Conversation

If you assume the average span of control in the world is 7, the hierarchy of the world would have ~12 levels 🤔
3
28
L10 in faang is really just L7 in the world org chart POTUS is like L8. The top 4 levels of world org chart, about 400 people, are full of transient people who have no idea they’re there and don’t care. The top person lasts less than a day in the job.
6
33
I’ve always known the heuristic that the height of a hierarchy scales roughly as log_(span-of-control)(group size), but never thought to derive it: For a full hierarchy of large group size P, and span of control S<<P, if the height is k levels, then k_approx = log_S(P) Why?…
1
4
If hierarchy is full 1+S+S^2+…+S^k=P (S^(k+1)-1)/(S-1)=P //sum of squares formula S^(k+1)=(S-1)P+1 k=log((S-1)P+1)/log(S)-1 If P is very large k~=log((S-1)P)/log(S) = log(S-1)/log(S)+log(P)/log(S) ~= 1+log(P)/log(S) k_approx = log_S(P)+1
1
1
#FermiEstimation is fun The visual intuition here is that if you draw the hierarchy, the branching factor is 7 (or whatever the span of control is) so obviously you raise that by powers as you add levels, which means you have to take a log with 7 as base to get the height
1
2