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This paper aims to show how a sociological description – a swarm analysis of the Nazi dictatorship – initially made with the means borrowed from George Spencer-Brown’s Calculus of Indications, can be transformed into a digital circuit and with which methods and tools of digital mathematics this digital circuit can be analyzed and described in its behavior. Thus, the paper also aims to contribute to a better understanding of Chapter 11 of “Laws of Form.”

The analysis uses methods of automata theory for finite, deterministic automata. Basic set operations of digital mathematics and special set operations of the Boolean Differential Calculus are used to calculate digital circuits. The software used is based on ternary logic, in which the binary Boolean logic of the elements {0, 1} is extended by the third element “Don’t care” to {0, 1, −}.

The paper confirms the method of transforming a form into a digital circuit derived from the comparative functional and structural analysis of the Modulator from Chapter 11 of “Laws of Form” and defines general rules for this transformation. It is shown how the indeterminacy of re-entrant forms can be resolved in the medium of time using the methods of automata theory. On this basis, a refined definition of the degree of a form is presented.

The paper shows the potential of interdisciplinary approaches between sociology and information technology and provides methods and tools of digital mathematics such as ternary logic, Boolean Differential Calculus and automata theory for application in sociology.

Chemistry as an applied science suffers from the fact that its necessarily close connection with various branches of industry is ill defined and generally very unsatisfactory in character. One result of this is that those who have made chemistry their profession find themselves more often than not in the position of having to subordinate their professional instincts to the temporary exigencies of some particular branch of trade and to find their professional status called in question and criticised by those who are not in the profession itself and who have no right to criticise.

Industry in rural, agriculturally based Northwest Tennessee has traditionally been apparel, textile, and footwear. In recent years, globalization has resulted in area plant closings, plant relocations and layoffs throughout the region. This paper examines the impact on former employees interviewed four years after a major plant closing in Obion County. This study presents the case study of the Brown Shoe Company that opened in 1923 and closed in 1994. The findings from this exploratory study suggest that the impacts of plant closures in the footwear industry are similar to other textile and garment factory closings. As in previous studies, workers were concerned with financial and health benefits issues and experienced emotional trauma. Dislocated workers were predominately female, and high poverty rates for families and female heads of households still exist almost eight years after the closing. Longitudinal research is suggested to further inform policy and governmental action in the wake of further plant closings, especially as such economic restructuring affects women and communities in rural southern areas of the USA.

Blake is relatively well-known, but who was J M Robertson? What's his connection with George Spencer-Brown? And how exactly did J M Robertson influence George Spencer-Brown?

George Spencer-Brown (1923–2016) is the author (among other works) of the undeservedly little-known book, Laws of Form (1969/2011), which was a key inspiration for Niklas Luhmann (1927–1998). But what inspired George Spencer-Brown? This paper explores two key influences on George Spencer-Brown and his work: the English poet and artist, William Blake (1757–1827) and the Scottish rationalist, politician and author, J M Robertson (1856–1933).

The paper points to a broken link between George Spencer-Brown's work and Niklas Luhmann's.

These questions are explored from two perspectives: first, George Spencer-Brown's works and their debt to (1) Blake's work, from which he quotes in a number of instances and to (2) J M Robertson's (in particular, the latter's Letters on Reasoning (1905) and Rationalism (1912)); second, my personal connection to Spencer-Brown, who mentored me through Laws of Form and with whom I developed a close friendship involving regular weekly telephone conversations for the greater part of the last four years of Spencer-Brown's life. I share anecdotes and stories that connect George Spencer-Brown and J M Robertson that span George Spencer-Brown's lifetime – from his school days to his dying days. Both Blake's and Robertson's influences are relevant to Spencer-Brown's view of morality. The paper looks at specific connections between Blake's work and J M Robertson's on the one hand and George Spencer-Brown's on the other.

The paper uncovers a mathematical error in George Spencer-Brown's genesis of re-entry. It distinguishes between the two interpretations of re-entry presented in “Laws of Form”: recursive versus sequential. The Indeterminacy inferred by George Spencer-Brown from his recursive genesis of re-entry is refuted in three different ways. The calculation of the Modulator from “Laws of Form” demonstrates that only the sequential interpretation of re-entry is reasonable. This contributes to the demystification of re-entry and enables a deeper understanding. Finally, six differences between the concept of form from “Laws of Form” and Niklas Luhmann's sociological systems theory are presented.

Methodologically, the paper uses the ternary logic of discrete mathematics, which extends {0, 1} by “don't care” to {0, 1, -}. George Spencer-Brown's Indeterminicy is refuted by using three different methods: complete induction, Theorems 14 and 15 and the software XBOOLE. For the calculation of the Modulator, the only practical application of re-entry in “Laws of Form”, techniques from automata theory are used.

The paper reveals a mathematical error in George Spencer-Brown's genesis of the re-entry of “Laws of Form” and refutes the assumption of Indeterminicy. The analysis of the only practical application of re-entry presented by George Spencer-Brown shows that the functioning of this Modulator can only be described correctly with the sequential interpretation of re-entry.

The paper emphasizes the interdisciplinary potential of sociology and information technology and provides methods and tools of discrete mathematics for use in the analysis of the works of George Spencer-Brown and Niklas Luhmann.

This article presents a history of the visual merchandising of American firearms from the mid-19th century until the present day. Although the scholarly literature has investigated visual representations of guns in advertising and popular media, it has paid far less attention to how sellers have displayed these objects at or near the point of purchase.

Primary sources include frescoes, engravings and photographs, plus papers, advertising and illustrations in popular newspapers and trade magazines. These and other period visual data are supplemented by secondary sources from a variety of fields, especially retailing and firearms history.

Evidence shows that American firearms were merchandised visually by Samuel Colt at three world expositions in the 1850s, by gunmakers and retailers in the latter 19th century, by Winchester and Remington dealers in the 1920s and 1930s, by high- and low-end retailers in New York in the first half of the 20th century and by gun stores, auctions and shows up to the present day.

The history of visual merchandising generally has focused upon major department stores, their alluring street-front windows and their fancy interior displays. This research explores past and present visual merchandising of firearms by manufacturers and smaller retailers. To the best of the author’s knowledge, it is the first such history of the subject.

George Spencer Brown is best known for his book Laws of Form, which elaborates a primary algebra of distinctions and forms capable of dealing with self-referential equations reflective of paradoxes in logic. The book has received little attention in mathematics, but it has greatly influenced cybernetics, communications, and ecological theories. But Spencer Brown also published poetry and stories, often under different names, and he practiced as a psychotherapist. Our chapter elaborates the utility of Laws of Form relating to organizational paradox before considering Spencer Brown’s other works in relation to his mathematics. Invoking philosophy, psychoanalysis and art, we suggest that these indicate a further distinction that sets all forms against the “nothing”: a wholeness or unity from out of which all distinctions, all words, meaning and life – but also all silence, nonsense and death – emerge in paradoxical opposition. Reading Spencer Brown not through the prism of mathematics, but as an evocative invitation to engage with the fissures that animate art and human life, highlights the paradoxical interplay of organization and violence; and how tragedy, suffering, sympathy and love should be more prominent in organizational research.