Saturday, March 20, 2010


JSH: Trying to stop posting

I don't like angry people who insult me in posts, and for years I've made it a point to NOT stop posting partly to infuriate them (what idiots, like trying to force people out of a public park), but also because I like posting, and there are ideas I'm pursuing that I like talking out and arguing.

One philosophy I noted years ago is that math ideas don't care. If you think you have a good idea in math, argue against it, at least to yourself. The correct ideas don't care. They don't need you. But arguing for your ideas as well at least can help you figure out if they are correct.

There is some hard to explain joy in arguing over your own ideas. And as time went on I highlighted that joy by emphasizing "my math". It's my math. But of course correct ideas—notice my emphasis on correct not saying mine are—really don't belong to anyone. Some are just privileged to find them. But once found they don't come with a signature tag. They can't. But if you post a lot about them on Usenet at least people know they came into this world through you. I liken it to giving birth in a good mood. Taking a crap when you're constipated in a bad one.

Finding ideas is PAINFUL. Whether they are correct or not! If you don't expect pain then you don't understand discovery.

Pain is part of the process.

If you don't hate yourself often while trying to find new things then you're not really trying.

Ok, enough with slogan attempts I might try to put on t-shirts. But reality is that having people insult you, yes, is painful, but it is NOTHING compared to the pain that will be inflicted upon you just by the belief that you have brand spanking new important ideas.

I don't know why exactly. I think it's unfair. But it is I think a lot of why you are probably done with math discovery by the age of 40. In your youth you press on. As you grow older you just don't have the energy to push through all that pain any more.

Oh, so I'm trying to bring it down. Stop posting. But doing it on my own terms. Not because some idiots called me "subhuman" or ordered me to stop. Not because some people berated me endlessly about the worthlessness of my efforts. It's my math. They are MY efforts. I CHOOSE. I choose what's important to me. Not strangers on Usenet.

But eventually you get older and times change and it becomes time to shift. So I'm going to try to shift! Other posters don't need to do anything different. It is not and never has been their decision. I want to emphasize that point.

You can't call me crazy and force me off of Usenet. Stupid people tried for over a decade and it didn't work, but didn't stop them from trying.

But I can choose to move on. So here's giving it the "old college try". I'll stop typing after the signature.

Sunday, March 14, 2010


JSH: Twin primes probability correlation

With twin primes a simple approach rips the prime distribution out of the equation.

My twin primes probability probability calculation works by taking the ACTUAL COUNT of prime numbers in the interval p_{j-1}^2 to p_j^2, and multiplying times:

prob = ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*…*(1/2)

The result is easy as it is just multiplying the probability for each prime x in that interval that it is NOT true that

x + 2 ≡ 0 mod p

which probability is just the result of dividing one minus the number of non-zero residues by the total number of residues together to get the total probability that a prime plus 2 is also prime.

For example, between 5^2 and 7^2, there are 6 primes. The probability then is given by:

prob = ((5-2)/(5-1))*((3-2)/(3-1) =3D (3/4)*(1/2) =3D 0.375

And 6*0.375 =3D 2.25 so you expect 2 sets of twin primes in that interval. And those twin primes are 29, 31 and 41, 43.

(Compare the simplicity of the calculation with traditional approaches which leave in the prime distribution itself which generates a LOT more complexity.


Since the result equals prediction correlation is 1.

But that's just one example, and you need to do a lot of them.

Within the bigger picture I've also predicted a smaller impact related to the distance p_j - p_{j-1}. Where I have hypothesized that the greater that distance the greater the accuracy of the prediction, which is also a mathematically precise statement as "accuracy" has a mathematical meaning in this context as does "correlation".

Thursday, March 11, 2010


JSH: Math, logic, pragmatic reality and primes

Years ago I noted that with math people I was stuck unable to convince them with mathematical proof, which doesn't quite make sense, and it puzzled me for years, and of course on Usenet posters claimed otherwise (I found it to be true off Usenet as well, for instance with mathematical journals), but now you can see it in action with what I call my prime residue axiom.

Years ago I noticed that you could consider twin primes probability in a fairly simple way by assuming that primes have no preferred residue modulo each other, which gives a nice little formula:

prob = ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*…*(1/2)

where you look at the interval p_{j-1}^2 to p_j^2, as my simple idea was to use the actual count of primes WITHIN that interval with the prob calculation, so it keeps shifting, as you go higher, you get more primes, and my simplification works rather well.

