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Language and the Rise of the Algorithm

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.


Language and the Rise of the Algorithm is an original and insightful, not to mention magisterial, work. Jeffrey M. Binder’s mastery of startlingly diverse sources—philosophical, mathematical, and literary—spread over four centuries is enormously impressive. His command of scholarly fields ranging from Renaissance theories of language to modern computer science is both broad and deep, and his knowledge of the lives and thought of dozens of characters, some famous, others less so, is nothing less than encyclopedic. Most critically, however, the book’s argument is both timely and compelling. In an age when boundaries between human and machine are tested as never before, Binder offers an insightful analysis of the present moment and a powerful narrative of how we got to this point.”

Amir Alexander, University of California, Los Angeles

“In order to better understand—and perhaps transform—our understanding of algorithms in the present, Jeffrey M. Binder argues persuasively that we need to reopen historical debates on the relationship between language and symbols. Language and the Rise of the Algorithm is a welcome addition to the history of computing that convincingly demonstrates the line between technical algorithms and their social meanings is, itself, socially constructed.”

Jessica Otis, George Mason University

“Jeffrey M. Binder has written a wonderful, thought-provoking book on the relationship between theories of language and symbolism in mathematics. Language and the Rise of the Algorithm has much to offer to the digital humanities and media studies, but this important work will also be read and studied with interest by historians of science and technology.”

Alma Steingart, Columbia University

Table of Contents

Chapter One
   Symbols and Language in the Early Modern Period
Chapter Two
   The Matter Out of Which Thought Is Formed
Chapter Three
   Symbols and the Enlightened Mind
Chapter Four
   Language without Things
Chapter Five
   Mass Produced Software Components
   The Age of Arbitrariness

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