Purpose

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.”

Design/methodology/approach

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, −}.

Findings

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.

Originality/value

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.

中文翻译：

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表格的数字分析

目的

本文旨在展示社会学描述——对纳粹独裁统治的群体分析——最初是用从乔治·斯宾塞-布朗的《指示演算》中借来的手段进行的，如何转化为数字电路，以及使用哪些数字数学方法和工具来实现这一点。可以分析和描述数字电路的行为。因此，本文还旨在帮助更好地理解“形式法则”第 11 章。

设计/方法/方法

该分析将自动机理论的方法用于有限的确定性自动机。数字数学的基本集合运算和布尔微分的特殊集合运算用于计算数字电路。所使用的软件基于三元逻辑，其中元素{0, 1}的二进制布尔逻辑由第三个元素“Don't care”扩展为{0, 1, -}。

发现

本文确认了将形式转换为数字电路的方法，该方法源自“形式法则”第 11 章中调制器的比较功能和结构分析，并定义了这种转换的一般规则。展示了如何使用自动机理论的方法在时间媒介中解决可重入形式的不确定性。在此基础上，提出了一种形式度的细化定义。

原创性/价值

该论文展示了社会学和信息技术之间跨学科方法的潜力，并提供了数字数学的方法和工具，如三元逻辑、布尔微分和自动机理论，以应用于社会学。