, you could just try coding it and see if it works.
[...]
JSH
wrote:
> JSH <jst...@gmail.com> writes:
>
> [...]
>
> > Good one! Yuck I'm having problems with it myself. Well THAT is why
> > I put these things out on Usenet, just in case someone can find a
> > problem before I call in the cavalry.
>
> It feels like just a couple of days since you said
> <http://groups.google.com/group/sci.crypt/msg/0d8cfe4849ffb4ba>:
>
> >> You're describing basic research. In getting to the latest results I
> >> had LOTS of missteps and failures.
The poster Enrico gave a false alarm. He said he couldn't get the
answer for q=2, N = 161 = 7(23) using my approach.
I take such claims seriously.
When I didn't get an answer quickly, I naturally got worried, so
posted the same.
> >> [...]
>
> >> That is a HIGHLY specific result and looks like something that might
> >> come from years of basic research, with lots of failures and
> >> missteps.
>
> Of course, you could just try coding it and see if it works.
Enrico just had problems. I DID find the answer using my approach but
further out than I'd like which made me wonder about the probability
that I've said is associated with it. But it IS a probabilistic
approach yet I don't want to use that to ignore surprisingly bad
outcomes.
What amazes me is how giddy people like you clearly get with even the
hint that I'm wrong versus wishing that someone, anyone, would find
something new and interesting.
So ONE LITTLE appearance of an issue and you're stomping and shouting
and hollering with glee.
But the method worked. It's actually a bit scarier now as there is
increasing evidence that it is actually is a valid approach.
James Harris
rossum
wrote:
>Enrico just had problems. I DID find the answer using my approach but
>further out than I'd like which made me wonder about the probability
>that I've said is associated with it.
Why did you have to wonder James? Could it be that you just tried
your method on a couple of small examples and thought that it looked
as if the probability was about 50% without actually checking on
enough examples to be sure?
>But it IS a probabilistic approach yet I don't want to use that
>to ignore surprisingly bad outcomes.
Then you need to test it over a wide range of values and actually see
what probability you get. What results do you get from testing it on
50,000 values in the range 10,000 to 2,000,000 for example?
>
>What amazes me is how giddy people like you clearly get with even the
>hint that I'm wrong versus wishing that someone, anyone, would find
>something new and interesting.
What amazes us James is that you claim such immense importance for
results that you have obviously spent all of five minutes checking.
We know from previous experience that your initial version of anything
is almost certain to have errors in it; that has been the case for as
long as I have been following your work. You have cried "wolf" a
great many times, only to say "Whoops, I found a mistake."
>
>So ONE LITTLE appearance of an issue and you're stomping and shouting
>and hollering with glee.
Because it was you who were stomping and shouting and hollering with
glee because you had solved the factoring problem and how we were all
going to have to appear before the SCotUS to justify ourselves. You
holler at us and we will holler straight back. You are reaping what
you sowed earlier James.
>
>But the method worked. It's actually a bit scarier now as there is
>increasing evidence that it is actually is a valid approach.
No James. Your method finds a solution, but it finds that solution no
faster than existing methods. Speed is of the essence James. We
already have plenty of slow solutions; we are now looking for fast
solutions. You have not shown that your latest solution is fast.
rossum
>
>
>James Harris
Bruce Stephens
[...]
> The poster Enrico gave a false alarm. He said he couldn't get the
> answer for q=2, N = 161 = 7(23) using my approach.
>
> I take such claims seriously.
Even when you have a proof?
[...]
> So ONE LITTLE appearance of an issue and you're stomping and shouting
> and hollering with glee.
I'm not doing that. I still suggest that if you've got something that
works, you should code it. The numbers you're trying by hand are so
small you'd have to work quite hard to avoid factoring them. You can
wait for other people to code it, I suppose, but that's never worked
well for you in the past.
> But the method worked. It's actually a bit scarier now as there is
> increasing evidence that it is actually is a valid approach.
We already have methods that work slowly. We're missing methods that
work fast enough that they'll work on larger numbers, and for that
you'll either have to do some kind of complexity analysis or you'll have
to code it and see if it works.
Enrico
>
> - Show quoted text -
====================================================
One thing still missing from James' method is how j is selected.
Enrico
Lits O'Hate
> Beautiful mathematics made to dance for the crowd so that maybe
> they'll toss their pennies.
Or their cookies.
--
"Here with absolute mathematical proofs I know without a doubt
that an entire planet is wrong about my ideas." -- James Harris
JSH
No, not really. There are size issues as T needs to be roughly equal
to N^2 for 50% probability with a=1, which I knew from the surrogate
factoring research, but kind of forgot.
