Complexity and complication

Complexity is subject to a large number of researches. It relates to many fields: hard sciences (mathematics with information theory, entropy in physics, etc.), but also disciplines such as ecology, psychology, sociology, economics or computing. The interesting aspect of complexity is that it constitutes a major stake for all human activities on which it interferes, usually in a negative way. The wide variety of concerned fields makes possible a relative generalization of the underlying concepts and a better understanding of reality by setting down unequivocally and in a very broad sense the problem of what is simple and what is complicated.

These concepts however have not produced a single and homogeneous formalization of the topic. Each different theoretical approach describes a particular aspect of the complexity (e.g. the complexity theory in mathematics or the redundancy in computer science or linguistics). With certain exceptions, they analyze the reality as it is, and not the future reality which is elaborated within a design process. In other words, very few methods help us to make it simple when everything needs to be built and while we have at our disposal tools that can evaluate the complexity of what has been carried out.

Therefore, to design an object, system or service that be simple is a difficult activity to supervise. The only assistance we can expect from considerations and studies undertaken so far, regards the implementation of the basic concepts they have generated, the description and the estimation of the complexity in clear terms – primarily descriptive – throughout the phase of objectivation. It will always be necessary, aiming simplification, to balance the impacts of the generated results and to adjust the targets.

Admittedly, if one is to take into account all issues relating to complexity starting from the design and analysis phases, it will not really be of concern to most of us. It seems that the decision in itself to proceed by following a logical step is enough a guarantee for a simplicity in solutions. This curious propensity to ignore or consider complexity as a minor phenomenon probably hides the will to avoid excessive design efforts whilst at the same time we know for a fact that any reality is tainted with it. We frequently are confronted to the annoying if not catastrophic consequences of not staying simple and of avoiding to control or circumscribe complexity. However, this does not seem to be a reason enough to change the things.

A correct understanding of complexity presupposes a capacity to make the distinction between what is complicated and what is complex.

In the dictionaries of everyday usage these terms have the same meaning, one term explaining the other and vice-versa. This confusion is not trivial because it makes impossible the dichotomy disorder-structure. There is a fundamental difference between “complication” that designates the fact that everything is composed of a large number of parts functionally and logically articulated between them (e.g., an airplane is made of thousands of components) and “complexity”, which connotes the unknown and the uncertain (it is partly the case of the weather forecast obtained after many calculations). Complication can thus be rationalized: one has only to explain the various components and the logic of their interactions to have a hold on reality – even this requires quite an effort to achieve. Complexity on the other hand is linked to imprecision or to the imponderable.

To rationalize reality is therefore to detect and circumscribe the part of the random aspect (complexity) and to structure all that can be subject to logical and reasoned considerations (complication).

Complexity can also be subject to simplification just by using a methodological approach of syntax and semantics (not presently the subject of this article).

To rationalize what can be rationalized does not always lead to the expected results. One might even say that complexity typically occurs during the development of the rational part when the latter becomes too complicated. A correct description of the components of an object and the interactions between its parts should ensure a perfect mastery of reality, with only two prerequisites: time and effort. But one should not forget factors such as the dimensions and the depth of the analysis, as well as the number of components and the richness of interactions.

A good way to manage complication is to provide an indicator whose primary function is not to define in an absolute manner the difficulty of appropriating reality but rather to offer a tool capable to compare two solutions and to measure the evolution of an object that needs to be enriched by new aspects or functionalities.

Before describing this indicator (it will be the subject of a forthcoming article), it is important to show that complication may induce complexity. Indeed, at some point of the design or the analysis phases, one must stop the rationalization process and acknowledge that the solution, however perfectly defined, becomes unrealizable.

Let us take the example of the brain. The human brain is composed of 100 billion neurons in average. For simplification purposes, let’s consider the neuron as the only constitutive entity and furthermore suppose that these neurons ensure the “functional logic” just by means of their synaptic connections. This definition of the brain viewed from this angle alone is complicated but not complex.

In physics, a manner of defining the complexity of a system is to count the number of states. The more important the number is, the more complex is the system. By extension, we will say that the brain is complicated, using as an indicator the number of possible states that it can take and assuming that certain states will induce a precise physiological answer (e.g., the focusing of the eyes on an object).

