Although only a small proportion of dancers know how to write down dances on paper using notation, most major dance companies in the world now depend on notated scores for the maintenance of their repertoires. All have the problem of reducing a four dimensional manifold to two dimensions. The basic method of compressing the dimensionality is by quantization. This process also limits the detail representable, control of which is then given by the number of symbols used. Any process for reducing the dimensionality must also lose some direct representation of the symmetries inherent in the higher dimension domain.
Many notations have extra symbols for representing commonly used symmetry operations.
Examples of these are shown in Figures 6 and 7. These notations are very different in the ways they treat space and time. Benesh quantizes time and Laban quantizes space. The figure is initially standing facing downstage left on a bent left leg, the rigth leg extended in front. The right leg is swung to the side and then brought in rapidly as the figure rise on point, and then pirouettes.