On Apr 11, 12:53 pm, geremy condra <debat...@gmail.com> wrote: > On Sun, Apr 10, 2011 at 7:49 PM, harrismh777 <harrismh...@charter.net> wrote: > > Chris Angelico wrote: > > >>> > All software can be expressed as lambda calculus. The point being, > >>> > all > >>> > software is mathematics... > > >> With enough software, you can simulate anything. That means that the > >> entire universe can be expressed as lambda calculus. Does that mean > >> that nothing can ever be patented, because it's all just mathematics? > > > Great question... the simple answer is, no. But the extended answer is a > > little complicated and not well understood by most folks, so its worth > > talking about, at least a lot. You may skip to the last paragraph for the > > main point... or stay tuned for the explanation. > > Mathematical processes and algorithms are not patentable (by rule) > > because they are 'natural' and 'obvious'. In other words, a natural set of > > laws (mathematics, just one example) are universally used naturally and > > obviously by all humans in the course of thinking, creating, expressing, > > &etc., and therefore these ideas are not patentable because they are the > > natural and obvious 'stuff' from which and through which the human mind > > processes the natural world. You cannot patent the Pythagorean theorem. You > > cannot patent addition, nor subtraction, nor the logical concepts for > > boolean algebra.... nor can you patent lambda calculus. These are just > > examples. > > You cannot patent the mathematical concept of nand gate; however, > > Motorola may patent the mechanical electrical implementation of the nand > > gate (CMOS 4011 quad nand). Also, Texas Instruments may patent their > > mechanical electrical implementation of the nand gate concept (TTL sn7400n > > quad chip). The chips are patentable, but the mathematical concept 'behind' > > the chips is not patentable. > > Software is another sort of animal entirely. Because software is not just > > based on mathematics--- IT IS mathematics. > > 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. > > Geremy Condra
----------------- ... the widespread belief, incorrectly known as the Church-Turing thesis, that no model of computation more expressive than Turing machines can exist. Yet Turing's original thesis only refers to the computation of functions and explicitly excludes other computational paradigms such as interaction. In this paper, we identify and analyze the historical reasons for this widespread belief. Only by accepting that it is false can we begin to properly investigate formal models of interaction machines. We conclude the paper by presenting one such model, Persistent Turing Machines (PTMs). PTMs capture sequential interaction, which is a limited form of concurrency; they allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of Turing machines and of the Church-Turing thesis. ------------------------ From http://www.cse.uconn.edu/~dqg/papers/cie05.pdf may be of interest (and also other papers of Peter Wegner questioning the universality of Turing machines lambda calculus etc) -- http://mail.python.org/mailman/listinfo/python-list
