### Saturday, June 30, 2007

## JSH: Bored, bored, bored again

So Ferry is yet again a big fat liar, but it is remarkable to me that a simple idea for factoring can just kind of sit out there without being settled. I DID program it, so I have a sense of how well it works in a certain arena which indicates to me that maybe it can be made to work for factoring huge numbers but I'd think that'd take some effort and expertise.

I feel now that I passed some limit or other with the Bulletin as there has been no reply to my latest paper, which is currently at my Extreme Mathematics group so hey, I've got it out there anyway, so who cares if some journal picks it up?

At least now it's settled that the AMS and I do not even need to bother playing at being civil any more.

I am bored, bored, bored again, and it seems to me that our world is remarkable for not having much new happening. Sure there is a little bit of this, and a lot of that, where that is people mindlessly killing each other, but the stupidity of the human race is old news.

I don't think there are a lot of intelligent people positive about our future at this point.

There is an insistent need to die in our behaviour, or kill. As if no matter how much people try to get away from that baseline, human nature always remains true so now the most dominant nation on the planet is also becoming the scariest. But hey, we have nuclear weapons.

And you know, we are capable of nuking you.

So that's where it ends. WE are capable of nuking you. We the people of the United States in pursuit of happiness and in great accord with democracy can sit back and let you die, and if you doth protest to much and dare to interfere with our pursuits make no mistake, WE ARE CAPABLE OF NUKING YOU.

So you will sit quiet, like nice little doggies and let us do what we want, or you will die.

My country scares the hell out of me, and I don't know what to do.

So much hope and so many dreams of what could have been destroyed in such a short period of time, from the tragedy of 9–11 to its exploitation by psychopaths who did what the terrorists never could have done.

Our government took away hope.

We the people of the United States of America…were betrayed…but we let them betray us, so in the end, we betrayed ourselves.

The idea of the United States was not big enough for the reality of human nature. Our nature.

Our ability to destroy others believing that protected us, when in so doing, we took away anything worth protecting.

I feel now that I passed some limit or other with the Bulletin as there has been no reply to my latest paper, which is currently at my Extreme Mathematics group so hey, I've got it out there anyway, so who cares if some journal picks it up?

At least now it's settled that the AMS and I do not even need to bother playing at being civil any more.

I am bored, bored, bored again, and it seems to me that our world is remarkable for not having much new happening. Sure there is a little bit of this, and a lot of that, where that is people mindlessly killing each other, but the stupidity of the human race is old news.

I don't think there are a lot of intelligent people positive about our future at this point.

There is an insistent need to die in our behaviour, or kill. As if no matter how much people try to get away from that baseline, human nature always remains true so now the most dominant nation on the planet is also becoming the scariest. But hey, we have nuclear weapons.

And you know, we are capable of nuking you.

So that's where it ends. WE are capable of nuking you. We the people of the United States in pursuit of happiness and in great accord with democracy can sit back and let you die, and if you doth protest to much and dare to interfere with our pursuits make no mistake, WE ARE CAPABLE OF NUKING YOU.

So you will sit quiet, like nice little doggies and let us do what we want, or you will die.

My country scares the hell out of me, and I don't know what to do.

So much hope and so many dreams of what could have been destroyed in such a short period of time, from the tragedy of 9–11 to its exploitation by psychopaths who did what the terrorists never could have done.

Our government took away hope.

We the people of the United States of America…were betrayed…but we let them betray us, so in the end, we betrayed ourselves.

The idea of the United States was not big enough for the reality of human nature. Our nature.

Our ability to destroy others believing that protected us, when in so doing, we took away anything worth protecting.

### Tuesday, June 26, 2007

## JSH: Why I am distancing

I have mathematical results which may eventually show me to be an important figure in human history, and it should be clear by now that I am distancing myself as rapidly as I can from the mathematical community.

Years ago I remember how I excited I was when my computer screen filled with prime numbers, so excited as I thought, finally I had what I needed to convince math people that there was value to the problem solving techniques I used and in my ideas.

Months of arguing where I'd stress point after point only to have people on newsgroups just deny or ignore those points kind of put me into shock. It took years for me to work out all the details and understand how and why people in the math field deny crucial mathematical results.

Now that I understand completely I also know that there are no results that can break through with the current community and I'm turning my problem solving skills to other areas.

I grew up with a "smart" label. Years of being in gifted programs, doing things like going to Duke University as a teenager, getting a scholarship to Vanderbilt University, and having a sense of my ability to learn quickly and apply what I learned to problems and get solutions got me used to thinking that was just the way most people experienced the world.

But it's not.

So some people fake it.

And I kept hoping so I talked about my prime counting function, but I moved on from there and even got published and the people who were fakes could always just lie. I never knew how people could just lie until this experience.

I looked in other areas so unlike most of you I was a part of the discussion in the run-up to war with Iraq, and got a version of a letter published in TIME magazine where I stressed caution.

As we've learned what the real evidence was and was not, and as people in this country have continued for the most part without concern as they have their lives in order I understand so much better how most of you continue as long as you feel you have your lives in order.

You are not truly human. There is something missing in you. There is a loss of soul, a loss of that wonder that some of us have with learning, and being certain we have the truth.

I call you parasitic but you are so much less, as many of you seem to think that there is something to you valuable, when how can there be?

You eat, you drink, you defecate, you procreate, and you will die, but when you die, what will you leave?

Animals do more. Many of you will leave nothing but whatever of this history remains as long as it does that like Bush and others who have nothing of value in themselves or their lives that they truly appreciate, to you other human beings are just things that you manipulate.

You want to know what button to push to make the thing do what you want. What to say to get the money, to get the praise. So you can do whatever it takes to get the things—the other human beings—to do what makes you happy.

Makes you happy for whatever time you have on this planet until you die, then nothing.

So you are nothing. You believe in nothing.

And the destiny that creatures like you bring to those other human beings that you cannot see as more than things, as mechanisms that you try to figure out how to push to do what you want, is death.

Our future looks more and more like death from parasites who look like human beings, who act like human beings to get what they want from human beings, but who can kill like Bush without a thought, without concern about any reason other than to them, it's ok.

Mathematics is more than just a word or some people posturing, presenting themselves as brilliant.

It is a field where the truth can be determined by mathematical proof.

To the extent that you have broken that field you have broken the human species itself, and for those who doubt the reality of where we are, the continuing war in Iraq is a taste of what the future brings to us all.

A world where death walks freely not because of what we can't do, but because of what we cannot see—the parasites who live among us.

Years ago I remember how I excited I was when my computer screen filled with prime numbers, so excited as I thought, finally I had what I needed to convince math people that there was value to the problem solving techniques I used and in my ideas.

Months of arguing where I'd stress point after point only to have people on newsgroups just deny or ignore those points kind of put me into shock. It took years for me to work out all the details and understand how and why people in the math field deny crucial mathematical results.

Now that I understand completely I also know that there are no results that can break through with the current community and I'm turning my problem solving skills to other areas.

I grew up with a "smart" label. Years of being in gifted programs, doing things like going to Duke University as a teenager, getting a scholarship to Vanderbilt University, and having a sense of my ability to learn quickly and apply what I learned to problems and get solutions got me used to thinking that was just the way most people experienced the world.

But it's not.

So some people fake it.

And I kept hoping so I talked about my prime counting function, but I moved on from there and even got published and the people who were fakes could always just lie. I never knew how people could just lie until this experience.

I looked in other areas so unlike most of you I was a part of the discussion in the run-up to war with Iraq, and got a version of a letter published in TIME magazine where I stressed caution.

As we've learned what the real evidence was and was not, and as people in this country have continued for the most part without concern as they have their lives in order I understand so much better how most of you continue as long as you feel you have your lives in order.

You are not truly human. There is something missing in you. There is a loss of soul, a loss of that wonder that some of us have with learning, and being certain we have the truth.

I call you parasitic but you are so much less, as many of you seem to think that there is something to you valuable, when how can there be?

You eat, you drink, you defecate, you procreate, and you will die, but when you die, what will you leave?

Animals do more. Many of you will leave nothing but whatever of this history remains as long as it does that like Bush and others who have nothing of value in themselves or their lives that they truly appreciate, to you other human beings are just things that you manipulate.

You want to know what button to push to make the thing do what you want. What to say to get the money, to get the praise. So you can do whatever it takes to get the things—the other human beings—to do what makes you happy.

Makes you happy for whatever time you have on this planet until you die, then nothing.

So you are nothing. You believe in nothing.

And the destiny that creatures like you bring to those other human beings that you cannot see as more than things, as mechanisms that you try to figure out how to push to do what you want, is death.

Our future looks more and more like death from parasites who look like human beings, who act like human beings to get what they want from human beings, but who can kill like Bush without a thought, without concern about any reason other than to them, it's ok.

Mathematics is more than just a word or some people posturing, presenting themselves as brilliant.

It is a field where the truth can be determined by mathematical proof.

To the extent that you have broken that field you have broken the human species itself, and for those who doubt the reality of where we are, the continuing war in Iraq is a taste of what the future brings to us all.

A world where death walks freely not because of what we can't do, but because of what we cannot see—the parasites who live among us.

### Sunday, June 24, 2007

## JSH: Issue is justification

Taking funding from academia is the kind of thing that smart academics can holler long and hard about in a very convincing way, so it's not like you can just come out and say, hey, these people lie, they make up stuff just for their careers, which means it's just about money, and they have no qualms about trying to block crucial research if they think it hurts their careers.

That is, you cannot just say that there are these professors who are con artists and be very convincing.

It takes more.

Luckily, truly brilliant minds would see the writing on the wall, but these are NOT truly brilliant minds so as we step through the final steps necessary to drastically remove funding from the academic world—en toto—they cannot see it coming.

For me it is remarkable to see how much these people invest in political processes as I've studied the various techniques used in fighting my research over the years by people who clearly seem very impressed with what they're doing!!!

They are fools.

When I shut the door and end this idiocy, and thereby give humanity at least a fighting chance of survival despite the parasitic human beings crowding every corner they can, those parasites will be the most surprised.

The preamble is all about building to a point where a clever con artist crying about how important research money is and how insane it is to just CUT CUT CUT funding for colleges and universities and for research—except for medical, materials science, biology, especially genetic, and anything important for national security—will not get sympathy.

So the cuts will go forward.

Take away the money, and we get a real scientific field again.

That is, you cannot just say that there are these professors who are con artists and be very convincing.

It takes more.

Luckily, truly brilliant minds would see the writing on the wall, but these are NOT truly brilliant minds so as we step through the final steps necessary to drastically remove funding from the academic world—en toto—they cannot see it coming.

For me it is remarkable to see how much these people invest in political processes as I've studied the various techniques used in fighting my research over the years by people who clearly seem very impressed with what they're doing!!!

They are fools.

When I shut the door and end this idiocy, and thereby give humanity at least a fighting chance of survival despite the parasitic human beings crowding every corner they can, those parasites will be the most surprised.

The preamble is all about building to a point where a clever con artist crying about how important research money is and how insane it is to just CUT CUT CUT funding for colleges and universities and for research—except for medical, materials science, biology, especially genetic, and anything important for national security—will not get sympathy.

So the cuts will go forward.

Take away the money, and we get a real scientific field again.

