My paper topic was to look at social phenomenon through the theoretical and visual tools established by nonlinear optical theory. If interested you should read the section of the paper that gives a brief introduction about optics. The thrust of it is simply that Social Systems can be considered complex nonlinear dynamical systems and so fall under a regime where it is possible to apply theory from other nonlinear systems to model and visualize it. One important concept in nonlinear system is that of the Soliton, a structure that can propagate indefinitely in time and space due to a balancing effect between dispersive and nonlinear, self-focusing effects.

Stable social structures such as cities and people groups can be thought of as a social Soliton. In my paper I only looked at the behavior of just one such structure. Now I will consider how two might interact to see if the analogy can indeed by extended to group interactions. Do they model a friendly get together, a war, or simple coexistence.

Soliton as the name may suggest are self-sufficient and solitary by nature. They are very happy being by themselves. The fundamental property of their collision is that they asymptotically preserve their shape. This means that when two solitons collide there may be distortion of one or both of the solitons, but with time those distortions will be ironed about and the solitons will return to its original shape. In a high resolution simulation of a collisions between two solitons, one larger than the other, the solitons were found to emerge with the larger one slight larger than before and the smaller one slight smaller than before and both carrying small perturbations on the trailing edge, [Lamb 1998].

These results have two important features: exchange of energy and residual perturbations. When two people groups interact, say in some form of competition, whether its war or a friendly game of soccer, we can expect that one wins, the other looses and both are shaken up a little. The energy exchange can come in the form of popularity, influence as well as money and booty, as in the case of war. We also should not be surprised that the larger soliton stole from the smaller soliton.

Yet both are shaken up, not simply the smaller one. Even the larger powerful countries or parties cannot avoid ripples in its structure it if wants to pick a fight. Yet it takes the smaller structure longer to iron itself out where as for the larger the ripples are nearly inconsequential.

Here I presented a brief exploration of social collisions through the formalism of soliton collisions. Two important conclusions are that in any such interaction there is a power exchange from weaker party to the stronger party, and residual oscillations for both parties which are ironed out with time. This model has a tunability such depending on the relative magnitude of the two solitons and the resulting energy exchange and residual, it can model both peaceful coexistence to all out war.

Kevin G. Lamb (1998)

Are Solitary Internal Waves Solitons?

Studies in Applied Mathematics 101 (3), 289–308.

doi:10.1111/1467-9590.00094