**WHAT DOES MOUNT EYJAFJALLAJOKULL TEACHES US ABOUT COMPLEXITY ?**

As I sit next to the beautiful Lake Como, I ponder on the complexity concepts I have learned in the past few days from Dr Jacek Marczyk. Why, because as one search for answers in life, one do get the rare opportunity to challenge your fundamental principles which drives your reasoning and logic. During my stay in the Italian town Como, I had the opportunity to visit the Volta museum on the shores of the lake. One can only stare at amazement of this man who mixed philosophy, engineering, science and biology to develop the forerunner of the modern battery nearly two hundred years ago. Being willing to learn and borrow from various disciplines certainly is important to the process of innovation!

Why this title, and why Volta? Well, let us first start with the concept - “optimal”. If you are an engineer you are trained to optimize; spending countless hours trying to find the best algorithm for the optimal solution. Unfortunately this doesn’t stop here; most of us pursue optimal ways to live our lives. What happens if you find the optimal solution? Is it at great expense? Can we ensure that the solution stays optimal at all cost? What will happen to this optimal solution if the slightest changes are introduced? Will your solution stay optimal?

In a few short days I came to the conclusion that “optimisation” and the way we think and apply it, might be a fallacy. Maybe there is something else that we rather should consider. What about “survival”? What if survival is a better approach to the minimization or maximisation of the system? Thus, our objective not to seek the optimal solution, but rather one which tries to avoid being destroyed at the optimal point of operation.

Very few people agree to the meaning of the word “complexity”. Maybe the simplest understanding of complexity is that complexity is the place where a system’s structure experience variation. To measure is to have the ability to manage; how do we then manage complexity? Especially if we start to use words such as “fuzzy”, “entropy” and “robustness” associated with complexity. In order to measure complexity, we need to understand the concept of “fragility”. Fragile means that at some point the object will break if placed under force; fragility of a system means that at some point a system will collapse if it is subject to more variation (“fuzziness”). Dr Jacek takes this to the level where he describes the fragility of a system as a function of the “uncertainty” of its environment and the complexity of the system itself.

If we focus on the complexity of a system; we can express the complexity of it in terms of structure and variation. Thus, a system operates its structure under the conditions of uncertainty, or variation. The structure is simply the objects in the system performing functions, each of them have relationships with other objects in the system. These relationships will not be stable over time for any system due to the energy in the system. As the second law of thermodynamics states, entropy (energy) in a system will increase over time. Entropy can be measured by the variation in relationships between the different functions. If the system comes to a point where all relationships operate close to large variations, the system can lose structure and collapse. In Figure 3 and Figure 4, the image on the left contains 50% more entropy between variable 3 and variable 1, than the relationship between variable 2 and variable 1.

Why this title, and why Volta? Well, let us first start with the concept - “optimal”. If you are an engineer you are trained to optimize; spending countless hours trying to find the best algorithm for the optimal solution. Unfortunately this doesn’t stop here; most of us pursue optimal ways to live our lives. What happens if you find the optimal solution? Is it at great expense? Can we ensure that the solution stays optimal at all cost? What will happen to this optimal solution if the slightest changes are introduced? Will your solution stay optimal?

In a few short days I came to the conclusion that “optimisation” and the way we think and apply it, might be a fallacy. Maybe there is something else that we rather should consider. What about “survival”? What if survival is a better approach to the minimization or maximisation of the system? Thus, our objective not to seek the optimal solution, but rather one which tries to avoid being destroyed at the optimal point of operation.

Very few people agree to the meaning of the word “complexity”. Maybe the simplest understanding of complexity is that complexity is the place where a system’s structure experience variation. To measure is to have the ability to manage; how do we then manage complexity? Especially if we start to use words such as “fuzzy”, “entropy” and “robustness” associated with complexity. In order to measure complexity, we need to understand the concept of “fragility”. Fragile means that at some point the object will break if placed under force; fragility of a system means that at some point a system will collapse if it is subject to more variation (“fuzziness”). Dr Jacek takes this to the level where he describes the fragility of a system as a function of the “uncertainty” of its environment and the complexity of the system itself.

If we focus on the complexity of a system; we can express the complexity of it in terms of structure and variation. Thus, a system operates its structure under the conditions of uncertainty, or variation. The structure is simply the objects in the system performing functions, each of them have relationships with other objects in the system. These relationships will not be stable over time for any system due to the energy in the system. As the second law of thermodynamics states, entropy (energy) in a system will increase over time. Entropy can be measured by the variation in relationships between the different functions. If the system comes to a point where all relationships operate close to large variations, the system can lose structure and collapse. In Figure 3 and Figure 4, the image on the left contains 50% more entropy between variable 3 and variable 1, than the relationship between variable 2 and variable 1.