### Wednesday, June 20, 2007

## Composite factorization coupling

For quite some time mathematicians have focused on factoring composites as a global problem, where they would focus efforts on a single number, which is following in the footsteps of past mathematicians, like good little soldiers.

But past mathematicians didn't have computers.

Being trained as a problem solver since I was a little kid, I thought to re-think the problem, and wonder if it wouldn't be possible to shift factoring one number into factoring a lot of other numbers and found that hey, it's easy to do with trivial algebra.

That's modern problem solving which it takes YEARS to master. And here is why it's so important as often a seemingly hard problem becomes simple with a small shift in perspective.

Given a target composite T, you start with the traditional—see no throwing out the old—difference of squares:

x^2 = y^2 + aT

Then you add in a very small extra which is the new, where yes, b must have k as a factor:

2xk = k^2 - bT

And bringing together the old with the new, where you already have the classical difference of squares to start, you now get ANOTHER difference of squares to finish:

(x+k)^2 = y^2 + 2k^2 + (a-b)T

and you have coupled one factorization to another, so that the factorization of aT is connected directly to the factorization of 2k^2 + (a-b)T.

So mathematically EVERY composite factorization comes with another factorization connected to it, so no composite factorization stands alone.

And that's over infinity.

Now to Fermat, or Euler, Newton or Gauss there might have been a, so what?

As for them, with their pencils and paper or pen and paper, figuring stuff out was hard enough on its own, without showing that one factorization could lead to another.

But we are children of the modern age and we have computers.

Computers can whir through millions of calculations of alternate factorizations without trouble, but seem to bog down if you do two things:

And so what if it is? In the blink of your slow eye, a modern computer can whir through a tremendous number of alternates until it finds one connected to your target and thereby gets the factorization of the product of two large primes.

That is modern problem solving—where you think out of the box.

The trouble is that MOST MATHEMATICIANS DO NOT DO MODERN PROBLEM SOLVING.

Instead they waste time learning a lot of abstruse stuff and a lot of techniques and styles, and they also learn how to ignore brilliant ideas that make them look stupid.

Now I know this from my other mathematical research where mathematicians can just blissfully continue no matter what I prove, but my emphasis on factoring is about stupid people pretending to be smart who will ignore ANYTHING because their entire lives are invested in the act.

Their entire lives are invested in the act.

They are wannabe actors pretending to be great mathematical minds.

I feel pity for some of you because of the years you've spent trying to learn dumb crap that doesn't actually work because you trust groups of people who tell you that it's brilliant and YOU are stupid if you find it hard to understand or realize that hey, a lot of this stuff just doesn't make sense!

But you see, a lot of modern math is hard because it's wrong, and modern math people are invested in keeping things the way they are so that they can make easy money.

I call it white collar welfare.

[A reply to someone who wrote that all his previous tests of James' ideas have shown that they can factor numbers but are slower than trial factorisation.]

Remember I have said recently that you need a number that is roughly as hard to factor as your target.

The method is a booster method that is an adjunct to other methods and there are more than enough headlines coming out to scare real mathematicians.

But you people are not real mathematicians, now are you?

United has a mysterious shut-down of its computers for two hours.

How would you demonstrate to a buyer that you could crack systems if you were a hacker looking to make millions?

The Pentagon(?) has to shut down its email because of some thing or other. Or was it the Department of Defense?

You people want the world to turn on its head, end the domination of the United States and usher in an era of anarchy, based on your ability to hold, hold, hold people who might do something just long enough until it's too late.

(Is that it? You are enemies of the United States? You WANT the global economy to crash to embarrass and remove the US from power?)

And people may die as a result, but you parasites just can't see beyond your limited needs.

It's a sad world because too many people trust too many others who are, parasitic humans who are not that smart, and care not a whit for the rest of the world.

But past mathematicians didn't have computers.

Being trained as a problem solver since I was a little kid, I thought to re-think the problem, and wonder if it wouldn't be possible to shift factoring one number into factoring a lot of other numbers and found that hey, it's easy to do with trivial algebra.

That's modern problem solving which it takes YEARS to master. And here is why it's so important as often a seemingly hard problem becomes simple with a small shift in perspective.

Given a target composite T, you start with the traditional—see no throwing out the old—difference of squares:

x^2 = y^2 + aT

Then you add in a very small extra which is the new, where yes, b must have k as a factor:

2xk = k^2 - bT

And bringing together the old with the new, where you already have the classical difference of squares to start, you now get ANOTHER difference of squares to finish:

(x+k)^2 = y^2 + 2k^2 + (a-b)T

and you have coupled one factorization to another, so that the factorization of aT is connected directly to the factorization of 2k^2 + (a-b)T.

So mathematically EVERY composite factorization comes with another factorization connected to it, so no composite factorization stands alone.

And that's over infinity.

Now to Fermat, or Euler, Newton or Gauss there might have been a, so what?

As for them, with their pencils and paper or pen and paper, figuring stuff out was hard enough on its own, without showing that one factorization could lead to another.

But we are children of the modern age and we have computers.

Computers can whir through millions of calculations of alternate factorizations without trouble, but seem to bog down if you do two things:

- Get two very large primes, and multiply them together.
- Try to factor them.

And so what if it is? In the blink of your slow eye, a modern computer can whir through a tremendous number of alternates until it finds one connected to your target and thereby gets the factorization of the product of two large primes.

That is modern problem solving—where you think out of the box.

The trouble is that MOST MATHEMATICIANS DO NOT DO MODERN PROBLEM SOLVING.

Instead they waste time learning a lot of abstruse stuff and a lot of techniques and styles, and they also learn how to ignore brilliant ideas that make them look stupid.

Now I know this from my other mathematical research where mathematicians can just blissfully continue no matter what I prove, but my emphasis on factoring is about stupid people pretending to be smart who will ignore ANYTHING because their entire lives are invested in the act.

Their entire lives are invested in the act.

They are wannabe actors pretending to be great mathematical minds.

I feel pity for some of you because of the years you've spent trying to learn dumb crap that doesn't actually work because you trust groups of people who tell you that it's brilliant and YOU are stupid if you find it hard to understand or realize that hey, a lot of this stuff just doesn't make sense!

But you see, a lot of modern math is hard because it's wrong, and modern math people are invested in keeping things the way they are so that they can make easy money.

I call it white collar welfare.

[A reply to someone who wrote that all his previous tests of James' ideas have shown that they can factor numbers but are slower than trial factorisation.]

Remember I have said recently that you need a number that is roughly as hard to factor as your target.

The method is a booster method that is an adjunct to other methods and there are more than enough headlines coming out to scare real mathematicians.

But you people are not real mathematicians, now are you?

United has a mysterious shut-down of its computers for two hours.

How would you demonstrate to a buyer that you could crack systems if you were a hacker looking to make millions?

The Pentagon(?) has to shut down its email because of some thing or other. Or was it the Department of Defense?

You people want the world to turn on its head, end the domination of the United States and usher in an era of anarchy, based on your ability to hold, hold, hold people who might do something just long enough until it's too late.

(Is that it? You are enemies of the United States? You WANT the global economy to crash to embarrass and remove the US from power?)

And people may die as a result, but you parasites just can't see beyond your limited needs.

It's a sad world because too many people trust too many others who are, parasitic humans who are not that smart, and care not a whit for the rest of the world.

## JSH: How stupid can you be?

A math journal dies after retracting a paper by a "crackpot" that just so happens to cast doubt on over a hundred years of number theory, and that "crackpot" talks about solving the factoring problem to punish people he says are con artists and a corporation mysteriously retracts monetary prizes for a problem that supposedly is one of the hardest in mathematics and you sit like the dumb fools you are.

History is all about people like you who sit and wait until you lose because you are not brilliant. You are not geniuses. You are not smart enough to get out of the way.

What I like about these kind of messages is that they are like lights to deer.

I want you to freeze.

Sit you morons who dared to think you were brilliant and lose everything.

Sit and wait until the world comes and takes you down like you deserve because you dared to think you were brilliant, you dared to corrupt my field.

You dared to call yourself mathematicians.

And for that reason you will lose everything you hold dear. You will be broken, and humiliated.

You will suffer pain like you have no comprehension of because you are too damn stupid to understand what this world is like, no matter what you see on the news.

Soon enough the headlines will be about YOU.

Look at the news today, and consider the worst things that are happening in this world, and consider that that is the lesson that is being delivered to you.

I want you to freeze.

You are the prey. You are the deer being shocked into motionlessness.

And I am the hunter.

History is all about people like you who sit and wait until you lose because you are not brilliant. You are not geniuses. You are not smart enough to get out of the way.

What I like about these kind of messages is that they are like lights to deer.

I want you to freeze.

Sit you morons who dared to think you were brilliant and lose everything.

Sit and wait until the world comes and takes you down like you deserve because you dared to think you were brilliant, you dared to corrupt my field.

You dared to call yourself mathematicians.

And for that reason you will lose everything you hold dear. You will be broken, and humiliated.

You will suffer pain like you have no comprehension of because you are too damn stupid to understand what this world is like, no matter what you see on the news.

Soon enough the headlines will be about YOU.

Look at the news today, and consider the worst things that are happening in this world, and consider that that is the lesson that is being delivered to you.

I want you to freeze.

You are the prey. You are the deer being shocked into motionlessness.

And I am the hunter.

### Sunday, June 17, 2007

## Integer factorization, probability

I've discovered that integer factorization can be generalized using the following equations, which link every factorization to another secondary factorization:

With T the target composite to be factored, letting

x^2 = y^2 + aT and 2xk = k^2 - bT

you can solve to find

(x+k)^2 = y^2 + 2k^2 + (a-b)T

so that it is clear that 'a' and 'b' need not be determined as you need a-b, which is chosen to be some non-zero integer, as is k.

Trivially, if you introduce integer factors f_1 and f_2, you can have

4f_1*f_2 = 2k^2 + (a-b)T

then y = f_1 - f_2 and

x = f_1 + f_2 - k

and an example, which took a single iteration, so it took one try, where I arbitrarily chose to let k = floor(T/30) and I picked a-b=2, consider

T = 732367903, k=floor(T/30) = 24412263, a-b = -2

2k^2 + (a-b)T = 1191915704826532 = ( 2^2 )( 7 )( 73 )( 583129014103 )

f_1 = 7/2 and f_2 = 85136836059038

y=-170273672118069/2 and x=170273623293557/2

so, x+y=-24412256, which has 223 as a factor.

T = 732367903 = (223)(3284161)

and you can see that it can work where you factor this one number to get to your target, but what is the probability that it WILL work?

Good question. I've talked about these simple methods for a few months now and gotten a lot of dismissive replies which never answer that question.

My own research indicates that if 2k^2 + (a-b)T is roughly as hard to factor as T, then you have about a 67% chance of factoring your target, so if you try to make it smaller so that it's easier to factor that probability drops and you need more iterations, so you can go to smaller numbers but would need to check more possibilities as the probability drops.

I state that without proof because it seems to me that at a minimum with the factoring problem, people willing to dismiss a simple method that can be shown to work, should be forced to present SOME mathematics in their rebuttals—like walk through an argument giving the probability of factoring.

Now I think that the modern math world has long gotten away with bluffing its way, and that modern mathematicians learned style over substance—the appearance of proof versus actual proof—so that they can lie.

