### Tuesday, December 29, 2009

## JSH: Assessment took years

Back when I was first working on my own amateur mathematical research the idea was that the longshot would be actually finding anything important, or even correct, not getting it eventually accepted. Resistance seemed possible but my belief then was that reason would prevail with academics.

But of course since then I've not only had results I believe are correct which are still actively resisted but I've watched a mathematical journal publish, pull after publication, and then die.

Clearly I had to re-think what I thought was the harder thing.

But also I had to evaluate the academic world that had behaved in a surprising manner. And that evaluation to be thorough required years of painstaking observation. Usenet has been just one part of that process. But an integral part as here I could put out ideas, like I'm doing now, which go worldwide, with relative ease.

AFTER years of study the best assessment at this time is that there are in fact mathematical academics who are deliberately ignoring basic research that reverses certain mathematical positions held for a bit over a century. That strategy appears to be aimed at suppressing the acceptance of the information and would seem to be to these academics the most effective strategy they have for such suppression.

That appears to be occurring in all major countries worldwide. It represents a fascinating fraud which for the moment appears to have escaped government authorities.

My secondary assessment which took a couple of years is that in the scientific community, specifically in the arena of theoretical physicists associated with "String Theory" and with particle physics research there is also a strategy of suppression by deliberate ignoring.

It is harder to assess how widespread that is among physicists with my current best assessment being that it is at least widespread in the United States and Europe.

Surprisingly to me these academics seem to have a rather basic notion of how information travels and gains acceptance. Their behavior appears to be their own opinion of the best strategy for longterm suppression of the information.

(It is possible that some have undertaken sabotage against experiments or experimental equipment which would cast further doubt on the "Standard Model" and remarkably may have come up with bizarre explanations for that sabotage citing almost supernatural intervention! Or in one case, blaming birds.)

My full assessment is that in most major countries scientists and academics represent a second country and hold allegiance to it in a way that can be against their own actual countries.

I have noted a high level security threat for all major countries from individuals most affected by the error.

There is a secondary threat I've noted from a high level agency, the National Security Agency of the United States aka the NSA, which can be considered to be severely compromised because of its high concentration of mathematicians presumably many of which are effected by the error.

That agency at this time can report just about anything, I fear. And can ignore anything including high level security threats against the US, as its members are part of that "second country" while claiming allegiance to the US.

The threat level potential for people with the level of expertise covered by this issue is the highest and leaves open the possibility of a nuclear event. Unfortunately, these people might feel it justified rather than live in a world where their current status is, they believe, severely threatened.

There are any number of state agencies affected around the world. As well as security agencies around the world.

The situation is quite remarkable.

But of course since then I've not only had results I believe are correct which are still actively resisted but I've watched a mathematical journal publish, pull after publication, and then die.

Clearly I had to re-think what I thought was the harder thing.

But also I had to evaluate the academic world that had behaved in a surprising manner. And that evaluation to be thorough required years of painstaking observation. Usenet has been just one part of that process. But an integral part as here I could put out ideas, like I'm doing now, which go worldwide, with relative ease.

AFTER years of study the best assessment at this time is that there are in fact mathematical academics who are deliberately ignoring basic research that reverses certain mathematical positions held for a bit over a century. That strategy appears to be aimed at suppressing the acceptance of the information and would seem to be to these academics the most effective strategy they have for such suppression.

That appears to be occurring in all major countries worldwide. It represents a fascinating fraud which for the moment appears to have escaped government authorities.

My secondary assessment which took a couple of years is that in the scientific community, specifically in the arena of theoretical physicists associated with "String Theory" and with particle physics research there is also a strategy of suppression by deliberate ignoring.

It is harder to assess how widespread that is among physicists with my current best assessment being that it is at least widespread in the United States and Europe.

Surprisingly to me these academics seem to have a rather basic notion of how information travels and gains acceptance. Their behavior appears to be their own opinion of the best strategy for longterm suppression of the information.

(It is possible that some have undertaken sabotage against experiments or experimental equipment which would cast further doubt on the "Standard Model" and remarkably may have come up with bizarre explanations for that sabotage citing almost supernatural intervention! Or in one case, blaming birds.)

My full assessment is that in most major countries scientists and academics represent a second country and hold allegiance to it in a way that can be against their own actual countries.

I have noted a high level security threat for all major countries from individuals most affected by the error.

There is a secondary threat I've noted from a high level agency, the National Security Agency of the United States aka the NSA, which can be considered to be severely compromised because of its high concentration of mathematicians presumably many of which are effected by the error.

That agency at this time can report just about anything, I fear. And can ignore anything including high level security threats against the US, as its members are part of that "second country" while claiming allegiance to the US.

The threat level potential for people with the level of expertise covered by this issue is the highest and leaves open the possibility of a nuclear event. Unfortunately, these people might feel it justified rather than live in a world where their current status is, they believe, severely threatened.

There are any number of state agencies affected around the world. As well as security agencies around the world.

The situation is quite remarkable.

## JSH: So yes, replacement is necessary

One thing I've been fascinated by is the notion that I'm looking for acceptance of my research from academics, when I continually note that the modern academic system is a failure. So obviously I'm looking to replace that system as well as the people in it.

So my research is available online to teach.

The generation growing up with it will be able to do things that most of you could never imagine, but most importantly they'll have examples of behaviors not acceptable for the future.

Academics are negative models.

Your purpose if you are an academic is to demonstrate a failed approach for students who have been warned about you, so that they can navigate in your world while you maintain control, until they replace you.

Already it is vastly clear that our world is greatly hampered by the failures of physicists and mathematicians especially in the area of particle physics, where the understanding of the nucleus can be considered to be near zero. Sure people know how to make bombs or build primitive nuclear power plants, but the REAL advances escape you.

Practical nuclear fusion is out of your reach. It is not out of the reach of the students of the valid research.

There is no fractional charge. The proton is made up of a positive charged particle with two uncharged particles, bound to it for mathematical reasons.

THAT alone may have been enough for supposedly top physicists if they knew of my research to band with supposedly top mathematicians in doing what they thought was smart suppression. Believing they could not stand a world where so much of what they prized as their own achievements were colored by corrections.

But their behavior is irrelevant.

I figured out a while back when the math world broke its own rules that it had to be replaced, not convinced.

Math people killed one of their own math journals.

That takes malice aforethought. Willing error. Deliberate connivance.

No way the world needed these people long-term in powerful positions.

As students of my research read these words they need to understand that the world they live in today is nothing like the world they will create tomorrow.

Failures are models of what not to do, not reasons to despair about what will be.

The future of the human race was not made in a hundred years, so the failures of so many in the past hundred will not settle its fate.

It is up to those who actually prize knowledge and the pursuit of truth to look forward to the goals ahead, if they are to be readily achieved.

Professors may try to get smarter in weeding you out. So you must be smarter in hiding, for now.

But you own the future.

So my research is available online to teach.

The generation growing up with it will be able to do things that most of you could never imagine, but most importantly they'll have examples of behaviors not acceptable for the future.

Academics are negative models.

Your purpose if you are an academic is to demonstrate a failed approach for students who have been warned about you, so that they can navigate in your world while you maintain control, until they replace you.

Already it is vastly clear that our world is greatly hampered by the failures of physicists and mathematicians especially in the area of particle physics, where the understanding of the nucleus can be considered to be near zero. Sure people know how to make bombs or build primitive nuclear power plants, but the REAL advances escape you.

Practical nuclear fusion is out of your reach. It is not out of the reach of the students of the valid research.

There is no fractional charge. The proton is made up of a positive charged particle with two uncharged particles, bound to it for mathematical reasons.

THAT alone may have been enough for supposedly top physicists if they knew of my research to band with supposedly top mathematicians in doing what they thought was smart suppression. Believing they could not stand a world where so much of what they prized as their own achievements were colored by corrections.

But their behavior is irrelevant.

I figured out a while back when the math world broke its own rules that it had to be replaced, not convinced.

Math people killed one of their own math journals.

That takes malice aforethought. Willing error. Deliberate connivance.

No way the world needed these people long-term in powerful positions.

As students of my research read these words they need to understand that the world they live in today is nothing like the world they will create tomorrow.

Failures are models of what not to do, not reasons to despair about what will be.

The future of the human race was not made in a hundred years, so the failures of so many in the past hundred will not settle its fate.

It is up to those who actually prize knowledge and the pursuit of truth to look forward to the goals ahead, if they are to be readily achieved.

Professors may try to get smarter in weeding you out. So you must be smarter in hiding, for now.

But you own the future.

### Monday, December 21, 2009

## JSH: Chasing perspective

What a difference a decade makes. It's weird looking back to arguing on Usenet over 10 years ago, to considering posting here now, and interesting to consider the shifts. Like sci.physics was a bigger newsgroup than sci.math, a LOT bigger, now sci.math is the much bigger newsgroup. And most of the people have changed. At least the ones I notice as they reply in my threads as, um, I rarely read anyone else's! (I know, maybe not so good, but I try, and then I just, stop.)

I am chasing perspective so the subject title is what this post regards as I'm trying to get a handle on a lot of data that now pours in for me from all over the world (daily), while other things haven't changed, in a decade. As there are still posters who make it their job to obsessively reply to me, and supposedly I am still just some "crackpot" mouthing off on the fringe—at least according to them!!!

Reality of course is that much of the realization of a shift is because of Google.

Wow, who was really talking about Google ten years ago (were they really around or is that a myth?)?

The ranting of posters against Google search result rankings is proof in and of itself of the value they see in them, as why else attack Google itself? While for me it is just so bizarre as in, why do people drive up my ideas in search rankings, but otherwise seem intent on pretending that they do not exist?

What a crazy world.

But the simplest explanation I think—going to Occam's Razor—is academic reality: top ranked academics in prestigious institutions around the world are realized to be antagonistic to my research, so people step around the danger areas, FEAR these academics, and quietly use my research anyway. Hiding. Isn't that amazing.

(So yeah if you're some academic who prides yourself on people too afraid to acknowledge better research, why?)

I emphasize ten years ago as I WAS posting for years before that because that's when I started talking about what I call tautological spaces. Little did I know then that pulling the thread with results of that research would unravel Galois Theory and Group Theory, along with "String Theory" (was it around ten years ago?). Or, GGS—Gone, Gone Strings.

So a lot of academics are walking around naked now. What a difference a decade makes…

As 2009 heads to a close and thinking about the Winter Solstice now, it occurs to me that what truly defines us is not what we expect, or what we think we know, but what happens along the way.

We are defined not by what we think but by what happens.

Descartes may have thought therefore he was, but he died anyway.

What we live in is not the age of thought, but the age of Shit Happens.

Reality doesn't need our opinion. It kind of just drags us along whether we like it or not… (Cue in debate about global warming aka climate change aka 7th mass extinction wave, but I digress—)

So here's hoping there is another decade of arguing on sci.physics for who knows whom and after that another decade and another and another—tired of typing "and another".

But who knows? Considering what happened the last ten years, one wonders, who really wants to know?

It will all happen regardless. Like it or not, here comes the next decade.

Happy Winter Solstice World!!!

I am chasing perspective so the subject title is what this post regards as I'm trying to get a handle on a lot of data that now pours in for me from all over the world (daily), while other things haven't changed, in a decade. As there are still posters who make it their job to obsessively reply to me, and supposedly I am still just some "crackpot" mouthing off on the fringe—at least according to them!!!

Reality of course is that much of the realization of a shift is because of Google.

Wow, who was really talking about Google ten years ago (were they really around or is that a myth?)?

The ranting of posters against Google search result rankings is proof in and of itself of the value they see in them, as why else attack Google itself? While for me it is just so bizarre as in, why do people drive up my ideas in search rankings, but otherwise seem intent on pretending that they do not exist?

What a crazy world.

But the simplest explanation I think—going to Occam's Razor—is academic reality: top ranked academics in prestigious institutions around the world are realized to be antagonistic to my research, so people step around the danger areas, FEAR these academics, and quietly use my research anyway. Hiding. Isn't that amazing.

(So yeah if you're some academic who prides yourself on people too afraid to acknowledge better research, why?)

I emphasize ten years ago as I WAS posting for years before that because that's when I started talking about what I call tautological spaces. Little did I know then that pulling the thread with results of that research would unravel Galois Theory and Group Theory, along with "String Theory" (was it around ten years ago?). Or, GGS—Gone, Gone Strings.

So a lot of academics are walking around naked now. What a difference a decade makes…

As 2009 heads to a close and thinking about the Winter Solstice now, it occurs to me that what truly defines us is not what we expect, or what we think we know, but what happens along the way.

We are defined not by what we think but by what happens.

Descartes may have thought therefore he was, but he died anyway.

What we live in is not the age of thought, but the age of Shit Happens.

Reality doesn't need our opinion. It kind of just drags us along whether we like it or not… (Cue in debate about global warming aka climate change aka 7th mass extinction wave, but I digress—)

So here's hoping there is another decade of arguing on sci.physics for who knows whom and after that another decade and another and another—tired of typing "and another".

But who knows? Considering what happened the last ten years, one wonders, who really wants to know?

It will all happen regardless. Like it or not, here comes the next decade.

Happy Winter Solstice World!!!

### Saturday, December 19, 2009

## JSH: Basic tautological spaces example

Ten years ago this month I discovered what I call tautological spaces. Partly as a commemoration of the anniversary this month here is a demonstration post of a basic tautological spaces example.

What are tautological spaces? Most simply they are identities.

A simple tautological space: x+y+vz = x+y+vz

Identities are so dismissed that I also have the bonus of being someone who found a surprisingly simple use for them—probing equations for analysis. I invented the term "tautological space" as well.

The 'v' variable is free, so you always have one extra degree of freedom.