Being an Industrial Engineer by training, I live in a world of conceptual and mathematical models. Quite important for me as I use them to understand, construct and optimise business systems! Business systems in itself is a difficult and “fuzzy” concept since it hinges around man, machine and money – “man” being a highly complex system on its own. Now to make things interesting, one complex system (“man – the business owner”) creates products or services (tangible or intangible) in a complicated system (“the factory”) to sell to other complex systems (“man – the customer”), using money and all different kinds of machines through some more intangibles; business processes.

In my quest I have resorted to visual descriptions of systems through the concept of “things” or objects, and their “relationships”. Being exposed to optimisation techniques, I have yet found anything that could aid me in the understanding and description of a high level, seemingly complex system which evolves over time. From modeling techniques such as the Integrated Definition Language (IDEF) to Soft Systems Methodology (SSM), advanced business intelligence algorithms, process mining, and social network analysis; one can create a picture; but it doesn’t provide any analytical insight into the overall construction and design of the complexity of the system.

So, if one wants to measure and understand complexity, a fundamental philosophy needs to be adopted towards the principles of “complicated versus complex”, “complexity versus precision”, “mathematical models” and “fragility”.

There is a difference between whether a system is complicated, or whether the system is complex. Complicated systems don’t have the characteristic of being “stochastic”. Take a Breitling watch for example; it has over 1000 handcrafted mechanical parts to ensure that it delivers its purpose – telling time. No one wants a watch which has elements of randomness when you want an answer from its function - “What is the time?”

Opposite to this, experiencing a crowd at Euro Disney during the summer holidays is quite the opposite to that of a complicated system. Here individuals form a complex system where they move according to their own individual needs and wants. A complex system doesn’t necessarily have to have thousands of moving parts; if it has stochastic behaviour in its structure, it is complex.

The Law of Incompatibility (as defined by L. Zadeh) states that as a system becomes more complex, the less precise it can be. If you take another look at Figure 3 and Figure 4 you will notice that Figure 3 depicts a seemingly more random system than Figure 4. So one will have greater difficulty describing it more precisely. Figure 4 can quite easily be defined by the linear equation, y = a + bx. A logical conclusion if one thinks about complexity as variation in structure!

Wow, that is quite a lot of concepts, but let me explain it with a practical example. I got stranded in Italy because of the Mount Eyjafjallajokull volcano eruption in Iceland, three thousand kilometers away. Even worse than the 9/11 incident, Eurocontrol enforced a no fly zone over most of European airspace for five full days, closing many airports.

In the F = U x C equation I will take my system fragility, F, as being dependant on the uncertainty of my system (U), times my system complexity (C). My system complexity consists of the functions “family”, “business”, and “available resources”. My environment whilst travelling abroad, defined as the functions of “location” and “travel”.

As all European airports shutdown, the critical system of travel becomes unstable and collapses. Airports such as Frankfurt, Amsterdam and Paris form critical hubs for airlines throughout the world, making this collapse severe. Suddenly millions of people can’t travel as more than 60 000 flights a day gets cancelled all over the world for five consecutive days. Here, the uncertainty of my environment skyrockets as the travel system collapses; even spilling over to accommodation, car rental and railway infrastructures.

In order for my system fragility to hold, I have one choice, immediately reduce my system complexity. This means that I address the relationships between my “family”, “business” and “resources”. The immediate actions to be carried out involve outsourcing, rescheduling, communication and redundancy. Nice management terms, but it means getting the family to support my wife and kids, the accountant to act as proxy for me in business matters, temporary delegations to my business partners, immediate communication with clients and suppliers, and finding alternative ways to return to South Africa within a feasible budget.

Using this approach I didn’t seek for an optimal solution to my problem but adapted to the approach where I was looking for survival, that is ensuring that the although difficult, social structures are taken care of, business structures remained intact, and personally by accepting some things are not in my control. Although this crisis was immensely inconvenient to my system, it proves that the philosophy of complexity management is sound. So rather than trying to forecast a crisis, one can manage your system, or a business system not to edge of being optimal, but rather to the point where the complexity of it is such that it will not be too fragile in the case of changes in its environment.

One should understand that in a system, whether it is business, economy, government or personal; it is more important to survive, than to strive for being optimal. One cannot predict the future as Nature constantly changes, or understand or calculate the probability of events happening (as preached in traditional risk management approaches). However, you can ensure that the structure of the system is robust; that is; living a good distance from the system’s critical complexity where things may change abruptly! If this sounds like a risk management strategy; yes it is.

