[btrettel]

These types of techniques are already big in certain fields. E.g., in fluid dynamics and heat transfer, "dimensional analysis" is frequently used to simplify and generalize models. Sometimes models can be nearly fully specified up to a constant of proportionality based solely on dimensional considerations. Beyond what is typically seen as "data" the information here is a list of variables involved in the problem and the dimensions of the variables.

As far as I can tell "dimensions" in this sense are a purely human construct. For two variables to have different dimensions, it means that they can not be meaningfully added, e.g., apples and oranges.