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Friday, June 29, 2018

Relief on academia

Am relieved to be back to feeling that academia on the whole works ok. And feel like gained quite a bit from my education including my four years of college for my degree in physics. But also am looking at a current situation which highlights I think where academia can fail, but shows how the web is helping much.

The situation in mathematics with number theory is in MY OPINION, a total fail, where a demonstrated flaw with number theory has not been properly addressed now for over 15 years. And 14 years since a published paper with a wacky story that I think is telling. But mathematicians were weird about things anyway. ONE of their big claims was that their field was immune from upheavals, like had happened, ironically in fields like physics.

They were wrong.

However, it is of interest to muse a bit as am thankful to be back to being confident that MOST of academia prizes best knowledge. Which is probably mostly correct. So is interesting to consider how one of the most logical could go so wrong.

And yeah, mathematics is potentially dominated by logic and what can be proven. But what if people knowingly claim something shown to be false is actually still true? Then what? Oh well academics are not SUPPOSED to do that right? But what protections if they do anyway?

And there is the problem. Possibly we're lucky then that a problem can be shown where absolute proof lets us know, and then we can puzzle over why humans would behave that way.

We are communal creatures. Human beings can easily believe things NOT true for the sake of community. While knowledge can be very disruptive.

So with my situation, have demonstrated valuable information which is needed, and web let's me know. Web lets others know as well. But is like with my improvement on binary quadratic Diophantine reduction. People can just use the best and STILL support the current math community.

So you get an academic version and what people who want to actually best solve a problem use.

Which is the great news actually. As attention is indefinitely and relentlessly gathered to the correct result that will dominate over time. Web just lets discoverers watch, which is different from the past.

Means you can relax about many things. And is very wild actually though I try to talk casually. But more and more appreciate how things draw attention. And yeah, reality is MOST people are not listening direct to academics in any area. If academics try to force that one, notice what happens. Reality is at best you might get a snooze-fest. People just do not want to be forced to hear them. Though occasionally some popularizer may gain a bit of celebrity, but in math? Not any that I've noticed.

And even among academics in a particular field, most are unlikely to pay attention much to any particular academic at any given time.

In our times, appears that pursuing the traditional paths is often a way to be lost in the herd. You will never be noticed much. (But then again, why would you want to be?) Whereas here, look at what I have.

For someone like me there is a 24 hours a day global attention reality enabled by the web. Am POTENTIALLY known in over 100 countries. I find that troubling often. However that is checkable from objective and third party sources.

Reality is, am personally, bigger than most math departments can ever imagine being. And can conceivably rank with the biggest and most prestigious on the planet. But of course, I like to joke, they'd be terrified to invite me to talk my math. I'd crush them on every level. Which is sad to me, but true. They cannot compete with me. I wish they could. I wish they would try to be better.

Sounds so arrogant, but is the truth that explains so much behavior. May as well state it. Is the socially disruptive reality. Have thought about for over a decade now. Still find it hard to process. But is much easier now than before! So there is progress. I simply have some of the best math ideas out there right now. Still just feels so, off. And is easy for me to watch my ego just go wild.

It IS important for me to try to stay grounded. And I make myself rely much on data from others. Where there has been nothing like that ability to check in human history before.

And there is just no way to compete against that attention reality and there should not be. Is a pure merit reality.

Academia has long been built to give advantage to establishment people which I think will go away. We DO need institutions dedicated to bodies of knowledge and a best process for bringing new people into those organizations and taking care of them.

But from my own experience I know you do not need to reward people to convince them to discover.

Worse you can end up with those who pursue the rewards and rely on fraud, and work to hide that reality. So the reward can be counter-productive. For me is comforting to just be outside such things. And has been important for instance that I am NOT a mathematician.

Academia should focus on best knowledge without inappropriate credence given to assumed authority bestowed upon humans, as we know better now.

The knowledge is what will last. And how do we know really?

Truth demonstrates.


James Harris

Monday, June 25, 2018

Some of my explanation

Mathematics is one of the most prestigious areas of human intellectual activity. And it makes sense to step carefully when making challenging assertions, where will admit have bounced around as to how I talk certain things. Here will give my own explanations for what I think has happened around my own mathematical discovery.

Like to me one of the coolest things ever is:

Where pj is the jth prime:

P(x,n) = x - 1 - sum for j=1 to n of {P([x/pj],j-1) - (j-1)}

That summation will count primes if you make sure n equals the count of primes up to sqrt(x), but no higher. And an example of what it gives is P(100,4) = 25.

Which I copied just now from one of the posts where I talk my prime counting discovery.

That result leads to a partial differential equation and is part of the explanation of the link between the count of prime numbers and continuous functions. Which makes it one of the greatest discoveries in the history of mathematics, in my opinion. So now I hedge.

