While working with clients in the last years of his life, Gordon Pask produced an axiomatic scheme for his Interactions of Actors Theory, less well-known than his Conversation Theory. "Interactions of Actors (IA), Theory and Some Applications", as the manuscript is entitled, is essentially a concurrent spin calculus applied to the living environment with strict topological constraints. One of the most notable associates of Gordon Pask, Gerard de Zeeuw, was a key contributor to the development of Interactions of Actors theory.
Interactions of Actors Theory (IA) is a process theory. As a means to describe the interdisciplinary nature of his work, Pask would make analogies to physical theories in the classic positivist enterprises of the social sciences. Pask sought to apply the axiomatic properties of agreement or epistemological dependence to produce a "sharp-valued" social science with precision comparable to the results of the hard sciences. It was out of this inclination that he would develop his Interactions of Actors Theory. Pask's concepts produce relations in all media and he regarded IA as a process theory. In his Complementarity Principle he stated "Processes produce products and all products (finite, bounded coherences) are produced by processes".
Most importantly Pask also had his Exclusion Principle. He proved that no two concepts or products could be the same because of their different histories. He called this the "No Doppelgangers" clause or edict. Later he reflected "Time is incommensurable for Actors". He saw these properties as necessary to produce differentiation and innovation or new coherences in physical nature and, indeed, minds.
In 1995 Pask stated what he called his Last Theorem: "Like concepts repel and unlike concepts attract". For ease of application Pask stated the differences and similarities of descriptions (the products of processes) were context and perspective dependent. In the last three years of his life Pask presented models based on Knot theory knots which described minimal persisting concepts. He interpreted these as acting as computing elements which exert repulsive forces in order to interact and persist in filling the space. The knots, links and braids of his entailment mesh models of concepts, which could include tangle-like processes seeking "tail-eating" closure, Pask called "tapestries".
His analysis proceeded with like seeming concepts repelling or unfolding but after a sufficient duration of interaction (he called this duration "faith") a pair of similar or like-seeming concepts will always produce a difference and thus an attraction. Amity (availability for interaction), respectability (observability), responsibility (able to respond to stimulus), unity (not uniformity) were necessary properties to produce agreement (or dependence) and agreement-to-disagree (or relative independence) when Actors interact. Concepts could be applied imperatively or permissively when a Petri (see Petri net) condition for synchronous transfer of meaningful information occurred. Extending his physical analogy Pask associated the interactions of thought generation with radiation : "operations generating thoughts and penetrating conceptual boundaries within participants, excite the concepts bounded as oscillators, which, in ridding themselves of this surplus excitation, produce radiation"
In sum, IA supports the earlier kinematic Conversation Theory work where minimally two concurrent concepts were required to produce a non-trivial third. One distinction separated the similarity and difference of any pair in the minimum triple. However, his formal methods denied the competence of mathematics or digital serial and parallel processes to produce applicable descriptions because of their innate pathologies in locating the infinitesimals of dynamic equilibria (Stafford Beer's "Point of Calm"). He dismissed the digital computer as a kind of kinematic "magic lantern". He saw mechanical models as the future for the concurrent kinetic computers required to describe natural processes. He believed that this implied the need to extend quantum computing to emulate true field concurrency rather than the current von Neumann architecture.
Reviewing IA he said:
Interaction of actors has no specific beginning or end. It goes on forever. Since it does so it has very peculiar properties. Whereas a conversation is mapped (due to a possibility of obtaining a vague kinematic, perhaps picture-frame image, of it, onto Newtonian time, precisely because it has a beginning and end), an interaction, in general, cannot be treated in this manner. Kinematics are inadequate to deal with life: we need kinetics. Even so as in the minimal case of a strict conversation we cannot construct the truth value, metaphor or analogy of A and B. The A, B differences are generalizations about a coalescence of concepts on the part of A and B; their commonality and coherence is the similarity. The difference (reiterated) is the differentiation of A and B (their agreements to disagree, their incoherences). Truth value in this case meaning the coherence between all of the interacting actors.
He added:
It is essential to postulate vectorial times (where components of the vectors are incommensurate) and furthermore times which interact with each other in the manner of Louis Kaufmann's knots and tangles.
In experimental Epistemology Pask, the "philosopher mechanic", produced a tool kit to analyze the basis for knowledge and criticize the teaching and application of knowledge from all fields: the law, social and system sciences to mathematics, physics and biology. In establishing the vacuity of invariance Pask was challenged with the invariance of atomic number. "Ah", he said "the atomic hypothesis". He rejected this instead preferring the infinite nature of the productions of waves.
Pask held that concurrence is a necessary condition for modeling brain functions and he remarked IA was meant to stand AI, Artificial Intelligence, on its head. Pask believed it was the job of cybernetics to compare and contrast. His IA theory showed how to do this. Heinz von Foerster called him a genius, "Mr. Cybernetics", the "cybernetician's cybernetician".
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