You should have seen that in your results where as N gets bigger it
takes longer and longer to get an answer, kind of like there are zones
where you CANNOT get the answer, as there are zones where answers are
far less likely.
James Harris
Enrico
======================================================
>
> You should have seen that in your results where as N gets bigger it
> takes longer and longer to get an answer, kind of like there are zones
> where you CANNOT get the answer, as there are zones where answers are
> far less likely.
>
What I see in my results are pairs of periodic impulse functions of
periods
equal to the pairs of primes in N. Intersections of the two functions
show
where solutions exist and the whole thing has a period of N, plus
reflection symmetry
In your solution yesterday for X^2 = 2 mod 161, you used
f1 = 143 and j = 111
143 divides 2q + jN evenly ONLY at the places where both
a solution to X^2 = 2 mod 161 and a factorization of 161 exist.
(Your right - it looks elegant)
There are 4 such places at intervals of 161.
Of any such group of 4, only 2 give nontrivial factorizations.
I assume thats the source of your 50% probability claim.
Is it significant that f1 = 143 is itself a solution to X^2 = 2 mod
161 ?
Is it significant that j = 111 is related to another solution of X^2
= 2 mod 161:
X = 74 via 74 * 3 / 2 = 111 ?
Evil, Lying Mathematicians want to know
Enrico
amzoti
>
> You should have seen that in your results where as N gets bigger it
> takes longer and longer to get an answer, kind of like there are zones
> where you CANNOT get the answer, as there are zones where answers are
> far less likely.
>
> James Harris
What twilight 'zone' do you exist in where anyone accepts this
nonsensical gibberish?
Are you delusional?
You are totally zoned in on the women and don't want to do the math.
Shame on you!
JSH
I worked backwards using f_1 = 3 mod 7 and f_1 = 5 mod 23, which gives
f_1 = 143 mod 161.
> I assume thats the source of your 50% probability claim.
That seems more and more to me like a guess having to do with
quadratic residues being so significant.
But I'm looking back over a year and it all gets fuzzy. My past self
seemed to think that was the probability, but I'm not really sure any
more why.
> Is it significant that f1 = 143 is itself a solution to X^2 = 2 mod
> 161 ?
Two key underlying surrogate factoring equations are:
f_1 = ak mod p, and f_2 = a^{-1}(1 + a^2)k mod p
where with N, p is a prime factor of N, and those equations are not
necessarily valid for N, but still end up being valid for some prime
factor of it. I've been using a=1, so if they are valid for both,
then yeah, k will equal f_1, and for the prime case you'd see that is
always the case.
Using k = 3^{-1}(f_1 + f_2) mod N, though works regardless though it's
true mod p, as well, of course. I thought that was cool as I just
jumped to mod N from mod p, and it's not always true that everything
carries over.
> Is it significant that j = 111 is related to another solution of X^2
> = 2 mod 161:
> X = 74 via 74 * 3 / 2 = 111 ?
I don't know. These surrogate factoring equations can be interesting
to unravel as you're always dealing with two factorizations.
Your pulling information out of one from the other or vice versa so
there are all these underlying mathematical relationships where they
connect to each other.
> Evil, Lying Mathematicians want to know
>
> Enrico
Hey, to me it's interesting mathematics and easily qualifies as of
interest for "pure math" reasons which I toss out because there are
posters who keep taunting about factoring a large number.
But the underlying mathematics is really this connection between TWO
factorizations, so who knows what you might see playing with it
enough. I suspect some of what you might see would look like
interference patterns.
IN any event, success with a=1 depends no certain things. You might
find more success with a=2. Also T can be even or odd. I often use
odd T, just because. (I kind of don't like messing with a lot of
factors of 2.)
I'm guessing now for various reasons that the probability of success
with a>1 is roughly: ((a-1)/a)*(50%).
With a=1, I'm guessing you have 50% probability with T>N^2, but it
still may work with smaller T but I'm not sure what the probability is
(lots of competing factors come into play).
James Harris
Chris McDonald
>I'm guessing now for various reasons that the probability of success
>with a>1 is roughly: ((a-1)/a)*(50%).
>With a=1, I'm guessing you have 50% probability with T>N^2, but it
>still may work with smaller T but I'm not sure what the probability is
>(lots of competing factors come into play).
This may be a significant result, worthy of investigation.
I postulate that for any positive integer, 50% to be an upper-bound on
the probability of it being prime, and thus a possible prime factor from
James' factorization techniques. It's amazing.
--
Chris.