ࡱ> UWT3 ;DbjbjOO "b--?;c]RRRR8 <C\ZZ(      $ ".S|.cRRZcccpR8RRRRc&cVwFr o?$ Axioms from Interactions of Actors Theory Mr N Green FCybS Real Time Study Group Department of Computer Science University of Wales, Cardiff www.cyberneticsassociates.co.uk While working with clients in the last years of his life Gordon Pask produced an axiomatic scheme from Interactions of Actors Theory which supports Conversation Theory. These axioms are discussed as characteristic of field concurrence and the second order cybernetic canon. In 1994 while consulting with clients Gordon Pask made a clear statement of axioms or properties governing his Conversation Theory, CT (Pask 1976), the means by which concepts are shared, and its underlying support Interactions of Actors Theory, IA (Pask 1992). As Bateson (1980) has it Nature and Mind are one. To Pask, also, a concept is the product of self-organisation (Pask 1996) whether in a star or a brain. There are two parts to an interacting participant or Actor. First the P-individual which is a dynamic productive and incidentally reproductive, adaptive, evolving and learning collection or entailment mesh of concepts. Second the M-individual which is a mechanical or biological medium e.g. a brain or a star, which supports the P-Individual and the strains its concepts produce. To Pask all observation was a Conversation between participant and observer with interpretation of the P-individual in the M-individual. The constraints on the Second Order paradigm of Cybernetics, the observer as part of the system, are made plain with the axioms. Pask (1990) won an award from Old Dominion University, Virginia for his Process/Product Complementarity principle. "Every process produces a product, every product is produced by a process" e.g. electromagnetic waves and photons or in the case of CT applied concepts and descriptions. This may be written Ap(Conz(T)) => Dz(T) where => means produces, z is a participant and T the current topic or concept from the domain of the participants. So the description, D, of T is produced by the Ap operator on the Con operator on T. The dual character is denoted: . P and M-Individuals are also dual process/product pairs. Pask wrote this as: denoting an Actor or participant to Interaction or Conversation. Ap, Con and D are operators in Pask's protolanguage Lp. The axioms or properties below apply to both Conversation and Interactions of Actors Theory with the exception that Conversations of P-individuals have Begins and Ends and may be interrupted by other conversations and so be nested whilst Actors, M-individuals, interact eternally. The closed toroidal processes which comprise the concepts of P-individuals exist as stable triples in which any pair is analogous to the other and distinguished by the third. Any two concepts may generate the third because of their resonant similarities and differences. The spatial form of the concept triples was under study at the time I joined Pask Associates in 1993. Borromean Rings and the prismatic tensegrity of Buckminster Fuller, as a tractable force model, were configured as elements of a potential concurrent computer. The concepts nest recursively in triples within each other. They form tori like wires in a multi-core electric cable. Repulsive forces are exerted by the concepts generating a carapace or hard protective shell around them. These forces further distinguish the domain of Interactions of Actors Theory from Conversation Theory in that Pask asserted IA to be a kinetic theory and CT to be kinematic because of its implicit begins and ends. Forces cause thoughts to change and we have the Last Theorem as Pask called it which states "Like concepts repel, unlike concepts attract". This statement is intended to embody all forces: weak, strong, gravitational and electric or magnetic, which give rise to the self-organising character we see in Nature. Here "+" directs into the not void (or something) and "-" means orthogonal to and "deflects similar concepts" Pask (1992 p47).  