5 ms·
There's maybe a two-to-three-order-of-magnitude difference between the difficulty of monads and the difficulty of this stuff.
by gjm11 2y ago
There's maybe a two-to-three-order-of-magnitude difference between the difficulty of monads and the difficulty of this stuff.
- mrtranscendence 2y agoMonads are just monoids in the category of endofunctors, after all.
- jacknews 2y agoof course my post was slightly a joke but is the relative difficulty, in human understanding, or a 'fundamental' difference in complexity? surely the later is something mathematicians can and have measured?
- tux3 2y agoComplexity has different meanings. People don't generally go and assign objective metrics of complexity to proofs, besides how long it is. You could try to draw the stack of abstractions necessary to understand the proof and see how high it stacks, and you could try to call that fundamental complexity, but I don't think many people would be happy with that. So yes, it's a difficulty in human understanding. What else could it be?
- thaumasiotes 2y agoIt's very common to track how many different axioms are needed for some result, and consider results with lower requirements to be more fundamental. "Less complex", probably not so much, but the issue is something that a number of people care about.
- tux3 2y agoVery common might vary by area. If you work near the foundations, I could see that, sure.