Re: Surrogate factoring, mapping, hyperbolas

From: Nora Baron (norabaron_at_hotmail.com)
Date: 04/20/05 

Date: 20 Apr 2005 09:10:39 -0700

jst...@msn.com wrote:
> Nora Baron wrote:
> > jst...@msn.com wrote:
> > > A sci.math poster has turned to just outright lying, putting up a
> > > thread claiming that surrogate factoring has completely failed.
> > >
> >
> > I am not sure whether you are referring to my post and that of
> > Rick Decker regarding numerators of rational factors of M that
> > are produced by implementing your algorithm. However, as I
> > pointed out in the other thread:
> >
> > 1. My result applies when you start with INTEGER factors
> > "a" and "b" of -T j^2, and when you apply your algorithm
> > in the most natural way, i.e., taking "plus" signs in
> > front of square roots that result from use of the
> > quadratic formula. In that situation, my result combined
> > with Rick Decker's proof implies that your "theorem" gives
> > only trivial factors of M.
>
> <deleted>
>
> The problem though is that "Nora Baron" has worked for *YEARS* to
> convince people that my research is wrong, and often turns to
> obfuscation with overlong posts and supposed "results" that send you
> chasing your tail for a long time before you can find out where the
> poster screwed up.
>
> It's a tactic.
>
> Now the fact that the SFT connects two hyperbolas ends the need for a
> very long post by allowing most to undertand rapidly what I mean, so
> what does "Nora Baron" do in response?
>
> The poster put up a long post, of course.
>
> I've truncated a bit to

  leave out as much of the math as possible and

> focus your attention and to remind you that,
> yes, I'm sorry to tell you, but there are bad people who lie to you,
> make things up, and work to ruin your knowledge of mathematics, and
> why?
>
> Who knows.
>
>
> > > If you trace out the graphs you get two hyperbolas.
> > >
> > > The theorem requires that you get the full hyperbolas over
> rationals,
> > > and the most astute of you can look at the theorem and see that
> > > actually it would work over complex numbers to map two hyperbolas
> > > together over the complex plane.
> > >
> >
> > Yes. So ?
> >
>
> The SFT equations connect two hyperbolas over the complex plane, so
> there is NO WAY that you can skip over solutions to one hyperbola or
> the other that represent what people consider non-trivial factors,
> destroying all claims against the SFT.
>
> It can't skip as if it skips then it does not map two hyperbolas
> completely.
>

  Put this another way. If it skipped then would not be a
"complete" map of the two hyperbolas.

  What you have done here is nothing but reword the definition
of 'skip'.

  You have not proven that your "theorem" defines a mapping
from one hyperbola ONTO the other. Even if you did, you
still would have a long way to go to get what you want.

> People can visualize hyperbolas which makes it easier to explain
versus
> talking about infinity.
>
> >
> > > So it's not rational to claim that you only get one type of
factor
> > that
> > > matters to human beings, as the connection is between two
> hyperbolas.
> > >
> >
> >
> > Here you are making one of your great classic leaps off the
> > edge of a cliff. You have absolutely no proof that if the
> > dots on one hyperbola represent trivial factorizations, those
> > on the other hyperbola must represent nontrivial factorizations.
>
> Um, poster, the SFT maps the hyperbolas together, so EVERY rational
> solution of each hyperbola is mapped to a rational solution of the
> other.
>

  Your "theorem" does not prove this. Your "theorem" shows that
you can generate rational solutions a and b to the equation

        a*b = M^2.

  It does not show that you generate ALL such solutions. Even
if it did, you still need to show that your "theorem" will
generate NONTRIVIAL solutions with a significant probability.

  All you need to do to convince people of the latter is: write
a little program that implements your theorem. Try it with
some target numbers M which are the product of two large
primes. See how often it gives nontrivial solutions.

  That's ALL you have to do. Why haven't you done it?

> It can't skip if it's completely mapped.
>

  Again, you are just saying: it can't skip if it doesn't
skip. This is not an informative statement.

> Oh wait, your comment seems to indicate that one hyperbola can have
> only non-trivial points while the other has trivial points.
>

  No - that's not what I meant and certainly I don't think it is
true. What I meant was, the correspondence that your trivial
"theorem" provides between these two curves does not necessarily
associate trivial factors on one parabola with nontrivial factors
on the other one.

> You can't be that stupid. Are you?
>

  Hey, in your immortal words from the past, I am 'dumber than
dog poop'. You even once called me a "Magidin mathematician".
That one I considered an honor. Thanks.

> Don't you know anything about graphing curves?
>

  Tell me all about it.

> Using rationals only, you can graph a hyperbola which will appear to
be
> fully connected, like on your computer screen, though technically
it's
> not continuous. (Or is it? Doesn't a limit argument prove it is?)
>

  Not if you are only considering rationals. Or are you now
interested in *irrational* factors of M ?

> The rationals that make up the points of that hyperbola will
alternate
> between being what people can call trivial factors to being
> non-trivial.
>

  More accurately: trivial factors and nontrivial factors are
both dense subsets of both parabolas. So what? This does
not prove what you need, which is that your trivial "theorem"
produces a significant probability of generating nontrivial
factors. There is one very easy way for you to show that and
convince everyone: Write a little program and post it and the
results. I DARE you.

> Do you understanding graphing?
>

  Feel free to explain it.

> > This is just transparent B.S. wishful thinking. If you think
> > this is an actual mathematical argument, you are way out of touch
> > with what mathematics actually is. Symmetry of the kind you are
> > wishing for here is not automatic.
> >
>

  At this point Mr. Harris enters full Grandstand mode. He
climbs to the top of Mt. Olympus, or at least a hillock
somewhere in Atlanta. A golden beam of light shines down
from the Heavens, and there is a blare of trumpets. He
begins to speak in sepulchral tones ...

> The "Nora Baron" poster is credited with teaching many readers
> mathematics.
>
> Some of you seem to think I'm a threat, but I actually love
> mathematics--correct mathematical arguments--while the "Nora Baron"
> poster is into lying about it, and worse, convincing other people of
> things that are not true, so who do you think has the negative
impact?
>

  Grandstand: "Tell us, O Wise Master!"

> When those people who cherished what they thought was real knowledge
> coming from such a person figure out that they were so easily
> manipulated and lied to, and were also taught false mathematical
ideas,
> do you think they'll come back later to ever praise the math
community?
>

  Grandstand: "Never! No, never, O Wise Master! They shall be scourged

               and stoned and cruelly beaten and tormented with whips
               and electrical dog-obedience devices!"

> More likely they may be some of the most virulent and hostile people
> you will ever see.
>

  Grandstand: "Verily, O Wise Master, the Apocalypse will be at hand!
               Thou shalt wield Thy Mighty Hammer!.

              "But tell us, O Wise Master - why do you refrain from
               smiting these cheating liars by showing them the
               results of a simple Program, which will prove them
               wrong?"

  Deep Booming Voice from the Heavens: "James, my Son, put down thy
               Mighty Hammer. Thou hast Fucked Up, and thou art
               continuing to *** Up.. Unless thou canst write a
               little Program showing that thine Ideas are actually
               worth a cupful of warm spit, thou must crawl all thy
               days in misery upon thy Belly, seeking in vain for fame,

               fortune, and gullible but gorgeous chicks."

  Nora B.

>
> James Harris