Space-time unit notation
Part of my units pages
Units involving distance and time are fundamental to many areas, including everyday life. They can be composed to form various combinations, like velocities (ms⁻¹), accelerations (ms⁻²), areas (m²), volumes (m³), frequencies (s⁻¹), etc. Unfortunately, this exponent-based notation can cause ambiguity.
If we instead represent these fundamental dimensions graphically, we get an unambiguous alternative which makes cancellation straightforward.
Instead of “m”, metres can be written with 𒀹, and multiple arrows can “stack”; e.g. 3µ𒑳 is 3µ(m³).
Instead of “m⁻¹”, inverse metres can be written as 𒀹. Up and down arrows then cancel out.
We could also use the “forwards” (rightwards) direction for time, writing seconds as 𒀹 and inverse seconds as 𒀹.
In this notation, the acceleration at Earth’s surface would be written as g = 9.81𒀹𒃵.