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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. T

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.
  - Natsu 16y ago
    Software "processes" merely turn one number into another algorithmically. What part of that isn't math? Is it because the computer usually tells you that the very large numbers in question are pictures, documents, web pages, or whatever else? As far as the computer is concerned, it's a very long number and it's no different from all the other numbers stored on your computer.

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.
- Natsu 16y ago
  Software "processes" merely turn one number into another algorithmically. What part of that isn't math? Is it because the computer usually tells you that the very large numbers in question are pictures, documents, web pages, or whatever else? As far as the computer is concerned, it's a very long number and it's no different from all the other numbers stored on your computer.