As for my final thought, pick up a design patterns book, and read it. Think about it in light of the two basic patterns of thought that I described for mathematics. If you can't see how it more closely resembles the algebraic mode of thought, then I probably didn't describe it clearly enough. For the real explanation I'd have to inflict a few months of advanced math on you. After you'd experienced figuring out, say, how homology groups work (for a demonstration of algebra) and various epsilon-delta proofs (for a taste of analysis), then you'd know directly the distinction that I am trying to describe.