From BRIAN CLEMENT
Jim Lesurf’s article ‘Chaos on the circuit board’ is actually an explanation
of the more complex form of chaos reported by William Bown in the same issue
(Science, 30 June). Negative resistance can be achieved in electronic gyrator
circuits configured so that the combination of a capacitance with a number
of resistors behaves as if it were an inductor at a specific audio frequency.
This is a question of phase relationships.
Gyrators are frequency-selective, and a system of negative resistance
filters would clearly offer multiple paths of least resistance. The transformation
of a square onto eight segments could be achieved by devising a system of
mutually orthogonal pathways. The new form of chaos described would then
become entirely predictable. The necessary manipulations can be derived
by inspection of the usual topological representations of the projective
plane, the torus and the Klein bottle as orthogonal vectors arranged in
the form of a square. These are also phase relationships. If superconductivity
is taken to be the ultimate expression of negative resistance, then so-called
chaos is the dissipation of energy in phase transitions taking place along
determinate pathways. This would constitute progressive entropy reduction
in a dynamic flow system equivalent to the generation of information.
Brian Clement Crickhowell Powys