The properties of the axioms can be appreciated as characteristic of Interaction in field concurrent N-body systems, like the Newtonian Solar system or the electrically charged protons and electrons of an atom or molecule. Interpretation of Pask's force of self-organisation is on going. Note stable elliptical orbits are rare in N-Body simulations with random initial conditions but equal masses. Choreographies, by contrast, are common when masses are equal eg Carlos Simo (undated pre-print from Paris Observatory). For simulation tools see Acheson (1997). Asymmetric attractive, sticky, aggregative generation (Witten and Sander 1981) producing a non-uniform Bakian 1/f( distribution of masses (Bak 1997) is probably necessary for the stable seeming elliptical orbits we all expect. Whilst the laws of electric and magnetic attraction and repulsion are familiar recall again the closed curved Newtonian process. There is a repulsion without electromagnetic law in the resistance of a gyroscope to a couple. Note also in the asymmetric Tippe (sometimes spelt Tippy) Top there is conflict of the minimisation principles of Fermat, Maupertius and Hamilton. The top turns up-side down at some critical frequency, achieving a spinning equilibrium but raising its centre of gravity. A picture of Fermi and Bohr watching an inverting Tippe Top is held in the Bohr Library of the American Institute of Physics. The stiffening of a soft carapace, as IA might interpret it, has been demonstrated by vertical periodic excitation at a resonant frequency of a curtain wire. David Acheson (1993), the discoverer, calls this "Not quite the Indian Rope Trick". Interactions of Actors Axioms Context Perspective Responsible Respectable Amity Agreement Agreement-to-disagree Purpose Unity not uniformity Faith Beginnings and Ends (CT) Eternally interacting (IA) Similarity and Difference Adaptation Evolution Generation Kinetic (IA) Kinematic (CT) Conservation of Meaningful Information Transfer both Permissive (Ap) and Imperative Application (Im) Informational openness and Organisational closure. Void and Not-Void  The setting up of counting and in particular state counting or variety may prove an interesting first challenge to elegance and chosen notation. The apparent simplicity of the Similarities and Differences in Actors Axiom are what may be deployed. It should be noted that a difference is the feedback of first order cybernetics. Amity and Faith have caused much concern. Amity means availability for interaction. It is a nearest neighbour criterion for least noticeable difference or distinction. In the human context we may say "willingness" to interact where will implies a shared Purpose or Unity which is not Uniformity. This in turn may lead us to use the term love, certainly where Generative interaction (or aggregative growth) is implied. Graham Barnes' (1994) celebrated primer on Psychotherapy "Justice, Love and Wisdom" can be seen in greater relief and in all its unbounded applicability when this clarification is made. Justice is defined here as "reflective balance", wise homeostasis applied in the manner of Rawls (1973) or, indeed, Rescher (1965). Faith is a property of an assertion and persists until a contradictory counter example is found. To interact or do a proper experiment, for example, faith is required. We cannot forecast the outcome, whatever we may claim, otherwise the experiment or interaction would not be worth conducting. It may be seen as a kind of concurrent Halting Problem or signal identification with noise. Permissive and Imperative application of a stress producing concept may be distinguished by freedom of choice: when the strains of concepts internal to a P-individual lead to autonomous action rather the than action forced by another participant. We see clearly how delicate the balance between permissive and imperative application necessarily is. Pask claimed Void and Not Void, or "something" as not void may be called, were required distinctions in IA. They distinguish M-Individuals. In CT although voids may be invoked they are not required. The begins and ends of CT may be seen as abstractions of the void/not void. If begins and ends are actual void/not void crossings an interesting question arises. Is Gibbs ringing seen around the begins and ends of the void when the closed, periodic processes in a signal are counted with Fourier spectral analysis? Agreement can be seen as trajectories between bodies in phase lock coupling or copying as in Wiener self-organisation. But the usual distinctions from CT of similarity and difference may apply here. This