Key deficiency of the fusion and annihilation gates is that, when implemented in media other than excitable spatially-extended systems, they do not preserve physical quantity of signals, e.g. when two signals merge the output signal will have a double mass of a signal input signal. This deficiency is overcome in the conservative logic, proposed by Fredkin and Toffoli in 1978 . The logical value are represented by solid elastic bodies, aka billiard balls, which deflect when made to collide with one another (figure ). Intact output trajectories of the balls represent and-not function, output trajectories of deflected balls represent and function. The gates based on elastic collision led to development of a reversible (both logically and physically) gate: Fredkin and Toffoli gates, which are the key elements of low-power computing circuits , and amongst the key components of quantum and optical computing circuits.