Fastfission said:
Effort does not have anything to do with whether something is
copyrightable. If they don't have a copyrightable form of "creativity" involved, then they aren't copyrightable. Now, again, I don't know if that applies to mathematical proofs, but I would suspect that it might not -- at least the strict mathematics of it.
Well, you raise some very interesting points. I know that research papers in math have a copyright attached to them...I have always assumed that this meant something along the lines of "don't photocopy this and sell it". (As if that's going to happen.) The copyright of math research papers always seemed bizarre to me -- mathematicians *WANT* their papers photocopied and distributed without permission!! Maybe not their textbooks or monographs, but certainly their research papers. It promotes their ideas. It gets people interested in their field and problems. It advances their careers. As far as researh papers are concerned, the entire copyright issue only exists because of publishing houses. We'd be perfectly content to do our own peer review, trade papers electronically, etc. And this is starting to be done.
To be honest, the only thing math people really care about with regard to research is attribution and rigour. I could take someone's paper and paraphrase all their results and proofs, and then sell it to people. Is that a copyright violation? Depends, I guess. If I'm just changing "x"'s to "t"'s or what not, then yes. If I'm really giving a novel presentation of the results, (e.g. presenting them in a pedagogically novel way) then no. There is no easy answer.
But if they are strictly "facts", as they claim to be, then they
aren't copyrightable. The catch-22 here is that if they are entirely fanciful, then they are clearly copyrightable. But if they are just juggling numbers (however intelligently), then I'm not so sure. But again, I don't know for sure -- it would come down to a decision of whether or not a proof was a fact of nature or whether it was an act of creativity. I don't know how a court would rule.
It's an issue that philosophers of math aren't agreed upon, let alone judges!!
I think this is a case of the community largely policing itself. Mathematicians would intuitively have a sense of when something was just "stealing" vs. an original contribution.
I think part of the problem here is that much of what you are arguing
as the mathematical way of proof requires a certain level of mathematical understanding to agree with. Things which would be self-evident to a mathematician would not be so to me. So in the end it is tempting to see it as a simple argument from authority, "This is right because I am right." Now if we had two people saying that, I wouldn't honestly know which one to go with, unless one of them could say, "And furthermore, this very formulation appears in Pearson's Wonderful World of Math on page 54" which I could easily verify.
Now the obvious solution here, were I in this imaginary content
arbiter role (a nonsensical proposition in itself posited only for the sake of argument), if such a citation was not able to be produced, would be to either appeal to an established authority (have some professor type look it over) or appeal to a number of mathematically adept Wikipedians with good edit records to look it over for me.
Exactly! We agree! People get caught up in citations to the literature as an end unto itself, rather than a *means* to an end. After all, why do we cite the literature? Because when something is in the literature, it has passed peer review and has been given the stamp of approval by qualified experts. All it means is, "Someone sent this paper to a human being(s), who read it, researched it, checked it, and proclaimed it good." Now, it's possible to interpret this as merely an "argument from authority"! After all, in a sense, *all* citations are just "arguments from authority"! They just say, "This person checked it, thought about it, verified it, and we should trust them." What is that, except an argument from authority?!? And that's all that goes on when I say, "suppose a proof is easily verifiable by any professional editor in the field at wikipedia". There's little difference between that and submitting something for peer review -- it's the same process.
But it is an interesting question, either way, when it comes to things like NOR. I think a large part of the fear is that people will use
their "mathematical reasoning" to do things which are known to be impossible (i.e. square the circle) and hide their clever trickery using the sorts of tricks that mathematicians can do (I know a number of former mathematicians who do such things for fun amongst themselves).
Well, that's what the experts are here for...to catch such things. Just like they catch such things in peer reviewed journals.
This is an interesting discussion (IMO).
darin