Re: Partial difference equation, primes

From: James Harris (jstevh_at_msn.com)
Date: 08/23/04 

Date: 23 Aug 2004 16:04:08 -0700

Marcel Martin <mm@ellipsa.no.sp.am.net> wrote in message news:<41298DB8.4C4DFD36@ellipsa.no.sp.am.net>...
> James Harris a écrit :
> >
> > Marcel Martin <mm@ellipsa.no.sp.am.net> wrote in message news:<41277B22.8D5D4AF9@ellipsa.no.sp.am.net>...
> > > Ok, so I still don't know what you call a "partial difference
> > > equation". But don't worry, it has no importance.
> >
> > I handled that topic with a separate thread.
> >
> > But it's not complicated--no matter what a sci.math'er might try to
> > insinuate--as a partial difference equation is the discrete analog to
> > a partial differential equation.
>
> Ok. So, dS(x,y) is what you call a PDE.
>

Sigh. And yes readers, this is how the sci.math'ers operate. If you
look through the entire posts you will see the poster Marcel Martin
has become a lot more foul.

I beat them at their claims and the sci.math'ers get ruder and ruder,
but manage to never really back down to the facts.

Later, after some time, when I post again, they make their original
claims all over again, and the entire drama starts anew.

Sometimes I think I wait a bit just to see them wind up and come again
with the same old song, just out of curiousity.

It's like they're automatons or something with one record they keep
playing over and over again, but of course they claim that's the way I
am, which is part of their record...

> > There is no other known in recorded history used to count prime
> > numbers besides my dS(x,y) and yes, I'm talking about all of human
> > history here.
>
> You might be right. Who would be moronic enough to compute
> pi(y) - pi(y-1) in order to check the primality of y?
>

So now it's clear that my work IS indeed different from what
mathematicians found and use, but from the sci.math'er--oddly enough
acknowledging the facts for once--suddenly it's also moronic.

These people are not what you and I would call sane.

> > To me that's a simple enough claim that it should either be refutable
> > by you sci.math'ers, or if you're sane, you'll quit trying to
> > insinuate that it's not a big deal.
> >
> > I fear you're not exactly what most people would call sane.
>
> Do you mean that I could write things like "I am the barbarian at the
> gates..."? :-)
>

I am the barbarian at the gates. I am a revolutionary, a discoverer,
a guy who didn't just try, but did, who didn't just wonder, but
accomplished.

After all, you've conceded my main point, as sci.math'ers have been
repeating over and over again that my work is not new, but I've beaten
you down to acknowledging a clear difference, even if you childishly
call it moronic.

I'm the guy who went out and found--from scratch--some beautiful
little formulas that count PRIME numbers:

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)

That dS(x,y) is NOT moronic as anyone who read through the derivation
and *understood* it can appreciate.

Not surprisingly the derivation of the prime counting function is one
of the most beautiful in mathematics:

See http://mathforprofit.blogspot.com/

> > > 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?
> >
> > You're lying because you're insinuating that mathematicians have in
> > fact used a partial difference equation to count prime numbers when
> > they have not.
>
> No. I wanted to be sure that what you call a PDE is also what I call
> a PDE. Experience proves that, with you, the meaning of a word can
> vary from any-thing to almost-all.
>

Sigh. There you go again.

The "pure math" prime counting formula is clearly something important
from the derivation, where *each* piece of it is highly significant.

Sure, algorithms derived from it will be different, but that doesn't
change the beauty and elegance of the mathematics from which they are
based!!!

Here sci.math'ers are caught on the most fundamental thing--beauty in
mathematics--with a purest of the pure function, which people who read
the derivation can understand completely.

It's mathematics not only concise, but understandable, as well as
beautiful.

My work represents problem solving at its purest.

And no mean sci.math'er, rude to the discoverer, can change that
reality.

> > It's not complicated here. You may think you can parse the language
> > to fool everyone on sci.physics or that the other sci.math'ers will
> > just go along with you as they have for over two years now, but it
> > doesn't change the facts.
> >
> > I say that no one in recorded human history has used a partial
> > difference equation to count prime numbers.
> >
> > That is a fairly straightforward claim, and if it's not true you can
> > just give some other partial difference equation, but instead you try
> > to spin the facts, like what in the hell is "F(x,y)"?
>
> F(x,y) is any function I can call a PDE. So, with something like
> "z(x,y) = Sum(i=a to y, F(x,i))", trivially I have F(x,y) = z(x,y) -
> z(x,y-1) and it allows me to claim that all the stuff is new because
> there is a PDE. Neat, isn't it? Yes, I read "The art of bullshitting"
> by JSH.
>

See? The sci.math'er gets ruder. These sci.math'ers hate mathematics
when it suits them.

