Category Archives: Complexity

Navigating Chaos and Model Thinking

An inherent property of a chaotic system is that slight changes in  initial conditions in the system result in a disproportionate change    in outcome that is difficult to predict. Chaotic systems appear to create outcomes that appear to be random: they are generated by simple and non-random processes but the complexity of such systems emerge over time driven by numerous iterations of simple rules. The elements that compose chaotic systems might be few in number, but these elements work together to produce an intricate set of dynamics that amplifies the outcome and makes it hard to be predictable. These systems evolve over time, doing so according to rules and initial conditions and how the constituent elements work together.

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Complex systems are characterized by emergence. The interactions between the elements of the system with its environment create new properties which influence the structural development of the system and the roles of the agents. In such systems there is self-organization characteristics that occur, and hence it is difficult to study and effect a system by studying the constituent parts that comprise it. The task becomes even more formidable when one faces the prevalent reality that most systems exhibit non-linear dynamics.

 

So how do we incorporate management practices in the face of chaos and complexity that is inherent in organization structure and market dynamics?  It would be interesting to study this in light of the evolution of management principles in keeping with the evolution of scientific paradigms.

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Newtonian Mechanics and Taylorism

Traditional organization management has been heavily influenced by Newtonian mechanics. The five key assumptions of Newtonian mechanics are:

  1. Reality is objective
  2. Systems are linear and there is a presumption that all underlying cause and effect are linear
  3. Knowledge is empirical and acquired through collecting and analyzing data with the focus on surfacing regularities, predictability and control
  4. Systems are inherently efficient. Systems almost always follows the path of least resistance
  5. If inputs and process is managed, the outcomes are predictable

Frederick Taylor is the father of operational research and his methods were deployed in automotive companies in the 1940’s. Workers and processes are input elements to ensure that the machine functions per expectations. There was a linearity employed in principle. Management role was that of observation and control and the system would best function under hierarchical operating principles. Mass and efficient production were the hallmarks of management goal.

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Randomness and the Toyota Way

The randomness paradigm recognized uncertainty as a pervasive constant. The various methods that Toyota Way invoked around 5W rested on the assumption that understanding the cause and effect is instrumental and this inclined management toward a more process-based deployment. Learning is introduced in this model as a dynamic variable and there is a lot of emphasis on the agents and providing them the clarity and purpose of their tasks. Efficiencies and quality are presumably driven by the rank and file and autonomous decisions are allowed. The management principle moves away from hierarchical and top-down to a more responsibility driven labor force.

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Complexity and Chaos and the Nimble Organization

Increasing complexity has led to more demands on the organization. With the advent of social media and rapid information distribution and a general rise in consciousness around social impact, organizations have to balance out multiple objectives. Any small change in initial condition can lead to major outcomes: an advertising mistake can become a global PR nightmare; a word taken out of context could have huge ramifications that might immediately reflect on the stock price; an employee complaint could force management change. Increasing data and knowledge are not sufficient to ensure long-term success. In fact, there is no clear recipe to guarantee success in an age fraught with non-linearity, emergence and disequilibrium. To succeed in this environment entails the development of a learning organization that is not governed by fixed top-down rules: rather the rules are simple and the guidance is around the purpose of the system or the organization. It is best left to intellectual capital to self-organize rapidly in response to external information to adapt and make changes to ensure organization resilience and success.

 

Companies are dynamic non-linear adaptive systems. The elements in the system are constantly interacting between themselves and their external environment. This creates new emergent properties that are sensitive to the initial conditions. A change in purpose or strategic positioning could set a domino effect and can lead to outcomes that are not predictable. Decisions are pushed out to all levels in the organization, since the presumption is that local and diverse knowledge that spontaneously emerge in response to stimuli is a superior structure than managing for complexity in a centralized manner. Thus, methods that can generate ideas, create innovation habitats, and embrace failures as providing new opportunities to learn are best practices that companies must follow. Traditional long-term planning and forecasting is becoming a far harder exercise and practically impossible. Thus, planning is more around strategic mindset, scenario planning, allowing local rules to auto generate without direct supervision, encourage dissent and diversity, stimulate creativity and establishing clarity of purpose and broad guidelines are the hall marks of success.

