Wednesday, November 22, 2006

 

Attacking reformulations, prime contradictions

One thing that is clear at this point is the position by several posters arguing with me that my prime counting function is a useless reformulation of information already known about prime counting.

There is much to support that view:

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

That prime counting function in its sieve form clearly has elements that can be found in prior prime counting research, and, guess what?

It gives the same answer as the count of primes is the same.

So what good is a reformulation?

Well, posters in going to so much trouble to proclaim my research old have repeatedly pointed out links between my prime counting function and previously known algorithms for counting primes and functions like the sieve function phi(x,a) used in those algorithms.

Um, but that sounds like they're saying that with one function, I can do everything that mathematicians previously did with multiple functions like using pi(x) and phi(x,a), so where before you had two or more, with my ideas, you have one function, which posters repeatedly point out can be optimized in EXACTLY THE SAME WAYS as what was previously known.

So this reformulation captures everything you need and you can work from it alone to do prime counting, going over old ground, so saying the reformulation is worthless can have some merit, right?

After all, prime counting isn't advanced by it, as I've finally acknowledged though early on I had high hopes that you could find much faster prime counting algorithms with it, so the reformulation despite its scope and size is a waste of time?

Well, hold on a minute. Sure, my prime counting function can be used to do everything known before, so you can say that it is going over old ground, so that if history had been different there might never have been a phi(x,a) function or even a one variable pi(x) function as you can do everything with my multi-variable function. But history shows humanity didn't go that route, so that's it, right?

BUT, the function I give—look back if you need to refresh yourself—recursively calls itself and directly counts primes, so you can use something simple, where I'll go to the classical prime counting function to show it:

pi(x) - pi(x-1)

with a natural number x greater than 3 is only non-zero if x is prime.

Because of that my prime counting function can go from being a sieve function, so that instead of having P(x,n) where n is a count of primes, you can use P(x,y) where y is just a natural number like x, as the function can call itself to sieve out the primes on its own, without human aid.

Hmmm…that sounds like more than just a reformulation now.

And besides, remember reformulations aren't necessarily all bad. How about Laplace Transforms? Or Hamiltonians?

Why just hate reformulations? Posters here clearly do as they repeatedly attack my research.

Yes I've made grand claims at times and had to back-track, but I acknowledge being excited about my own ideas and discoveries and hoping that they are grander than they may be, and I can stand corrected.

But even the reformulation argument begins to fall apart when the P(x,y) function arrives, able to do what no other "prime counting function" has ever been known to do in mathematical history.

And posters attack that noting that algorithms counting primes are now slow.

Um, is all prime counting just about fast prime counting, as excuse me, but isn't there something called the Riemann Hypothesis which gives methods that are even slower?

If speed actually counting primes is all that matters, why in the hell does anyone care about the Riemann Hypothesis?

Of course, it's not just about speed counting primes, and here the objections of posters go into hysteria and denial as they bounce all over the map, to ignore a unique feature of my research, but hey, this is Usenet.

Usenet is known for having people who are at the extremes of human behavior, who can say just about anything, and it's not like the math world is ruled by Usenet.

Nope. My research is not blocked by strange people objecting in weird ways on Usenet and calling me nasty names.

It is blocked by mathematicians at universities allowing that to go on by refusing to acknowledge my research, no matter how much I try to get them to pay attention.

So no, it's not about the posters calling me nasty names, and not even Erik Max Francis calling me a crackpot on his website, but aboutprofessors at universities, sitting quietly.

And that is why I say that the academic world today is a dinosaur with medieval crap like tenure giving them too much leeway, so that they can sit without fear of reprisals if the truth is known.

Do you think ANY math professor on this planet is brave enough to quietly sit by while my research is wrongly reviled on Usenet and the web if they thought it could impact their own careers?

If they thought they would be tossed out of their universities and forced to get a real job in the outside world, where results actually matter?

I doubt it. They don't strike me as being brave people.

But they are smart enough to know that today's academic world makes them almost bullet-proof when it comes to consequences for ignoring my research and leaving it to fringe people on Usenet to wrongly go after it, while they sit quietly, knowing they are safe from consequences, while also knowing that they are the key to having important research like my prime counting function properly acknowledged.

If they sit quietly long enough, they can hope that it will all just go away and the knowledge will be lost, with their academic careers safely protected.





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