(where formula_40 is the flat space metric, and the above equation expresses that formula_41, when written in terms of the basis formula_36, is locally flat). (Formulating general relativity with triads instead of metrics was not new.) The densitized triads are not unique, and in fact one can perform a local in space rotation with respect to the internal indices formula_14. The canonically conjugate variable is related to the extrinsic curvature by formula_44. But problems similar to using the metric formulation arise when one tries to quantize the theory. Ashtekar's new insight was to introduce a new configuration variable,