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Here's an example. You stumble on a bunch of psychology papers in which psychologists noticed that whenever 6+ kids get together, there are either three mutual

by xamuel 8y ago

Here's an example. You stumble on a bunch of psychology papers in which psychologists noticed that whenever 6+ kids get together, there are either three mutual friends, or three mutual non-friends. The psychologists think this has something to do with child psychology and have written 10,000 pages on it. You immediately recognize it has nothing to do with psychology and is just basic Ramsey Theory [1]. Should you have to review thousands of pages before being allowed to chip in? [1] https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Example:_R(3,_3)_=_6 https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Example:_R(... A less hypothetical example: You're Bertrand Russel and you discover Russel's paradox, a one-liner which negates thousands of pages of Frege's not-yet-published logic textbook. Do you have to wait for him to publish it, and then you read it, before raising your voice?

joe_the_user 8y ago
Some scientific subfields are ridiculous on their face. But there's a crucial difference between that and the way original rule is phrased. The fields one has to dismiss are characterized by things one knows is false by physics or combinatorics or other common sense things. Theories of telepathy, the flat earth, creation science or whatever. The "you can't show me one good paper on the subject" is an appealing-seeming pronouncement but it's really dumb way to do it. Just say, "that doesn't make sense and you'd need huge evidence to prove it". Paper quality isn't really the question.
- uncle_d 8y ago
  Regarding telepathy... https://www.sheldrake.org/research/animal-powers/a-dog-that-seems-to-know-when-his-owner-is-coming-home-videotaped-experiments-and-observations https://www.sheldrake.org/research/animal-powers/a-dog-that-...
  - Elrac 8y ago
    Sheldrake is my go-to example of bad science. In one of his experiments monitored by another scientist, when the dog didn't respond in a way that met Sheldrake's criteria, Sheldrake changed the criteria in mid-experiment. That one incident alone should be enough to dismiss any results coming from Sheldrake. He's not only dishonest but blithely unaware that he's being blatantly so.
mherdeg 8y ago
What immediately comes to mind is the 1994 paper "A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves", which drew a lot of attention immediately after it was published, with such follow-up articles as "Tai's Formula Is the Trapezoidal Rule".
varjag 8y ago
Not a psychologist, but I don't see the immediate connection to Ramsey Theory other than matching numbers. Is there a proof somewhere that human relationships are isomorphic to colored complete graphs? Why not for example hypergraphs, where Ramsey combinatoric figures should be different?
- xamuel 8y ago
  The isomorphism is: let the kids be nodes. Between kids x and y, place a red edge if x and y are friends, or place a blue edge if x and y are not friends.
  - varjag 8y ago
    Psychologic findings are statistical. Cliques do not form perfectly reliably; there are kids who would have no friends, kids who have common friend but hate each other, or yes all six could be friends indeed. R(3,3) doesn't seem universal enough here to be touted as "isomorphism"; it is not giving any particular insight except the most trivial (that child cliques sometimes can be represented as monochromatic sets of a complete graph). Am certain one can do a number of other graph-theoretic or algebraic relationships here with zero insight or predictive force.
    - xamuel 8y ago
      R(3,3) doesn't say a clique necessarily forms. It says a clique forms or an anti-clique forms (or both). If all six are friends, then there are (6 choose 3) cliques. If all six hate each other, there are (6 choose 3) anti-cliques. If one kid is hated by everyone, that in some sense decreases the odds of a clique but simultaneously increases the chances of an anti-clique, and R(3,3)=6 guarantees that in some sense these increases/decreases balance each other out.
  - mattkrause 8y ago
    My point, above, is that this isn't necessarily a good abstraction. The edges could be directed (A considers B a friend, B does not consider A a friend). The graph may not actually be complete (maybe absence of friendship is different from non-friendship), and so on. So yes, if kids' friendships form a complete undirected graph, then sure, your result is not at all surprising. But maybe they don't.
ipioxu15 8y ago
> The psychologists think this has something to do with child psychology and have written 10,000 pages on it. If you mean that 10000 pages in total in 10-page papers, you have read the literature, and become the hero child psychology needs by writing a paper refuting this. On the other hand, if you did not read the literature wider, how do you know that you are first to do so, or that the misconception is even shared by other than the authors of those papers. Of course, the implicit assumption in all this is that psychologists are stupid.
mattkrause 8y ago
In my experience, the vast majority of scientists would love to have that Ramsey’s Theory conversation with you. Some people might get prickly if you lead with “This is trivial and I can’t believe you don’t know that....” but I suspect the vast majority of my colleagues would hear you out. On the other hand....Ramsey’s theorem applies to compelete (undirected) graphs. Friendship is not necessarily symmetric: Alice could consider Bob a friend, but not vice versa. It could also be context-dependent, especially with kids: Alice and Charlie get along, but not when Bob is around. The thousands of pages that you don’t want to read probably address some of these “details” that your spherical cow model totally ignores. I think it’s totally fair for someone to say “That’s interesting, but have you read X,Y, and Z? They show that your model doesn’t apply because....”
- 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 :)