Yup, I think that modern mathematicians as a group routinely lie having learned that they can get away with it.

Their motivation in lying about factoring is that the factoring problem being hard means more jobs for mathematicians and a dodge from embarrassment because the Internet is currently secured based on it supposedly being a hard problem, while the simple equations I've presented here may show a way that smart people can break that

security system.

RSA has taken away the money prizes for its challenges since I started presenting this research. Coincidence? I hope so, but mathematics is not just about hope.

Modern mathematicians I feel are capable of ignoring such a result based on a hope and a prayer because the PR disaster of the truth coming out is great enough that they will just wait, and hope that no one notices, unless, of course, I'm wrong!

As, after all, I've made it very clear that I will tell the world that mathematicians routinely lie if my research breaks through. If they do lie routinely about their research, why wouldn't they hide a stupid mistake where they gave the world a security system breakable with some simple algebra?

You think they are "beautiful minds" and I think they are con artists, but I could be wrong.

But if I'm wrong, then cannot a supposedly very advanced mathematical community present a mathematical argument that shows what the probability of factoring with the system of equations I've presented actually is?

With T the target composite to be factored, letting

x^2 = y^2 + aT and 2xk = k^2 - bT

you can solve to find

(x+k)^2 = y^2 + 2k^2 + (a-b)T

so that it is clear that 'a' and 'b' need not be determined as you need a-b, which is chosen to be some non-zero integer, as is k.

Trivially, if you introduce integer factors f_1 and f_2, you can have

4f_1*f_2 = 2k^2 + (a-b)T

then y = f_1 - f_2 and

x = f_1 + f_2 - k

and an example, which took a single iteration, so it took one try, where I arbitrarily chose to let k = floor(T/30) and I picked a-b=2, consider

T = 732367903, k=floor(T/30) = 24412263, a-b = -2

2k^2 + (a-b)T = 1191915704826532 = ( 2^2 )( 7 )( 73 )( 583129014103 )

f_1 = 7/2 and f_2 = 85136836059038

y=-170273672118069/2 and x=170273623293557/2

so, x+y=-24412256, which has 223 as a factor.

T = 732367903 = (223)(3284161)

and you can see that it can work where you factor this one number to get to your target, but what is the probability that it WILL work?

Good question. I've talked about these simple methods for a few months now and gotten a lot of dismissive replies which never answer that question.

My own research indicates that if 2k^2 + (a-b)T is roughly as hard to factor as T, then you have about a 67% chance of factoring your target, so if you try to make it smaller so that it's easier to factor that probability drops and you need more iterations, so you can go to smaller numbers but would need to check more possibilities as the probability drops.

I state that without proof because it seems to me that at a minimum with the factoring problem, people willing to dismiss a simple method that can be shown to work, should be forced to present SOME mathematics in their rebuttals—like walk through an argument giving the probability of factoring.

Now I think that the modern math world has long gotten away with bluffing its way, and that modern mathematicians learned style over substance—the appearance of proof versus actual proof—so that they can lie.

Yup, I think that modern mathematicians as a group routinely lie having learned that they can get away with it.

Their motivation in lying about factoring is that the factoring problem being hard means more jobs for mathematicians and a dodge from embarrassment because the Internet is currently secured based on it supposedly being a hard problem, while the simple equations I've presented here may show a way that smart people can break that

security system.

RSA has taken away the money prizes for its challenges since I started presenting this research. Coincidence? I hope so, but mathematics is not just about hope.

Modern mathematicians I feel are capable of ignoring such a result based on a hope and a prayer because the PR disaster of the truth coming out is great enough that they will just wait, and hope that no one notices, unless, of course, I'm wrong!

As, after all, I've made it very clear that I will tell the world that mathematicians routinely lie if my research breaks through. If they do lie routinely about their research, why wouldn't they hide a stupid mistake where they gave the world a security system breakable with some simple algebra?

You think they are "beautiful minds" and I think they are con artists, but I could be wrong.

But if I'm wrong, then cannot a supposedly very advanced mathematical community present a mathematical argument that shows what the probability of factoring with the system of equations I've presented actually is?

## JSH: Natural pause

One of the fun things to me about this wacky saga is that every once in a while--every few years or so—I talk about the method behind the apparent madness, kind of like a behind the scenes episode on some movie or some television show.

Those who hate such things can tune out at this point…for the rest here is the rationale that I use in deciding to post and what I think is kind of sort of the point.

First off, the rule of Usenet and Internet is attention has to happen first.

If no one reads you then there is no way you can get any message across, no matter how valid you think that message is!

Second thing, people don't like nice, and they don't like agreement as it's boring.

Posts where people ask nicely for help, congratulate each other, and then talk about how great this process is and isn't it wonderful to be able to share information in such an agreeable place, are boring.

Our world thrives on conflict. Disagreement drives Usenet. Without it, you don't get that thing I mentioned above—attention.

So yes, a lot of what you see in postings from my side is just for show, as they say, merely meant to keep the antagonism up, keep the hostilities up, so that there is a continual tension and sense of conflict to draw in readers.

Over the years I've refined techniques that tend to play to what works and manages a rag-tag group of posters who come and go, kind of like circus players, as over the years I've had a LOT of them, come and go.

I do at times try to tone things down a bit as well, when it gets too outrageous even for me, often with limited success, where the thing that does work is for me to just stop posting for a while, and I'm finding that I have to do that more and more as things get more advanced.

With all of that said there is a lot of real drama taking place as the attention is not the purpose, but keeping the light on my mathematical research IS, and the reality that academics at some very prestigious institutions are not doing their jobs is the underlying theme.

There really was that publication in SWJPAM for instance where the editors withdrew my paper after emails from several sci.math posters (not certain about how many emailed them), and subsequently the journal DID die, and Cameron University, its host, DID wipe all record of its nine year existence from its webpages.

I do have multiple rejections from top journal of papers that are now found on my websites, and I do have very simple mathematical results which cannot be disputed as to correctness—though some posters still try—which inexplicably are ignored by math people who claim they care about "pure math".

My take on it is that to them "pure math" means that they have the right to ignore ANY mathematical result no matter how important it can be shown to be, as long as they do not personally like it!

So "pure math" means "personal math" or "my math" which goes to the bit of side humor in the title of my math blog, when you consider the way math people actually behave.

And that kind of covers the gist of the show as well as the reasons for it.

I am an American who very much studies how modern media works, and one thing we know how to do in this country, is get attention! So when you see all those news stories about celebrities here and their wild behavior, you may just wonder, while I study.

Like Paris Hilton is a remarkable person in terms of giving you some sense of the concept, as make no mistake, our modern world runs as much on attention as it does on oil.

You have to be able to get it, to get anything done, as otherwise, no one knows who you are, or what you have found, no matter what it is you have found.

Those who hate such things can tune out at this point…for the rest here is the rationale that I use in deciding to post and what I think is kind of sort of the point.

First off, the rule of Usenet and Internet is attention has to happen first.

If no one reads you then there is no way you can get any message across, no matter how valid you think that message is!

Second thing, people don't like nice, and they don't like agreement as it's boring.

Posts where people ask nicely for help, congratulate each other, and then talk about how great this process is and isn't it wonderful to be able to share information in such an agreeable place, are boring.

Our world thrives on conflict. Disagreement drives Usenet. Without it, you don't get that thing I mentioned above—attention.

So yes, a lot of what you see in postings from my side is just for show, as they say, merely meant to keep the antagonism up, keep the hostilities up, so that there is a continual tension and sense of conflict to draw in readers.

Over the years I've refined techniques that tend to play to what works and manages a rag-tag group of posters who come and go, kind of like circus players, as over the years I've had a LOT of them, come and go.

I do at times try to tone things down a bit as well, when it gets too outrageous even for me, often with limited success, where the thing that does work is for me to just stop posting for a while, and I'm finding that I have to do that more and more as things get more advanced.

With all of that said there is a lot of real drama taking place as the attention is not the purpose, but keeping the light on my mathematical research IS, and the reality that academics at some very prestigious institutions are not doing their jobs is the underlying theme.

There really was that publication in SWJPAM for instance where the editors withdrew my paper after emails from several sci.math posters (not certain about how many emailed them), and subsequently the journal DID die, and Cameron University, its host, DID wipe all record of its nine year existence from its webpages.

I do have multiple rejections from top journal of papers that are now found on my websites, and I do have very simple mathematical results which cannot be disputed as to correctness—though some posters still try—which inexplicably are ignored by math people who claim they care about "pure math".

My take on it is that to them "pure math" means that they have the right to ignore ANY mathematical result no matter how important it can be shown to be, as long as they do not personally like it!

So "pure math" means "personal math" or "my math" which goes to the bit of side humor in the title of my math blog, when you consider the way math people actually behave.

And that kind of covers the gist of the show as well as the reasons for it.

I am an American who very much studies how modern media works, and one thing we know how to do in this country, is get attention! So when you see all those news stories about celebrities here and their wild behavior, you may just wonder, while I study.

Like Paris Hilton is a remarkable person in terms of giving you some sense of the concept, as make no mistake, our modern world runs as much on attention as it does on oil.

You have to be able to get it, to get anything done, as otherwise, no one knows who you are, or what you have found, no matter what it is you have found.

### Friday, June 15, 2007

## JSH: Suing universities

The very next thing I'll do if my research breaks through is begin pushing plans forward for suing major universities along the legal lines I've outlined before during an important brainstorming period.

My two top choices are Harvard and Princeton, and I'll use Mazur for Harvard, and the editors of the Annals for Princeton, as well as anybody else I can net for some very big cases.

Now some may say that is about ego and looking for something big to do next, but a lot of it is just about anger, and just being tired of people getting away with lying thinking they are safe because they are at some prestigious university.

I want to make an example that the world will never forget.

And Princeton and Harvard will make that possible because before I'm done, if I have my way, their endowments will be cut by at least half.

And they will just be the start, especially as I open the door and show people how it's done.

My two top choices are Harvard and Princeton, and I'll use Mazur for Harvard, and the editors of the Annals for Princeton, as well as anybody else I can net for some very big cases.

Now some may say that is about ego and looking for something big to do next, but a lot of it is just about anger, and just being tired of people getting away with lying thinking they are safe because they are at some prestigious university.

I want to make an example that the world will never forget.

And Princeton and Harvard will make that possible because before I'm done, if I have my way, their endowments will be cut by at least half.

And they will just be the start, especially as I open the door and show people how it's done.

## JSH: Bursting bubbles

I'll admit that at times I try to find a silver lining in my situation by just bursting bubbles.

Plenty of supposedly brilliant top theoretical physicists muttered stuff about primes and physics, as oh my, maybe they could connect the great Riemann Hypothesis from those math guys over to the world of physics and isn't it all just grand?

But they happily ignore simple findings that could tie everything together.

Remember Occam's Razor?

Problem with that thing is that it doesn't get you research grants!!!

When I was a naive undergrad in physics, young and idealistic, I used to admire physicists who I believed were people who sought the truth, but now I know, hey they got to eat!

They want stuff like other people. And to get stuff in our world you need, money.

And if you do not lie in our world, then it is harder to get, money.

There is not a true top physicist in the world today. Not one. I have a contempt for them.

They are all corrupted.

The sad thing about this story is that if it does break my way, it will be because of money and ways I have figured out to help other people out there make more of it—far from the sciences and mathematics.