My innovation moving forward from Gauss was to use "mod" with identities:

x+y+vz = 0(mod x+y+vz), which is the equivalent of x+y+vz = x+y+vz

You use tautological spaces with non-identities which I call conditionals.

Here's using tautological spaces with x^2 + y^2 = z^2.

x+y+vz = 0(mod x+y+vz), so x+y = -vz(mod x+y+vz), squaring both sides:

x^2 + 2xy + y^2 = v^2 z^2 (mod x + y + vz), now subtract out

x^2 + y^2 = z^2, giving

2xy = (v^2 - 1) z^2 (mod x+y+vz), which is

(v^2 - 1) z^2 = 2xy (mod x+y +vz), so:

(v^2 - 1)z^2 - 2xy = 0 (mod x+y+vz)

and I can get rid of x, with x = -y-vz (mod x+y+vz), so I have:

(v^2 - 1)z^2 + 2vyz + 2y^2 = 0 (mod x+y+vz)

which just says that for ANY v you choose, you have that x+y+vz, will be a factor of what's on the left hand side which is the residue.

And that is not really ring specific, as if you don't use "mod" you can do it all explicitly. But it's most meaningful in rings where "factor" is meaningful.

So like with v=1, I have 2yz + 2y^2 = 0 (mod x+y+z), and trivially with x=3, y=4, z=5, you have:

2(4)(5) + 2(16) = 72 has 12 as a factor.

So you get the result that if x^2 + y^2 = z^2, then 2y(z+y) has x+y+z as a factor.

Notice that is true over infinity. Tautological spaces give answers over infinity in general. So their use always encapsulates an infinite set.

They add on to existing knowledge, as notice you can analyze x^2 + y^2 = z^2 separately, or throw anything you want at its residue using the variable 'v' which is your control variable.

Now this month ten years of tautological spaces! A fascinatingly simple idea using identities, which just so happens to capture infinity.

What are tautological spaces? Most simply they are identities.

A simple tautological space: x+y+vz = x+y+vz

Identities are so dismissed that I also have the bonus of being someone who found a surprisingly simple use for them—probing equations for analysis. I invented the term "tautological space" as well.

The 'v' variable is free, so you always have one extra degree of freedom.

My innovation moving forward from Gauss was to use "mod" with identities:

x+y+vz = 0(mod x+y+vz), which is the equivalent of x+y+vz = x+y+vz

You use tautological spaces with non-identities which I call conditionals.

Here's using tautological spaces with x^2 + y^2 = z^2.

x+y+vz = 0(mod x+y+vz), so x+y = -vz(mod x+y+vz), squaring both sides:

x^2 + 2xy + y^2 = v^2 z^2 (mod x + y + vz), now subtract out

x^2 + y^2 = z^2, giving

2xy = (v^2 - 1) z^2 (mod x+y+vz), which is

(v^2 - 1) z^2 = 2xy (mod x+y +vz), so:

(v^2 - 1)z^2 - 2xy = 0 (mod x+y+vz)

and I can get rid of x, with x = -y-vz (mod x+y+vz), so I have:

(v^2 - 1)z^2 + 2vyz + 2y^2 = 0 (mod x+y+vz)

which just says that for ANY v you choose, you have that x+y+vz, will be a factor of what's on the left hand side which is the residue.

And that is not really ring specific, as if you don't use "mod" you can do it all explicitly. But it's most meaningful in rings where "factor" is meaningful.

So like with v=1, I have 2yz + 2y^2 = 0 (mod x+y+z), and trivially with x=3, y=4, z=5, you have:

2(4)(5) + 2(16) = 72 has 12 as a factor.

So you get the result that if x^2 + y^2 = z^2, then 2y(z+y) has x+y+z as a factor.

Notice that is true over infinity. Tautological spaces give answers over infinity in general. So their use always encapsulates an infinite set.

They add on to existing knowledge, as notice you can analyze x^2 + y^2 = z^2 separately, or throw anything you want at its residue using the variable 'v' which is your control variable.

Now this month ten years of tautological spaces! A fascinatingly simple idea using identities, which just so happens to capture infinity.

## JSH: Understanding Usenet as theater Corrected Version

Saw more errors than I liked in my previous posting. So here it is again, with corrections!

In our incredibly connected Information Age, one of the FASTEST ways to get a worldwide audience is through Usenet. For that reason there are a lot of players in this environment, and a tremendous amount of competition, where understanding how it works effectively depends I think on seeing a lot of postings as theater.

Here there is TREMENDOUS competition. Understand that—you are competing with everyone else!!!

I don't know how many times over the years I've seen some poster begrudge the attention my posts get, wondering why he (it's always another guy), can't get nearly as much with postings he thinks are relevant, carefully reasoned out, and polite.

While I throw up half-baked ideas, readily engage in insult battles, have errors scattered all over the place, and often will rant on just about anything that suits my purposes of the moment!

What gives?

REALITY is that Usenet is a pure attention zone.

Quite simply, you must hold people's attention to be read.

If you are read, you are getting attention.

So I have the phenomena of posters who stalk my postings telling people not to read them! Because that way they get read themselves. So I call them attention parasites or liken them to barnacles on a ship at sea.

They know what they're doing. And it does work.

Theater is about conflict.

If you take any basic creative writing courses you'll get that thrown at you a LOT. Conflict.

Agreement does not draw interest. It bores people.

Drama is about an antagonist and protagonist. Usenet is a lot about drama.

Get it right and over time you are influential.

My postings can be so dominant on newsgroups that I am now careful about which ones I use. As I can simply squash everyone else on small newsgroups or skew the postings even on big ones like sci.physics, which doesn't usually suit my purposes.

It's not just about getting attention. It's about getting influence by getting attention to your ideas.

Objections are simply fuel for the fire.

Handling objections I liken to tacking into the wind.

Consider that years ago I was just one of many arguing out my own ideas and research on Usenet, where I focused on mathematics. Today after years of arguing I am a dominate figure across any number of media (not pop culture, yet, so, no, no television, radio or movies…yet) where I like pointing to search engines as it's easy for others to check.

So Google says I have the definition of mathematical proof. Cool.

When posters give you instructions about using Usenet that emphasize being polite, kissing butt (otherwise known as respecting what is mainstream or profusely thanking others for help) remember they are teaching you how to be ignored.

Not saying you shouldn't thank others for help! Just be careful how you do it.

If people give you advice on Usenet, pay attention to what they do. Not what they say.

The people with the greatest longevity you'll notice on newsgroups are just about all insult machines!

(Sadly)

Conflict. Take a course on creative writing. Learn how to be argumentative.

Try things. Mistakes are not a bad thing.

And join the theater that is called Usenet. It may often be a theater of the absurd, but worldwide attention is just about reality.

Today I'm read in over 50 countries—every 30 days. Not counting Usenet. That's just my math blog.

Conflicts here can be your friends. It may bruise your ego. Hurt your feelings.

But without objection, you are not interesting.

And learn to write, then re-write. And if you feel like it, re-write again. Mistakes are not a bad thing. Just a thing.

In our incredibly connected Information Age, one of the FASTEST ways to get a worldwide audience is through Usenet. For that reason there are a lot of players in this environment, and a tremendous amount of competition, where understanding how it works effectively depends I think on seeing a lot of postings as theater.

Here there is TREMENDOUS competition. Understand that—you are competing with everyone else!!!

I don't know how many times over the years I've seen some poster begrudge the attention my posts get, wondering why he (it's always another guy), can't get nearly as much with postings he thinks are relevant, carefully reasoned out, and polite.

While I throw up half-baked ideas, readily engage in insult battles, have errors scattered all over the place, and often will rant on just about anything that suits my purposes of the moment!

What gives?

REALITY is that Usenet is a pure attention zone.

Quite simply, you must hold people's attention to be read.

If you are read, you are getting attention.

So I have the phenomena of posters who stalk my postings telling people not to read them! Because that way they get read themselves. So I call them attention parasites or liken them to barnacles on a ship at sea.

They know what they're doing. And it does work.

Theater is about conflict.

If you take any basic creative writing courses you'll get that thrown at you a LOT. Conflict.

Agreement does not draw interest. It bores people.

Drama is about an antagonist and protagonist. Usenet is a lot about drama.

Get it right and over time you are influential.

My postings can be so dominant on newsgroups that I am now careful about which ones I use. As I can simply squash everyone else on small newsgroups or skew the postings even on big ones like sci.physics, which doesn't usually suit my purposes.

It's not just about getting attention. It's about getting influence by getting attention to your ideas.

Objections are simply fuel for the fire.

Handling objections I liken to tacking into the wind.

Consider that years ago I was just one of many arguing out my own ideas and research on Usenet, where I focused on mathematics. Today after years of arguing I am a dominate figure across any number of media (not pop culture, yet, so, no, no television, radio or movies…yet) where I like pointing to search engines as it's easy for others to check.

So Google says I have the definition of mathematical proof. Cool.

When posters give you instructions about using Usenet that emphasize being polite, kissing butt (otherwise known as respecting what is mainstream or profusely thanking others for help) remember they are teaching you how to be ignored.

Not saying you shouldn't thank others for help! Just be careful how you do it.

If people give you advice on Usenet, pay attention to what they do. Not what they say.

The people with the greatest longevity you'll notice on newsgroups are just about all insult machines!

(Sadly)

Conflict. Take a course on creative writing. Learn how to be argumentative.

Try things. Mistakes are not a bad thing.

And join the theater that is called Usenet. It may often be a theater of the absurd, but worldwide attention is just about reality.

Today I'm read in over 50 countries—every 30 days. Not counting Usenet. That's just my math blog.

Conflicts here can be your friends. It may bruise your ego. Hurt your feelings.

But without objection, you are not interesting.

And learn to write, then re-write. And if you feel like it, re-write again. Mistakes are not a bad thing. Just a thing.

## JSH: Understanding Usenet as theater

In our incredibly connected Information Age, one of the FASTEST ways to get a worldwide audience is through Usenet. For that reason there are a lot of players in this environment, and a tremendous amount of competition, where understanding how it works effectively depends I think on seeing a lot of postings as theater.

Here there is TREMENDOUS competition. Understand that—you are competing with everyone else!!!

I don't know how many times over the years I've seen some poster begrudge the attention my posts get, wondering why he (it's always another guy), can't get nearly as much with postings he things are relevant, carefully reasoned out, and polite.

While I throw up half-baked ideas, readily engage in insult battles, have errors scattered all over the place, and often will rant on just about anything that suits my purposes of the moment!

What gives?

REALITY is that Usenet is a pure attention zone. Quite simply, you must hold people's attention to be read.

If you are read, you are getting attention.

So I have the phenomena of posters who stalk my postings telling people no to read them! Because that way they get read themselves.

I call them attention parasites or liken them to barnacles on a ship at sea.

They know what they're doing. And it does work.

Theater is about conflict. If you take any basic creative writing courses you'll get that thrown at you a LOT. Conflict.

Agreement does not draw interest. It bores people.

Drama is about an antagonist and protagonist. Usenet is a lot about drama.

Get it right and you are influential.

My postings can be so dominant on newsgroups that I am now careful about which ones I use. As I can simply squash everyone else on small newsgroups or skew the postings even on big ones like sci.physics, which doesn't usually suit my purposes.

Objections are simply fuel for the fire.

Consider that years ago I was just one of many arguing out my own ideas and research on Usenet, where I focused on mathematics. Today after years of arguing I am a dominate figure across any number of media (not pop culture, yet, so, no, no television, radio or movies…yet) where I like pointing to search engines as it's easy for others to check. So Google says I have the definition of mathematical proof. Cool.

When posters give you instructions about using Usenet that emphasize being polite. Kissing butt (otherwise known as respecting what is mainstream or profusely thanking others for help) remember they are teaching you how to be ignored.

Pay attention to what they do. Not what they say.

The people with the greatest longevity you'll notice on newsgroups are just about all insult machines.

Conflict. Take a course on creative writing. Learn how to be argumentative. Try things. Mistakes are not a bad thing.

And join the theater that is called Usenet. It may often be a theater of the absurd, but worldwide attention is just about reality.

Today I'm read in over 50 countries—every 30 days.

Not counting Usenet. That's just my math blog.

Conflicts here are your friends. It may bruise your ego. Hurt your feelings.

But without objections, you are not interesting.

Here there is TREMENDOUS competition. Understand that—you are competing with everyone else!!!

I don't know how many times over the years I've seen some poster begrudge the attention my posts get, wondering why he (it's always another guy), can't get nearly as much with postings he things are relevant, carefully reasoned out, and polite.

While I throw up half-baked ideas, readily engage in insult battles, have errors scattered all over the place, and often will rant on just about anything that suits my purposes of the moment!

What gives?

REALITY is that Usenet is a pure attention zone. Quite simply, you must hold people's attention to be read.

If you are read, you are getting attention.

So I have the phenomena of posters who stalk my postings telling people no to read them! Because that way they get read themselves.

I call them attention parasites or liken them to barnacles on a ship at sea.

They know what they're doing. And it does work.

Theater is about conflict. If you take any basic creative writing courses you'll get that thrown at you a LOT. Conflict.

Agreement does not draw interest. It bores people.

Drama is about an antagonist and protagonist. Usenet is a lot about drama.

Get it right and you are influential.

My postings can be so dominant on newsgroups that I am now careful about which ones I use. As I can simply squash everyone else on small newsgroups or skew the postings even on big ones like sci.physics, which doesn't usually suit my purposes.

Objections are simply fuel for the fire.

Consider that years ago I was just one of many arguing out my own ideas and research on Usenet, where I focused on mathematics. Today after years of arguing I am a dominate figure across any number of media (not pop culture, yet, so, no, no television, radio or movies…yet) where I like pointing to search engines as it's easy for others to check. So Google says I have the definition of mathematical proof. Cool.

When posters give you instructions about using Usenet that emphasize being polite. Kissing butt (otherwise known as respecting what is mainstream or profusely thanking others for help) remember they are teaching you how to be ignored.

