Monday, January 08, 2007
JSH: Re-cap, when is unique also important?
What is not in doubt is that back in 2002 after a problem solving effort I found my own way to count prime numbers where last week I kept talking about the sieve form of my prime counting function.
But that's not what I found years ago.
To understand the issues now you need to understand just a bit about counting prime numbers, as in all of human history there have been only two basic ways to count them:
The brute force method doesn't work that well, so people have figured out smart ways with the second approach. And with it you have sieve methods, where again, you use primes to count more primes.
In thousands of years of human history there have been just these two ways known to exactly count prime numbers, until I found my prime counting function, where crucial here is in understanding what hasn't been mentioned.
I did not find a sieve function. Years ago when I posted I did not post a sieve function.
What I found is a function that unlike any other previously known, finds the primes it needs to do counting the smarter way, where you just tell it that 2 is prime and it figures out the rest.
That is a P(x,y) function. Where y is like x, just another natural number.
In contrast with sieve functions like my prime counting function in its sieve form P(x,n), there n is a count of prime numbers—the helper primes you need to count primes.
Guess what? I didn't first give the sieve form of my prime counting function as it was a sci.math poster named Wim Benthem who did so, years ago, after I put up something unlike anything mathematicians had ever seen before—a function that did what people did, count primes by first finding primes, on its own.
For days last week I argued with posters about whether or not there is another known multi-variable prime counting function, as several posters lied until cornered and then switched to saying my prime counting function could be trivially related to a previously known phi function.
But they lied again, as that's not the function I actually discovered.
And the one I actually discovered cannot be so related to anything else known. It cannot be directly related to any sieve function.
If I am wrong a poster should relate my P(x,y) function to something previously known.
Those who followed the discussion may remember I asked posters if there was anything else unique about my prime counting function besides being multi-variable, and you may notice they did not give you the answer I give to you now.
So you have the lies about there being another multi-variable prime counting function, collapsing into lies that my prime counting function was just trivially related to another multi-variable function, when in fact what I actually discovered and posted about those years ago, can't be related to anything else known, and it can do what no other known mathematical function can do.
So what gives?
Why would mathematicians lie if it's so grand, and is there anything else to this prime counting function of mine?
Well some of you know that modern mathematics can get a little complicated. You may also know that mathematicians can get a lot of schooling to study difficult topics for years to gain expertise in their subject areas.
It can be a difficult business with extreme complexity, difficult arguments and years of effort just to understand the basics.
And I might have cut the Gordian knot in one of the most high profile areas—prime numbers.
Imagine you are a Ph.D in mathematics specializing in prime numbers, and you sent a grant proposal for federal funds totalling $500,000 US to fund your research where most of that is your SALARY for five years of research. And then some nobody, from nowhere comes up with a simple damn function that opens the door to a simple explanation and your research is not needed.
Do you just give up on half a million dollars over the next five years?
Didn't think of it that way? Don't understand how mathematical research gets funded?
I give a simple answer, and mathematicians lose income—if they acknowledge it.
If they don't, and notice, they didn't, those research grants keep coming, the money keeps flowing, and that mathematics Ph.D is still worth something.
Alternative explanations?
Give them please.
You have a unique function that does what no other in human history has ever done in counting prime numbers. Yet mathematicians have done their best to completely ignore it for over four years.
Oh yeah, is there anything else to its uniqueness?
In its simplicity may be found the answers to the 'why' of prime numbers. Answers so simple, they might even make sense to non-mathematicians.
A slashing breakdown of complexity, replaced with beautiful simplicity.
Yet most mathematicians completely ignore it, while you get Usenet posters who lie about its details, continually getting caught in lies and omissions.
Come on, deep down, you knew it had to be about money.
So simple answer is, they lie about it because of the money.
[A reply to someone who said that James' algorithm is not essentially different from the very earliest work done on the subject, and that, although it is an achievement for James to come up with it independently, it yields no new insights.]
In actuality it explains the prime distribution giving answers looked for by some of the greatest minds in mathematical history, as the P(x,y) prime counting function, not the sieve function posters continually try to bring up instead, is a fully mathematicized prime counting function, which just kind of blabs out the answer at you.
It says that the prime count varies from other mathematical functions—the prime gap shown by the prime number theorem—because you have to specially constrain the partial difference equation on which the P(x,y) function relies.
So it just tosses the answer out there, easy. An easy answer in one of the areas where other research is quite complicated.
The partial difference equation on which my prime counting function in its full glory as a fully mathematicized function relies, leads to a partial differential equation, which can be integrated, to get an approximation to the prime count.
There is NOTHING even close in ANY of the mathematical literature.
And to lie about it posters have to just dodge that assertion in detail and depend on flatly denying it as there is NOTHING even close in ANY of the mathematical literature.
Nothing.
So they cannot show.
To lie here posters have to lie as flatly as if you asserted that 2+2=5, as there is nothing in all of human history that covers the territory I covered with some simple ideas.
Nothing.
Such an absolute statement does not need rhetoric in response but concrete facts.
To the extent that posters in reply rely on rhetoric, you know they are lying to you.
But that's not what I found years ago.
