" 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."

I think you missed the point, actually.

They have argued, and precedent until yesterday was: It is patentable because it is implemented on a computer, because it "transforms the computer" into a "specific device". IE that the computer, programmed, makes something unpatentable, patentable.

"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. "

As a patent attorney, having fought software patents for many many years now, i'm just going to say this is completely and totally false.