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Above I said I didn't agree that software is "math", but didn't expound on that. I will do so very briefly here.
I look at Microsoft Excel, and in my opinion:
Microsoft Excel is neither a mathematical formula that was derived, nor a mathematical principle that was discovered. It's a state machine implemented as software, and that software was constructed, not derived or discovered like a mathematical formula or mathematical principle. This is why I don't consider software to be "math".
OK, that's my brief expounding. Now for some philisophical and metaphysical rambling.
I don't think the "software is math" argument is relevant to patents. Look at Amazon's "1-click" patent. Most people hold that that patent is absurd. But not because it's "math". The idea of "1-click" (including a description of how it works (in the case of "1-click" the idea and the description of how it works are essentially one and the same)) isn't "math", even if the software (i.e. the source code or compiled binary code) is considered such. And it's the idea of "1-click", not the software, that was patented. Or does the "software is math" crowd argue that the ideas themselves are "math" even before they are implemented as software (in which case, again the "software is math" argument is rendered irrelevant)?
I get the feeling that the "software is math" crowd feels that all mathematical principles already exist in the abstract, just waiting to be discovered, and therefore since they already exist, they can't be patented; and/or that all mathematical formulas already exist in the abstract, just waiting to be derived, and therefore since they already exist, they can't be patented. And they want to say that software is "math" (I guess because software can be represented as a series of 1's and 0's or can be interpreted using an abstract Turing machine, or some similar notion), and therefore all software already exists in the abstract, just waiting to be derived or discovered, therefore can't be patented.
If that's the line of thinking, then could one not take the next step and argue that non-software inventions also already exist in the abstract (see Plato or Aristotle), just waiting to be discovered, therefore nothing (software and non-software) can be patented? Or could one not at least argue that since the *idea* of every non-software invention can be represented as a series of 1's and 0's (ASCII text, for example), that therefore every *idea* itself is "math", and therefore every idea already exists in the abstract, just waiting to be derived or discovered, and therefore no inventions can be patented, software or non-software?
(Reminds me of a "proof" I once saw that said that since every idea can be generally described in 500 words, and every word can be represented as 1's and 0's, that therefore there is an absolute limit to the number of ideas that can and will ever exist. :p