This paper aims to introduce the concept and praxis for eigenform in the context of second-order cybernetics.
Abstract
Purpose
This paper aims to introduce the concept and praxis for eigenform in the context of second-order cybernetics.
Design/methodology/approach
The paper is designed as a formal (partly mathematical) introduction with excursions into the applications and meanings of these constructions. Mathematics studies what a distinction would be if there could be a distinction. Mathematics is a special form of fictional design. This study raises the question of “What it would mean to go beyond mathematics or for mathematics to go beyond itself?”.
Findings
This study shows how objects in the author’s experience can be seen to be eigenforms and that in this context such objects are a construct of their interactions, linguistic and otherwise experiential. In this way, the author can investigate scientifically without the need for an assumption of objectivity. The author cocreates the universe through the discovery of distinctions and eigenforms in their dialogue with what can be.
Research limitations/implications
The implications of this research are profound for the performance and exploration of science. The author can explore their role in that creation and find that what they create is independent of significant subsets of their actions.
Practical implications
The practical implications of this study are strongest for the logical understanding of the author’s constructions and actions. They have used eigenform and reflexivity to maintain a clear view of their participation in their own worlds.
Social implications
The social implications are in accordance with the practical implications. The author can now admit that they each produce eigenform models of the others and for themselves. These models have in-depth usage, in that it is understood that one is not identical with their models.
Originality/value
This paper presents a highly original and very simple way to incorporate second-order cybernetics into all thought and action.
Details
Keywords
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…
Abstract
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 puts 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 a transformation 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.
Details
Keywords
Discusses the relationship between computer proof and human proof. These issues are discussed both in general and specifically regarding the recent solution of the Robbins problem…
Abstract
Discusses the relationship between computer proof and human proof. These issues are discussed both in general and specifically regarding the recent solution of the Robbins problem via a proof generated by computer. The Robbins problem was a long‐standing open problem about axioms for Boolean algebra. One point of this paper is to show that the proof of the Robbins conjecture, generated by a computer, can be filled in and understood by human beings. We accomplish this aim in the present paper by presenting a notational reformulation of Boolean algebra and the Robbins problem. The notational/linguistic issue developed here is of cybernetic, linguistic and semiotic interest. It is our contention that mathematics can behave non‐trivially under change of notation. Change of notation can be as significant as change of language. In the present case the change of language afforded by an appropriate change of notation makes a mathematical domain accessible to human beings that has heretofore been only accessible to computers.
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Abstract
Details
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Sara L. Cochran and Donald F. Kuratko
The world is changing very rapidly with events that alter the landscape for students during a time when entrepreneurs are needed more than ever. This chapter explores trends in…
Abstract
The world is changing very rapidly with events that alter the landscape for students during a time when entrepreneurs are needed more than ever. This chapter explores trends in entrepreneurship research that are focused in areas of the entrepreneurial mindset, alleviation of poverty through entrepreneurship, social entrepreneurship, portfolio thinking about entrepreneurial venture types, the crucial nature of racial diversity, and the drive of women entrepreneurs. It also examines COVID-19’s disparate impact on smaller ventures and Black entrepreneurs, while highlighting its impact on spurring entrepreneurial innovations causing an entrepreneurial explosion. Most importantly, this chapter focuses on how the emerging research trends amidst the COVID-19 pandemic have prompted entrepreneurship educators to enact educational innovations. The chapter includes tools and tips to integrate into the changing nature of university programs and entrepreneurship curriculums facing a dynamic future.
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Kristen A. Gilbert, Robert H. Voelkel and Christie W. Johnson
Research suggests effective immersive simulations that rely on augmented reality enhance teachers’ self-efficacy and skills (Badiee & Kauffman, 2015). However, there is a gap in…
Abstract
Research suggests effective immersive simulations that rely on augmented reality enhance teachers’ self-efficacy and skills (Badiee & Kauffman, 2015). However, there is a gap in the literature as studies have largely ignored their uses in educational leadership programs (Bradley & Kendall, 2015). This study investigated the relationship between application of critical skills within an immersive simulation environment and 26 school or district leaders’ perceptions of self-efficacy in leading a professional learning community (PLC). Two overarching themes materialized from participants: improved general confidence in leading a PLC, and a sense of refined or expanded skills in the context of new approaches to leading PLC. Further studies are needed on the use of immersive simulation as a pedagogical tool and to examine impact for educational leadership practitioners.
Kristen A. Gilbert, Robert H. Voelkel and Christie W. Johnson
Research suggests effective immersive simulations that rely on augmented reality enhance teachers’ self-efficacy and skills (Badiee & Kauffman, 2015). However, there is a gap in…
Abstract
Research suggests effective immersive simulations that rely on augmented reality enhance teachers’ self-efficacy and skills (Badiee & Kauffman, 2015). However, there is a gap in the literature as studies have largely ignored their uses in educational leadership programs (Bradley & Kendall, 2015). This study investigated the relationship between application of critical skills within an immersive simulation environment and 26 school or district leaders’ perceptions of self-efficacy in leading a professional learning community (PLC). Two overarching themes materialized from participants: improved general confidence in leading a PLC, and a sense of refined or expanded skills in the context of new approaches to leading PLC. Further studies are needed on the use of immersive simulation as a pedagogical tool and to examine impact for educational leadership practitioners.
The history of the field of entrepreneurship and the entrepreneurship program at Saint Louis University is discussed, along with the descriptions of the Gateways to…
Abstract
The history of the field of entrepreneurship and the entrepreneurship program at Saint Louis University is discussed, along with the descriptions of the Gateways to Entrepreneurship Conferences and the creation of the Advances in Entrepreneurship, Firm Emergence, and Growth (AEFEG) series given in relation to those national- and campus-level contexts. The growth and development of the AEFEG series is discussed and the editorial contributors are noted, which could be of use to those interested in editorial roles and processes. Based on these elements, the chapter concludes with observations on the field of entrepreneurship and some ideas about its future.