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> (As an Oxford mathematician, Martin Gould, has explained, Ramsey theory tells us, for instance, that among any six users of Facebook there will always be eith

> (As an Oxford mathematician, Martin Gould, has explained, Ramsey theory tells us, for instance, that among any six users of Facebook there will always be either a trio of mutual friends or a trio in which none are friends.) What is the sensible/true version of this? Clearly it’s not correct as stated. You could have three pairs of two mutuals. You could have five mutuals and a singlet. Or six mutuals. Is it more a statement about probabilities?

MaysonL 6y ago
Three pairs of two mutuals: take one from each pair, that's a trio with no friendships. Five mutuals: take any three and there's a trio of mutuals.
- mordymoop 6y ago
  Thanks. I still think the wording of the original description isn’t great. If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are friends, not that all of them are friends and therefor three of them are friends. But I suppose I will choose not to die on the hill of slightly misleading language and admit I was just wrong.
  - renewiltord 6y ago
    This is a classical joke among new students to Mathematics to break the habit of the English language description being translated to the Mathematical problem statement. It goes in a question and answer format something like: "You knew a girl in high-school. In situation A, you find out years later that she is a stage actor and a dancer. In situation B, you find out years later that she is a stage actor. Compare how likely the second one is to the first one" In plain English there's an implied meaning of "she is a stage actor and not a dancer" in situation B. But that is not the statement. Situation B is as likely or more than Situation A but not if you use the English language description which suddenly is under-specified without real-world information. Obviously you pick the things to play to the priors of the person you're asking so that if they think actors frequently dance you put that in there. That leads them down the false rabbit hole of whether it's "stage actor and dancer" vs. "stage actor and not dancer" that you're comparing.
  - dllthomas 6y ago
    > If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are friends, not that all of them are friends and therefor three of them are friends. In pragmatics (a subfield of linguistics) this is called "conversational implicature" - in particular it's an example of the "maxim of quantity". Which is to say, you are correct about how the language works and mathematicians are a little weird.
wging 6y ago
https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Example:_R(3,_3)_=_6 https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Example:_R(... Let the 6 nodes be users, and color edges between two users red if they are friends, blue if they are not. I think it's true as stated, as another comment claims.

MaysonL 6y ago

Three pairs of two mutuals: take one from each pair, that's a trio with no friendships. Five mutuals: take any three and there's a trio of mutuals.

mordymoop 6y ago
Thanks. I still think the wording of the original description isn’t great. If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are friends, not that all of them are friends and therefor three of them are friends. But I suppose I will choose not to die on the hill of slightly misleading language and admit I was just wrong.
- renewiltord 6y ago
  This is a classical joke among new students to Mathematics to break the habit of the English language description being translated to the Mathematical problem statement. It goes in a question and answer format something like: "You knew a girl in high-school. In situation A, you find out years later that she is a stage actor and a dancer. In situation B, you find out years later that she is a stage actor. Compare how likely the second one is to the first one" In plain English there's an implied meaning of "she is a stage actor and not a dancer" in situation B. But that is not the statement. Situation B is as likely or more than Situation A but not if you use the English language description which suddenly is under-specified without real-world information. Obviously you pick the things to play to the priors of the person you're asking so that if they think actors frequently dance you put that in there. That leads them down the false rabbit hole of whether it's "stage actor and dancer" vs. "stage actor and not dancer" that you're comparing.
- dllthomas 6y ago
  > If I point at a group of six people sitting at a table and say “three of them are friends”, the natural assumption is that three and only three of them are friends, not that all of them are friends and therefor three of them are friends. In pragmatics (a subfield of linguistics) this is called "conversational implicature" - in particular it's an example of the "maxim of quantity". Which is to say, you are correct about how the language works and mathematicians are a little weird.

wging 6y ago

https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Example:_R(3,_3)_=_6 https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Example:_R(... Let the 6 nodes be users, and color edges between two users red if they are friends, blue if they are not. I think it's true as stated, as another comment claims.