Prologue We usually treat mathematical structures as things we look at—diagrams on a page, symbols in a line, objects to be manipulated by the intellect. But they are not objects. They are environments. They are the invisible architectures that determine what is possible, what is impossible, and what is necessary. You do not just solve … Continue reading The Axiom Engine: A Phenomenology of Abstract Structures
Tag: freedom
Constraints Liberate, Liberties Constrain
https://www.youtube.com/watch?v=GqmsQeSzMdw Interesting throughout. Main points: Build in abstractions, with symbols and functions.Counter-intuitively, abstractions make precision possible.The more expressive a language, the more ambiguous the content.Or more generally, freedom at one level implies constraints at another level.Plan for interoperability and extension, which also implies limits.As much authority is necessary, but no more.The more something can do, … Continue reading Constraints Liberate, Liberties Constrain
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