Wiener Medalist, worked all his life with charm and
great care to bring Cybernetics into the
mainstream. Dr Bernard Scott reviews the early
work leading to the kinematic Conversation
Theory. Scott was instrumental in the seventies in developing CASTE and
Thoughsticker at System Research Ltd, Pask's consulting company which he described as an Epistemological Laboratory.
Pangaro's PhD thesis
work with Thoughtsticker and Lp, the protologic put force into entailment meshes as a distinction mechanism.
A principle concern was the nature of analogies in concept entailment meshes (or topic maps). Analogies established dependence between participants and could indicate difference, distinction, contradiction, ambiguity or innovation depending on the perspective of the participants. In research discussion at the time, the late 1970s, the repulsive force of the carapace
distinguishing concepts, the vacuity of master clocks in concurrent systems (his approach to holism) and the associated relativistic constraints were continuing if perplexing themes.
Interactions of Actors Theory
In the late eighties Pask achieved rigour by taking the dual
of the static "stick and ball" Conversation Theory producing
the kinetic "Interactions of Actors Theory". The consequent attractions and
link and evolve into the minds containing the
persisting closed loops which we call concepts. In effect this is a generalisation
of Cannon homeostasis.
Heinz von Foerster called Pask "Mister Cybernetics,
the Cybernetician's Cybernetician". But Pask preferred
the term Cybernetist to evoke the physical nature
of his IA Theory. "Interactions of Actors (IA), Theory and Some Applications" is essentially a concurrent spin calculus applied to the living environment.
The year before he died Gordon was awarded his
third Doctorate, an ScD, one of very few given by
Downing College Cambridge from where he took
his second higher degree in 1949.
He famously regarded the Spencer-Brown
distinction as a repulsive force, still not accepted by many
cyberneticians or Spencer-Brown himself. Time and more thought will tell. Gordon's rejection of master clocks to comply with a Relativistic Geometry and the avoidance of serial (Goedel/Turing) pathology with field concurrence, made his approach very strict. He said simply and very profoundly "Time is incommensurable for Actors". He would say "There are no doppelgangers". Actors will have unique acceleration histories making their clocks non-uniform. Not everyone appreciated this. Levels and their associated master clocked vectors of relaxation times were so very useful to many of us interested in linguistic systems theory, but this was naive, merely classical, to Pask.
He argued that to be distinct a repulsive force must be exerted at a boundary otherwise a Hilbertian "mark on paper", a concept in a brain, or a brick becomes a smear. If a diffusion process at a boundary is dominant an entity cannot persist or be described. His dynamic Lp, the concurrent calculus, still has some surprises in store for us. The productions, as he would call them, of these deep assumptions have yet to be fully established. They introduced force into cybernetics at a fundamental level.
Concepts are force exerting, persisting,
closed, Brunnian in threes at least, braids
recursively packed in toroidal processes ("like multicore telephone cable" or ""onion skins") in
any medium, solid, liquid,
gas, plasma or, indeed, brains. Their spins exert a residual parity within a coherence.
Epistemologically at least two concurrently
existing concepts are required to make a
There's no such thing as input or output.
There are only fields exerting forces. Tubes and
wires etc. act as wave guides.
Every process produces a product. Every
product is produced by a process. Gordon called this "Product/Process Complementarity". Compare with Bohr's Complementarity principle.The illogicality of the co-existence of waves and particles was rejected by Einstein, Schroedinger and others e.g. by Fritz London in 1939 (Phillip Anderson, Nature vol 437 29 Sept 2005 p.625). Heisenberg's Uncertainty Principle produced the Copenhagen interpretation and became the new orthodoxy. Today it is attacked for putting physics in the dark ages for seventy years by Carver Mead who, like Pask, favours Wave Mechanics. Pask is saying, simply, waves produce particles through interactions resolving the difficulty with Bohr. Pask "products" are solitons with beginnings and ends. Anderson remarks that slits are not rigid in interference experiments but superpositions of "unimaginably large numbers of different quantum states", an entangled coherence is produced with the slit which divides into a decoherent diffraction pattern.
Pask won a
prize for his Complementarity Principle from Old Dominion
University-O.D.U. This captures Gabor's uncertainty
Δf • Δt ≈ 1
An eternal actor of frequency f+Δf will produce a Conversation of duration Δt and the Actor's frequency will be reduced to f.