The lack of immediate pickup--and appropriate cheering--from people who claim to prize mathematical knowledge is easily explained, by a result I found later. I figured out could make an argument that looked like a correct mathematical proof by the accepted rules, which could also be shown to be flawed--by those accepted rules. And the paper is dated 2003, but actually was published in 2004, where things got wacky after. Give a good recent overview I think with post:


So what gives then? Well I figured out there were some numbers...well. I covered a lot more recently with a basic generalized factorization:

In the complex plane:

P(x) = (g1(x) + 1)(g2(x) + 2)

where P(x) is a primitive quadratic with integer coefficients, g1(0) = g2(0) = 0, but g1(x) does not equal 0 for all x.

Taken from this post, which I look at LOTS. Figured out how to solve for the g's to show how you can get all algebraic integers, and then keep going, and realize there are other numbers previously not catalogued. Where is like if you stumble across people who only know evens, and then claim that 2 and 6 are coprime, and you end up arguing with them about the existence of 3.

Is boring. Today I face problems I consider to be about people for whom the truth is irrelevant, like they have a math religion now. And mathematicians are the priesthood, and they just believe what they are told, I guess. As these things are old news.

And have done things I think are cool in lots of mathematical areas. Like even found something that apparently puzzled Ramanujan, but am not sure, of course.  And Euler did work in the same area too! Which I thought was great. I DO wonder what they'd make of my BQD Iterator and the simple explanation.

Of course also managed more recently to be able to group myself with Euler with my own modular inverse discovery, which is about as cool as it can get in mathematics.

So yeah have a little bit of lots, and just gave some highlights which occurred to me now as both definitive and easy for me to trot out, without having to work too hard.

So what gives with other people talking? I really do not know. Actually am not sure what people are talking or not. This blog pulls global attention according to Google Analytics. But then am puzzled at what am not noticing happen. Which doesn't mean is not maybe happening. Feel confident though that if certain things were happening, I would notice.

Oh, some may think race is a factor. I figured out long ago why it is not. Turns out that American racism is primarily a problem of the United States as modern version was invented here. Nation ran into a contradiction with claims of believing in merit rules, and people having slaves: so invented what is commonly considered to be race. And science has debunked race as a social construct.

Mathematics is global. The United States is influential but not that influential. American racism in my assessment has had no impact on my story with my mathematical discovery. Turns out quite simply that humans challenged with the truth can resist it. Like check out this story for sad and bizarre perspective, on my blog Beyond Mundane:


So yeah, simpler explanation is that I have big enough math results that challenge enough people they just have far as I can tell decided to simply not acknowledge them. And just keep doing what they were doing! Which does not mean understanding numbers as well as they could.

There is a certain amount of naive too, I think. Modern web is SO new. Where will admit am very lucky that web is here. But yeah, certain people who do not fully understand how the web works, may be unable to accept how information travels.

People DO know, but then what? Gets very complicated there and often involves perceived self-interest but also pragmatism, especially with confronting establishment things. Besides a lot of people are VERY cynical about much. Mathematicians doing fake research? To them may not at all be a surprise.

I WAS surprised for years. Now I'm not. Is harder for me though.

You have to believe in so much to learn enough to discover as I have. And then to have that discovery shatter so much of my faith in so many institutions? Was VERY difficult for me. But now am more at peace with much which is really about time.

Of course helps to have kept getting monster discoveries routinely too! Guess that's natural.

Truth can be hard to handle for lots of reasons. And yeah there are people who prefer the lie. Or can believe with what I think is religious fervor, and for them is just a matter of faith.

But, for the truly curious that is not a path they would take. Is not satisfying. And more and more am trying to speak more to that audience of folks I figure appreciate the truth. Numbers do not care. These discoveries are way cool, and for people who want to understand mathematics, the truth matters more, am sure.

And yeah, may as well note, these answers intrigue me as well. Is just still surreal to think of as, answers I figured out. As years go by is easier to distance myself though, which is also kind of weird. I figured out, but...how really. Does it matter. Yeah to me! But then again, don't I know? I guess so.

So much that are simple answers though. Math really does not care what we think.

Let those others who are the lost keep with their mathematics as a religion. History will catch up eventually. Which is what history teaches us.

In the meantime, we can just have fun, appreciate the truth, and appreciate how hard it can be to know, and accept.

Would I speed things up if I could? Like get official recognition and changing math textbooks, and getting interviews with global press on the constant? In the past would have said yes, and now am thankful for the time. So no, and believe in a process. More and more feel like world knows better about how these things should go.