Pay attention to what they do. Not what they say.

The people with the greatest longevity you'll notice on newsgroups are just about all insult machines.

Conflict. Take a course on creative writing. Learn how to be argumentative. Try things. Mistakes are not a bad thing.

And join the theater that is called Usenet. It may often be a theater of the absurd, but worldwide attention is just about reality.

Today I'm read in over 50 countries—every 30 days.

Not counting Usenet. That's just my math blog.

Conflicts here are your friends. It may bruise your ego. Hurt your feelings.

But without objections, you are not interesting.

## JSH: Importance of use

To a large extent my Usenet postings are stylized reflecting years of experience on which types of post achieve whatever my current objective might be which DOES shift. With that said there are times I like to just put something that is more along the lines of just kind of chatting or something less, focused.

One reality of how I've looked at things recently is on the importance of use. And unlike posters who routinely dismiss any and all evidence they think supports me in any way, I look at Google search results as evidence of use, albeit, hidden use.

Google seems to be showing a weird case where people are going to what works, but are still paying lip service to what is accepted.

The implications are fascinating, but it's hard to tell now what exactly is happening, though presumably some break-even point will be reached and the ideas that are in use will take over, or so I've surmised.

To some extent I've thought of the full idea as a little dangerous as I'm still not sure how far resistance to my research really reaches. It may be safer for certain academics to feel safe in their Ivory Towers. I'm now letting them in on the secret.

Usage could I guess still be low, though it clearly is worldwide.

But it might be profound. Web analytics data shows a very steadily high country count of visits to my math blog in the 50+ range, while the Google search results still have my research dominating often over everything else previously known, yet searches on me in particular still bring up the Crank.net page.

Usage will change the situation, so in a sense I do have the benefit of the Internet and web search results.

So I have a luxury others may not have. My ideas already clearly dominate, worldwide. And that dominance is growing.

And I do check others besides Google, and can detect patterns indicating usage there as well, so I'm not just relying on Google, but then again, Google is the primary web search engine, so it's definitely a big deal.

But also Google dominates because it is the best, where I'm biased in that direction now by simply watching how rapidly my own research gets picked up by Google versus other search engines, which is a weird way to check, but hey, I have the definition of mathematical proof! According to Google.

Oh yeah, the evidence of hidden usage around the world where people are using the research but quietly may indicate a real fear of challenging the current system.

And that could mean quite a lot.

So possibly some of you reading this post who are established scientists are not really so much believed, as feared, even among your colleagues, as people who might challenge your positions realize they have little to no chance.

I repeat, you may not be so much believed—as feared.

Part of the reason I bring up Google searches has been to test them as well as to see whether or not my talking about them might influence things, maybe even make the high ranking for my research disappear! I've gone even further in such challenges by actually writing to two of my Congressional representatives—which happen to be Speaker Nancy Pelosi, and Senator Feinstein—asking them to investigate how search engines get their search results. I've talked badly at times about Google, just to see if that might impact.

While over the years Yahoo! has bounced around as has other search engines, Google search results tend to remain consistent, along with Google's fortunes. Possibly the lesson here is that people want what they want. I've had the privilege of watching search engines in relation to my own research so I know of things or suspect things that I don't go into detail about because I don't want to get sued!!! By Yahoo! or Microsoft, or maybe others.

But also I'm not certain, but I may know some things about how some people operate, where Google appears to actually be the best, at simply doing what it says it does.

If fear rules acceptance of mainstream ideas more than some scientists wish to admit such that more powerful ideas can be quietly picked up so that the best evidence is from Google search results then clearly our academic and scientific worlds do not behave as advertised.

So the importance of use is a determinant, which will decide the outcome.

IN other words, I like to say that Sir Isaac Newton isn't around to promote or defend his research!!!

But his research is still around because it worked and works.

Now I wonder how many "super stars" of their time from the past would be surprised to not be known at all today, possibly in their era they were the feared ones. Even Newton was feared. But he was also right. The others are footnotes in history or forgotten, and while many may think they know history so that they know who they all were, I doubt it.

Considering some of the big names in science or mathematics today who I know will not stand the test of time, I suspect that maybe some of the bigger names in their time get white-washed out of history, by a world that later repudiates them, trying to forget it ever thought they were great. So it tries to wipe away their very existence.

Regardless, forget about the Usenet arguments. A lot of it to me is theater anyway and worthless in the big picture.

All that matters is use. And if you have your own ideas you think are great: all that matters is use.

The good ideas get picked up, eventually. People can DO things with them that they can't do with the other stuff.

And that is ultimately the only thing that matters.

One reality of how I've looked at things recently is on the importance of use. And unlike posters who routinely dismiss any and all evidence they think supports me in any way, I look at Google search results as evidence of use, albeit, hidden use.

Google seems to be showing a weird case where people are going to what works, but are still paying lip service to what is accepted.

The implications are fascinating, but it's hard to tell now what exactly is happening, though presumably some break-even point will be reached and the ideas that are in use will take over, or so I've surmised.

To some extent I've thought of the full idea as a little dangerous as I'm still not sure how far resistance to my research really reaches. It may be safer for certain academics to feel safe in their Ivory Towers. I'm now letting them in on the secret.

Usage could I guess still be low, though it clearly is worldwide.

But it might be profound. Web analytics data shows a very steadily high country count of visits to my math blog in the 50+ range, while the Google search results still have my research dominating often over everything else previously known, yet searches on me in particular still bring up the Crank.net page.

Usage will change the situation, so in a sense I do have the benefit of the Internet and web search results.

So I have a luxury others may not have. My ideas already clearly dominate, worldwide. And that dominance is growing.

And I do check others besides Google, and can detect patterns indicating usage there as well, so I'm not just relying on Google, but then again, Google is the primary web search engine, so it's definitely a big deal.

But also Google dominates because it is the best, where I'm biased in that direction now by simply watching how rapidly my own research gets picked up by Google versus other search engines, which is a weird way to check, but hey, I have the definition of mathematical proof! According to Google.

Oh yeah, the evidence of hidden usage around the world where people are using the research but quietly may indicate a real fear of challenging the current system.

And that could mean quite a lot.

So possibly some of you reading this post who are established scientists are not really so much believed, as feared, even among your colleagues, as people who might challenge your positions realize they have little to no chance.

I repeat, you may not be so much believed—as feared.

Part of the reason I bring up Google searches has been to test them as well as to see whether or not my talking about them might influence things, maybe even make the high ranking for my research disappear! I've gone even further in such challenges by actually writing to two of my Congressional representatives—which happen to be Speaker Nancy Pelosi, and Senator Feinstein—asking them to investigate how search engines get their search results. I've talked badly at times about Google, just to see if that might impact.

While over the years Yahoo! has bounced around as has other search engines, Google search results tend to remain consistent, along with Google's fortunes. Possibly the lesson here is that people want what they want. I've had the privilege of watching search engines in relation to my own research so I know of things or suspect things that I don't go into detail about because I don't want to get sued!!! By Yahoo! or Microsoft, or maybe others.

But also I'm not certain, but I may know some things about how some people operate, where Google appears to actually be the best, at simply doing what it says it does.

If fear rules acceptance of mainstream ideas more than some scientists wish to admit such that more powerful ideas can be quietly picked up so that the best evidence is from Google search results then clearly our academic and scientific worlds do not behave as advertised.

So the importance of use is a determinant, which will decide the outcome.

IN other words, I like to say that Sir Isaac Newton isn't around to promote or defend his research!!!

But his research is still around because it worked and works.

Now I wonder how many "super stars" of their time from the past would be surprised to not be known at all today, possibly in their era they were the feared ones. Even Newton was feared. But he was also right. The others are footnotes in history or forgotten, and while many may think they know history so that they know who they all were, I doubt it.

Considering some of the big names in science or mathematics today who I know will not stand the test of time, I suspect that maybe some of the bigger names in their time get white-washed out of history, by a world that later repudiates them, trying to forget it ever thought they were great. So it tries to wipe away their very existence.

Regardless, forget about the Usenet arguments. A lot of it to me is theater anyway and worthless in the big picture.

All that matters is use. And if you have your own ideas you think are great: all that matters is use.

The good ideas get picked up, eventually. People can DO things with them that they can't do with the other stuff.

And that is ultimately the only thing that matters.

### Friday, December 18, 2009

## JSH: Consideration of idea worth

Having gone through getting at least an undergraduate degree in physics I can appreciate how annoying it can be when some person thinks he has VERY important ideas, which challenge orthodoxy, while now I can appreciate that feeling that you have something important and someone should listen.

So what's the resolution? Well for me I've tossed things out there and do my arguing for my own purposes or posts like this one as well, and figure, things will work out.

But I have that luxury.

Ten years ago this month I had the privilege of finding a simple extension of mathematical ideas pioneered by Gauss himself, which I called tautological spaces (I even got to do a cool name, bonus).

A simple tautological space: x+y+vz = x+y+vz

So yeah, this post is partly to commemorate that ten year anniversary.

Identities are so dismissed that I also have the bonus of being someone who found a surprisingly simple use for them—probing equations for analysis.

The 'v' variable is free, so you always have one extra degree of freedom and I like to say it was designated by me 'v' for Victory.

My innovation moving forward from Gauss besides using special identities was to use "mod".

x+y+vz = 0(mod x+y+vz), which is the equivalent of x+y+vz = x+y+vz

Here's using tautological spaces with x^2 + y^2 = z^2.

x+y+vz = 0(mod x+y+vz), so x+y = -vz(mod x+y+vz), squaring both sides:

x^2 + 2xy + y^2 = v^2 z^2 (mod x + y + vz), now subtract out x^2 + y^2 = z^2, giving

2xy = (v^2 - 1) z^2 (mod x+y+vz), which is (v^2 - 1) z^2 = 2xy mod (x+y+vz), so:

(v^2 - 1)z^2 - 2xy = 0 (mod x+y+vz)

and I can get rid of x, with x = -y-vz (mod x+y+vz), so I have:

(v^2 - 1)z^2 + 2vyz + 2y^2 = 0 (mod x+y+vz)

which just says that for ANY v you choose, you have that x+y+vz, will be a factor of what's on the left hand side which is the residue. And that is not really ring specific, as if you don't use "mod" you can do it all explicitly. But it's most meaningful in rings where "factor" is meaningful.

So like with v=1, I have 2yz + 2y^2 = 0 (mod x+y+z), and trivially with x=3, y=4, z=5, you have:

2(4)(5) + 2(16) = 72 has 12 as a factor.

So you get the result that if x^2 + y^2 = z^2, then 2y(z+y) has x+y+z as a factor.

So why should physics people care?

Because you can put ANY equation from the canons of physics or any other area of human endeavor through a tautological space, subtracting it from an identity, and poke at it by setting v to whatever value you wish. (Higher order tautological spaces are available depending on the number of variables or other aspects of the equation. For instance, I used x^2 + y^2 + vz^2 = 0(mod x^2 + y^2 + vz^2) to prove Fermat's Last Theorem.)

v is yours entirely, no matter what the equation.

It is quite simply, a mathematical probing tool.

Which means I can say that tautological spaces encapsulate all prior human mathematical knowledge.

ALL prior human mathematical knowledge.

For the theoretical physicist looking for an edge it can't hurt to be able to grab the essence of any mathematical equation in your field, get a residue, and poke at it, at will.

Given that I've taken identities and turned them into a powerful analysis technique and named the field of study, the resistance against the ideas is fierce.

Fierce resistance is a challenge. Overcoming it is a thrill.

But that just means I can point out that people using these techniques have an edge.

You now know they have an edge.

They lose nothing from what was currently known, but may find out surprising things with a super-powered technique, so I'm thinking it probably is already secretly used by people wanting that edge.

Just for fun I handled binary quadratic Diophantine equations. The entire field.

Ten years. Years ago I was desperate for answers. Today I celebrate my successes and ponder how fascinating the journey has been. Yes, I do dominate discussions in odd ways, while still supposedly being fringe. But you do not know what advances may secretly have depended on my ideas. You do not know if you're behind today because that guy in front of you, was smarter in a way you didn't realize.

Which is how it should be, I guess. In any event that's how it is.

I've noted that Google searches around mathematical fields related to this research are dominated by my research.

So yeah, you can get backup to my having handled the ENTIRE FIELD of binary quadratic Diophantine equations, just with a Google search.

The entire field.

Weirdly enough, I covered 2000 years worth of research in a few days, re-discovering some things along the way. 2000 years, in a few days.

2000 years of human effort. With tautological spaces, I could match that by myself in a few days. Wow.

Happy Birthday Tautological Spaces! Now ten years old. And what a brilliant child of mine you are!

So what's the resolution? Well for me I've tossed things out there and do my arguing for my own purposes or posts like this one as well, and figure, things will work out.

But I have that luxury.

Ten years ago this month I had the privilege of finding a simple extension of mathematical ideas pioneered by Gauss himself, which I called tautological spaces (I even got to do a cool name, bonus).

A simple tautological space: x+y+vz = x+y+vz

So yeah, this post is partly to commemorate that ten year anniversary.

Identities are so dismissed that I also have the bonus of being someone who found a surprisingly simple use for them—probing equations for analysis.

The 'v' variable is free, so you always have one extra degree of freedom and I like to say it was designated by me 'v' for Victory.