To remain simple, if a neuron at a given moment, can assume two states (yes or no), the number of possible states of the brain, will be 2 for one neuron, 2×2=4 for two neurons, 2x2x2=8 for three neurons and 2 multiplied 100 billion times (noted 2100,000,000,000) for the entire brain. This number is huge (it has 30 billion figures and exceeds by far, as a comparison, the estimated number of atoms in the universe which are about 1080). Thus, complication is primarily induced by the interactions between the neurons and not by their number.

Although this example is very simplified (the fact, for example, that each neuron is on average connected to 10,000 other neurons significantly reduces the number of possible states which nevertheless still remains enormous) it means that it would be unrealistic to seek to analyze, design or model the human brain. Nevertheless the description we have made is perfectly rational, but the passage to reality (such as for example to analyze the cerebral activity by means of the medical imagery), can only be achieved by reducing the number of possible states. The solution is to define cerebral zones by aggregation of enormous quantities of neurons. These zones then make feasible the study of cerebral operation to the detriment of a precise and reasoned description of intimate workings. We then transferred a part of the rationality (the complication) to the complexity by creating a statistical imprecision (which neurons are included in an area? how do they impact on the macroscopic state of the zone? etc.) and by deliberately reducing its operation to a limited number of states.

In other words, complication, when it becomes impracticable, requires a change of the conceptual level (the transition from the neuron to the macroscopic brain region). It is not then possible anymore to explain by causes and effects links, the dynamic of reality because it presents a random aspect inducing risks of inadequacy between our definition of reality and reality itself.

One should not believe that the example of the brain is an atypical case. The number of states induced by the various components of an object is always very high. Thus, the recipe of a cake requiring ten ingredients and ten objects to its manufacture (flour, salt, oven, bowl, balance, …) whose states would be reduced, for simplification purposes, in the only condition of availability (yes or no) – for example, do I have enough flour? – comprises approximately 315,000 possibilities.

However, as opposed to what a large number of states could make us believe, to make a cake is not difficult. Isn’t this concept of complication over-estimated?

It all depends on the stage of rationalization in which we are.

A neophyte who never entered a kitchen will have to examine each of the 315,000 cases to determine if the cake is realizable (a tiresome process because there is only one case meeting the requirement). A chef will simply check the availability of all the ingredients and utensils and will only have to deal independently with the 20 states of the components of the recipe: if all answers are positive then the cake is realizable.

Confronted with the objectivation of the brain, we are neophytes. Faced with the realization of a cake, we are experts.

When for the first time we are vis-à-vis a reality, we must imperatively adopt the behavior of the neophyte. This behavior is essential because in a contrary case, we believe we make rationality when in fact we increase the complexity by presumption of expert skills. All the states of the components that we identify will be incorporated in the various states of the entire reality. A logical process of reduction of states will then make possible a significant and controlled drop of the number of states while we preserve the integrity of the explanation of reality.

It should however be stressed that in a very large number of projects, the process of identification and simplification of the states is not applied. The proposed solution takes after the spontaneous generation. It emerges immediate, certain and seldom subject to doubt. An insidious and unconscious transfer happens at that moment towards complexity of an issue that could have been solved in the complication domain.

The number of states has consequently the merit to pose the problem of the richness of reality and the need to initiate the process of rationalization in a realizable context even if it means to increase complexity, but here in a deliberated and measured way when the weight of states becomes too important. It also has the merit of making necessary an approach based on the formalization of the states of each part composing the whole.

To objectify (to make concrete) reality (the real thing) in the effort of rationalization can thus imply informational sacrifices. The reality then escapes to some extent, from the laid down objective of a whole and total control of the world which surrounds us and which we propose to build.

The practice of complexity/complication in the process of objectivation can then be summarized as follows:

  • reality always comprises a complex part whatever the will and efforts of rationalization
  • it is essential to identify the components and their states because it is the combination of the two which provides an indicator of the complication
  • complication can hide complexity
  • when one is confronted with the reality for the first time, the indicator of complication must be maximal
  • there are no rational states outside of what has been defined in the space of the rational possibilities (the complication part)
  • if the reality shows aspects or dynamics different from what has been constructed logically, these issues belong to complexity
  • the complexity has a cost: the cost of disasters
  • the complication has a cost: the cost of design, analysis and development.
  • Posted in Complexity | Tagged , | Leave a comment