Besides I have my global status, but without so much of the fuss. More I learn, more appreciate how great so much actually is with how things have gone. Takes years to process. Is just reality.


James Harris

Monday, June 18, 2018

When truth matters more

Much shifted positively for me with my find May of last year of a new way to calculate the modular inverse. It was important for the world of course. But for me personally it was a different experience could compare with my discovery of the prime count to continuous function explanation, now over fifteen years ago.

To me there are similarities in terms of ease of checking from others, and celebrity around the subject area. Where yeah, celebrity is kind of boring, because is simply human chatter, but hey, is curious too.

Also importantly for others provided something really easy to check, and could give perspective on social aspects to the mathematical community not necessarily so easy to delineate without such a result.

People can claim all kinds of things, but how often in human history do you have a major mathematical find with which to test an influential group of them? Very rarely actually.

I like to say let's you x-ray certain social things, as a metaphor for how much can then peer into both the math community and into minds within that community. Where will admit have puzzled over thoughts revealed for over a decade now.

Mathematics can enable perfect tests, of human beings. And you can trap people into giving their actual feelings beyond any possibility of useful lies.

Is weird though, as now over a year later, yup, think same pattern is trying to play out that happened with my prime counting finds. Is actually a bit more refined as well, as if certain people believe they have learned lessons from there.

Which is a depressing subject which have decided to avoid talking much. Besides is weird: what kind of delusion would lead anyone to think can actually suppress major mathematical results? Has never succeeded in human history, with good reason. And regardless, why would any human try?

For me of course is fascinating to watch. The effort betrays a lack of basic understanding of knowledge, and why we humans appreciate, and how we use. Looks like some believe in celebrity as the basis for ALL interest, which is not even remotely close to reality. One reason I decry the celebrity model for academics. And routinely now dismiss those who clearly crave attention to themselves for their discovery.

World needs the knowledge. The knowledge is what our species will keep using for benefit of humanity.

Celebrity is actually not well understood in our times. I studied it carefully, and understand better how much is illusion.

Especially with modern celebrity which actually is: simply excited human discussion around a person, topic or event, usually. Which is why fades so quickly, always. People will only talk excitedly for so long. Disrupting celebrity is actually surprisingly easy--just shift the conversation. Eventually am confident we will crush celebrity out of intellectual areas including mathematics and the sciences.

Knowledge is best valued on use.

For those who wonder, web enables worldwide attention very rapidly, so useful knowledge sweeps the planet very quickly.

Have watched over and over again through the years and regardless find it, unsettling.

How people discuss though? Can be complicated.

The result also validated for me an approach which focuses more on discovery. Is just more fun to keep figuring things out than worry about, human chatter on the subject of what you discovered! Is more cool too.

Also shows irrelevance of official recognition in the modern age. World apparently is in a slow meltdown of prior systems and couldn't care less. And am a fan of the journal system, but relish a lack of need for journals. But am in a unique position.

As the world's latest major mathematical discoverer, of course I don't need journals.

Wonder when will have to stop saying am latest? For now there doesn't seem to be any competition there though. When there is another, I'll just note am a major discoverer, I guess. Should I even bother though?

Checking me is easy. But who has the will to let the truth matter more? That intrigues me as well.

Is a dynamic arena but have found my results with some web searches.

Like search: modular inverse innovation

Or search: modular inverse discovery

Others may work as well, of course.

Is dynamic as, is about others. I have no control over web search results, of course.

So yeah, this post was really for people who may have wondered: was there something wrong with the reaction? Answer of course is, yeah. But is lots naive really. And I wouldn't worry over it.

Of course I've lost nothing. Recognition at best comes from those who can appreciate the accomplishment. And the web helps you to know. Thank you to those who do.

Good thing though is how easily can check my math, if you wish. And then have no further doubts, if you had any.

Know it helped me. But I'm at the center of the storm is how I feel it is, and is like, out there are the hurricane force winds, and here, is calm.


James Harris

Friday, June 01, 2018

Simpler modular form for BQD Iterator

Was surprised to discover that considering x2 - Dy2 = F mod N, is also the path to a simpler form for my BQD Iterator.

Key is the factorization available from:

x2 - Dy2 = x2 - m2y2 = (x-my)(x+my) = F mod N

Where, for some residue r, x + my = r mod N, and x - my = Fr-1 mod N

And I can iterate to get: x + Dy + m(x + y) = r' mod N

Then x + my + Dy + mx = x + my + m(my+x) = r + mr = r(m+1) = r' mod N

And have the result then: r' = r(m+1) mod N

Then with k iterations, have for kth iteration: rk = r(m+1)k mod N

So can use r to iterate modularly with a very simple result.

Where intrigues me is VASTLY simpler than what can get with the explicit form.


James Harris