## Poly Math: Exponential Complexity in Poly Relationships

One of the common comments I hear about polyamory is that it seems complex. And you know what? It certainly can be. When you have two people in a relationship, each person only has one other person to keep in mind. But when you're in relationship with two, you now have two people to keep in mind. In relationship with 3 people, and now you have 3 to keep in mind. Add to this, that in each relationship you tend to be at least a slightly different person. You have a different shared history, a different vocabulary for communication, a different set of common interests, different set of common friends, different pet names and a different emotional reaction.

So.. if you're in relationship with 3 people, it's just 3 relationships to keep on top of, right?

Nope. It gets far more complex than that. If you're in relationship with 3 people, that's a total of 4 people. Now, all four people may not be romantically involved with each other, but they do each have a relationship of some sort with each other. That relationship may range from general knowledge of each other all the way to a very close friendship, or perhaps even a romantic connection. Because in polyamory, there's no hiding of relationships.

**Let's take a look at a hypothetical 4 person relationship:**

Alice | Bob |

John | Susan |

Regardless of who is sleeping with whom, there are 6 different dyadic couplings within a 4-person relationship. Each one of these pairings has it's own unique relationship and interactions. The overall strength of this four person group is highly dependent upon the strength of each of the pairings within the group. Even the non-romantic pairings. Sometimes, especially the non-romantic pairings. Let's take a look at the 6 different pairings in this hypothetical quad:

Alice-Bob | Married for 10 years |

Bob-Susan | Dating for about a year |

Susan-John | Married for 5 years |

John-Alice | Friends via their spouses dating |

Alice-Susan | Have personality conflicts, tolerate sharing Bob |

Bob-John | Have become good friends via shared interest in video gaming |

Because Bob and John really enjoy video gaming they have been able to enjoy each other's company, and through sharing their common interests they have formed a pretty solid friendship. They're both sharing Susan romantically, and since they're both comfortable with each other and don't feel either one of them is being possessive or territorial, they have no problems sharing.

Alice and Susan however only barely tolerate each other, perhaps they have a personality conflict, or one of them holds resentment over sharing Bob. Whatever their underlying issues are, they're not dealing with them and avoid getting to know each other and establishing trust. Even though Alice and Susan are not in a romantic relationship, their relationship with each other can become a real problem in all of the other relationships.

For example, Bob and Susan would like to take a long weekend together to celebrate their 1 year anniversary. John has no problem with this, he has a good relationship with Bob and trusts him and Susan. However, Alice reacts negatively to the idea, as she hasn't built up trust and respect for Susan. She respects Bob's relationship with Susan, but because she and Susan haven't established a solid respect for each other as individuals, Alice is not comfortable with the situation.

This is just a simple situation. It can obviously play out in several ways, some more dramatic and negatively than others. But you can see that just one of the six pairings not functioning can create problems for the entire group to overcome.

**Six is more than four, but not so bad?**

6 relationships to keep up with when you involve 4 people together. Sounds like a lot. But wait.. it gets more complicated. Not only do you have the 6 pairings, you also have 4 different threeway relationships: Alice-Bob-Susan, Bob-Susan-John, Susan-John-Alice, John-Alice-Bob. And yup, you guessed it, in each tripling you can have a completely different energy going on. Perhaps because Bob and John are so comfortable with each other, they can both enjoy spending time with Susan together so that threesome tends to get a lot of energy. But because Alice and Susan aren't totally comfortable with each other, when they hang out with Bob together it's fairly non-comfortable for everyone. The guys rarely get a chance to just spend with Alice, and Susan rarely hangs out with Alice and John. Those are groupings that just don't naturally occur often. In this case, it might be useful for the ladies to both hang out with John for a bit, as a way to get the women interacting with each other without the constant reminder that they are sharing Bob.

And of course, there's an entirely different energy when all four people are hanging out together than in any of the other configurations. How do Alice and John interact when they see Bob and Susan together? Are Bob and Susan able to give authentic attention to their respective spouses when all four are together?

Let's add up the total number of relationships between four people:

Pairings | 6 |

Triplings | 4 |

Quad | 1 |

Total |
11 |

11 unique relationships exist between 4 people. And if any one of those relationships is unhealthy enough, it can crumble the overall relationship (or at the very least, make it highly unstable and problematic). So energy should be put into developing all 11 of those relationships.. and this is on top of the all important time and energy needed to be devoted to your relationship with yourself.

**Are you exhausted yet?**

So, that's just with 4 people. What happens if you have more than four people in a relationship together? It gets exponentially more complicated. Just by adding one more person to the mix, let's say Alice starts dating Tom, you now have 26 unique relationships. Make it 6 people, and you have 57 relationships. Or how about the intimate network of 15 people I'm involved with? 32,752 unique relationships.

Mind boggling.

Oh, and how did I figure all this out? By using this handy-dandy formula:

This formula was created at a party I recently hosted. A bunch of poly math geeks sat around sipping wine and nibbling on cookies and came up with this formula after about an hour of deliberation. I host *really* wild parties, as you can tell.

Yes, there is a simpler formula of 2^n - n - 1 that will derive the same thing. But I like the above formula better:

1) It looks better on a T-shirt (Yes, we created a t-shirt!)

2) It illustrates the point of the formula better - the more people you add, the more complexity you get!

And you know what? None of this is really new stuff. You get the same dynamics and complications anytime you put people together. Whether it be a group of people working on a project, a group of friends, a sports team, roommates, a family with children, etc. Just in the case of polyamory, you're mixing this up with some potentially touchy emotions, expectations and interrelationships that just make for all sorts of opportunity for ... challenges.