But did they actually modify OS X or did they just provide a software adapter so that it could be installed on the machine? Like how Windows runs on Macs through Boot Camp.

Seems to me that this would be allowed unless Apple tied the copyright of the hardware and software together.

I agree with everything you've said. However the fact remains that the behavior of atoms can or at least will be completely explainable through mathematics. Same with electrons. Same with any subatomic construct. Therefore, by your logic, no mechanical patents are possible as well because it can all be explained through math.

That's about the process, a different kind of patent.

Quicksort is not implicit to math. Show me how to derive quicksort from set theory. You can't. Show me how to derive a basic bubble sort from set theory. You can't. It is a function that can be explained using set theory but is not contained within it. Even the Fibonacci sequence is not implicit to mathematics. It was created by someone, patentable or not.

But these are all concepts that lie outside the core of mathematics. Everything in mathematics is intrinsic to the rules of mathematics: the axioms. Meaning that while new equations can be discovered, they are all derived from a core theory.

The act of choosing a way to select element p is in and of itself outside of mathematics. You chose the first element? Middle? Some logarithmic? OK. You still chose a way, not the math. This is precisely why software cannot be derived from mathematics. Hence, why the "math is not patentable" theory does not work when applied to software patents.

Where is the mathematics for this part? Or many other parts of the algorithm. It is explained in a rigorous mathematical way, but that doesn't make it mathematics.

Many algorithms can be explained and profiled using mathematics, but they aren't a subset of mathematics. Take quicksort for example. Sorting data has nothing to do with mathematics. It just so happens that a mathematical model can predict the performance of the algorithm.

Mathematicians work on axioms and the like. There is no axioms for a lot of things in software. Saying software patents should be outlawed because it's based on logic is like saying that mechanical patents should be outlawed because it's all based on the atoms that produce the end product.

Yes, in the majority of cases more competition is better. Then there are operating systems.

Until applications and data are built on completely open standards -- interoperable with ANY capable device -- this multiple OS business is just a hassle for consumers.

Imagine if your must-have pizza topping was incompatible with any other company's pizzas!

I don't agree with you. It's funny how my dad is a machine electrician and I am a programmer. There is grunt work to be done in both fields, but every time we talk about our work it always comes down to design.

Knowing how to make the machine do what doesn't make a strong programmer. I'm sure that you are a good programmer: how many times have you forgotten a cast or how to do a certain operation. I'm betting just as much as any other good programmer. If you forget these things you can easily look it up or check out some reference code.

The real strength of a programmer is in design: re-usability, extendability, readability, robustness, and performance. The good programmers balance these factors to produce a solution that works well now and can be easily adapted to new problems.

The irony is that this follows for many careers: farming, electricians, medicine, surgery, programming, mechanics. The ones who know what makes a good solution, not just how to implement those solutions, are the ones with the real skills.