The Lebanese Differential Equation

Ok. Quick review for those who have forgotten, and a short introduction for those who never dealt with it. A differential equation, in its simplest form, relates the present to current inputs and to the past. It's the foundation of mathematical sciences (for example, it defines classical mechanics, quantum mechanics, circuits, optimization, chemical reactions, fluid mechanics, thermodynamics, etc.), but besides all that, it is also used to model visual effects (by companies such as "Industy, Light, and Magic" and Pixar) in movies such as Monster's Inc. (remember the scene with the doors? all differential equations), and is used in both economics and sociology (there are computer programs that simulate social networks and growth of communities). It includes feedback loops and time-variant relationships. In short, it explains every dynamical system, and one can even go as far as saying that life itself is simply a differential equation (albeit an infinitely complicated one).

So what is the Lebanese Differential Equation? It is a system of nonlinear equations consisting of multiple variables (as well as their n-th order rate of change) and time-varying coefficients. It can be used to define the breakdown of Lebanese society (by knowing the breakdown, you can also model the cohesion) as a function of America, France, Israel, Syria, Saudi Arabia, Sectarianism, Collective memory, social inequalities, Hezbollah, Aoun, Lahoud, Jumblatt, Hariri, Seniora, etc. It models the dynamics of Lebanon, and allows the approximate understanding of the effects each of its variables has.

This dynamical system becomes harder to model if more details are to be retained. Yet at a certain level, it is necessary. Too many of us, myself included, have been guilty of putting forth an opinion based on our own observations and understanding of what we have seen and read, but such experiences are not comprehensive enough to accurately model much. With an explicit model, we would be able to understand what effect Western "advice" has. Would it increase the breakdown of the Lebanese state? A simple dynamical system with positive coefficients predicts that it would exponentially increase. That doesn't seem to be the case. Other inputs and other relationships counteract such an increase, possible by damping the result. Or maybe that coefficient is simply negative.

This is where the government would come in. It's optimal action is modeled as an input that would minimize the breakdown by counteracting and possibly limiting the other inputs, and by damping past changes. With constant inputs (this is a reasonable approximation with a short time frame), a steady-state solution would hopefully be reached, but that does not imply stability, since a sudden impulse might throw the system into disarray, in which the output would not decay back to a finite value. Stability would only be obtained if the government would actually be able to control the effects the different inputs have, or if it could actually limit them.

Mustapha discusses how the government is not doing enough. Assuming we can model the entire social and political dynamic system that we call Lebanon, we can then compensate for the inputs (be it America, Israel, Hezbollah, Syria, Aoun, Jumblatt, etc.). But there will always be sporadic jolts to the system, such as the Mehlis Report, Bashar's recent speech, Hezbollah's attacks, Israel's current political shakeup, which could completely rearrange past relationships. Should the government's job be only to react? Or should it attempt to change the system itself so that its input is dominant and so the intervariable coefficients are under its control? This is what the government is lacking.

The past does affect the present, in the same way the present will affect the future. Predicting this, considering that we do not know the future inputs, is an estimation problem, and is considerably difficult. I had no idea, when I jotted down two years ago that "Disregarding the aftershocks on regional and world politics, the loss of life is enough to make all of us shed at least one tear" with regards to the Iraqi invation, that Iraq would turn into the nightmarish quagmire it is today. That may be an extreme example, so let's look at Egypt. The US has been trying to promote rapid "democratic change", but has begun to back off because of the strong gains the Muslim Brotherhood has made. Simply put, they incorrectly modeled the dynamical system. And now they are attempting to correct it by reducing the magnitude of their input (in this case, interference). Will that be successful? Time will tell. A key point to keep in mind is that seemingly benign inputs today may blow the system up tomorrow. It isn't logical just to compare two ills and then say that the "less dangerous one" is the one we will support, without fully understanding their effects.

So does the Lebanese model exist? Not yet. This blogger does not have the time nor the information to even attempt such a gargantuan (and probably impossible) task. But even if people did have the time and the means, they simply do not have the information. A fundamental source of information that would shed the initial light on the coefficients of interdependency are unknown, simply because a census has not been taken since 1932. Lebanon can't even be approximated. Who can understand the basics if a comprehensive census does not exist? We each have our own theories on how Lebanon would react to different events, and some may be closer to reality than others, but who can know?

Yes, such a census may reveal shockingly disproportionate demographics, and would reveal surprising social inequalities, but that should come in second place when compared to understanding the Lebanese dynamics (apparently, Jordan publishes the population size in the newspaper ... on a daily basis). With the foundation a census would provide, and with more detailed analysis, Lebanon might be understood in terms of an approximate model. The government's job is to attempt and manipulate that model in order to minimize the result - which is the breakdown of Lebanon. The alternative is to continue doing what we do now - second-guess those that have destructive and constructive influence, and then just sit on the sidelines and wait to see how close our guesses were.

Apologies for the mathematical analogies ... tomorrow is Thanksgiving ... I had an hour to kill before leaving town ... and ... what better way to spend it than to write something that intertwines two things I enjoy.

posted by Lazarus, 8:50 PM