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Butterflies in Islam: Why a little is a lot
"So what about the stuff we can hardly measure, the things we consider unimportant or trivial in our daily lives? -- a smile, a simple kind gesture, for example? What place do they have in our day-to-day encounters?"
"In whatever business thou mayest be and whatever portion thou mayest be reciting from the Qur'an and whatever deed ye (humankind) may be doing We are Witnesses thereof when ye are deeply engrossed therein. Nor is hidden from thy Lord (so much as) the weight of an atom on the earth or in heaven. And not the least and not the greatest of these things but are recorded in a clear Record." (10:61)
To paraphrase, I believe that Allah is telling us that in whatever you are occupied, be it your occupation, when you recite the Qur'an, and in any other work you may be doing, Allah and the angels are a witness to your actions, and even the smallest things that you do are recorded.
For me, the question that arises first after reading this verse is: Why is everything so important, even something that is physically or figuratively less than an atom's weight? Is it to increase our already burdensome lives? Are we not all caught up in the rat-race, working to live, and barely alive enough to work or extend ourselves any further? Is this the burden of Muslims that the other monotheistic religions balk at, suggesting that Islam, unlike other religions, guarantees nothing in the end, that our fate is always in the balance, and that we must always be on guard? On top of all this, it is not just the big things that Allah is aware of, but also the tiniest little things!
Well, the psychology of behavior modification is beyond the scope of this article and beyond my area of expertise, but I feel that if Islam is a prescription for internal and external peace, then change must come about by active application, not benign neglect. We are told in the Qur'an: "Surely Allah does not change the condition of a people until they change their own condition." (13:11)
I suppose that having a slight scientific bent has given me an alternate perspective on the Qur anic teaching that every minute thing is recorded by Allah. I believe that it is not so much to burden us with having to watching every little thing we do, but to tell us that everything we do has a significant impact on us, our families, our communities, and ultimately society as a whole. Wow! What a burden -- or, what an opportunity! Yes, an opportunity that derives from certain fundamental physical principals which we cannot wiggle our way out of. These principles have been captured in the term "butterfly effect," and derive from concepts fully developed in chaos theory.
Now I do not profess to be an expert in either theology or mathematics. I am, however, an optimist and the first quoted verse brings me much peace when given a certain physical context. So, what about this "butterfly effect"?
It began with Edward Lorenz, a meteorologist who modeled convection currents on computers. Given the lengthy computations necessary on the large and slow computers of his day (the early 1960s), Lorenz decided to write down the intermediate values in his study and continue his simulation at a later time. As he recorded these values, he took the liberty of rounding some of them off to three decimal places or so. But when he later re-started the computer simulation where it had left off, he realized that as the calculations progressed, the results departed from those of an uninterrupted simulation.
The departure from the expected result was not miniscule, even though the discrepancy in starting values was. Apparently, as time passed, the departure grew exponentially! The effect became known as "sensitivity to initial conditions." Given the fact that Lorenz was modeling weather patterns, it was remarked "if the theory (chaos theory) were correct, one flap of a seagull's wings would be enough to alter the course of the weather forever." Lorenz extended this analogy in the title of his lecture, "Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?" Hence, the "butterfly effect."
There are two major concepts relevant to this piece that arise out of chaos theory and each has something to do with systems governed by a defined set of rules. Systems with defined rules, as for example a system of mathematical equations, are said to be "deterministic." Deterministic systems, even very basic ones, like simple mathematical equations, can show rather complicated behaviors, which have often been described as "seemingly random." But such behavior isn't really random: because it is being generated from a mathematical equation, it just looks very complicated.
Thus, chaos is not really that intuitive sense of disorder we have grown up associating with the word. Rather, it is at times very complicated behavior that emerges from a specific set of rules. Actually it is through rules (or, equations) that the typical behavior of a given system is manifested. If we think of weather, for example, there are a finite amount of weather patterns that can happen, simply because physical rules have to be obeyed; but we are unable to predict which one will occur, or when. We can't expect to get wholly new kinds of weather -- that would be weird and frankly, unnatural. Everything in our physical and spiritual environment follows rules, whether we like it or not, and whether we can explain it or not as we are told in the Qur'an:
"Seek they other than the religion of Allah when unto Him submitteth whosoever is in the heavens and the earth, willingly or unwillingly." (3: 83).
