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This is the URL I'm sending people to when I want to point out just how far domain-specific gibberish can go. Or just to mess with people... "I was looking fo

This is the URL I'm sending people to when I want to point out just how far domain-specific gibberish can go. Or just to mess with people... "I was looking for an experimental proof assistant for synthetic ∞-categories and stumbled across this awesome project..." "It's wicked cool! It uses a version of second-order abstract syntax which is great for lambda extraction." The project description sounds like something that MIT automated gibberish research paper generator would come up with.

mathisfun123 3y ago
what is the substance of this complaint? if i pull the API for django or react or ...anything else, how much should i be expected to understand without any prior exposure? how is "domain-specific gibberish" any different? you make up words to represent groups of other words in order to capture concepts. it's literally just how language works. let me translate for you: proof assistant: program that checks your work (writing a proof) and helps you find new proofs. synthetic: math where the axioms "represent" the objects instead of the other way around (they're "synthesized" from the objects) 1-category: a collection with objects and functions between them 2-category: a collection with objects, functions between them, and functions between those functions (called homotopies) k-category: you get the idea ∞-category: the limit as k -> ∞ second-order abstract syntax which is great for lambda extraction: syntax specifically suited for this kind of stuff and you know what? even though i am not a category theorist i was able to figure this out. you know how? i quickly skimmed the "docs" https://ncatlab.org/nlab/show/synthetic+%28infinity%2C1%29-category+theory https://ncatlab.org/nlab/show/synthetic+%28infinity%2C1%29-c...
- danidiaz 3y ago
  I'm not a mathematician, but I feel the "syntethic"/"analythic" distinction in mathematics is an interesting and useful concept. "In modern mathematics, an analytic theory is one whose basic objects are defined in some other theory, whereas a synthetic theory is one whose basic objects are undefined terms given meaning by rules and axioms"—Michael Shulman In programming terms, I guess "synthetic" mathematics feels a bit like programming to an abstract interface. https://ncatlab.org/nlab/show/synthetic+mathematics https://ncatlab.org/nlab/show/synthetic+mathematics In the first part of this video Cédric Villani gives (in French) a nice explanation of the distinction: https://youtu.be/xzVk56EKBUI?t=258 https://youtu.be/xzVk56EKBUI?t=258 Edit: an English explanation, also by Villani: https://www.youtube.com/watch?v=AIrLXbwyYXQ https://www.youtube.com/watch?v=AIrLXbwyYXQ
- electrozav 3y ago
  I didn't read it as a complaint, more of a humorous observation. Either way, there's no need to get aggressive onto someone that hasn't figured it out yet.

mathisfun123 3y ago

what is the substance of this complaint? if i pull the API for django or react or ...anything else, how much should i be expected to understand without any prior exposure? how is "domain-specific gibberish" any different? you make up words to represent groups of other words in order to capture concepts. it's literally just how language works. let me translate for you: proof assistant: program that checks your work (writing a proof) and helps you find new proofs. synthetic: math where the axioms "represent" the objects instead of the other way around (they're "synthesized" from the objects) 1-category: a collection with objects and functions between them 2-category: a collection with objects, functions between them, and functions between those functions (called homotopies) k-category: you get the idea ∞-category: the limit as k -> ∞ second-order abstract syntax which is great for lambda extraction: syntax specifically suited for this kind of stuff and you know what? even though i am not a category theorist i was able to figure this out. you know how? i quickly skimmed the "docs" https://ncatlab.org/nlab/show/synthetic+%28infinity%2C1%29-category+theory https://ncatlab.org/nlab/show/synthetic+%28infinity%2C1%29-c...

danidiaz 3y ago
I'm not a mathematician, but I feel the "syntethic"/"analythic" distinction in mathematics is an interesting and useful concept. "In modern mathematics, an analytic theory is one whose basic objects are defined in some other theory, whereas a synthetic theory is one whose basic objects are undefined terms given meaning by rules and axioms"—Michael Shulman In programming terms, I guess "synthetic" mathematics feels a bit like programming to an abstract interface. https://ncatlab.org/nlab/show/synthetic+mathematics https://ncatlab.org/nlab/show/synthetic+mathematics In the first part of this video Cédric Villani gives (in French) a nice explanation of the distinction: https://youtu.be/xzVk56EKBUI?t=258 https://youtu.be/xzVk56EKBUI?t=258 Edit: an English explanation, also by Villani: https://www.youtube.com/watch?v=AIrLXbwyYXQ https://www.youtube.com/watch?v=AIrLXbwyYXQ
electrozav 3y ago
I didn't read it as a complaint, more of a humorous observation. Either way, there's no need to get aggressive onto someone that hasn't figured it out yet.