Figure 2.1 – NIST Subway Diagram

So, what is direction, really?

Currently, direction is an orphan when it comes to understanding physical quantities and how they relate to one another.  The basic unit that is used to define an angle, the radian, is the disconnected unit at the lower right in the NIST diagram.  Why is that?  And why is the unit of the solid angle, the steradian, a component of luminous flux?  What’s up with that?

It’s our new understanding that a quantity related to the radian is actually the eighth base quantity, and it belongs on the left-hand side of the diagram, probably just below length.   Then, those three base quantities (sometimes referred to as dimensions in physics) of length, direction, and time can be understood as comprising spacetime.

This idea that there are fundamental physical properties that can be related or equated to one another gives rise to an entire method of dimensional analysis that is used for examining physical phenomena and theories and inferences about their underpinnings.  The foundation for such a view is the understanding that everything can be expressed as a quantity of something.  This ability to equate the property to a quantity is the key here, and this website is dedicated to learning how and why direction can be expressed as an actual quantity.

The SI base units and their physical quantities are the metre for measurement of length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for temperature, the candela for luminous intensity, and the mole for amount of substance.  The turn (or revolution) is the manifestation of a generalized property that is expressed as orientation or direction.  It is possible that the physical quantity of $\|\pi\|$ should be incorporated for the amount of direction, or orientation. There’s a legitimate argument to be made that $\|\tau\|$ is a better value to use for deriving the base unit, and we’re starting to lean in that direction.