Author 
Message 
Tim Peters science forum Guru
Joined: 30 Apr 2005
Posts: 426

Posted: Mon Jul 17, 2006 3:39 am Post subject:
Re: Loose connectivity, factoring and residues



[jstevh@msn.com]
Quote:  ...
Now then, if you find a solution
x^2  y^2 = 0 mod T
where x = 1 mod T, then you will also find that
S = 2*x*k mod T
solves to give
k = S*(2*x)^{1} mod T
so if you solve for k FIRST, with x_res = 1 mod T, then you get the
SAME ANSWER if k is a residue modulo T, understand?
That is an important point.

Not really. As I said, I'm done with this method, but I'll take time to
spell out an implication you missed in my last message (I didn't spell out
every step then  I will now).
No matter what you pick for anything, or how you go about it, these are
/requirements/ of the method:
x^2  y^2 = 0 (modulo T) [1]
x^2  y^2 = S  2*x*k [2]
2*S*k = x_res (modulo T) [3]
Solving for S in [2] and substituting into [3] gives:
2*(x^2  y^2 + 2*x*k)*k = x_res (modulo T)
But by [1], x^2  y^2 is congruent to 0, so that becomes:
2*(2*x*k)*k = x_res (modulo T)
or
4*x*k^2 = x_res (modulo T) [4]
Then in any solution that doesn't work purely by luck, you also need:
x = x_res (modulo T)
so that [4] becomes:
4*x*k^2 = x (modulo T) [5]
Then acknowledging that it's a miracle if x isn't coprime to T (if it isn't,
use gcd(x, T) to factor and forget the rest), x has an inverse modulo T, and
[5] is then equivalent to:
4*k^2 = 1 (modulo T) [6]
You may have noticed that I derived the same thing in the context of my
specific "work backwards" example, but the derivation was shorter there
because it used specific numbers. But in fact [6] depends on nothing about
the way I picked x or x_res: if you want to pick x_res=1 instead, fine, [6]
_still_ applies. Picking S first and then solving for k doesn't change that
either. You can't get away from it. As just demonstrated, it's _inherent_
to this method that it needs to find k satisfying the quadratic congruence
[6], and that's equivalent to solving the modular square root problem, and
that in turn is known (has been proved) to be exactly as hard as factoring
T.
Nothing you say, hope, wish for, or believe can worm around that fact. If
you can solve [6] efficiently, sure, you can factor efficiently too. So
demonstrate you can solve [6] efficiently, or let go and move on. And by
"solving [6]" I mean solving it for a /given/ T, not goofiness like picking
k first and then finding T for which [6] holds (that's trivial to solve, and
irrelevant).
Quote:  ...
Look over my roadmap of discoveries. Why do you think your
mathematical insights are better than mine?

Partly because I believe most of your claimed discoveries are wrong (i.e,
your "roadmap of discoveries" reads like a recital of mostly unacknowledged
failures to me, with a few wildly overvalued correct results), and in the
specific case of factoring integers because I routinely see how one of your
methods has to end in minutes, instead of the days, weeks, or months you
continue to struggle with one. That's not because I'm "lucky".
If you haven't noticed, I've also had much more success factoring integers
with your methods than you've had. The reason for that is that I generally
understand what your methods /actually/ do more deeply than you do.
Quote:  Just because you've seen a lot of my failures?

No. All I take from those is that for someone trying to do mathematics,
you're extraordinarily careless, generally know little about the areas you
tackle, often have trouble thinking and writing clearly, and have enormous
difficulty letting go of failed ideas. Those alone don't preclude you from
making worthwile discoveries (but certainly don't help you either).
Quote:  But could you have ANY of my successes?

But I'm not willing to call incorrect claims successes, neither yours nor
mine. That puts me at a severe disadvantage, you know 

Back to top 


OM science forum beginner
Joined: 01 Jul 2005
Posts: 4

Posted: Mon Jul 17, 2006 5:03 am Post subject:
RE: Responding to Brad Guth  ENOUGH!



