[leumassuehtam]

I like to think of an algebra the same as a language. You want to define and constrain your language such that you can describe elements of your universe is clear and consice.

For example, if I am trying to describe a art piece in the museum, I need concepts and words that connect what I am seeing to reality. In the same way in electromagnetism, proper time is part of the reality and it is an experimental fact, so it must be included in the algebra. Another example is a functional programming language where you identify high-level functions as the building concepts of many computer science problems.

Defining an algebra tailored for the problem you're working with actually highly constrain the space, and this is what makes many problems trivial.