My innovation moving forward from Gauss besides using special identities was to use "mod".

x+y+vz = 0(mod x+y+vz), which is the equivalent of x+y+vz = x+y+vz

Here's using tautological spaces with x^2 + y^2 = z^2.

x+y+vz = 0(mod x+y+vz), so x+y = -vz(mod x+y+vz), squaring both sides:

x^2 + 2xy + y^2 = v^2 z^2 (mod x + y + vz), now subtract out x^2 + y^2 = z^2, giving

2xy = (v^2 - 1) z^2 (mod x+y+vz), which is (v^2 - 1) z^2 = 2xy mod (x+y+vz), so:

(v^2 - 1)z^2 - 2xy = 0 (mod x+y+vz)

and I can get rid of x, with x = -y-vz (mod x+y+vz), so I have:

(v^2 - 1)z^2 + 2vyz + 2y^2 = 0 (mod x+y+vz)

which just says that for ANY v you choose, you have that x+y+vz, will be a factor of what's on the left hand side which is the residue. And that is not really ring specific, as if you don't use "mod" you can do it all explicitly. But it's most meaningful in rings where "factor" is meaningful.

So like with v=1, I have 2yz + 2y^2 = 0 (mod x+y+z), and trivially with x=3, y=4, z=5, you have:

2(4)(5) + 2(16) = 72 has 12 as a factor.

So you get the result that if x^2 + y^2 = z^2, then 2y(z+y) has x+y+z as a factor.

So why should physics people care?

Because you can put ANY equation from the canons of physics or any other area of human endeavor through a tautological space, subtracting it from an identity, and poke at it by setting v to whatever value you wish. (Higher order tautological spaces are available depending on the number of variables or other aspects of the equation. For instance, I used x^2 + y^2 + vz^2 = 0(mod x^2 + y^2 + vz^2) to prove Fermat's Last Theorem.)

v is yours entirely, no matter what the equation.

It is quite simply, a mathematical probing tool.

Which means I can say that tautological spaces encapsulate all prior human mathematical knowledge.

ALL prior human mathematical knowledge.

For the theoretical physicist looking for an edge it can't hurt to be able to grab the essence of any mathematical equation in your field, get a residue, and poke at it, at will.

Given that I've taken identities and turned them into a powerful analysis technique and named the field of study, the resistance against the ideas is fierce.

Fierce resistance is a challenge. Overcoming it is a thrill.

But that just means I can point out that people using these techniques have an edge.

You now know they have an edge.

They lose nothing from what was currently known, but may find out surprising things with a super-powered technique, so I'm thinking it probably is already secretly used by people wanting that edge.

Just for fun I handled binary quadratic Diophantine equations. The entire field.

Ten years. Years ago I was desperate for answers. Today I celebrate my successes and ponder how fascinating the journey has been. Yes, I do dominate discussions in odd ways, while still supposedly being fringe. But you do not know what advances may secretly have depended on my ideas. You do not know if you're behind today because that guy in front of you, was smarter in a way you didn't realize.

Which is how it should be, I guess. In any event that's how it is.

I've noted that Google searches around mathematical fields related to this research are dominated by my research.

So yeah, you can get backup to my having handled the ENTIRE FIELD of binary quadratic Diophantine equations, just with a Google search.

The entire field.

Weirdly enough, I covered 2000 years worth of research in a few days, re-discovering some things along the way. 2000 years, in a few days.

2000 years of human effort. With tautological spaces, I could match that by myself in a few days. Wow.

Happy Birthday Tautological Spaces! Now ten years old. And what a brilliant child of mine you are!

### Sunday, December 13, 2009

## JSH: The Error, executive summary

Here is a post meant to be an executive summary of the issues around an error of ideas found in algebraic number theory.

A problem was introduced into human mathematics back in the late 1800's. Proving the problem is trivial using a special construction which is only different from normal factorizations in that it doesn't involve polynomial factors:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

(The above was derived. But that derivation is not necessary to understand the implications.)

The a's can be found using the quadratic formula:

a_1(x) = ((7x - 1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2

a_2(x) = ((7x - 1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2 or vice versa.

Letting b_1(x) = a_1(x) + 1, assuming a_2(0) = 0, I have a_1(x) = b_1(x) - 1, and substituting gives:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

Now at x=0, b_1(0) = a_2(0) = 0, so the functions can be said to be normalized.

In the field of complex numbers it is then clear by the distributive property how the 7 was multiplied.

Notice that a*(b+c) = a*b + a*c, is still valid with a*(f(x) + b) = a*f(x) + a*b, so the result is simply an application of the distributive property. Since the distributive property is valid on the complex plane the result follows from the field of complex numbers for that reason.

But the result from the complex plane is contradicted by results from another mathematical area.

In what is called the ring of algebraic integers, defined to be the set of roots of monic polynomials with integer coefficients it can be proven that neither of the roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

can have 7 itself as a factor in that ring when the roots are non-rational. (Notice trivially at x=0 one does, as it is 0.)

So there is a direct contradiction. You can prove one thing from the field of complex numbers, and appear to prove its opposite in the ring of algebraic integers.

Algebraic integers are the base ring around which the field of algebraic numbers is developed. They are also the base from which Galois Theory is developed. This result leads to the conclusion that there must be a problem with the use of Galois Theory.

The ability to appear to prove something false means this error can allow mathematicians to appear to prove just about anything.

One spectacular example of such a flawed argument known as a proof is that of Andrew Wiles, who is believed to have proven Fermat's Last Theorem.

So if recognized this error would have a devastating impact on the mathematical community.

It probably would have a devastating impact on mathematical physicists as well.

It also may indicate problems in particle physics and an explanation of why there are issues with the Standard Model, which relies on group theory.

At this time it is not clear if the error will be acknowledged any time soon because experts in the fields affected appear to be in active denial.

Issues here are relevant to all nations. Governments should consider it an area of national security. Scientists and academics in the implicated fields are to be considered now known security risks. Nations around the world are to consider the NSA to be the world agency most directly affected by this error in terms of personnel risk. Its actions are not to be simply trusted even by NATO allies, or Interpol.

The NSA has possibly the greatest concentration of powerful people directly affected by this error. Exploit potential of NSA staffers by hostile governments exploiting the error may be high.

Threat from this problem is at the highest level. Confrontation with people affected by this error should be done with extreme caution especially if they have access levels that could give them significant negative options.

Suicide risk among those affected may be high, as well as potential acting out of destructive anger against others including nations.

Threat level is near maximum, as potential exists on worst case scenarios for a nuclear exchange, or catastrophic economic collapse.

A problem was introduced into human mathematics back in the late 1800's. Proving the problem is trivial using a special construction which is only different from normal factorizations in that it doesn't involve polynomial factors:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

(The above was derived. But that derivation is not necessary to understand the implications.)

The a's can be found using the quadratic formula:

a_1(x) = ((7x - 1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2

a_2(x) = ((7x - 1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2 or vice versa.

Letting b_1(x) = a_1(x) + 1, assuming a_2(0) = 0, I have a_1(x) = b_1(x) - 1, and substituting gives:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

Now at x=0, b_1(0) = a_2(0) = 0, so the functions can be said to be normalized.

In the field of complex numbers it is then clear by the distributive property how the 7 was multiplied.

Notice that a*(b+c) = a*b + a*c, is still valid with a*(f(x) + b) = a*f(x) + a*b, so the result is simply an application of the distributive property. Since the distributive property is valid on the complex plane the result follows from the field of complex numbers for that reason.

But the result from the complex plane is contradicted by results from another mathematical area.

In what is called the ring of algebraic integers, defined to be the set of roots of monic polynomials with integer coefficients it can be proven that neither of the roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

can have 7 itself as a factor in that ring when the roots are non-rational. (Notice trivially at x=0 one does, as it is 0.)

So there is a direct contradiction. You can prove one thing from the field of complex numbers, and appear to prove its opposite in the ring of algebraic integers.

Algebraic integers are the base ring around which the field of algebraic numbers is developed. They are also the base from which Galois Theory is developed. This result leads to the conclusion that there must be a problem with the use of Galois Theory.

The ability to appear to prove something false means this error can allow mathematicians to appear to prove just about anything.

One spectacular example of such a flawed argument known as a proof is that of Andrew Wiles, who is believed to have proven Fermat's Last Theorem.

So if recognized this error would have a devastating impact on the mathematical community.

It probably would have a devastating impact on mathematical physicists as well.

It also may indicate problems in particle physics and an explanation of why there are issues with the Standard Model, which relies on group theory.

At this time it is not clear if the error will be acknowledged any time soon because experts in the fields affected appear to be in active denial.

Issues here are relevant to all nations. Governments should consider it an area of national security. Scientists and academics in the implicated fields are to be considered now known security risks. Nations around the world are to consider the NSA to be the world agency most directly affected by this error in terms of personnel risk. Its actions are not to be simply trusted even by NATO allies, or Interpol.

The NSA has possibly the greatest concentration of powerful people directly affected by this error. Exploit potential of NSA staffers by hostile governments exploiting the error may be high.

Threat from this problem is at the highest level. Confrontation with people affected by this error should be done with extreme caution especially if they have access levels that could give them significant negative options.

Suicide risk among those affected may be high, as well as potential acting out of destructive anger against others including nations.

Threat level is near maximum, as potential exists on worst case scenarios for a nuclear exchange, or catastrophic economic collapse.

### Saturday, December 12, 2009

## JSH: Kind of a weird story, I guess

Admittedly it is sort of a big deal to have to explain that over one hundred years ago a rather profound and somewhat subtle error entered into number theory, and the error propagated, so now it appears it impacted particle physics in the form of group theory, so, um, you don't quite know nearly as much as you may think you know about subatomic particles.

For years I've talked about this issue not entirely to convince others but to convince myself.

So Usenet has helped me to slowly get used to the idea, accept it, and realize its full consequences (I think).

Along the way I advanced mathematics as well. THAT has taken a while to get used to as well. (Just seems so strange but do a search on tautological spaces.)

So the story is kind of weird, but also rather fascinating, and it raises some serious implications about science and technology, as in, um, we're not really started yet.

If the human species is working with slightly off theories when it comes to particle physics, and is using flawed mathematics then of course that could hold things up in terms of advancement.

The scarier thing that may result from removing those blocks is an explosion of development.

I've considered that resistance to my research—after all I have mathematical proofs to back it—may be a reflex reaction of humanity as a whole to prevent a serious increase in the rate of technological advance.

Maybe some kind of natural break that the species unconsciously uses in order to limit change.

Or I've thought it could be aliens.

The correct mathematical ideas and understanding of particle physics could lead to technology that would allow us to leave our planet, so an alien species might see a low tech and possibly "legal" way in their arena of holding humanity to planet earth by blocking acceptance of mathematical advances.

And that is nutty. But I've had to contemplate it as a serious issue, as of course, if it were true, and the aliens saw me as a person who could move things forward then that might not be such a good thing. Some of my posts have probed this issue and offered the possibility that I might just kind of do other things if needed. After all, if there were some alien species interfering, I wouldn't have a snowballs chance in hell. Real life is not a sci-fi movie. No miracle solutions. But I've decided that alien interference appears to be very unlikely, or if it exists, there are rules preventing the aliens from blocking me further, or more directly.

Oh yeah, another possibility are modern day Luddites. People who hate science and technology, who might see a quantum leap in human understanding which could lead to incredible scientific advance as a threat.

They could actually be scarier than aliens.

IN any event, looks like I've been right on the math. It's probable that physics is screwed up in some ways. Not terribly clear what advances would come from the correct math. And who knows? Maybe there are aliens interfering.

But what can you do?

For years I've talked about this issue not entirely to convince others but to convince myself.

So Usenet has helped me to slowly get used to the idea, accept it, and realize its full consequences (I think).

Along the way I advanced mathematics as well. THAT has taken a while to get used to as well. (Just seems so strange but do a search on tautological spaces.)

So the story is kind of weird, but also rather fascinating, and it raises some serious implications about science and technology, as in, um, we're not really started yet.

If the human species is working with slightly off theories when it comes to particle physics, and is using flawed mathematics then of course that could hold things up in terms of advancement.

The scarier thing that may result from removing those blocks is an explosion of development.

I've considered that resistance to my research—after all I have mathematical proofs to back it—may be a reflex reaction of humanity as a whole to prevent a serious increase in the rate of technological advance.

Maybe some kind of natural break that the species unconsciously uses in order to limit change.

Or I've thought it could be aliens.

The correct mathematical ideas and understanding of particle physics could lead to technology that would allow us to leave our planet, so an alien species might see a low tech and possibly "legal" way in their arena of holding humanity to planet earth by blocking acceptance of mathematical advances.

And that is nutty. But I've had to contemplate it as a serious issue, as of course, if it were true, and the aliens saw me as a person who could move things forward then that might not be such a good thing. Some of my posts have probed this issue and offered the possibility that I might just kind of do other things if needed. After all, if there were some alien species interfering, I wouldn't have a snowballs chance in hell. Real life is not a sci-fi movie. No miracle solutions. But I've decided that alien interference appears to be very unlikely, or if it exists, there are rules preventing the aliens from blocking me further, or more directly.

Oh yeah, another possibility are modern day Luddites. People who hate science and technology, who might see a quantum leap in human understanding which could lead to incredible scientific advance as a threat.

They could actually be scarier than aliens.

IN any event, looks like I've been right on the math. It's probable that physics is screwed up in some ways. Not terribly clear what advances would come from the correct math. And who knows? Maybe there are aliens interfering.

But what can you do?

## JSH: Sadly cynical I guess

So yeah, I had an epiphany recently that if people realized they could humiliate academics with this error then maybe there'd be progress which is sadly cynical.

After years of trying the positive routes—like publication, wow they killed the entire freaking math journal—or even negative ones with rants against academics I felt were lying or willfully remaining ignorant, I've concluded that giving ordinary citizens the power to shred the dignity of professors is the last most potent route left.

And THAT will interest people.

Forget about abstract math and the fate of humanity or the importance of science and discovery, but making some proud professor at, say, Harvard look like an idiot? Now THAT will interest people.

And it can be done.

The error is a key into an exclusive world.

It is a way for regular people to shred down the Ivory Tower.

To humble proud people.

And that is too appealing I think to pass up.

