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Thursday, January 18, 2018

Finding knowledge rules

We get born and get told things. And to me knowledge is useful information and folks in the modern era get PLENTY. However, humans found that knowledge, right? And the process can have problems, where we have humans at the front lines called scientists as well as others who keep figuring things out.

To me is an awesome process and definitely respect while also find it fascinating when people are told facts and believe you are trying to convince them of something.

In mathematics there is mathematical proof. And proof is definitive.

If knowledge is available, yet you believe things not true, where that can be determined by fact, then I suspect you have problems with determination of fact, or have not been informed.

With those able to access the web, who have training will admit my belief is: ability to determine fact when available represents a valuable skill.

And I also believe that some people lack ability to determine fact and simply rely on what they are told. Which is NOT necessarily a terrible thing! Most people must simply rely upon what they are told. Like with medicine, am going to listen to that medical doctor. Probability can challenge with authority and better my own health versus endanger? Very small. Or nonexistent.

Our human reality is vastly complex with too much knowledge for any one human to have much of a grasp of it all. However, it is still possible to determine fact, if you have the skills. While some apparently require the majority to believe fact, when is determined or they may instead believe false information which to me is simply, not knowledge.

This blog audience focus from now on is to be directed towards those who can determine mathematical fact.

The ability to find knowledge should be cheered and supported. And in my analysis people who depend primarily on the social group to know, who either lack ability to check for fact or refuse to check, can only be convinced by that social group they believe. And effort in their direction is simply wasted.

Tuesday, January 16, 2018

When people work harder reducing

The burden on me to establish certainty with my own research should be vastly hard, especially with ideas that challenge the status quo. We have had a lot of great humans who have done great things, which work great too. And people flying all over with all kinds of cool technology, in countries with great freedoms, along with so much else in support of my views there. Greatness works.

So I must take my time and accept great difficulty in establishing unimpeachable certainty. Which is fun! It pushes me to understand my own research and has even aided further discovery. But also there is so much demonstrative now, done.

One of those ideas that demonstrates has to do with Diophantine equations like:

c1x2 + c2xy + c3y2 = c4 + c5x + c6y

Where is binary because you have unknowns x and y, and is also called two-variable. Diophantine just means looking for integer solution. I figured out a best way to reduce to something simple.

For example:

x2 + 2xy + 3y2 = 4 + 5x + 6y

Where I just tried something simple and was lucky there ARE integer solutions. My method for reducing gives:

(-4(x+y) + 10)2 + 2s2 = 166

And turns out you can easily solve from there and find integer solutions:

x = 4, y = -2, or x = 5, y = -2

More recently played around and had to work harder for this example, as wanting something simpler in ways:

x2 + y2 = xy + x+y + 102

Which my method reduces to give:

(-3(x+y) + 6)2 + 3s2 = 3708

And figured out solutions: x = -10, so y = -8, or x = 3, y = -8

Copying from prior posts.

Reference posts: Reducing binary quadratic Diophantines, Reducing a quadratic Diophantine to find solutions

My method for reducing is I think the best in the world, and supersedes methods that trace back to Carl Gauss who is a HUGE hero of mine. And his methods now include wasted effort finding something called a discriminant, which is not needed for reducing these equations.

People wasting their mental energy though is not surprising to me, or a great concern. Others might value their efforts more highly than I do, as is a telling failure, in my opinion.

From my perspective, is more telling when people work harder than necessary, when they could do better than those who find better.

Those who seek truth best, interest me more than those who do not.

May seem cold, but many may wish to be something they are not. To me is important how to figure out those with potential. Finding the truth when is so easily available? When easy to find on the web?

If you can't do that easy then how can you find the things waiting to be discovered, when that can be so hard?

Challenges are met by people with ability. Why I deeply appreciate the challenges in front of me, as I learn so much more about what I can do.

Everything testable and each statement of mine checkable though I wonder if am reaching in claiming is the best possible. But I think not. Like consider, how I got something important.

Use my method to reduce on: x2 - Dy2 = F

Gives the BQD Iterator.


James Harris

Monday, January 15, 2018

Thoughts on infinite depth

Correct mathematics will check out correct over infinity. There is no error or possibility for error. And that is a perfect test. I like to call it--infinite depth. As incorrect mathematics on the surface can look ok, but will lead to contradiction.

Questions of whether or not mathematics can have rules that lead to contradiction were handled most famously with the work of Kurt Gödel being of signature importance. Lots of people talk him, but the essence of the desire with mathematics is what I stated.

People can though get excited over the question of: can you have valid mathematics which leads to something wrong? And I'd say simply: no.

