  Quantum groups and non-commutative spaces have been repeatedly utilized in
approaches to quantum gravity. They provide a mathematically elegant cut-off,
often interpreted as related to the Planck-scale quantum uncertainty in
position. We consider here a different geometrical interpretation of this
cut-off, where the relevant non-commutative space is the space of directions
around any spacetime point. The limitations in angular resolution expresses the
finiteness of the angular size of a Planck-scale minimal surface at a maximum
distance 1/\sqrt{Lambda} related the cosmological constant Lambda. This yields
a simple geometrical interpretation for the relation between the quantum
deformation parameter q=exp[i Lambda l_{Planck}^2 ] and the cosmological
constant, and resolves a difficulty of more conventional interpretations of the
physical geometry described by quantum groups or fuzzy spaces.
