In physics and also in biology, dimensional analysis can help the scientist achieve qualitative understanding without detailed calculations. One of the chief impediments to studying complex systems like cells and cities is that we have no clue as to what the dimensions are. For example, in order to characterise a city, should:
- Inflows of people and goods be along the same dimension or separate dimensions?
- All energy sources be clubbed into one dimension?
Any rational analysis of a complex system has to start with identifying the relevant dimensions. Given a system S, what is the procedure for identifying its relevant dimensions?