....Kids, enough is enough. Brad Guth is a known troll, who's mental
processes are totally corrupted from the fact that he was not only
molested by his father and his uncle at an early age, he actually bent
over and took it *willingly*, and enjoyed the experience. This being
now understood, it should also be understood that he's not a victim,
but a worthless sack of s**t pretending to be intelligent life, and
therefore should simply be killfiled.
....So, with all these facts laid out for you, if you can't put the
retarded bastard into your killfiles, at least remove
sci.space.history from the followups so we don't have to put up with
the responses to his blatherings that you kids keep polluting our
group with. Everyone on ssh that counts has him killfiled, so please
put him out of our misery once again, eh?
Thanks.
OM

]=====================================[
] OMBlog  http://www.io.com/~o_m/omworld [
] Let's face it: Sometimes you *need* [
] an obnoxious opinion in your day! [
]=====================================[ 

Back to top 


Proginoskes science forum Guru
Joined: 29 Apr 2005
Posts: 2593

Posted: Mon Jul 17, 2006 5:56 am Post subject:
Re: Loose connectivity, factoring and residues



Tim Peters wrote:
Someone must have touched a sensitive nerve (i.e., proven JSH wrong);
JSH is deleting posts from Google Groups again.
 Christopher Heckman (who never deletes his Usenet posts) 

Back to top 


Tim Peters science forum Guru
Joined: 30 Apr 2005
Posts: 426

Posted: Mon Jul 17, 2006 6:43 am Post subject:
Re: Loose connectivity, factoring and residues



[Tim Peters, to JSH, shows that if x is congruent to x_res modulo T,
and x is coprime to T, then every solution for k must satisfy:]
Quote:  ...
4*k^2 = 1 (modulo T) [6]

[and then leaps to an incorrect conclusion of his own:]
Quote:  ...
If you can solve [6] efficiently, sure, you can factor efficiently too.
So demonstrate you can solve [6] efficiently, or let go and move on.

I apologize for not noticing that [6] is of a special form with two easily
found solutions (assuming T is odd, and only considering solutions in [1,
T)):
k = (T+1)/2
and
k = (T1)/2
Finding the other two solutions (when T=p*q is the product of two distinct
odd primes) is still as difficult as factoring T: [6] boils down to finding
the square roots of 1 (solve (2*k)^2 = 1 for 2*k, and then use 2^1=(T+1)/2
to isolate k), and the solutions above correspond to +/1. The other two
square roots of 1 are mod(+/(p^(q1)  q^(p1)), T), and there's no
efficient way to find those without knowing p and q.
So you can find two solutions to [6] very easily after all. I don't know
whether they're useful solutions, but you're not going to get anywhere if
[6] isn't satisfied, and the other solutions are hard to find, so these are
worth pursuing. 

Back to top 


Norm De Plume science forum beginner
Joined: 19 May 2005
Posts: 3

Posted: Mon Jul 17, 2006 6:46 am Post subject:
Re: Responding to Brad Guth  ENOUGH!



100% of the people who believe that the moon landings were faked also
have wives and/or girlfriends who always fake their orgasms.
Coincidence? 

Back to top 


a_plutonium@hotmail.com science forum Guru
Joined: 11 Sep 2005
Posts: 1063

Posted: Mon Jul 17, 2006 6:51 am Post subject:
mass and space functionality equals charge Re: gravity a fictional force in the Atom Totality



a_plutonium@hotmail.com wrote:
Quote: 
I am going to refer to Feynman's Lectures on Physics page 210 of the
Table 23 of Elementary Interactions:
Coupling Strength Law
photon to charged particle approx 10^2 law known
gravity to all energy approx 10^40 law known
weak decays approx 10^5 law partly known
mesons to baryons approx 1 law unknown some rules known
Let us consider the Coulomb force as the Unification force where
weakforce combines with strongforce to become a Nuclear Coulomb in
the above table. That comes to some agreement in the above table for it
is very much approx.
Agreement in that 10^2 is a midpoint of functionality of 1 and 10^5.
So that combining Weakforce with Strongforce results in a Nuclear
Coulomb force.

