3 ms·

This kind of proves the point. You're misunderstanding the mathematics. Asymmetry of friendship is irrelevant. Whether the friendships have non-local dependency

by xamuel 8y ago

This kind of proves the point. You're misunderstanding the mathematics. Asymmetry of friendship is irrelevant. Whether the friendships have non-local dependency is irrelevant. The kids' friendship and non-friendship IS a colored complete graph: between any two nodes (kids), there is either a red edge (if those two are friends--in the context of the group, if you want), or there is a blue edge (if those two are not friends--in the context of the group, if you want).

mattkrause 8y ago
Asymmetry is relevant because your bound comes from undirected graphs. The number for a complete digraph is different.
- xamuel 8y ago
  Oh, now I see what you're saying. Ok, you're right, to be pedantic, the original phenomenon should be reworded: Whenever 6+ kids get together, either there are 3 mutual friends, or there are 3 kids K1,K2,K3 such that for any two K_i, K_j, either K_i is not K_j's friend, or K_j is not K_i's friend. I was implicitly using "A and B are friends" to mean "A is B's friend, and B is A's friend". Thanks for pointing that out :)
  - mattkrause 8y ago
    No problem! My bigger point was that the literature on any given topic is chock full of discussions like this. Is friendship directional? Is it binary, or does it make more sense to consider weights on these edges (casual acquaintance/best friend)? Can an outside observer infer friendship, or do you need to rely on self-reports? If so, how consistent are they? And so on. The more patient researchers are happy to walk you through these sorts of considerations, especially when you're introducing them to a new tool or something. However, if you catch someone who's busy—or grumpy—you might get blown off with "That won't work. Haven't you read the literature?" Personally, I think this happens too often, but you can sorta see how people might get sick of regurgitating the same arguments over and over. This is not to say that "read it and come back" can't be used as a moat, or that ideas "from the literature" shouldn't be revisited and questioned, but I think insisting that people do a bit of reading is not usually meant in bad faith.

by xamuel 8y ago

mattkrause 8y ago

Asymmetry is relevant because your bound comes from undirected graphs. The number for a complete digraph is different.

xamuel 8y ago
Oh, now I see what you're saying. Ok, you're right, to be pedantic, the original phenomenon should be reworded: Whenever 6+ kids get together, either there are 3 mutual friends, or there are 3 kids K1,K2,K3 such that for any two K_i, K_j, either K_i is not K_j's friend, or K_j is not K_i's friend. I was implicitly using "A and B are friends" to mean "A is B's friend, and B is A's friend". Thanks for pointing that out :)
- mattkrause 8y ago
  No problem! My bigger point was that the literature on any given topic is chock full of discussions like this. Is friendship directional? Is it binary, or does it make more sense to consider weights on these edges (casual acquaintance/best friend)? Can an outside observer infer friendship, or do you need to rely on self-reports? If so, how consistent are they? And so on. The more patient researchers are happy to walk you through these sorts of considerations, especially when you're introducing them to a new tool or something. However, if you catch someone who's busy—or grumpy—you might get blown off with "That won't work. Haven't you read the literature?" Personally, I think this happens too often, but you can sorta see how people might get sick of regurgitating the same arguments over and over. This is not to say that "read it and come back" can't be used as a moat, or that ideas "from the literature" shouldn't be revisited and questioned, but I think insisting that people do a bit of reading is not usually meant in bad faith.