And you know what I'll do then?

I'll challenge the world to push survival of the fittest—and actually honest--in the academic world by starving funding. I will do my best to shut down entire research departments at major universities as I think they mostly teach lying.

I will push Congress in the United States to slash research budgets in all areas except:

wasted teaching people how to lie and "publish or perish" so that they'll ignore ANY research because first they look around to see if it will help their careers or not.

I think there are too many scientists worldwide, clogging up the works, and that human progress depends on forcing the bad ones out by starving them of money.

The great scientists will find a way. The rest will find jobs elsewhere.

Plenty of supposedly brilliant top theoretical physicists muttered stuff about primes and physics, as oh my, maybe they could connect the great Riemann Hypothesis from those math guys over to the world of physics and isn't it all just grand?

But they happily ignore simple findings that could tie everything together.

Remember Occam's Razor?

Problem with that thing is that it doesn't get you research grants!!!

When I was a naive undergrad in physics, young and idealistic, I used to admire physicists who I believed were people who sought the truth, but now I know, hey they got to eat!

They want stuff like other people. And to get stuff in our world you need, money.

And if you do not lie in our world, then it is harder to get, money.

There is not a true top physicist in the world today. Not one. I have a contempt for them.

They are all corrupted.

The sad thing about this story is that if it does break my way, it will be because of money and ways I have figured out to help other people out there make more of it—far from the sciences and mathematics.

And you know what I'll do then?

I'll challenge the world to push survival of the fittest—and actually honest--in the academic world by starving funding. I will do my best to shut down entire research departments at major universities as I think they mostly teach lying.

I will push Congress in the United States to slash research budgets in all areas except:

- Those crucial to national security, including materials science which I'll mention next.
- Material science.
- Biological and medical research, especially research involving genetics.

wasted teaching people how to lie and "publish or perish" so that they'll ignore ANY research because first they look around to see if it will help their careers or not.

I think there are too many scientists worldwide, clogging up the works, and that human progress depends on forcing the bad ones out by starving them of money.

The great scientists will find a way. The rest will find jobs elsewhere.

### Thursday, June 14, 2007

## JSH: The search for truth

Pain and discovery have always gone hand in hand. After all, if it were easy, everybody would do it.

The real story of the path of humanity from the trees to the plains to cities and our modern world is filled with a lot of pain from a lot of people who will never be named.

They suffered so that we could live a different, hopefully better life, and most of them died without ever making a mark beyond the knowledge they gained—and passed on.

Who invented glass? What was the name of the first human being that made fire? Or the first ones who were brave enough to use natural fire rather than run from it like the other animals?

They died a long time ago, and there was no immortality for them in their discovery.

We discover because that is who we are. It is as natural for human beings to learn as it is to breathe, but it is a painful process.

For me the greatest disappointment in the modern mathematical community is in what I see as a lack of humanity, a retrograde movement, a recidivism, against the search for truth.

And why?

I think it's for jobs. I think that a modern mathematician today would rather lie about prime numbers than endanger research funding by telling the truth. And that way that professor can keep money for HIS kids. He can buy his wife some comfort. Pay his mortgage and to him that is more than enough reason.

And that is what makes him less than human.

What good is it to give that kid a meal and a home and take away the future?

If a man like these professors were facing fire, would he have run away, would we be here today?

Prometheus angered the gods in Greek legend by daring to challenge them, and bring knowledge to a hungry race, and in so doing he was punished.

We who discover are the children of Prometheus. It is our fate to be forever punished for the gift of knowledge.

But we do it anyway.

There is always a challenge. There are always anti-humans who create the battles and make the wars necessary as their parasitic nature demands it because without it doing it they cannot feed their children.

They cannot feed their children on truth.

But the progress of this planet depends on those who not only search for fire, they embrace it, and in the burning, the pain, the misery, and in the blindness of that light that forces its way through you, you learn that no matter what may come and all that will go, this time, and in this place you stood where greatness stood before, and on the shoulders of giants you rode.

The world will forget. It always does.

But its memory is not the reason, and the gods punished Prometheus and his children not for some simple thoughts of creatures they disdained.

They punished them for daring…and that was always enough.

The real story of the path of humanity from the trees to the plains to cities and our modern world is filled with a lot of pain from a lot of people who will never be named.

They suffered so that we could live a different, hopefully better life, and most of them died without ever making a mark beyond the knowledge they gained—and passed on.

Who invented glass? What was the name of the first human being that made fire? Or the first ones who were brave enough to use natural fire rather than run from it like the other animals?

They died a long time ago, and there was no immortality for them in their discovery.

We discover because that is who we are. It is as natural for human beings to learn as it is to breathe, but it is a painful process.

For me the greatest disappointment in the modern mathematical community is in what I see as a lack of humanity, a retrograde movement, a recidivism, against the search for truth.

And why?

I think it's for jobs. I think that a modern mathematician today would rather lie about prime numbers than endanger research funding by telling the truth. And that way that professor can keep money for HIS kids. He can buy his wife some comfort. Pay his mortgage and to him that is more than enough reason.

And that is what makes him less than human.

What good is it to give that kid a meal and a home and take away the future?

If a man like these professors were facing fire, would he have run away, would we be here today?

Prometheus angered the gods in Greek legend by daring to challenge them, and bring knowledge to a hungry race, and in so doing he was punished.

We who discover are the children of Prometheus. It is our fate to be forever punished for the gift of knowledge.

But we do it anyway.

There is always a challenge. There are always anti-humans who create the battles and make the wars necessary as their parasitic nature demands it because without it doing it they cannot feed their children.

They cannot feed their children on truth.

But the progress of this planet depends on those who not only search for fire, they embrace it, and in the burning, the pain, the misery, and in the blindness of that light that forces its way through you, you learn that no matter what may come and all that will go, this time, and in this place you stood where greatness stood before, and on the shoulders of giants you rode.

The world will forget. It always does.

But its memory is not the reason, and the gods punished Prometheus and his children not for some simple thoughts of creatures they disdained.

They punished them for daring…and that was always enough.

### Tuesday, June 12, 2007

## JSH: Ok, what DOES amuse me

I will admit that I find it fascinating how much stock math people put in put downs, as if some wacky postings on some website, or a bunch of people continually calling you crazy actually makes a difference.

Maybe it does in your world, but not in mine.

People just do not care. They have bigger things to worry about in their lives.

To me it has long been a source of amusement to watch so many of you get so excited as if you had this great big thing to have some weird posting or something I said that you'd get excited about as if, "gotcha!"

You're such children. Look around you at the big wide world and see if anybody actually cares.

So yeah, it is kind of fun to poke at you people. The wacky postings seem to elicit a predictable reaction, which I find fascinates me.

But what makes any of you think that will make a difference if any of my ideas get known to be valuable to the world?

Think they will pause for one second because I said something weird here, or something weird there?

I think some of you do because you are STUPID.

And that makes you even funnier.

Maybe it does in your world, but not in mine.

People just do not care. They have bigger things to worry about in their lives.

To me it has long been a source of amusement to watch so many of you get so excited as if you had this great big thing to have some weird posting or something I said that you'd get excited about as if, "gotcha!"

You're such children. Look around you at the big wide world and see if anybody actually cares.

So yeah, it is kind of fun to poke at you people. The wacky postings seem to elicit a predictable reaction, which I find fascinates me.

But what makes any of you think that will make a difference if any of my ideas get known to be valuable to the world?

Think they will pause for one second because I said something weird here, or something weird there?

I think some of you do because you are STUPID.

And that makes you even funnier.

## Generalizing integer factorization

Stepping just slightly away from equation familiar from a congruence of squares gives a generalized factoring method which shows a means to balance the difficulty of factoring a number against computational resources.

Beginning with

x^2 = y^2 + aT and k^2 = 2xk + bT

where T is the target composite to be factored, you can easily solve to find

(x+k)^2 = y^2 + 2k^2 + (a-b)T

so that it is clear that 'a' and 'b' need not be determined as you need a-b, which is chosen to be some non-zero integer as is k.

Trivially, if you introduce integer factors f_1 and f_2, you can have

4f_1*f_2 = 2k^2 + (a-b)T

then y = f_1 - f_2 and

x = f_1 + f_2 - k

so by factoring 2k^2 + (a-b)T you can potentially non-trivially factor your target composite T.

Experiments with this method show that the larger 2k^2 + (a-b)T is, the more likely you are to factor the target T by factoring it, but that means it can be roughly as hard to factor as your original composite!

But there are a couple of saving graces, the most important being that the method focuses on the smaller primes first—pulling them out of the composite preferentially.

And, for composites 2k^2 + (a-b)T very close in factoring difficulty to your target composite T, the method works approximately 67% of the time.

So it is a method that allows you to adjust depending on what factoring probability you can handle with your computational power.

Beginning with

x^2 = y^2 + aT and k^2 = 2xk + bT

where T is the target composite to be factored, you can easily solve to find

(x+k)^2 = y^2 + 2k^2 + (a-b)T

so that it is clear that 'a' and 'b' need not be determined as you need a-b, which is chosen to be some non-zero integer as is k.

Trivially, if you introduce integer factors f_1 and f_2, you can have

4f_1*f_2 = 2k^2 + (a-b)T

then y = f_1 - f_2 and

x = f_1 + f_2 - k

so by factoring 2k^2 + (a-b)T you can potentially non-trivially factor your target composite T.

Experiments with this method show that the larger 2k^2 + (a-b)T is, the more likely you are to factor the target T by factoring it, but that means it can be roughly as hard to factor as your original composite!

But there are a couple of saving graces, the most important being that the method focuses on the smaller primes first—pulling them out of the composite preferentially.

And, for composites 2k^2 + (a-b)T very close in factoring difficulty to your target composite T, the method works approximately 67% of the time.

So it is a method that allows you to adjust depending on what factoring probability you can handle with your computational power.

## JSH: Reading them is what matters

Quite simply to elaborate on another post in another thread where I point out that I make posts to be read, the main thing for me is to get you to read my posts.

And the wackier ones are the ones where at times I am working the hardest, which is why they are that wacky. That pulls you in, so it is the bait.

I am a great student of human psychology and physiology of the brain.

The idea in those posts is to shift you without you knowing it is being done or understanding exactly what is being done.

Some of them are meant to actually change your brain chemistry.

I, myself, will not read most of them again. Nor am I dumb enough to sit and read a bunch of them in a row.

Maybe the greatest test of my real abilities versus your perceptions that I have none are what those posts are doing as we speak, and what they do to people who read them—whether they wish it or not.

Quite simply, no matter what you think of me, they will change you.

Of course, you can consider this post to be reverse psychology, so go read my wacky posts, and see what happens…

And the wackier ones are the ones where at times I am working the hardest, which is why they are that wacky. That pulls you in, so it is the bait.

I am a great student of human psychology and physiology of the brain.

The idea in those posts is to shift you without you knowing it is being done or understanding exactly what is being done.

Some of them are meant to actually change your brain chemistry.

I, myself, will not read most of them again. Nor am I dumb enough to sit and read a bunch of them in a row.

Maybe the greatest test of my real abilities versus your perceptions that I have none are what those posts are doing as we speak, and what they do to people who read them—whether they wish it or not.

Quite simply, no matter what you think of me, they will change you.

