On Mon, Apr 11, 2011 at 2:10 AM, Steven D'Aprano <steve+comp.lang.pyt...@pearwood.info> wrote: > On Mon, 11 Apr 2011 00:53:57 -0700, geremy condra wrote:
<snip> >> I am extremely skeptical of this argument. Leaving aside the fact that >> you've randomly decided to drop the "decidable" qualifier here- a big >> problem in its own right- it isn't clear to me that software and >> computation are synonymous. Lambda calculus only models computation, and >> software has real properties in implementation that are strictly >> dependent on the physical world. Since perfectly predicting those >> properties would seem to require that you perfectly model significant >> portions of the physical universe, I think it's quite reasonable to >> contend that the existence of lambda calculus no more rules out the >> applicability of patents to software (which I detest) than it rules out >> the applicability of patents to hardware (which I find only slightly >> less ridiculous) or other meatspace inventions. > > I agree with all of this: I too detest software patents, and find > hardware patents problematic but pragmatic. But if there's a reason for > accepting one and rejecting the other, it's far more subtle than the hand- > waving about mathematics. I believe that the reason falls more to > *pragmatic* reasons than *philosophical* reasons: software patents act to > discourage innovation, while hardware patents (arguably) act to encourage > it. After all, encouraging innovation is what patents are for. > > M Harris' argument fails right at the beginning: > > "Mathematical processes and algorithms are not patentable (by rule) > because they are 'natural' and 'obvious'." > > It's not clear to me how the Banach-Tarski paradox can be described as > 'natural': > > Using the axiom of choice on non-countable sets, you can prove > that a solid sphere can be dissected into a finite number of > pieces that can be reassembled to two solid spheres, each of > same volume of the original. No more than nine pieces are needed. > ... This is usually illustrated by observing that a pea can be > cut up into finitely pieces and reassembled into the Earth. > > http://www.cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node36.html > > > And I think anyone who knows the slightest bit of mathematics would be > falling over laughing at the suggestion that it is 'obvious'. I'd quibble with you over terminology here. BTP arises naturally- ie, without being explicitly constructed- in certain axiomatic systems. But I get your point. > Of course, some mathematics is obvious, or at least intuitive (although > proving it rigorously can be remarkably difficult -- after 4000 years of > maths, we still don't have an absolutely bullet-proof proof that 1+1=2). Erm. This is getting a bit far afield, but yes, we do. The statement you provide above part of Presbuger arithmetic, which is both complete and decidable. > But describing mathematics as 'obvious' discounts the role of invention, > human imagination, ingenuity and creativity in mathematics. There's > nothing obvious about (say) asymmetric encryption, or solving NP-complete > problems like the knapsack problem, to mention just two examples out of > literally countless examples.[1] Meh. Obvious is in the eye of the beholder, and I doubt we'll wind up coming up with a satisfying and rigorous definition here. I'd therefore rest on the concept of 'natural' I outlined earlier, which would clearly forbid patenting the product of discovery but allow patenting inventions. > If it were just a matter of joining the dots, there would be no unsolved > problems, since Euler would have solved them all 200 years ago.[2] > > Part of the patent problem is that the distinction between discovery of a > fact (which should not be patentable) and invention (which, at least > sometimes, should be patentable) is not clear. The iPod existed as a > Platonic ideal in some mathematical bazillion-dimensional abstract design > space long before it was invented by Apple; does that make it a discovery > rather than an invention? On the other hand, it is doing Apple a great > disservice to ignore their creativity in finding that design point, out > of the infinite number of almost-iPods that suck[3] or don't work. I agree. Of course, your post existed as a billion-point platonic ideal beforehand, so you can't really claim credit (man, Plato figured *everything* out!), but still. Geremy Condra -- http://mail.python.org/mailman/listinfo/python-list