On 10/27/05, Brown, Darin Darin.Brown@enmu.edu wrote:
That's funny...given that a lot of mathematical papers consist almost entirely of proofs, are you saying that copyright does not apply to them? I think the publisher would beg to differ.
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.
WestLaw likes to pretend that they can copyright legal briefs but the courts keep telling them that they can't. Phone books take a tremendous amount of effort and cost to put together but they aren't copyrightable. Publishers aren't the best source for information on what is copyrightable.
This is my point -- statements of theorems don't have different "versions" of themselves. (Maybe *equivalent* versions, that's another issue.) Or at least, there's very little room for tinkering.
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.
But several times I've seen a math person raise an issue like this outside of the math community, and people just pounce on them -- imposing their own view of a policy to a situation they don't even understand.
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.
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).
But again -- it only really will "matter" if it bubbles up out of the limited scope of the mathematics-based articles. It's highly unlikely that I would ever run across such a dispute.
FF