Cumulative Coordination founded upon Dyadic and Triadic Relationships
(resent in order for it to appear here with the actual author included)
My apologies for taking so long to produce this supplement to my essay -- it has been tricky deciding on the best way to formulate these rather intricate concepts, the eventual outcome being to a considerable extent informed by the approaches of Barad and Yardley. In the essay itself I took biology as the foundation, with biosemiotics (the use of Peirce's sign theory in the context of biology) as an essential mechanism underlying the effectiveness of biological processes. I have since realised (a) that a number of Peirce's ideas are relevant in a wider context than biology, and (b) as discussed in Barad's work, processes involving patterns of change feature in biology in a different way to how they feature in physical systems generally. The argument that follows begins with a discussion of Peirce's dyadic and triadic relationships, the latter being a somewhat unusual kind of situation, which does however naturally manifest in certain situations such as with Jupiter's satellites. Whereas the kinds of order studied in physics can often be characterised purely in terms of dyadic relationships, in biology triadic relationships play an equally important part, giving rise to dynamic phenomena of a radically different character, with a complexity rendering conventional kinds of analysis problematic, though other approaches appear feasible. The phenomenon of language appears to be explicable in terms of the concepts proposed here, providing a dramatic illustration of the power of the type of organisation that will be discussed.
Peirce's sign theory invokes two kinds of relationships between systems, secondness and thirdness, the former involving two systems exerting a significant influence on each other, and the latter a more complex situation where a relationship exists between three systems but not between any of the pairs. The latter is exemplified by the case of Jupiter's three satellites Io, Europa and Ganymede, between whose orbital phases there exists the linear relationship:
[math]$\Phi \equiv \lambda_{Io} - 3 \times \lambda_{Eu} 2 \times \lambda_{Ga} = 180^\circ$[/math]
The stability of this relationship against other influences present, such as that of Jupiter's fourth major satellite, Callisto, implies that the order involved in the relationship will emerge spontaneously should the three-satellite system at some point find itself in a situation where it is approximately satisfied. On the other hand, a sufficiently large disturbance could lead to a situation involving large deviations from the relationship concerned. The situation envisaged here is one where relationships are being continually formed and dissolved, with alternating stability and instability, leading to the emergence of constructs that are progressively more resistant to instability, and effective in their ability to stabilise.
Triadic relationships enter naturally in biology, as for example when a third element defining a process links the current situation to some desired state. Elementary computations of this kind can be concatenated into highly complex but effective computations, in which connection note that regular electronic circuitry makes use of systems of this kind, transistors with their three leads providing triadic relationships whilst other circuit elements such as resistors involve simply dyadic relationships. The idea now is that learning has as its basis systems settling into such triadic relationships. Two conditions must be satisfied before this can happen, that the required constituents be available, and that the process associated with the triadic relationship should support stability of the outcome. This may be thought of as a process of trial and error, changes continually being made until some error is resolved. The first requirement involves in principle a meta-process that determines which systems are active at any given time. It is here that significance arises, given that particular aspects of a given situation are relevant for success in that situation. These metasystems are the equivalent of the semiotic scaffolding of the approach of Hoffmeyer.
Two other aspects relevant to the understanding of the intricacies of the situation being addressed are those of the role of signs, and Yardley's concept of oppositional dynamics, which is related to Barad's intra-action. The latter involves two entities X and Y that cooperate to generate some specific process. Such cooperation is a consequence of the error-correction process discussed, involving a situation where, as the consequence of previous acts of error correction no further error correction is needed in the given situation. Thus if X is fixed then under certain conditions its complement Y can be built up over over time through error correction. This in addition provides a mechanism for replication, since if Y is fixed a complement similar to X can also be built up over time. Language provides an instructive example, X being the processes involved in producing speech and Y processes involved in interpreting speech. Here language learners have to learn how to interpret the productions of others (creating Y from X), as well as how to produce speech that others can interpret (creating X from Y), the criteria in both cases being that of success in whatever additional process is involved on the side.
One function of signs, related to the above, involves their potential role as proxy. This can be accomplished with two systems x and X linked in the manner indicated, so that a system related to an entity X becomes reversibly linked with a system related to the corresponding sign. The utility of signs lies partly in the fact that they form a comparatively stable aspect of a given situation that may be adaptable to many different situations by acting in conjunction with systems adapting to the context (this is the concept of code duality. In other words, the same sign x may linked to different Xs in different situations, an example of a triadic relationship (involving X, x and a system related to the context). Human language can be seen as an advanced form of this process, enhanced by syntactic mechanisms sensitive to relevant aspects of speech. This is all about the existence of mechanisms able to generate specific actions, and the fact that specific systems work together, supporting each other.
Yardley's circles can provide a useful general picture to help understand the above. A circle can be envisaged as an object, with a structure that supports an activity. This activity can create or manipulate other circles in ways discussed in detail, including moving from a state of affairs more in accord with a single entity and one more in accord with a pair of entities. Such close relationships between two entities can form a basis for the emergence of oppositional dynamics.
The above is essentially a sketch, intended as a starting point to encourage more detailed research by others involving more resources than those available to the author, starting perhaps with detailed specification of specific situations, and appropriate models, thereby testing the validity of concepts such as oppositional dynamics. Previously, a student working with the author was able to test ideas of mathematician Nils Baas in this way. On the basis of similar developments it should be possible to critique in detail proposals of authors such as Barad and Yardley. Ultimately one would hope to establish connections with current physics, and end up establishing the picture proposed here as a definitive extension of current theories in physics, including demonstrating its applicability to situations where mind and meaning play roles denied to them in current physics.
