A great deal of what we do in software is a direct consequence of a couple of fundamental assumptions we make: postulates of software development. Only by questioning and changing those assumptions can we bring about fundamental change in the way we build software.

Postulates or axioms are rarely discussed or thought about. We just accept them, like breathing air or walking on the ground. Changing a postulate or assumption normally results in a cascade of consequences that changes a great deal.

Geometry: The Parallel Postulate

We can understand postulates in software by seeing how they work in geometry. In Euclidean geometry, there are four fundamental postulates, and a pivotal fifth one, the parallel postulate. This is the one that says, basically, if the angle between two lines isn't exactly 180 degrees, the lines will eventually cross; otherwise, they are parallel, and never meet.

What's important about this postulate (and the others) is that all the rest of Euclidean geometry is derived from them. Given the postulates, all the theorems are implied.

For example, the famous Pythagorean Theorem is one of the many theorems whose truth grows out of the small seeds of the postulates.

In the diagram above, the theorem states that a² + b² = c².

Non-Euclidean Geometries

What if parallel lines can meet? Think it's impossible? Well, think about lines on a globe.

Lines that are parallel end up meeting — and this is business as usual in Elliptic Geometry. What's worse, the Pythagorean Theorem does not hold in non-Euclidean geometries in general, and spherical geometry in particular.

This isn't just textbook stuff. For example, Einstein's General Theory of Relativity is based on non-Euclidean geometry. In fact, questioning the Parallel Postulate and devising ways of thinking about and describing non-Euclidean spaces was essential to the development of modern physics. So long as geometry was Euclidean and only Euclidean, progress was impossible.

The Postulates of Software

So what are the software equivalents of the Euclidean Postulates? There are few questions that are more important, because only when the foundation is questioned and changed is rational, constructive, internally consistant change possible. Only with new postulates can we derive a whole new set of theorems to define software practice. Only then is fundamental change and improvement possible.