820:
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
122:. 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
137:. 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". He saw these properties as necessary to produce differentiation and innovation or new coherences in physical nature and, indeed, minds.
32:: 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.
153:
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
210:
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
913:
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
638:(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.
819:
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
193:
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
140:
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
184:
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
164:
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
148:
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
917:
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
152:
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),
218:
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.
662:: 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
169:'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
95:
236:. 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.
231:
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
185:
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
161: : "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"
898:
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
268:. 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
77:
The figure shows Pask's "repulsive carapace" force surrounding a concept. It is shown by the minus sign, it has a clockwise or anticlockwise spin – compare Spin. The spin signature is determined by the residual
202:
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.
66:, 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,
102:
of a minimal concept. The red, blue and green rods exert compressive repulsions, the black lines represent attractive tensions. The
Borromean link shown is regarded as a resonance form (c.f.
82:
of a braid which is the thick line enclosed by the cylinder. The plus sign labels a process seeking closure by "eating its own tail". Three of these toroidal structures can produce a
165:
mathematics or digital serial and parallel processes to produce applicable descriptions because of their innate pathologies in locating the infinitesimals of dynamic equilibria (
859:(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
505:
483:
458:
436:
414:
392:
370:
348:
326:
304:
157:) condition for synchronous transfer of meaningful information occurred. Extending his physical analogy Pask associated the interactions of thought generation with
260:
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
51:(see "Mind and Nature: A Necessary Unity" 1980). Pask's nexus of analogy, dependence and mechanical spin produces the differences that are central to
934:
Scott, B (2009). Conversations, Individuals and
Concepts: Some key concepts in Gordon Pask's Interaction of Actors and Conversation Theories.
875:
Pask distinguishes
Imperative (written &Ap or IM) from Permissive Application (written Ap) where information is transferred in the
74:
215:. "Ah", he said "the atomic hypothesis". He rejected this instead preferring the infinite nature of the productions of waves.
635:
233:
722:(required for the production of the quanta of thought: the transfer of "set-theoretic tokens", as Pask puts it in 1996).
828:
for A and B, would account for this for example. On occasion a second knotted string was tied to the bar representing
1133:
895:
845:
634:
Conversation is defined as having a beginning and an end and time is vectorial. The components of the vector are
265:
134:
127:
130:
he stated "Processes produce products and all products (finite, bounded coherences) are produced by processes".
174:
646:'s kinematic domain (bounded by beginnings and ends) where times are commensurable and in the eternal kinetic
841:
848:: "All processes produce products and all products are produced by processes". This can be written:
276:) of different, evolving, persisting and coherent forms. Two proofs are presented both due to Pask.
58:
While working with clients in the last years of his life, Pask produced an axiomatic scheme for his
643:
29:
488:
466:
441:
419:
397:
375:
353:
331:
309:
287:
220:
145:
666:
medium (stars, liquids, gases, solids, machines and, of course, brains) that produce relations.
40:
Interactions of actors theory was developed late in Pask's career. It is reminiscent of Freud's
1039:
Heinz von
Foerster's Self-Organisation, the Progenitor of Conversation and Interaction Theories
170:
111:
914:
philosopher, wanted to apply these ideas to bring a new kind of rigour to cybernetic models.
900:
891:
273:
79:
829:
269:
261:
67:
45:
25:
507:
be the start and finish times for the transfer of meaningful information, we can write:
948:
808:
AA = A(A) is not equal to BA = B(A) and vice versa, hence, there are no Doppelgangers.
719:
123:
119:
83:
41:
94:
1127:
821:
212:
166:
910:
905:
880:
207:
952:
114:
nature of his work, Pask would make analogies to physical theories in the classic
825:
257:
186:
142:
103:
52:
48:
21:
659:
115:
110:
Interactions of actors theory is a process theory. As a means to describe the
87:
223:
called him a genius, "Mr. Cybernetics", the "cybernetician's cybernetician".
70:, was a key contributor to the development of interactions of actors theory.