THAT is ALL from over 3 1/2 years ago. I pushed the idea further back then, realized you should be able to do something similar for prime gaps of arbitrary even size, and realized some depressing things. If true, my simple idea PROVED the twins prime conjecture and DISPROVED Goldbach's Conjecture. But in a probabilistic proof!

All that is from over 3 1/2 years ago. I argued about a few things on Usenet and wandered off, and recently brought the subject up again and decided I had an axiom which I called the prime residue axiom.

Arguments erupted and posters argued both sides: some claimed I didn't have an axiom, others claimed that what I had was already proven but so what?

Oh, and I forgot, you can also find ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*…*(1/2), in the twin primes constant!


Now I know how people can ignore bold facts like seeing a formula from a probabilistic interpretation in established literature, which does a rather good job of predicting twin primes probability with a simpler formula than what is currently taught, and argue BOTH SIDES as if it were nothing at all!

People can in fact confidently proclaim that 2+2=5 and believe it, if you understand human nature and how the mind works.

So there is no doubt that this approach is a simplification, it ties in easily with prior known research, and has scary implications like that you can prove the Twin Primes Conjecture and disprove Goldbach's Conjecture with one interpretation.

But you may have noticed that the math world isn't exactly buzzing with the news!

If you know your math history you know that study of twin primes got big about the time I say a rather remarkable error entered into the mathematical field, where I've proven that the ring of algebraic integers can be trivially shown to contradict with the field of complex numbers!

That allows you to appear to prove things without having actually done so, and as it has been in the field for over a hundred years it has selected people who are tolerant of the error.

Such people can believe two different and contradictory things at the same time.

The mathematical flaw at the heart of established number theory SELECTS such people, as people who are not so capable could not be number theorists WITH THAT FLAW.

That is, if you were not a person with that peculiar ability, even if you did not understand that something was wrong with the ring of algebraic integers thoroughly, you might have some weird feeling that would push you into a different field, like topology.

Ok, so back to prime numbers! Turns out I have multiple results around prime numbers. The people who can believe two different and contradictory things always say that none of them are important! The prime residue axiom though leads to a prime gap equation. It took me a while to get that correct but I think I have the correct equation as of now on my math blog (though I haven't posted it on Usenet, having put up flawed prior versions).

So why not just use the prime gap equation over a wide range to prove I'm right?

Because it won't matter to the people who can believe two different and contradictory things at the same time, who have been selected into number theory by the core error I found, which means they cannot be moved by mathematical proof, as given ANY proof they can believe it's opposite just as easily as believe in the proof itself. Damn inconvenient, eh?

It's a conundrum. These people dominate number theory because the error dominates number theory.

I assure you they are special people whose brains allow them to believe two different and contradictory things at the same time.

The error that entered into number theory over a hundred years ago is perfect for these type of people and they found a comfortable home in number theory and fashioned "pure math" to secure that home. Notice 'pure math" came into the field at about the time of the error and at about the time that the twin primes conjecture was made.

To themselves they are normal!!!

You will NOT get anywhere trying to explain to them that it's not normal to be able to believe two opposite and contradictory things at the same time, as their brains work that way. To them it's as natural as breathing.

The situation is actually kind of fascinating in many ways. God only knows what can break the hold of these people on number theory. But I assure you that facts and therefore mathematical proof, cannot.

Tuesday, March 09, 2010


JSH: Why fame is lame

One of the things that gets posters who argue with me more hot and bothered than anything else is this notion that I'm trying to get famous. I'm not. In fact, it's quite dangerous to get famous. Or to be a celebrity which is not necessarily famous in my opinion but is more well-known as a THING, and in fact, celebrities in the US have a life expectancy of 55 years of age, less than black males.

The tales that so enthrall people of celebrity meltdowns are indicative of an illness associated with it. Somehow it seems to mess people up, maybe because human beings were not built for it.

So let's look at some famous people and I'll look at science and math people because it's math newsgroups:

Turing: did a lot of great work during World War II to protect his country, breaking German codes and such. After the war he was hounded for being gay, chemically castrated, and pushed to suicide. (His mother thinks he was murdered). He was treated horribly and the British government recently apologized for that treatment.