 

Principles of Leadership in a New Age

We have already explored the fact that traditional leadership models originated in the context of mass production and efficiencies. These models are arcane in our information era today, where systems are characterized by exponential dynamism of variables, increased density of interactions, increased globalization and interconnectedness, massive information distribution at increasing rapidity, and a general toward economies driven by free will of the participants rather than a central authority.

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Complexity Leadership Theory (Uhl-Bien) is a “framework for leadership that enables the learning, creative and adaptive capacity of complex adaptive systems in knowledge-producing organizations or organizational units. Since planning for the long-term is virtually impossible, Leadership has to be armed with different tool sets to steer the organization toward achieving its purpose. Leaders take on enabler role rather than controller role: empowerment supplants control. Leadership is not about focus on traits of a single leader: rather, it redirects emphasis from individual leaders to leadership as an organizational phenomenon. Leadership is a trait rather than an individual. We recognize that complex systems have lot of interacting agents – in business parlance, which might constitute labor and capital. Introducing complexity leadership is to empower all of the agents with the ability to lead their sub-units toward a common shared purpose. Different agents can become leaders in different roles as their tasks or roles morph rapidly: it is not necessarily defined by a formal appointment or knighthood in title.

Thus, complexity of our modern-day reality demands a new strategic toolset for the new leader. The most important skills would be complex seeing, complex thinking, complex knowing, complex acting, complex trusting and complex being. (Elena Osmodo, 2012)

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Complex Seeing: Reality is inherently subjective. It is a page of the Heisenberg Uncertainty principle that posits that the independence between the observer and the observed is not real. If leaders are not aware of this independence, they run the risk of engaging in decisions that are fraught with bias. They will continue to perceive reality with the same lens that they have perceived reality in the past, despite the fact that undercurrents and riptides of increasingly exponential systems are tearing away their “perceived reality.”  Leader have to be conscious about the tectonic shifts, reevaluate their own intentions, probe and exclude biases that could cloud the fidelity of their decisions,  and engage in a continuous learning process. The ability to sift and see through this complexity sets the initial condition upon which the entire system’s efficacy and trajectory rests.

 

Complex Thinking: Leaders have to be cognizant of falling prey to linear simple cause and effect thinking. On the contrary, leaders have to engage in counter-intuitive thinking, brainstorming and creative thinking. In addition, encouraging dissent, debates and diversity encourage new strains of thought and ideas.

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Complex Feeling: Leaders must maintain high levels of energy and be optimistic of the future. Failures are not scoffed at; rather they are simply another window for learning. Leaders have to promote positive and productive emotional interactions. The leaders are tasked to increase positive feedback loops while reducing negative feedback mechanisms to the extent possible. Entropy and attrition taxes any system as is: the leader’s job is to set up safe environment to inculcate respect through general guidelines and leading by example.

 

Complex Knowing: Leadership is tasked with formulating simple rules to enable learned and quicker decision making across the organization. Leaders must provide a common purpose, interconnect people with symbols and metaphors, and continually reiterate the raison d’etre of the organization. Knowing is articulating: leadership has to articulate and be humble to any new and novel challenges and counterfactuals that might arise. The leader has to establish systems of knowledge: collective learning, collaborative learning and organizational learning. Collective learning is the ability of the collective to learn from experiences drawn from the vast set of individual actors operating in the system. Collaborative learning results due to interaction of agents and clusters in the organization. Learning organization, as Senge defines it, is “where people continually expand their capacity to create the results they truly desire, where new and expansive patterns of thinking are nurtured, where collective aspirations are set free, and where people are continually learning to see the whole together.”

 

Complex Acting: Complex action is the ability of the leader to not only work toward benefiting the agents in his/her purview, but also to ensure that the benefits resonates to a whole which by definition is greater than the sum of the parts. Complex acting is to take specific action-oriented steps that largely reflect the values that the organization represents in its environmental context.

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Complex Trusting: Decentralization requires conferring power to local agents. For decentralization to work effectively, leaders have to trust that the agents will, in the aggregate, work toward advancing the organization. The cost of managing top-down is far more than the benefits that a trust-based decentralized system would work in a dynamic environment resplendent with the novelty of chaos and complexity.