But I see it as, if mathematics leads to something wrong, then is NOT valid. So that idea of a check possible, to me answers the question.

But how can you know? We can't check infinity with infinite tests one-by-one. Where I rely much on tautologies for my work.

Like: x+y+vz = 0(mod x+y+vz) is logically a tautology and mathematically is called an identity.

Is equivalent to: x+y+vz = x+y+vz

Much of my mathematical research reduces back to validity if that identity is valid.

Actually have a reference post from 2014 that is demonstrative:
Example, showing truth, logic and absolute proof

Identities by definition are valid; therefore, a result that so reduces is perfectly checked.

Functionally that means that a person like myself can make a mathematical statement, and find that statement implies something else. Where readily admit have come across such or had them brought to my attention and even when I know have a mathematical proof can be that emotion of FEAR.

Then test the implication and look at a new result. Discovery rules. Fear turns then to elation. But regardless, emotion is irrelevant. The math behaves perfectly. Infinite depth means there can be no mistake. And I marvel to myself or chatter a bit about it, like maybe here on this blog.

So have given the logic. Emotion can mean something else. One phrase like to use, over and over again is--math and emotion do NOT go well together. Like one way I check people is to ask, if they say absolutes do not exist, if they believe: 2+2 = 4

Number authority is so useful. With questions of truth can still be of interest to ask a person, why do you so believe? Most people will of course not debate you over such a thing, but why not?

Simple enough, yes, but there are humans who will debate you over it. I find it to be a telling human check.


James Harris

Thursday, January 11, 2018

Some math perspective and pep talk

The math sustains me like to say, and getting going into a new year is useful to reflect on just a bit, some of how that works.

Like one of those results will use for comfort:

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

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

My way to count primes in its sieve form.

That is SO compact! The math has a succinct efficiency I appreciate. One of my favorite posts talking is actually on my blog Beyond Mundane: Simple and fast prime counter

One of the last results where I got lots of criticism over a decade ago, where what I saw as specious comparison to known methods ignored the new. Yes, basic concepts were same, so?

The innovation involved is how is simply displayed and compact, which is also obvious in comparison.

Love considering as the time passes. As over 15 years now and yeah, look over what math people still teach, as if a world of students cannot also find easier on the web.

And something that so floored me only a few years ago, realizing can easily find all integer solutions for:

x2 + (m-1)y2 = mn+1

From: Squares and nth powers

Not surprisingly to me, using this result, which follows from my BQD Iterator could make for popular shares. Like:

12 + 32 = 10

82 + 62 = 102

262 + 182 = 103

282 + 962 = 104

3162 + 122 = 105

From: Sum two squares to power of 10

Simplicity has HUGE benefits as if people get curious can check you on EVERY math detail. Web enables a lot as well, as folks can know. They can just check you on the facts.

Can also check what they thought they knew, about others in a high profile area. For me was lots of surprise for years.

Now these results are comforting, while less exciting, for me.

There is that thing about the math where when you discover you get a different emotional connection to your discoveries, which I know from how I look at my math discoveries versus math from others.

The math does not care. That actually IS a comfort. Because the knowledge is more important to me.

So yeah, this pep talk is working for me like usual. And what discoveries to pick? Is just about my mood. Could talk my better than Gauss's way to reduce binary quadratic Diophantine equations. Could go on again about my modular inverse method, but am on pause there. Still relishing it though.

Or lots of other things.

Pep talk complete! Well I feel better now. Who knows why humans who come and go might fight against mathematical discovery, and do we really care?

The math feels like a friend to me. And I know the math does not care. Convincing myself, I should not either. We humans have choice.

Knowledge should be about reinforcing choice. The math has given me more choice. Am thankful.


James Harris

Wednesday, January 10, 2018

Power of math

That correct mathematics has a power of its own sustains me. And what I call the social problem is much about people who clearly do not believe it does.

Lies? Have to be supported constantly. That human energy can only last so long. And besides, the truth can crush lies even when LOTS of people keep trying to push them.

The valid math wins over time. And I have a unique opportunity, as NO major discoverer at my level has ever faced such opposition.

My predecessors would be jealous am sure. But they're long dead. Gives me different perspective on their lives as well. They had to fight their own battles too. History tends to be glossed over as to full reality. Still realize how much better it is, here am thankful. I get to know so much more than they ever could in ways, I think. Yeah it is different between understanding possibility and living in this modern reality.

Gist of it is, opportunity like no other as in challenges, I simply learn more useful.

From my best perspective is simply an interesting exercise.


___JSH