Equilibrium, Resonance, Stability, Rep and Reproduction
Although Generation and Reproduction are part of the Lp canon both in VSM Theory and CT/IA there is no explicit treatment of conditions for new concept formation: for CT to become a theory of Intercourse, as it were or VSM Theory to generate a new system one, although the variety requirement- its food- is well established.
From the stable concept Triple we find a general rule that any two concepts can make a third. It is a resonance structure like benzene or the fullerenes. The components are in a dynamic equilibrium exchanging roles to maintain stability. Presumably this satisfies the potential for crossover and mutation. We need to clarify if single and double concepts can exist unsupported and their field properties. It may turn out to be trivial. Gordon's work was often generous in this respect.
A treatment of this with unified terminology and perhaps with appeals to Stewart's Tern theory, for example, to establish a rigorous VSM hierarchy and leave Lp unmodified but applied to Pask's Rep generatively.
The primary need would be to recognise VSM as representable first with the shorthand system/metasystem, then to recognise that any non-trivial VSM must have at least two Systems One- thus rendering VSM tractable to stable triple analysis (collapsing it into a 4-3-2 structure might also work). Stewart's levels might be applied as Relaxation times but it introduces meta linguistic levels into Pask's concept triples which Pask scholars might resist. An insistence on the inclusion of M-Individuals may actually decide the question. They would stand for the Physics (of the Tern) and subsequent interpretation as bandwidth (Secondary Domain) that supplies a filter (Tertiary Domain) for meaningful concepts. Incidentally this provides the opportunity to use von Foerster SO in the consideration of unused bandwidth. Comments please. More when I have it. Time to consider how Wienerian SO- self referential coupling- might be applied here. Thus a coherent Story of Generation may emerge. This may satisfy the cosmological requirement implicit in the epistemological constraint of "Understanding". But perhaps only in the sense of void and pleroma.
The present conventional requirement for the emergence of Higgs Bosons from (inflationary) virtual photons may be redundant when a hard (but elastic) carapace can be easily accounted for by a repulsive force. A re-examination of photonics from the (Second Order) cybernetic perspective is implied. A "box" full of photons with light (not heavy) and light (electromagnetically) reflecting walls is attracted to the source of a gravitational field. The box may be static, not moving in some co-ordinate
system or context. The photon as product of wave might be very helpful here. The implication of Gordon's Concept Triples interpreted as (Super)Strings may also be considered wherein the "Trouser Diagram" can account for fusion and fission of strings and their products. A further interpretation of Rep might provide a basis for the integration via Radical Constructivism with Autopoiesis and Metasystem Transition Theory might be facilitated but not for the faint hearted!
A Note on Rep
Rep was a key early operator in Lp. It accounted for invariance and stability. To say a table reproduced itself to be stable was remarkable. A most helpful remark from Mike Elstob about Gordon's work during a discussion of stability, dynamic equilibrium and the steady state. Later the application of Rep to memory seemed trivial. Rep(Description), Rep(Procedure) were all discussed. One fairly startling series of Rep produced a kind of cosmic zoom:
The full canon went something like:
- Rep(Planet)=Solar System
- Rep(Solar System)=Universe
We might tentatively introduce some further Lp notation here by saying strictly it is only the interpretation of the concept that produces the description etc.
Thus Interp(Rep(Con(T)))= D(T) where D is description.
Since Interp implies Rep in addition to compilation and interpretation the Rep may be dropped. So might a typical notation checking session with Gordon be conducted. In his later work his interest in Rep waned in favour of Prod. Simply Reproductive mental operations were not seen as sufficiently novel. The Myth of Invariance and the myth of stability combining make Rep's reputation less
respectable. For those of us who always knew stability or persistence to be a dynamic process the difficulties still require consideration.
Now again, strictly T is a topic in conversational domain of Z participants so we may write
or even in some circumstances
The major concern was the correct placement of sub and superscripts and attempting clear understanding of the means of subscripting the topic or concept, under interpretation or any T and subscripting the operator
The Interpretation of the Description yielding a Procedure or public action implies a hierarchy of thought which, again, might be simplified because Interp(ConZT) may imply ProcZ(T). Thence we come to the Ap operator wherein the interpretation in an M-Individual actually occurred after the Reps implied by Con (none) D (one) Proc (two). Other Pask Scholars please comment!
Some time was taken in correctly subscripting the expression Interp(Proc(T)) or even Interp(Prog(T)) with one subscript to distinguish serial processing. A pair of subscripts for parallel and a triple for true field concurrent processing. Always with a z as an index for a particular participant and a T to denote a pruning under a particular concept or topic.
This we must write, for a truly concurrent thought process:
There is some concern about his use of Con. Clearly a concept to start with. But with a few Reps deleted or, perhaps, more precisely condensed as in the primary arithmetic initials of Laws of Form we have ConZ(T) meaning perhaps the informational transfer of the concept or topic T by means of the Con operator. Thus the useful distinctions of conversation and conceptualisation were examined and considered. More strictly one might add: for application with Ap to an appropriate M-Individual. Which is what happens when something is done.
For information transfer to occur (across some interface, an M-Individual incarnation(?) itself often subject to subscripting) a Petri-like condition must be met. This established synchrony between a pair of participants. The Cognitive Reflector of Conversation Theory requires an act to be performed in a shared medium wherein the Petri-like transfer can occur. This make the private concept public and potentially agreeable between the pair of participants.
And so we have Ap(Con(T)) which may also be expressed
Ap(Proc(Rep(T))) = Ap(Proc(Con(T))) = Ap(Rep(Con(T))) in Z, suitably inscribed with i, j, k subscripting the P-individual herein implied and in a suitably subscripted M-Individual. "=" here means is notationally identical or equivalent to. This becomes complicated when two topics say TA and TB in two minds are exchanged.
In later work ==> was used to mean "produces" and "incidentally reproduce".
Revelling in process/product complementarity Pask refers to process/product pair
So Ap actually produced the result. Con* was introduced as a concept operator operating on other concepts. Since concepts contain concepts the deficiency made up is not immediately apparent. <Con*, Con> become complementary product/process pairs.
This allows (shorn of a potentially considerable number of subscripts, up to three for each operator or term)
Ap(Con*Z(<ConZ(T), DZ(T)>))=<ConZ(T), DZ(T)> as a legal expression. Operations of this kind are routine in Laws of Form. It might be seen as an identity statement.
All concepts are generalisations and the value of a conversation is an analogy. Further notes in due course may explicate this and the residual parity that produces forces acting between concepts.
So does Rep support crossover and mutation? It could, indeed, it must to account for production and innovation if mutation is seen as a unique difference or distinction. Pask developed his Calculus (Interaction Calculus- IC?) to make any mutation explicit rather than implicit as, perhaps, with the early days of Rep. Does it pass the per Bak test? Bak claims Holland's Genetic Algorithm fails. Can IC generate a Power Law distribution? Since coin-tossing run-lengths can I would say concepts combined with spin can. A formal proof might be of interest.