  Our purpose is to offer a logical analysis of the system of units and to
explore possible paths towards a consistent and unified system with an original
perspective. The path taken here builds on the fact that, thanks to optical or
matter-wave interferometry, any measurement can be reduced to a dimensionless
phase measurement and we follow this simple guiding line. We finally show how
one could progress even further on the path of a synthetic framework for
fundamental metrology based upon pure geometry in five dimensions.
