Interactions of actors theory
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In information theory, Interactions of actors theory is a theory developed by Gordon Pask and Gerard de Zeeuw. It is a generalisation of Pask's earlier
conversation theory Conversation theory is a cybernetic and dialectic framework that offers a scientific theory to explain how interactions lead to "construction of knowledge", or "knowing": wishing to preserve both the dynamic/kinetic quality, and the necessity for th ...
: The chief distinction being that conversation theory focuses on analysing the specific features that allow a conversation to emerge between two participants, whereas interaction of actor's theory focuses on the broader domain of conversation in which conversations may appear, disappear, and reappear over time.


Overview

Interactions of actors theory was developed late in Pask's career. It is reminiscent of Freud's
psychodynamics Psychodynamics, also known as psychodynamic psychology, in its broadest sense, is an approach to psychology that emphasizes systematic study of the psychological forces underlying human behavior, feelings, and emotions and how they might relate t ...
, Bateson's
panpsychism In the philosophy of mind, panpsychism () is the view that the mind or a mindlike aspect is a fundamental and ubiquitous feature of reality. It is also described as a theory that "the mind is a fundamental feature of the world which exists thro ...
(see "Mind and Nature: A Necessary Unity" 1980). Pask's nexus of analogy, dependence and mechanical spin produces the differences that are central to
cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson ma ...
. While working with clients in the last years of his life, Pask produced an axiomatic scheme for his interactions of actors theory, less well-known than his conversation theory. ''Interactions of Actors, 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 is a process theory.Gordon Pask (1993), ''Interactions of Actors, Theory and Some Applications'' As a means to describe the
interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several other fields like sociology, anthropology, psychology, ec ...
nature of his work, Pask would make analogies to physical theories in the classic positivist enterprises of the
social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of s ...
s. 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 A process theory is a system of ideas that explains how an entity changes and develops. Process theories are often contrasted with variance theories, that is, systems of ideas that explain the variance in a dependent variable based on one or more ...
. 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".Gordon Pask (1996). ''Heinz von Foerster's Self-Organisation, the Progenitor of Conversation and Interaction Theories''. 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 In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...
knot A knot is an intentional complication in cordage which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bends, loop knots, and splices: a ''hitch'' fastens a rope to another object; a ...
s which described minimal persisting concepts. He interpreted these as acting as computing elements which exert repulsive forces 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 A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that ...
) condition for synchronous transfer of meaningful information occurred. Extending his physical analogy Pask associated the interactions of thought generation with
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
: "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 Anthony Stafford Beer (25 September 1926 – 23 August 2002) was a British theorist, consultant and professor at the Manchester Business School. He is best known for his work in the fields of operational research and management cybernetics. ...
'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 Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
to emulate true field concurrency rather than the current
von Neumann architecture The von Neumann architecture — also known as the von Neumann model or Princeton architecture — is a computer architecture based on a 1945 description by John von Neumann, and by others, in the '' First Draft of a Report on the EDVAC''. T ...
. 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 In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...
, metaphor or
analogy Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject ...
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 Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epi ...
Pask, the "philosopher mechanic", produced a tool kit to analyse the basis for knowledge and criticise 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 The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of ever ...
. "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 modelling 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 Heinz von Foerster ( German spelling: Heinz von Förster; November 13, 1911 – October 2, 2002) was an Austrian American scientist combining physics and philosophy, and widely attributed as the originator of Second-order cybernetics. He was twice ...
called him a genius, "Mr. Cybernetics", the "cybernetician's cybernetician".


Hewitt's actor model

The Hewitt, Bishop and Steiger approach concerns sequential processing and inter-process communication in digital, serial, kinematic computers. It is a parallel or pseudo-concurrent theory as is the theory of concurrency. See Concurrency. In Pask's true field concurrent theory kinetic processes can interrupt (or, indeed, interact with) each other, simply reproducing or producing a new resultant force within a coherence (of concepts) but without buffering delays or priority.


No Doppelgangers

"There are no Doppelgangers" is a fundamental
theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...
,
edict An edict is a decree or announcement of a law, often associated with monarchism, but it can be under any official authority. Synonyms include "dictum" and "pronouncement". ''Edict'' derives from the Latin edictum. Notable edicts * Telepinu Proc ...
or
clause In language, a clause is a constituent that comprises a semantic predicand (expressed or not) and a semantic predicate. A typical clause consists of a subject and a syntactic predicate, the latter typically a verb phrase composed of a verb wit ...
of
cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson ma ...
due to Pask in support of his theories of learning and interaction in all media: conversation theory and interactions of actors theory. It accounts for physical differentiation and is Pask's exclusion principle. It states no two products of concurrent interaction can be the same because of their different dynamic contexts and perspectives. No Doppelgangers is necessary to account for the production by interaction and
intermodulation Intermodulation (IM) or intermodulation distortion (IMD) is the amplitude modulation of signals containing two or more different frequencies, caused by nonlinearities or time variance in a system. The intermodulation between frequency comp ...
(c.f. beats) of different, evolving, persisting and coherent forms. Two proofs are presented both due to Pask.


