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 learner's mind)
• The achievement of a result in mathematics by extending analogies from the axioms
• Did analogy have the same status of Generalisation?
  

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.

Analogies exist when there is a shared similarity between two topics, ideas, thoughts, descriptions or concepts. There also exist differences.

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, matter).
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 T2.

The derivations T8 and T9 are shown to add rigour.

T6,T7,T10 and 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 concepts attract"

(Pask's Last Theorem)

Concepts contain concepts to any arbitrary depth.

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)

Some Axioms

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 kinetic.

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.

Gordon Pask

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 evolves.
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 object.
In 1929 Cannon coined the word "homeostasis" to describe this phenomenon of maintaining dynamic equilibrium in physiology. Wallace regarded it as a mechanism for Evolution.
This universal principle is not taught in schools. It should be!
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.