The Golden Ratio (GR) Helix

Posted on 14th April 2012 in Theory

Golden Ratio Helix Fractal

What direction are you going and how are you going to get to your destination? What is your trajectory?


Unfortunately, for most of you I guess, there are things you call mathematical equations that offer a reasonable representation of how things are moving through time-space. I prefer the term “relationship” instead of “equation” because that is what it is. We’re investigating the nature of your motion through time space. This motion may be of your body, it may be of your mind, it may be of the balance of your bank account. Whatever the case, leave it to a scientist to find some set of equations to describe the universe. Better yet, let’s get rid of the term scientist and replace it with philosopher and simply say that a bloke or bird is trying to come up with a description of what is going on with something – a set of relationships describing a natural occurrence. In this case, you’re the natural occurrence and we, or I, am going to come up with a set of relationships to explain your behavior. Well, yes, we’re all somewhat predictable.


Anyway, I just wanted to get that out of the way because scientists have such a bad rap for being cold sterile reductionists with a pole up their ass who miss the big picture. This is so with many of the scientists I have known, but some of us are, in fact, decent, pole-less, creatures who simply utilize the tools of mathematics to help us understand nature’s complexities and don’t actually need to control or manipulate anything to make money. There is a difference.


The Golden Ratio Helix is a beautiful model to describe the desired trajectory of conflict. Ahhh, desired trajectory of conflict you are wondering. What the hell does he mean by that. Well, think about it. What is the desired outcome of an event? Do you want to know how much fuel per body stack you need to get the pile of bodies to burn by themselves? Do you want to find a way to peaceful resolution of a situation? Well it works both ways and has been employed to both ends. I hope those of you reading this are more interested in mutual beneficence than you are in personal gain through the exploitation of others. In any case, whatever your disposition, you’ll probably appreciate this – at least once I get done talking and get on with the cool images.


For those of you who done know what a helix looks like, here are some visuals:


The most famous of the helices

kick your ass helix









For those of you who don’t know what the golden ratio looks like, it is based on a simple mathematical progression and the ratio of successive terms which, as the sequence is propagated, the ratio of successive terms approximates a number which is called the golden ratio.  This ratio appears all over the place in nature. The following images illustrate the GR’s appearance in many forms in nature:golden ratio in  plant
golden ratio in a plant



If you put the helix together with the spiral you get the GR helix. The nature of the helix – depending on which way you travel along it –  is an ever diverging or converging trajectory. With respect to conflict, we travel one way along it and we are spiralling towards convergence – which I argue represents a state of stability. Travelling in the other direction represents a divergence, or escalation of conflict. In one case one is spiraling into control. In the other case one is spiralling out of control. The idea, however, is taken to represent the fact that, in the normal course of action of Conflict Transformation (CT), one hopes to reduce the term and severity of conflict towards a state of peace such that each time conflict arises, the intensity and duration of the conflict diminishes. It should be noted, of course, that motion along these trajectories can be, and often is, controlled directly by external forces with a clear intention. That is to say that some peoples, groups, governments are in the business of conflict escalation.


Think about this in terms of one of your personal relationships. Each time you engage in conflict with your partner, hopefully the duration and intensity of the conflict diminishes. If not, you are definitely lost (or maybe wandering) in the enchanted prison. In the case of warring parties (great phrase), we should hope that the behavior is the same. However, due to the complex nature of internal and external forces in, say, the case of Palestine (the Palestinian peoples vs the Israeli government), where the nature and origin of the forces are so complex that peaceful resolve, as we have seen, is the more difficult road to travel as conflict escalation seems to be the name of the game. If the external forces could be isolated and eliminated (i.e. if the US would stop funding the Israeli military – yes, I realize it is not only the US government, I am only providing one example),  the dynamic would be more manageable.


Of course, if the interests of different state, and non-state,  actors in the Middle East were based on human needs and human rights, the conflict helix…the game… would be of a much different nature. In fact, if the goal were mutually assured creation there would  be little or no conflict and we would be talking about the peace helix in which an inversion of trajectories would take place and the divergent trajectory along the spiral would represent an unbounded growth of mutual inclusion and mutual beneficence – a veritable transcendence of ego (on the personal level) and nationalism. The inward spiral along the trajectory would represent a collapse into selfishness.


How do you deal with the internal and external forces in your life and the lives of other as you spiral along the Golden Ratio (conflict/peace) Helix?


As we shall investigate later, your well being is intimately tied to the well being of others. Yeah, there’s some math for that – there are a set of relationships which show how we are all intimately intertwined (and, as you expect, some of the visual representations of these dynamics are pretty cool). The more your government, your god, your parents, your partner, etc, can condition you away from this understanding of the infinite relationships we are continuously engaged in, the more you will be content serving your term in the enchanted prison.


The next topic shall be on “Transcending Nationalism for a Soft Landing into Extinction” or something along those lines – coming in the next day or two.