 

Complex Being: This is the ability of the leaser to favor and encourage communication across the organization rapidly. The leader needs to encourage relationships and inter-functional dialogue.

 

The role of complex leaders is to design adaptive systems that are able to cope with challenging and novel environments by establishing a few rules and encouraging agents to self-organize autonomously at local levels to solve challenges. The leader’s main role in this exercise is to set the strategic directions and the guidelines and let the organizations run.

Chaos as a system: New Framework

Chaos is not an unordered phenomenon. There is a certain homeostatic mechanism at play that forces a system that might have inherent characteristics of a “chaotic” process to converge to some sort of stability with respect to predictability and parallelism. Our understanding of order which is deemed to be opposite of chaos is the fact that there is a shared consensus that the system will behave in an expected manner. Hence, we often allude to systems as being “balanced” or “stable” or “in order” to spotlight these systems. However, it is also becoming common knowledge in the science of chaos that slight changes in initial conditions in a system can emit variability in the final output that might not be predictable. So how does one straddle order and chaos in an observed system, and what implications does this process have on ongoing study of such systems?

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Chaotic systems can be considered to have a highly complex order. It might require the tools of pure mathematics and extreme computational power to understand such systems. These tools have invariably provided some insights into chaotic systems by visually representing outputs as re-occurrences of a distribution of outputs related to a given set of inputs. Another interesting tie up in this model is the existence of entropy, that variable that taxes a system and diminishes the impact on expected outputs. Any system acts like a living organism: it requires oodles of resources to survive and a well-established set of rules to govern its internal mechanism driving the vector of its movement. Suddenly, what emerges is the fact that chaotic systems display some order while subject to an inherent mechanism that softens its impact over time. Most approaches to studying complex and chaotic systems involve understanding graphical plots of fractal nature, and bifurcation diagrams. These models illustrate very complex re occurrences of outputs directly related to inputs. Hence, complex order occurs from chaotic systems.

A case in point would be the relation of a population parameter in the context to its immediate environment. It is argued that a population in an environment will maintain a certain number and there would be some external forces that will actively work to ensure that the population will maintain at that standard number. It is a very Malthusian analytic, but what is interesting is that there could be some new and meaningful influences on the number that might increase the scale. In our current meaning, a change in technology or ingenuity could significantly alter the natural homeostatic number. The fact remains that forces are always at work on a system. Some systems are autonomic – it self-organizes and corrects itself toward some stable convergence. Other systems are not autonomic and once can only resort to the laws of probability to get some insight into the possible outputs – but never to a point where there is a certainty in predictive prowess.

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Organizations have a lot of interacting variables at play at any given moment. In order to influence the organization behavior or/and direction, policies might be formulated to bring about the desirable results. However, these nudges toward setting off the organization in the right direction might also lead to unexpected results. The aim is to foresee some of these unexpected results and mollify the adverse consequences while, in parallel, encourage the system to maximize the benefits. So how does one effect such changes?

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It all starts with building out an operating framework. There needs to be a clarity around goals and what the ultimate purpose of the system is. Thus there are few objectives that bind the framework.

  1. Clarity around goals and the timing around achieving these goals. If there is no established time parameter, then the system might jump across various states over time and it would be difficult to establish an outcome.
  2. Evaluate all of the internal and external factors that might operate in the framework that would impact the success of organizational mandates and direction. Identify stasis or potential for stasis early since that mental model could stem the progress toward a desirable impact.
  3. Apply toll gates strategically to evaluate if the system is proceeding along the lines of expectation, and any early aberrations are evaluated and the rules are tweaked to get the system to track on a desirable trajectory.
  4. Develop islands of learning across the path and engage the right talent and other parameters to force adaptive learning and therefore a more autonomic direction to the system.
  5. Bind the agents and actors in the organization to a shared sense of purpose within the parameter of time.
  6. Introduce diversity into the framework early in the process. The engagement of diversity allows the system to modulate around a harmonic mean.
  7. Finally, maintain a well document knowledge base such that the accretive learning that results due to changes in the organization become springboard for new initiatives that reduces the costs of potential failures or latency in execution.
  8. Encouraging the leadership to ensure that the vector is pointed toward the right direction at any given time.

