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The term ‘algorithm’ is believed to derive from the French bastardization of the name of the ninth-century Persian mathematician al-Khwārizmī, the author of the oldest known work of algebra. Being originally employed in medieval Western Europe to indicate the novel calculation methods alternative to those based on Roman numerals, in more recent times the term has come to mean ‘any process of systematic calculation […] that could be carried out automatically’ (Chabert 1999: 2). As Chabert remarks in his book A History of the Algorithm: ‘algorithms have been around since the beginning of time and existed well before a special word had been coined to describe them’ (1999: 1). Euclid’s algorithm for determining the greatest common divisor of two integers, known since the fourth century BCE, is one of the earliest examples.

More generally, algorithms can be intended as computational recipes, that is, step-by-step instructions for transforming input data into a desired output (Gillespie 2014). According to Gillespie (2016: 19), algorithms are essentially operationalized procedures that must be distinguished from both their underlying ‘model’ – the ‘formalization of a problem and its goal, articulated in computational terms’ – and their final context of application, such as the technical infrastructure of a social media platform like Facebook, where sets of algorithms are used to allocate personalized content and ads in users’ feeds. Using a gastronomic metaphor, the step-by-step procedure for cooking an apple pie is the algorithm, the cookbook recipe works as the model, and the kitchen represents the application context. However, in current public and academic discourse, these different components and meanings tend to be conflated, and the term algorithm is broadly employed as a synecdoche for a ‘complex socio-technical assemblage’ (Gillespie 2016: 22).

‘Algorithm’ is thus a slippery umbrella term, which may refer to different things (Seaver 2017). There are many kinds of computational recipes, which vary based on their realms of application as well as on the specific ‘algorithmic techniques’ employed to order information and process data (Rieder 2020). A single task, such as classifying texts by topic, may concern domains as diverse as email ‘spam’ filtering, online content moderation, product recommendation, behavioural targeting, credit scoring, financial trading and more – all of which involve a plethora of possible input data and outputs. Furthermore, text classification tasks can be executed in several – yet all ‘algorithmic’ – ways: by hand, with pen and paper only; through rule-following software applying models predefined by human programmers (e.g. counting topic-related word occurrences within texts); or via ‘intelligent’ machine learning systems that are not explicitly programmed a priori. These latter can be either supervised – i.e. requiring a preliminary training process based on data examples, as in the case of naive Bayes text classifiers (Rieder 2017) – or unsupervised, that is, machine learning techniques working without pre-assigned outputs, like Latent Dirichlet Allocation in the field of topic modeling (Bechmann and Bowker 2019).

This book does not aim to offer heavily technical definitions, nor an introduction to algorithm design and AI technologies; the reader can easily find such notions elsewhere.² Throughout the text, I will frequently make use of the generic terms ‘algorithm’ and ‘machine’ to broadly indicate automated systems producing outputs based on the computational elaboration of input data. However, in order to highlight the sociological relevance of the quali-quantitative transition from Euclid’s calculations to today’s seemingly ‘intelligent’ artificial agents like GPT-3 and AlphaGo, some preliminary conceptual distinctions are needed. It is apparent, in fact, that the everyday socio-cultural implications of algebraic formulas solved for centuries by hand or via mechanical calculators are not even close in magnitude to those of the algorithms currently governing information networks.

Below I briefly outline the history of algorithms and their applications – from ancient algebra to rule-following models running on digital computers, and beyond to platform-based machine learning systems. This socio-technical evolution can be roughly broken into three main eras, visually summarized in Figure 1 at the end of this section. Without pretending to be exhaustive, the proposed periodization focuses especially on the emergence of ‘public relevance algorithms’ (Gillespie 2014: 168), that is, automated systems dealing with the social matter of human knowledge, experience and practice.