Of course, you can consider this post to be reverse psychology, so go read my wacky posts, and see what happens…

### Sunday, June 10, 2007

## JSH: Statement of the problem

Mathematicians are so completely disconnected from the real world that they can no longer be trusted to tell the truth even about mathematics itself. Their world is ruled by vote, and in its democracy, mathematical proof can be useless against the group opinion.

In fact, mathematicians today no longer believe in proof outside of their opinion.

See: http://www.maa.org/devlin/devlin_06_03.html

Independent research can simply be ignored by the current mathematical community without regard to even basic proof of value by measures that most people including experts in other academic areas are known to consider the most compelling reasons for importance, like uniqueness in an important area.

So I can have a find of mathematical function that finds prime numbers and counts them in a way never before seen, as it uses the summation of a partial difference equation, which is distinguished by allowing you to move to a partial differential equation, and mathematicians can simply state that is not of interest, and not be compelled to do what most would consider the right thing.

Worse, even publication no longer matters, as with other mathematical research of mine I did get published, following a well laid out process involving formal peer review, and that publication was not only reversed by a few emails from posters of the sci.math newsgroup falsely claiming error in my paper, but later the journal itself simply shut down, and the hosting school Cameron University went so far as to remove all mention of the now defunct journal.

That journal and the papers that had been published in it for nine years would have simply gone into total limbo if not for the efforts of EMIS, which continues to provide the published editions on its mirror servers.

See: http://www.emis.de/journals/SWJPAM/

The full problem then is that mathematicians are capable not only of ignoring mathematical proof, but also of ignoring important research easily seen to be unique by people in other fields, which can be made relevant to other fields, as I've pointed out by noting that at the heart of my prime counting function is a discrete damped oscillator.

The article I link to above is titled "When is a proof?" and is written by Keith Devlin, a mathematician at Stanford. He talks of two types of "proof", where one is proof as most people think of it and the other is the following quote:

"The left wing answer (fuzzy, democratic, and human centered) is that a proof is an argument that convinces a typical mathematician of the truth of a given statement."

I emailed him an early draft of the paper that did eventually get published by the now defunct SWJPAM and retracted, before that event, and his reply was that it was the left wing type.

Um, I use VERY basic mathematics deliberately now with a focus on quadratics (simplifying from the paper which used cubics), and it does not matter, as mathematicians seem to have escaped completely to a position that a proof is only what they want to be a proof.

And you have a dead math journal as some evidence of how big this issue is.

But it is bigger than mathematics because it goes to how academia does research.

Editors as proven by those at SWJPAM can make bizarre decisions that are all about fuzzy, democratic, human-centered stuff, and nothing about the value of the research.

I suggest to you that the current system of formal peer review is out-dated and itself defunct, and it is past time for a system of independent measures probably including cross-disciplinary evaluations.

Mathematicians have good reason to fear my discoveries as they can either help close doors on research that many mathematicians around the world are working on—getting pay and often state funding, as well as prizes—or show errors in the field itself, so protecting against the truth is about academic fraud.

But more importantly than their will to ignore important research is the ability to get away with it on this scale.

I suggest to you that academics in almost any area of research can potentially do the same because the system is not setup for proper policing despite the tremendous advantage members of a discipline can get by dissembling as a group about information in their field.

Only independent evaluations by people who are not themselves invested can bring back some degree of certainty beyond the verisimilitude of academic assertions. Are they actually true based on all the information available, or is it just that for some academics the appearance of truth is important for funding and their careers?

My own personal belief is that the mathematicians have shown the flaws in an out-dated academic system that carries too much from medieval times and ignores what we know today about human nature and the ability of even large groups of highly intelligent people to ignore inconvenient truths.

It is past time that academics lost the glow of being better than ordinary people, and we accepted that they too can engage in large scale fraud at a level so high that even the death of a journal can be tossed off as just an ordinary, every day thing just so that they do not have to handle the truth.

When the future of our species depends on how we handle the truth, the issue is more than just, academic.

The problem as stated I think needs to be answered but I do not know what the answer is.

I present it to the group for suggestions:

Is there any solution to academics deciding against acceptance of inconvenient truths in their own field? Or specifically, can mathematicians be made to accept proof that they do not want as it is inconvenient to their careers?

If so, how?

In fact, mathematicians today no longer believe in proof outside of their opinion.

See: http://www.maa.org/devlin/devlin_06_03.html

Independent research can simply be ignored by the current mathematical community without regard to even basic proof of value by measures that most people including experts in other academic areas are known to consider the most compelling reasons for importance, like uniqueness in an important area.

So I can have a find of mathematical function that finds prime numbers and counts them in a way never before seen, as it uses the summation of a partial difference equation, which is distinguished by allowing you to move to a partial differential equation, and mathematicians can simply state that is not of interest, and not be compelled to do what most would consider the right thing.

Worse, even publication no longer matters, as with other mathematical research of mine I did get published, following a well laid out process involving formal peer review, and that publication was not only reversed by a few emails from posters of the sci.math newsgroup falsely claiming error in my paper, but later the journal itself simply shut down, and the hosting school Cameron University went so far as to remove all mention of the now defunct journal.

That journal and the papers that had been published in it for nine years would have simply gone into total limbo if not for the efforts of EMIS, which continues to provide the published editions on its mirror servers.

See: http://www.emis.de/journals/SWJPAM/

The full problem then is that mathematicians are capable not only of ignoring mathematical proof, but also of ignoring important research easily seen to be unique by people in other fields, which can be made relevant to other fields, as I've pointed out by noting that at the heart of my prime counting function is a discrete damped oscillator.

The article I link to above is titled "When is a proof?" and is written by Keith Devlin, a mathematician at Stanford. He talks of two types of "proof", where one is proof as most people think of it and the other is the following quote:

"The left wing answer (fuzzy, democratic, and human centered) is that a proof is an argument that convinces a typical mathematician of the truth of a given statement."

I emailed him an early draft of the paper that did eventually get published by the now defunct SWJPAM and retracted, before that event, and his reply was that it was the left wing type.

Um, I use VERY basic mathematics deliberately now with a focus on quadratics (simplifying from the paper which used cubics), and it does not matter, as mathematicians seem to have escaped completely to a position that a proof is only what they want to be a proof.

And you have a dead math journal as some evidence of how big this issue is.

But it is bigger than mathematics because it goes to how academia does research.

Editors as proven by those at SWJPAM can make bizarre decisions that are all about fuzzy, democratic, human-centered stuff, and nothing about the value of the research.

I suggest to you that the current system of formal peer review is out-dated and itself defunct, and it is past time for a system of independent measures probably including cross-disciplinary evaluations.

Mathematicians have good reason to fear my discoveries as they can either help close doors on research that many mathematicians around the world are working on—getting pay and often state funding, as well as prizes—or show errors in the field itself, so protecting against the truth is about academic fraud.

But more importantly than their will to ignore important research is the ability to get away with it on this scale.

I suggest to you that academics in almost any area of research can potentially do the same because the system is not setup for proper policing despite the tremendous advantage members of a discipline can get by dissembling as a group about information in their field.

Only independent evaluations by people who are not themselves invested can bring back some degree of certainty beyond the verisimilitude of academic assertions. Are they actually true based on all the information available, or is it just that for some academics the appearance of truth is important for funding and their careers?

My own personal belief is that the mathematicians have shown the flaws in an out-dated academic system that carries too much from medieval times and ignores what we know today about human nature and the ability of even large groups of highly intelligent people to ignore inconvenient truths.

It is past time that academics lost the glow of being better than ordinary people, and we accepted that they too can engage in large scale fraud at a level so high that even the death of a journal can be tossed off as just an ordinary, every day thing just so that they do not have to handle the truth.

When the future of our species depends on how we handle the truth, the issue is more than just, academic.

The problem as stated I think needs to be answered but I do not know what the answer is.

I present it to the group for suggestions:

Is there any solution to academics deciding against acceptance of inconvenient truths in their own field? Or specifically, can mathematicians be made to accept proof that they do not want as it is inconvenient to their careers?

If so, how?

## JSH: They shut the door

If there is one thing that truly shocks me about the modern mathematical community is that it just completely shuts the door.

So these people will label you a crackpot or a crank and destroy anything, even their own stuff, to make that stick and it does not matter what you can prove.

When I was thinking about meddling in the mathematical world and looking for my own proofs, I thought to myself that I'd use simple or what are often called elementary methods not only to help myself not get muddled into very complex mathematics, but also to make it easier to explain.

But that makes it despairingly easy to know these people actually, quite deliberately, lie about mathematical proof.

So I got published and you can do a web search on "SWJPAM" and look through posts on the sci.math newsgroup when they were attacking that journal for publishing a paper of mine, and see the conspiracy to email the editors against my paper planned out in posts.

They shut the door. I played by the rules. I wrote a paper representing years of research, and months of effort which I passed through a number of mathematicians. I sent the paper to a peer reviewed mathematical journal which took months of review before it told me the reviewers liked it and they published it.

Then some people sent some emails, and they made fun of me when in despair I posted about how my parents had been proud, or how my teacher's had been proud of the publication and I had to try and explain the odd retraction. My own father thinks I'm crazy and told me so because he doesn't believe that something this massively wrong could be happening. So he thinks I must be wrong.

They have no limits. People on the newsgroup made fun of my having to explain to my family and teachers this situation. It's like they're inhuman if you cross them. Like, to them, nothing is sacred.

The math people do not follow their own rules, and they get away with it.

The example I've given with the prime counting function is meant to let you go beyond rhetoric. As is your ability to do a search on the now dead journal and see that it did exist. See how long it existed, and see what happened to it now.

What if you had a paper published in that journal?

People from the math community take the time and trouble to smear me across the web.

That kind of political behavior is learned, and to be effective it has to be practiced.

But why? Why do mathematicians need high level political attack skills?

I say, because they have learned to lie because it's so hard to check many of their claims and those claims are worth money, from funding to math prizes, to just having jobs as professors and researchers at universities, the lies are worth money.

And when you lie a lot for money, you need to be good at it, like politicians.

Maybe it is inevitable that the search for truth is finally lost by every species before it dies, when people find that the effort and energy involved in getting to real answers is beyond them, so a civilization turns to pretend.

Maybe the real story of our future is that our world finally becomes mostly actors pretending to be people who are mathematicians, or physicists, or before the final crumble, even doctors or lawyers because the hardest thing to find or handle can be the truth.

[A reply to someone who wondered what would James' father think about this post or about this one.]

What's wrong with those messages?

In both I'm contemplating a thorny issue as for a while I concluded that a final solution to the problem of getting my research acknowledged would be to figure out an answer to the factoring problem, which underlies the security of the Internet itself.

My fear with that was that, hey, I might succeed! And if I did it could have dramatic consequences for a lot of people, and I went through a lot of moral and ethical searching about the problem.

At the time of the second message I was afraid I had succeeded and had decided to release the information, and thought that two particular posters might get in trouble if it did cause some negative consequences as they had spent to much time attacking the research.

Kind of like if before September 11th, someone had been posting warnings on Usenet about hijackers flying planes into buildings in a terrorist attack, and a couple of posters had been criticizing the idea and that person as a crackpot and then it happened.

My belief in the past was that they might face severe negative consequences, while today I think they'd probably just get ignored as most people do not think of Usenet as a credible source.