 

Once a framework and the engagement rules are drawn out, it is necessary to rely on the natural velocity and self-organization of purposeful agents to move the agenda forward, hopefully with little or no intervention. A mechanism of feedback loops along the way would guide the efficacy of the direction of the system. The implications is that the strategy and the operations must be aligned and reevaluated and positive behavior is encouraged to ensure that the systems meets its objective.

edge of chaos

However, as noted above, entropy is a dynamic that often threatens to derail the system objective. There will be external or internal forces constantly at work to undermine system velocity. The operating framework needs to anticipate that real possibility and pre-empt that with rules or introduction of specific capital to dematerialize these occurrences. Stasis is an active agent that can work against the system dynamic. Stasis is the inclination of agents or behaviors that anchors the system to some status quo – we have to be mindful that change might not be embraced and if there are resistors to that change, the dynamic of organizational change can be invariably impacted. It will take a lot more to get something done than otherwise needed. Identifying stasis and agents of stasis is a foundational element

While the above is one example of how to manage organizations in the shadows of the properties of how chaotic systems behave, another example would be the formulation of strategy of the organization in responses to external forces. How do we apply our learnings in chaos to deal with the challenges of competitive markets by aligning the internal organization to external factors? One of the key insights that chaos surfaces is that it is nigh impossible for one to fully anticipate all of the external variables, and leaving the system to dynamically adapt organically to external dynamics would allow the organization to thrive. To thrive in this environment is to provide the organization to rapidly change outside of the traditional hierarchical expectations: when organizations are unable to make those rapid changes or make strategic bets in response to the external systems, then the execution value of the organization diminishes.

Margaret Wheatley in her book Leadership and the New Science: Discovering Order in a Chaotic World Revised says, “Organizations lack this kind of faith, faith that they can accomplish their purposes in various ways and that they do best when they focus on direction and vision, letting transient forms emerge and disappear. We seem fixated on structures…and organizations, or we who create them, survive only because we build crafty and smart—smart enough to defend ourselves from the natural forces of destruction. Karl Weick, an organizational theorist, believes that “business strategies should be “just in time…supported by more investment in general knowledge, a large skill repertoire, the ability to do a quick study, trust in intuitions, and sophistication in cutting losses.”

We can expand the notion of a chaos in a system to embrace the bigger challenges associated with environment, globalization, and the advent of disruptive technologies.

One of the key challenges to globalization is how policy makers would balance that out against potential social disintegration. As policies emerge to acknowledge the benefits and the necessity to integrate with a new and dynamic global order, the corresponding impact to local institutions can vary and might even lead to some deleterious impact on those institutions. Policies have to encourage flexibility in local institutional capability and that might mean increased investments in infrastructure, creating a diverse knowledge base, establishing rules that govern free but fair trading practices, and encouraging the mobility of capital across borders. The grand challenges of globalization is weighed upon by government and private entities that scurry to create that continual balance to ensure that the local systems survive and flourish within the context of the larger framework. The boundaries of the system are larger and incorporates many more agents which effectively leads to the real possibility of systems that are difficult to be controlled via a hierarchical or centralized body politic Decision making is thus pushed out to the agents and actors but these work under a larger set of rules. Rigidity in rules and governance can amplify failures in this process.

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Related to the realities of globalization is the advent of the growth in exponential technologies. Technologies with extreme computational power is integrating and create robust communication networks within and outside of the system: the system herein could represent nation-states or companies or industrialization initiatives. Will the exponential technologies diffuse across larger scales quickly and will the corresponding increase in adoption of new technologies change the future of the human condition? There are fears that new technologies would displace large groups of economic participants who are not immediately equipped to incorporate and feed those technologies into the future: that might be on account of disparity in education and wealth, institutional policies, and the availability of opportunities. Since technologies are exponential, we get a performance curve that is difficult for us to understand. In general, we tend to think linearly and this frailty in our thinking removes us from the path to the future sooner than later. What makes this difficult is that the exponential impact is occurring across various sciences and no one body can effectively fathom the impact and the direction. Bill Gates says it well “We always overestimate the change that will occur in the next two years and underestimate the change that will occur in the next ten. Don’t let yourself be lulled into inaction.” Does chaos theory and complexity science arm us with a differentiated tool set than the traditional toolset of strategy roadmaps and product maps? If society is being carried by the intractable and power of the exponent in advances in technology, than a linear map might not serve to provide the right framework to develop strategies for success in the long-term. Rather, a more collaborative and transparent roadmap to encourage the integration of thoughts and models among the actors who are adapting and adjusting dynamically by the sheer force of will would perhaps be an alternative and practical approach in the new era.

