# Key word "eigenform"

Chansky D. (2017) In the Eigenform of the Beholder. Constructivist Foundations 12(3): 326–328. Fulltext at http://cepa.info/4183

Chansky D.
(

2017)

In the Eigenform of the Beholder.
Constructivist Foundations 12(3): 326–328.
Fulltext at http://cepa.info/4183
Open peer commentary on the article “Audience and Eigenform: Cybersemiotic Epistemology and the “Truth of the Human Spirit” in Performance” by Tom Scholte. Upshot: Truthfulness, for both actors and their audiences, emerges at the intersection of physiology and social embeddedness, according to Scholte’s argument for the importance of parsing eigenforms. But an understanding of this process on the part of actors and embedding it in their training cannot alone effectuate the social change for which Scholte calls absent change in what is presented in visible, mainstream venues in productions willing to deploy analogous progressive insights and techniques.

Christy Jr. L. F. (2017) Performance as an Epistemological Tool Describing the Envelope of Perception. Constructivist Foundations 12(3): 331–332. Fulltext at http://cepa.info/4185

Christy Jr. L. F.
(

2017)

Performance as an Epistemological Tool Describing the Envelope of Perception.
Constructivist Foundations 12(3): 331–332.
Fulltext at http://cepa.info/4185
Open peer commentary on the article “Audience and Eigenform: Cybersemiotic Epistemology and the “Truth of the Human Spirit” in Performance” by Tom Scholte. Upshot: Scholte’s counterintuitive use of the arts as laboratories of perceptual inquiry investigates meaning, language and formation of perceptual systems. Theory of Logical Types offers one way of understanding the power of theatre as a tool revealing the contextual organizing structures of perception.

Collings A. M. (2016) Eigenforms, Coherence, and the Imaginal. Constructivist Foundations 11(3): 501–502. Fulltext at http://cepa.info/2859

Collings A. M.
(

2016)

Eigenforms, Coherence, and the Imaginal.
Constructivist Foundations 11(3): 501–502.
Fulltext at http://cepa.info/2859
Open peer commentary on the article “Cybernetics, Reflexivity and Second-Order Science” by Louis H. Kauffman. Upshot: This commentary reflects broadly on the concept of eigenform and reflexive domains, focusing on the idea that second-order science is neither the same as nor completely distinct from ordinary living.

de Zeeuw G. (2017) Eigenform and Expertise. Constructivist Foundations 12(3): 258–260. Fulltext at http://cepa.info/4166

de Zeeuw G.
(

2017)

Eigenform and Expertise.
Constructivist Foundations 12(3): 258–260.
Fulltext at http://cepa.info/4166
Open peer commentary on the article “Eigenform and Reflexivity” by Louis H. Kauffman. Upshot: Kauffman proposes to understand scientific thinking as including not only observations but also the act that enables their intentional use. This provides a constructivist opportunity: extending scientific thinking to gaining personal expertise.

Espejo R. (2017) “The Truth of the Human Spirit” and Interaction Mechanisms. Constructivist Foundations 12(3): 334–336. Fulltext at http://cepa.info/4187

Espejo R.
(

2017)

“The Truth of the Human Spirit” and Interaction Mechanisms.
Constructivist Foundations 12(3): 334–336.
Fulltext at http://cepa.info/4187
Open peer commentary on the article “Audience and Eigenform: Cybersemiotic Epistemology and the “Truth of the Human Spirit” in Performance” by Tom Scholte. Upshot: Scholte’s article offers a most valuable reflection on cybernetics and acting. This commentary reflects on interaction mechanisms between actors and audiences.

Fields C., Hoffman D. D., Prakash C. & Prentner R. (2017) Eigenforms, Interfaces and Holographic Encoding: Toward an Evolutionary Account of Objects and Spacetime. Constructivist Foundations 12(3): 265–274. Fulltext at http://cepa.info/4168

Fields C., Hoffman D. D., Prakash C. & Prentner R.
(

2017)

Eigenforms, Interfaces and Holographic Encoding: Toward an Evolutionary Account of Objects and Spacetime.
Constructivist Foundations 12(3): 265–274.
Fulltext at http://cepa.info/4168
Context: The evolution of perceptual systems and hence of observers remains largely disconnected from the question of the emergence of classical objects and spacetime. This disconnection between the biosciences and physics impedes progress toward understanding the role of the “observer” in physical theory. Problem: In this article we consider the problem of how to understand objects and spacetime in observer-relative evolutionary terms. Method: We rely on a comparative analysis using multiple formal frameworks. Results: The eigenform construct of von Foerster is compared to other formal representations of observer-environment interactions. Eigenforms are shown to be encoded on observer-environment interfaces and to encode fitness consequences of actions. Space and time are components of observational outcomes in this framework; it is suggested that spacetime constitutes an error-correcting code for fitness consequences. Implications: Our results contribute to an understanding of the world in which neither objects nor spacetime are observer-independent. Constructivist content: The eigenform concept of von Foerster is linked to the concepts of decoherence and holographic encoding from physics and the concept of fitness from evolutionary biology.

