The structure of the new SI

The "new" Syst\`eme international d'unit\'es (SI), which became effective May 20, 2019, defines and is defined by a set of constants. These include the speed of light, the Planck constant, the Boltzmann constant, and the constant relating the elementary electric charge to the coulomb. Interpreting such constants as conversion factors organizes the units they relate into a unifying geometric framework. In this framework, units appear (perhaps raised to some power) either as rows/columns in a single conversion table or as entries in a list of dimensionless numbers. This organization clarifies the distinction between "fundamental" physical constants with values that are set by people, like those defined in the SI, and those with values that are set by nature. It also reveals geometry permeating our theories of physics that is normally hidden by a surplus of units.