I win on the facts, and they start cursing.

> > I've seen how you sci.math'ers operate for over two years now, and you
> > have a contempt for the truth, and a demonstrated contempt for
> > mathematics.
> >
> > > > >
> > > > > > That's only with the "pure math" implementation.
> > > > >
> > > > > !?
> > > >
> > > > Shown above.
> > >
> > > What I meant was that '"pure math" implementation' is a mere nonsense.
> >
> > Yet people can see that it is not nonsense most dramatically by
> > looking at it, and I've put it on my blog:
> >
> > http://mathforprofit.blogspot.com/2004_03_01_mathforprofit_archive.html
>
> Have you a dictionnary at hand? Search for 'implementation'. Maybe you
> will learn something today.
>

If you implement the pure math function itself--that is use no
speed-ups--it's rather slow.

But if you do the same thing with the Fourier Transform--it's slow.

You sci.math'ers wish to throw out the baby with the bathwater by
creating dumb criteria.

Like suddenly, if there are fast algorithms the base mathematics is
junk!!!

Oh wait, even you probably aren't socially stupid enough to try and
toss out the Fourier Transform, so you sci.math'ers are *picky* about
where you apply your rules.

If I discover something, you make up one rule, but you dare not
challenge Fourier!!!

Wait, if Fourier were making his discovery today, and posted on
sci.math, you'd probably challenge him because that's what you
sci.math'ers do.

> > > > 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 :-)
> >
> > No.
>
> But then, what about your claim according to which your method leads
> to the fastest possible prime counting?
>

What about 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.
> >
> > That's what it looks like.
>
> But then, since your "technology" makes use of a list, what about your
> claim 'It does not need a list'?
>

The prime counting function does not need a list.

The explicit prime counting function necessarily looks as shown.

So what is the *explicit* prime counting function?

It's where the dS values are set by formulas, like

dS(x,2) = floor(x/2) - 1

is simple enough that you should understand what I mean.

The *explicit* prime counting function is infinite in size, but pieces
of it can be derived and looked at, and those pieces only look ONE
WAY, as the math is rigid.

> > The math is simply rigid here, no matter how much you might like to
> > make more out of it.
> >
> > It just is.
> >
> > > > 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.
> >
> > Then give a single wrong point I've made.
> >
> > Give ANYTHING mathematical which will stand up to scrutiny.
>
> My prefered one is "the algebraic integer ring is not complete"
> (consequence of your irrefutable proof of FLT).
>

Trying to change the subject?

I say that's a concession that I have NOT made a single wrong point.

> > Do more than insinuate, like talk straight for once.
>
> But I insinuate nothing. I am clearly saying you're a dead loss in
> math. Anybody can read any of the billion posts you sent to sci.math
> and can see that all what you say in math is always either trivial
> or wrong (this is even sometimes trivially wrong).
>

It sounds like you've quit even trying to use mathematics and now are
just trying to convince with words.

You can't win, don't you understand that?

Mathematics is not a social convention. It doesn't change depending
on whether or not people believe you or not.

Why can't you just rely on math itself?

Mathematically my prime counting function stands out clearly in
several ways.

Why fight the truth?

> > > > 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***?
> >
> > Technology refers as a word to state of the art.
>
> So, the state of the art in math is technology... I love the poetic
> quality of such a sentence, don't you :-)
>

Actually the state of the art in mathematics IS technology:

Main Entry: tech·nol·o·gy
Pronunciation: -jE
Function: noun
Inflected Form(s): plural -gies
Etymology: Greek technologia systematic treatment of an art, from
technE art, skill + -o- + -logia -logy
1 a : the practical application of knowledge especially in a
particular area
...

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=technology&x=0&y=0

By technology I refer to the *explicit* prime counting function.

Like

dS(N,3) = floor((N-4)/6) with N even.

It is the least computationally complex formula for calculating the
count of odd composites with 3 as a factor up to and including N.

That technology is state of the art, as mathematicians cannot do
better.

They also cannot do better--or even math without my research--the the
other dS values I can give, like

dS(N,5) = floor((N-16)/10) - floor((N-16)/30), with even N>6,

wher that's the count of odd composites, NOT divisible by 3, that have
5 as a factor.

Since I can give the most compact, most efficient formulas for each dS
count, I can define the most efficient prime counting possible.

Like I said, on every point I'm way ahead of mathematicians and the
technology I have is state of the art.

James Harris