My recent career in a sentence …
Computers and algorithms may be getting faster, cheaper and easier, but they simply cannot handle a blind search through the eight-or-more-dimensional parameter space.
— Squires, T. M., Messinger, R. J., & Manalis, S. R. (2008). Making it stick: convection, reaction and diffusion in surface-based biosensors. Nature Biotechnology, 26(4), 417–426.
From the same article is one of the more persuasive arguments for finding nondimensional groups of parameters.
Before beginning, however, we would like to dwell on the obvious. Nothing can be large except by comparison with something else. A retrovirus is too small to see, yet is enormous from an atomic standpoint. Similarly, flows are neither fast nor slow, solutions neither concentrated nor dilute, and sensors neither big nor small without standards for comparison. Meaningful ‘apples to apples’ comparisons can be made only between quantities with the same physical units— for example, length versus length. The (dimensionless) ratios of two effects under comparison are incredibly informative and play an extremely important role in the study of fluids and transport.