Einstein: ostracized by his colleagues as irrelevant, in his later life this greatest of scientists worked futility and alone on the "great proof" so he was a crackpot in his later life, having already BEEN famous for his prior work. He married his 2nd cousin—so why not some beautiful super model or something (ok, there weren't any back then but why his dowdy 2nd cousin?).

Newton: history says he died a virgin. It also says he was really mean.

My favorite though is Tesla. He fell in love with pigeons. Said that women's jewelry scared him. He died alone in a hotel room divisible by 3 because he wouldn't stay in any other room. Oh and he was really into pigeons and called the greatest love of his life one particular pigeon which when it died he said there was no reason left for him to discover anything further as his inspiration had left him.

Archimedes: slaughtered by a Roman soldier. Various tales as to how it all happened.

One remarkable theme that is recurring is problems with love interests or a lack of one. Einstein with his 2nd cousin. His "normal" relationship was BEFORE his Nobel prize, when he actually fathered children. Turing hounded for being gay. Tesla, in love with pigeons. Newton, a virgin.


My theory is that major discovery angers men around you. The major discoverer is automatically a threat as he's appealing to women and emasculating to men, so they make his life miserable. One way to be certain he's miserable is to remove romantic interests.

Einstein was pushed aside deliberately by his physics colleagues who said his ideas were not relevant any more.

That is typical. When you make major discoveries at a high enough level, you will get hurt for it. Guaranteed.

The major mathematical figure who seemed to best all of it that I've noted is Gauss. Somehow he managed to escape all of the above, have a lot of kids, and not fall in love with pigeons.

It's worse in our modern age. People like a winner but love to attack a winner. Most of the attacks are hidden from view.

You learn to be guarded as people ARE out to get you. But saying so is dangerous as they'll just say you're paranoid and crazy.

Safer to just fall in love with pigeons.

Monday, March 08, 2010


JSH: Biggest mystery, pondering again hostility

I've been curious for years about hostile reactions to my postings, and for lots of reasons, including in the past worrying that posters were working to block widespread acceptance of my research, which is a concern which has faded. It's not that I don't think negative claims against my work have an impact. I think they do. It's just that I now see an advantage in the "blocking" as I see it, as it allows me to work on problems without being bothered with concerns of anyone stealing my ideas, often for years at a time. Reality is that mathematicians probably feel terror at the idea of continuing any of my research, knowing they will face outright hostility and rage in response. That protects my research directions.

However it does remain puzzling, as one benefit I've gained over the years has been the gift of just being occupied with my various mathematical musings, which I've noted are of great interest to me. To be upfront, I even call it, my math. I even named my math blog, my math. It IS my math.

Now some will berate me for posting about my math musings as if it's this terrible thing for me to put it forward as important when I think it's important. Which doesn't seem to work I've noticed. Somehow posts still seem to keep coming out about my math despite their efforts, despite years of trying by them, and many more besides them, most of whom years ago gave up.

So what gives? Many of these posters routinely tell me I'm a failure, and claim that I have nothing to show for years of effort. Um, but I have an entire blog of my math. I like it. They may claim that no one else does. And that my efforts are pointless and futile, and I wonder, why?

If I say I like keeping myself occupied and have done so with my math, how can they claim that my efforts are pointless and futile as they continue to work at convincing me to stop posting, when after over a decade such efforts have failed?

Why do they keep doing the same thing over and over again without any change in the result?

Even more intriguingly, they claim I am the one who does that, but today I have my prime counting function. It counts primes. It works. They say, it's not new or interesting, but to me, it is my math. If you had your own three-dimensional prime counting function, a P(x,y) function while the math world still has a pi(x), two-dimensional function, would you not at least consider that kind of cool as YOUR math?

I discovered tautological spaces. They say that's not new or interesting. But it's my math. I came up with my own definition of mathematical proof. They say there are plenty of such definitions. But I say, it's my math.

My math is the object ring. I find it interesting. I find my prime residue axiom (even if you don't think it's an axiom, I do), fascinating. With it I have a prime gap equation, which can predict counts if twin primes, or other gaps. It's my math. I like it.

Result after result has intrigued me for years. Yes, some of those results I feel should be important to others and I've said as much, as, for instance, part of my math is showing the ring of algebraic integers contradicting the field of complex numbers which I think should interest SOMEONE, but they say, it's wrong. They say it's not interesting. I say, it's my math.

So what is the mystery?

How can seemingly intelligent people keep doing the same thing over and over again, year after year, without any change in the result?

