It dates back at least to Adam Smith’s exposition in The Wealth of Nations (1776), which Hegel also commented upon already in his Jena lectures (1805–6). The thesis that labor has to become “mechanical” on its own, before machinery replaces it, is an old fundamental principle that has simply been forgotten. To affirm, as did the introduction, that labor is a logical activity is not a way of abdicating to the mentality of industrial machines and corporate algorithms, but rather of recognizing that human praxis expresses its own logic (an anti-logic, some might say)-a power of speculation and invention, before techno-science captures and alienates it. The initial chapter emphasized this aspect by highlighting how ancient rituals, counting tools, and “social algorithms” all contributed to the making of mathematical ideas. ![]() The concern, however, has not been to repeat the separation of the concrete and abstract domains but to see their coevolution throughout history: eventually to investigate labor, rules, and automation, dialectically, as material abstractions. This book began with a simple question: What relation exists between labor, rules, and automation, i.e., the invention of new technologies? To answer this question, it has illuminated practices, machines, and algorithms from different perspectives-from the “concrete” dimension of production and the “abstract” dimension of disciplines such as mathematics and computer science. In the 1890s, the German anatomist Christian Wilhelm Braune and Otto Fischer published a series of papers on the biomechanics of human gait under loaded and unloaded conditions. The analogy is relevant, I think, for all machines and also for machine learning, whose abstract models do in reality encode a concretion of social relations and collective behaviors, as this book has tried to demonstrate in reformulating the nineteenth-century labor theory of automation for the age of AI. 4 In the passage from Capital quoted above, Marx suggested a similar analogy that resonates with today’s science and technology studies: in the same way in which fossil bones disclose the nature of ancient species and the ecosystems in which they lived, similarly, technical artifacts reveal the form of the society that surrounds and runs them. There will be a day in the future when current AI will be considered an archaism, one technical fossil to study among others. Instruments of labour not only supply a standard of the degree of development which human labour has attained, but they also indicate the social relations within which men work. It is not what is made but how, and by what instruments of labour, that distinguishes different economic epochs. Relics of bygone instruments of labour possess the same importance for the investigation of extinct economic formations of society as do fossil bones for the determination of extinct species of animals. Politically Mathematics manifesto, 2019 2 Like any other human activity, it carries the possibilities of both emancipation and oppression. ![]() With digital data, mathematics has become the dominant means in which human beings coordinate with technology … Mathematics is a human activity after all. The social law has become interwoven with models, theorems and algorithms. ![]() We live in the age of digital data, and in that age mathematics has become the parliament of politics. How do the tools work? Who finances and builds them, and how are they used? Whom do they enrich, and whom do they impoverish? What futures do they make feasible, and which ones do they foreclose? We’re not looking for answers.
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