Sets of natural units, like ‘atomic units’, are sometimes used to simplify the equations of physics.
This choice of units can be seen as a way of showing the relationships between quantities in their
simplest form, in specialised situations, while still being correct. The unit system used for
teaching, the SI, is instead designed primarily to be a set of units that can be applied
consistently across all areas of science, commerce and industry. The SI also gives priority to
emphasising the distinction between different quantities, by (most of the time) giving different
units to different quantities, rather than producing the simplest possible equations. It is not
widely appreciated that the SI treats the radian as the natural unit for angle, the only unit to be
treated this way, with consequent issues for clear distinctions between quantities involving angles.
The system that the SI would become if this anomaly were removed is presented. Rather than
advocating this major c…