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Lately there has been a lot of discussion around climate change. It has been argued, with good reason and empirical evidence, that environment can be adversely impacted on account of mass industrialization, increase in population, resource availability issues, the inability of the market system to incorporate the cost of spillover effects, the adverse impact of moral hazard and the theory of the commons, etc. While there are demurrers who contest the long-term climate change issues, the train seems to have already left the station! The facts do clearly reflect that the climate will be impacted. Skeptics might argue that science has not yet developed a precise predictive model of the weather system two weeks out, and it is foolhardy to conclude a dystopian future on climate fifty years out. However, the alternative argument is that our inability to exercise to explain the near-term effects of weather changes and turbulence does not negate the existence of climate change due to the accretion of greenhouse impact. Boiling a pot of water will not necessarily gives us an understanding of all of the convection currents involved among the water molecules, but it certainly does not shy away from the fact that the water will heat up.

History of Chaos

Chaos is inherent in all compounded things. Strive on with diligence! Buddha

Scientific theories are characterized by the fact that they are open to refutation.  To create a scientific model, there are three successive steps that one follows: observe the phenomenon, translate that into equations, and then solve the equations.

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One of the early philosophers of science, Karl Popper (1902-1994) discussed this at great length in his book – The Logic of Scientific Discovery. He distinguishes scientific theories from metaphysical or mythological assertions. His main theses is that a scientific theory must be open to falsification: it has to be reproducible separately and yet one can gather data points that might refute the fundamental elements of theory. Developing a scientific theory in a manner that can be falsified by observations would result in new and more stable theories over time. Theories can be rejected in favor of a rival theory or a calibration of the theory in keeping with the new set of observations and outcomes that the theories posit. Until Popper’s time and even after, social sciences have tried to work on a framework that would allow the construction of models that would formulate some predictive laws that govern social dynamics. In his book, Poverty of Historicism, Popper maintained that such an endeavor is not fruitful since it does not take into consideration the myriad of minor elements that interact closely with one another in a meaningful way. Hence, he has touched indirectly on the concept of chaos and complexity and how it touches the scientific method. We will now journey into the past and through the present to understand the genesis of the theory and how it has been channelized by leading scientists and philosophers to decipher a framework for study society and nature.

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As we have already discussed, one of the main pillars of Science is determinism: the probability of prediction.  It holds that every event is determined by natural laws. Nothing can happen without an unbroken chain of causes that can be traced all the way back to an initial condition. The deterministic nature of science goes all the way back to Aristotelian times. Interestingly, Aristotle argued that there is some degree of indeterminism and he relegated this to chance or accidents. Chance is a character that makes its presence felt in every plot in the human and natural condition. Aristotle wrote that “we do not have knowledge of a thing until we have grasped its why, that is to say, its cause.” He goes on to illustrate his idea in greater detail – namely, that the final outcome that we see in a system is on account of four kinds of influencers: Matter, Form, Agent and Purpose.

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Matter is what constitutes the outcome. For a chair it might be wood. For a statue, it might be marble. The outcome is determined by what constitutes the outcome.

Form refers to the shape of the outcome. Thus, a carpenter or a sculptor would have a pre-conceived notion of the shape of the outcome and they would design toward that artifact.

Agent refers to the efficient cause or the act of producing the outcome. Carpentry or masonry skills would be important to shape the final outcome.

Finally, the outcome itself must serve a purpose on its own. For a chair, it might be something to sit on, for a statue it might be something to be marveled at.

However, Aristotle also admits that luck and chance can play an important role that do not fit the causal framework in its own right. Some things do happen by chance or luck. Chance is a rare event, it is a random event and it is typically brought out by some purposeful action or by nature.

