> Software algorithms are mathematical expressions. I don't need to show prior art to prove that having a patent on 46,456,456 + 235,566 = 46,692,022 is meaningless even if nobody has done that particular calculation before me.

Straw-man argument by over-generalization.

A better analogy would be that software systems are machines that can be fully specified in some formal system.

But then, so are physical machines, for most useful levels of abstraction.

The distinction is simply not as clear-cut as you're making it. If a software system can simulate a physical system, should there be a difference in patentability?

If you're speaking narrowly of individual algorithms, then perhaps you have an argument, but what's important is how you pull all the various algorithms you need together.

According to Donald Knuth[1]:

"[To a computer scientist] every algorithm is as mathematical as anything could be... An algorithm is an abstract concept unrelated to physical laws of the universe."

[1]http://www.pluto.it/files/meeting1999/atti/no-patents/brevet...

And this proves what? I can find quotes to support an arbitrary position too. :P

It proves nothing of course. I just think that Knuth makes a compelling argument and I tend to agree with him. Mathematics by definition has no relationship to the physical world. When we create these relationships they fall outside of mathematics and become things like physics or chemistry. Patenting mathematical formulas is kind of meaningless, but more importantly, very harmful. If we were to patent them, we couldn't afford to teach them for example.

Next, the question is whether algorithms fall under mathematic. Knuth argues that they do and I agree.

Ok, this isn't an answer to your points, but have you read Tegmark's Mathematical Universe Hypothesis?http://arxiv.org/abs/0704.0646

"I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems."

I have not. From a quick look this stuff feels like String theory, which we conveniently cannot prove. Once again, only a mathematical concept with no connection to the real world that we need to concern ourselves with. It's also a "theory of everything" which I have learned not to trust (these theories tend to overlook some big issues, like the fact that quantum effects only show themselves at roughly atomic scales and just assume that the cumulative effect at large scales does not cancel out).

I realize that combinations of algorithms are still algorithms, but where do you stop?

The main problem with software patents for me are that

1) They stifle innovation by killing small projects or forcing innovators to not care about infringing (for which they can be sued later).

2) A lot of them are BS. There may be not prior art in the patent database, but for a specialist in the field, they're obvious.

3) It costs too much to patent, which puts too much power in large companies' hands. They can spam the USPTO with brain farts, with some non-zero probability of having them approved. If I save for a year, I can make one patent application per year.

In other words, there's no problem with software (or other) patents in theory, but currently the pragmatics are out of whack. Software patents are no different than other forms of patents except that many of the coefficients involved are very different from other industries, which significantly changes the calculus. Complete elimination of software patents would be preferable to what we have now, but IMO wouldn't necessarily be the optimal solution.

Questions:

1) How would you classify a non-reprogrammable hardware device that performs a computation?

2) Would it matter to your classification if it was programmed through the simple arrangement of wires, rather than some source code?

3) How is an arrangement of levers that performs a computation different? Would you argue that a specific physical machine capable of performing a computation is patentable, while the algorithm itself is not?

3b) Since computers are a form of universal machine, if the answer to (3) is yes, then what constitutes the specific physical machine, where the machine is specified in software?

4) Finally, would you simply argue that nothing should be patentable, in which case splitting hairs is irrelevant?

If you build a physical calculator that can add 2 and 2 in a novel way, you get a patent for the way you've built the machine. By the same token if Intel figures out how to build a quantum CPU they get a patent. You don't get a patent for 2 + 2 = 4, and Intel cannot patent the quantum mechanics formulas, just the blueprints of their device. As for (4), patents serve a purpose in some industries, etc.

So if I invent, say, a genuinely novel new form of public key exchange, or a new psychoacoustic model that drastically improves audio compression, or a novel forward error correction scheme --- these things shouldn't be patentable, but a new kind of bicycle kickstand should be?

In my opinion, that's exactly how it should be. Patents do not exist to serve corporations, developers, inventors or investors. They exist to foster innovation so that the public can reap the benefits.

Can you invent, market and sell a new type of bicycle stand without patents? No. The concept will be copied as soon as it hits the market.

Can you invent, market and sell a new type of algorithm without patents? Arguably yes. Startups do it all the time. A patent is neither necessary nor sufficient for success in this case. In fact, it seems that on balance, patents are far more harmful than they are good to legitimate software companies.

> They exist to foster innovation so that the public can reap the benefits.

Fair enough, but dislosure fosters innovation. Two companies making the same bicycle stand is no more innovative than just one.

> Can you invent, market and sell a new type of bicycle stand without patents? No. The concept will be copied as soon as it hits the market.

If a copier can market and sell a new type of bicycle stand, why can't the inventor do the same?

I note that many things, both physical and virtual, are sold without patent protection, so it's unclear why you think that patents are essential for physical things but not virtual.

Won't copyright and trade secrets offer enough protection?

No. Imagine I'm a 4-person startup hoping to capitalize on my revolutionary new psychoacoustic library. Copyright protections don't prevent Microsoft from reading my library, learning how they work, and creating a clean-room reimplementation. Similarly, it's hard to create a trade secret out of something that will need to run on every customer's machine.

Will patents help you against Microsoft? Does your four person startup really have the resources to take on a major legal team? From the patents question in the interview at http://www.nature.com/news/2010/101007/full/news.2010.525.ht..., it sounds like defending a patent isn't a pretty or an affordable business.

Patents take 5-7 years to issue and cost hundreds of thousands of dollars to litigate. They're more like claymores rigged to a dead man's switch than they are a real defense.

But that's orthogonal to the question that was just asked.

However, if that idea is worth selling, you will be ahead in the market. Microsoft will need to catch up. They may buy you out. Software typically goes obsolete for reasons other than the "need" for protection.

Besides, by the time Microsoft does that, some other algorithm could quite possibly be created by somebody else.

I'm no fan of software patents but comparing a simple arithmetic operation to an algorithm is a bad way to argue about software patents. Algorithms are a higher level of abstraction that can be quite complex in the end. And they are rarely the unique way to do something. It can even be almost impossible that an algorithm is really the best choice in your case.

Do I think software patents (or any patents) make sense? No, but I won't call software algorithms simple mathematical expressions similar to adding 1+1.