Füllsack M. & Riegler A. (2017) Thinking in Eigenbehaviors as a Transdisciplinary Approach. Constructivist Foundations 12(3): 239–245. Fulltext at http://cepa.info/4161

Füllsack M. & Riegler A.
(

2017)

Thinking in Eigenbehaviors as a Transdisciplinary Approach.
Constructivist Foundations 12(3): 239–245.
Fulltext at http://cepa.info/4161
Context: By proposing to regard objects as “tokens for eigenbehavior,” von Foerster’s seminal paper opposes the intuitive subject-object dualism of traditional philosophy, which considers objects to be instances of an external world Problem: We argue that this proposal has two implications, one for epistemology and one for the demarcation between the natural sciences and the humanities. Method: Our arguments are based on insights gained in computational models and from reviewing the contributions to this special issue. Results: Epistemologically, von Foerster’s proposal suggests that what is called “reality” could be seen as an ensemble of eigenforms generated by the eigenbehavior that arises in the interaction of multiple dynamics. Regarding science, the contributions to this special issue demonstrate that the concept of eigenbehavior can be applied to a variety of disciplines from the formal and natural sciences to the humanities. Its universal applicability provides a strong argument for transdisciplinarity, and its emphasis on the observer points in the direction of an observer-inclusive science. Implications: Thinking in eigenbehavior may not only have implications for tearing down the barriers between sciences and humanities (although a common methodology based on von Foerster’s transdisciplinary approach is still to crystalize), a better understanding of eigenbehaviors may also have profound effects on our understanding of ourselves. This also opens the way to innovative behavior design/modification technologies.

Kauffman L. H. (2005) EigenForm. Kybernetes 34(1/2): 129–150. Fulltext at http://cepa.info/1271

Kauffman L. H.
(

2005)

EigenForm.
Kybernetes 34(1/2): 129–150.
Fulltext at http://cepa.info/1271
Purpose: Discusses the notion of eigenform as explicated by Heinz von Foerster wherein an object is seen to be a token for those behaviors that lend the object its apparent stability in a changing world. Design/methodology/approach – Describes von Foerster’s model for eigenforms and recursions and put this model in the context of mathematical recursions, fractals, set theory, logic, quantum mechanics, the lambda calculus of Church and Curry, and the categorical framework of fixed points of Lawvere. Findings: Determines that iterating an object upon itself is seen to be a key to understanding the nature of objects and the relationship of an observer and the apparent world of the observer. Originality/value – Contemplates the concept of recursion in the context of second-order cybernetics.

Kauffman L. H. (2009) Reflexivity and Eigenform: The Shape of Process. Constructivist Foundations 4(3): 121–137. Fulltext at http://cepa.info/133

Kauffman L. H.
(

2009)

Reflexivity and Eigenform: The Shape of Process.
Constructivist Foundations 4(3): 121–137.
Fulltext at http://cepa.info/133
Purpose: The paper discusses the concept of a reflexive domain, an arena where the apparent objects as entities of the domain are actually processes and transformations of the domain as a whole. Human actions in the world partake of the patterns of reflexivity, and the productions of human beings, including science and mathematics, can be seen in this light. Methodology: Simple mathematical models are used to make conceptual points. Context: The paper begins with a review of the author’s previous work on eigenforms - objects as tokens for eigenbehaviors, the study of recursions and fixed points of recursions. The paper also studies eigenforms in the Boolean reflexive models of Vladimir Lefebvre. Findings: The paper gives a mathematical definition of a reflexive domain and proves that every transformation of such a domain has a fixed point. (This point of view has been taken by William Lawvere in the context of logic and category theory.) Thus eigenforms exist in reflexive domains. We discuss a related concept called a “magma.” A magma is composed entirely of its own structure-preserving transformations. Thus a magma can be regarded as a model of reflexivity and we call a magma “reflexive” if it encompasses all of its structure-preserving transformations (plus a side condition explained in the paper). We prove a fixed point theorem for reflexive magmas. We then show how magmas are related to knot theory and to an extension of set theory using knot diagrammatic topology. This work brings formalisms for self-reference into a wider arena of process algebra, combinatorics, non-standard set theory and topology. The paper then discusses how these findings are related to lambda calculus, set theory and models for self-reference. The last section of the paper is an account of a computer experiment with a variant of the Life cellular automaton of John H. Conway. In this variant, 7-Life, the recursions lead to self-sustaining processes with very long evolutionary patterns. We show how examples of novel phenomena arise in these patterns over the course of large time scales. Value: The paper provides a wider context and mathematical conceptual tools for the cybernetic study of reflexivity and circularity in systems.

Kauffman L. H. (2010) Reflexivity, eigenform and foundations of physics. In: Reflexivity: Proceedings of ANPA 30 June 2010. Fulltext at http://cepa.info/1819

Kauffman L. H.
(

2010)

Reflexivity, eigenform and foundations of physics.
In: Reflexivity: Proceedings of ANPA 30 June 2010.
Fulltext at http://cepa.info/1819
This essay is a discussion of the concept of reflexivity and its relationships with self-reference, re-entry, eigenform and the foundations of physics.

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