The Mathematical Theory of Groups
The Mathematical Theory of groups was composed by a barely 20 year old French man named Evariste Galois. He wrote the entire theory in one night. A total of sixty pages in which he frantically kept scribbling in the margins, “I haven’t the time, I haven’t the time.” This last because he had a duel to attend the next morning and he was correct in his assumption. He was shot the next day in the intestine and left to die because there was no doctor around.
I hate math. Typically I like things that are concrete and have a logical sequence, but all higher level math becomes abstract and while I am a visual learner, I have difficulty incorporating abstract symbols in the forms of Greek letters into math formulas comprised of numbers. My OCD mind doesn’t like mixing what I consider two very different sets of symbols. Letters shouldn’t have a meaning if standing alone. They should only represent something when combined to form words. But I digress.
I am using this theory in my internship. For some reason applying it to people and relationships gives it meaning that its simple formulas did not. Group Theory has 4 main tenants:
1.) It is composed of members that are all alike in one common characteristic, while their actual nature is otherwise irrelevant for the purpose of the theory. The outcome of any combination of two or more members is itself a member of the group. The numbers on a clock for example: 1+2= 3 which is another member of the group.
2.) Combining members in varying sequences still ends with the same outcome. Using the clock scenario: 12+2= 2 o’clock because the group itself is circular in nature. The outcome will always be a time of day that progresses forward. One cannot go back in time. If you put this in the context of relationships it means that no matter how many changes members implement the result is the same. Ashby’s homeostat is a good example of this. In a couple relationship there is a sort of homeostasis that is maintained despite the actions taken by either partner. One partner might make a change in order to become closer to the other partner, but the other partner inevitably and simultaneously makes a change to move back. It’s like two people dancing. The maintenance of this distance is necessary for the dance to work. One partner moves forward, the other back, and they are never moving closer to each other than the original distance they began with but that is what makes things function.
3.) The group contains an identity member such that the combination of it with any member of the group gives that other member, which means it maintains that other member’s identity. 5+0=5. This other member is a reflector of sorts. But this null member (0), maintains homeostasis.
4.) Every group member has an opposite, and the combination of the two gives the group identity member. 5 + (-5)= 0. Thus the group identity is maintained. In families it would look like this: If the family’s identity is currently one of a family in crisis dealing with a troubled teen, then what happens when the troubled teen changes. If the troubled teen turns into its opposite, the responsible child, often the other child in the family, the previously responsible other child, will become problematic in an effort to maintain group identity. Therefore, in spite two drastic changes in the family, homeostasis is maintained. The identity remains the same.
This of course is the problem of group theory when reflected in relationships. It never moves past first order change (a change within the system that does not change the system.) The system becomes known as a game without end. There are never any solutions. No purpose the group is working towards because even if it tried infinite in group changes it would never achieve a second order change (change within the system that alters the system). The groups natural tendency is to sustain itself in its current form.
I’m learning in my internship how to help people find second order change. I’m not having bad dreams about it anymore. Ultimately I am not a member of the group. I cannot change it. But I can help a member find a way, even the smallest of changes, that can bring about a shift in the entire system. For the first time in 3 almost four years I feel passionate about my future again. I have been so sure these past years that God brought me to this place for a reason, and I’ve been so disappointed. I missed my old dreams and I felt certain that my future would be a service of sacrifice. Our dean spoke to the school once about how our ministry might not always be something we love but simply something we must do and I hated that because I was sure that that would be me. I am hopeful now that I will be passionate in my new career, maybe not always happy, but I will have purpose. That’s what excites me. I’m not sure that God brought me here because I will be a great help to others, I think it is probably the opposite, he brought me here because there was a need that would fill my own.