876:
158:
154:
99:
890:
was a condition he required for the persistence of concepts. He endorsed
245:
190:
625:
253:
964:
249:
93:
73:
72:
90:
could be used as a model for the interaction in a Borromean link.
824:
during interaction, recoil or the differences in relativistic
879:
manner, the token appearing as a hole in a torus producing a
86:
model of the minimal stable concept. Pask said the prismatic
194:
meaning the coherence between all of the interacting actors.
951:
and the inadequacy of serial (digital computer) modelling
173:
to emulate true field concurrency rather than the current
785:
AB = A(B) = <Con A(B), D A(B)>, A's Concept of B.
780:
AA = A(A) = <Con A(A), D A(A)>, A's Concept of A,
977:
492:
470:
445:
423:
401:
379:
357:
335:
313:
291:
976:
Aspects of these structures can be investigated with
491:
469:
444:
422:
400:
378:
356:
334:
312:
290:
1009:
Interactions of Actors, Theory and Some Applications
64:
Interactions of Actors, Theory and Some Applications
887:
647:
499:
477:
452:
430:
408:
386:
364:
342:
320:
298:
149:"tail-eating" closure, Pask called "tapestries".
840:To set in further context Pask won a prize from
284:Consider a pair of moving, dynamic participants
62:, less well-known than his conversation theory.
753:) = <Con B(T), D B(T)>, B's Concept of T,
737:) = <Con A(T), D A(T)>, A's Concept of T,
244:"There are no Doppelgangers" is a fundamental
106:) of Pask's minimal persisting concept triple.
797:given that for all Z and all T, the concepts
8:
1033:
1031:
1029:
1027:
1025:
1019:Pask (1996) p.355 and Postulate (20) p. 359
28:. It is a generalisation of Pask's earlier
1003:
1001:
999:
997:
995:
1059:von Foerster pp 35–42 in Glanville (1993)
490:
468:
443:
421:
399:
377:
355:
333:
311:
289:
883:containing recursively packed concepts.
658:The second proof is more reminiscent of
650:domain where times are incommensurable.
967:. At cybsoc.org. Retrieved 1 July 2008.
927:
416:will be different from the duration of
954:Retrieved 9 June 2008 at cybsys.co.uk
789:and vice versa, or, in general terms
642:No Doppelgangers applies in both the
7:
350:. Their separation will vary during
801:TA = A(T) is not equal to TB = B(T)
691:means "description of" and <Con
133:Most importantly Pask also had his
98:Prismatic tensegrity space filling
793:ZZ = Z(Z) = <Con Z(Z), D Z>,
14:
1104:Green, Nick. "On Gordon Pask."
1077:Pask (1993) para 82 and Table 4
947:Short discussion in context of
938:. 4(3): 151-158 (pp. 155-156).
772:) = <Con Z (T), D Z(T)>,
1:
886:Pask's "hard" or "repulsive"
60:interactions of actors theory
18:Interactions of actors theory
989:Pask (1993) fig.35 para. 219
714:produces A's description of
500:{\displaystyle \textstyle T}
478:{\displaystyle \textstyle T}
453:{\displaystyle \textstyle B}
431:{\displaystyle \textstyle T}
409:{\displaystyle \textstyle A}
387:{\displaystyle \textstyle T}
365:{\displaystyle \textstyle T}
343:{\displaystyle \textstyle T}
321:{\displaystyle \textstyle B}
299:{\displaystyle \textstyle A}
710:)> reads A's concept of
226:
1150:
936:Constructivist Foundations
141:presented models based on
896:coherence theory of truth
846:complementarity principle
328:producing an interaction
128:complementarity principle
20:is a theory developed by
1068:Pask 1993 paras 100, 130
1050:Pask 1993, paragraph 84.
175:von Neumann architecture
1108:30.5/6 (2001): 673-682.
