Q: What is complexity?

There doesn’t exist a widely accepted definition of complexity. Many of the popular definitions refer to complexity as a ”twilight zone between chaos and order”. It is often sustained that in this twilight zone Nature is most prolific and that only this region can produce and sustain life. Others claim that  the phenomena of self-emergence or spontaneous self-organization are manifestations of complexity. Clearly, such definitions do not lend themselves to any practical use since they don’t suggest any measure or quantity. We define complexity as function of structure and uncertainty.  Complexity, according to our approach, is not a phenomenon, it is a property of every system, just like energy, or potential.

Humans instinctively try to stay away from highly complex scenarios because of one fundamental reason – high complexity implies a capacity to deliver surprising behavior. However, at the same time, higher complexity means more functionality. This is why, for example, in our biosphere evolution strives to attain higher complexity as a means of increasing the survivability of species.

Q: How is complexity measured?

Complexity is a function of structure, entropy. Structure describes the way information flows within a given system. This may be represented via maps (graphs). Entropy represents uncertainty, both in the system as well as in its environment.  The "natural" metric of complexity which Ontonix has devised possesses remarkable properties. The metric, for example, peaks. In other words, it confirms the existence of the so-called critical complexity, in the proximity of which systems transition to states of high instability and unpredictability. It is therefore of paramount importance to know one's critical complexity and to stay away from it at all times.
 

Q: What are the salient properties of complexity?

Complexity possesses many interesting properties. One can mention, for example, the following:

• A highly complex system is more difficult to understand and manage than a simpler one (more complexity = more management effort)
• A highly complex systems is capable of delivering surprises (that's why people instinctively prefer a simpler life over a complex life!)
• A highly complex systems is (for the above reason) more risky
• High complexity is created by parameters that vary a lot AND are related to each other. If everything is constant, complexity = 0
• A highly complex systems is generally less efficient than a simpler one
• High complexity is the biggest enemy of a business

Q: Why and when does complexity increase?

Complexity doesn’t necessarily always increase. It is precisely the objective of management actions to keep complexity under control. However, in a closed system entropy can only increase – consequence of the Second Law of Thermodynamics - and this will inexorably increase complexity. But complexity doesn’t only increase due to increase in entropy. Increase in structure can also lead to higher complexity with the same amount of entropy. It is important to keep in mind that an increase in entropy implies an increase in complexity but not vice-versa.

Q: Does there exist an upper complexity limit?

Complexity cannot increase indefinitely. For every system there exists a critical upper threshold of complexity beyond which it is impossible to evolve further. At critical complexity levels, even small increments of entropy will destroy structure (links in the map) and the system will experience loss of functionality and fitness. At such levels one may either drain entropy from the system or add new structure. Critically complex systems are fragile. For most systems the critical complexity levels are unknown. This is due to the fact that even though the so-called “complex behaviour” (often called spontaneous self-organization) has been extensively studied in disparate fields, in very few circumstances has the measurement of the evolution of complexity been quantified.
 

Q: What is fragility?

Fragility manifests itself in a sudden loss of functionality or collapse. The most important feature of fragility is that there is no early warning before the collapse. Imagine how a slab of glass breaks. The rupture is brittle and sudden. In the case of metals, for example, one clearly observes plastification before rupture. When a system is fragile – i.e. close to its critical complexity – a very small perturbation can bring the system down. In many parts of the world today we see fragile societies or socio-economical systems. When systems collapse, either partially or totally, the event is accompanied by a loss of complexity. Fragility, therefore, is inversely proportional to the distance that separates the complexity of system from its critical complexity limit.
 

Q: How is fragility related to risk?

Given that there exists an upper limit of complexity for each system, and due to the fact that at critical complexity levels systems become fragile – i.e. can lose functionality without early warning – the higher the complexity of a given system the higher the risk of collapse. If the critical state is unknown, higher complexity automatically implies higher risk. Advanced risk management may be accomplished by measuring the complexity of a given system, tracking its evolution in time and, most importantly, establishing the corresponding critical levels of complexity.
 
Q: What is complexity management?