This identity establishes Actor and Conversation Theory as a quantum/wave theory with Conversations reducing the curvature of space and reducing the temperature of the Universe as frequencies are divided down in an expanding Universe. Combined with the incommensurability of time for any pair of coherent Actors and their asynchronous interaction we have General Relativistic compliance. Quite a feat. A conversation between Human participants will be packed with many such events. A conversation between superstrings or even smaller events that are real and exert forces might contain one such event. Asynchronous coherent distinction producing closure is all that is required and this is applicable to all forces and interactions of any size.
Processes produce distinctions which are their
Causality: proof of causality depends on
begins and ends. The converse is also true:
causality cannot be demonstrated when
interactions are circular or eternal. (Collected by
Adams who served on several of Pask's companies' boards.)
Concepts are covered in a repulsive shell or
carapace. (First heard in the seventies.)
Concepts persist minimally as stable dynamic resonating
triples linked in the Borromean manner. They
exist in three dimensions, at least. (First heard
in the nineties.)
Space is punctuated with voids and not-voids
yielding a torus of countably infinite
Continuity around a three dimensional void is denoted by the
Borromean link. ("Avoid a void" Spike Hawkins' shortest poem and discussed with the poet at a memorable Athenaeum Dinner)
Pask's Last Theorem (PLT):"Like concepts
repel unlike concepts attract" ("I have my last
Theorem", said Gordon."It's in a drawer." As far
as is know it never was written down.) He insisted it applied to all forces electromagnetic, gravitational, strong and weak. This can be seen as the superposition principle applied to force.
Osborne and Pope have proposed "like spins repel" and "unlike spins attract" in their angular momentum synthesis of gravitational and electromagnetic force.
This implies the minimally 3-braided trajectories of a concept repel when they touch and attract when they link. This is a general theory of force produced by linking and touchings of the force normal to the braided trajectories of closure. This diagram from the Interactions of Actors Theory manuscript shows the forces of repulsion which when linked produce attraction when a knot forms with "tail-eating" closure. A 3-braid when closed produces the Borromean Link. Ideas about coherence at these surfaces are sought.
Pask asserted these in one
of his seminars to Norsk Hydro in 1995:
The explanations are by
Nick Green who worked with Pask in his last
Context: may be the same or different
for Interacting Actors.
Perspective: Is always different for
each actor in the same context. For this reason
we have the famous no Doppelgangers clause."There
are no Doppelgangers". No two minds,
P-individuals or states in bodies are the
Respectability: An Actor is
respectable when it can be observed.
Responsibility: An Actor may require
stimulation to become respectable, in which case
it is responsible.
Similarity: By PLT produces repulsion
and unfoldment of concepts.
Difference: By PLT produces attraction
as a feedback which may produce closure and coherence. The beats produced may account for 1/f noise and the lifetime or viability of the coherence
Amity: Availability for Interaction or
we can speak of love when appropriate.
Faith: Is required while an
interaction persists until it ends or is
interrupted or until a product is produced.
Agreement: Is the result of meaningful
information transfer or learning. It produces a
repulsion and a new coherence. In agreement-to-disagree an
attraction is maintained after meaningful
information transfer. (Wiener considered serial
coupling is repulsive and parallel
Unity which is not uniformity: is a
property of purpose. More simply a
similarity or description shared by a group of
Actors interpretable as a shared goal.
Adaptivity: an elastic property
tending to restore equilibrium comparable with
Newton's third Law and Le Chatelier's Principle.
Generation: aggregation through
attraction. Evolution: aggregative
differences resulting from learning or transfer
of meaningful information.
The starts and finishes
characteristic of Conversation Theory, supported
by eternal interaction, are equivalent to
kinetic interaction punctuated by
kinematic events or products, with
begins and ends.
Void and not-void: The
structure of Euclidian space.
A participant Actor produces forces by
Permissive or Imperative
Conservation of Ap and
parity. The conventional conservation laws
operate. Outputs become inputs with closure. A
triple shows residual clockwise or anti-clockwise
Concurrent processes require at least
three indexes to distinguish. Serial requires one
index and parallel two indexes.
For serial processes we add variety to
resolve undecidability or render controllable.
In the concurrent case we acquire a concept to
resolve ambiguity or conflict by
innovation. This is the difference that
separates a pair of analogous
"For every force there is an orthogonal force" which may produce closure.