In the process, make no mistake, they'll probably end academia as it currently operates.

But I warned you on that score.

I'm enlisting an army. That army will go to war against your pride, your prestige, and ultimately, your position as a professor, if you are one.

The last thing to go.

Better re-think your retirement plans. Some of you will need new careers to replace the one you're about to lose.

After years of trying the positive routes—like publication, wow they killed the entire freaking math journal—or even negative ones with rants against academics I felt were lying or willfully remaining ignorant, I've concluded that giving ordinary citizens the power to shred the dignity of professors is the last most potent route left.

And THAT will interest people.

Forget about abstract math and the fate of humanity or the importance of science and discovery, but making some proud professor at, say, Harvard look like an idiot? Now THAT will interest people.

And it can be done.

The error is a key into an exclusive world.

It is a way for regular people to shred down the Ivory Tower.

To humble proud people.

And that is too appealing I think to pass up.

In the process, make no mistake, they'll probably end academia as it currently operates.

But I warned you on that score.

I'm enlisting an army. That army will go to war against your pride, your prestige, and ultimately, your position as a professor, if you are one.

The last thing to go.

Better re-think your retirement plans. Some of you will need new careers to replace the one you're about to lose.

## JSH: Mathematical impossibility and Galois Theory

Showing an important result in complex numbers allows me to prove absolutely a problem with some well-established number theory which underpins Galois Theory, which removes use of Galois groups, at least, useful use. But being able to prove something absolutely is not as big a convincer as you might suppose, as, I've done it before.

What's different now is I'm pointing out to people that this result CAN be used to humble any, oh, string theorist you wish to torture with it. Human nature is odd. People might not care about some massive error in the abstract, but knowing they can blow up another human being's world with it, now that gets their attention.

So here's the result in the field of complex numbers yet again, where notice it's easy to show absolute proof.

I use a special construction:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

The a's can be found using the quadratic formula, but are so ugly I usually don't bother to give them, but maybe it'll help for those who wonder what they look like:

a_1(x) = ((7x - 1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2

a_2(x) = ((7x - 1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2 or vice versa.

At x=0, one of the a's is 0, while the other is -1, as a^2 + a = 0, has those solutions (you can check with the explicit equations as well if you wish). So it pays to get functions where both are 0 at x=0, as that trivially finishes the exercise.

Letting b_1(x) = a_1(x) + 1, assuming a_2(0) = 0, I have a_1(x) = b_1(x) - 1, and substituting gives:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

So now in the field of complex numbers you have the interesting result that the 7 was multiplied in only one way, which is the way I picked as fundamentally the example is no different from 7(x^2 + 3x + 2) = (x + 2)(7x + 7).

If I'd picked another way, you might have:

7(175x^2 - 15x + 2) = (5b_1(x) + 14)(5a_2(x) + 1)

If I'd wanted to split the 7 with square roots, you could have:

7(175x^2 - 15x + 2) = (5b_1(x) + 2sqrt(7))(5a_2(x) + sqrt(7))

So over the complex plane you have the answer as to what I wanted and the only way the 7 could have multiplied.

That is a mathematical absolute. It's mathematically impossible for the 7 to have multiplied any different way with:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

where b_1(0) = a_2(0) = 0.

But that says that with

a^2 - (7x-1)a + (49x^2 - 14x) = 0

only one of the roots is a product of 7, and I say it that weird way as I'm on the complex plane and "factor" isn't really meaningful.

And here's where a lot of algebraic number theory blows up which brings into question the usefulness of Galois Theory, and rather than go into that a lot, I'll point out that you're looking at a really easy absolute proof.

After all, if the 7 is being multiplied times one factor, so that only one root is a product of 7 and something else, then how in the hell could its factors end up in the other root?

But mathematicians teach that it DOES if with integer x

a^2 - (7x-1)a + (49x^2 - 14x) = 0

has non-rational roots.

Their mistake was easy to make, and the mistake was made over a hundred years ago, and it just took a while for someone (me) to come along and put it out there boldly what that mistake was, and predictably with an over one hundred year error there has been resistance.

It's actually kind of fascinating to watch posters try to dance around what you can determine in the field of complex numbers!

So what's different now? I've explained that the result is valid over the complex field before.

Again, it's that simple thing: the ability to humiliate others.

I'm guessing there are people in this world who will love the opportunity to screw with academics, to laugh at them, to show them up.

String theorists are a sad lot, if you know of this error, or they're a funny group of people whom you can watch with endless humor.

You can laugh and laugh and laugh as they go on about what the universe might be like, or claim that this or that notion of theirs actually works in the REAL WORLD.

When mathematicians claim some BIG RESULT, you can chuckle. I know I do.

I can dismiss awards yearly. I see the dark humor in it.

They're funny people.

What I've given is the key to seeing people with no clothes on, as the saying goes.

You can laugh at department heads. An undergrad can smile knowingly at her math professor. She may do the homework assigned. Take the tests. Do the bogus math because what's her choice? But deep down she knows she's dealing with a fool.

One time I got so in a mood I actually made a post about how the village idiots took over number theory.

Am I being too mean?

Nope. They had their chance. They've had YEARS. But they seem to believe that they can run.

Ok, now they can see the consequences. Humiliation.

They will be the world's next big laugh, and cry. Especially for the parents of the students taught the bogus research over the last six years. Those parents may just cry. So much for a Harvard education, eh?

Through the humiliation of academics, the truth can come out and that tragedy can end.

The betrayal of young minds by their professors.

Yeah, I have full justification to wreck the pride of arrogant idiots who betrayed so much for so little, who in trying to run from an absolute error, only set themselves up to be shown for what they are.

What they truly are.

They had a duty to tell the truth. Now it's your duty to make them pay.

What's different now is I'm pointing out to people that this result CAN be used to humble any, oh, string theorist you wish to torture with it. Human nature is odd. People might not care about some massive error in the abstract, but knowing they can blow up another human being's world with it, now that gets their attention.

So here's the result in the field of complex numbers yet again, where notice it's easy to show absolute proof.

I use a special construction:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

The a's can be found using the quadratic formula, but are so ugly I usually don't bother to give them, but maybe it'll help for those who wonder what they look like:

a_1(x) = ((7x - 1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2

a_2(x) = ((7x - 1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x)))/2 or vice versa.

At x=0, one of the a's is 0, while the other is -1, as a^2 + a = 0, has those solutions (you can check with the explicit equations as well if you wish). So it pays to get functions where both are 0 at x=0, as that trivially finishes the exercise.

Letting b_1(x) = a_1(x) + 1, assuming a_2(0) = 0, I have a_1(x) = b_1(x) - 1, and substituting gives:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

So now in the field of complex numbers you have the interesting result that the 7 was multiplied in only one way, which is the way I picked as fundamentally the example is no different from 7(x^2 + 3x + 2) = (x + 2)(7x + 7).

If I'd picked another way, you might have:

7(175x^2 - 15x + 2) = (5b_1(x) + 14)(5a_2(x) + 1)

If I'd wanted to split the 7 with square roots, you could have:

7(175x^2 - 15x + 2) = (5b_1(x) + 2sqrt(7))(5a_2(x) + sqrt(7))

So over the complex plane you have the answer as to what I wanted and the only way the 7 could have multiplied.

That is a mathematical absolute. It's mathematically impossible for the 7 to have multiplied any different way with:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

where b_1(0) = a_2(0) = 0.

But that says that with

a^2 - (7x-1)a + (49x^2 - 14x) = 0

only one of the roots is a product of 7, and I say it that weird way as I'm on the complex plane and "factor" isn't really meaningful.

And here's where a lot of algebraic number theory blows up which brings into question the usefulness of Galois Theory, and rather than go into that a lot, I'll point out that you're looking at a really easy absolute proof.

After all, if the 7 is being multiplied times one factor, so that only one root is a product of 7 and something else, then how in the hell could its factors end up in the other root?

But mathematicians teach that it DOES if with integer x

a^2 - (7x-1)a + (49x^2 - 14x) = 0

has non-rational roots.

Their mistake was easy to make, and the mistake was made over a hundred years ago, and it just took a while for someone (me) to come along and put it out there boldly what that mistake was, and predictably with an over one hundred year error there has been resistance.

It's actually kind of fascinating to watch posters try to dance around what you can determine in the field of complex numbers!

So what's different now? I've explained that the result is valid over the complex field before.

Again, it's that simple thing: the ability to humiliate others.

I'm guessing there are people in this world who will love the opportunity to screw with academics, to laugh at them, to show them up.

String theorists are a sad lot, if you know of this error, or they're a funny group of people whom you can watch with endless humor.

You can laugh and laugh and laugh as they go on about what the universe might be like, or claim that this or that notion of theirs actually works in the REAL WORLD.

When mathematicians claim some BIG RESULT, you can chuckle. I know I do.

I can dismiss awards yearly. I see the dark humor in it.

They're funny people.

What I've given is the key to seeing people with no clothes on, as the saying goes.

You can laugh at department heads. An undergrad can smile knowingly at her math professor. She may do the homework assigned. Take the tests. Do the bogus math because what's her choice? But deep down she knows she's dealing with a fool.

One time I got so in a mood I actually made a post about how the village idiots took over number theory.

Am I being too mean?

Nope. They had their chance. They've had YEARS. But they seem to believe that they can run.

Ok, now they can see the consequences. Humiliation.

They will be the world's next big laugh, and cry. Especially for the parents of the students taught the bogus research over the last six years. Those parents may just cry. So much for a Harvard education, eh?

Through the humiliation of academics, the truth can come out and that tragedy can end.

The betrayal of young minds by their professors.

Yeah, I have full justification to wreck the pride of arrogant idiots who betrayed so much for so little, who in trying to run from an absolute error, only set themselves up to be shown for what they are.

What they truly are.

They had a duty to tell the truth. Now it's your duty to make them pay.

### Wednesday, December 09, 2009

## JSH: Galois Theory problem and resolution in complex plane

I found a problem with some old mathematics which takes out the usefulness of Galois Theory, but it's hard to get people to believe that unless they try to do the math, so I gave a challenge to give to a mathematician which should be simple as it's removing an excess factor of 7. Now I'm sure some of you would love a nifty little mathematical challenge with which you could confound your colleagues, and I especially like to pick on string theorists, but first you need to BELIEVE it will, so here's why.

First the challenge.

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

To understand what is happening you need to go to the complex plane. Next you need normalized functions.

With x=0, you know you zero one of the functions as then:

a^2 + a = 0, so one is 0, and the other is -1. That trivially works:

7( 2) = (5(0) + 7)(5(-1) + 7)

where I arbitrarily picked a_1(0) = 0, a_2(0) = -1, as of course it could be vice versa. You're halfway there.

Remember we're in the complex plane. Now to normalize I can leave one of the a's and add 1 to the other, so, let:

b_2(x) = a_2(x) + 1, so a_2(x) = b_2(x) - 1, then:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5b_2(x) + 2)

and you know that the 7 could only have multiplied times the first factor—even though it's the complex plane.

Why? Because you see the 7 there with the normalized functions. 7*1 = 1.

If it had multiplied times the other factor then you'd have:

7(175x^2 - 15x + 2) = (5a_1(x) + 1)(5b_2(x) + 14)

Because 7*2 = 14, even on the complex plane.

Yup, I picked the first way. I MADE this example up to show a problem, and yes, with an extraneous factor like 7, it takes human choice to force it to go one way, as like: 7(x^2 + 3x + 2) = (7x + 7)(x + 2), there is a CHOICE.

I simply used an example that blows up some faulty math ideas.

So now you know from the complex plane how the multiplication had to go, so what's the big deal?

Well, now you know that only one of the roots of:

a^2 - (7x-1)a + (49x^2 - 14x) = 0

can actually have 7 as a factor! Trying x=1, you find that a^2 - 6a + 35 = 0, and

a_1(x) = 3 +/- sqrt(-26), and a_2(x) = 3 -/+ sqrt(-26)

or vice versa. But you cannot SEE the factor that is 7 because the square roots obscure it, but from the complex plane you know it is there, for one case, but it's indeterminable which one.

Now then, you have seen me easily give you the answer from the complex plane, so why does this remove the usefulness of Galois Theory?

Well mathematicians will tell you that provably NEITHER of the roots have 7 as a factor in something called the ring of algebraic integers. And that's true!

Contradiction.

Isn't that fun! You now know a real live mathematical contradiction. And it's a doozy.

So the ring of algebraic integers contradicts the complex plane. But algebraic number theory is built using the ring of algebraic number theory, and Galois Theory is built on algebraic number theory.

Pull the support and they all fall down.

So then, you now have conclusive proof that you CAN screw up the world of any string theorist in the world with this result!

You can sneak it on a blackboard, or write it on some paper and slip it under their door. Anything.

Any person in the world can use this result to make any string theorist go batshit.

I'm picking on string theorists but you can use it on any mathematical physicist, or even better, use it on a mathematician.

Be forewarned though, they may react in unpredictable ways. If they physically assault you, do not blame me.

Consider, in a moment you can crash the entire world of some person who may have a lot of prestige in this world. You can humble heads of major departments. Crush arrogant brats who've been told they are the future of physics.

Destroy people's life's work in a moment.

Now you know why posters argue with me year after year after year after year on this result. And how I got published on an earlier version and the math journal died:

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

http://www.emis.de/journals/SWJPAM/vol2-03.html

I didn't withdraw it. The editors did. EMIS has been kind enough to put a link though to my original paper:

http://www.emis.de/journals/Annals/SWJPAM/Vol2_2003/2.ps.gz

So I am a published author on this subject!

So yeah, they destroyed a freaking math journal over this result. You can certainly screw up the world of any math person you choose with it.

YOU have the power now. Use it wisely.

The correct mathematics may transform our world.

Just imagine you do not really know physics, especially particle physics, yet.

First the challenge.

