15 ms·
I know this is barely relevant, but anyway: if we're all the average of our 5 closest friends, it means we're all identical, unless the population is split into
by pingswept 15y ago
I know this is barely relevant, but anyway: if we're all the average of our 5 closest friends, it means we're all identical, unless the population is split into disjoint subgroups that have no friendships between them.
If that's not the case, how could the highest-quality person have 5 friends? By definition, they're all worse than her, so their average can't be equal to her, unless we're all equal.
Anyway, back to the anecdotes about Eventbrite or whatever.
- eipipuz 15y agoConsider an icosahedron. At each vertex a person with a vector pointing outwards. In this example, people are normalized and can be understood by 3 dimensions. There you have 12 unique persons, each of them an average of the 5 surrounding it. Pick one of them as the best, you will see that doesn't in any way violate that it is still the average. Anyway, yeah, it also smells bad, but it could have a grain of truth.
- pingswept 15y agoAh, and I had assumed we were scalars! But you're right, and what's even better is that the icosahedron case generalizes to people walking on the surface of a sphere (assuming they're evenly spaced).
- Eliezer 15y agoErm, I could be wrong but wouldn't the icosahedron be the maximum "evenly spaced" set of people on the surface of a sphere (that weren't all confined to a great circle)? Lots of regular polygons, rather fewer regular polyhedra. (Of course if we make the jump to a 4D sphere we can put 600 people into the largest regular polytope, the hexacosichoron. http://en.wikipedia.org/wiki/Convex_regular_4-polytope http://en.wikipedia.org/wiki/Convex_regular_4-polytope) EDIT: I am wrong, it'd only take a uniform polyhedron, not a regular one. E.g. http://en.wikipedia.org/wiki/Icosidodecahedron http://en.wikipedia.org/wiki/Icosidodecahedron