People are not getting patents for some sequence of calculations, they're getting patents for producing a useful, new effect on the world. Yes all computers are universal in what they can compute, but I see no reason why coming up with a new, greatly improved and economically useful way of using such a restricted machine should not be patentable.

Furthermore, people seem to think that just because a computer program can be described as a sequence of mathematical steps that it is therefore a mathematical algorithm and shouldn't be patentable. Algorithms have no effect on the world, they do not improve anything in a tangible way, but software absolutely does (and it's why you can read this now!) and it is the processes that lead to producing these useful effects that is patentable. I can't patent an algorithm without specifying why it is useful to the population at large.

Finally, people seem to have got the bizarre notion that there are patents claiming computers which are capable of performing a certain task, which is just absurd and untrue. The claims are usually directed to a system which actually does perform the steps in the process, not one which is capable of it (therefore allowing them to exclude competitors who make their own implementation of some software process that has been patented and attempt to make money from it).

I think this is the heart of your argument here. (Correct me if I'm wrong.)

The problem is that in terms of calculation, computers are not limited. In fact, that was proven not once, but twice, in 1939. Any computation that can be performed can be done with any general-purpose computer. The Church-Turing Thesis proves that that computer need not even be specialized: it only requires the ability to manipulate symbols deterministically in some general manner.

What these patents cover is, in fact, only those computations with the aid of a general-purpose computer, and the only reason those patents have been allowed is by this fallacious argument that a general-purpose computer somehow becomes a special-purpose computer when it is programmed. This is not how computers work. A general-purpose computer does not become special-purpose merely by assigning some numbers to a pool of memory any more than an FPGA becomes an ASIC by uploading a ROM image. It is still a general-purpose computer, and its nature does not change.

If, perhaps, by programming a computer, the program magically became a new, immutable physical wiring, your argument might have merit. But we do not live in a world of magic.

>If software can be patented then that patent would infringe itself.

To infringe a patent, you must make, use or sell a product incorporating the invention. A patent by itself does none of those and hence cannot infringe anything.

If you want something physically-grounded you'd have to say: I want to implement this idea on that specific computer with these specific physical manifestations. And even if you got that patent, it would be effectively worthless. Changing what we view as trivial details of the implementation (e.g. swapping a Pentium for a Pentium Pro) would totally change the physical manifestations at the level of electrons and molecules. In other words, that would completely avoid any claims in the patent that are described at the physical level.

And the minute you retreat to considering claims at the functional level (i.e. what our collections of electrons and molecules mean) you're no longer talking about doing something physical to achieve a useful result: you're talking about combining abstract ideas with a wide range of possible physical implementations to achieve a useful result, which is something entirely different.

The problem with this type of argument is that it essentially says everything is an unlimited physical process that could be patented through competent drafting, because everything always affects change at some level. Heck, even the process of observation affects things at a physical level. Allowing things to be patented, simply because they can be described as a physical process, without anything more, is ridiculous.

This was not was anyone had in mind when they created the patent system, nor was it even allowed until recently.

The problem is that the physical aspects of the computer are not what infringes the patent. They exist in the prior art. A mechanical or biological computer would infringe the same as an electrical computer because the physical aspects are irrelevant to the software. You're essentially try to claim that authors should be able to patent literary works because a pen or a printing press is a physical machine that moves all manner of ink molecules around into a particular configuration.