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We had briefly discussed the Laplace demon and he summarized this wonderfully: “We ought then to consider the resent state of the universe as the effect of its previous state and as the cause of that which is to follow. An intelligence that, at a given instant, could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be uncertain, and the future, like the past, would be open to its eyes.”  He thus admits to the fact that we lack the vast intelligence and we are forced to use probabilities in order to get a sense of understanding of dynamical systems.

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It was Maxwell in his pivotal book “Matter and Motion” published in 1876 lay the groundwork of chaos theory.

“There is a maxim which is often quoted, that “the same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more than once, so that the causes and effects cannot be the same in all respects.  There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts “That like causes produce like effects.” This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied: but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the points cause a railway train to run into another instead of keeping its proper course.” What is interesting however in the above quote is that Maxwell seems to go with the notion that in a great many cases there is no sensitivity to initial conditions.

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In the 1890’s Henri Poincare was the first exponent of chaos theory. He says “it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.” This was a far cry from the Newtonian world which sought order on how the solar system worked. Newton’s model was posted on the basis of the interaction between just two bodies. What would then happen if three bodies or N bodies were introduced into the model. This led to the rise of the Three Body Problem which led to Poincare embracing the notion that this problem could not be solved and can be tackled by approximate numerical techniques. Solving this resulted in solutions that were so tangled that is was difficult to not only draw them, it was near impossible to derive equations to fit the results. In addition, Poincare also discovered that if the three bodies started from slightly different initial positions, the orbits would trace out different paths. This led to Poincare forever being designated as the Father of Chaos Theory since he laid the groundwork on the most important element in chaos theory which is the sensitivity to initial dependence.

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In the early 1960’s, the first true experimenter in chaos was a meteorologist named Edward Lorenz. He was working on a problem in weather prediction and he set up a system with twelve equations to model the weather. He set the initial conditions and the computer was left to predict what the weather might be. Upon revisiting this sequence later on, he inadvertently and by sheer accident, decided to run the sequence again in the middle and he noticed that the outcome was significantly different. The imminent question that followed was why the outcome was so different than the original. He traced this back to the initial condition wherein he noted that the initial input was different with respect to the decimal places. The system incorporated the all of the decimal places rather than the first three. (He had originally input the number .506 and he had concatenated the number from .506127). He would have expected that this thin variation in input would have created a sequence close to the original sequence but that was not to be: it was distinctly and hugely different.  This effect became known as the Butterfly effect which is often substituted for Chaos Theory. Ian Stewart in his book, Does God Play Dice? The Mathematics of Chaos, describes this visually as follows:

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“The flapping of a single butterfly’s wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month’s time, a tornado that would have devastated the Indonesian cost doesn’t happen. Or maybe one that wasn’t going to happen, does.”

Lorenz thus argued that it would be impossible to predict the weather accurately. However, he reduced his experiment to fewer set of equations and took upon observations of how small change in initial conditions affect predictability of smaller systems. He found a parallel – namely, that changes in initial conditions tends to render the final outcome of a system to be inaccurate. As he looked at alternative systems, he found a strange pattern that emerged – namely, that the system always represented a double spiral – the system never settled down to a single point but they never repeated its trajectory. It was a path breaking discovery that led to further advancement in the science of chaos in later years.

Years later, Robert May investigated how this impacts population. He established an equation that reflected a population growth and initialized the equation with a parameter for growth rate value. (The growth rate was initialized to 2.7). May found that as he increased the parameter value, the population grew which was expected. However, once he passed the 3.0 growth value, he noticed that equation would not settle down to a single population but branch out to two different values over time. If he raised the initial value more, the bifurcation or branching of the population would be twice as much or four different values. If he continued to increase the parameter, the lines continue to double until chaos appeared and it became hard to make point predictions.

There was another innate discovery that occurred through the experiment. When one visually looks at the bifurcation, one tends to see similarity between the small and large branches. This self-similarity became an important part of the development of chaos theory.

