This is a good analogy, spike. But right now I am in the throes of mathematical mania, and so I have rejiggered the problem for myself once again. Consider what is to be proven: P != 2nmodp + pk. The modulo operation here can be rewritten as 2n- p[2n/p] (where brackets denote the floor function). So we have: 2n-p[2n/p] +pk != P. Dividing by p gives this: 2n/p - [2n/p] +k != P/p. This is wonderful. We have restated the question as such: If the fractional part of 2n/p (p being any applicable prime) cannot equal the fractional part of P/p, there is a hole in the sieve and the conjecture is true. But I belive the fractional parts will never be equal,. because P/p will always produce an "odd" fractional part and 2n/p an even one.<br>
<br>kyew ee dee?<br><br><div class="gmail_quote">On Sat, Nov 28, 2009 at 12:59 PM, spike <span dir="ltr"><<a href="mailto:spike66@att.net">spike66@att.net</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
On Behalf Of Will Steinberg<br>
Subject: Re: [ExI] Goldbach Conjecture<br>
<br>
<br>
> If it can be proved that every two-way sieve of eratosthenes has at<br>
least one hole, the conjecture can be proven. What this means is that<br>
(since oles are at 2k, 3k, 5k, nmod2+2k, nmod5+5k, etc.) ...What is needed<br>
to continue is a way to prove there will always be a p that doesn't equal<br>
nmodp +pk. Will Steinberg<br>
<br>
<br>
2009/11/28 spike <<a href="mailto:spike66@att.net">spike66@att.net</a>><br>
<br>
> ...On Behalf Of Giulio Prisco (2nd email)<br>
> Subject: Re: [ExI] Goldbach Conjecture<br>
><br>
> I think the Goldbach conjecture is probably false, with<br>
> probability 1 (that means, certainly false). Here is<br>
why:... Giulio<br>
<br>
<br>
I disagree sir, however I confess my line of reasoning is<br>
not as well developed as the one you offer... spike<br>
<br>
<br>
Clearly I took an engineer's approach to the question, which sidesteps the<br>
real question. With this I reveal myself as merely an engineer who likes<br>
math and not the genuine article. I offer for your Saturday morning<br>
entertainment the frisbee analogy to the Goldbach conjecture, along with the<br>
extropian and transhumanist angle to this discussion.<br>
<br>
In my teens I had a doberman who loved to play frisbee, but wasn't quite<br>
capable of catching the device in flight. He would chase it, knock it down,<br>
carry it back, have a blast, but he couldn't quite leap and catch. He was<br>
close, often attempted it, never managed the task. My dog was a terrific<br>
athlete, brave, fierce, fast, coordinated, a magnificent beast was he. He<br>
once slew a rattlesnake single-pawedly, or single-mouthedly(?) but in any<br>
case without help from me or Mister Twelve Gage. Oddly he had a close<br>
relative (in human terms his niece) who could catch a frisbee in flight.<br>
His niece was actually a clumsy dog in some ways, but not in that. She got<br>
better at it over time. My dog would watch her catch that frisbee with a<br>
kind of amazement, as if to say "How does that bitch do it?"<br>
<br>
Catching the frisbee is an example of a skill that is right on the ragged<br>
edge of that particular breed's abilities. Most dobies cannot, a few can.<br>
If we bred only the catchers, I can easily imagine we could create a frisbee<br>
catching breed. On the other hand, actually throwing the frisbee is a skill<br>
outside the abilities of any dog that I know of. If my dog could throw a<br>
frisbee, what fun he and the other dogs could have! The dogs would watch in<br>
amazement as I and the other two-legged beasts would throw that frisbee back<br>
and to. They worshipped us.<br>
<br>
The great unsolved mathematical conjectures such as Goldbach, my own search<br>
for an odd perfect number, and (until 1995) Fermats, are examples of<br>
humanity's version of the dobies' frisbee problem. These are questions<br>
right on the ragged edge of our species' abilities. Guys like Andrew Wiles<br>
demonstrate that these kinds of problems can be solved, given enough effort.<br>
We have solved a number of rattlesnake problems, but these questions are our<br>
frisbees.<br>
<br>
We as a species have before us some immediate and urgent frisbee problems,<br>
such as the energy generation. Eugene, Keith, <a href="http://et.al" target="_blank">et.al</a>. have outlined the<br>
problem and offered possible solutions. Having tasks right at the ragged<br>
edge of the envelope gives us something at which to aim. In this case the<br>
stakes could not be higher. Transhumanists and extropians are examples of<br>
humans who can *almost* catch, people who believe that the object is<br>
catchable, people who are taking a flying leap at that frisbee.<br>
<br>
spike<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
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</blockquote></div><br>