Ilm Al-raml: A Case Study in Mathematizing Divination Systems Using Modular Arithmetic

Abstract

The study of divination and divination systems, particularly in non-technological societies, presents a set of unusual problems that challenge the core of rational and epistemic thought. Notwithstanding the bulk of research on cultural genres such as religion, magic, and myth, efforts fall short of distinguishing the constituent theoretical and ontological underpinnings of divinatory practices. Employing modular arithmetic principles, this study proposes a case for situating mathematical concepts within atypical cultural and historical contexts that essentialize mathematical thought as embodied expressions of human endeavors. This article presents an investigation into the mathematical structures underlying an ancient historical and cultural divination practice known as ilm al-raml (Arabic translation of sand science). Principled by sociohistorical and sociocultural lenses, the study employs an ethnomathematical methodology. Coined by D’Ambrosio (1985 , 1999 ) and Knijnik’s (2000) seminal ethnographic research, ethnomathematical methodology can be interpreted as delineating a way to track and analyze the processes of generation, transmission, diffusion, and formalization of mathematical knowledge in diverse cultural systems. By reflecting on the concepts of synchronicity and acausal events, I show that ilm al-raml presents an algorithmic divination system that is based on fundamental computational rules based on Boolean algebra laws with a probabilistic time ordering of events specifically designed to predict future outcomes.