sentences:  It is not immediately obvious that this new singularity is better, as both singularities have multiplicity 2 and are given by the sum of monomials of degrees 2, 3, and 4.A natural idea for improving singularities is to blow up the locus of the "worst" singular points.The Whitney umbrella "x"2 = "y"2"z" has singular set the "z" axis, most of whose point are ordinary double points, but there is a more complicated pinch point singularity at the origin, so blowing up the worst singular points suggests that one should start by blowing up the origin.