by xamuel 8y ago

joe_the_user 8y ago

Some scientific subfields are ridiculous on their face. But there's a crucial difference between that and the way original rule is phrased. The fields one has to dismiss are characterized by things one knows is false by physics or combinatorics or other common sense things. Theories of telepathy, the flat earth, creation science or whatever. The "you can't show me one good paper on the subject" is an appealing-seeming pronouncement but it's really dumb way to do it. Just say, "that doesn't make sense and you'd need huge evidence to prove it". Paper quality isn't really the question.

uncle_d 8y ago
Regarding telepathy... https://www.sheldrake.org/research/animal-powers/a-dog-that-seems-to-know-when-his-owner-is-coming-home-videotaped-experiments-and-observations https://www.sheldrake.org/research/animal-powers/a-dog-that-...
- Elrac 8y ago
  Sheldrake is my go-to example of bad science. In one of his experiments monitored by another scientist, when the dog didn't respond in a way that met Sheldrake's criteria, Sheldrake changed the criteria in mid-experiment. That one incident alone should be enough to dismiss any results coming from Sheldrake. He's not only dishonest but blithely unaware that he's being blatantly so.

mherdeg 8y ago

What immediately comes to mind is the 1994 paper "A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves", which drew a lot of attention immediately after it was published, with such follow-up articles as "Tai's Formula Is the Trapezoidal Rule".

varjag 8y ago

Not a psychologist, but I don't see the immediate connection to Ramsey Theory other than matching numbers. Is there a proof somewhere that human relationships are isomorphic to colored complete graphs? Why not for example hypergraphs, where Ramsey combinatoric figures should be different?

xamuel 8y ago
The isomorphism is: let the kids be nodes. Between kids x and y, place a red edge if x and y are friends, or place a blue edge if x and y are not friends.
- varjag 8y ago
  Psychologic findings are statistical. Cliques do not form perfectly reliably; there are kids who would have no friends, kids who have common friend but hate each other, or yes all six could be friends indeed. R(3,3) doesn't seem universal enough here to be touted as "isomorphism"; it is not giving any particular insight except the most trivial (that child cliques sometimes can be represented as monochromatic sets of a complete graph). Am certain one can do a number of other graph-theoretic or algebraic relationships here with zero insight or predictive force.
  - xamuel 8y ago
    R(3,3) doesn't say a clique necessarily forms. It says a clique forms or an anti-clique forms (or both). If all six are friends, then there are (6 choose 3) cliques. If all six hate each other, there are (6 choose 3) anti-cliques. If one kid is hated by everyone, that in some sense decreases the odds of a clique but simultaneously increases the chances of an anti-clique, and R(3,3)=6 guarantees that in some sense these increases/decreases balance each other out.
- mattkrause 8y ago
  My point, above, is that this isn't necessarily a good abstraction. The edges could be directed (A considers B a friend, B does not consider A a friend). The graph may not actually be complete (maybe absence of friendship is different from non-friendship), and so on. So yes, if kids' friendships form a complete undirected graph, then sure, your result is not at all surprising. But maybe they don't.

ipioxu15 8y ago

> The psychologists think this has something to do with child psychology and have written 10,000 pages on it. If you mean that 10000 pages in total in 10-page papers, you have read the literature, and become the hero child psychology needs by writing a paper refuting this. On the other hand, if you did not read the literature wider, how do you know that you are first to do so, or that the misconception is even shared by other than the authors of those papers. Of course, the implicit assumption in all this is that psychologists are stupid.

mattkrause 8y ago

In my experience, the vast majority of scientists would love to have that Ramsey’s Theory conversation with you. Some people might get prickly if you lead with “This is trivial and I can’t believe you don’t know that....” but I suspect the vast majority of my colleagues would hear you out. On the other hand....Ramsey’s theorem applies to compelete (undirected) graphs. Friendship is not necessarily symmetric: Alice could consider Bob a friend, but not vice versa. It could also be context-dependent, especially with kids: Alice and Charlie get along, but not when Bob is around. The thousands of pages that you don’t want to read probably address some of these “details” that your spherical cow model totally ignores. I think it’s totally fair for someone to say “That’s interesting, but have you read X,Y, and Z? They show that your model doesn’t apply because....”

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 :)