Units, fundamental constants, dimensional analysis, and all that stuff

That is what is being discussed in this wonderful thread at The n-Category Café. It is one of those tricky subjects where everybody thinks it is all so simple, the true answer to all questions is obvious... and then everybody gives different answers. How many fundamental constants are there? Must fundamental constants be dimensionless? What are units? Do coordinates in GR have units, or are they in the metric tensor, or where? I once spent a couple of hours discussing these questions after lecture hours with my particle physics teacher, and no conclusion was reached. Great food for thought. (You can also check this paper for more.)