Benoit Mandelbrot started to study this self-similarity pattern in chaos. He was an economist and he applied mathematical equations to predict fluctuations in cotton prices. He noted that particular price changes were not predictable but there were certain patterns that were repeated and the degree of variation in prices had remained largely constant. This is suggestive of the fact that one might, upon preliminary reading of chaos, arrive at the notion that if weather cannot be predictable, then how can we predict climate many years out. On the contrary, Mandelbrot’s experiments seem to suggest that short time horizons are difficult to predict that long time horizon impact since systems tend to settle into some patterns that is reflecting of smaller patterns across periods. This led to the development of the concept of fractal dimensions, namely that sub-systems develop a symmetry to a larger system.

Feigenbaum was a scientist who became interested in how quickly bifurcations occur. He discovered that regardless of the scale of the system, the came at a constant rate of 4.669. If you reduce or enlarge the scale by that constant, you would see the mechanics at work which would lead to an equivalence in self-similarity. He applied this to a number of models and the same scaling constant took effect. Feigenbaum had established, for the first time, a universal constant around chaos theory. This was important because finding a constant in the realm of chaos theory was suggestive of the fact that chaos was an ordered process, not a random one.

Sir James Lighthill gave a lecture and in that he made an astute observation –

“We are all deeply conscious today that the enthusiasm of our forebears for the marvelous achievements of Newtonian mechanics led them to make generalizations in this area of predictability which, indeed, we may have generally tended to believe before 1960, but which we now recognize were false. We collectively wish to apologize for having misled the general educated public by spreading ideas about determinism of systems satisfying Newton’s laws of motion that, after 1960, were to be proved incorrect.”

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Distribution Economics

Distribution is a method to get products and services to the maximum number of customers efficiently.

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Complexity science is the study of complex systems and the problems that are multi-dimensional, dynamic and unpredictable. It constitutes a set of interconnected relationships that are not always abiding to the laws of cause and effect, but rather the modality of non-linearity. Thomas Kuhn in his pivotal essay: The Structure of Scientific Revolutions posits that anomalies that arise in scientific method rise to the level where it can no longer be put on hold or simmer on a back-burner: rather, those anomalies become the front line for new methods and inquiries such that a new paradigm necessarily must emerge to supplant the old conversations. It is this that lays the foundation of scientific revolution – an emergence that occurs in an ocean of seeming paradoxes and competing theories. Contrary to a simple scientific method that seeks to surface regularities in natural phenomenon, complexity science studies the effects that rules have on agents. Rules do not drive systems toward a predictable outcome: rather it sets into motion a high density of interactions among agents such that the system coalesces around a purpose: that being necessarily that of survival in context of its immediate environment. In addition, the learnings that follow to arrive at the outcome is then replicated over periods to ensure that the systems mutate to changes in the external environment. In theory, the generative rules leads to emergent behavior that displays patterns of parallelism to earlier known structures.

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For any system to survive and flourish, distribution of information, noise and signals in and outside of a CPS or CAS is critical. We have touched at length that the system comprises actors and agents that work cohesively together to fulfill a special purpose. Specialization and scale matter! How is a system enabled to fulfill their purpose and arrive at a scale that ensures long-term sustenance? Hence the discussion on distribution and scale which is a salient factor in emergence of complex systems that provide the inherent moat of “defensibility” against internal and external agents working against it.

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Distribution, in this context, refers to the quality and speed of information processing in the system. It is either created by a set of rules that govern the tie-ups between the constituent elements in the system or it emerges based on a spontaneous evolution of communication protocols that are established in response to internal and external stimuli. It takes into account the available resources in the system or it sets up the demands on resource requirements. Distribution capabilities have to be effective and depending upon the dynamics of external systems, these capabilities might have to be modified effectively. Some distribution systems have to be optimized or organized around efficiency: namely, the ability of the system to distribute information efficiently. On the other hand, some environments might call for less efficiency as the key parameter, but rather focus on establishing a scale – an escape velocity in size and interaction such that the system can dominate the influence of external environments. The choice between efficiency and size is framed by the long-term purpose of the system while also accounting for the exigencies of ebbs and flows of external agents that might threaten the system’s existence.

