If you assume the average span of control in the world is 7, the hierarchy of the world would have ~12 levels 🤔
Conversation
Org chart of the world 🤔
1
16
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
2
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
For S=7, P=7.5b, you get
k_exact=12.61
log_7(P)=11.68
A better approximation would be log_S(P)+1
12.68~=12.61
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
Replying to
Kevin Bacon taught us that there 7 degress of separation, in which case log_x(7.5B) = 7, and x ~= 26. So, the span of control in Kevin Bacon's world is roughly 26
1