Complexity management is not simply reduction of components, products or business units or, generally speaking, streamlining of a business process. This definition, which has been established by numerous business consulting firms, which claim to offer complexity management services, delivers only part of the truth. The reduction of components is neither necessary nor sufficient toward the reduction of complexity. One may in fact reduce complexity by increasing the number of components and by simultaneously re-arranging entropy. However, the most important issue in complexity management measuring it. If you can’t measure it you can’t manage it.


Q: Why Should Complexity be Managed?

There are many good reasons to measure, monitor and manage complexity. However, we can mention the following as the most important:

• First of all, highly complex systems are less profitable. This is intuitive and this is why many corporations pursue lean business models.
• Secondly, an excessively complex business is inherently fragile and vulnerable. It is also less sustainable. This is because excessive complexity is the source of exposure.
• A more complex business is less responsive to change and extreme events - it is less resilient.
• Last but not least, in a turbulent economy, complexity management overcomes the limitations of conventional risk management.

Q: What are the common misconceptions on complexity?

Very often complex is thought to be equivalent to complicated. Complex does not mean complicated, or difficult, although one could, with great caution, equate complexity to sophistication (functionality). Another common misconception regards the number of components in a system. Often, a large number of components or parts is thought to imply high complexity. This is not necessarily the case. Systems with a small number of components may be far more complex than systems with a very large number of components. Let us not forget that complexity is computed not only as function of the system map, it also includes entropy.


Q: Is entropy always synonymous to destruction?

No. Entropy is one of the fundamental entities in Nature and it reflects such things as uncertainty, randomness, information content, amount of organization or capacity to perform work. It is important, however, to remark that uncertainty, which is by most people perceived to be something adverse, is necessary in order to create novelty. Without uncertainty it is impossible to evolve and to reach higher states of complexity. The complexity metric conceived by Ontonix shows in fact how entropy can actually create new structure (new links in the system map) and not just destroy it.


Q: How can complexity be used in management or decision-making?

Complexity is an extremely useful tool in advanced management, strategy and decision-making. Suppose that a decision maker has different equivalent options to chose from. Which option should he select? The least complex option – with all things being equal – should be chosen as its distance to the corresponding critical complexity level will be greater. It will therefore be less vulnerable. Excessive complexity, even if we are far from criticality, implies also that the system in question is more difficult to manage and control. This is in part due to high interdependency which implies more constraints and conflicts within the system. 

Because complexity is a property of all physical systems, it establishes an objective and "natural" Key Performance Indicator of immense value to businesses operating in a turbulent economy.

Q: How does complexity relate to redundancy and robustness?

Redundancy and robustness are not the same thing, although both concepts are ultimately related. Robustness reflects the system’s ability to maintain intact the topology of its system map in the presence of uncertainties. More precisely, we can state that robustness is proportional to the partial derivative of complexity with respect to entropy. Robustness, therefore, specifies how well the system is able to maintain its functionality. Redundancy is a property linked exclusively to the topology of the system map and reflects, globally speaking, the density of the map itself. In densely connected systems, information can flow between different components along multiple channels and the average number of these channels quantifies how much reserve there is in the system from a fail-safe perspective.


Q: How does the Ontonix complexity measure differ from the conventional measures?

There exist numerous complexity measures. One could mention, for example, the (deterministic) Kolmogorov-Chaitin complexity, which is the smallest length in bits of a computer program that runs on a Universal Turing Machine and produces a certain object x. There are also other measures such as Computational Complexity, Stochastic Complexity, Entropy Rate, Mutual Information, Cyclomatic Complexity, Logical Depth, Thermodynamic Depth, etc. Some of the above definitions are uncomputable. Some are applicable to either computer programs, strings of bits, or specific mechanical or themodynamic systems. In general, the above definitions cannot be used to treat generic multi-dimensional systems from the standpoint of structure, entropy and coarse-graining. This is precisely what our metric accomplishes. Moreover, our metric connects such concepts and quantities as fitness, fragility, controllability, functionality and robustness and shows how entropy can both build and destroy structure.

Source: www.ontonix.com with the kind permission of Ontonix, S.R.L.