This leaves the Universe with only one force, a Coulomb force. Where
the WeakNuclear and StrongNuclear form a NuclearCoulomb. It is not by
accident that Coulomb is 10^2 and the midpoint between WeakNuclear
10^5 and StrongNuclear at 1.
Circa 1999 and the first several years of 2000s I thought gravity has
an antigravity force and when combining these two would make a
ElectronRegionCoulomb force just as WeakNuclear and StrongNuclear is
the nuclear region coulomb. So that a specific region of any atom has
combinations of forces which add up to a Coulomb force. So all forces
are merely Coulomb forces when combined. The NuclearCoulomb is the
broken symmetry of the Nucleus.
But now I am of the opinion that gravity has no antigravity force and
that gravity is merely a residue of Coulomb between protons holding
together electrons in an atom. Gravity is a fictional force such as
centrifugal to centripetal.
Quote: 
Now to resolve gravity as a fictional force (or a residue of the
Coulomb force considering that the Cosmos is the inside of a gigantic
atom).
In an atom, whether in chemistry lab or the Atom Totality itself, most
of the mass is the nucleus and thus it bends the space around the
nucleus so that the electrons travel in that bent space and we see it
as an attraction force the Coulomb attraction.. Protons repulse other
protons but in the nucleus of an atom, we have a new particle called a
nuclearelectron. This is a special kind of electron because it is a
whole electron and not an electrondotcloud. Every neutron has a
nuclearelectron inside itself and this nuclearelectron when inside
the space of a nucleus runs out and runs around holding together the
protons in the nucleus of atoms larger than hydrogen in atomic mass.

Never did I think I would someday have to use the idea "mass bends
space". But now I must use it to reconcile how all the galaxies being a
part of the electrons of the Atom Totality can have gravity. Since we
know that electron to electron charge repulses one another.
So I need the concept that "mass bends space" to reconcile electron to
electron repulsion.
Quote:  But the NuclearElectron does not concern us with the night sky of our
cosmos. Our cosmos is purely the electrondotcloud of the 231Pu Atom
Totality. Galaxies are pieces of the 94 electrons of 231Pu, ditto for
Sun and Earth. What we see in the night sky is all the pieces of the 94
electrons of 231Pu. Now, why do we see a force which we call "gravity"?
It is identical to the Coulomb force when we replace charge with mass,
only it is about 10^40 weaker in strength.
Charge is mass, and mass bends space around that mass.
The easy solution is that mass is charge as a function of geometry.

Here I need functionality, where mass and space are functions of one
another and which creates charge. Charge is the functionality of mass
and space. I cannot say much more about this now. I can give examples
to make clear.
Example: An electron inside a neutron is a ball and not an
electrondotcloud. The ball is small and compact and so the ball has
all the mass and very little space. In contrast, the electron of
hydrogen atom of its 1s is electrondotcloud. As if the electron had
been smashed of its mass and tiny pieces of its mass scattered around
the proton nucleus. Here the electron is a combination of the
electrondotcloud and the large space those electron dots are
scattered.
If we take two protons and put them close together their space may not
even be a ball shape but something different because they are repulsing
one another. The proton to electron in a hydrogen atom of 1s is
perfectly spherical because it is attractive and forms a symmetrical
geometry.
So charge as a physics concept is the function of mass and space.
Quote: 
This means that gravity is fictional force.

Fictional because now we can view Coulomb force with its charge terms
as a combination of functionality of mass to space.
Planet Earth is part of the 94th electron of 231Pu ditto for the Sun.
Yet Sun and Earth attract one another, while electrons repel one
another. But this is explained in that charge is not a separate concept
from that of mass and space. The dots of electrondotcloud do not
repel one another, instead, they create space around them and bend
space around them and we perceive this as "gravity".
Most people reading this have the notion that space exists independent
of mass. What I am saying is that space does not exist until electrons
or an electron becomes a dotcloudelectron. A nuclear electron or a
electron moving in a wire of electricity is a collapsed electron into a
ball and lacks the enormous space.
And the reason neutrons hold together protons is because the nuclear
electron inside the neutrons devotes its space to that of gluing
together the protons.
Quote: 
In astronomy there is a very big problem of a "missing mass". It is
called the Missing Mass Problem. The solution is that the mass of the
cosmos is 99% in the Nucleus of the Atom Totality.
Now we all know the formula E = mc^2. And we know that c = 3 X 10^8
m/s. Now can I derive the approx 10^40 force strength by Feynman's
above table for the 231Pu Atom Totality. Let me give it a rough shot.
The energy term E would be the 5 shells of 231Pu. This is the "5f"
energy shell. This is the geometry or space functionality.