In my quest I have resorted to visual descriptions of systems through the concept of “things” or objects, and their “relationships”. Being exposed to optimisation techniques, I have yet found anything that could aid me in the understanding and description of a high level, seemingly complex system which evolves over time. From modeling techniques such as the Integrated Definition Language (IDEF) to Soft Systems Methodology (SSM), advanced business intelligence algorithms, process mining, and social network analysis; one can create a picture; but it doesn’t provide any analytical insight into the overall construction and design of the complexity of the system.

So, if one wants to measure and understand complexity, a fundamental philosophy needs to be adopted towards the principles of “complicated versus complex”, “complexity versus precision”, “mathematical models” and “fragility”.

**Complicated versus complex**There is a difference between whether a system is complicated, or whether the system is complex. Complicated systems don’t have the characteristic of being “stochastic”. Take a Breitling watch for example; it has over 1000 handcrafted mechanical parts to ensure that it delivers its purpose – telling time. No one wants a watch which has elements of randomness when you want an answer from its function - “What is the time?”

Opposite to this, experiencing a crowd at Euro Disney during the summer holidays is quite the opposite to that of a complicated system. Here individuals form a complex system where they move according to their own individual needs and wants. A complex system doesn’t necessarily have to have thousands of moving parts; if it has stochastic behaviour in its structure, it is complex.

**Precision versus Complex**The Law of Incompatibility (as defined by L. Zadeh) states that as a system becomes more complex, the less precise it can be. If you take another look at Figure 3 and Figure 4 you will notice that Figure 3 depicts a seemingly more random system than Figure 4. So one will have greater difficulty describing it more precisely. Figure 4 can quite easily be defined by the linear equation, y = a + bx. A logical conclusion if one thinks about complexity as variation in structure!

**Mathematical Models**

A system, especially a highly complex one cannot be estimated by mathematical equations; Nature evolves around structure and its energy. What model will start to describe Figure 3 in more detail, or the tree in Figure 6? Therefore images are more important in capturing the complexity of a system.**Fragility**

The fragility (F) of a system is dependent on the Uncertainty (U) of its Environment times the Complexity (C) of the System (F = U X C).Wow, that is quite a lot of concepts, but let me explain it with a practical example. I got stranded in Italy because of the Mount Eyjafjallajokull volcano eruption in Iceland, three thousand kilometers away. Even worse than the 9/11 incident, Eurocontrol enforced a no fly zone over most of European airspace for five full days, closing many airports.

In the F = U x C equation I will take my system fragility, F, as being dependant on the uncertainty of my system (U), times my system complexity (C). My system complexity consists of the functions “family”, “business”, and “available resources”. My environment whilst travelling abroad, defined as the functions of “location” and “travel”.

As all European airports shutdown, the critical system of travel becomes unstable and collapses. Airports such as Frankfurt, Amsterdam and Paris form critical hubs for airlines throughout the world, making this collapse severe. Suddenly millions of people can’t travel as more than 60 000 flights a day gets cancelled all over the world for five consecutive days. Here, the uncertainty of my environment skyrockets as the travel system collapses; even spilling over to accommodation, car rental and railway infrastructures.

In order for my system fragility to hold, I have one choice, immediately reduce my system complexity. This means that I address the relationships between my “family”, “business” and “resources”. The immediate actions to be carried out involve outsourcing, rescheduling, communication and redundancy. Nice management terms, but it means getting the family to support my wife and kids, the accountant to act as proxy for me in business matters, temporary delegations to my business partners, immediate communication with clients and suppliers, and finding alternative ways to return to South Africa within a feasible budget.

Using this approach I didn’t seek for an optimal solution to my problem but adapted to the approach where I was looking for survival, that is ensuring that the although difficult, social structures are taken care of, business structures remained intact, and personally by accepting some things are not in my control. Although this crisis was immensely inconvenient to my system, it proves that the philosophy of complexity management is sound. So rather than trying to forecast a crisis, one can manage your system, or a business system not to edge of being optimal, but rather to the point where the complexity of it is such that it will not be too fragile in the case of changes in its environment.

One should understand that in a system, whether it is business, economy, government or personal; it is more important to survive, than to strive for being optimal. One cannot predict the future as Nature constantly changes, or understand or calculate the probability of events happening (as preached in traditional risk management approaches). However, you can ensure that the structure of the system is robust; that is; living a good distance from the system’s critical complexity where things may change abruptly! If this sounds like a risk management strategy; yes it is.

So, forget about optimal solutions or traditional risk management approaches, rather start to focus on how to survive with a system that is robust, and has sufficient degrees of freedom to simplify the system if disaster struck. Remember, you cannot forecast the future (as the Iceland Volcano taught us), but you can ensure a robust system!