842:Old Dominion University
16:In information theory,
648:interactions of actors
640:
501:
479:
454:
432:
410:
388:
366:
344:
322:
300:
204:
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180:Reviewing IA he said:
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91:
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502:
480:
455:
433:
411:
389:
367:
345:
323:
301:
200:
182:
97:
76:
1117:Pask (1993) para 188
1086:Pask (1993) para 102
1037:Gordon Pask (1996).
1007:Gordon Pask (1993),
489:
467:
442:
420:
398:
376:
354:
332:
310:
288:
227:Hewitt's actor model
978:Scharein's KnotPlot
963:Nick Green (2003).
644:conversation theory
266:exclusion principle
135:exclusion principle
118:enterprises of the
30:conversation theory
1134:Information theory
815:A mechanical model
654:Reproduction proof
497:
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450:
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428:
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384:
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372:. The duration of
362:
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340:
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318:
317:
296:
295:
221:Heinz von Foerster
211:the invariance of
108:
92:
1095:R.D. Laing (1970)
776:also, in general
611:
610:
171:quantum computing
112:interdisciplinary
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901:G. Spencer Brown
892:Nicholas Rescher
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240:No Doppelgangers
206:In experimental
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836:Further context
830:coordinate time
817:
757:or, in general
656:
630:Pask remarked:
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270:intermodulation
262:differentiation
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120:social sciences
68:Gerard de Zeeuw
38:
26:Gerard de Zeeuw
12:
11:
5:
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949:upper ontology
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822:Doppler shifts
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755:
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720:Dirac notation
677:) ≠
669:Here we prove
655:
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609:
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495:
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438:observed from
426:
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394:observed from
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281:
280:Duration proof
278:
264:and is Pask's
241:
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189:, metaphor or
124:process theory
84:Borromean link
42:psychodynamics
37:
34:
13:
10:
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3:
2:
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636:commensurable
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1008:
985:
972:
959:
943:
935:
930:
916:
911:distinctions
906:Laws of Form
904:
885:
881:Klein bottle
874:
855:(T)) => D
850:
839:
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208:Epistemology
205:
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183:
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163:
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139:
132:
109:
63:
59:
57:
39:
17:
15:
965:Gordon Pask
826:proper time
258:cybernetics
234:Concurrency
187:truth value
143:Knot theory
104:tautomerism
53:cybernetics
49:panpsychism
22:Gordon Pask
1106:Kybernetes
922:References
918:lucidity.
863:<Ap(Con
718:, evoking
660:R.D. Laing
198:He added:
116:positivist
88:tensegrity
980:software.
877:Petri net
805:and that
159:radiation
155:Petri net
126:. In his
100:unit cell
46:Bateson's
1128:Category
888:carapace
871:(T)>.
844:for his
36:Overview
867:(T)), D
811:Q.E.D.
246:theorem
191:analogy
851:Ap(Con
626:Q.E.D.
272:(c.f.
254:clause
80:parity
909:that
613:Thus
274:beats
250:edict
146:knots
485:and
463:Let
306:and
24:and
903:'s
894:'s
699:),
685:).
664:any
256:of
252:or
1130::
1024:^
994:^
832:.
764:=
762:TZ
745:=
743:TB
729:=
727:TA
619:≠
600:≠
585:≠
570:≠
559:,
552:≠
543:,
536:≠
527:,
520:≠
460:.
248:,
177:.
55:.
44:,
1041:.
869:Z
865:Z
857:Z
853:Z
770:T
768:(
766:Z
751:T
749:(
747:B
735:T
733:(
731:A
716:T
712:T
708:T
706:(
704:A
701:D
697:T
695:(
693:A
689:D
683:T
681:(
679:B
675:T
673:(
671:A
621:B
617:A
605:B
602:T
598:A
595:T
590:A
587:T
583:A
580:T
575:B
572:T
568:A
565:T
557:B
554:T
550:A
547:T
541:B
538:T
534:B
531:T
525:B
522:T
518:A
515:T
494:T
472:T
447:B
425:T
403:A
381:T
359:T
337:T
315:B
293:A
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