Plutonium does have 5 energy levels of 5f6. And if Charge is a
functionality between Mass and Space then the speed of light to the 5th
power does yield a force strength of approx 10^40. I need to work on
this more. And it implies that gravity is different in the nucleus then
in the electronspace region of an atom. And here we can set up
experiments to verify the differences. The old way of thinking is that
gravity is the same in all places and regions of the Universe. I am
saying that gravity would be different in the nucleus of an atom
compared to its electron space region.
Quote: 
Notice that when I take 3x10^8 to the 5th power, I end up with approx
10^40. The same approx 10^40 that Feynman has in his table above.
Summary: In an Atom Totality all the forces unify into one force
Coulomb Force. The force of gravity in an Atom Totality is merely a
sideeffect of Coulomb. We think gravity is independent of Coulomb,
when in fact it is a result of the Cosmos being a big atom held
together by the Coulomb force.

I feel somewhat satisfied with gravity a fictional force, because I can
dispel the need to reconcile with a carrier particle for gravity, such
as the mythical graviton or the neutrino. A fictional force has no
carrier particle.
I am not sure yet of the mathematics involved, whether I am dealing
with composite functions for mass to space to form charge or something
more complicated. Thus I call it "functionality" at the moment.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electrondotcloud are galaxies 

Back to top 


Pat Flannery science forum beginner
Joined: 30 Jun 2005
Posts: 35

Posted: Mon Jul 17, 2006 7:59 am Post subject:
Re: Responding to Brad Guth  ENOUGH!



OM wrote:
Quote:  ...So, with all these facts laid out for you, if you can't put the
retarded bastard into your killfiles, at least remove
sci.space.history from the followups so we don't have to put up with
the responses to his blatherings that you kids keep polluting our
group with. Everyone on ssh that counts has him killfiled, so please
put him out of our misery once again, eh?

Trying to argue a logical point with Brad is like petting a porcupine
the porcupine won't appreciate the gesture, and if you're smart you will
only try it once.
Pat 

Back to top 


Tim Peters science forum Guru
Joined: 30 Apr 2005
Posts: 426

Posted: Mon Jul 17, 2006 9:22 am Post subject:
Re: Loose connectivity, factoring and residues



Quote:  [Tim Peters, to JSH, shows that if x is congruent to x_res modulo T,
and x is coprime to T, then every solution for k must satisfy:]
...
4*k^2 = 1 (modulo T) [6]

And that was wrong, based on copying the erroneous:
Quote:  2*S*k = x_res (modulo T) [3]

from an older post that should have said:
2*x_res*k = S (modulo T)
instead. My apologies for that again.
Quote:  ...
So you can find two solutions to [6] very easily after all. I don't
know whether they're useful solutions, but you're not going to get
anywhere if [6] isn't satisfied, and the other solutions are hard to
find, so these are worth pursuing.

So there's no mistake, [6] is irrelevant. Then again, those values for k
appear to work as well as any others 

Back to top 


Tim Peters science forum Guru
Joined: 30 Apr 2005
Posts: 426

Posted: Mon Jul 17, 2006 9:22 am Post subject:
Re: Loose connectivity, factoring and residues



[Tim Peters, to JSH]
Quote:  ...
No matter what you pick for anything, or how you go about it, these are
/requirements/ of the method:
x^2  y^2 = 0 (modulo T) [1]
x^2  y^2 = S  2*x*k [2]
2*S*k = x_res (modulo T) [3]

Jeez Louise, I /am/ hallucinating today. [3] was copied from a post with a
transcription error, and should have been:
2*x_res*k = S (modulo T) [3]
instead. No particular constraint on k^2 follows after that correction. 

Back to top 


Tim Peters science forum Guru
Joined: 30 Apr 2005
Posts: 426

Posted: Mon Jul 17, 2006 5:23 pm Post subject:
Re: Loose connectivity, factoring and residues



[Proginoskes]
Quote:  Someone must have touched a sensitive nerve (i.e., proven JSH wrong);

