The difference is that in the software case the patent claims are completely divorced from the computer's physical operation. You could be using a gravity-based computer built out of planets and stars and it would infringe all the same. Because the computer isn't required to do something, it is only required to calculate something.

Let's try this another way. You understand that it is possible to build a computer out of anything. Let's build a computer out of nothing. We want to perform a calculation without building anything whatsoever, so all we are going do is observe nature. There are any number of ways to represent a calculation. If there are three pigeons and five more arrive then you have only to observe the resulting number of pigeons to learn the sum of three and five, etc. Nature is going to do lots of calculations we don't care about the answers to, so we ignore those and only pay attention to the ones necessary according to the algorithm to be executed.

By doing this you can execute any algorithm. Doing strictly nothing but observing natural phenomena. There is no machine. Because the result you are trying to obtain is not a thing, it is a representation of information. And information can be encoded into anything and the representation is defined by the context. By changing the context -- an entirely intellectual undertaking -- you determine what information is represented by the physical state. What the machine (or the birds or the stars) do is comprehensively irrelevant, as long as things are happening you can use them to represent the execution of computer software.