  We consider the relations between de Vaucouleurs-Ikeuchi diagram and
generalized commutation relations among the coordinates and momenta. All
physical objects in the Universe ranging from elementary particles to super
cluster of galaxies are confined within the Triangle of the de
Vaucouleurs-Ikeuchi diagram on the matter density versus scale length plane.
These three boundaries are characterized by the quantum uncertainty principle,
gravitational event horizon, and cosmological constant. These are specified by
the non-zero commutation relations $[x_\mu,p_\nu], [x_\mu, x_\nu]$ (strictly
$[x_i,t]$) and $[p_\mu,p_\nu]$, respectively. The canonical commutation
relation $[x_i,p_j]$ are slightly modified, which preserves the self
consistency as a whole.
