I appreciate that the abacus has prior art (counting units on fingers and tens on feet). My mind experiment was to ask a question about the migration of an insight regarding physical objects to a software representation. If the physical abacus were invented in an innovation vacuum with no prior art, I would think that another inventor's software representation would be infringing to the first inventor. Likewise, if there were no related prior art and I invented the iPhone abacus APP, I would consider a physical stone and wood model to infringe my software version.
The abacus is an improved method of counting compared to moving stones (called calculi by the Romans :-) around on an unconstrained surface. But there are many ways of constraining how stones move, and I bet people had already been using others (such as grooves and pits) long before the advent of metal-working permitted beads on wires. An abacus simply automates a mathematical counting process already understood, and it's perfectly legal for others to automate that same mathematics using other physical hardware.
I'm sure that other readers can think of better examples, but the one that comes to mind is the abacus. If you were the first person to invent the abacus, wouldn't a software abacus APP on a smart phone violate your invention even though it contained no beads, no metal rods, no wooden frame, no corner brackets, and no moving parts? It seems to me that as soon as many physical inventions are disclosed that the software implementation suddenly becomes "obvious".
If I invent a piece of hardware that does something physical, your software could not possibly do the same thing because software by itself does not have a physical manifestation -- it just does mathematics. So as a non-lawyer, I cannot see how it can infringe since it does not actually do anything physical. If you add hardware to your software so that it then does the physical thing my hardware does, it's no longer software-only and could then possibly infringe.
The issues raised by this case are clearly keeping the lawyers busy. I'd like to pose a simpler question. If you invent a piece of hardware and get a patent on it, should I be able to implement the same invention in software and get around your patent?