Wasn't me Proving there's no possible efficient way to pick the free
variables so that "it works" would, I think, be messy. For a while I was
under the illusion (based on a transcription error in one of the equations)
that the method necessarily relied on solving a hard modular square root
problem "to work", but that's not obviously so after all.
It was rarely possible to prove (with finite effort) that last year's
methods couldn't possibly work efficiently either, and for a similar reason:
there's not much you can say about the congruence class of i+j across all
<i, j> pairs s.t. i*j = n for some fixed n. Instead mod(i+j, T) acts much
like a lowquality pseudorandom number generator (which is consistent with
observations, then and now, that the method behaves similarly to, but worse
than, the randomgcd factoring algorithm, at least in the absence of an
intelligent way to pick the free variables). However, that cuts both ways:
since there's not much you can say, it gets in the way of trying to prove it
/can/ work efficiently too.
Here _one_ of the questions is whether you can pick integer S, x_res, k, f_1
and f_2 efficiently s.t.
f_1 + f_2 = 2*(x_res + k) (modulo T)
and
f_1 * f_2 = S + k^2
and
S = 2 * x_res * k (modulo T)
And the answer is "yes": S = x_res = k = f_1 = f_2 = 0 works, leading to
the true conclusion that 0^2  0^2 = 0 (modulo T). Not terribly useful,
though ;)
Quote:  JSH is deleting posts from Google Groups again.
 Christopher Heckman (who never deletes his Usenet posts)

Indeed! Me neither. Does /anyone/ else? Doing so routinely is antisocial.
But then I suppose we're not performing noble social experiments in
information destruction either 

Back to top 


Proginoskes science forum Guru
Joined: 29 Apr 2005
Posts: 2593

Posted: Mon Jul 17, 2006 6:16 pm Post subject:
Re: Loose connectivity, factoring and residues



Tim Peters wrote:
Quote:  [Proginoskes]
Someone must have touched a sensitive nerve (i.e., proven JSH wrong);
JSH is deleting posts from Google Groups again.
 Christopher Heckman (who never deletes his Usenet posts)
Indeed! Me neither. Does /anyone/ else? Doing so routinely is antisocial.
But then I suppose we're not performing noble social experiments in
information destruction either

It's strange, though. When I go to sci.math, all of his posts are
missing, but if I go to alt.math.recreational or alt.math, they're
still there.
Maybe if you crosspost, and delete the post from Google Groups, it
only wipes out the post from the thread in the first newsgroup. Or
(more likely) JSH forgot about the other newsgroups.
 Christopher Heckman 

Back to top 


Dr.Colon.Oscopy@gmail.com science forum beginner
Joined: 17 Jul 2006
Posts: 1

Posted: Mon Jul 17, 2006 8:55 pm Post subject:
Re: Responding to Brad Guth  ENOUGH!



Well put, however I bristle when the analogy of a Porcupine is used in
this situation as it denegrates the poor animal (porcupines are well
armed) and unlike the porcupine, the Brad has no point(s)..........Doc
Pat Flannery wrote:
Quote:  OM wrote:
...So, with all these facts laid out for you, if you can't put the
retarded bastard into your killfiles, at least remove
sci.space.history from the followups so we don't have to put up with
the responses to his blatherings that you kids keep polluting our
group with. Everyone on ssh that counts has him killfiled, so please
put him out of our misery once again, eh?
Trying to argue a logical point with Brad is like petting a porcupine
the porcupine won't appreciate the gesture, and if you're smart you will
only try it once.
Pat 


Back to top 


ma740988 science forum beginner
Joined: 18 Jul 2006
Posts: 2

Posted: Tue Jul 18, 2006 12:38 am Post subject:
Re: maths for programming C++



Robbie Hatley wrote:
[...]
Quote: 
"uttre"
(1) sometime ago i read a blog of SteveyDrunken's on "Maths everyday".
the distinctional points he proposed in his blog are exactly similar to
the ones i have got after doing some programming for 6 months. but he
had his points by reading "John Von Neumann and the Origins of Modern
Computing". I dont know him & neither i read that book but the points
he noticed & points i noticed are similar in many respects.
Taht's all very nice, but has absolutely nothing whatsoever to
do with the C++ programming language, so it's 100% offtopic here.
As you may have noticed, you got a lot of replies, but none
that really helped you a lot. That's what happens when you get
waaaaay offtopic.
Try these newsgroups instead:
sci.math (I set followup here)
alt.math
alt.math.moderated
I think you'll get MUCH better responses there.
The reason is, computer programming is a skill which requires
relatively little mathematics. About all you need to know is:
1. Gradeschool arithmetic.
2. A little boolean algebra (and, or, not, DeMorgan's Law, etc)
3. A little bit of highschool algebra helps sometimes (optional)
That's it. Any 14yearold knows those things already.
Now, if you're doing programming in a heavily mathematical field
(say, university mathematics research, or theoretical physics, or
climate modeling, or advanced cartography using fancy projections)
then you may need to learn more math. But for most programming,
little math is required. So most programmers here are not
advanced mathematicians, and can't advise you very well on
highermathematics textbooks.

