Technology and Culture

Language and the Rise of the Algorithm is a timely book. In the last two decades, the notion of an algorithm has turned from an abstract mathematical concept into an opaque predictive machine learning system, while large language models such as GPT-4 are forcing us to revisit the relationship between algorithms and natural language. This book puts such developments into a much-needed context. It follows the history of symbolic abstraction underlying the notion of an algorithm, starting from the early modern period, and shows that the nature of the algorithm and its relationship to language has undergone multiple transformations over time.

The main focus of the book is on the notions of a universal language and an algorithm, representing "hard" logic on the one hand, and their [End Page 427] relationships to natural language, representing "soft," messy human communication on the other. In the first four chapters, the book follows the emergence of symbolic notations and attempts to create universal languages by Gottfried Wilhelm Leibniz and Nicolas de Condorcet, as well as George Boole's system, which eventually developed into Boolean logic. In those developments, we see the changing relationship between symbolic systems and the messy world. For Leibniz, learning his universal language "does not involve learning a new set of ideas [because] the notions are already there in the mind" (p. 67). The symbols of the universal language represented idealized real-world concepts. For Boole, symbols became arbitrary abstract signs. His system "would include no encyclopedic catalog of things" and focused instead on capturing structural relationships: "Making its results meaningful was a matter of interpretation" (p. 126).

In the last chapter and the coda, the book moves to the discussion of algorithms in computer science, the ALGOL programming language, the recent recasting of algorithms as predictive machine learning systems, and finally, the emerging large language models. The relationship between symbols and the messy world is reversed again. In ALGOL, symbols are "arbitrary tokens with no inherent meanings beyond the roles assigned to them in code" (p. 223), while large language models are rooted in "people's linguistic practices" and make it hard "to judge where algorithm ends and language begins" (p. 3).

The parallels between the precomputer era of algebra and the modern era of programming are inspiring, but they require careful reading. Binder is cautious not to suggest that a particular development in programming languages was directly influenced by algebra. Following how exactly abstract symbols and the notion of an algorithm entered the world of computing remains an intriguing task for historians, who can draw inspiration from the studies of the notions of a program (De Mol and Bullynck, "Roots of 'Program' Revisited," 2021) and programming language (Nofre, Priestley, and Alberts, "When Technology Became Language," 2014). For symbolic notations, much remains to be said. The first symbolic names in the early assembly languages, preceding ALGOL, were far from arbitrary—they referred to physical storage locations (accumulators) of the computers.

For historians of technology, the book provides a welcome framing for thinking about algorithms. The transformations documented by Binder provide the backdrop for discussing the emergence of algorithmic bias and societal shifts that will inevitably come with the rise of large language models. The transformations of the notion of an algorithm, finely documented by Binder, also point to a more general problem in the epistemology of computing. Other computer science concepts have evolved too, and with a few exceptions (such as Kell's brief essay, "In Search of Types," 2014), those key transformations remain invisible. Even if we uncover such transformations, how should we engage with such elusive concepts? [End Page 428]

Binder's book should also be of interest to technologists designing new programming systems. An intriguing thread documented in the book is the role of abstraction. In the case of algebra and computer science algorithms, abstraction allowed them to develop independently of specific applications and be applicable to any domain. At the same time, abstraction disconnected computation from communication and...