"Meaning is emotion": the production of an imperative force from a permissive force
"No flag waving": recently interpreted as let the user apply cybernetics to the domain of choice but also dissmisive of appeals to irrational group loyalty.
"Compare and contrast": the means by which Cybernetics may be conducted.
"No ether is necessary only an orthogonal force."
"They will come to know" said somewhat archly of colleagues struggling with his "new" cybernetics.
On system boundaries, autopoiesis and organisational closure: "The boundaries of the system, far from being pre-fabricated, are created by the activities of the system. This is the prescient notion of autopoiesis (as developed by Maturana and Varela), or organisational closure, as we called it at Brunel University and in my own laboratory, System Research."
Three paraphrased remarks from
Dr Larry Richards who was then Founding Chair of Engineering Management at O.D.U. under whose auspices Product/Process Complementarity was produced.
Concept: an organizationally-closed process continuously generating a "static" product--a description (the carapace).
Organization is to structure as process is to product--complementary pairs. Organization/process generates structure/product and structure/product supports organization/process.
(Further comment on the Maturana/Varella approach.)
With respect to the metaphor of "pillars": Architectural pillars are not "static", but participants in a dynamic equilibrium; and the architecture can, of course, change significantly, as when subjected to an earthquake.
This, above, from the late eighties may be seen as a precursor to Pask's use of structural modelling. He used the Fuller-Snelson prismatic tensegrity as a model of the forces exerted in the Borromean Triple. Surprsingly this shows three repulsive forces under dynamic equilibrium will adopt a sixty degree architecture. The proof, which is concurrent, requires three equal rods joined at the ends by string or elastic. The three repulsions of the rods are balanced by the nine attractions of the strings. There are two enantiomporhic forms with left and right twist. This is the form of a minimal object: three spins (or concepts), exerting a residual spin parity, clockwise or anti-clockwise resonating to fill space persistently. The differences are attractive according to the Last Theorem. The figure shows a Venn diagram model of the coherence of three concepts (1) interpreted as the three repulsive forces, the rods and strings, of a minimal space filling form (2) and the associated Borromean spin diagram (3).
This may be extended to modelling entailment meshes of concepts as spin networks.
Unexpectedly in a simulation study P McGuinness,W Drenckhan and D Weaire "The optimal tap: three-dimensional nozzle
design" (J. Phys. D: Appl. Phys. 38 (2005) 3382–3386) showed that in spraying fluids a triangular nozzle design, rather than circular, produces smaller droplets. This sugests that the braiding form of (2) is indeed important in fluid structure.
More recent work suggests the axioms and properties may be produced by a strict analysis of coherence phenomena as Pask himself first suggested in the 1961 Namur Cybernetic Congress paper "The cybernetics of evolutionary processes and of self organizing systems". Here he remarks "The idea of Self Organization belongs to the present and imperfect search for coherence" (1.8.1). Coherence as a both a defining and dynamic process is a major theme in the IA manuscript.
Coherence generates persisting repulsive boundaries and transitory decoherence permits communication between domains. This can lead to coalescence but where repulsive distinctions persist, differentiation. This produces a general kinetic mechanism of evolutionary learning in all media. The repulsive distinction can be seen as thermostatically error-correcting, an attractive difference.
In 1972 Gordon wrote the entry for Cybernetics in Encyclopaedia Britannica. He discusses von Foerster's hand-eye paradigm and introduces analogy as productive of differences. Apart from its cogency it is fascinating to review in light of his later work.
Dr Ranulph Glanville and Dr Bernard Scott prepared a list of 259 of Pask's publications in part II of the Pask Memorial Edition of Kybernetes vol. 30 no. 7/8 2001 pp1031-1043
Heisenberg Uncertainty is written Δp • Δx ≥ h where p is momentum and x is a distance. For a photon of wavelength λ momentum = h/λ where h is Planck's constant. By definition fλ = c where f is frequency and c is the velocity of light. There is a full proof by MacLennan (Appendix A). However to distinguish a frequency of f we need a duration, t, of at least 1/f: we know Δt≥ 1/Δf. Thus we obtain Δf • Δt ≥ 1
D. Gabor, "Theory of Communication", J. Inst. Electr. Engineering, London, Vol. 93 (III), 1946, pp. 429-457