Re: Partial difference equation, primes

From: Marcel Martin (mm_at_ellipsa.no.sp.am.net)
Date: 08/21/04 

Date: Sat, 21 Aug 2004 18:41:06 +0200

James Harris a écrit :
>
> Marcel Martin <mm@ellipsa.no.sp.am.net> wrote in message news:<41257489.17E05AC2@ellipsa.no.sp.am.net>...
> > James Harris a écrit :
> > >[...]
> > > My prime counting function uses a partial difference equation.
> >
> > What do you call a "partial difference equation"?
>
> dS(x,y) = [p(x/y, y-1) - p(y-1, sqrt(y-1))][ p(y, sqrt(y)) - p(y-1,
> sqrt(y-1))],
>
> S(x,1) = 0, p(x, y) = floor(x) - S(x, y) - 1, and S(x,y) is the sum of
> dS from dS(x,2) to dS(x,y).
>
> Here dS(x,y) is a partial difference equation. And p(x,sqrt(x)) gives
> the count of prime numbers up to and including x.
>
> Source: http://mathforprofit.blogspot.com/2004_03_01_mathforprofit_archive.html

Ok, so I still don't know what you call a "partial difference
equation". But don't worry, it has no importance.

Do you understand that the fact that "your" formula contains or not
a PDE has absolutely no impact on the way we could use it to compute
pi(x)? Do you understand that with many formulas containing
something like F(x,y), one could claim that F(x,y) is a PDE? Of course,
one could do it but what would it change?
 
> >
> > > That's only with the "pure math" implementation.
> >
> > !?
> >
>
> Shown above.

What I meant was that '"pure math" implementation' is a mere nonsense.
 
> Posters continually use the world "algorithm" in a derisive manner,
> when actually the prime counting function is just a formula.

Ok. So, if a program based on your formula is slow it's not inherent
in your formula but it is due to computer scientists who are quite
unable to efficiently program it :-)

> Algorithms can be *derived* from it, but it's no more an algorithm
> than
>
> e = mc^2
>
> though some nutcase *could* call that an algorithm, if they were
> trying to argue that it was not important.
>
> But it's a formula, not an algorithm.
>
> Algorithms are based off of formulas, not the other way around.
>
> > > You can also move to an explicit representation, for instance,
> > >
> > > dS(N,2) = N/2 - 1, with even N,
> > >
> > > dS(N,3) = floor((N-4)/6), if N is even, and N>2, and
> > >
> > > dS(N,5) = floor((N-16)/10) - floor((N-16)/30), N even, and N>6, while
> > >
> > > dS(N,7) = floor((N-8)/14) - floor( (N-22)/42) - floor((N-106)/70) +
> > > floor( (N-106)/210) - 2, N even, N>36,
> > >
> > > and now, what gets put on the stack now?
> >
> > Huh? Isn't "dS(N,2), dS(N,3), dS(N,5), dS(N,7), ..." a list? And why
> > do you index it with prime values (which, btw, makes useless your
> > (p(y,sqrt(y)) - p(y-1,sqrt(y-1))) whereas you claim you do not need
> > a list of primes?
>
> The compressed explicit prime counting function exists as I've shown.

Which one makes use of an IMPLICIT list of values.

> Notice it too is a formula and not an algorithm.
>
> It just so happens that's what it looks like when you have it take
> into account that N is even and 2 is prime.
>
> The math is rigid.

Yes and that's your main problem. That's precisely because the math is
rigid that you're almost always wrong. If making math was singing, you
would sing out of tune.
 
> What I've given are the least computationally complex ways to do the
> calculations shown, which makes them technology beyond what
> mathematicians had before my work.

Ways? Technology? You just said you gave a formula, just a formula!
Is a formula a way? Is a formula a technology? Or did you give a
formula, a way and a technology but NOT an algorithm?
Frankly, are you not a little tired to continuously bull***?

> And again it's proof that my research IS in fact new and cutting edge.

No, it is not new. It might be new for you but it is not for others.
 
> If not, then I challenge you to give formulas that have less
> computational complexity,

What does mean "having less computational complexity"?

> or even just show that mathematicians had
> these formulas before me.

Legendre.
 
> The reality is that I'm far ahead of mathematicians at every level,
> when it comes to counting prime numbers:

You already claimed the same about FLT, Goldbach Conjecture and
integer factorization. And yet, I am not aware of all your 'research'.
 
> 1. My prime counting function derivation is just neat.

Subjective point of view.
 
> 2. My prime counting function itself is beautiful and compact.

Subjective point of view.
 
> 3. I can outline the full theory that determines computational
> complexity for fast prime counting.

Wrong. A program using your Legendre variant CANNOT be fast.
 
> I win on all counts.

In your reality, maybe, but not in mine.
 
> Mathematicians win on obstinacy and sheer refusal to accept reality
> that they don't like.
>
> They're weak.

Whereas you're strong. Do you really believe that you could explain
to M. Schumacher how he should drive? Well, considering your math
level, that's exactly what you are doing with mathematicians when
you claim that you can teach them something.
 
> > > It's a social thing. I like being the revolutionary as I can sit back
> > > and look at you and wonder how sad it would be if I were such a sheep
> > > and so easily lied to and so easily manipulated by so few people using
> > > such dumb arguments.
> > >
> > > But I'm not a sheep...I'm a discoverer.
> >
> > I agree on the fact you are not a sheep. I don't believe that a sheep
> > can be schizophrenic.
>
> Yeah, right, toss insults when I win on all the FACTS.

Who did insult who?
1) When you wrote 'I can sit back and look at you and wonder how sad
it would be if I were such a sheep', you clearly insulted me.
2) When I wrote 'I agree on the fact you are not a sheep. I don't
believe that a sheep can be schizophrenic.', it was not an insult but
a diagnosis.
 
> The reality is that I can prove each and every one of my points to an
> extraordinary degree.

Are you able to write more than 3 lines without starting to rave?
 
> In fact, my proofs for my work are far more detailed than
> mathematicians can ever usually manage for their own works!!!
> As a person trained by physicists I have a deep appreciation for what
> it means to challenge versus follow.
>
> Mathematicians teach and are taught to follow.
>
> Physicists are taught to challenge and discover.

Even if it were true what would it change? Though a physicist can be
schizophrenic, you are not a physicist. 

-- 
mm
http://www.ellipsa.net/
mm@ellipsa.no.sp.am.net  ( suppress no.sp.am. )
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