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http://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis http://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis It's pretty trivial to show that software i

http://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis http://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis It's pretty trivial to show that software is in fact math. Not "approximative with math", like a mechanical device with the laws of physics perhaps, but actually math^. If you want to express OpenOffice.org terms more easily recognizable to the layman as "math", simply translate the program from whatever it may be written in to lisp, at which point a conversion to lambda calculus is quite clear. (^ Unless perhaps you also have a definition of "math" that precludes something like the Pythagorean Theorem as well, which is absurd.) EDIT: Addendum: even if you for some reason don't agree with this, it remains a fact that someone that does hold software patents to be invalid for this reason can easily and reasonably criticize a software patent without first reading it.

tzs 16y ago
Would you say I'm doing math when I write down my recipe chocolate chip cookies? I'd say I'm just describing steps to be executed in order to accomplish a particular real world task. Software is the same--it is steps to execute on a machine to accomplish a task. Software can be described in ways that sometimes make it amenable to mathematical analysis, but that doesn't make it math. The Pythagorean Theorem is math--and you can't patent it. However, if you designed, say, a new way to truss bridges, and a key aspect of that was that certain things were of lengths that formed right triangles via the Pythagorean Theorem, it would not be patenting math if a patent were issued on your truss system.
- burgerbrain 16y ago
  As per the Church Turing Thesis, computation that you do with step by step instructions and computation that you preform with lambda calculus are equivalent. That you think Pythagorean Theorem is math, but "software" somehow isn't, seems to indicate to me that you are restricting your definition of math to something like arithmetic and symbolic manipulation. That, or similar definitions, is all fine and dandy, but the field of math is not actually limited to such opinions. Regardless of opinion, you can show with math that software is math. It's just using a different notation than small subset of math they teach you in primary school. EDIT: If you're still not convinced, check out what Knuth has to say about the issue. I suspect he is a far more rigorous mathematician than either of us will ever be, and his writing is certainly better than my own: http://eupat.ffii.org/gasnu/knuth/swpatknuth.en.pdf http://eupat.ffii.org/gasnu/knuth/swpatknuth.en.pdf
  - Natsu 16y ago
    You can go further. Show them the Curry-Howard correspondence: http://www.haskell.org/haskellwiki/Curry-Howard-Lambek_correspondence http://www.haskell.org/haskellwiki/Curry-Howard-Lambek_corre... "Interestingly, the isomorphism maps programs (functions in Haskell) to (constructive) proofs in logic (and vice versa)." So not only is software equivalent to math, there are people out there actually writing the software program equivalent to ZFC (one of the most commonly used sets of axioms in mathematics): http://us.metamath.org/index.html http://us.metamath.org/index.html If that program is math, then all software is math. If that program is not math, please tell me what is. From what I've seen, lawyers love to draw lines in the air, creating distinctions between things that are, in fact, formally equivalent. I have no doubt that they can, in fact, write some distinction that satisfies them legally, but in doing so, they will be creating a legal fiction wholly alien to mathematicians. I believe it was Knuth who pointed out that there's no difference between numbers and other kinds of precise information.
    - tzs 16y ago
      The distinction is between the thing and the use of the thing. For instance, you can't get a patent on wood. You can get a patent on using wood to make some particular thing if the use of the wood there is novel, useful, and non-obvious. Same with software and math. Software patents do not cover the mathematical aspects of software--they cover the use of the mathematics in a novel, useful, non-obvious way (at least when the patent office does its job during examination...).
      - burgerbrain 16y ago
        The logical conclusion of what you're saying is that while you cannot patent the Pythagorean Theorem, you could patent using the Pythagorean Theorem to solve triangles, perhaps in the context of architecture. That is of course, patently absurd. "Software patents do not cover the mathematical aspects of software" As Knuth explicitly notes in the materials I've already linked, trying to separate the math from the rest of software is a fundamentally flawed endeavor.
      - 16y ago

tzs 16y ago

Would you say I'm doing math when I write down my recipe chocolate chip cookies? I'd say I'm just describing steps to be executed in order to accomplish a particular real world task. Software is the same--it is steps to execute on a machine to accomplish a task. Software can be described in ways that sometimes make it amenable to mathematical analysis, but that doesn't make it math. The Pythagorean Theorem is math--and you can't patent it. However, if you designed, say, a new way to truss bridges, and a key aspect of that was that certain things were of lengths that formed right triangles via the Pythagorean Theorem, it would not be patenting math if a patent were issued on your truss system.

burgerbrain 16y ago
As per the Church Turing Thesis, computation that you do with step by step instructions and computation that you preform with lambda calculus are equivalent. That you think Pythagorean Theorem is math, but "software" somehow isn't, seems to indicate to me that you are restricting your definition of math to something like arithmetic and symbolic manipulation. That, or similar definitions, is all fine and dandy, but the field of math is not actually limited to such opinions. Regardless of opinion, you can show with math that software is math. It's just using a different notation than small subset of math they teach you in primary school. EDIT: If you're still not convinced, check out what Knuth has to say about the issue. I suspect he is a far more rigorous mathematician than either of us will ever be, and his writing is certainly better than my own: http://eupat.ffii.org/gasnu/knuth/swpatknuth.en.pdf http://eupat.ffii.org/gasnu/knuth/swpatknuth.en.pdf
- Natsu 16y ago
  You can go further. Show them the Curry-Howard correspondence: http://www.haskell.org/haskellwiki/Curry-Howard-Lambek_correspondence http://www.haskell.org/haskellwiki/Curry-Howard-Lambek_corre... "Interestingly, the isomorphism maps programs (functions in Haskell) to (constructive) proofs in logic (and vice versa)." So not only is software equivalent to math, there are people out there actually writing the software program equivalent to ZFC (one of the most commonly used sets of axioms in mathematics): http://us.metamath.org/index.html http://us.metamath.org/index.html If that program is math, then all software is math. If that program is not math, please tell me what is. From what I've seen, lawyers love to draw lines in the air, creating distinctions between things that are, in fact, formally equivalent. I have no doubt that they can, in fact, write some distinction that satisfies them legally, but in doing so, they will be creating a legal fiction wholly alien to mathematicians. I believe it was Knuth who pointed out that there's no difference between numbers and other kinds of precise information.
  - tzs 16y ago
    The distinction is between the thing and the use of the thing. For instance, you can't get a patent on wood. You can get a patent on using wood to make some particular thing if the use of the wood there is novel, useful, and non-obvious. Same with software and math. Software patents do not cover the mathematical aspects of software--they cover the use of the mathematics in a novel, useful, non-obvious way (at least when the patent office does its job during examination...).
    - burgerbrain 16y ago
      The logical conclusion of what you're saying is that while you cannot patent the Pythagorean Theorem, you could patent using the Pythagorean Theorem to solve triangles, perhaps in the context of architecture. That is of course, patently absurd. "Software patents do not cover the mathematical aspects of software" As Knuth explicitly notes in the materials I've already linked, trying to separate the math from the rest of software is a fundamentally flawed endeavor.
    - 16y ago