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-   -   Poly Math (http://www.polyamory.com/forum/showthread.php?t=2573)

saudade 04-18-2010 06:57 PM

Poly Math
 
So, there's this thread started by Jools on the downsides to being poly:

http://www.polyamory.com/forum/showthread.php?t=2506

LovingRadiance, SchrodingersCat, Twig, and I wound up on a math tangent. I thought it might be more appropriate to put it in its own place, so here we go...

LR:
Quote:

When we add a partner we now have twice as many issues to deal with.
SC:
Quote:

would say adding a partner more than doubles the issues. You still have your own issues as an individual, plus their issues as an individual, plus your mutual issues as a couple.

Theorem: the number of issues for n people in a poly arrangement is multiplied by 2^n - 1

So for 3 people, you have 3 people's individuals (3x) + the couple-wise issues (3x) + the issues as a 3-some (1x) = 7x

4 people, you have 15x the issues as a single person. And so on.
(4x individual + 6x pairs + 4x triples + 1x quad = 15x)

Hey, maybe there's a joint-math/psych thesis in here... lol yeah ok, I think it's bedtime, brain's getting silly...
Twig:
Quote:

Schrodinger, your math isn't quite right. I would agree that that adding a partner more than doubles your issues. By your formula moving from single to just one partner would only double the number of issues. You should make n=2 a special case and apply 2^n-1 to n>2.

I wonder what happens when you add imaginary partners. Are they represented by i/ You would start having trigonometric issues.

If you haven't guessed I'm a math geek.
Twig, I'd rather not have a solution with exceptions. :p Seems too in-elegant. It also seems appropriate, if we're doing this properly, not to assume that each person/relationship has the same # of issues. That does, however, throw the math utterly out the window (which is what happens when you let a social scientist get involved!).

Twig, who's looking over my shoulder, recommends a branch of math called network theory...

Any thoughts? Any math on other poly topics?

PS: I couldn't think of any appropriate tags. Feel free to add some!

rubyfish 04-18-2010 08:17 PM

Mine's not math, but chemistry. Equally geeky, but in a different direction.

I was thinking that lots of poly people use letters to describe their relationships (V or N or W). But there are a lot of configurations that just doesn't work for. So I had a flash of brilliance. Assume each person is a carbon atom in a hydrocarbon. Use organic nomenclature. So a V is a propane. A triad becomes cyclopropane. Okay, so if you want to stick with actual molecules, each person would be limited to four partners, but love doesn't care whether carbon has five bonds.

Okay, I'm finished with my moment of geek. Continue onwards with your math.

twig 04-18-2010 10:23 PM

My original reply was made after a night of no sleep. After some sleep and caffeine I see that I was mistaken. There is nothing wrong with Schrodinger's math. I think if we work at it we can come up with a model of relationship issues that takes into account not only that different people have different number of issues but also that different issues interact with each other differently.

saudade 04-18-2010 11:33 PM

Working it all out in my head
 
@Ruby, I'd rename the thread "Poly Geekery" if I could. (Mods, could you?) Thanks for broadening the geeking!

@Math ppl:

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:
  • 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.

My initial answer: 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:

N=(2^x)-1 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:
  1. The equation is show the number of possible combinations of all the X's (people), including combinations of one X.
  2. A combination with no X's present is theoretically possible.
  3. 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.

SchrodingersCat 04-19-2010 06:15 AM

Quote:

Originally Posted by saudade (Post 26920)
Low and behold, he pointed out that SC's formula represented this data:

N=(2^x)-1 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:
  1. The equation is show the number of possible combinations of all the X's (people), including combinations of one X.
  2. A combination with no X's present is theoretically possible.
  3. 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.

Oh goody, a math thread! I love combinatorics! (that's the kind of math concerned with, as the name implies, combinations of things).

-1 is a VERY important constant, much more important that Pi! You can do a lot of math without Pi, but without -1, all you can do is add stuff, you can never subtract (since by definition, 5-3 is actually 5 + (-1) * 3). So then if I'm a goat farmer and I sell you a goat, how would I know how many goats I have without counting them again? And how would I know whether one had wandered off or if I was only missing the one I sold you? But that's all besides the point...

Actually, 2^N-1 shows up in a lot of places in math. In this case, 2^N-1 is just the number of "non-empty subsets" of a group of N people, i.e. the number of smaller groups that actually have people in them. But you pointed that out.

