Powering is the self-multiplication of a number. Second powering, or squaring, is usually identified in geometry with the mensuration of areas. In synergetics second powering is associated with the number of external vertices of a (polyhedral) system.
Fuller gives simple formulae, involving the first four prime numbers, for calculating the number of such vertices, given the frequency or modular subdivision of the system, and the type of system (tetrahedral, icosahedral, etc.).
The rationale for this is bound up with Fuller's rejection of unreal objects such as continuous surfaces or solid volumes, which he sees as mere abstractions. He goes on to relate this principle to physics:
"The second and third power point aggregations identify the energy quanta of systems and their radiational growth or their gravitational contraction. They eliminate the dilemma in which physics failed to identify simultaneously the wave and the particle". (Synergetics 223.41)
Beyond this is the suggestion that synergetics facilitates conceptual modelling in four, five, or six dimensions (Synergetics 432.01).
© Paul Taylor 2001