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What Is an Algorithm?

Matteo Pasquinelli:

"The term “algorithm” comes from the Latinization of the name of the Persian scholar al-Khwarizmi. His tract On the Calculation with Hindu Numerals, written in Baghdad in the ninth century, is responsible for introducing Hindu numerals to the West, along with the corresponding new techniques for calculating them, namely algorithms. In fact, the medieval Latin word “algorismus” referred to the procedures and shortcuts for carrying out the four fundamental mathematical operations—addition, subtraction, multiplication, and division—with Hindu numerals. Later, the term “algorithm” would metaphorically denote any step-by-step logical procedure and become the core of computing logic. In general, we can distinguish three stages in the history of the algorithm: in ancient times, the algorithm can be recognized in procedures and codified rituals to achieve a specific goal and transmit rules; in the Middle Ages, the algorithm was the name of a procedure to help mathematical operations; in modern times, the algorithm qua logical procedure becomes fully mechanized and automated by machines and then digital computers.

Looking at ancient practices such as the Agnicayana ritual and the Hindu rules for calculation, we can sketch a basic definition of “algorithm” that is compatible with modern computer science: (1) an algorithm is an abstract diagram that emerges from the repetition of a process, an organization of time, space, labor, and operations: it is not a rule that is invented from above but emerges from below; (2) an algorithm is the division of this process into finite steps in order to perform and control it efficiently; (3) an algorithm is a solution to a problem, an invention that bootstraps beyond the constrains of the situation: any algorithm is a trick; (4) most importantly, an algorithm is an economic process, as it must employ the least amount of resources in terms of space, time, and energy, adapting to the limits of the situation.

Today, amidst the expanding capacities of AI, there is a tendency to perceive algorithms as an application or imposition of abstract mathematical ideas upon concrete data. On the contrary, the genealogy of the algorithm shows that its form has emerged from material practices, from a mundane division of space, time, labor, and social relations. Ritual procedures, social routines, and the organization of space and time are the source of algorithms, and in this sense they existed even before the rise of complex cultural systems such as mythology, religion, and especially language. In terms of anthropogenesis, it could be said that algorithmic processes encoded into social practices and rituals were what made numbers and numerical technologies emerge, and not the other way around. Modern computation, just looking at its industrial genealogy in the workshops studied by both Charles Babbage and Karl Marx, evolved gradually from concrete towards increasingly abstract forms."



Matteo Pasquinelli:

"In a fascinating myth of cosmogenesis from the ancient Vedas, it is said that the god Prajapati was shattered into pieces by the act of creating the universe. After the birth of the world, the supreme god is found dismembered, undone. In the corresponding Agnicayana ritual, Hindu devotees symbolically recompose the fragmented body of the god by building a fire altar according to an elaborate geometric plan. The fire altar is laid down by aligning thousands of bricks of precise shape and size to create the profile of a falcon. Each brick is numbered and placed while reciting its dedicated mantra, following step-by-step instructions. Each layer of the altar is built on top of the previous one, conforming to the same area and shape. Solving a logical riddle that is the key of the ritual, each layer must keep the same shape and area of the contiguous ones, but using a different configuration of bricks. Finally, the falcon altar must face east, a prelude to the symbolic flight of the reconstructed god towards the rising sun—an example of divine reincarnation by geometric means.

The Agnicayana ritual is described in the Shulba Sutras, composed around 800 BCE in India to record a much older oral tradition. The Shulba Sutras teach the construction of altars of specific geometric forms to secure gifts from the gods: for instance, they suggest that “those who wish to destroy existing and future enemies should construct a fire-altar in the form of a rhombus.” The complex falcon shape of the Agnicayana evolved gradually from a schematic composition of only seven squares. In the Vedic tradition, it is said that the Rishi vital spirits created seven square-shaped Purusha (cosmic entities, or persons) that together composed a single body, and it was from this form that Prajapati emerged once again. While art historian Wilhelm Worringer argued in 1907 that primordial art was born in the abstract line found in cave graffiti, one may assume that the artistic gesture also emerged through the composing of segments and fractions, introducing forms and geometric techniques of growing complexity. In his studies of Vedic mathematics, Italian mathematician Paolo Zellini has discovered that the Agnicayana ritual was used to transmit techniques of geometric approximation and incremental growth—in other words, algorithmic techniques—comparable to the modern calculus of Leibniz and Newton. Agnicayana is among the most ancient documented rituals still practiced today in India, and a primordial example of algorithmic culture.

But how can we define a ritual as ancient as the Agnicayana as algorithmic? To many, it may appear an act of cultural appropriation to read ancient cultures through the paradigm of the latest technologies. Nevertheless, claiming that abstract techniques of knowledge and artificial metalanguages belong uniquely to the modern industrial West is not only historically inaccurate but also an act and one of implicit epistemic colonialism towards cultures of other places and other times. The French mathematician Jean-Luc Chabert has noted that “algorithms have been around since the beginning of time and existed well before a special word had been coined to describe them. Algorithms are simply a set of step by step instructions, to be carried out quite mechanically, so as to achieve some desired result.” Today some may see algorithms as a recent technological innovation implementing abstract mathematical principles. On the contrary, algorithms are among the most ancient and material practices, predating many human tools and all modern machines:

Algorithms are not confined to mathematics … The Babylonians used them for deciding points of law, Latin teachers used them to get the grammar right, and they have been used in all cultures for predicting the future, for deciding medical treatment, or for preparing food … We therefore speak of recipes, rules, techniques, processes, procedures, methods, etc., using the same word to apply to different situations. The Chinese, for example, use the word shu (meaning rule, process or stratagem) both for mathematics and in martial arts … In the end, the term algorithm has come to mean any process of systematic calculation, that is a process that could be carried out automatically. Today, principally because of the influence of computing, the idea of finiteness has entered into the meaning of algorithm as an essential element, distinguishing it from vaguer notions such as process, method or technique.

Before the consolidation of mathematics and geometry, ancient civilizations were already big machines of social segmentation that marked human bodies and territories with abstractions that remained, and continue to remain, operative for millennia. Drawing also on the work of historian Lewis Mumford, Gilles Deleuze and Félix Guattari offered a list of such old techniques of abstraction and social segmentation: “tattooing, excising, incising, carving, scarifying, mutilating, encircling, and initiating.” Numbers were already components of the “primitive abstract machines” of social segmentation and territorialization that would make human culture emerge: the first recorded census, for instance, took place around 3800 BCE in Mesopotamia. Logical forms that were made out of social ones, numbers materially emerged through labor and rituals, discipline and power, marking and repetition.

In the 1970s, the field of “ethnomathematics” began to foster a break from the Platonic loops of elite mathematics, revealing the historical subjects behind computation. The political question at the center of the current debate on computation and the politics of algorithms is ultimately very simple, as Diane Nelson has reminded us: Who counts? Who computes? Algorithms and machines do not compute for themselves; they always compute for someone else, for institutions and markets, for industries and armies."