Monday, July 24, 2017

When truth is your hammer

Readily admit I will turn to absolute proof and even number authority itself, when need reassurance. And when you wield truth in a certain way it can be necessary to hammer through against people who rely more on feeling than fact, as we humans can be recalcitrant at times. And there are people who think truth is a moving target or most amazing to me, some think truth is about human opinion.

So yeah I posted this thing recently:

349672 + 7522 + 1128+ 1880+ 26322 + 41362 + 48882 = 357212


An absolute truth it doesn't care what you think of it, or me.

And I'd summed five squares before and the math is easy, but it just felt good. And I like to stare at it when get philosophical or, yeah need that reassurance.

Human beings will come and go.

Here in this time, when some may think that they have a will that can overcome mathematical proof.

Let them try.

When you are someone like me who wields truth as a hammer when necessary, or has the infinity results, then you can look at others with curiosity, to see what they believe.

Try to break the hammer, see what happens.

I'm curious. I, at least, am human. But in the end?

The math is not human. The math knows you. But you do not control the math.

The math does not care what you believe.

Possibly some of you as well will feel that urge to wield truth.

Do you have what it takes? Few can handle the truth at certain levels, who can find the most powerful infinity results and present to their world.

I could. I have.

This post was SO much fun. Yeah am a fan of comic books. But I read them a little differently than others am sure, now. And the movies? Are so much more fun, for me.

Takes someone like me.

Can you stand with truth as your best protector?

Or would you bend in fear?

I know.

For me maybe is more fun this way anyway, as suits my flair for the dramatic.

Coming up on 15 years since I discovered my prime counting function as just one example. Can you imagine? Could you simply stand for truth?

Challenge demands a certain person. Reality? Knows.

The math knows. The math chose. Reality bends not for you.

The future demands the one who will get it done.

There are more results out there--an infinity of them. Reality will choose those who will get it done.

Can you stand for truth? Come what may?

Readily admit as much as I LOVE discovery of my own, more and more wonder, where can these ideas lead that others might find?

Truth is out there.

James Harris

Thursday, July 20, 2017

Progression, abstraction and two conics equation

Worth noting the progression to my latest result, which has a lot to do with reducing the general equation for what I like to call a binary quadratic Diophantine equation which is also called a two variable one:

c1x2 + c2xy + c3y2 = c4 + c5x + c6y

Here x and y are the two unknowns to be figured out. The base result comes from this post from September 2008. But checking published posts, was referenced talking a general method for reducing binary quadratic Diophantine equations on this blog in this post in May 2011.

And copying from this post, where also note that with my method for reducing can get to the general reduced form:

u2 - Dv2 = C

Where u and v are unknowns. And while I've talked about with C=1 as the two conics equation before, the more general also gives two so that is just the unary case. Letters don't matter of course and like to show as:

x2 - Dy2 = F

where all variables are non-zero integers. And yeah a LOT of abstraction, in that progression, where now you can solve for x and y modularly. Looks like I figured that out in September of 2012.

With a non-zero integer N for which a residue m exists where--m2 = D mod N, and r, any residue modulo N for which Fr-1 mod N exists then a solution is:

2x = r + Fr-1 mod N and 2my = Fr-1 - r mod N

And use that to solve for the modular inverse.

 r-1 = (n-1)(r + 2my0) - 2md mod N

Where y0 is chosen as is m, with m not equal to r, and n and d are to be determined. They are found from:

2mdF0 = [F0(n-1) - 1](r + 2my0) mod N


F0 = r(r+2my0) mod N


And felt an urge to put all together to kind of see that progression from the most general form, to abstraction to the more basic two conics form, and then to a solution for the modular inverse.

So you end up going from something to do with binary quadratic Diophantine equations to something more general than them.

James Harris

Wednesday, July 19, 2017

Correct matters most

When found mathematical results have an absolute aspect you can find difficult to find elsewhere, like maybe only in logic. When you have the correct mathematical result, it is absolutely true. And have given an example of absolute proof.

However emotion can lead us astray as human beings and have been lead astray in the past by my emotions and did not like it when found out! Where could be SO confident and certain, when thought had a correct mathematical argument only to finally have that wrong belief dramatically collapse when finally could see my error.

That elicits a terrible feeling and I do not like it. I try not to repeat such failure.

The joy in believing you have something important is not worth it, if it is not even correct, as such a thing is completely empty.

Correct matters most, as only when absolutely correct do you have the mathematical proof, as proof is perfect.

To check against emotion I now employ a process which I think helps protects others as well, as while not good to lead one's self astray, so much worse to lead others! Which means I try to focus objectively, consider results as facts only when well established, and refrain from emotional appeals.

So please do not be surprised at a steady process which does not involve trying to convince you, but is sharing of mathematical ideas and process as well, so that truth can be determined.

For those who appreciate truth, working for the truth should be a privilege.

Am lucky in that most of what I have requires only what are generally called elementary methods. I like that phrase. Elementary methods.

Numbers have fascinated me in special ways for as long as I can remember. Like friends with personalities who are anxious to tell you cool things. And they never lie. But can lie to myself if I'm not careful so yeah, focus on--correct matters most.

And explanation helps.

Labels below this post consider various areas around the social aspect of presenting mathematics from celebrity, to what I call the social problem, and also instructional. Click on a label for more posts in that area! And thank you for your interest.

I try not to try to convince you, but I do appreciate your time and attention.

James Harris