The Quadratic Law of Resentment

January 12, 2001 7:15 AM

The Quadratic Law of Resentment If you combine N people, there are N(N-1)/2 possible ways in which arguments can break out. [via A&LD] This seems rather salient to a site like Metafilter...
posted by rushmc (9 comments total)

4349775 ways for metafilterers to fight!
posted by sonofsamiam at 9:22 AM on January 12, 2001

Now, how many of you are gonna check it to see if it's right? ;)
posted by sonofsamiam at 9:50 AM on January 12, 2001

Would you get mad if someone did check your calculation? :)
The good news is that it's not doubling or tripling anymore. When member 2951 joins we can only fight 2950 more ways. In fact, for every person that joins, we can only fight N-1 more ways. That's pretty negligible considering the possible ways that we can already fight.
posted by iceberg273 at 10:08 AM on January 12, 2001

Them's fighin' words!
posted by jennyb at 10:37 AM on January 12, 2001

jennyb: Them's fightin' words, too.
posted by allaboutgeorge at 11:06 AM on January 12, 2001

If this were real life I'd throw a chair at you right now...
posted by jennyb at 11:19 AM on January 12, 2001

Is anyone else reminded of the opening of Something Happened?
posted by grimmelm at 11:37 AM on January 12, 2001

Is there a proof for this theorem anywhere?
posted by Succa at 12:51 PM on January 13, 2001

Succa, I'm guessing here, and I certainly don't agree with the numbers, but let's say (for simplicity) that N=5. There's five people, coincidentally enough named Person 1, Person 2, Person 3 Person 4 and Person 5. Or, P₁5 for easy writing.

5(4)/2 = 20, so that's the number we're trying to achieve.

Alright, I'm too lazy to bother with subscripting, though I'm sure it would look nice. P1 through P5.

P1 can start an arguement with P2, P3, P4 or P5, so that's 4 ways.
P2 can start an arguement with P1, P3, P4, or P5, 4 more
P3 can start an argument with P1, P2, P4, or P5, +4
P4 " " " " " P1, P2, P3, or P5, +4
P5 " " " " " P1, P2, P3, P4.

4+4+4+4+4=20, as I'm sure you've already guessed. I know, I could have probably stopped after P2, but it was getting fun. :-)

It's not a factorial function because who started the argument is apparently important. I personally thing there are far more ways an argument can start in a group of N people.

N says Blogs suck, N+1 says Blogs are valuable, N+3 chips in and says only the A-List are cool and N+2 smacks them all upside the head.

posted by cCranium at 2:52 PM on January 13, 2001