Thread: Poly Math
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Old 04-19-2010, 06:15 AM
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Originally Posted by saudade View Post
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.

As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.
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