requires externalisation, in a medium shared by at least two participants, of a behaviour induced by one participant as a result of a communication act. The acknowledgement by the second participant, with whom there also exists the analogical dependence of meaningful information transfer or communication, constitutes agreement. Agreement to Disagree is clearly the recognition by a pair of participants that this condition has not been achieved. Begins and ends are implicit here. These bounding singularities are indicated here by a rapid change in radius of curvature of trajectory or an encounter with the void (and the possibility of the Gibbs phenomenon around a discontinuity). Adaptation, Generation and Evolution are deeply intertwined, as indeed are all the axioms, but key features can be distinguished. Adaptation is a dynamical change perhaps elastic in character. Generation is a sticky, attractive, aggregative process (with death as disaggregative, or entering the void). Evolution requires meaningful information transfer or learning. Context and Perspective, the neighbourhood and your position in it, can be literally interpreted with no special caveats. Unity without uniformity is simply an expression of identity wherein distinct parts cohere. Purpose is the intended or perceived outcome of a process, it may be another word for product. Nevertheless purpose is important in the emergence of Cybernetics and key to its interdisciplinary success. IA is also a theory of process. The term distinction is widely known from Spencer-Brown (1969) and might be included for its power in setting up closure and minimal difference. We know, for example, A ( A but what that means except as denoting a minimal difference is not clear. It is enough, however, to make it a required axiom though it may more properly be called a value, albeit subject to careful definition. The terms Organisational Closure and Informational Openness are nowadays widely accepted as defining a system eg Maturana and Varela (1980) and the IA scheme is coherent with this approach. They are supported but not required given a suitable supply of Actors who self-organise. The IA axioms are widely applicable. The applicability of an early version of Pask's work to psychotherapy, for example, of both individuals and organisations is shown by Barnes (1994). The IA scheme is designed for concurrent application so it should shed light on concurrent computation. Various hardware configurations continue to be considered. No confusion with quantum computing should be permitted where current proposals limit concurrence to the quantum registers in an emulation of the conventional serial digital computer. IA was in part a mission to Artificial Intelligence (AI) research to map a physics of self-organisation into common sense. It may yet come to the rescue if AI is to become more than attempts at advanced von Neumann machine programming. Sceptics may say "Why speak of 'Respect' when you mean observable, why speak of 'Responsibility' when you mean response or 'Faith' when you mean tenacity?" No great damage is done we hope but applicability is greatly facilitated. In particular the putting of the so-called "soft sciences": psychology, sociology, politics etc. and law on a sounder basis. One capable of producing sharp values (as distinct from Zadeh fuzzy values) of a precision equal to any obtainable in the so called hard sciences of Physics or Chemistry. We recognise the need to make assumptions and restrictions on the ideals equivalent to those made as the Euclidean becomes the Newtonian thence the relativistic and quantum in science. Pask scholars and collaborators continue to discuss the potential and we may be facing a Bourbakian task of putting Cybernetics on an axiomatic basis. There seem to be immediate applications in putting Criticism on a more rigorous basis indeed making Criticism into a human science. The hermeneutic constraints of Post Modernism seem fully satisfied. Others may care to challenge that. The applications of these axioms to Beer's Principles of Organisation (Beer 1985) and Pask's own "Properties of Self-Organised Systems and their consequences for a company" (Green 2001, footnote 11) may also form an interesting objective for future research. De Zeeuw's observation (de Zeeuw 