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Wednesday, November 19, 2014

Finding solid ground

There is an extra to the extraordinary issue of thinking you've found a problem where the mathematical field has an important error in that the field prides itself on not only not having error, but being the one major discipline where such a thing is impossible. Worse, if you "prove" the problem you also have to deal with where do you go talk about it? To the very people who couldn't see it before? Some of whom may have relied on it to build their careers?

But the personal side of it was far bigger for me for a long time. I grew up solidly within the system, went to a top college on an academic scholarship. Got my degree in physics. Was thoroughly indoctrinated in the mainstream, and didn't expect to find a problem with it. It took me a long time to work through things, and at times I'd try to discuss, but I now realize that the "personal" part means it isn't helpful to others.

So what about someone who comes across my mathematical research and now has to struggle with its implications? I'm ready to finally help there.

And I think that is a responsibility I should accept. For those who just dismiss my ideas of course it's irrelevant. Such people will not be convinced by what I say here. But this post is not for them.

First off, is the question of--how do we know anything? And in mathematics you can hear a lot of talk about mathematical proof and axioms, but also, especially after my research came out, unfortunately, you can see pushback where mathematicians are claiming that "mathematical proof" is actually about the weight of the opinion of mathematicians! So I gave a post, stepping you through an absolute mathematical truth for demonstration purposes:

somemath.blogspot.com/2014/10/example-showing-truth-logic-and.html

And the BIG thing that should jump out is that I rely a lot on identities. Like x = x is an identity. And of course that's true! So like if I'm thinking about arguments someone might make against my research, it's like there's a point where you can jump off. If some person wishes to debate whether or not x=x is true then you really aren't going to be able to reach common ground, you know?

But for those who will accept it, then it's not very far to solid ground. Then I have arguments that rely on identities with conditions. Like, if x2 + y2 = z2 then under those conditions these things that follow from identities must be true. Not complicated.

When you're pondering "truth" or what some person claims is truth, then you have to find that thing you accept from which all else must follow and I like that I can say: it's identity. If you believe in mathematical identities then you can get the rest.

It's important to have that linchpin.

So what about acceptance? Why can't you go to some mathematical conference on say, my work on the problems with using algebraic integers? Or why can't you read up on my prime counting function from others? Or the partial differential equation that follows from it from others?

There I have to hedge that maybe you can find others discussing such things, but to my knowledge the only other people I know of who talked about them publicly were people years ago arguing with me against their importance online.

It's up to other people where they choose to engage and what they choose to discuss publicly.

So the short answer is, I don't control what other people choose to engage upon publicly.

They do.

So the choice tells you more about them than me.

From a personal perspective though, it can be a lot about who you are. So it's like, if you conclude that something is true, like that identity is key, and everything else follows, but then get stuck on--but what about these experts in the field who aren't talking about this thing?--then you're dealing with two different issues.

And I've been there. Spent a lot of time there. That's one of those personal things I realized wasn't doing anyone any good by discussing publicly, like on this blog.

My research has drawn the attention one would expect, which means that on the social side I can put forward ideas that promptly and rapidly zip around the planet. That does take a while to really feel ok. Maybe it will never really feel ok to me, but that's not a good reason for me not to help other people.

After all, coming across these ideas, you can have a real concern about how to know if they are correct or not.

And that I can understand and feel I have a responsibility to give that help.


James Harris
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