To the memory of our father Hasan SARAL.
“the chemist Kekule came upon one of the most important discoveries of organic chemistry, the structure of the benzene ring, in a dream. Having pondered the problem for some time, he turned his chair to the fire and fell asleep:’Again the atoms were gamboling before my eyes…. My mental eye…could now distinguish larger structures…all twining and twisting in snkae-like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke.” The spontaneous inner image of the snake biting its own tail suggested to Kekule that organic compounds, such as benzene, are not open structures but closed rings[1].”
Everyday, we fight with many difficulties of many kinds. Some of these are as simple and short as loosening of the shoelaces. Some of them are as difficult and long as making an invention and some of them as abrupt and serious as a traffic accident… If you have a look at the many problems that we fight with you will notice that we can categorize them and their solutions in different groups. Although these groups may carry similarities in their quantity, quality and content attributes, their use by individual persons and the importance assigned to them may differ. Also, even though the problems and their solutions may be similar the personalities of the individuals that they interact may cause them to appear different.
Studying the nature of problems makes it possible for us to solve similar problems easily and also understand ourselves better We can categorize problems in various ways. For example, problems that repeat endlessly are called chronic in medicine. I am afraid, some of our political problems may be called the same. On the other hand some problems are seasonal. For example, opening the streets to transportation by cleaning the snow. These problems repeat with more or less a certain period. Acute problems happen suddenly and are serious to handle. For example, a sewage pipe gets broken in your house… Some problems are ubiqutious. You meet them in many areas of life. Some are wide spread with in a limited area. Your computer program does not work. When nothing works at all you have made a main mistake with wide results. Focused problems affect a certain functionality and the system recovers as soon as you fix it. Like a tooth ache…
Some problems are light but persist for a long duration. In fact, we can group the problems by their durations that they sustain, short – long etc. or according to their largeness. The way the problems happen may be classified also. Few or many in quantity. Fighting with more than one problem at the same time increases the total difficulty. The way we categorize problems is not constant. It changes according to the subject of the problem and the context it happens. To put a tiny piece of thread through a sewing needle may be percieved as difficult while a much more concentration demanding computer programming task may be percieved easier, just like a technical problem may be percieved much more difficult after midnight than at noon.
The fact that our perception of the problems is variable makes our categorization of the problems more difficult and hence reduces the benefit that arises from the categorization. If you are throwing anything you get hold of to your target in a chaos that you can not apprehend you have come to that point where you have to take a deep breath and try to categorize the problems correctly. If you can categorize the problems as convenieint as possible to reach the target your chance of hitting your target via a similar solution. Solving problems is basically a problem of classification.
I had mentioned the chronic problems in the beginning. The word ‘chronic’ means ‘: marked by long duration or frequent recurrence’ by Merriam-Webster. The most apparent characteristic of a chronic problem
is repetition or continuity. Reduction of the repetition intervals indicates that the problem gets severe or light. For example, a severe crisis give way to the lighter ones but more frequent or irregular problem periods, or the increase in the severity of problems and the increase of the frequency may indicate a worsening.
The repetition of the problem in chronic problems may happen in various ways:
1-The problem arises in a flow of random events. The crux of the issue here is; the events other than the chronic problem are random and carry no relation with the problem.
2- The chronic problem happens after a chain of happening events. After each occurence things repeat the same iteration of events. In this case, repeating event is not only the chronic problem but the events that prepare it.
The events’ iteration does not have to be constant array of events. The presence of some events may be obligatory, but two seperate iterations may be composed of completely different events. But most of the events that form the iteration belong to the set of events that form the reasons of chronic problem.
If we look at a chronic problem from a closer point of view, we may observe that a single crisis begins at a moment in time, continues and finishes, or the problem has begun at a moment and continues for a long duration without any interruption. Aset of the general conditions that prepare the outbreak of the crisis, a set of the causes that push the events to happen and a set of the triggers which may come just before the crisis may be observed. In the case of the repeating crisis, there is a set of conditions that prepare, a set of causes that make it happen and a set of triggers that initiate the end of the crisis.
