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