But based on my past belief I felt I should warn them, and it turned out I was wrong.

The Internet's security system is not currently known in wide areas to be broken, there has been no major correction to the world's stock exchanges based on it being broken, and no crash of the world economy followed by a great depression in the United States.

So my fears did not materialize into reality.

[A reply to someone who wrote that, in both posts, Jame expressed no doubt whatsoever and that, instead of that, he wrote as if he was absolutely certain.]

I was certain, and I was wrong.

Maybe there is where I think mathematicians and physicists go totally different ways as I think that statement can make sense to a physicist, but the concept seems to give mathematicians all kinds of bizarre trouble.

Certainty is not proof—it's a feeling.

So if certainty is not proof how do we actually know anything?

In physics we concern ourselves not so much with absolute certainty as with what works in the real world, so we know something in physics on the basis of repeatability and predictability.

Knowledge should give us something in the real world in terms of knowing something will happen, acting to make that something happen and then seeing it happen as expected.

That is knowledge, and repetition of the above gives us a feeling of certainty, but it is not proof of absolute truth.

So these people will label you a crackpot or a crank and destroy anything, even their own stuff, to make that stick and it does not matter what you can prove.

When I was thinking about meddling in the mathematical world and looking for my own proofs, I thought to myself that I'd use simple or what are often called elementary methods not only to help myself not get muddled into very complex mathematics, but also to make it easier to explain.

But that makes it despairingly easy to know these people actually, quite deliberately, lie about mathematical proof.

So I got published and you can do a web search on "SWJPAM" and look through posts on the sci.math newsgroup when they were attacking that journal for publishing a paper of mine, and see the conspiracy to email the editors against my paper planned out in posts.

They shut the door. I played by the rules. I wrote a paper representing years of research, and months of effort which I passed through a number of mathematicians. I sent the paper to a peer reviewed mathematical journal which took months of review before it told me the reviewers liked it and they published it.

Then some people sent some emails, and they made fun of me when in despair I posted about how my parents had been proud, or how my teacher's had been proud of the publication and I had to try and explain the odd retraction. My own father thinks I'm crazy and told me so because he doesn't believe that something this massively wrong could be happening. So he thinks I must be wrong.

They have no limits. People on the newsgroup made fun of my having to explain to my family and teachers this situation. It's like they're inhuman if you cross them. Like, to them, nothing is sacred.

The math people do not follow their own rules, and they get away with it.

The example I've given with the prime counting function is meant to let you go beyond rhetoric. As is your ability to do a search on the now dead journal and see that it did exist. See how long it existed, and see what happened to it now.

What if you had a paper published in that journal?

People from the math community take the time and trouble to smear me across the web.

That kind of political behavior is learned, and to be effective it has to be practiced.

But why? Why do mathematicians need high level political attack skills?

I say, because they have learned to lie because it's so hard to check many of their claims and those claims are worth money, from funding to math prizes, to just having jobs as professors and researchers at universities, the lies are worth money.

And when you lie a lot for money, you need to be good at it, like politicians.

Maybe it is inevitable that the search for truth is finally lost by every species before it dies, when people find that the effort and energy involved in getting to real answers is beyond them, so a civilization turns to pretend.

Maybe the real story of our future is that our world finally becomes mostly actors pretending to be people who are mathematicians, or physicists, or before the final crumble, even doctors or lawyers because the hardest thing to find or handle can be the truth.

[A reply to someone who wondered what would James' father think about this post or about this one.]

What's wrong with those messages?

In both I'm contemplating a thorny issue as for a while I concluded that a final solution to the problem of getting my research acknowledged would be to figure out an answer to the factoring problem, which underlies the security of the Internet itself.

My fear with that was that, hey, I might succeed! And if I did it could have dramatic consequences for a lot of people, and I went through a lot of moral and ethical searching about the problem.

At the time of the second message I was afraid I had succeeded and had decided to release the information, and thought that two particular posters might get in trouble if it did cause some negative consequences as they had spent to much time attacking the research.

Kind of like if before September 11th, someone had been posting warnings on Usenet about hijackers flying planes into buildings in a terrorist attack, and a couple of posters had been criticizing the idea and that person as a crackpot and then it happened.

My belief in the past was that they might face severe negative consequences, while today I think they'd probably just get ignored as most people do not think of Usenet as a credible source.

But based on my past belief I felt I should warn them, and it turned out I was wrong.

The Internet's security system is not currently known in wide areas to be broken, there has been no major correction to the world's stock exchanges based on it being broken, and no crash of the world economy followed by a great depression in the United States.

So my fears did not materialize into reality.

[A reply to someone who wrote that, in both posts, Jame expressed no doubt whatsoever and that, instead of that, he wrote as if he was absolutely certain.]

I was certain, and I was wrong.

Maybe there is where I think mathematicians and physicists go totally different ways as I think that statement can make sense to a physicist, but the concept seems to give mathematicians all kinds of bizarre trouble.

Certainty is not proof—it's a feeling.

So if certainty is not proof how do we actually know anything?

In physics we concern ourselves not so much with absolute certainty as with what works in the real world, so we know something in physics on the basis of repeatability and predictability.

Knowledge should give us something in the real world in terms of knowing something will happen, acting to make that something happen and then seeing it happen as expected.

That is knowledge, and repetition of the above gives us a feeling of certainty, but it is not proof of absolute truth.

### Saturday, June 09, 2007

## JSH: Math people ARE different

To me arguing comes naturally in the search for truth as people have different points of views and might see something you miss or catch you on mistakes that you cannot easily see on your own.

The big surprise for me from the math community was figuring out that they argue to deny the truth, and do so as a group, so like, when I had a paper on some of my mathematical research published, as a group the sci.math newsgroup reacted in fury and some of them emailed the mathematical journal editors against my paper.

But what was really weird to me about that story was that in attacking the publication against my paper the math people attacked journals in general, claiming they often published wrong papers!!!

So they attacked the entire system. But later when I noted that they claimed they didn't!

Ultimately they seemed to settle on a paper only being important if it were published in a major journal and had general acceptance in the math community.

All that reaction was to me getting published and the rest of the story is the journal editors yanked my paper out of the published journal, as it was electronic so they could just change the file, managed one more edition and then quietly shut down.

The journal with the initials SWJPAM—on which it is the easiest to search for it—was a publication of Cameron University which previously had links to it on its websites, but it removed all of those so that the journals editions—and the papers published in it over nine years—would have been lost except that EMIS, a mirror server, decided to keep the journal alive.

See: http://www.emis.de/journals/SWJPAM/

Imagine, the university was willing to just toss over nine years of published mathematical papers!!! And nary a word in protest that I've noticed from the mathematical community.

What EMIS says at that link is the most I've heard on this entire thing from what one might call an official source.

That's the mathematical world and I think some of you have some weird noble idea of that world that is nothing like the reality as that story is factual. It is about the actual math world and what is possible within it.

My take on it is that it is a highly political world. Math people care about consensus first and foremost.

And they can deny ANYTHING.

Like I have talked about my find of a discrete damped oscillator as that makes it physics relevant but since 2002, when I made this discovery, I have talked about it in the math world because it counts prime numbers and it does so by summing a partial difference equation.

Turns out, there is no other known function, or any other research for that matter, where you get anything like it, as not only do you have this first of using a partial difference equation, so it actually finds primes on its own as it counts, but you can move to a partial differential equation, which is just mind-blowing, so it's easy to step through all the ways this research is unique.

But I can't get any traction in the math world, and in fact, on direct points over uniqueness I end up in bizarre arguments, admittedly on math newsgroups, with people who just deny the facts.

So, if you are naive or trusting in human nature, you may ask, why can't I just ask them to show something else like what I found?

I do. They lie in reply. These people seem to have nothing sacred.

They lie about prime numbers, they lie about simple equations and when I looked to find a reason, the only one that makes sense is that they do not wish to accept what is mathematically true for some rather basic reasons:

Yup, what I'm talking about is academic fraud.

Can it be stopped?

I think the odds are long. There's no sense in my mind that this post, for instance, will matter much more than any of the previous ones, and let's face it, mathematicians get away with this because, for instance, prime numbers are NOT really that important to the business of most of the world.

What they do is not relevant or meaningful anymore. Even in physics most of the mathematics that is needed was discovered long ago. These people may not have anything important to do!

In a sense they have a point that their world is no longer relevant, so it doesn't really matter much to what everyone else is doing if they are wrong, or ignore important research, and they do need to eat!

But they are different I think from physics people who are driven to find answers, and get to the truth—not just be convincing and keep getting paid.

Or I like to think they are. Who really knows and does it really matter?

Eventually our species like so many others before it will be extinct. In the meantime, well, we do what we do because, what else would we do?

And reality is that for most people perception IS reality. It's more important to believe that we're doing important things than to actually be doing important things.

Still it is sad. Often I feel sorry for these people who spend so much energy on things that are just not true that on some level they must know are not true.

But then again, other people make bigger sacrifices to care for themselves and their children.

People will do a lot to have a life, have kids, live comfortably. Lying is common in society's around the world.

Lying about math is not that big of a reach, not when a comfortable life, for you and your children, can be realized by just not caring about what is true about some math stuff.

But I do hope physics can to some extent escape falling into the same decline as the mathematics field has, but maybe it's inevitable.

Maybe species like humanity do die with a whimper, as I think many of us suspect—failing in every way, including in the search for truth.

Learning that pretend knowledge is better than truth, so that some people can feel comfortable, may just be a sign that a species is on its last legs.

The big surprise for me from the math community was figuring out that they argue to deny the truth, and do so as a group, so like, when I had a paper on some of my mathematical research published, as a group the sci.math newsgroup reacted in fury and some of them emailed the mathematical journal editors against my paper.

But what was really weird to me about that story was that in attacking the publication against my paper the math people attacked journals in general, claiming they often published wrong papers!!!

So they attacked the entire system. But later when I noted that they claimed they didn't!

Ultimately they seemed to settle on a paper only being important if it were published in a major journal and had general acceptance in the math community.

All that reaction was to me getting published and the rest of the story is the journal editors yanked my paper out of the published journal, as it was electronic so they could just change the file, managed one more edition and then quietly shut down.

The journal with the initials SWJPAM—on which it is the easiest to search for it—was a publication of Cameron University which previously had links to it on its websites, but it removed all of those so that the journals editions—and the papers published in it over nine years—would have been lost except that EMIS, a mirror server, decided to keep the journal alive.

See: http://www.emis.de/journals/SWJPAM/

Imagine, the university was willing to just toss over nine years of published mathematical papers!!! And nary a word in protest that I've noticed from the mathematical community.

What EMIS says at that link is the most I've heard on this entire thing from what one might call an official source.

That's the mathematical world and I think some of you have some weird noble idea of that world that is nothing like the reality as that story is factual. It is about the actual math world and what is possible within it.

My take on it is that it is a highly political world. Math people care about consensus first and foremost.

And they can deny ANYTHING.

Like I have talked about my find of a discrete damped oscillator as that makes it physics relevant but since 2002, when I made this discovery, I have talked about it in the math world because it counts prime numbers and it does so by summing a partial difference equation.

Turns out, there is no other known function, or any other research for that matter, where you get anything like it, as not only do you have this first of using a partial difference equation, so it actually finds primes on its own as it counts, but you can move to a partial differential equation, which is just mind-blowing, so it's easy to step through all the ways this research is unique.

