Software as complexity management (part 1)

Software exists to solve problems, primarily problems in business. Solutions to those problems pay for the people who write the software who solve them. Even free software runs on corporate money. Especially free software.

If we want to write better software, we need to have a solid understanding of what a problem is. Instead of problems, it's useful to talk about the problemspace. I often find it useful to imagine a problem as a surface in N-dimensional space, each dimension representing a competing concern. For me, the surface describes the complexity floor of the solutionspace. It's the theoretically ideal solution - the absolute zero of software perfection.

So, the ideal software is the implementation that is closest to the complexity floor. Can we describe the complexity axes? Can we describe some rules for how to minimize them? What do you think?