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

To understand what is happening you need to go to the complex plane. Next you need normalized functions.

With x=0, you know you zero one of the functions as then:

a^2 + a = 0, so one is 0, and the other is -1. That trivially works:

7( 2) = (5(0) + 7)(5(-1) + 7)

where I arbitrarily picked a_1(0) = 0, a_2(0) = -1, as of course it could be vice versa. You're halfway there.

Remember we're in the complex plane. Now to normalize I can leave one of the a's and add 1 to the other, so, let:

b_2(x) = a_2(x) + 1, so a_2(x) = b_2(x) - 1, then:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5b_2(x) + 2)

and you know that the 7 could only have multiplied times the first factor—even though it's the complex plane.

Why? Because you see the 7 there with the normalized functions. 7*1 = 1.

If it had multiplied times the other factor then you'd have:

7(175x^2 - 15x + 2) = (5a_1(x) + 1)(5b_2(x) + 14)

Because 7*2 = 14, even on the complex plane.

Yup, I picked the first way. I MADE this example up to show a problem, and yes, with an extraneous factor like 7, it takes human choice to force it to go one way, as like: 7(x^2 + 3x + 2) = (7x + 7)(x + 2), there is a CHOICE.

I simply used an example that blows up some faulty math ideas.

So now you know from the complex plane how the multiplication had to go, so what's the big deal?

Well, now you know that only one of the roots of:

a^2 - (7x-1)a + (49x^2 - 14x) = 0

can actually have 7 as a factor! Trying x=1, you find that a^2 - 6a + 35 = 0, and

a_1(x) = 3 +/- sqrt(-26), and a_2(x) = 3 -/+ sqrt(-26)

or vice versa. But you cannot SEE the factor that is 7 because the square roots obscure it, but from the complex plane you know it is there, for one case, but it's indeterminable which one.

Now then, you have seen me easily give you the answer from the complex plane, so why does this remove the usefulness of Galois Theory?

Well mathematicians will tell you that provably NEITHER of the roots have 7 as a factor in something called the ring of algebraic integers. And that's true!

Contradiction.

Isn't that fun! You now know a real live mathematical contradiction. And it's a doozy.

So the ring of algebraic integers contradicts the complex plane. But algebraic number theory is built using the ring of algebraic number theory, and Galois Theory is built on algebraic number theory.

Pull the support and they all fall down.

So then, you now have conclusive proof that you CAN screw up the world of any string theorist in the world with this result!

You can sneak it on a blackboard, or write it on some paper and slip it under their door. Anything.

Any person in the world can use this result to make any string theorist go batshit.

I'm picking on string theorists but you can use it on any mathematical physicist, or even better, use it on a mathematician.

Be forewarned though, they may react in unpredictable ways. If they physically assault you, do not blame me.

Consider, in a moment you can crash the entire world of some person who may have a lot of prestige in this world. You can humble heads of major departments. Crush arrogant brats who've been told they are the future of physics.

Destroy people's life's work in a moment.

Now you know why posters argue with me year after year after year after year on this result. And how I got published on an earlier version and the math journal died:

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

http://www.emis.de/journals/SWJPAM/vol2-03.html

I didn't withdraw it. The editors did. EMIS has been kind enough to put a link though to my original paper:

http://www.emis.de/journals/Annals/SWJPAM/Vol2_2003/2.ps.gz

So I am a published author on this subject!

So yeah, they destroyed a freaking math journal over this result. You can certainly screw up the world of any math person you choose with it.

YOU have the power now. Use it wisely.

The correct mathematics may transform our world.

Just imagine you do not really know physics, especially particle physics, yet.

### Tuesday, December 08, 2009

## JSH: How you know, Galois Theory lost, group theory lost?

I can give the mathematical demonstration, but if you refuse to accept mathematical proof, it's kind of hard but I'll put it up again and explain how you have to lie to yourself to not realize this example blows up some things.

It asks you to try and DO something.

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

If any of you are worth a damn, first thing you should notice is that the functions are not normalized.

Checking at x = 0, gives a^2 + a = 0, so a=0 or a=-1, which means a_1(0) = 0 or -1, and a_2(0) = -1, or 0.

Which means that if you are a well-trained student of physics you will normalize the functions. Just like I did, years ago.

If you normalize the functions then the answer jumps out at you.

One normalization is a_1(x) = b_1(x) - 1, as that gives b_1(0) = 0, and then you can assume a_2(0) = 0, so:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

with normalized function as b_1(0) = a_2(0) = 0.

And now there's no mystery as there is only one way that 7 gets there now.

Notice that's true even in the field of complex numbers.

So to disbelieve that the 7 multiplied in one particular way is to distrust even the field of complex numbers which gives the same result because even in a field 7*1 = 7.

Divide off the 7 now:

175x^2 - 15x + 2 = (5b_1(x) + 2)(5a_2(x)/7 + 1)

There is NO OTHER WAY. It's trivial math. 7*1 = 7. That is true in the field of complex numbers. It's true in the field of algebraic numbers ,and it's even true in the ring of algebraic integers.

But it is NOT true in the ring of algebraic integers in general that a_2(x) has 7 as a factor.

So you have an easy mathematical proof of a problem with a ring many of you may not remember hearing about until I started going on and on about this issue. But the ring of algebraic integers is a base ring for number theory which was used for the mathematical ideas around the field of algebraic numbers, which is what's used with Galois Theory.

Algebraic numbers are ratios of algebraic integers. i.e. x/y where x and y are algebraic integers, and y is nonzero.

But you don't have to know all the abstractions behind the mathematics many of you probably take for granted, because all you need to know is that math people not only argue with me about the result above, but they killed a freaking mathematical journal that published a paper on the problem.

It is BIG.

Now then, posters can reply to me claiming error when there is none. You can verify the mathematics YOURSELF.

When you see people arguing against what you know has to be correct, get a clue!!!

Now then, what can you do?

Well, you can ask a mathematician to work through the problem. Give them the task to divide off the 7.

Why bother?

Because right now they may believe I'm just one guy, ranting on Usenet, with no one listening.

I think many of you ARE listening, realize the problem, and feel overwhelmed.

So first step is to say: start small. You ask someone to divide off the 7. If mathematicians are too intimidating, pick a mathematical physicist.

Pick a string theorist.

One by one you can around the world remove the delusion from these mathematicians that I'm the only one who knows.

These are proud people. They cherish prestige. They love accolades.

The analogy is to swimming naked: They're swimming naked. Drain the pool.

This result is mathematics and at least then you know it was always true. People make mistakes and can compound them.

The story could have been mathematicians acknowledge a major error in "core" number theory found by an amateur with a degree in physics working at solving math problems as a hobby, but they chose to kill the math journal, and run away.

So now it's up to physics people to go catch them.

It asks you to try and DO something.

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

If any of you are worth a damn, first thing you should notice is that the functions are not normalized.

Checking at x = 0, gives a^2 + a = 0, so a=0 or a=-1, which means a_1(0) = 0 or -1, and a_2(0) = -1, or 0.

Which means that if you are a well-trained student of physics you will normalize the functions. Just like I did, years ago.

If you normalize the functions then the answer jumps out at you.

One normalization is a_1(x) = b_1(x) - 1, as that gives b_1(0) = 0, and then you can assume a_2(0) = 0, so:

7(175x^2 - 15x + 2) = (5b_1(x) + 2)(5a_2(x) + 7)

with normalized function as b_1(0) = a_2(0) = 0.

And now there's no mystery as there is only one way that 7 gets there now.

Notice that's true even in the field of complex numbers.

So to disbelieve that the 7 multiplied in one particular way is to distrust even the field of complex numbers which gives the same result because even in a field 7*1 = 7.

Divide off the 7 now:

175x^2 - 15x + 2 = (5b_1(x) + 2)(5a_2(x)/7 + 1)

There is NO OTHER WAY. It's trivial math. 7*1 = 7. That is true in the field of complex numbers. It's true in the field of algebraic numbers ,and it's even true in the ring of algebraic integers.

But it is NOT true in the ring of algebraic integers in general that a_2(x) has 7 as a factor.

So you have an easy mathematical proof of a problem with a ring many of you may not remember hearing about until I started going on and on about this issue. But the ring of algebraic integers is a base ring for number theory which was used for the mathematical ideas around the field of algebraic numbers, which is what's used with Galois Theory.

Algebraic numbers are ratios of algebraic integers. i.e. x/y where x and y are algebraic integers, and y is nonzero.

But you don't have to know all the abstractions behind the mathematics many of you probably take for granted, because all you need to know is that math people not only argue with me about the result above, but they killed a freaking mathematical journal that published a paper on the problem.

It is BIG.

Now then, posters can reply to me claiming error when there is none. You can verify the mathematics YOURSELF.

When you see people arguing against what you know has to be correct, get a clue!!!

Now then, what can you do?

Well, you can ask a mathematician to work through the problem. Give them the task to divide off the 7.

Why bother?

Because right now they may believe I'm just one guy, ranting on Usenet, with no one listening.

I think many of you ARE listening, realize the problem, and feel overwhelmed.

So first step is to say: start small. You ask someone to divide off the 7. If mathematicians are too intimidating, pick a mathematical physicist.

Pick a string theorist.

One by one you can around the world remove the delusion from these mathematicians that I'm the only one who knows.

These are proud people. They cherish prestige. They love accolades.

The analogy is to swimming naked: They're swimming naked. Drain the pool.

This result is mathematics and at least then you know it was always true. People make mistakes and can compound them.

The story could have been mathematicians acknowledge a major error in "core" number theory found by an amateur with a degree in physics working at solving math problems as a hobby, but they chose to kill the math journal, and run away.

So now it's up to physics people to go catch them.

### Sunday, December 06, 2009

## JSH: Core error and Galois Theory

A few years back I did my own amateur research in what I thought was abstract number theory, and even briefly got published before some sci.math people ruined that with some emails. But funny thing. The ENTIRE math journal then died.

http://www.emis.de/journals/SWJPAM/vol2-03.html

Later I simplified the argument now to a seemingly simple task that I give, but pulling on the thread I've pointed out that the "core error" is not just some abstract problem for number theorists as it removes the usefulness of Galois Theory. And because group theory comes from Galois Theory it brings into question, group theory.

The math part is easy:

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

The 7 on the left hand side looks like a trivial factor. Standard teaching is just to divide off such routine factors, for instance:

7(x^2 + 3x + 2) = (7x + 7)(x + 2)

becomes x^2 + 3x + 2 = (x + 1)(x + 2), as the factor of 7, is useless, and provides no important information.

The example I've given above in many ways is just as trivial, the 7 is just as extraneous and it's removed just as easily as:

175x^2 - 15x + 2 = (5a_1(x)/7 + 1)(5a_2(x) + 7)

or

175x^2 - 15x + 2 = (5a_1(x) + 7)(5a_2(x)/7 + 1)

as it implies that one of the a's has 7 itself as a factor, but that means that:

a^2 - (7x-1)a + (49x^2 - 14x) = 0

has 7 as a factor of only one root, and if you let x=1, you get a^2 - 6a + 35 = 0, and

a_1(1) = 3 +/- sqrt(-26), or a_2(1) = 3 -/+ sqrt(-26) or vice versa.

So now you know that one of those has 7 as a factor, though it's invisible because of the square root.

But that blows up a lot of algebraic number theory and that's where all the arguing starts and the dead math journal and lots of unpleasantness and namecalling often ensues.

The problem is that with:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

it's insane to claim that the 7 is a function of x. It's a 7. 7 is just a number. It's NOT a function. Also you KNOW that excess factors can just be divided off. The value of x is irrelevant, but the number theory that blows up actually teaches that how the 7 divides off in the ring of algebraic integers depends on the value of x.

That algebraic integer theory formed the basis of the mathematical ideas underpinning the field of algebraic numbers which is about ratios of algebraic integers, and you get Galois Theory from the field of algebraic numbers.

Remember: dead math journal, years of arguing, math people claiming that 7 divides off as a function, weird things.

If you lose group theory then yeah, that brings into question the Standard Model. So the "core error" if you pull the string really goes places, which is fascinating in and of itself.

Anyone wish to lay odds on mathematicians and physicists losing so many pet cows?

Yeah, so now you see the problem.

Math is easy.

You have to do weird things to believe in the old stuff. The new stuff works great and fits with simple things taught to kids about extra factors. I can explain it all. Easy. Even got published!—until they killed the entire goddamn journal AFTER my paper was pulled.

Isn't that overkill?

Why trash the math journal AFTER they managed to get my paper pulled?

If I'm right then the wrong math can only go so far and problems will arise, but if these people are too invested, they'll just make up stuff, call you a crackpot if you cross them, and do wrong things until something breaks, I guess.

That's the way it goes.

But if you know the math you know to just let them go on their way and waste their lives without investing your precious time in stupidity.

I know I do. I don't even bother reading newspaper reports about physics research any more. Waste of time.

It's not really research any more when people are willfully in error. They're just playing a game.

And a stupid one too.

http://www.emis.de/journals/SWJPAM/vol2-03.html

Later I simplified the argument now to a seemingly simple task that I give, but pulling on the thread I've pointed out that the "core error" is not just some abstract problem for number theorists as it removes the usefulness of Galois Theory. And because group theory comes from Galois Theory it brings into question, group theory.

The math part is easy:

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

The 7 on the left hand side looks like a trivial factor. Standard teaching is just to divide off such routine factors, for instance:

7(x^2 + 3x + 2) = (7x + 7)(x + 2)

becomes x^2 + 3x + 2 = (x + 1)(x + 2), as the factor of 7, is useless, and provides no important information.

