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You might be looking for a kind of understanding that doesn't exist in math. John von Neumann said, "In mathematics, you don't understand things. You just get u
by dkarl 2y ago
You might be looking for a kind of understanding that doesn't exist in math. John von Neumann said, "In mathematics, you don't understand things. You just get used to them." So even one of the greatest mathematicians of all time didn't feel like he "understood" concepts that he was adept at applying to both abstract and real-world problems.
This is why there are monad tutorials that use dozens of different analogies for monads, and nobody feels like they understand anything better after reading them. But if you use monads enough, eventually you get used to how they work and how to accomplish things with them. And then you stop caring if you "understand" them.
- Krei-se 2y agoSpeak for yourself, monads are easily understood from the philosophical pov: https://en.wikipedia.org/wiki/Monad_(philosophy) https://en.wikipedia.org/wiki/Monad_(philosophy) which they are derived from in category theory, so maybe go that way if you still need foundation for the concept of the concept that bore all concepts?
- School-Cotton 2y agoAs far as I can tell this is totally unrelated to the concept of monad in mathematics or programming.
- ahoka 2y agoHow does it make it easy? That’s like saying to understand object oriented programming one just needs to study Plat’s theory of forms.
- Krei-se 2y agoIts the point where you start from in CT. Having the problem of not being able to talk about a concept is the absurd function and part of Chapter 1 (!!) in books about category theory. So instead of circling around this topic, welcome, this means you are inside the problem domain of category theory ;)
- Koshkin 2y agoNot such a bad idea TBH
- dkarl 2y agoEasily understood? Looking at that link, the term has been used by many different philosophers with many different meanings. Leibniz's monads are the most famous, and they have nothing in common with category theory monads except the name.[0] The mathematical concept was in use for years before anybody decided to call it a "monad" anyway. According to Wikipedia: "The notion of monad was invented by Roger Godement in 1958 under the name 'standard construction'. Monad has been called 'dual standard construction', 'triple', 'monoid' and 'triad'. The term 'monad' is used at latest 1967, by Jean Bénabou."[1] [0] https://en.wikipedia.org/wiki/Monadology#Summary https://en.wikipedia.org/wiki/Monadology#Summary [1] https://en.wikipedia.org/wiki/Monad_(category_theory)#Terminological_history https://en.wikipedia.org/wiki/Monad_(category_theory)#Termin...
- Krei-se 2y agoSo what? If you call it god around 0 BC and monad in the 1970 it's still the same concept. If the notation and meanings change in your pov and that gives you headaches, that's maybe related to the fact, that you cannot call an absurd function, but you can derive structure from combining it.
- jasomill 2y agoIn other words, God is just a monoid in the category of endofunctors‽
- Krei-se 2y agoIs this taken word by word from wikipedia? A monad is an entity that has no purpose other than relation to itself, but can be part of a structure that employs functionality or meaning. I think the problems around this concept for most is, that causality is not a requirement yet, so things don't have to make sense to be part of constructing upon them. An analogy in IT might be, that worrying about traversal of a graph is a problem domain in time and space and causality that involves questions around loop detection and recursion because you deal from a pov that has those constraints. But that's not a problem yet in the domain of structure as it. This took some brain, so i hope it's a good try on explanation.
- chongli 2y agoCategory theory does not derive the idea of a monad from philosophy, it merely reuses the word for an entirely unrelated purpose. It's like how a frog [1] to a farrier has nothing to do with the frog [2] from everyday use, nor to the frog [3] from railroading. [1] https://en.wikipedia.org/wiki/Frog_(horse_anatomy) https://en.wikipedia.org/wiki/Frog_(horse_anatomy) [2] https://en.wikipedia.org/wiki/Frog https://en.wikipedia.org/wiki/Frog [3] https://en.wikipedia.org/wiki/Frog_(disambiguation)#Railroads https://en.wikipedia.org/wiki/Frog_(disambiguation)#Railroad...
- grugagag 2y agoIf it is intuitive understanding you’re talking about then I feel that there are things in math that are more intuitive and less intuitive and harder to grasp.