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Topic: SF: Finally, surrogate factoring
Replies: 86   Last Post: Jun 10, 2006 11:51 PM

 Messages: [ Previous | Next ]
 Rick Decker Posts: 1,356 Registered: 12/6/04
Re: JSH: SF: Finally, surrogate factoring
Posted: Jun 6, 2006 8:54 PM

Tim Peters wrote:
> [Rick Decker]
>

>>...
>>So completing the square w.r.t y first yields
>>
>> (2*y + 10*z + 5*f_1 - f_2)^2 = (4*z + 3*f_1 - f_2)^2 + 4*T
>>
>>Completing the square w.r.t. z first yields
>>
>> (42*z + 10*y - 3*f_2 + 19*f_1)^2 = (4*y + 3*f_2 - 5*f_1)^2 + 84*T
>>
>>and rewriting both these as differences of squares yields the same
>>(useless) factorization of T:
>>
>> T = (y + 3*z + f_1)(y + 7*z + 4*f_1 - f_2)

>
>
> Macsyma agrees ;-)
>
>

>>and it's not hard to verify that
>>
>> g_1 = y + 3*z + f_1
>>
>> g_2 = y + 7*z + 4*f_1 - f_2

>
>
> Given that James started with (although it was obscured by the
> presentation):
>
> f_1 = w + x - 2*z
> f_2 = w + 3*x + 2*y + 2*z
> g_1 = w + x + y + z
> g_2 = 3*w + x - y - 3*z
>
> that's immediate. So, after small mountains of tedious manipulation, we get
> back a minor respelling of the initial assumptions.

Of course. My observation was nothing more than a verification
that all of this completing-the-square taradiddle was indeed correct
(and, as you indicate below, trivial). Nice typesetting, BTW.
>
> What I don't understand is how anything other than that outcome could be
> _hoped_ for here. No amount of rearranging and cross-substituting the
> initial equations (whatever they may be) is going to yield new information,
> and there's never a step that even requires the quantities to be integers
> (as opposed to, e.g., arbitrary complex numbers). How can someone imagine
> that insight into integer factorization could result from this insight-less
> symbol-pushing?

I think that what we interpret as obfuscation on James' part is actually
a consequence of the fact that his understanding is extremely shallow.
This is, I think, the reason that he thinks his "prime counting
function" is truly new and innovative--he really is incapable of even
the slightest bit of abstraction that to all mathematicians is as
natural as breathing.
>
> As usual, I couldn't make sense of his original writeup before you showed
> the correct result of completing the square wrt y first, at which point I
> could work backward from that to deduce what you thought James was trying to
> say. Also as usual, you got that right. Therefore :-) you must also know
> why he thinks this kind of approach _could_ yield something useful.
>

See above. The kind of self-editing we're accustomed to by inclination
and training is something he simply doesn't get. For example, a tiny bit
of thinking makes it obvious that no matter what collection of linear
equations one starts with, as long as they have a unique solution
the end result of the "small mountain of tedious manipulation" will
be the completely unsurprising T = g_1 * g_1, which we knew from the
start.

> Or is this another case where you know he's right, and are keeping silent
> about which initial equations actually do work just to protect your career?
> Clever, if so ;-)
>

Clever you for deducing that. True, I've found that a simple
modification of James' argument will allow one to factor N in
log^2 (log N) steps, but I'm witholding it (a) to protect my career
and (b) to crack all those RSA codes out there and make a bazillion
bucks by theft, deceit, and blackmail.

Be afraid, be very afraid.

Regards,

Rick

Date Subject Author
6/4/06 JAMES HARRIS
6/5/06 Doug Schwarz
6/5/06 Tim Peters
6/5/06 Doug Schwarz
6/5/06 Christopher J. Henrich
6/5/06 Gib Bogle
6/5/06 Proginoskes
6/5/06 William L. Bahn
6/5/06 JAMES HARRIS
6/5/06 Abstract Dissonance
6/5/06 Abstract Dissonance
6/5/06 Salami Man
6/5/06 William L. Bahn
6/6/06 Brian Quincy Hutchings
6/5/06 guenther.vonKnakspott@gmx.de
6/6/06 Matthijs Hebly
6/6/06 Salami Man
6/5/06 Abstract Dissonance
6/5/06 Gordon Burditt
6/5/06 Sebastian Gottschalk
6/5/06 dkguru
6/5/06 Ed Weir \(ComCast\)
6/5/06 Abstract Dissonance
6/5/06 Andrew Swallow
6/5/06 gjedwards@gmail.com
6/5/06 Salami Man
6/5/06 Gib Bogle
6/6/06 TC
6/6/06 Salami Man
6/5/06 Sebastian Gottschalk
6/5/06 JAMES HARRIS
6/5/06 marc.t.davies@gmail.com
6/5/06 gjedwards@gmail.com
6/5/06 LarryLard
6/5/06 William L. Bahn
6/5/06 Richard Henry
6/5/06 Salami Man
6/5/06 Bob Marlow
6/5/06 Bob Marlow
6/5/06 none
6/5/06 rossum
6/5/06 Rick Decker
6/5/06 JAMES HARRIS
6/5/06 jshsucks@yahoo.com
6/5/06 Salami Man
6/5/06 Tim Peters
6/5/06 JAMES HARRIS
6/5/06 Tim Peters
6/6/06 Rick Decker
6/6/06 Rick Decker
6/6/06 Tim Peters
6/6/06 Rick Decker
6/7/06 David C. Ullrich
6/7/06 Rick Decker
6/7/06 Jesse F. Hughes
6/7/06 Rick Decker
6/8/06 David C. Ullrich
6/7/06 Bertie Reed
6/6/06 JAMES HARRIS
6/6/06 JAMES HARRIS
6/7/06 Rick Decker
6/7/06 Tim Peters
6/7/06 Rick Decker
6/8/06 JAMES HARRIS
6/8/06 Jose Carlos Santos
6/8/06 Rick Decker
6/8/06 LarryLard
6/8/06 David Bernier
6/8/06 Rick Decker
6/9/06 Tim Peters
6/9/06 david250@gmail.com
6/9/06 marcus_b
6/8/06 Richard Henry
6/8/06 jshsucks@yahoo.com
6/8/06 Paul Sperry
6/8/06 LarryLard
6/8/06 Denis Feldmann
6/8/06 David Bernier
6/8/06 David C. Ullrich
6/8/06 David Moran
6/8/06 David Bernier
6/8/06 Tim Peters
6/8/06 Proginoskes
6/10/06 Tim Peters
6/10/06 Tim Peters
6/6/06 gjedwards@gmail.com
6/6/06 Proginoskes