The example I've given above in many ways is just as trivial, the 7 is just as extraneous and it's removed just as easily as:

175x^2 - 15x + 2 = (5a_1(x)/7 + 1)(5a_2(x) + 7)

or

175x^2 - 15x + 2 = (5a_1(x) + 7)(5a_2(x)/7 + 1)

as it implies that one of the a's has 7 itself as a factor, but that means that:

a^2 - (7x-1)a + (49x^2 - 14x) = 0

has 7 as a factor of only one root, and if you let x=1, you get a^2 - 6a + 35 = 0, and

a_1(1) = 3 +/- sqrt(-26), or a_2(1) = 3 -/+ sqrt(-26) or vice versa.

So now you know that one of those has 7 as a factor, though it's invisible because of the square root.

But that blows up a lot of algebraic number theory and that's where all the arguing starts and the dead math journal and lots of unpleasantness and namecalling often ensues.

The problem is that with:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

it's insane to claim that the 7 is a function of x. It's a 7. 7 is just a number. It's NOT a function. Also you KNOW that excess factors can just be divided off. The value of x is irrelevant, but the number theory that blows up actually teaches that how the 7 divides off in the ring of algebraic integers depends on the value of x.

That algebraic integer theory formed the basis of the mathematical ideas underpinning the field of algebraic numbers which is about ratios of algebraic integers, and you get Galois Theory from the field of algebraic numbers.

Remember: dead math journal, years of arguing, math people claiming that 7 divides off as a function, weird things.

If you lose group theory then yeah, that brings into question the Standard Model. So the "core error" if you pull the string really goes places, which is fascinating in and of itself.

Anyone wish to lay odds on mathematicians and physicists losing so many pet cows?

Yeah, so now you see the problem.

Math is easy.

You have to do weird things to believe in the old stuff. The new stuff works great and fits with simple things taught to kids about extra factors. I can explain it all. Easy. Even got published!—until they killed the entire goddamn journal AFTER my paper was pulled.

Isn't that overkill?

Why trash the math journal AFTER they managed to get my paper pulled?

If I'm right then the wrong math can only go so far and problems will arise, but if these people are too invested, they'll just make up stuff, call you a crackpot if you cross them, and do wrong things until something breaks, I guess.

That's the way it goes.

But if you know the math you know to just let them go on their way and waste their lives without investing your precious time in stupidity.

I know I do. I don't even bother reading newspaper reports about physics research any more. Waste of time.

It's not really research any more when people are willfully in error. They're just playing a game.

And a stupid one too.

## JSH: Losing Galois Theory

One of the more depressing things that happened several years ago was that a line of amateur mathematical research took away the usefulness of Galois Theory. Turns out it's now trivial to prove, with a simple demonstration:

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

You may have seen me post that before as a challenge to mathematicians and string theorists (who happen to often be heavily into mathematics), but you may not understand its full significance—or how it takes away Galois Theory, so here is the rest.

Try to divide off the 7 in the most general way possible, consider functions,

w_1(x) and w_2(x), such that:

w_1(x)*w_2(x) = 7, and dividing off the 7 above gives:

175x^2 - 15x + 2 = (5a_1(x)/w_1(x) + 7/w_1(x))(5a_2(x)/w_2(x) + 7/w_2(x))

and suppose that they are factors such that

a_1(x) = b_1(x)*w_1(x), and a_2(x) = b_2(x)*w_2(x), then:

175x^2 - 15x + 2 = (5b_1(x) + w_2(x))(5b_2(x) + w_1(x))

and you may think that all is ok, but notice—a residue of 7 remains in the form of the factors w_1(x) and w_2(x).

The freaky bastards don't want to go away!!!

They are ghosts that remain in the thing.

But for those who know their Galois Theory that is unacceptable, as the class number uniquely holds those factors so it really is saying that SOMETHING is left, even though the 7 is gone from the left hand side—and that something can't just disappear by the rules of Galois Theory—in the ring of algebraic integers.

It is there permanently. But that is nonsensical. The 7 has divided off, so what can be left?

With an example from integers:

7(x^2 + 3x + 2) = (7x + 7)(x+2),

divide off the 7: x^2 + 3x + 2 = (x+1)(x+2). Done.

And if someone told you that a trace of the 7 had to remain you'd call them an idiot.

You may know that physicists seem to think that Galois Theory has usefulness in physics with group theory, but if you can comprehend the mathematics above, you now know it can't, because Galois Theory is about unit factors, which for that reason can always just divide off and disappear.

Unless you believe in math ghosts…

Try to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

You may have seen me post that before as a challenge to mathematicians and string theorists (who happen to often be heavily into mathematics), but you may not understand its full significance—or how it takes away Galois Theory, so here is the rest.

Try to divide off the 7 in the most general way possible, consider functions,

w_1(x) and w_2(x), such that:

w_1(x)*w_2(x) = 7, and dividing off the 7 above gives:

175x^2 - 15x + 2 = (5a_1(x)/w_1(x) + 7/w_1(x))(5a_2(x)/w_2(x) + 7/w_2(x))

and suppose that they are factors such that

a_1(x) = b_1(x)*w_1(x), and a_2(x) = b_2(x)*w_2(x), then:

175x^2 - 15x + 2 = (5b_1(x) + w_2(x))(5b_2(x) + w_1(x))

and you may think that all is ok, but notice—a residue of 7 remains in the form of the factors w_1(x) and w_2(x).

The freaky bastards don't want to go away!!!

They are ghosts that remain in the thing.

But for those who know their Galois Theory that is unacceptable, as the class number uniquely holds those factors so it really is saying that SOMETHING is left, even though the 7 is gone from the left hand side—and that something can't just disappear by the rules of Galois Theory—in the ring of algebraic integers.

It is there permanently. But that is nonsensical. The 7 has divided off, so what can be left?

With an example from integers:

7(x^2 + 3x + 2) = (7x + 7)(x+2),

divide off the 7: x^2 + 3x + 2 = (x+1)(x+2). Done.

And if someone told you that a trace of the 7 had to remain you'd call them an idiot.

You may know that physicists seem to think that Galois Theory has usefulness in physics with group theory, but if you can comprehend the mathematics above, you now know it can't, because Galois Theory is about unit factors, which for that reason can always just divide off and disappear.

Unless you believe in math ghosts…

### Friday, December 04, 2009

## JSH: Confronting your colleagues

I've found a rather potent error in some number theory, where it's kind of like a place where given 7x = 7x, the error stops you from dividing off the 7. But rather than explain it in detail I want you to ask a mathematician you know to do something that may seem simple. Which when you first see it may look trivial:

The request is, ask a mathematician to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

Now you do not need to know what an algebraic integer is, or why this particular request is so important, but you just need to be able to read the mathematician to see how he, or she reacts to this request.

The request shows a very devastating error that entered into number theory in the late 1800's but lurks in "pure math" areas so it probably doesn't effect much math that physicists use, though it may blow apart string theory, as people there go to more mathematical approaches and may have gone far enough to have this error impact, but you can give it to a string theorist as well as a mathematician and see what he does.

My fear is that your colleague, if the person is a colleague, will lie to you. He may be lying to himself.

But I think you will be able to tell.

That's why this test is so potent. It's easy to give. That expression IS kind of funky, with that 7 on the left hand side, so why can't it just divide off? Like with 7x = 7x, you can divide off, to get x = x. You can do it in complex number of course, but here it's a number theory issue where that "algebraic integers" part is important.

The expression IS an identity as it's a factorization.

So it is like 7x = 7x, fundamentally.

I think some of you know about this error because of my prior posts and you can see I'm taking a different tack. I think some of you deep down wish to see how a math person will react to this thing. Or maybe you know it IS a massive problem, so you will not do it, to try and protect fellow academics. Or out of your own fear of the response.

It's a fascinating error. How it has lurked in mathematics for over a hundred years is fascinating as well, as is the difficulty in getting mathematicians to face it. But what you do or do not do is important here.

It is not an academic exercise.

The request is, ask a mathematician to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

Now you do not need to know what an algebraic integer is, or why this particular request is so important, but you just need to be able to read the mathematician to see how he, or she reacts to this request.

The request shows a very devastating error that entered into number theory in the late 1800's but lurks in "pure math" areas so it probably doesn't effect much math that physicists use, though it may blow apart string theory, as people there go to more mathematical approaches and may have gone far enough to have this error impact, but you can give it to a string theorist as well as a mathematician and see what he does.

My fear is that your colleague, if the person is a colleague, will lie to you. He may be lying to himself.

But I think you will be able to tell.

That's why this test is so potent. It's easy to give. That expression IS kind of funky, with that 7 on the left hand side, so why can't it just divide off? Like with 7x = 7x, you can divide off, to get x = x. You can do it in complex number of course, but here it's a number theory issue where that "algebraic integers" part is important.

The expression IS an identity as it's a factorization.

So it is like 7x = 7x, fundamentally.

I think some of you know about this error because of my prior posts and you can see I'm taking a different tack. I think some of you deep down wish to see how a math person will react to this thing. Or maybe you know it IS a massive problem, so you will not do it, to try and protect fellow academics. Or out of your own fear of the response.

It's a fascinating error. How it has lurked in mathematics for over a hundred years is fascinating as well, as is the difficulty in getting mathematicians to face it. But what you do or do not do is important here.

It is not an academic exercise.

### Thursday, December 03, 2009

## JSH: To parents

I you are reading this message maybe you're looking at the newsgroup with curiosity about what your child is reading, or you have been directed here by that child to read this message, which is somewhat of a difficult one for me, as I'm here to ask you to do something which may sound strange.

You need to ask a mathematician to do something which may reveal to you that that person is knowingly living a fraud, which is important to you as they may be TEACHING that fraud to your child.

Your child may have directed you here as she or he needs your help with this extraordinary situation.

The request is, ask a mathematician to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

The mathematics is as simple as I can get it. I've worked for years to boil things down to a level where it is very easy to explain, but still there are I'm sure elements which will not make sense to you. That is ok. You are to use your knowledge of human nature here, and everything in that piece above is needed, including the part about algebraic integers.

If you're wondering about the principle here it is like how with 7x = 7x, you can get to x = x. Trivial, I know. But over a hundred years ago a bizarre but somewhat subtle error entered into the mathematical field, where that trivial thing is violated in the example I wish you to use in this thing called the ring of algebraic integers.

I discovered this some years ago. I even got a paper on it published, but some math people got it retracted by spooking the editors, who yanked it against my wishes: http://www.emis.de/journals/SWJPAM/vol2-03.html

That link is to the archives of the journals maintained by a European organization called EMIS, which keeps up with electronic mathematical journals from around the world: http://www.emis.de/journals/index.html

The mathematical journal itself shut down not too long after pulling my paper. Its hosting university scrubbed all mention of its existence from its website. EMIS actually saved that journal from vanishing completely.

If your child has brought you to this post, consider what he or she faces: a massive error in the field of number theory, for which a journal may have been destroyed, where people in the field may be knowingly perpetuating a fraud. For that child to progress in the mathematical field she or he may have to knowingly learn false mathematics, just to get by, take tests, do homework, knowing it is bogus.

Why would mathematics professors do such a thing?

You as an adult may be aware that people can do very wrong things when faced with extreme loss. The error may invalidate the entire careers of people who may have spent decades, working hard, thinking they were brilliant, believing in their work.

With so much of their lives invested, it may seem easier to them to live a lie, maybe even to deny in their own minds the truth.

But to that they are sacrificing the future of your child in mathematics.

You do not have to believe all of that to act. If you know a mathematician simply ask them to divide the 7 off. If they satisfy you in answering that request, and ask why, you can say some strange nutty person on Usenet or the Internet was babbling nonsense.

The point here is not your mathematical knowledge. It is your human knowledge. If they are under the stress of the knowledge of a fraud as immense as I say, you'll pick that up.

Your situation is shared by parents all over the world.

This problem is an issue for parents in China, as well as the United States, in Russia, as well as Japan, in Singapore, Australia, New Zealand, Mozambique, Mexico, Czechoslovakia, Britain, Ireland, Venezuela, Malta, Vietnam, Iran, South Korea, North Korea and hundreds more.

If you have read to here, then your judgement is what's necessary for the next decision. I'm trying to enlist the aid of parents around the world to stop this nonsense of fraudulent information being taught to their children as all else has failed.

It is up to you now. And all you have to do is ask some mathematician, to divide off a 7.

You need to ask a mathematician to do something which may reveal to you that that person is knowingly living a fraud, which is important to you as they may be TEACHING that fraud to your child.

Your child may have directed you here as she or he needs your help with this extraordinary situation.

The request is, ask a mathematician to divide off the 7:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0 in the ring of algebraic integers.

The mathematics is as simple as I can get it. I've worked for years to boil things down to a level where it is very easy to explain, but still there are I'm sure elements which will not make sense to you. That is ok. You are to use your knowledge of human nature here, and everything in that piece above is needed, including the part about algebraic integers.

If you're wondering about the principle here it is like how with 7x = 7x, you can get to x = x. Trivial, I know. But over a hundred years ago a bizarre but somewhat subtle error entered into the mathematical field, where that trivial thing is violated in the example I wish you to use in this thing called the ring of algebraic integers.

I discovered this some years ago. I even got a paper on it published, but some math people got it retracted by spooking the editors, who yanked it against my wishes: http://www.emis.de/journals/SWJPAM/vol2-03.html

That link is to the archives of the journals maintained by a European organization called EMIS, which keeps up with electronic mathematical journals from around the world: http://www.emis.de/journals/index.html

The mathematical journal itself shut down not too long after pulling my paper. Its hosting university scrubbed all mention of its existence from its website. EMIS actually saved that journal from vanishing completely.

If your child has brought you to this post, consider what he or she faces: a massive error in the field of number theory, for which a journal may have been destroyed, where people in the field may be knowingly perpetuating a fraud. For that child to progress in the mathematical field she or he may have to knowingly learn false mathematics, just to get by, take tests, do homework, knowing it is bogus.

Why would mathematics professors do such a thing?

