# Proofing the Pythagorean theorem and what this means for Domain-Driven Design

According to Wikipedia the Pythagoraen theorem is the theorem with the highest number of known proofs, citing a book containing over 370 of them.

What does this mean for modelling under the Domain-Driven Design paradigm?

In discussions with other developers I often hear the opinion, that you should develop the model of a software entirely disconnected from technical decisions as long as possible and fully abstracted from the choices.

I held this opinion myself for a long time.

Discussing this with a colleague today I found a nice analogy to describe my growing pain with this approach, something I wasn’t able to formulate before.

Maybe the analogy is a bit of a stretch.

The Pythagoraen theorem shows that you can find an entirely different solution for the same problem by using a different toolbox. Finding one or more proofs for the theorem depends on your knowledge of different fields of mathematics. And depending on the toolbox, the solution is simple and elegant, or complex and theoretical.

The reverse conclusion could be, that if you develop a model (theorem) entirely abstracted from the future implementation and toolbox, then it must increase in generality and complexity to take into account the potential implementation with any kind of toolbox. Or the problem space is simple like the Pythagoraen theorem that its description allows many implementations.

Consequently, if you make technical decisions and restrict yourself to fewer approaches/toolboxes before building the model, then the resulting model can be simpler under the assumption that you only need it to be solved under the given technical constraints.

For example, take Redis as a choice of database. Its built in support for more complex data-types allows to implement extremely simple abstractions directly on top of Redis. If you know you use Redis up front for a problem that can be solved with lists, sets or maps, then the model and code describing this domain logic could be extremely simplified compared a solution that makes no assumptions about the data storage.