Digital logic and the Turing machine are the bases of the computer revolution which began in the mid-twentieth century and is still very much in progress. We have produced ever more powerful hardware and software to do syntactical processing operating within fixed rules and fixed environments. We don’t appear, however, to be close to providing a machine which has the power to 'think' beyond these limitations. Nor does the human brain appear to operate like a Turing machine. Is there a logic, a grammar, that can be applied to something like the human brain? My argument will be that there is, and that it is not a digital logic, which is a particular outcome of a more fundamental logic, but one to which uncertainty is intrinsic.

From evidence from systems organised at many different scales, it will be proposed that a logical structure can be developed which encompasses the general class of self-organising systems, and which is based on a universal rewrite system and the principle of nilpotency or squaring to zero, in which the system and environment have (in mathematical terms) a space-time variation, defined by the phase, which preserves a dualistic mirror-image relationship. Ways of achieving this relationship in physical terms include quantum holography and the holographic principle. Thermodynamically, it seems to connect with systems organised as quantum Carnot engines.

The programme of the Cybernetics Machine Group of the British Computer Society is to develop the theory and applications relating to this process. The principal investigators are Peter Rowlands, Peter Marcer, Bernard Diaz, Vanessa Hill, and Walter Schempp, a unique combination of experts in physics, computer science, biology and mathematics. A physical realisation appears to be already available in the form of magnetic resonance imaging, where the systematic theorising of Walter Schempp is leading to advanced practical results.