But I can't get any traction in the math world, and in fact, on direct points over uniqueness I end up in bizarre arguments, admittedly on math newsgroups, with people who just deny the facts.

So, if you are naive or trusting in human nature, you may ask, why can't I just ask them to show something else like what I found?

I do. They lie in reply. These people seem to have nothing sacred.

They lie about prime numbers, they lie about simple equations and when I looked to find a reason, the only one that makes sense is that they do not wish to accept what is mathematically true for some rather basic reasons:

- My research helps settles questions thought big and open on which a lot of mathematicians are currently doing research. So accepting it would take away jobs.
- They feel invulnerable because society accepts them as experts and believes in them, trusts them, so even when they blatantly lie on something as seemingly obvious as whether or not a partial difference equation has EVER been used to count prime numbers, there's little I can do.

Yup, what I'm talking about is academic fraud.

Can it be stopped?

I think the odds are long. There's no sense in my mind that this post, for instance, will matter much more than any of the previous ones, and let's face it, mathematicians get away with this because, for instance, prime numbers are NOT really that important to the business of most of the world.

What they do is not relevant or meaningful anymore. Even in physics most of the mathematics that is needed was discovered long ago. These people may not have anything important to do!

In a sense they have a point that their world is no longer relevant, so it doesn't really matter much to what everyone else is doing if they are wrong, or ignore important research, and they do need to eat!

But they are different I think from physics people who are driven to find answers, and get to the truth—not just be convincing and keep getting paid.

Or I like to think they are. Who really knows and does it really matter?

Eventually our species like so many others before it will be extinct. In the meantime, well, we do what we do because, what else would we do?

And reality is that for most people perception IS reality. It's more important to believe that we're doing important things than to actually be doing important things.

Still it is sad. Often I feel sorry for these people who spend so much energy on things that are just not true that on some level they must know are not true.

But then again, other people make bigger sacrifices to care for themselves and their children.

People will do a lot to have a life, have kids, live comfortably. Lying is common in society's around the world.

Lying about math is not that big of a reach, not when a comfortable life, for you and your children, can be realized by just not caring about what is true about some math stuff.

But I do hope physics can to some extent escape falling into the same decline as the mathematics field has, but maybe it's inevitable.

Maybe species like humanity do die with a whimper, as I think many of us suspect—failing in every way, including in the search for truth.

Learning that pretend knowledge is better than truth, so that some people can feel comfortable, may just be a sign that a species is on its last legs.

### Wednesday, June 06, 2007

## Fully discretized physics, my discrete damped oscillator

It was back in 2002 when I discovered a discrete damped oscillator as an accident as it was the heart of a prime counting function that I was actually looking to find.

Here is the damped discrete oscillator:

With natural numbers, if y<sqrt{x} then

P(x,y) = x-1-\sum_{k=2}^y {((P([x/k],k-1)-P(k-1,sqrt{k-1}))\Delta P(k,sqrt{k})}

else P(x,y) = P(x,sqrt{x}) where

Delta P(k,sqrt{k}) = P(k,\sqrt{k})-P(k-1,\sqrt{k-1})

whenever k is not prime Delta P(k, sqrt{k}) equals 0, while it equals 1 if k is prime, so you get this oscillation, and program it and you can watch it drop as you iterate from k=2 up to sqrt{x}.

Oh yeah, it happens to also count primes but that is secondary here.

Now it turns out that discrete mathematics can be really, really hard, which is one of the reasons that continuous functions are so big in physics—they're easier.

But quantum mechanics brought in a discrete viewpoint, and I think it's just a matter of time before physics is fully discretized.

Now I've known about this for years without emphasizing it a lot, partly because I've been mulling it all over, but also because I'm a curious person, and THIS result allowed me to test the mathematicians with something relatively simple, where I could see how they operate.

Which gave me time to mull the questions over, and I've taken a few years and now feel like it's time to point out that, hey, here might be a key function in a fully discretized physics.

But don't expect help from mathematicians because they've been heaping scorn on me for years.

Ok, so yeah, I admit it, I have a thing against mathematicians. I remember back when I was an undergrad I had a professor who just ragged and ragged against them, and you know what?

He was right.

They don't understand science.

They go on and on about being "pure" but while this idea of mine was just a "pure" prime counting function, they ignored it, or on Usenet, ripped on it.

These people have lost touch with reality, so they've finally lost touch with mathematics as well, as mathematics as we know it is a tool we need to figure out reality.

Without a reason beyond what makes them feel good, mathematicians today are lost.

There is no other known way to count prime numbers using a discrete summation of a partial difference equation.

How could they just act like it doesn't exist?

I contacted a guy named Odlyzko who is like tops in this area, and he told me my research was of no interest after I pushed him a bit when he dumped me on a colleague who programmed that prime counting function in C. I posted his program later on the newsgroup sci.math and was not surprised when it was ripped upon by nasty posters.

That was just fun, but it was telling fun. Math people are disconnected from reality.

If these people actually gave a damn about anything other than pretending to actually care about the pursuit of knowledge they'd have been all over this years ago.

Mathematicians are not scientists. There are mathematicians who call themselves physicists who are NOT scientists, and some of them probably babble about primes and relating them to physics because of some muddled nonsense they trot out about the Riemann Hypothesis.

I don't expect them to give a damn either about my find as it's too simple for such people.

Who wants a partial difference equation that picks out prime numbers and sums to also give a count? I mean, like, what intellectually minded person could be interested in such a thing?

What intellectually minded person could not?

These people are not very bright. They are pretend bright.

They cannot find real theories that work in the real world, and they cannot help with the next physics revolution, when discrete mathematics takes over the field, and the easier continuous functions are only used maybe to teach or when people just want a quick rough guess.

The demonstration is in front of you. Brilliant mathematics reviled by mathematicians, where the ace I had to play was to point out that it is actually a discrete damped oscillator.

For years I've made my disdain of mathematicians known. If these people had an ounce of sense they'd have expected this sort of gambit, where I'd let them show their contempt for purity for years, so that I could come in and checkmate them on the physics.

To them "pure math" is whatever makes them look prettier or gives them money, like with a prize or a some fat federal grant.

They are NOT very bright. They are just pretenders, who fool a lot of the people, most of the time, including many of you who probably naively look up to mathematicians who cannot do physics, even to save their own skins.

Here is the damped discrete oscillator:

With natural numbers, if y<sqrt{x} then

P(x,y) = x-1-\sum_{k=2}^y {((P([x/k],k-1)-P(k-1,sqrt{k-1}))\Delta P(k,sqrt{k})}

else P(x,y) = P(x,sqrt{x}) where

Delta P(k,sqrt{k}) = P(k,\sqrt{k})-P(k-1,\sqrt{k-1})

whenever k is not prime Delta P(k, sqrt{k}) equals 0, while it equals 1 if k is prime, so you get this oscillation, and program it and you can watch it drop as you iterate from k=2 up to sqrt{x}.

Oh yeah, it happens to also count primes but that is secondary here.

Now it turns out that discrete mathematics can be really, really hard, which is one of the reasons that continuous functions are so big in physics—they're easier.

But quantum mechanics brought in a discrete viewpoint, and I think it's just a matter of time before physics is fully discretized.

Now I've known about this for years without emphasizing it a lot, partly because I've been mulling it all over, but also because I'm a curious person, and THIS result allowed me to test the mathematicians with something relatively simple, where I could see how they operate.

Which gave me time to mull the questions over, and I've taken a few years and now feel like it's time to point out that, hey, here might be a key function in a fully discretized physics.

But don't expect help from mathematicians because they've been heaping scorn on me for years.

Ok, so yeah, I admit it, I have a thing against mathematicians. I remember back when I was an undergrad I had a professor who just ragged and ragged against them, and you know what?

He was right.

They don't understand science.

They go on and on about being "pure" but while this idea of mine was just a "pure" prime counting function, they ignored it, or on Usenet, ripped on it.

These people have lost touch with reality, so they've finally lost touch with mathematics as well, as mathematics as we know it is a tool we need to figure out reality.

Without a reason beyond what makes them feel good, mathematicians today are lost.

There is no other known way to count prime numbers using a discrete summation of a partial difference equation.

How could they just act like it doesn't exist?

I contacted a guy named Odlyzko who is like tops in this area, and he told me my research was of no interest after I pushed him a bit when he dumped me on a colleague who programmed that prime counting function in C. I posted his program later on the newsgroup sci.math and was not surprised when it was ripped upon by nasty posters.

That was just fun, but it was telling fun. Math people are disconnected from reality.

If these people actually gave a damn about anything other than pretending to actually care about the pursuit of knowledge they'd have been all over this years ago.

Mathematicians are not scientists. There are mathematicians who call themselves physicists who are NOT scientists, and some of them probably babble about primes and relating them to physics because of some muddled nonsense they trot out about the Riemann Hypothesis.

I don't expect them to give a damn either about my find as it's too simple for such people.

Who wants a partial difference equation that picks out prime numbers and sums to also give a count? I mean, like, what intellectually minded person could be interested in such a thing?

What intellectually minded person could not?

These people are not very bright. They are pretend bright.

They cannot find real theories that work in the real world, and they cannot help with the next physics revolution, when discrete mathematics takes over the field, and the easier continuous functions are only used maybe to teach or when people just want a quick rough guess.

The demonstration is in front of you. Brilliant mathematics reviled by mathematicians, where the ace I had to play was to point out that it is actually a discrete damped oscillator.

For years I've made my disdain of mathematicians known. If these people had an ounce of sense they'd have expected this sort of gambit, where I'd let them show their contempt for purity for years, so that I could come in and checkmate them on the physics.

To them "pure math" is whatever makes them look prettier or gives them money, like with a prize or a some fat federal grant.

They are NOT very bright. They are just pretenders, who fool a lot of the people, most of the time, including many of you who probably naively look up to mathematicians who cannot do physics, even to save their own skins.

### Tuesday, June 05, 2007

## Quadratic residue method for finding primes

Here's an idea that I tossed out some months ago on sci.math only to be informed it was well-known, but I'm suspicious now of that claim so I thought I'd toss it out here.

The idea is to get quadratic residues modulo some non-square and iterate up with them.

Start with, say 29 and let 17 be the non-square.

That gives

29^2 - 17 = 824 = 8*103

and 103 is prime, so now you use 103^2 - 17 = 32*331, giving you 331, and now I'm wondering why I picked 17.

It's maybe quicker to just use n^2 - 2, as then you get mostly primes at first though as you go farther out with bigger numbers you do tend to get composites.

The idea just shifts you to another distribution of primes—primes with a quadratic residue of 17 or 2 or whatever non-square you pick—so the probability is higher that you will get primes than just going with naturals.

Hmmm…let me do one more iteration, so 331^2 - 17 = 8*13693, so it's starting to pick up a little steam. So I went from 29 to 103, to 331, to 13693, in three iterations.

Next would be 13693^2 - 17 = ( 2^3 )( 19 )( 43 )( 28687 ).

Then next is 28687^2 - 17 = ( 2^4 )( 1429 )( 35993 ).

So this thing is going slow, oh well, so maybe it's not so great an idea for that reason?