2^N-1 does indeed assume that all individuals, couples, etc have the same number of issues. Of course, that's completely ridiculous. You can't even find two people who have the same number of issues, plus if I'm married to someone who has issues, then his issues become my issues, which is separate from the issues we generate as a couple.

So if his daughter is having trouble with life, then that's not a "relationship issue" specifically. But she's his daughter, so it becomes an issue for him, which in turn makes it an issue for me too. So does that count as one or two issues? Or is it one issue with multiplicity = 2?

What about if we're both afraid of heights. Is that two different issues?

Then of course on the flip side, the more people you have in your life, the more possible solutions you have access to for dealing with issues. Maybe as a single parent, child care is an issue. But suddenly I'm in a relationship with 3 other parents, well that's not likely to be much of an issue anymore!

Some issues just naturally clear up when you're in a relationship. e.g. Loneliness. Now, that's an issue that ideally you should deal with on your own, find ways to not feel lonely, without relying on someone else to make it go away. But ideals and reality don't always jive.

Or if my mother were constantly bugging me about "have you found a man yet?" then that would be an issue that I can't actually deal with on my own, assuming my mother has not listened to anything I had to say about not NEEDING a man. But if I get in a relationship with a man, then she's instantly off my back and that issue goes away.


Hmm, environment being the "-1" ... that's interesting. The thing is, if you're talking about how "the environment affects you" then it's an "individual issue." If you're talking about how the environment "affects your relationship" then it's a "relationship issue." For example, the layout of your condo isn't a problem in and of itself, i.e. when it's just sitting there empty. It's only a problem in relation to the number of people living there. So if it's too small for 3 people but big enough for 2, then it's a problem of the 3-person-groups. If you cram 4 people in there, then it's a problem of all the 3-person-subsets as well as the 4 person set.

I think the "-1" is the issues that the world has as a whole, with or without you even being alive. War in Iraq, American economy, earthquakes in Haiti... maybe those are the "-1"


Technically, we should be doing this as set theory, not combinatorics... so since every person, couple, threesome, etc has different numbers of issues, here's what we do: Take a 3 person example. People are A, B, C. Sets of issues are denoted X(P) where P = a subset of {A,B,C}
the symbol "U" means union, so something is said to be in the set "X U Y" if it's in either X or Y... The symbol "^" means intersection, so something is in "X ^ Y" if it's in X and it's in Y.
Ok, that sums up set theory 101. Actually, that's like the first day of set theory 101, but it's enough for this theory (have I lost everyone yet??)

So all the issues of the three people are the set:
X(A) U X(B) U X(C) U X(A,B) U X(B,C) U X(C,A) U X(A,B,C)

Now we've allowed for all possible issues between those three people. If both A and B are afraid of heights, it will be in there with "multiplicity 2" which means it's the same thing, but it's in there twice.


*giggles*

SchrodingersCat 04-19-2010 06:19 AM

Quote:

Originally Posted by twig (Post 26891)
Schrodinger, your math isn't quite right. I would agree that that adding a partner more than doubles your issues. By your formula moving from single to just one partner would only double the number of issues. You should make n=2 a special case and apply 2^n-1 to n>2.

I wonder what happens when you add imaginary partners. Are they represented by i/ You would start having trigonometric issues.

If you haven't guessed I'm a math geek.

I know you already retracted your statement, but just to clear it up for everyone else... 2^2 - 1 = 4 - 1 = 3 --> 3x the issues of 1 person.

Even for n = 0, a non-existant person has 2^0 - 1 = 1 - 1 = 0 issues......... but that depends on whether you're a nihilist or not!

As for imaginary partners... Then things get complex!!!!!!!!!! :D :D :D

EugenePoet 04-20-2010 02:43 AM

Geez. Let I = issues, B = baggage, and A = attitude... :p

LovingRadiance 04-20-2010 04:09 AM

Quote:

Originally Posted by rubyfish (Post 26910)
So a V is a propane.

Maca wants to know if that means we are highly explosive and smell like rotten eggs? He says he wants to know because that just does not work for him. :D

Isn't the stinky egg smell ADDED. It's not natural right? So that "highly explosive" part isn't so bad.....:eek:

rubyfish 04-20-2010 04:25 AM

Pure propane has virtually no odor. Some thing with natural gas. It's added to make leaks super noticeable.

And propane is perfectly safe, if handled correctly. Like poly relationships :).

LovingRadiance 04-20-2010 04:28 AM

LMAO!!

Maca says, "ok then I accept it and not only do I accept it, I like that definition."

Go rubyfish!!!


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