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Tuesday, November 14, 2017

But does it factor?

One of my first results with what I now call the BQD Iterator was talked couple years after found it in this post with this result.

Given x2 - Dy2 = 1:


(D-1)j2 + (j+1)2 = (x+y)2, where j = ((x+Dy) -1)/D

or

(D-1)j2 + (j-1)2 = (x+y)2, where j = ((x+Dy) +1)/D

Where the two cases only matter for finding integer solutions, as j will be an integer if j = 1 mod D, for the first one, or j = -1 mod D for the second.

And gave this example back then:

With D=2, and x=17, y=12, you solve as 172 - 2(12)2 = 1, and going with the minus of the plus or minus:

j = ((17+2(12)-1)/2 = 20 is a solution giving:

202 + 212 = 292

So D-1 a perfect square relates to circles but otherwise gives non-circular ellipses.

And also I noted the rational solutions for x and y:

x = (D + t2)/(D - t2) and y = 2t/(D - t2)

Because that means you can get integer solutions for an ellipse, using those solutions, because of how those squares are distributed. But like with the first one, have always wondered about:

(D-1)j2  = (x+y)2 -  (j+1)2 = (x + y + j + 1)(x + y - j - 1),  j = ((x+Dy) - 1)/D

Because you can force that to be all integers with rational solutions as all the denominators can be multiplied out. And I never checked it, to see if it ever factored D-1 non-trivially.

But have wondered, for years. Why will I not check it?

My guess? Is one of THE control equations for ALL integer factorizations. The other results from the other variant. That thing I suspect, helps control all integer factorization, across infinity. But maybe not.

May be key to integer factorization the way that x2 + y2 = 1 is key to trigonometry. Showing value of what I now call unary two conics equation. Maybe that thing controls ALL integer factorizations! To the math would be just about logic. For us? Would be so remarkable.

Maybe it just kind of scares me.

To just look at something that maybe controls so much, and wonder.


James Harris

Analyzing psychological space

Was surprised over a decade ago. Did think maybe that math grad student would be honest and help when he realized I was correct. Have had time to consider my example social problem case quite a bit through the years. And part of it is, training? Number theorists rule their roost with psychological precision. Doubt is an accident.

Over a hundred plus years to probably notice their number theory tools were not really working well, if at all. And now very practiced at deflecting attention to the reality, including bouncing off people like myself talking it.

Feel like am playing catch up, as for a LONG time felt like just needed to keep piling up discoveries, but they are more and more immune to it! Like are adapting, and learning can get away with it.

Need to abstract them. Ok, what is currently known?

Math students can't seem to be enticed with further discovery potential, as have tried that angle. Can't be trusted to turn on them when erroneous math is proven. And willingly apparently continue, even when must be clear that the analysis they are doing is actually worthless. Troubling.

So odd is why have been puzzled for so long. Mathematical results? Useless with them. Even if some excitement is generated for a bit? Gets dampened out, somehow. Yet, they think they're interested in mathematics? How is this cognitive dissonance maintained, except by very powerful psychological tools? Or am I assuming too much. Could be stupid simple, eh? Ponder here more?

Institutions are well trained to accept them like any other experts. And IS weird how deep that trust goes, even as web security breaches embarrass. Why not question underlying system?

US Government apparently is completely hacked and doesn't even seem to care too much. I just assume all its systems are leaking, and then world events make more sense. Shows power of military might over good sense. So figure we're safe regardless or would be more concerned.

These are psychological forces that go deep into the human animal. Behavior is very communal, and number theorists are tapping into controls that suspend human reasoning, which is really surface anyway. Human beings are NOT rational. Emotion has been noted as key.

People identifying communally must be separated from seeing as a benefit. Failure realty should be emphasized? Key? Must be some kind of reward system that creates such tight binding against mathematical proof! Absolute truth can be deflected only certain ways? Or no? Yeah by casting doubt on concept of mathematical proof, which HAVE caught them doing in the past.

Over a hundred years of history of apparent success current ones can check of people who may have owed that appearance to the error. Could be reassuring to them. They may no longer believe in truth. They may no longer believe in social systems. They may feel safe with believing that even their fake research will last indefinitely, or definitely long enough to live a seemingly successful life. Interesting.

Psychological assessment space generated. Will consider and edit over time as needed.


James Harris

Further defining social problem space

Discovering the math was apparently first problem solving exercise and after over two decades of successful discovery, am now realizing need to focus on what I call the social problem.

What have established beyond mathematical doubt is that there is a problem with use of ring of algebraic integers, where recently posted in detail talking historical reality entered field in late 1800's.

Mathematicians at that time, ironically were trying to solidify the foundations of mathematics as a discipline, and screwed up.

Problem with math error is it makes it easier to look like you prove something which is actually taught to math students. In this case erroneous ideas were not outed because also push went to supposedly pure research. With that even as a theory, would expect MORE people would crowd into the easier area, and looks like that's what happened, with number theorists dominating.

Initially did not realize math people had to be aware on some level. Now believe they were, as looking at sophisticated blocking to maintain the error, which primarily relies on silent treatment.

And can easily prove the math. Have however watched as people do not react as have expected when realize am correct, which posted earlier on, as have studied for more than a decade. As I solidify the mental adjustment. Means is not enough to just inform. Must consider human psychology more carefully.

People look to experts. Is forced on us in a complex world. In this case, with a problem so old, very much entrenched at ALL levels in mathematical community.

A practical wrinkle did enter though, as number theorists presented integer factorization as a hard problem, and web emerged using techniques like public key encryption for security. It is now doubtful that lack of ability with integer factorization was because of difficulty, but simply may have been because of lack of ability, of number theorists. And yeah, lots of web security problems consistent with that theory, but also an area where governments are SUPPOSED to check.

