Pask's Protolanguge, Dynamic Lp, the Protologic

The formal language of Conversation Theory and Interactions of Actors Theory

Introduction
A conversation produces concepts when meaningful transfer of information occurs between participants. These participants may be any individual giving rise to a persisting force of attraction or repulsion in any medium at any scale where forces act down to and beyond superstring. Dynamic Lp concerns learning as an act of self-organisation and outcomes that are the products of processes. Lp is a model of process and evolution as much as anything else.

It is an extraordinary achievement by the late Professor Gordon Pask PhD, ScD, DSc and Wiener Medal holder. Application ranges from his equilibrium of Imperative Forces producing Permissive Application of thought (or the ideal of freedom of choice) to the Borromean triple model of a stable concept and, indeed, now we realise, a distinctly cybernetic model of stable non-void space or continuity, itself. Pask sometimes spoke of his work as experimental epistemology.
Some primitive operators:
T Name of a Concept or Topic
Con Concept or Conversation process operator
D Description
AP Apply: Permissive serial, parallel or concurrent execution
IM Apply: Imperative serial, parallel or concurrent execution
z An index for participants in one or many brains.
A coversational domain, entailment or web.
A graph of Relations or derivations.
i, j, k Indices for Concepts or Topics. See also the note below on participants.
=> Means produces

For example consider:

p where pz : IM(Conz(T))=> AP(Conp(T))

This states there exists a participant p which is a subset of participants z such that the Imperative application of concept T in z can produce the permissive application of a concept T in participant p

Underlined words are axioms from Interactions of Actors (IA) Theory

Conservation of both Imperative and Permissive Meaningful Information Transfer:
Consider clockwise and anticlockwise moments of forces about a point of calm or equilibrium
Three Cases

  1. Serial:
    IM(Conz(iTjk1)) + AP(Conz(iTjk2)) => IM(Conz(iTjk3)) + AP(Conz(iTjk4)
    k1 = k3, k2 = k4

    This serial case generates time. An inplace change. A thinking experience or "change of mind", in this case irreversible

  2. Parallel:
    IM(Conz(iTj1k1)) + AP(Conz(iTj1k2)) => IM(Conz(iTj2k3)) + AP(Conz(iTj2k4)
    in parallel case an out of place change, possibly instantaneous. A transfer of information or restricted act of learning possibly within a single medium or brain.

  3. Concurrent:
    IM(Conz(iTj1k1)) + AP(Conz(i2Tj2k2)) => IM(Conp(i3Tj3k3)) + AP(Conp(i4Tj4k4)
    The General concurrent out of place case. An act of learning between a pair of distinct participants.

Minimum condition for Permissive Application is when there is an equilibrium of Imperative forces

IM(Conz(iTjk1)) - IM(Conz(iTjk2) => AP(Conp(iTjk))

Subscripts i, j, k, ∈ z, z∈ E3 i= i1, i2, i3, ...in; j =j1, j2, j3, ...jn; k= k1, k2, k3, ...kn; where concepts in the Entailment or concept map of Participant z. A bounded range in i, j, k, defines a participant which can subsequently defined A, B, C etc to reduced the complexity of subscripting. Depending on the complexity of the case under consideration indexes can be re-introduced assigned to a specific participant or concept in a participant domain.
Thus we may write the condition for Permissive Ap:
IM(Con(TB)) - IM(Con(TC) => AP(Con(TA))
The indexing schemes are generally liberal, like the definition of a participant. The requirement for three indexes in the concurrent case is strict.

While IM(Conz(iTjk1)) - IM(Conz(iTjk2) => null where "-" means difference.
then IM(Conz(iTjk1)) - IM(Conz(iTjk2) => AP(Conp(iTjk3)) <=◊=>Begin
where <=◊=> means is analagous to.

and when (|IM(Conz(iTjk1)) - IM(Conz(iTjk2)| > 0) <=◊=>End

Difference: Dz(i1Tj1k1) - Dz(i2Tj2k2) => Dz(i3Tj3k3) Unlike concepts attract

Similiarity: Dz(i1Tj1k1) - Dz(i2Tj2k2) => void Like concepts repel

Respectable: Dz(i1Tj1k1) => Dz-1(i1Tj1k1) participant is hot enough to be perceived by observer participant z-1.

Responsible: Dz(i1Tj1k1) + Dz(i1Tj1k2)=> Dz-1(i1Tj1k3) participant z is excited by Dz(i1Tj1k2) to render observable.

Perspective: Dz(i1Tj1k1) <> Dz(i1Tj1k2) where "<>" means not equal to. The transformation of k1 to k2 might be, for example, the outcome of an affine transformation.

Context: Dz(iTjk) <> Dz(lTmn) The context defined by the index triple in z of a concept determines its meaning.

Agreement: Dz(iTjk) => Dz-1(lTmn)

Agreement-to-Disagree: Dz(iTjk) <> Dz-1(lTmn)

Generation: Dz(iTjk) + Dz-1(lTmn) > Dz-1(lTmn)
Faith (the duration of an Interaction or experiment), Amity (the availability for Interaction), Purpose, Unity that is not uniformity, Eternal Interaction, Adaption, Evolution, Kinetic and Kinematic, Void and Not-void still need consistent treatment. A time subscript might be introduced, as Pask did in his last paper, for persistence and denoting begins and ends in applied concepts. This might make some definitions more straight forward but it would be more in the spirit of his enquiry to avoid time. In Lp time appears as an arbitrary master reference serialisation process, restricted to unreal non-concurrence, but assumed, perhaps unprovably, to be uniform.
A NOTE On Participants:
A conversational participant has two parts: The P-Individual, a collection of strains or concepts in a medium, the M-Individual, a brain or a star, which are closed, toroidal, self-referential, or loosely "circular", dynamically interacting processes packed recursively in stable Borromean triples "like wires in multi-core cable" and may be called entailment structures or meshes of topics or concepts, thoughts or Dawkins-like memes. Unlike the finite, bounded by begins and ends, interactions of Conversations, Actors which support P and M-individuals interact eternally with no begins and ends. Pask observed causality can only be shown where processes have begins and ends. In eternal Interaction causality cannot be demonstrated. A concept is the outcome of the self-organising process.

A NOTE On IM and AP:
When a concept(T) is executed an unfoldment occurs starting with the nearest neighbour entailed concepts. This is bounded by the topics or concepts in a participant but the foci from which to unfold and the truncation and selection is indeterminate (from Pask's unpublished Interactions of Actors: Theory and some Applications April 1993). This may be seen as a statement of the difficulty with Dynamical Methods in General.

Further Notes: Concerning Pask's Epistemology and the Atomic "Hypothesis"

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