Below we see Pask's analysis of an analogy. To Gordon
analogy "was everything".
- Dependence- a pre-condition for intelligible
communication of any kind
- Learning- the way a new concept is acquired
(by its relationship with an existing concept in a
- The achievement of a result in mathematics by
extending analogies from the axioms
- Did analogy have the same status of
Since invariance did not exist absolutely but only
within analogy and generalisations only exist because
they identify non-existent invariance, analogy might
claim precedence. Big Stuff indeed. Surely the assertion
of the primacy of analogy was itself a generalisation.
This is about the Theory of Theory: fundamental aspects
of Epistemology- the theory of knowledge and how we "come
to know" by acquiring Distinctions.
when there is a shared similarity between two topics,
ideas, thoughts, descriptions or concepts. There also
In the diagram above T1 is analogous to T2 where
T is a topic or concept in one or more
minds (or more generally M-Individuals: hardware, media,
Any T has derivations and to be
non-trivial its epistemology MUST imply concurrent
existence of more than one derivative concept. The
simplest interesting case is two and the two
distinguishing concurrent concepts for
T1 and T2 are shown.
The Analogy is shown by T4 as the topic or concept
shared by T1 and
The derivations T8 and
T9 are shown to add rigour.
T11 show the rigour necessary in
fully describing the derivations of the dependencies.
T4 must in
general(!) show the existence of a way of relating
T1 to T2 - a mapping and a necessary restriction on
the domain to render it finite, leading to the definition
of a distinction, are necessary properties of
T8 and T9
All these relations have beginnings and ends as topics
are executed in minds or M-individuals as their
associations bring them to consciousness. In Pask's later
Interaction of Actor Theory- see below- T1,
T2 and T4 became a stable
triple of concepts any two of which could make a third:
they were dynamic entities exerting forces on each other
(foretelling a new discipline of Neuromechanics).
"Like concepts repel and unlike
(Pask's Last Theorem)
Concepts contain concepts to any
This is a spin physics knot theory hybrid approach where the crossings of the orthogonal repulsions of braided trajectories produce attraction. It is a theory of force. See the recent paper Axioms from IA Theory.
Interactions of Actors (IA)
- No Begins and Ends: Interaction is
- Amity and Respect
- Unity that is not Uniformity
- Kinetics support Kinematics
- Imperative Action
- Agreement and Disagreement
- Organisational Closure
- Informational Openness
- Evolution or Adaptation
- Similarity and Difference
- Faith or Duration
- Permissive Action
Design Considerations from IA to realise AI
A primary distinction is made between serial or
parallel systems and Nature which is truly field
concurrent. Serial/parallel digital computing is seen as
kinematic and true field concurrent computing as
One conjecture is that a kinetic computer may be able to
solve scaled N-Body problems unlike mathematics or
iterative digital kinematic approximation where outcomes
of interesting cases, eg collisions, are made uncertain
by incomputable encounters with singularities.
Improving the precision of kinetic systems seems to be
the design issue. It is not yet clear why an inverse
square law space should enable possible real-time
optimisation unlike discrete space.
A Machine with analogue radio I/O might be most simple
to construct and without interrupts may satisfy the Pask
Condition for field concurrence. Machines might be
realised with hot wires. A ballistic gas machine can also
be considered. This might enable an elegant "Babel Fish"
language translator via a porous plug constructed, for
example, by electro-chemical diffusion limited
aggregation training. Which approach would best serve
e.g. the Travelling Salesman Problem remains to seen, but
the minimisation behaviour of bubbles according to Plateau's
rules- with its IA-like rule of three- gives a
glimpse of one approach.
Interactions of Actors Theory can be used as a hardware
theory of self-organisation. Pask insisted that minds
could not exist without interpretation in some physical
medium: the collection of concepts that make a mind, or
P-Individuals, are interpreted in M-Individuals.
This is an organising principle that makes minds is
general. Bateson's "Mind and Nature: a Necessary Unity"
provides a beautiful and clear discussion from a
different perspective for readers of all kinds.
Pask's Stable Concept Triples Interacting
Analogous to each other any two concepts can
make the third. A defining property.
A Note on Cybernetics:
Nowadays simply defined as the science of
differences that make a difference (Bateson) or
error detection and correction.
Wiener's discovery (in "Cybernetics: or Control and
Communication in the Animal and the Machine" 1948) was
that the regulation of complex systems behaviour by
negative feedback enabled purpose to be modelled into
behaviour. A universal purpose might be seen as the need
to keep warm as seen in the behaviour of the inanimate as
it approaches the solid state and the living as it
The control of speed in watches, steam engines and
thermostats all clearly embody this principle as, indeed,
does the way the eye helps the hand grasp an external
In 1929 Cannon coined the word "homeostasis" to describe
this phenomenon of maintaining dynamic equilibrium in
physiology. Wallace regarded it as a mechanism for
This universal principle is not taught in schools. It
Recent work by Pask in Second Order Cybernetics, with the
observer as part of the system, produced his Interaction
of Actor Theory. It may put the Deconstructionist
Post-modern approach, for example, on a rigorous basis
suggesting an axiomatic General Theory of Criticism or,
indeed, Error. The context and perspective axioms are
particularly powerful here in driving the necessary
interpretative or hermeneutic analysis.This is still the
subject of research.
Through the notational forms shown Concept Mapping
becomes possible with its attendant epistemological
concerns of relation, context, perspective and
interpretation. Responsibility, amity, purpose, eternal
and delimited interaction are all features.
Graham Barnes' Second Order "Justice, Love and Wisdom"
deals with problems in Therapy. Past critics (often
failed AI Researchers) spoke of Cybernetics having
"descended" into therapy. However insistence on an
axiomatic approach has lead to ready and facile
application. The rigour of regarding Love or Amity as a
readiness to interact, Justice as homeostatic balance
(Beer's "Point of Calm" in a complex system) and Wisdom
as knowledge of Requisite kind or Variety awaits counter
examples from Application.
Ashby's Requisite Variety measure, the number of states
of a stable system, its potential information content,
requires agreed constraints. Pask rejected it in
developing his work but applied it, when constraints
could be agreed, to practical problems.
Some of the primitives adopted by Pask in his
protolanguage, Lp, include Ap, Proc, Con, D, Interp to
denote Application of a Procedure, Con (Concept,
Conversation) distinct from a Description (D) and the
Interpretation of a Con on an M-Individual
He contended one index was required to describe a serial
process, two for a parallel process but three for a truly
field concurrent process.