To understand the issues now you need to understand just a bit about counting prime numbers, as in all of human history there have been only two basic ways to count them:
- Brute force, like from 1 to 10, you check that no natural numbers below 2 divide it, except 1, so it is prime, as is 3, then you find that 2 divides 4 so it's not, and then no naturals except 1 divide 5 so it is, and so on…
- Get smarter and notice that you can count the primes by first finding primes. That is, you find the primes below the positive square root of the number you're counting up to, and get counts using those primes.
The brute force method doesn't work that well, so people have figured out smart ways with the second approach. And with it you have sieve methods, where again, you use primes to count more primes.
In thousands of years of human history there have been just these two ways known to exactly count prime numbers, until I found my prime counting function, where crucial here is in understanding what hasn't been mentioned.
I did not find a sieve function. Years ago when I posted I did not post a sieve function.
What I found is a function that unlike any other previously known, finds the primes it needs to do counting the smarter way, where you just tell it that 2 is prime and it figures out the rest.
That is a P(x,y) function. Where y is like x, just another natural number.
In contrast with sieve functions like my prime counting function in its sieve form P(x,n), there n is a count of prime numbers—the helper primes you need to count primes.
Guess what? I didn't first give the sieve form of my prime counting function as it was a sci.math poster named Wim Benthem who did so, years ago, after I put up something unlike anything mathematicians had ever seen before—a function that did what people did, count primes by first finding primes, on its own.
For days last week I argued with posters about whether or not there is another known multi-variable prime counting function, as several posters lied until cornered and then switched to saying my prime counting function could be trivially related to a previously known phi function.
But they lied again, as that's not the function I actually discovered.
And the one I actually discovered cannot be so related to anything else known. It cannot be directly related to any sieve function.
If I am wrong a poster should relate my P(x,y) function to something previously known.
Those who followed the discussion may remember I asked posters if there was anything else unique about my prime counting function besides being multi-variable, and you may notice they did not give you the answer I give to you now.
So you have the lies about there being another multi-variable prime counting function, collapsing into lies that my prime counting function was just trivially related to another multi-variable function, when in fact what I actually discovered and posted about those years ago, can't be related to anything else known, and it can do what no other known mathematical function can do.
So what gives?
Why would mathematicians lie if it's so grand, and is there anything else to this prime counting function of mine?
Well some of you know that modern mathematics can get a little complicated. You may also know that mathematicians can get a lot of schooling to study difficult topics for years to gain expertise in their subject areas.
It can be a difficult business with extreme complexity, difficult arguments and years of effort just to understand the basics.
And I might have cut the Gordian knot in one of the most high profile areas—prime numbers.
Imagine you are a Ph.D in mathematics specializing in prime numbers, and you sent a grant proposal for federal funds totalling $500,000 US to fund your research where most of that is your SALARY for five years of research. And then some nobody, from nowhere comes up with a simple damn function that opens the door to a simple explanation and your research is not needed.
Do you just give up on half a million dollars over the next five years?
Didn't think of it that way? Don't understand how mathematical research gets funded?
I give a simple answer, and mathematicians lose income—if they acknowledge it.
If they don't, and notice, they didn't, those research grants keep coming, the money keeps flowing, and that mathematics Ph.D is still worth something.
Alternative explanations?
Give them please.
You have a unique function that does what no other in human history has ever done in counting prime numbers. Yet mathematicians have done their best to completely ignore it for over four years.
Oh yeah, is there anything else to its uniqueness?
In its simplicity may be found the answers to the 'why' of prime numbers. Answers so simple, they might even make sense to non-mathematicians.
A slashing breakdown of complexity, replaced with beautiful simplicity.
Yet most mathematicians completely ignore it, while you get Usenet posters who lie about its details, continually getting caught in lies and omissions.
Come on, deep down, you knew it had to be about money.
So simple answer is, they lie about it because of the money.
[A reply to someone who said that James' algorithm is not essentially different from the very earliest work done on the subject, and that, although it is an achievement for James to come up with it independently, it yields no new insights.]
In actuality it explains the prime distribution giving answers looked for by some of the greatest minds in mathematical history, as the P(x,y) prime counting function, not the sieve function posters continually try to bring up instead, is a fully mathematicized prime counting function, which just kind of blabs out the answer at you.
It says that the prime count varies from other mathematical functions—the prime gap shown by the prime number theorem—because you have to specially constrain the partial difference equation on which the P(x,y) function relies.
So it just tosses the answer out there, easy. An easy answer in one of the areas where other research is quite complicated.
The partial difference equation on which my prime counting function in its full glory as a fully mathematicized function relies, leads to a partial differential equation, which can be integrated, to get an approximation to the prime count.
There is NOTHING even close in ANY of the mathematical literature.
And to lie about it posters have to just dodge that assertion in detail and depend on flatly denying it as there is NOTHING even close in ANY of the mathematical literature.
Nothing.
So they cannot show.
To lie here posters have to lie as flatly as if you asserted that 2+2=5, as there is nothing in all of human history that covers the territory I covered with some simple ideas.
Nothing.
Such an absolute statement does not need rhetoric in response but concrete facts.
To the extent that posters in reply rely on rhetoric, you know they are lying to you.
# posted by James Harris @ 21:54 
