Math Geek Talks Polyamory

It is summer time and that gives me all sorts of time to think things. Since I am inclined to be a bit of a math geek, it gives me an opportunity to poke around on the far edges of mathematical theory, and contemplate what any of that might mean in relationship to the more grounded realities of my daily existence. It is heady stuff, and probably not to the taste of everyone, but I like it. I will also acknowledge right from the start here, that I am not in anyway a professional mathematician, and so my understandings and interpretations of the mathematics here should be taken with a grain of salt.

Areas that I am curious about: fractal geometry, chaos theory, game theory, graph theory, and knot theory. Today, I'm sort of wading around in knot theory, and wondering how or if knot theory might apply to relationship dynamics, and polyamory. That's the broad outline of where I am heading with this, so feel free to bail out now before it gets really deep...

Most of what follows; a basic discussion of knot theory, is taken from the Mega-Math website (and I didn't do very much with it -- it is lifted almost verbatim). I like Mega-math for this kind of introduction because it is written for young students, and so pretty easily accessible:

The mathematical theory of knots originated in the 19th century, but has made major advances in the past decade. One of the most exciting developments has been the discovery of deep connections between knot theory and the branch of physics that studies the fundamental particles and forces that are the building blocks of the universe. It has also been found that DNA is sometimes knotted, and knots may play a role in molecular biology.

Mathematicians envision knots as closed loops or paths that you can trace round and round with your finger. It is as though the two free ends of tangled rope have been spliced together. When knots are drawn or represented on paper, the places where the rope crosses itself are shown as a broken line and a solid line. The intent is to show that the part of the rope represented by the broken line is passing under the part represented by the solid line.

Mathematicians ask many of the same questions about knots as they have asked about numbers. One of these questions is, "Are these two knots equal?" If one knot can be untangled, without cutting, to look like another knot, the two are considered to be equal. This is the concept of knot equivalence. When two knots seem to be very different, it could very well be that one is just an extra-twisted-up verstion of the other, and that one knot can be transformed into the other by twisting and turning, but without cutting the rope and actually unknotting it.

Knot theorists are still seeking a straightforward and general method for determining whether two knots are equivalent. This is the notion of topological equivalence, and it is a very powerful idea that plays many roles throughout mathematics. The major insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. For example, the square and the circle have many properties in common: they are both one dimensional objects, and both separate the plane into two parts, the part inside and the part outside.

You can "add" two knots together if you make a cut in each one, and, without unknotting, splice the ends together so that each end is joined to an end from the other knot. Knot addition shows us how two knots can be added together to make a more complex knot. If you begin with a knot, then take a second piece of rope and make a knot out of it that is woven into the first knot, the result is what mathematicians call a link. Also, you can take a braid that is made of three or four, or any number of strands, you can splice the ends in a variety of ways. You can turn it into a knot, or you can turn it into a link made of several intertwined knots.


If you have waded through all of that, then you must be wondering what possible connection any of that has to polyamory and relationships.


I think that creating relationships is like adding knots, or sometimes like creating knot links. If we perceive each member in a relationship as a unique knot, each with their own particular patterns and complexities, then we can envision that joining non-equivalent knots can change the level of complexity that each one is a part of. It isn't necessarily the case that adding knots creates MORE complexity although it can. In the right combinations, knots can become less twisted, and this might also be true of some relationship dynamics.


Consider the societal norm in relatedness, which is "coupledness." When you have two people in a relationship, each person only has one other person to keep in mind. Sort of. In reality, of course, that is almost never the case. People come with a variety of attachments -- extended families, work committments, friendships, histories. Most of us are pretty twisted knots of relatedness in and of ourselves. Anyone who has ever tried to live in extended and intimate relationship with another person, can attest to the complexity of the endeavor.


Of course, relational twistedness isn't a constant. If I'm feeling strong and healthy; if my work life is going smoothly; if I feel good about the path that my children's lives are following; if my aging parents are in secure situations; if my friendships are fulfilling and nurturing; then things don't feel all that challenging. When, however, any of those facets of my life start to wobble, my ability to maintain all the linkages gets strained, and that complicates my intimate relationship dynamics.


Then, consider the notion of relating polyamorously. There is, within the poly community, an ongoing discussion about the nature of "poly math." It revolves around the numbers of actual (versus apparent) relationships that come into being when we engage in intimate connectedness with more than one partner. In relationship with 2 people or 3 people or more, there are several overlapping and interlocking relationships all existing simultaneously. Between each pair or couple, there is a dyadic relationship, and then there are triadic and quadratic relationships. More relationships add layers.


In every relationship, each of us tends to be at least a slightly different person. We share different histories, different emotional valances, different intersts, different shared friends, different pet names. Remember all those unique and non-equivalent knots? One of the basic precepts of knot theory is that if two knots are not equal, no amount of twisting and manipulation will turn the knot into an "unknot." Partners, as we relate to them, will retain their unique characteristics. We can't treat all our relationships or all our partners alike. Even if we manage to twist them into similar configurations, they remain what they are and who they are.


Knot theory might give us some visual clues about those connections and those levels of complexity. Playing with knots, we could come to have a more definitive sense of the shibari-style connectedness that pulls us first one way and then another.

And that's where my mind has been wandering. And if that isn't enough for you, this site can take you through a discussion of graph theory and polyamory. WooHoo!


swan