Semiotics and control systems Toward a non-classical model of communication By Robert de Beaugrande

Somehow the one electron seems to ‘know’ instantly what happens to the other; but that would require information to be transferred faster than the speed of light, the velocity physics insists is a true ‘constant’ and not to be exceeded.⁴ So two possibilities remain, both offensive to classical reality: either your observation itself has transferred the information; or the two events (spin-changes or whatever) are in some non-classical sense ‘the same one’.⁵

Hawkes (1977: 126) suggests that ‘in Peirce’s view, logic exists independently of both reasoning and fact’. But did not the formalists rather suppose that logic was the ultimate guarantee of the possibility of reasoning and fact? Only in this way could logic be expected to obviate the regress to reality. The Einsteinian belief in the self-sufficient existence of an external world matches up to the formalist belief in the self-sufficient existence of a logical world , both worlds being ultimately classical. Now, quantum reality — pushing Einstein’s theories in a direction he never accepted — shows that neither belief can be sustained, and provides a forceful impetus for non-classical models.

The ‘sum over histories’ model of Richard Feynman (1958) assumes that a single quon takes all possible paths, none of them any ‘better’ than the rest. However, interference comes to the rescue to keep the quon from roaming all over the universe. Every ‘wild path’, such as an arabesque of fantastic loopings, has a parallel path with exactly equal amplitude and opposite phase, and the two paths totally cancel each other. Only the paths of ‘least action” those near the classical trajectory of a straight line, are close enough in phase to produce additive amplitudes and survive. In this model, interference is precisely what saves the quon from utter randomness. So saying that reality is, or is generated by, an interference pattern makes good sense for the Feynman model and suspends the confrontation between the one-world and many-world models. We obtain not ‘the best of all possible worlds” nor even ‘the one most probable world” but a pattern of indissoluble interference among possible worlds. If we could ever cancel an but one (near-infinite certainty), reality could not be under­stood (near-infinite uncertainty). .

Such considerations indicate that we might do better to interpret a ‘dimension’ not as some measurability for ‘size’, ‘shape’, ‘extent’, ‘duration’, and the like, but as a mode of connectedness. A thing has a dimension if we can plot for it a. trajectory between two or more coordinate values. This interpretation places the focus not on the fixity of dimensions, as in classical science, but on their alterity, the indispensable potential of a value to be other than what may be determined on any one occasion - more fitting for quantum science.

As Nick Herbert (1985: 249) remarks, ‘one of the greatest scientific achievements imaginable would be the discovery of an explicit relationship between the waveform alphabets of quantum theory and certain human states of consciousness’.