@Ruby, I'd rename the thread "Poly Geekery" if I could. (Mods, could you?
) Thanks for broadening the geeking!
It's worth prefacing all this with the fact that my math background is rather unorthodox. I've been trained to try out my own solutions before trusting anyone else's.
This approach led me to trying to determine how many sets of issues any given relationship would have, without paying much attention to the already proposed answers. I wound up agreeing with SC initially, but since I enjoyed fleshing it out and my explanation might be useful to someone else, I'll provide it below (If you're not interested in the details of what I did and why, feel free to skip the next section.)
How I got my initial answer:
Let's pretend there's a person, X1. X1 has a set of issues that X1 is going to have no matter what, whether alone or in a relationship (like depression or time management issues). Then we have X2, who also has his/her own issue set. If X1 and X2 date, we have the issues of each individual, plus the issues that exist only when they are in relation to each other (different methods of showing affection, perhaps). Now, for every X we add to this relationship, we get one more set of an individual's issues, and then a set of issues for every way in which this person relates to another person or people. For a triad this is pretty simple: X1+X2, X1+X3, X2+X3, and X1+X2+X3.
It's worth making a few points here:
My initial answer:
- I don't think it matters whether the three people are a triad or a vee for these purposes. I think the two legs on a vee are just as capable of having relationship issues as two people in an equilateral triad. Similarly, as things get more complicated, I believe that any individual who has a significant involvement with a person in the group also has an issue set with every other member of the group, even if that person isn't romantically/sexually involved with anyone else.
- I also believe that any possible group of people out of the whole set (whether it's a pair out of a quad, the whole of a trio, or four random members of a large constellation, etc.) counts as a group in relation with its own issue set. I claim this because a group of three people is capable of having issues that no twosome out of its membership has-- it is its own relationship.
- For the purposes of this endeavor, it doesn't actually matter whether an issue set is intrinsic to one person, or exists in relation between several people. Mathematically, I'm just imagining all possible groups out of a set of of N people, including sets with one person.
- I don't see a way to account for variability in the size of issue sets-- one member of a quad is a drama queen, another is laid back, and the other two have wildly different moral codes. I was initially pretty concerned about this, but I've since decided it doesn't matter, which I'll come back to later.
Using this approach, I figured out how many issue sets a relationship has, based on the number of people involved:
0 people, 0 issue sets
1 person, 1 issue set
2 people, 3 issue sets
3 people, 7 issue sets
4 people, 15 issue sets
5 people, 32 issue sets
6 people, 63 issue sets
I then talked this data set over with Twig, resident mathematician, because I'm out of practice turning data sets (even basic ones like this) into formulas. Low and behold, he pointed out that SC's formula represented this data:
where N= total issue sets and X= number of people
A next step:
Now that I had my head around the formula, I began wondering about next steps, complications, etc. Specifically, I got curious about the -1 in the equation. It didn't look like some magic constant (like pi) that was necessary to smooth the equation over... which meant it had to represent something!
I've come to the conclusion (and would love some pushback on this) that the -1 is to remove the environment from the equation. Here's my logic:
- The equation is show the number of possible combinations of all the X's (people), including combinations of one X.
- A combination with no X's present is theoretically possible.
- Therefore the -1 in the formula removes that specific combination, so we only have combinations with people in them.
Why not include the environment? I can remember times, as an American, that having Bush, Jr. as president impacted the quality of my relationships. I'm currently co-housing with lots of friends and loves, and the layout of our townhome really does shape how we interact (both for good and ill). Is it possible that the relationship really is part of the equation, and there's one more set of issues to consider each time?
As for adjusting the formula to accommodate individual variations in issue quantity: given the rate of exponential growth, I suspect individual variation only matters in smaller relationships. One mono relationship might be wildly different from another, because individual variability has a great impact percentagewise, but when there's half a dozen people involved the number of relationships has to dwarf that variability.