You as an adult may be aware that people can do very wrong things when faced with extreme loss. The error may invalidate the entire careers of people who may have spent decades, working hard, thinking they were brilliant, believing in their work.

With so much of their lives invested, it may seem easier to them to live a lie, maybe even to deny in their own minds the truth.

But to that they are sacrificing the future of your child in mathematics.

You do not have to believe all of that to act. If you know a mathematician simply ask them to divide the 7 off. If they satisfy you in answering that request, and ask why, you can say some strange nutty person on Usenet or the Internet was babbling nonsense.

The point here is not your mathematical knowledge. It is your human knowledge. If they are under the stress of the knowledge of a fraud as immense as I say, you'll pick that up.

Your situation is shared by parents all over the world.

This problem is an issue for parents in China, as well as the United States, in Russia, as well as Japan, in Singapore, Australia, New Zealand, Mozambique, Mexico, Czechoslovakia, Britain, Ireland, Venezuela, Malta, Vietnam, Iran, South Korea, North Korea and hundreds more.

If you have read to here, then your judgement is what's necessary for the next decision. I'm trying to enlist the aid of parents around the world to stop this nonsense of fraudulent information being taught to their children as all else has failed.

It is up to you now. And all you have to do is ask some mathematician, to divide off a 7.

### Wednesday, December 02, 2009

## JSH: Factorizations are identities

Ok, starting to see a breakdown of understanding of the most basic of mathematics in replies to my previous threads so some points of reminder:

If I were having this discussion with Gauss and Dedekind that would be it. The demonstration would be enough.

But many of you are ready to toss mathematics entire, and declare it to be inconsistent today, only because of 100+ years with the error. Nothing more.

So at the end of the day, protestations of rigor and claim of love of mathematical truth were tossed by many of you based on time alone. Time with a massively devastating error, which just happens to show some people were wrong for over a hundred years.

People have been wrong for longer.

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

That special construction blows apart some flawed ideas. That's all. To hold on to those flawed ideas you have to dismiss mathematical consistency itself.

For any of you looking for authority, or looking to authority, you simply take that construction to your favorite math teacher, and ask him or her to divide off the 7 in the ring of algebraic integers.

It cannot be done. That ring breaks the identity principle. It grabs the 7 like a desperate lover—and refuse in general to let go.

A proper ring would not behave in such a way.

- Factorizations are identities!!!

So, like with x^2 + 3x + 2 = (x+1)(x+2), notice the SAME THING on both sides of the equals!!!

It just looks different one one side. But it's the SAME THING. A factorization is an identity.

The ring of algebraic integers bizarrely violates a principle in certain special cases with a special construction, which is equivalent then to blocking the case that given 7x = 7x, x=x, as it will not allow you to divide the 7 off. - If you do not address the issue properly then you have a fundamental mathematical contradiction!

So if you just say, no way, no problem is possible here, everything is ok, then you're also saying: mathematics contradicts!

So you're ultimately trashing all of human mathematics.

Mathematics does not allow shades of gray.

Posters get away with denying mathematics entire by people not accepting that mathematical logic does not allow you to say it's ok for the ring of algebraic integers to disobey basic principles of identity.

If you so allow you end mathematics itself. You declare it to be inconsistent. - The special construction is mathematically irrefutable. It shows a profound flaw with defining a ring as having only as members the roots of monic polynomials with integer coefficients.

If I were having this discussion with Gauss and Dedekind that would be it. The demonstration would be enough.

But many of you are ready to toss mathematics entire, and declare it to be inconsistent today, only because of 100+ years with the error. Nothing more.

So at the end of the day, protestations of rigor and claim of love of mathematical truth were tossed by many of you based on time alone. Time with a massively devastating error, which just happens to show some people were wrong for over a hundred years.

People have been wrong for longer.

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

That special construction blows apart some flawed ideas. That's all. To hold on to those flawed ideas you have to dismiss mathematical consistency itself.

For any of you looking for authority, or looking to authority, you simply take that construction to your favorite math teacher, and ask him or her to divide off the 7 in the ring of algebraic integers.

It cannot be done. That ring breaks the identity principle. It grabs the 7 like a desperate lover—and refuse in general to let go.

A proper ring would not behave in such a way.

### Tuesday, December 01, 2009

## JSH: Formally peer review and published

The results I'm giving showing a problem with the ring of algebraic integers are a simplification of research I had formally peer reviewed and published in a mathematical journal, where the editors later chickened out, caving to Usenet pressure, pulled my paper, and then could manage only one more edition before the journal DIED. Its archives are maintained by EMIS:

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

So yeah, last time I checked I'm listed as a published mathematical author. EMIS also revived the paper which the editors withdrew, where you can see again the famous link:

http://www.emis.de/journals/SWJPAM/vol2-03.html

I don't link though to the revived paper (but thanks EMIS!) as I've greatly simplified the argument to quadratics versus the cubics I was using before:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And I demonstrated in other threads that yes, since I am the one who is mathematically correct I can SHRED people who fight the argument. I hate doing it though. I feel terrible and have been so polite for so many years. Maybe only by being more brutal can I show some of you where you actually are.

I can walk into any major math department in the world and humiliate the head of that department in minutes.

But not just I. ANYONE who knows of this error, and realizes the ongoing academic fraud can do the same.

So yes, proud people. Maybe even arrogant people who are on paper major mathematicians, respected, with established positions, can at a moment face humiliation.

They live with it. Can you?

Can you blow your years learning bogus math, fighting to work your way through hard courses of study in number theory, to get good grades, to impress people I can humiliate in ten minutes with basic algebra?

To be one of them?

So why don't I do it? Why don't I say, ride over the University of Berkeley which is minutes away, and confront some mathematicians about this number theory error?

Because there is strength in numbers.

Even if I got into the math department a simple call to security, and some stupid sick idiot can go on with his life as if he really is a mathematician instead of being a fraud. A fake. A wannabe who actually failed to prove maybe anything as EVERYTHING he supposedly has proven depends on this error.

No. I'll teach people about it. And eventually they will come. So you can wait if you wish for that day, when someone puts some equations in front of you and SHREDS your delusions of being a mathematician. Like your supposed betters do.

Formally peer reviewed and published.

Just words when human beings hate mathematics in truth, based on their actions, no matter what anyone else may call them.

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

So yeah, last time I checked I'm listed as a published mathematical author. EMIS also revived the paper which the editors withdrew, where you can see again the famous link:

http://www.emis.de/journals/SWJPAM/vol2-03.html

I don't link though to the revived paper (but thanks EMIS!) as I've greatly simplified the argument to quadratics versus the cubics I was using before:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And I demonstrated in other threads that yes, since I am the one who is mathematically correct I can SHRED people who fight the argument. I hate doing it though. I feel terrible and have been so polite for so many years. Maybe only by being more brutal can I show some of you where you actually are.

I can walk into any major math department in the world and humiliate the head of that department in minutes.

But not just I. ANYONE who knows of this error, and realizes the ongoing academic fraud can do the same.

So yes, proud people. Maybe even arrogant people who are on paper major mathematicians, respected, with established positions, can at a moment face humiliation.

They live with it. Can you?

Can you blow your years learning bogus math, fighting to work your way through hard courses of study in number theory, to get good grades, to impress people I can humiliate in ten minutes with basic algebra?

To be one of them?

So why don't I do it? Why don't I say, ride over the University of Berkeley which is minutes away, and confront some mathematicians about this number theory error?

Because there is strength in numbers.

Even if I got into the math department a simple call to security, and some stupid sick idiot can go on with his life as if he really is a mathematician instead of being a fraud. A fake. A wannabe who actually failed to prove maybe anything as EVERYTHING he supposedly has proven depends on this error.

No. I'll teach people about it. And eventually they will come. So you can wait if you wish for that day, when someone puts some equations in front of you and SHREDS your delusions of being a mathematician. Like your supposed betters do.

Formally peer reviewed and published.

Just words when human beings hate mathematics in truth, based on their actions, no matter what anyone else may call them.

## JSH: Dividing off 7

Ok, I've gone on and on about a problem with dividing off 7 with a special example which shows how bizarre (insane) the ring of algebraic integers is, but can it be divided off in a saner ring? YES!

Here's the example again:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

If you arbitrarily pick a_1(x) = 7b(x), you get:

7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5a_2(x)+ 7)

and you can trivially divide off the 7:

175x^2 - 15x + 2 = (5b_1(x) + 1)(5a_2(x)+ 7)

Easy as pie. Some may wonder about the apparent 7 still remaining, especially as I talked of ghosts with 7 in a previous reply, but the situation is easily figured out with x=0, as then:

175(0)^2 - 15(0) + 2 = (5b_1(0) + 1)(5a_2(0)+ 7)

which is

2 = (1)(-5 + 7) = (1)(2)

no problems and no 7. You can remove the final appearance that 7 is still there with a_2(x) = b_2(x) - 1, giving:

175x^2 - 15x + 2 = (5b_1(x) + 1)(5b_2(x) + 2)

where you'll note the b's are now normalized, in that with x=0, b_1(0) = b_2(0) = 0.

(Isn't that neat? Now it looks a LOT like x^2 + 3x + 2 = (x+1)(x+2) and YES that was DELIBERATE! Isn't that clever?)

And now I can multiply back by 7 if I wish to get my original example, or I can multiply 8, or 27, or any number I wish.

See? Constants multiplied ARE easy to handle, just like you've been taught! So what's the big deal?

The big deal is that option is not available in the ring of algebraic integers, as it says one of the roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

has 7 as a factor, while the other does not.

But NEITHER of the roots have 7 as a factor, if that gives you a quadratic with integer coefficients and the a's are non-rational, in the ring of algebraic integers! The ring is insane!!!

Example: with x=1, you have a^2 - 6a + 35 = 0, so

a_1 = (6 +/- sqrt(36 - 4(35)))/2, a_2 = (6 -/+ sqrt(36 - 4(35)))/2

So you have simply enough a_1 = 3 +/- sqrt(-26), and a_2 = 3 -/+ sqrt(-26) where I arbitrarily picked that order.

And I don't see that either of them has 7 as a factor, but you have mathematical proof that one of them does, but not in the ring of algebraic integers! So what gives?

The mathematics is telling you that there can be situations where with combinations of radicals and integers, you can have an integer factor that is not visible to the naked eye, but provably there or mathematics contradicts!

Yup. Without that conclusion you run into mathematical contradiction.

So in a sense the people who keep arguing with me are arguing for the death of mathematics, by claiming it is fundamentally illogical.

They are then: anti-mathematicians

Yes, they can call themselves mathematicians. They can be called mathematicians by the world, but if you take a position that requires that mathematics itself be illogical, then you cannot in truth BE a mathematician.

Go back over it. Go back over everything in this post as much as you need. And realize the logical necessity or find an error in the reasoning.

I constructed a powerful little example that blows apart some human social structures. It reveals that some pretenders are claiming to be mathematicians when they are not. That's all. It's not complicated.

These things happen. Otherwise, human history would be rather boring.

Here's the example again:

7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

If you arbitrarily pick a_1(x) = 7b(x), you get:

7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5a_2(x)+ 7)

and you can trivially divide off the 7:

175x^2 - 15x + 2 = (5b_1(x) + 1)(5a_2(x)+ 7)

Easy as pie. Some may wonder about the apparent 7 still remaining, especially as I talked of ghosts with 7 in a previous reply, but the situation is easily figured out with x=0, as then:

175(0)^2 - 15(0) + 2 = (5b_1(0) + 1)(5a_2(0)+ 7)

which is

2 = (1)(-5 + 7) = (1)(2)

no problems and no 7. You can remove the final appearance that 7 is still there with a_2(x) = b_2(x) - 1, giving:

175x^2 - 15x + 2 = (5b_1(x) + 1)(5b_2(x) + 2)

where you'll note the b's are now normalized, in that with x=0, b_1(0) = b_2(0) = 0.

(Isn't that neat? Now it looks a LOT like x^2 + 3x + 2 = (x+1)(x+2) and YES that was DELIBERATE! Isn't that clever?)

And now I can multiply back by 7 if I wish to get my original example, or I can multiply 8, or 27, or any number I wish.

See? Constants multiplied ARE easy to handle, just like you've been taught! So what's the big deal?

The big deal is that option is not available in the ring of algebraic integers, as it says one of the roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

has 7 as a factor, while the other does not.

But NEITHER of the roots have 7 as a factor, if that gives you a quadratic with integer coefficients and the a's are non-rational, in the ring of algebraic integers! The ring is insane!!!

Example: with x=1, you have a^2 - 6a + 35 = 0, so

a_1 = (6 +/- sqrt(36 - 4(35)))/2, a_2 = (6 -/+ sqrt(36 - 4(35)))/2

So you have simply enough a_1 = 3 +/- sqrt(-26), and a_2 = 3 -/+ sqrt(-26) where I arbitrarily picked that order.

And I don't see that either of them has 7 as a factor, but you have mathematical proof that one of them does, but not in the ring of algebraic integers! So what gives?

The mathematics is telling you that there can be situations where with combinations of radicals and integers, you can have an integer factor that is not visible to the naked eye, but provably there or mathematics contradicts!

Yup. Without that conclusion you run into mathematical contradiction.

So in a sense the people who keep arguing with me are arguing for the death of mathematics, by claiming it is fundamentally illogical.

They are then: anti-mathematicians

Yes, they can call themselves mathematicians. They can be called mathematicians by the world, but if you take a position that requires that mathematics itself be illogical, then you cannot in truth BE a mathematician.

Go back over it. Go back over everything in this post as much as you need. And realize the logical necessity or find an error in the reasoning.

I constructed a powerful little example that blows apart some human social structures. It reveals that some pretenders are claiming to be mathematicians when they are not. That's all. It's not complicated.

These things happen. Otherwise, human history would be rather boring.