Right, and yet courts affirm patents where the only novel component is something that can be expressed in software. The reason they do, in my non-expert opinio

Right, and yet courts affirm patents where the only novel component is something that can be expressed in software. The reason they do, in my non-expert opinion, is that they see the slippery slope - every invention can be decomposed into logical steps (the algorithm) and simple physical processes carrying out those steps that aren't novel enough to be patented on their own. And for many or most inventions, the combination of the physical processes isn't even enough to be novel -- the algorithm is key. Consider, for example, synthesizing a chemical. You could have a chemical plant that's able to perform hundreds of basic processes, and the key component is the algorithm that describes which steps to perform in which order. Not allowing patents on these processes just because the important parts of them can be described with an algorithm would be a radical departure from the functioning of our patent system - much more radical than not following the reasoning in some past case to the letter. So courts have allowed this kind of patent on algorithms, but in my opinion have gotten the logic of it wrong. What I think they should do is distinguish between algorithms that are really mathematical in nature (as in, would be of interest to computer scientists or mathematicians) and algorithms that really just encode a physical process. This wouldn't be that radical of a departure from the cases you mention - they'd just need to refine what those cases meant by 'algorithm'. The problem with the way courts have ruled to date is that it actually affords less protection to the real mathematical algorithms that the clause was meant to protect, because everyone just slaps "on a machine" to the end of their patent and bam, you've got patentable subject matter. Linked lists on a machine. I'd much rather see the courts look at the crux of the algorithm being suggested (linked lists) and decide that it's too abstract for a patent.