I have lots of results that I call my math, which THEY say are all worthless, useless or previously known. But I like them, because they're my math.

Does anyone know why people would do the SAME THING year after year after year after year without any change in the result?

If I'd stopped years ago when the first posters started on the endless treadmill of trying to block free speech on Usenet by insulting me, then I don't think I'd have my own prime counting function, nor my object ring. I find it hard to believe I'd have my prime residue axiom, or my tautological spaces.


How do some define insanity?

Would you have listened to them? Did you? Do you now?

They protected my research for years because they could block so many of you worldwide off from fascinating mathematical concepts. Isn't THAT intriguing?

I find it fascinating. How much of my math would have been your math if that had not occurred? Thankfully that is a question that will never be answered. History would have changed. But maybe it was all fate. So many different things had to occur at just the right time, including the rise of the Internet, the arrival of Google, and now the dominance of Twitter.

Given what they knew at the time those posters had no way of knowing that years later, some company called Google would arrive, and a search on its search engine on the definition of mathematical proof would bring up a page on my math blog as #1 for people all over the world. Who knew? Who could have guessed?

Now I've been amused by those posters who do THE SAME THING YEAR AFTER YEAR WITH THE SAME RESULT declaring boldly that Google search results do not matter? Was I surprised by their assertions?


Oh, so why are they still so confident? Seems they have a rather naive definition of fame. Like most people they seem to think they know it when they see it. They say my aim is fame (and maybe fortune?) and that as long as I'm not famous by their standards then I have nothing.

What small minds. As if fame is a motivator for someone like me.

Friday, March 05, 2010


JSH: Depressing reality, prime reality

There is a lot of satisfaction with having my own axiom, which I had the honor of naming as I'm the discoverer, which is of course, the prime residue axiom, and yes, posters can reply in the negative or derisively, but there you see the difference between finding something and talk.

Anyone can rip on anything. But who could actually find the prime residue axiom? I did.

But now comes the depressing part, which I realize every time I discover something, which is another reason in actuality for me to stop, if I cared for recognition, because every discovery makes recognition more unlikely as it makes my research that much more threatening.

So it could be decades now. Having reached 40 it occurs to me that I don't have any juice left for major discoveries anyway. It is a young person's game, and unfortunately mostly a young man's game. Given my experiences I wonder if maybe there are fewer women discoverers because they don't like to argue! (Hmmm…does that sound right?) Or maybe it's just chance or something else. I feel confident there will be women who make major discoveries at my level and beyond, someday.

But it's a young person's game. Which is another way I think to understand that sadly, no, a lot of "mathematicians" today aren't doing valid research, in my opinion. Young people make the major breakthroughs. Not old geezers.

But old geezers running things in the math world today I'm sure do not give a damn about how primes behave between each other in a way that explains that sense of random with primes. I don't think the old geezers could care less about the answers. I think they're too old to care. They care more about their mortgages, the stature they've accrued, etc. crap that is ultimately meaningless, but oh so enticing to the weak minded.

I feel sorry for some of you. With answers to such deep questions so close to live in a world that may refuse to get to them because some people have their NEEDS. Like their need for tenure when I've promised to try and abolish it. Or their need to protect their egos when my research shatters the lie of their "accomplishments".

While I feel satisfied with the answers I have, so it's free and easy for me. And I get to live in a world where I know reality unlike anyone else, because I know how far some people can go to lie, and how the world lets them. But our world is an efficiency built upon billions of years. The only reality we have, it was here before any of us got here, it will be here long after we're gone.

I'm fine with reality. Its answers are beautiful and I know some of them. It's not my problem if most of you don't, won't, but will pretend that you do. When you're gone, the world will spin just the same.

I have my own axiom. It's so weird. I find it harder and harder to see myself the same way as each day goes by, and harder to do the things I did before, as I contemplate it. You know it took me over 3 1/2 years to even put it out as an axiom? Before I just posted it as, hey, primes might not care about their residues modulo each other. And didn't quite maybe consciously make the leap though on some level I'm sure I knew. And it took me over three years to dare say.

Sometimes I imagine myself as someone in a ship that moved a high velocity against first the sound barrier, to break through it, and shoot ever more rapidly in the ensuing silence. I can see myself as this dart of a ship that is a blur, all alone and moving more rapidly at increasing speed until…what's next?

There is a Universe in front of me.

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