> Right, I was not contemplating granting a monopoly over the thinking, but rather other applications of the invention such as selling of a machine that uses the algorithm.
First, though I realize this is generally overlooked, software is merely a passive description of an algorithm, qualitatively no different from the description in the patent application. A machine storing such software is qualitatively no different than the paper the patent application was written on--a medium containing a stored description of the algorithm. It is only when the machine is actually used that you could say that the algorithm is being used--by the owner or operator of the machine, not whoever manufactured or sold it.
However, we then run into the second issue: in attempting to avoid monopolizing people's thoughts, we've codified an excessively limited interpretation of the term "thinking". Increasingly, people are integrating computers into their day-to-day lives and routinely using them to aid their own thought processes. I would hate to formalize a legal distinction at this point between "thinking" which goes on entirely in one's brain and "thinking" which incorporates technology to a greater or lesser degree.
Without that distinction, however, any time a person evaluates an algorithm on a general-purpose computer they are "thinking". Ergo, if you exclude "thinking" from actions which can infringe on the patent, you are left with very little in the way of actual monopolies.
Finally, to approach the issue from a different direction, all the novelty is in the algorithm, not the machine, which is merely a general-purpose computer. In my opinion, at least, if you're not patenting the algorithm in its own right, any novelty in the algorithm shouldn't count toward fulfilling the overall requirements. That would be rather like inventing a novel kind of transistor, using it in a textbook-standard amplifier circuit, and then being granted a patent on that standard amplifier design incorporating the new transistors. (Correct me if I'm wrong, but I certainly *hope* you couldn't a patent like that...)
> ... it doesn't explain why there should be a patentability distinction between algorithm and not algorithm ...
The novelty criteria isn't limited to software patents, of course, but software patents suffer from the systemic issue that only the unpatentable abstract algorithm is actually novel--given the algorithm, a device which implements it via a general-purpose computer is nothing new or surprising. All software patents have this problem, which is why they're singled out.
> I'm not sure it would be easier for a judge to determine whether an invention is an algorithm or not than it would be to simply determine whether the invention meets those two underlying criteria.
I think you're making it sound harder to classify something as a software patent than it really is. One simple question would do: is the invention present before you load the software? If no, it's a software patent. Still, you might be right about the cost/benefit analysis being easier in some cases. Now if only patent examiners were permitted to reject applications simply because they feel the patent fails to provide sufficient public benefit... sweet, sweet chaos. I can't imagine the examiners or the applicants tolerating that degree of subjectivity. This, of course, is part of the reason inventions are classified into patentable and unpatentable subject matter.
Algorithms, as such, are already an unpatentable subject matter (math). The real question in this debate is how to interpret "novelty" and "obviousness" when patentable and unpatentable subjects are mixed together, particularly when it's just the non-patentable part which is novel or non-obvious.