On remediation: Media, repair, and the discipline of fantasy in the theory and practice of algorithmic modernity

Nothing ever works quite as imagined. When algorithms and mathematical systems work, to the extent they do, imagination makes all the difference. Work, imagination, and the space between them manifest in mediated practices of conceptual figuration sustained through regimes of remediation: repair, correction, backfilling, but also (as a pun) patterns of mediation and material transmutation. Such remediation links algorithmic practice and fantasy from early modernity to the present, from the elementary to the elite. It makes whole small errors and grand systems alike. I explore these remediations and their relationship to materials, labor, and fantasy through an episodic account of sixteenth-century arithmetic, nineteenth-century blackboards, twentieth-century projects to create global infrastructures and universal foundations, and twenty-first-century tests of the promises and limits of mediated imagination in mathematics.