# Group theory in change

Years ago, when I first encountered this material in Watzlavick’s “Change”, I had a feeling that it’s great, but I can’t quite grasp it in its fullness. Like there was a lot more to be understood for changework there, but I lacked the perspective for it.

I’ve recently come back to it, I think I get what it’s saying now, but, honestly, there are probably quite a few much smarter people among you here, so I figured I’d throw it out for everyone, as a useful thing to start with.

Now, the basis of this is group theory, with a little bit of class theory added in.

Group theory, as first conceived by the tragically brilliant Evariste Galois (and polished by his many successors), which – in a bit of a simplification, goes like this…

- Any group is composed of
**members**which are all alike in one common characteristic (all other aspects of their identity notwithstanding). So we can have groups of people, emotions, numbers, whatever you like. Furthermore, a**combination**(adding or subtracting members) of any members will still produce a member of the group. Now, this little thing is extremely important because as we will see, it will have a huge impact on group theory in changework. (Basically, since any combination of group members still leads us to the group, this limits the possible changes when basing them on members of the group.) - Members can be combined in a
**varying sequence**, but the outcome of this combination remains the same, no matter how the sequence changes – as long as all the same members are combined. 4+ 3 + 1 + 2 = 1 + 2 + 3 +4 - A group contains an
**identity member**, a member which, when combined with another member, maintains the identity of the other member. In a group of added numbers it’s 0, 1+0 = 1, 5+0 = 5. In a group of multiplied numbers it’s 1, 1x1 =1, 5x1 = 5, etc. In a group of people, it would be no one. John + no one = John. Etc. For changework it’s important in understanding that a member of the group may act and lead to no change in the identity of another member. There are “null&void” actions available, which can be mistaken for actions with actual consequences. - In any system which can be described as a group, each member has an
**opposite**, where the combination of a member and its opposite gives us the identity member. Now for addition this would be (-member), so 5+(-5)=0, which we know to be the identity member. (This is the point where we easily fall into typical opposites if we concentrate on addition alone, but take care that other combination rules could apply. For example, if the combination rule is multiplication, like in the group of 2, 4, 8, 16, etc. the identity member would be 1, so the opposite member for member 4 would actually be 0.25 ) For changework this is important to point out that what seems like significant change might still have us ending up in the middle of the group we had hoped to leave.

Now group theory is very useful for thinking about people’s situations, problems, the states of dynamic systems. What it does not actually allow us to do, is to think or talk about things that exceed the groups. For that, we need to talk about logical types, with its primary rule of “whatever involves **all** of a group must not be of the group”.

So, why care about this, if you are not one of the mathematically inclined? I’m not, to be honest, but I could see that there is something here, even years ago when I couldn’t quite put my hand on it.

Now what this gives us, for changework, is this- when people experience problems, their reactions to these problems tend to form a specific group. And when change often gets stuck, is because people tend to solve the situation while keeping within the group. (This is not to say, that problems cannot be solved within the group, by such a **first-level solution**. Often they can, but, honestly, people will rarely need assistance for that category of problems, so it’s not something a changeworker is likely to encounter.) In fact, what most people tend to do in such situations, is some variation of rule two – they attempt to change the sequence of the solutions. But, as long as the solutions are the same and all belong to the group, no change in the sequence will lead to a different result. It’s like taking a step into each of the cardinal directions – as long as you take exactly one step and the road isn’t blocked, you’ll get back to where you started, no matter if you did NSWE, ESNW or any other combination.

For these situations what must be done is to cause a change from outside the system, a **second-level solution**. For that you need to be able to map the original group, together with it’s identity member (and the opposites that come with it) and try to map structures above and beyond the original group. It seems a bit theoretical at first, but when you start to dig into it, it starts being a really useful perspective. As I said, a lot of you folks are smarter then me, so I figured you might find it useful to dig your teeth into this.