Duration proof

Consider a pair of moving, dynamic participants \textstyle A and \textstyle B producing an interaction \textstyle T. Their separation will vary during \textstyle T. The duration of \textstyle T observed from \textstyle A will be different from the duration of \textstyle T observed from \textstyle B. Let \textstyle T\textstyle s and \textstyle T\textstyle f be the start and finish times for the transfer of meaningful information, we can write: Thus ''A'' ≠ ''B'' Q.E.D. Pask remarked:
Conversation is defined as having a beginning and an end and time is vectorial. The components of the vector are commensurable (in duration). On the other hand actor interaction time is vectorial with components that are incommensurable. In the general case there is no well-defined beginning and interaction goes on indefinitely. As a result the time vector has incommensurable components. Both the quantity and quality differ.
No Doppelgangers applies in both the
conversation theory Conversation theory is a cybernetic and dialectic framework that offers a scientific theory to explain how interactions lead to "construction of knowledge", or "knowing": wishing to preserve both the dynamic/kinetic quality, and the necessity for th ...
's kinematic domain (bounded by beginnings and ends) where times are commensurable and in the eternal kinetic interactions of actors domain where times are incommensurable.


Reproduction proof

The second proof is more reminiscent of
R.D. Laing Ronald David Laing (7 October 1927 – 23 August 1989), usually cited as R. D. Laing, was a Scottish psychiatrist who wrote extensively on mental illnessin particular, the experience of psychosis. Laing's views on the causes and treatment of ...
: Your concept of your concept is not my concept of your concept—a reproduced concept is not the same as the original concept. Pask defined concepts as persisting, countably infinite, recursively packed spin processes (like many cored cable, or skins of an onion) in any medium (stars, liquids, gases, solids, machines and, of course, brains) that produce relations. Here we prove ''A''(''T'') ≠ ''B''(''T''). ''D'' means "description of" and reads A's concept of ''T'' produces A's description of ''T'', evoking
Dirac notation Distributed Research using Advanced Computing (DiRAC) is an integrated supercomputing facility used for research in particle physics, astronomy and cosmology in the United Kingdom. DiRAC makes use of multi-core processors and provides a variety o ...
(required for the production of the quanta of thought: the transfer of "set-theoretic tokens", as Pask puts it in 1996). : ''TA'' = ''A''(''T'') = , A's Concept of T, : ''TB'' = ''B''(''T'') = , B's Concept of T, or, in general : ''TZ'' = ''Z''(''T'') = , also, in general : AA = A(A) = , A's Concept of A, : AB = A(B) = , A's Concept of B. and vice versa, or, in general terms : ZZ = Z(Z) = , given that for all Z and all T, the concepts : TA = A(T) is not equal to TB = B(T) and that AA = A(A) is not equal to BA = B(A) and vice versa, hence, there are no Doppelgangers. Q.E.D.


A mechanical model

Pask attached a piece of string to a bar with three knots in it. Then he attached a piece of elastic to the bar with three knots in it. One observing actor, A, on the string would see the knotted intervals on the other actor as varying as the elastic was stretched and relaxed corresponding to the relative motion of B as seen from A. The knots correspond to the beginning of the experiment then the start and finish of the A/B interaction. Referring to the three intervals, where x, y, z, are the separation distances of the knots from the bar and each other, he noted x > y > z on the string for participant A does not imply x > z for participant B on the elastic. A change of separation between A and B producing
Doppler shift The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
s during interaction, recoil or the differences in relativistic
proper time In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval b ...
for A and B, would account for this for example. On occasion a second knotted string was tied to the bar representing
coordinate time In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. In many (but not all) coordinate systems, an event is specified by one time coordinate and three spatial ...
.


Further context

To set in further context Pask won a prize from
Old Dominion University Old Dominion University (Old Dominion or ODU) is a public research university in Norfolk, Virginia. It was established in 1930 as the Norfolk Division of the College of William & Mary and is now one of the largest universities in Virginia with ...
for his complementarity principle: "All processes produce products and all products are produced by processes". This can be written: Ap(ConZ(T)) => DZ (T) where => means produces and Ap means the "application of", D means "description of" and Z is the concept mesh or coherence of which T is part. This can also be written : Z (T)), DZ (T)>. Pask distinguishes Imperative (written &Ap or IM) from Permissive Application (written Ap)Pask (1993) para 188 where information is transferred in the
Petri net A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that ...
manner, the token appearing as a hole in a torus producing a
Klein bottle In topology, a branch of mathematics, the Klein bottle () is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a o ...
containing recursively packed concepts. Pask's "hard" or "repulsive"
carapace A carapace is a Dorsum (biology), dorsal (upper) section of the exoskeleton or shell in a number of animal groups, including arthropods, such as crustaceans and arachnids, as well as vertebrates, such as turtles and tortoises. In turtles and tor ...
was a condition he required for the persistence of concepts. He endorsed
Nicholas Rescher Nicholas Rescher (; ; born 15 July 1928) is a German-American philosopher, polymath, and author, who has been a professor of philosophy at the University of Pittsburgh since 1961. He is chairman of the Center for Philosophy of Science and was fo ...
's
coherence theory of truth Coherence theories of truth characterize truth as a property of whole systems of propositions that can be ascribed to individual propositions only derivatively according to their coherence with the whole. While modern coherence theorists hold that ...
approach where a set membership criterion of similarity also permitted differences amongst set or coherence members, but he insisted repulsive force was exerted at set and members' coherence boundaries. He said of G. Spencer Brown's ''
Laws of Form ''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems: * The "primary arithmetic" (described in C ...
'' that distinctions must exert repulsive forces. This is not yet accepted by Spencer Brown and others. Without a repulsion, or Newtonian reaction at the boundary, sets, their members or interacting participants would diffuse away forming a "smudge"; Hilbertian marks on paper would not be preserved. Pask, the mechanical philosopher, wanted to apply these ideas to bring a new kind of rigour to cybernetic models. Some followers of Pask emphasise his late work, done in the closing chapter of his life, which is neither as clear nor as grounded as the prior decades of research and machine- and theory-building. This tends to skew the impression gleaned by researchers as to Pask's contribution or even his lucidity.


References

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