Despite the above facts, suppose one were to adopt polar coordinates, and wish to say that r θ θ ˙ ˙ 2 is "centrifugal force", and reinterpret r ¨ ¨ as "acceleration" (without dwelling upon any possible justification). How does this decision fare when one considers that a proper formulation of physics is geometry and coordinate-independent? See the article on general covariance. To attempt to form a covariant expression, this so-called centrifugal "force" can be put into vector notation as: F θ θ ˙ ˙ = − − ω ω × × ( ω ω × × r ) , with: ω ω = θ θ ˙ ˙ k ^ ^ , and k ^ ^ , a unit vector normal to the plane of motion. Unfortunately, although this expression formally looks like a vector, when an observer changes origin the value of θ θ ˙ ˙ changes (see Figure 2), so observers in the same frame of reference standing on different street corners see different "forces" even though the actual events they witness are identical.