## Sunday, November 20, 2016

One result I stared at for quite a bit is the start of an infinite progression using what I now call the BQD Iterator:

The series starts with

1. x2 + Dy2 = F

2. (x-Dy)2 + D(x+y)2 = F(D+1)

3. ((1-D)x-2Dy)2 + D(2x + (1-D)y)2 = F(D+1)2

4. ((1-3D)x + (D2 - 3D)y)2 + D((3-D)x + (1-3D)y)2 = F(D+1)3

5. ((D2 - 6D + 1)x + (4D2 - 4D)y)2 + D((4-4D)x + (D2 - 6D + 1)y)2 = F(D+1)4

and that goes out to infinity.

Here is my reference post discussing it, wow back in 2008. So yeah back then hadn't named the BQD Iterator. Just kind of informally talked it for a long time. Naming it worked better, and think I came up with a cool one.

It's interesting looking through the post seeing my efforts to try and use that series to solve for x and y. Through the years have had mixed feelings about such efforts.

James Harris

### Our picky world

Thankfully years ago I learned to very wary of trusting myself when it came to my mathematical ideas. Sure I could tell myself that searching for the new can lead to false positives but it's another to live it. And have that gut-wrenching moment when realize something you'd convinced yourself to be true, was utterly false.

With the rise of the web I was also really lucky in that web allows me to not rely on myself, which is my continuing strategy.

Yeah but eventually that lack of trust in self can just get silly.

But am SO skeptical I like as the years go by to check, re-check, and check again. And at times I've done things to try and test the web interest.

The web flexes and shifts with any such efforts. It actually, well it can kind of mess with you as the new is so different than before.

The web behaves like an intelligent entity though I realize am seeing reflected the interest of LOTS of human beings. But for me often is like am dealing with one being. Can be, um, remarkable can say.

The world grabbed hold of my research as soon as it went public. I'd rationalize as watched the evidence. Tell myself things I realize now are not true so I could just mostly continue my life as if nothing had changed. Now I simply talk about things as the mood moves me. It's not necessary for me to say anything else about it, ever. There is relief in making that hard statement. But part of me wants to believe I still need to be working at it.

But it IS knowledge. Turns out I can't take it away even if I wished.

And had some thoughts on how I use the web to test things in a post here almost two years ago. But now realize I was still only JUST beginning to grasp how the world treats information.

That post fascinates me as it is remarkable to me how much more I know now compared to when was so sure had most figured out. And also now am free to focus more on things will admit might interest fans of the research! Which is LOTS more fun. So my posting behavior has shifted.

Finally as I stopped thankfully doing my own basic research started looking around and realized more and more our world is very picky. It is odd to consider that you can survey any number of people effortlessly just with a few searches.

Now will admit more and more I assess others. And web lets me do it with minimal effort. That's also more fun.

For years I convinced myself certain things had to happen or certain things should happen around my research, but I was wrong. The world does what it wants. The web though lets me watch in awe.

James Harris