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Can you expand on the utility of categories here? There's a lot of space between knowing what defines a monad, when something might be a monad, what you can do
by Y_Y 5y ago
Can you expand on the utility of categories here? There's a lot of space between knowing what defines a monad, when something might be a monad, what you can do with monadic structure etc.
Of course if an AI truly understood monads I it would be a bright line marking where the machines have finally surpassed the human mind.
Cool.
- archibaldJ 5y agoI think it's closely linked to the notions of semantics as approached in CS (ie. PLT) v.s. in linguistics where we are mostly concerned with the "micro-structures" and "meso-structures" that gave rise to qualia we humans experience (e.g. therefore languages with different structural systems such as English vs Chinese encode concepts (as well as intentions) very differently; (for an illustration, see Interality as a Key to Deciphering Guiguzi: A Challenge to Critics [1])), and not so much about how evaluation and execution came about (e.g. as studied from a compiler's persective in denotational semantics, or a more functional perspective in operational semantics, where things like natural transformations are ubiquitous) [1]: https://cjc-online.ca/index.php/journal/article/view/3187/3258 https://cjc-online.ca/index.php/journal/article/view/3187/32... And so categories naturally come in as a way to bridge and compose these two worlds, and that's just the beginning. There're so much more we don't understand yet, such as what understanding really is given a certain set of contexts and constraints as well as in regards to their relaxations. What is understanding if there are no doings? And what is doing with no understandings? How do things compose? These are great mysteries.
- Y_Y 5y ago> How do things compose? I think you pretty much summed it up right there.