Nice if it is a general feature of heavy-tailed distributions. Why do we expect tasks to be heavy tailed? It has some intuitive force certainly. Do you know of a formal argument?
The time to complete a task using a certain approach should be heavy-tailed because most approaches don’t work or are extremely impractical compared to the best ones. Suppose you’re trying to write an O(n log n) sorting algorithm. Mergesort is maybe easy to think of, heapsort would require you to invent heaps and take maybe 10x more time, and most ideas out of the space of all possible ideas don’t work at all. So the time for different approaches definitely spans many orders of magnitude.
The speed at which humans can do various cognitive subtasks also differs by orders of magnitude. Grandmasters can play chess >1000 times faster at equal skill level than lesser players, as evidenced by simuls. Filling in a clue in a crossword sometimes takes me 1 second but other times might take me an hour or longer if I didn’t give up first.
Nice if it is a general feature of heavy-tailed distributions. Why do we expect tasks to be heavy tailed? It has some intuitive force certainly. Do you know of a formal argument?
The time to complete a task using a certain approach should be heavy-tailed because most approaches don’t work or are extremely impractical compared to the best ones. Suppose you’re trying to write an O(n log n) sorting algorithm. Mergesort is maybe easy to think of, heapsort would require you to invent heaps and take maybe 10x more time, and most ideas out of the space of all possible ideas don’t work at all. So the time for different approaches definitely spans many orders of magnitude.
The speed at which humans can do various cognitive subtasks also differs by orders of magnitude. Grandmasters can play chess >1000 times faster at equal skill level than lesser players, as evidenced by simuls. Filling in a clue in a crossword sometimes takes me 1 second but other times might take me an hour or longer if I didn’t give up first.