Here's another iteration:

35993^2 - 17 = ( 2^5 )( 179 )( 226169 )

and one more

226169^2 - 17 = ( 2^5 )( 1598513017 )

and one last one:

1598513017^2 - 17 = ( 2^5 )( 229 )( 859 )( 1879 )( 216036409 )

Went backwards with that one. Oh well, just an idea—

One more to leave on a high note:

216036409^2 - 17 = ( 2^5 )( 19 )( 76762713838183 )

Looks like you get about 5 bits added to the length per iteration.

The idea is to get quadratic residues modulo some non-square and iterate up with them.

Start with, say 29 and let 17 be the non-square.

That gives

29^2 - 17 = 824 = 8*103

and 103 is prime, so now you use 103^2 - 17 = 32*331, giving you 331, and now I'm wondering why I picked 17.

It's maybe quicker to just use n^2 - 2, as then you get mostly primes at first though as you go farther out with bigger numbers you do tend to get composites.

The idea just shifts you to another distribution of primes—primes with a quadratic residue of 17 or 2 or whatever non-square you pick—so the probability is higher that you will get primes than just going with naturals.

Hmmm…let me do one more iteration, so 331^2 - 17 = 8*13693, so it's starting to pick up a little steam. So I went from 29 to 103, to 331, to 13693, in three iterations.

Next would be 13693^2 - 17 = ( 2^3 )( 19 )( 43 )( 28687 ).

Then next is 28687^2 - 17 = ( 2^4 )( 1429 )( 35993 ).

So this thing is going slow, oh well, so maybe it's not so great an idea for that reason?

Here's another iteration:

35993^2 - 17 = ( 2^5 )( 179 )( 226169 )

and one more

226169^2 - 17 = ( 2^5 )( 1598513017 )

and one last one:

1598513017^2 - 17 = ( 2^5 )( 229 )( 859 )( 1879 )( 216036409 )

Went backwards with that one. Oh well, just an idea—

One more to leave on a high note:

216036409^2 - 17 = ( 2^5 )( 19 )( 76762713838183 )

Looks like you get about 5 bits added to the length per iteration.

## Discrete damped oscillator, prime numbers

Back in 2000 I discovered a damped discrete oscillator, which I noticed later as I wasn't looking for that, as I was looking for a prime counting function.

Here is the damped discrete oscillator:

With natural numbers, if y<sqrt{x} then

P(x,y) = x-1-\sum_{k=2}^y {((P([x/k],k-1)-P(k-1,\sqrt{k-1}))\Delta P(k,\sqrt{k})}

else P(x,y) = P(x,\sqrt{x}) where

Delta P(k,\sqrt{k}) = P(k,\sqrt{k})-P(k-1,\sqrt{k-1})

and that is a damped oscillator as whenever k is not prime Delta P(k,sqrt{k}) equals 0, while it equals 1 if k is prime, so you get this oscillation that drops as you iterate from k=2 up to sqrt{x}.

Graph it. Looks like a bouncing ball.

Anyone have a clue how to figure out the period? That actually could be a good research question as you can move from summing a partial difference equation, which is what's being done above, to integrating a partial differential equation.

Could primes and bouncing balls be related? Like somehow wrapped up in a bouncing rubber ball is information about prime numbers?

I'm posting to a physics group as I've talked about this result with math people, well, since 2000!

I don't think they care, especially not about a physics question like, what is the period of the damped oscillation?

And, are there any other discrete damped oscillators known?

>From the run around they've given me over the years it is clear to me that mathematicians do not care about such things, but I'm including the sci.math newsgroup just in case.

I guess the result is not "pure" enough for them! After all, what do mathematicians care about damped oscillations?

The big question to me is, can any of you out there calculate the period? Oh, and yes, the discrete calculation gives the count of prime numbers, perfectly, out to positive infinity.

The mathematics is absolutely correct. Perfectly correct.

To get a prettier look at the equations as you can see the in a pdf, you have to go to my Extreme Mathematics Google Group:

http://groups.google.com/group/extrememathematics/web/counting-primes

I presented the paper to a couple of math journals but they all rejected it. Maybe I should re-write for a physics journal focusing on the damped oscillation?

Here is the damped discrete oscillator:

With natural numbers, if y<sqrt{x} then

P(x,y) = x-1-\sum_{k=2}^y {((P([x/k],k-1)-P(k-1,\sqrt{k-1}))\Delta P(k,\sqrt{k})}

else P(x,y) = P(x,\sqrt{x}) where

Delta P(k,\sqrt{k}) = P(k,\sqrt{k})-P(k-1,\sqrt{k-1})

and that is a damped oscillator as whenever k is not prime Delta P(k,sqrt{k}) equals 0, while it equals 1 if k is prime, so you get this oscillation that drops as you iterate from k=2 up to sqrt{x}.

Graph it. Looks like a bouncing ball.

Anyone have a clue how to figure out the period? That actually could be a good research question as you can move from summing a partial difference equation, which is what's being done above, to integrating a partial differential equation.

Could primes and bouncing balls be related? Like somehow wrapped up in a bouncing rubber ball is information about prime numbers?

I'm posting to a physics group as I've talked about this result with math people, well, since 2000!

I don't think they care, especially not about a physics question like, what is the period of the damped oscillation?

And, are there any other discrete damped oscillators known?

>From the run around they've given me over the years it is clear to me that mathematicians do not care about such things, but I'm including the sci.math newsgroup just in case.

I guess the result is not "pure" enough for them! After all, what do mathematicians care about damped oscillations?

The big question to me is, can any of you out there calculate the period? Oh, and yes, the discrete calculation gives the count of prime numbers, perfectly, out to positive infinity.

The mathematics is absolutely correct. Perfectly correct.

To get a prettier look at the equations as you can see the in a pdf, you have to go to my Extreme Mathematics Google Group:

http://groups.google.com/group/extrememathematics/web/counting-primes

I presented the paper to a couple of math journals but they all rejected it. Maybe I should re-write for a physics journal focusing on the damped oscillation?

### Friday, June 01, 2007

## JSH: War of attrition

The Math Wars are to me all about how some people with position and power forget the power of the pen, and sit letting the pot slowly come to a boil.

When I feel a bit down—like if insulting posters start getting to me—I can do things like do Google searches on my open source project "Class Viewer" which took the number one spot for that search string, years ago.

It is all over the world. I especially feel honored looking at the Chinese page, where words I typed years ago to describe my project have been translated.

That is an odd feeling. And that is just one thing.

Just a few days ago I started talking about a "managed copy" idea of mine and just typing up a post on my blog I found myself talking about it as digital media equipment self-encryption and of course went to the initials to designate it DMESE.

That is just one more thing.

Archimedes said that with a level long enough and a place to stand he could move the world because he could conceive of greatness on a scale that most people cannot.

I can move the world.

Not one of you can say the same.

My posts get translated to languages across the planet. I watch ideas of mine travel around the world.

Yet I am still stopped by academics who are dead-set on fighting the Math Wars to the bitter end, and mostly they just wait.

Yes, Princeton academics can stop me today. Yes, Harvard academics can hold the line today.

But they burn everything their universities have built up over the years in the process and I let them.

I emailed the University of California at Berkeley to note some unethical behavior by Arturo Magidin, and noticed at that point that Ralph McKenzie is listed as faculty, where it notes he is at my alma mater Vanderbilt University.

Yup, I know that as I visited him there years ago, before my paper was published, retracted after sci.math'ers including Magidin trumped the formal peer review system with some emails, and the freaking math journal died.

Academics can only sit and wait, while I move forward over time. Knowing that at the end, I go for the entire system to reform it.

And I will change their world.

I send papers to math journals and I damn well get a reply. Sure, they're polite rejections but they had better reply to me.

You people don't get it because I post among you, and you think that because I post I must be at your level.

Yeah only to use you in the Math Wars. I want mathematicians around the world to keep thinking about what you are thinking. I want them working hard to figure out how well they have you in hand.

I want them working to keep you.

I want them to demean themselves, crawl on their hands and knees to keep you believing in them.

And they are doing it.

While the war of attrition continues and it is all about inertia and momentum as I have always needed time.

If the world knew too quickly what my discoveries really are, then the true targets could have escaped, but now the net closes, and you are the fish that were always part of the trap.

You were always the bait.

They care so damn much about what you people think of them that they are willing to lose everything, grasping for what they cannot hold.

Public opinion is such a great thing. I love it. Public opinion is all about perception.

People like Andrew Wiles are nothing without the applause or the dreams of it. They'll hold on, and hold on, and hold on, and give their energy, their very life blood to hold on to it, even if that is the means that is used to build the energy to end the wars.

They give their life's blood for you to believe in them. And that is the energy that drives this forward.

That is the hope of the world.

It was always about time. I have always needed time.

When I feel a bit down—like if insulting posters start getting to me—I can do things like do Google searches on my open source project "Class Viewer" which took the number one spot for that search string, years ago.

It is all over the world. I especially feel honored looking at the Chinese page, where words I typed years ago to describe my project have been translated.

That is an odd feeling. And that is just one thing.

Just a few days ago I started talking about a "managed copy" idea of mine and just typing up a post on my blog I found myself talking about it as digital media equipment self-encryption and of course went to the initials to designate it DMESE.

That is just one more thing.

Archimedes said that with a level long enough and a place to stand he could move the world because he could conceive of greatness on a scale that most people cannot.

I can move the world.

Not one of you can say the same.

My posts get translated to languages across the planet. I watch ideas of mine travel around the world.

Yet I am still stopped by academics who are dead-set on fighting the Math Wars to the bitter end, and mostly they just wait.

Yes, Princeton academics can stop me today. Yes, Harvard academics can hold the line today.

But they burn everything their universities have built up over the years in the process and I let them.

I emailed the University of California at Berkeley to note some unethical behavior by Arturo Magidin, and noticed at that point that Ralph McKenzie is listed as faculty, where it notes he is at my alma mater Vanderbilt University.

Yup, I know that as I visited him there years ago, before my paper was published, retracted after sci.math'ers including Magidin trumped the formal peer review system with some emails, and the freaking math journal died.

Academics can only sit and wait, while I move forward over time. Knowing that at the end, I go for the entire system to reform it.

And I will change their world.

I send papers to math journals and I damn well get a reply. Sure, they're polite rejections but they had better reply to me.

You people don't get it because I post among you, and you think that because I post I must be at your level.

Yeah only to use you in the Math Wars. I want mathematicians around the world to keep thinking about what you are thinking. I want them working hard to figure out how well they have you in hand.

I want them working to keep you.

I want them to demean themselves, crawl on their hands and knees to keep you believing in them.

And they are doing it.

While the war of attrition continues and it is all about inertia and momentum as I have always needed time.

If the world knew too quickly what my discoveries really are, then the true targets could have escaped, but now the net closes, and you are the fish that were always part of the trap.

You were always the bait.

They care so damn much about what you people think of them that they are willing to lose everything, grasping for what they cannot hold.

Public opinion is such a great thing. I love it. Public opinion is all about perception.

People like Andrew Wiles are nothing without the applause or the dreams of it. They'll hold on, and hold on, and hold on, and give their energy, their very life blood to hold on to it, even if that is the means that is used to build the energy to end the wars.

They give their life's blood for you to believe in them. And that is the energy that drives this forward.

That is the hope of the world.

It was always about time. I have always needed time.