Kyle had a nice post on programming and how those symbolic systems evolve that's worth a read. On a secant, it reminds me of Brian Rotman's book Mathematics as Sign which is one of my all time favorite books. I'll have my ai amenuesis pull up a summary and draw out connects at the end.
\n\n\n\n1/ Programming has a strange relationship to nature.
\nAt the bottom, we’re stuck with hard constraints: computability, information theory, memory, latency, the speed of light, heat, hardware failure.
\nThese are not negotiable. We discover them.
\nBut software also lets us create new effective laws almost at will.
\n2/ A filesystem says these bits are a file, files have names, directories contain files, bytes persist after a process exits.
\nA database says a transaction is atomic—even though underneath, hundreds of fallible physical operations happen over time.
\nA language invents objects, types, promises, ownership.
\nNone of these things exist in physics. We made them up.
\nAnd then something curious happens: once we make them up, we have to start discovering their consequences.
\n3/ Humans invented the rules of chess, but we didn’t invent the fact that some position is mate in seven.
\nOnce the rules exist, objective facts about that world follow from them.
\nSoftware is like this everywhere.
\nWe choose transaction semantics and discover anomalies. We invent a rendering model and discover what identity must mean inside it. We define a protocol and discover behaviors nobody explicitly designed, but which follow inevitably from its rules.
\nAt the layer where you create an abstraction, you’re a legislator.
\nOne layer above, you’re a physicist.
\n4/ This is what makes abstractions so powerful: they don’t merely save code. They refactor reality for everything above them.
\nOnce the machinery is reliable enough, the upper layer stops seeing the mess below. It inhabits a simpler world with different apparent laws.
\nVenkatesh Rao’s “New Nature” is useful here: technology accumulates artificial lawfulness until it becomes part of the environment itself.
\nProgrammers do this recursively, at tiny scales, every day.
\n5/ Dennett’s idea of “cranes” explains how these worlds accumulate.
\nEvolution doesn’t start from scratch. Once it discovers a useful mechanism, that mechanism becomes part of the platform from which further complexity can emerge.
\nSoftware abstractions do the same.
\nFilesystems, databases, protocols, type systems, frameworks: each packages previous discoveries into structure that future systems simply assume.
\nA framework isn’t merely reusable code.
\nIt’s reusable theory—accumulated search the next program doesn’t have to repeat.
\n6/ So there’s a recursive process:
\ndiscovery → theory → mechanism → law → nature → new discovery
\nWe discover something about a world. We encode the discovery into an abstraction. The abstraction becomes part of the environment. The next programmer encounters our invention as nature and starts discovering its laws in turn.
\nSoftware is, in this sense, recursive nature-making.
\n\n
And as promised here is a GBG style connection.
\n[Rotman's starting move is to treat mathematics as a written, semiotic practice rather than a window onto a Platonic realm. Mathematics is something people do with marks on paper, chalk on boards, and diagrams. The question he keeps asking is: what kind of activity is this, and who is doing it?
\nHis answer is a three-part model of the mathematician:
\nMathematical reasoning, on this view, is a kind of disciplined thought experiment. The Subject imagines the Agent executing a procedure ("add one, then repeat") and predicts what it would produce. Proof persuades because it convinces us that the Agent's run would go a certain way. Rotman is explicit that this Agent looks a lot like a computer running a program, and that mathematical texts read like code addressed to it. He notices the two kinds of imperatives in mathematical writing:
\nThe essays build out from there. He looks at diagrams as genuine instruments of thought rather than mere illustrations, and at the "technology of persuasion" that makes a proof land. Then comes the more polemical turn of "taking God out of mathematics and putting the body back in." Classical mathematics quietly endows its Agent with godlike powers: it can count forever and complete infinite tasks. Rotman asks what happens if you take the physical limits of real counting seriously, including memory, energy, time, and the finite universe. The result is his sketch of a "non-Euclidean" arithmetic of physically realizable numbers, where iteration isn't presumed to go on without end.
\nThe resonance with Kyle's post is pretty direct. Kyle's legislator/physicist split is almost exactly Rotman's account of how invented signs yield discovered truths. We write the Code; the Agent's imagined behavior under it is then something we have to find out, just as nobody legislated mate-in-seven. Rotman dissolves the old fight between "math is invented" and "math is discovered" the same way Kyle dissolves it for software. Both are true, at different layers.
\nRotman's critique of the infinite Agent also lines up with Kyle's first point. Underneath every clean abstraction sit non-negotiable physical constraints: memory, latency, heat. Mathematics, like software, works by building an Agent that doesn't see that mess. The upper layer inhabits a simpler world with tidier laws. Rotman's contribution is to remind us that this simpler world is an achievement of sign-making, not a given. It's worth remembering which constraints got idealized away to produce it. In Kyle's terms, mathematics is one of the oldest cases of recursive nature-making. It is so successful that we forgot the Agent was imaginary and started treating its world as the real one.]
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