Any program you can write, you could build a physical machine to execute.

Now consider a physical general-purpose computer with your program loaded into it. Can you really argue that this is fundamentally a different kind of object than the special-purpose machine? They behave, let's suppose, identically.

Okay, maybe you would say, the program considered abstractly is still an object I can't kick, so it's not patentable; the only thing that's patentable is a physical computer with the program loaded into it. But that doesn't help you, because no one can actually use the program without loading it into a computer anyway. So if you get a patent on a computer with your program loaded, that has the same practical effect as a patent on the program itself. No?

Any algorithm has an infinite set of different physical machines that could be built that will execute it. A machine expressing an algorithm is not the same as the algorithm itself.