Derivations
Building a mathematical system that can 'act out' real world changes
The process of derivation 'loads' real world activity into equations. This loading process allows equations to 'act out' the changes in the world. The equation can thus be thought of as a symbol-based 'machine', which can mimic -- act out -- changes in the real world. As the symbol-based system can act out changes in the world, it can be used to explore, and predict, the changes in the real world. This makes the symbol-based system very useful, as it allows building and exploring many 'what-if' scenarios, without making (costly) changes to the real world.