2001) that IA makes it possible to search for Theory suggests Gordon's goal of a dynamic proto-theory may have been achieved. One characterisation of IA is as a dynamic incarnation of Lp, Pask's protolanguage, as distinct from the static CT version of Lp. As de Zeeuw so wittily observed at CybCon 2002 IA enables one to say things like "Love makes the World go round". The axioms provide a route to a robust seeming proof. One wonders where this might lead us. ______________________________ References Acheson, David (1997) "From Calculus to Chaos" OUP 1997 ISBN 0-19-850257-7 Acheson, David and Mullin, Tom (1993) Nature vol 366 pp215-216 (1993) Bak, Per (1997) "How Nature Works: The Science of Self-Organised Criticality" OUP 1997 ISBN 038798738 Barnes, Graham (1994) "Justice Love and Wisdom" Inform Lab 1994 ISBN 9531760179 Bateson, Gregory (1980) "Mind and Nature- A Necessary Unity" Bantam Books ISBN1572734345 Beer, Stafford (1985) "Diagnosing the System for Organisations" John Wiley ISBN 0-471-90675-1 Green, Nick (2001) "On Gordon Pask" Kybernetes vol 30 No 5/6 2001 pp673-682 Maturana, Humberto and Varela, Francisco (1980) "Autopoiesis and Cognition" Kluwer ISBN 9027710155 Pask, Gordon (1996) "Heinz von Foerster's Self Organisation, the Progenitor of Conversation and Interaction Theories" Gordon Pask, Systems Research vol 13, No 3 1996 pp 349-362 Pask, Gordon (1992) "Interactions of Actors, Theory and some Applications" Gordon Pask and Gerard de Zeeuw Volume 1 "Outline and Overview" (Draft June 1992) Pask, Gordon (1990) "Complementarity in the Theory of Conversations" in Nature, Cognition and System Carvalho, M (Ed.) Proceedings of Baden Baden Symposium 1990 Reichsuniversitiet, Gronigen Pask, Gordon (1976) "Conversation Theory" Elsevier Rawls, John (1973) "A Theory of Justice" Oxford OUP 1973 ISBN: 0674000781 Rescher, Nicholas (1966) "Distributive Justice" Bobbs-Merrill 1966 Simo, Carles (~2001) "New families of Solutions in N-Body Problems" Institut de Mecanique Celeste, Observatoire de Paris. Pre-print http://mat.uab.es/art3ecm/simo.pdf Spencer-Brown, George (1969) "Laws of Form" 3rd Edition 1979 Dutton ISBN 0-525-47544-3 Witten, Tom and Sander, Len (1981) "Diffusion-limited aggregation, a kinetic critical phenomenon" Physical Review Letters, vol 47, 1981 pp1400-1403 de Zeeuw, Gerard (2001) "Interaction of Actors Theory" Kybernetes vol 30, No 7/8 2001 pp971-983. Tippy or Tippe Top some references to studies Weisstein, Eric http://scienceworld.wolfram.com/physics/TippeTop.html A downloadable Threebody simulator, THREEBP.BAS at http://www.jesus.ox.ac.uk/~dacheson/programs/index.html see also Acheson's Vortex Research on curious self-organising vortex "leapfrogging" and his remarks on Kelvin's early knot theoretic "vortex atom" theory in "Elementary Fluid Dynamics" OUP 1990 pp168-172 including a Borromean Ring from Lord Kelvin (1869) Trans. R. Soc. Edinb. 25, pp217-260 reprinted in "Knots and Applications" ed. Louis Kauffman World Scientific 1995 ISBN 981-02-2030-8 Choreographies demonstration applet of the recent work of Simo, Chenciner and Montgomery http://www.soe.ucsc.edu/~charlie/3body/ Further discussion of Pask and his IA axioms at www.cyberneticsassociates.co.uk 8 October, 2002Nick Green  PAGE 5/ NUMPAGES 1 The Carapace of Repulsive Force around a section of a closed loop concept process from Pask 1992 > " # & ' / 0 1  ! $ % + , - 0<[\[\]-KϻϨϨϛ~v5CJOJQJ5B*CJOJQJhnH B*OJQJhnH  H*OJQJ jb5CJH*OJQJjOJQJUmH56OJQJ 6OJQJ5H*OJQJ 5OJQJOJQJ CJOJQJ6CJOJQJOJQJ>*B*OJQJ CJOJQJ5CJOJQJ-->Tsef 4 5   34DE$7$$$->Tsef 4 5   34DE:;-KS_kw}%0>M" # !!## % %(())++=->-U.V.W1X1 4!444688888899W9      ^:;-KS_kw}%0 & F$$ & F7$ h77$70>M" # !!## % %(())++=->-$7"$$l^ 0f $ & F$BGLQ@GKQZh# ( !!!!###$# %% '5'''''(((((())**++++f,g,H-y-888969X9g9ѵѭ֦֦ CJOJQJ5CJOJQJ j5CJOJQJjOJQJUmH 5OJQJOJQJ5CJOJQJB*OJQJhmH nH B*OJQJhnH 6B*OJQJhnH A>-U.V.W1X1 4!444688888899W9X9999::s:t:$$7$7$7W9X9999::s:t:::; ;t;;;7<C<D<<<====!>">e>f>>??g?h????U@`@a@@@@BABB!CICJCCCCCCCCCCC8D9D:D;D>g999:1:t:::: ;O;;;D<W<<<====">:>f>z>>??+?h????@a@s@@@@@ AAABBBBBB C!CJCzCCCCCCCCCCCCCCCCCCC:D;D0JmH0J j0JU CJOJQJ5>*B*CJOJQJB*CJOJQJ5B*CJOJQJ>*B*CJOJQJ5CJOJQJ CJOJQJGt:::; ;t;;;7<C<D<<<====!>">e>f>>??g?h???????U@`@a@@@@BABB!CICJCCCCCCCCCC $$l09 $$$??CCCC8D9D:D;D$ /R . 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