One component of the equation that gives rise to the chronic event is a function which may change by time but may also be accepted as constant for relatively short periods of time. This function may be related to the events in the past or to the material dependent on the nature of the interacting elements/participants of the problem.
When studided closely, the reasons, the causes and the triggers that lead to the outbreak of the crisis may be related to their own previous values and also may be related to the previous crises values. For example, the seriousness of a previous crisis, its duration, its attack/sustain/release durations. Sometimes the slowness of the evolution of the problem, namely slowness in its attack period, mathematically its 1st and 2nd derivatives being small, or precautions that balance and slow sudden changes may stop the forming of crisis episodes. The dependence of the reasons that form the chronic crisis to the characteristics of previous crises and to its own evolution leads to the unmanageable repetition of a chronic problem.
Above, I had mentioned a chronic problem that occurs among unrelated random events. There may be such problems that may be dependent on only themselves and their own past iterations. These self triggering chronic problems are recursive[3] in nature. In fact they may be evaluated as a special case of functions mentioned in the 2. item.
If I may return back to the beginning of this article, if we have a closer look at the story of the chemist who found the benzene ring, we may now come to appreciate the value of the symbol ‘the snake which bites its own tail’. The metaphor of ‘the snake which bites its own tail’ or ‘the scorpion biting itself’ is a method utilized in solving problems that are very difficult. The problem is so difficult that it can not be solved or cured by external effects such as, force, medicine etc. It becomes inevitable that the energy at the source of the problem may be used to kill itself. This kind of solutions may not be present or evident. I believe, chronic problems have the ability to be solved by using the metaphor of ‘the snake which bites its own tail’ on the premises of their own definition.
Ali R+ SARAL
Note: My simple article ‘A Mathematical Model of Chronic Problems’ is available at my blog
http://tekne-techne.blogspot.com in Turkish.
Kaynaklar:
[1] Rober H. McKim, Experiences in Visual Thinking , Brooks/Cole Pub. Co. Monterey, California, s. 11.
[2] Merriam-Webster Dictionary
Main Entry: chronic
Etymology: French chronique, from Greek chronikos of time, from chronos
Date: 1601
1 a: marked by long duration or frequent recurrence : not acute
Medical Merriam-Webster:.
1 a : marked by long duration, by frequent recurrence over a long time, and often by slowly progressing seriousness : not acute Chronic her b : suffering from a disease or ailment of long duration or frequent recurrence chronic
2 a : having a slow progressive course of indefinite duration -- used especially of degenerative invasive diseases, some infections, psychoses, and inflammations chronic-- comparre ACUTE 2b(1) b : infected with a disease-causing agent (as a virus) and remaining infectious over a long period of time but not necessarily expressing symptoms
[3] Merriam-Webster Dictionary
Main Entry: re•cur•sion
Pronunciation: \ri-ˈkər-zhən\
Function: noun
Etymology: Late Latin recursion-, recursio, from recurrere
Date: 1616
1: RETURN 2 : the determination of a succession of elements (as numbers or functions) by operation on one or more preceding elements according to a rule or formula involving a finite number of steps 3 : a computer programming technique involving the use of a procedure, subroutine, function, or algorithm that calls itself one or more times until a specified condition is met at which time the rest of each repetition is processed from the last one called to the first — compare ITERATION
Main Entry: it•er•a•tion
Pronunciation: \ˌi-tə-ˈrā-shən\
Function: noun
Date: 15th century
1: the action or a process of iterating or repeating: as a: a procedure in which repetition of a sequence of operations yields results successively closer to a desired result b: the repetition of a sequence of computer instructions a specified number of times or until a condition is met —compare RECURSION 2: one execution of a sequence of operations or instructions in an iteration
