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The Relevance of Algorithms

How would we begin to look at the pro­duc­tion of the algo­rith­mic? Not the pro­duc­tion of algo­rithms, but the pro­duc­tion of the algo­rith­mic as a jus­ti­fi­able, legit­i­mate mech­a­nism for knowl­edge pro­duc­tion. Where is that being estab­lished and how do we exam­ine it?