I’m taking a Linear Algebra course this fall. Last night, my instructor said something quite interesting:
“We are building a model of Euclidean geometry in our vector space. Then we can prove our axioms of geometry (as theorems).”
This would sound like technobabble to me even a week ago, but what he’s really saying is this:
“If you can implement one system’s basic rules or axioms in another system, you can build a model of that first system in the second.”
The beauty for those of us who work in the model is that we (theoretically) shouldn’t need to care what platform we run on. (In practice, there are differences, which is why we want platforms to implement standards, so we can concentrate on using the theoretical model we depend on.)
On the flip side, that also means that building and maintaining that fundamental system we build on top of has to be done very, very carefully. If you’re building something for others to use (and chances are, when you’re writing software, you’re doing exactly that), you really have to think about how you want others to use your system, and how others might try to use your system in ways you don’t expect.
It’s really quite a profound duty that we take on when we craft software for others to use.