My latest research result, figuring out a new primary way to do modular inverse could not be ignored by legitimate researchers, so can conclude they realize they are in error, and now are simply protecting, against further mathematical discovery which then is an enemy to their success.

Social problem then is fully revealed as a cadre of people who are succeeding at being mathematicians in appearance, with it possible they have no research of importance that is valid. Whose entrenchment may help explain widespread problems with web security. And they are apparently aware that they are in error and that their research is bogus. Where they have been acting to protect their situation.

Thorny problem, indeed.


James Harris

Knowledge as entertainment or sport

There is a great thing about mathematics that you do not need to work to convince, when is correct. And have noted past success with my own research in getting published, even though I also make sure to note chief editor tried to delete out my paper AFTER publication from a now dead electronic journal, which was back in 2004.

However, it occurs to me that people seem to think AM trying to convince, when am sharing mathematical truths, which of course is a position that can collapse if they evaluate.

Like shared that story of a math grad student who I guess thought he might be able to convince me I was wrong, over a decade ago, and what happened when he instead convinced himself.

He was deflated.

That is NOT fun to witness either. And have encountered more than once. So no, there is no flush of satisfaction as if won an argument. Math just is. For me there has usually been a bit of sadness for that person. The truth should not hurt, but is choice of that person, not me.

To me the rest of the story with mathematics in the modern age is NOT with whether or not you can prove, but how others react, and I think math for those who don't avoid it, who think they value it, is like entertainment or sport.

So yeah, can easily convince mathematicians--better yet, my math easily convinces mathematicians, as one would expect. There is no mathematical basis for denial of it. But it is disappointing for them emotionally.

Is maybe like watching a favorite team lose a sporting event, when someone finally realizes am correct. They deflate and slink off. Is that cruel? They disappear. That person so jumping up and down and excited like a fan cheering on the home team--the mathematical establishment, deflates and metaphorically, just goes home.

People who do not care if the math they do is correct as long as they FEEL good doing it, or talking about it. They represent a problem I find difficult to solve. Correct mathematical arguments? Just make them feel worse. The more proof given? Worse they feel. Then they just walk away from it, to keep doing what they like.

So yes! Have experienced winning the arguments for those who wonder. So no, you do not have anything to offer by agreeing with what I know to be true. And I've watched what people do next.

Have watched, as they, slink away from the truth.

And I have pondered the behavior, for years.

It is a difference of our times I think. Possibly a product of a culture where entertainment and sports are HUGE in lives of many, including me, where others maybe think they chose knowledge, but reality is they get pronouncements from people informing something is important. Same people also often saying is TOO DIFFICULT for most to understand. So yeah, for them? Is not about knowledge, but about trust and emotion. Their cheering of mathematics is no different than others cheering their favorite sports team or celebrities.

And when math bursts that bubble? They shrink away like a morose crowd upset with a loss by the home team.

Which I realized years ago. And I call it, the social problem. That in the 21st century people of the math community do NOT care if math is correct. They care how it makes them feel. Applied math is safe from this effect. In pure math it dominates. Notice where MOST of today's mathematicians are.

What can you do though, when the truth is not appealing?

Working on solving the social problem, like with this post. Solution is to get people to value the knowledge, not their emotion about the knowledge. But how? Is such a weird problem and remarkably difficult to solve. So no, is not needed for me to work to convince. Can simply share, and is EASY for me to get agreement on my math research.

Is math after all.

Math works that way.


James Harris

Monday, November 13, 2017

Some math and attention reality

Mathematics has a huge value to our species for what we can do with mathematical things and has developed to a level of abstraction where much of it can be distant for many.

That is true in lots of areas of human interest and recently noted to myself how little I know about paint, though see all over the place, and have painted things. But how much do I really need to know to live my life?

Reliance on expertise is a necessity in our world where so much was developed over so much time and mathematics is one of the oldest areas of human interest and effort. Yet can still surprise us with powerful tools. Like one of my personal favorites is my own discovery.

Given: u2 + Dv2 = F

then it must also be true that

(u-Dv)2 + D(u+v)2 = F(D+1)

-------------------------------------------------------------
Reference blog post: Binary Quadratic Diophantine Iterator

That is not complicated really. And yeah, if you THINK the only thing you need to do is discover something interesting, then you do NOT need to be an expert in that area.

One of my favorite examples made with it, so yeah have on repeat as I think tells SO much:

(462 + 482 + 722)(1722 + 258+ 430+ 6022 + 17622) = 


            615+ 30752 + 141452 + 159902  + 1884972   =  774*210

Do you know how was done? On this blog can see easily built--and explained.

Yeah we DO need people who can develop a deep knowledge most do not need to have, like about paint like do I need to ponder its chemical structure? No. However if I noticed something cool about paint, might I expect say a chemist who specialized in paints to find curious, if true? I think so.

Am NOT a mathematician. Am someone who has found some cool, relatively simple things, including ones that challenge what we think we know, about numbers. And went to the people who are establishment, repeatedly.

Math in its usefulness is how we have so much. As human beings learned more to do with what they had, have discovered more. To me that is SO cool.

Have watched as people from all over the world come to this blog, to look at things, presumably useful. I know I like playing with numbers.

Then I think a spectator mentality takes over. Especially when you've been trained to accept pronouncements of supposedly important math which very few people are expected to barely understand. Which is ok, is like with my paint example. We just need to know that expertise is real, you know?

While with me and my math discovery, is much emphasis on simple understanding and being able to DO something with the math, which is also am sure a great draw.

The math is the indicator. The attention flows naturally--to what works well.


James Harris