A wide-ranging history of the algorithm.

Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians well before the computer age: How do you draw the line between computational rules and the complexities of making systems comprehensible to people? By attending to this question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day.
 
Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz’s calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole’s nineteenth-century logic system; and the early programming language ALGOL, short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. Machine learning, in its increasing dependence on words, erodes the line between technical and everyday language, revealing the urgent stakes underlying this boundary.
 
The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction.

"“Binder’s book is excellent and if you have any interest in the topic at all then you should definitely read it. It certainly has the potential to become a classic in the tangled field of the histories of mathematics, language, logic, and computer science. . . . In his journey from al-Khwārizmī to GPT-3 Binder covers an incredible amount of complex material in a comparatively small number of pages. However, his writing is never cluttered or in any way incomprehensible; it is always clear, lucid, and easy to follow . . .”" - Renaissance Mathematicus

"“This book is a tightly packed, erudite contribution to the growing concern in the Humanities with algorithms.”" - LSE Review of Books

"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." - Technology and Culture

"This book offers a historical examination of the development of algorithmic expression. Binder brings together the histories of mathematics, computer science, and linguistics . . . This scholarly work with its extensive bibliography should appeal to a wide range of readers with interests encompassing the respective histories of language and computer science. The book should be in all university libraries." - Choice