The basic premise as I understand the OP's post surrounds the
application of higher level math in a programming context. So while
it's true that his/her post is offtopic, the advise received in
scimath may or may not be of much help. Simply put, most of the
respondents may not know a heck of alot about programming. Conversly
most of the respondents here may not know much about high level math.
With that in mind, I understand and feel the OP's pain. The difference
is I understand and appreaciate the higher level math pertaining to
pattern recognition ( one of the OP's desire ), image/signal
processing, boundary element methods etc. etc. For years and of
course  even today  matlab has been my analysis tool. For years, I
would hand matlab code to a developer and say  go code 'this'. Over
the last year or so I've done some role reversal. Granted, I'm no
Grade A programmer like most folks on here and I can't quote every
line of the standard. It remains true nonetheless, that the OP will
find that programming higher level math requires:
1. An appreciation for the standard library ( alot of those algorithms
in that library is a god send )
2. An appreciation for templates. ( I find this to be a real beast
from time to time. )
Rest assured there's quite a few programming books out there geared
towards the scientific community. Sadly, the vast majority of these
books  I've run across  are poorly written. 

Back to top 


stush@rocketmail.com science forum addict
Joined: 10 Nov 2005
Posts: 73

Posted: Tue Jul 18, 2006 12:57 am Post subject:
Re: maths for programming C++



ma740988 wrote:
Quote:  Robbie Hatley wrote:
[...]
"uttre"
(1) sometime ago i read a blog of SteveyDrunken's on "Maths everyday".
the distinctional points he proposed in his blog are exactly similar to
the ones i have got after doing some programming for 6 months. but he
had his points by reading "John Von Neumann and the Origins of Modern
Computing". I dont know him & neither i read that book but the points
he noticed & points i noticed are similar in many respects.
Taht's all very nice, but has absolutely nothing whatsoever to
do with the C++ programming language, so it's 100% offtopic here.
As you may have noticed, you got a lot of replies, but none
that really helped you a lot. That's what happens when you get
waaaaay offtopic.
Try these newsgroups instead:
sci.math (I set followup here)
alt.math
alt.math.moderated
I think you'll get MUCH better responses there.
The reason is, computer programming is a skill which requires
relatively little mathematics. About all you need to know is:
1. Gradeschool arithmetic.
2. A little boolean algebra (and, or, not, DeMorgan's Law, etc)
3. A little bit of highschool algebra helps sometimes (optional)
That's it. Any 14yearold knows those things already.

Simply not true unless you want to program like a 14 year old. 

Back to top 


jstevh@msn.com science forum Guru
Joined: 21 Jan 2006
Posts: 951

Posted: Tue Jul 18, 2006 1:13 am Post subject:
Re: Loose connectivity, factoring and residues



Proginoskes wrote:
Quote:  Tim Peters wrote:
[Proginoskes]
Someone must have touched a sensitive nerve (i.e., proven JSH wrong);
JSH is deleting posts from Google Groups again.
 Christopher Heckman (who never deletes his Usenet posts)
Indeed! Me neither. Does /anyone/ else? Doing so routinely is antisocial.
But then I suppose we're not performing noble social experiments in
information destruction either :(
It's strange, though. When I go to sci.math, all of his posts are
missing, but if I go to alt.math.recreational or alt.math, they're
still there.
Maybe if you crosspost, and delete the post from Google Groups, it
only wipes out the post from the thread in the first newsgroup. Or
(more likely) JSH forgot about the other newsgroups.
 Christopher Heckman

Hmmm...looks like I'll need to check those as well then!!!
Thanks for the head's up!!!!!!
___JSH 

Back to top 


Google


Back to top 



The time now is Tue Sep 19, 2017 5:08 pm  All times are GMT

