In this edited volume on “algorithmic modernity,” uniting several historians of science, no formal definition for “algorithm” is actually provided. Instead the authors start with popular perceptions of the role of algorithms in society, that is, as instruments of both liberation and alienation in the language as well as in daily life. Consequently, this volume transgresses well-posed definitions to track images thereof in people’s imaginations from roughly the 16th century up to the year 2000, through the prisms of the humanities and some social sciences. Almost no parallels are drawn to philosophy and religious thinking on these topics. As historians often do, the different authors sometimes illustrate their discussion through examples of calculations, processes, or decision making as used in science, education, daily life, or simple computer science. It is stated that this “volume keeps a clear focus on the emergence and continuous reconstitution of algorithmic practices alongside the ascendance of modernity,” and thus a strong research component is claimed inside the humanities.

Each chapter, although often linked to a historical period, highlights some aspects of the evolutions to society brought about by the use of algorithms. Chapter 1 focuses on the links between early geometrical and algebraic constructs to create understanding at different complexity levels. Chapter 2 starts at 1543, analyzing the emergence of some level of reasoning and the concept of misunderstandings or misprision; it criticizes formal approaches as hiding the error-bound roots of reasoning. In contrast, chapter 3 dwells upon a mechanistic understanding of algorithms during the Enlightenment, combined with the abstraction of the symbols involved enabling a universal applicability of reasoning steps. This paves the way for chapter 4’s discussion of the impact on knowledge production in multiple fields of science, creating universal and rule-based precision tools to address empirical problems. Chapter 5 shows how the scope of empirical problems got extended to the commercial arena, offering elements of power to those who could master such tools (even simple ones such as the rule of three). Chapter 6 focuses on two 19th-century mathematicians who promoted empiricism, logic, and inductive reasoning, in contrast to relying on rigor and precision, foreshadowing the use of computers. This trend is further examined in chapter 7, which dissects the practices of Harvard Observatory, around 1870, where manual calculation practices were supplemented by computational cultures (without computers); a comic opera had been created dramatizing workplace stratification and feminization.

The last three chapters deal with how reasoning gets supplemented by computers, and this is before artificial intelligence (AI) thinking emerged in historical waves with its utopian components. Chapter 8 analyzes how algorithmic business management strategies became, in the 1930s, an apparatus for state-driven control of society, for example, in industrial agriculture in relation to quality control; identified ingredients of such control are instability, probabilities, randomization, the law of large numbers, and inferential management. Chapter 9 describes the expansion of this algorithmically regulated control to social, behavioral, and managerial practices in the US, with statistical inference and significance testing as added components. The final chapter (10) demonstrates how number crunching enables black-box software to figure out if an outcome is significant or not, and links it up to supervised learning or decision trees from pattern recognition and AI. A conjecture is offered: the ritualized application of algorithms will soon lead to the termination of theoretical thinking and creative rigor.

The volume includes not only extensive notes for each chapter, but also an exceedingly long bibliography and an index of key people.

This collection of papers is of course relevant to historians of science interested in how information and reasoning have evolved, but also to political scientists seeking historical roots and shifts in the present Information Age and over time.

In view of current ethical and societal challenges, the editors would have been advised to add a transversal analysis of the risks and harms due to algorithmic modernity, and to refine their conjecture(s) by separating out algorithms from heuristics. Taking a wider perspective, maybe the actual and more philosophical research question underlying this volume is the definition of abstract truth and how it gets transformed when used as an instrument of influence.