As mentioned, the other important concept that arises out of chaos theory is "sensitivity to initial conditions," which means that small changes in variables (i.e. the values of mathematical equations) will create profound changes in that system as it evolves over time. These initial changes, or "perturbations," although tiny can dramatically alter the path a system could take. In chaotic systems, this rate of change can be quantified and is known as the lyapunov exponent. This rate of change actually represents the distance between two paths, one offset from the other by a small "perturbation." One can imagine that if the paths of a system kept diverging in this exponential fashion, the whole system would explode. Or, if the path of a system kept contracting exponentially, the system would collapse down to a singular point and implode. Chaotic systems that neither blow up, nor implode, must maintain a balance between expansion and contraction. In mathematical terms, these balanced systems contain both positive and negative lyapunov exponents. Is it any wonder that both "the Expander" and "the Constrictor" are among Allah's many attributes? Thus it appears that in Islam, ethereal as well as physical systems exist in a balance of opposing forces. (This can lead also to an in-depth discussion of the concept of "Moderation," which is another topic in and of itself.)
So what about the stuff we can hardly measure, the things we consider unimportant or trivial in our daily lives? -- a smile, a simple kind gesture, for example? What place do they have in our day-to-day encounters? Furthermore, what about more overt and profound actions, such as helping the needy, the orphaned, the homeless, the hungry, and the underprivileged? It is so easy to say, "What can I do? I am just one person, or "I can't make a difference."
That the small perturbations mentioned above result in exponential returns is iterated mathematically in Sura al-Baqarah verse 261, which states that The parable of those who spend their possessions for the sake of Allah is that of a grain out of which grow seven ears, in every ear a hundred grains: for Allah grants manifold increase to whom he wills; and Allah is infinite, all knowing . If one were to plot the mathematical progression stated in this verse as three points with co-ordinates (1, 1), (2, 7), and (3,700), any simple curve fitting algorithm would fit this to an exponential in the form of y = y0 + AeBx and yield values of y0 = 1.0, A = 0.00045, and B = 4.75. Regardless of the actual values of the parameters, this progression is well approximated by an exponential. Hence when we invest in the things that are important, as Allah has prescribed, then our small investment (1 grain), results in a huge return (700 grains). An exponential return! Remember though, this should be extended to all types of investments, be they investments of time, investments of effort, or investments of behavior. A kind word and the veiling of another s want is better than a charitable deed followed by hurt; and Allah is self sufficient, for-bearing (al-Baqarah, 263).
Well, if it is not enough that the Qur'an tells you every little thing counts, mathematics says the same thing! Everything does count, and the more we begin to believe and understand this, the less disenfranchised we will feel. We must believe this because it is a reality from which we cannot escape, it is inherent in the fact that we exist as part of a complex social and physical system, governed by rules and equations set down by our singular Creator, Allah. Let's not fool ourselves into thinking that by non-participation we effect no change. The absence of involvement is just as profound a "perturbation" in the universal system as is an active effort to do so.
So when we lament over the problem of the world's disjointed Ummah, we should take a step back and remind ourselves that human-engineered unity is, in and of itself, an unobtainable goal. We cannot just will unity to happen, it is a process. The process begins and ends by rigorously applying ourselves to all that the Qur'an prescribes for us. The unity we so yearn for is the natural endpoint of these efforts, provided we follow the prescriptions set forth. If we think social change will come about merely by ritualistic pursuits, then read Sura Al-Maun (Alms):
"Have you considered him who calls the judgment a lie? That is the one who treats the orphan with harshness and does not urge (others) to feed the poor. So woe to the praying ones, who are unmindful of their prayers, who do (good) to be seen, and withhold the necessaries of life". (107:1-7)
So, back to the "little things" in life. It is often said that the most successful among us are those who set themselves small, attainable goals. With consistent application to these attainable goals, life then becomes a series of positive reinforcements and ultimately we make it to the culminating point. Conversely, those who set huge, unrealistic goals are more likely to be destined for failure.
So if we haven't yet obtained the things we hope for as a community or as a society, then we should be looking at our own individual behaviors. It may be that when it was our time to flap our wings and change the weather in Texas, we were sitting in our basement and complaining about our next-door neighbors!
by courtesy & © 2003 Taufik A. Valiante
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