Analogies

At the place where I work there is a set of keys used by the employees around the work area. This particular set of keys is connected to a plastic keychain, similar to the ones pictured here. As a result of its being stretchy, bouncy, and exhibiting what Buckminster Fuller called tensegrity, playing with these keys is something that I do often. I think that most people have-to varying degrees-the tendency to nervously play around with things like this, but what I think is noteworthy about my playing around with this keychain, is that it exhibits dynamics that remind me of much more complex-and less concrete-situations.

I'm thinking about one dynamic pattern in particular, which occurs when the coils of the keychain are twisted with both hands at two different places simultaneously. I really wanted to capture this on video, but my phone is blocking me from using the video camera until I get a memory card, so a verbal description will have to suffice. I should state that, while this may be very hard to picture without such a keychain at hand, with one, it is very obvious.

Anyway, the dynamic response that I'm talking about occurs when the keychain is held by the thumb and index finger of both hands (which have between them about 2 complete rotations of the coil), and twisted by both hands simultaneously in opposite directions (clockwise and counter-clockwise). Doing this causes the coils to initially expand in diameter, but if the twisting continues, the coil will suddenly reorganize itself. The reorganization takes the form of an inverted twist in the coil that goes in the opposite direction of the rest. While this may be difficult to picture, everyone has seen it, either with a key ring, or a slinky that has an obvious imperfection in the coil.

I think it may be helpful to describe the process temporally: When the coil is twisted as described above, it keeps its shape and simply expands in size-at first. However, as the twisting continues, a point is reached at which a new inverted twist emerges. At that point, the coil could no longer maintain the original shape, and it reorganizes itself into a new form. Once an inverted coil has emerged, no further outside force is necessary to maintain it. One can let go and the inversion will persist. Interestingly, once the inversion is in the coil, it can be removed by applying both hands in the same way as was used to implement the twist, and twisting in the opposite directions. Also noteworthy is that, when implementing or removing the inverted coil, stretching the keychain while applying force will lead to the reorganization requiring a greater amount of force.

I see this dynamical reaction to be abstractly isomorphic to many phenomena that involve a system (a physical, biological or social structure) that is able to withstand a certain amount of stress before reorganizing itself in a predictable way. Of course, there are no limits to how one might look at simple physical events as being metaphoric for larger situations. I could, for example, comapre a breaking ruler with the downfall of a corporation. But the beauty of the keychain is that it exhibits a complexity that makes it suitable for modelling systems-specifically adaptive systems that reogranize themselves rather than dissipate when disturbed.

If we were to look at the way that a family responds to a crisis, we might see a reorganization occurring at a certain "breaking point"--similar to what is found in the keychain. The organization of the keychain is a function of the system reacting to two different kinds of forces: the outside twisting and the internal force that gives the keychain its shape in the first case. A family is also distorted by outside forces, but the possible reorganization is a function of both the outside forces as well as the internal forces that may serve to maintain the family as a soherent system. The reogranization of a family following a crisis is easily seen as resulting from the force of the crisis, but the reorganization itself may be a product of the existing forces of the family reacting with and persisting after the disturbance--just as in the keychain.

Now, the keychain is not necessarily the best model for a complex system like a family. Nevertheles, I think that it is very useful to realize the analogical properties of complex physical systems like this one which can be seen right in front of ones own eyes. By doing so, we gain physical experience with dynamical processes that we may use to get a grip on dynamical processes whose physical/temporal dimensions dwarf our potential for easy grasping. I'm inclined to take a closer look at children's toys to see if they have access to complex dynamical phenomena like those in the keychain. Perhaps early exposure to such dynamical processes (confined both temporally and spatially for easier comprehension) could have its benefits...