Partner Ecosystem

Since all systems are subject to the laws of entropy and the impact of unintended consequences, strategies have to be orchestrated accordingly. While it is always naïve to assume exactitude in the ultimate impact of rules and behavior, one would surmise that such systems have to be built around the fault lines of multiple roles for agents or group of agents to ensure that the system is being nudged, more than less, toward the desired outcome. Hence, distribution strategy is the aggregate impact of several types of channels of information that are actively working toward a common goal. The idea is to establish multiple channels that invoke different strategies while not cannibalizing or sabotaging an existing set of channels. These mutual exclusive channels have inherent properties that are distinguished by the capacity and length of the channels, the corresponding resources that the channels use and the sheer ability to chaperone the system toward the overall purpose.

social economics

The complexity of the purpose and the external environment determines the strategies deployed and whether scale or efficiency are the key barometers for success. If a complex system must survive and hopefully replicate from strength to greater strength over time, size becomes more paramount than efficiency. Size makes up for the increased entropy which is the default tax on the system, and it also increases the possibility of the system to reach the escape velocity. To that end, managing for scale by compromising efficiency is a perfectly acceptable means since one is looking at the system with a long-term lens with built-in regeneration capabilities. However, not all systems might fall in this category because some environments are so dynamic that planning toward a long-term stability is not practical, and thus one has to quickly optimize for increased efficiency. It is thus obvious that scale versus efficiency involves risky bets around how the external environment will evolve. We have looked at how the systems interact with external environments: yet, it is just as important to understand how the actors work internally in a system that is pressed toward scale than efficiency, or vice versa. If the objective is to work toward efficiency, then capabilities can be ephemeral: one builds out agents and actors with capabilities that are mission-specific. On the contrary, scale driven systems demand capabilities that involve increased multi-tasking abilities, the ability to develop and learn from feedback loops, and to prime the constraints with additional resources. Scaling demand acceleration and speed: if a complex system can be devised to distribute information and learning at an accelerating pace, there is a greater likelihood that this system would dominate the environment.

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Scaling systems can be approached by adding more agents with varying capabilities. However, increased number of participants exponentially increase the permutations and combinations of channels and that can make the system sluggish. Thus, in establishing the purpose and the subsequent design of the system, it is far more important to establish the rules of engagement. Further, the rules might have some centralized authority that will directionally provide the goal while other rules might be framed in a manner to encourage a pure decentralization of authority such that participants act quickly in groups and clusters to enable execution toward a common purpose.

push pull

In business we are surrounded by uncertainty and opportunities. It is how we calibrate around this that ultimately reflects success. The ideal framework at work would be as follows:

  1. What are the opportunities and what are the corresponding uncertainties associated with the opportunities? An honest evaluation is in order since this is what sets the tone for the strategic framework and direction of the organization.
  2. Should we be opportunistic and establish rules that allow the system to gear toward quick wins: this would be more inclined toward efficiencies. Or should we pursue dominance by evaluating our internal capability and the probability of winning and displacing other systems that are repositioning in advance or in response to our efforts? At which point, speed and scale become the dominant metric and the resources and capabilities and the set of governing rules have to be aligned accordingly.
  3. How do we craft multiple channels within and outside of the system? In business lingo, that could translate into sales channels. These channels are selling products and services and can be adding additional value along the way to the existing set of outcomes that the system is engineered for. The more the channels that are mutually exclusive and clearly differentiated by their value propositions, the stronger the system and the greater the ability to scale quickly. These antennas, if you will, also serve to be receptors for new information which will feed data into the organization which can subsequently process and reposition, if the situation so warrants. Having as many differentiated antennas comprise what constitutes the distribution strategy of the organization.
  4. The final cut is to enable a multi-dimensional loop between external and internal system such that the system expands at an accelerating pace without much intervention or proportionate changes in rules. In other words, system expands autonomously – this is commonly known as the platform effect. Scale does not lead to platform effect although the platform effect most definitely could result in scale. However, scale can be an important contributor to platform effect, and if the latter gets root, then the overall system achieves efficiency and scale in the long run.

Network Theory and Network Effects

Complexity theory needs to be coupled with network theory to get a more comprehensive grasp of the underlying paradigms that govern the outcomes and morphology of emergent systems. In order for us to understand the concept of network effects which is commonly used to understand platform economics or ecosystem value due to positive network externalities, we would like to take a few steps back and appreciate the fundamental theory of networks. This understanding will not only help us to understand complexity and its emergent properties at a low level but also inform us of the impact of this knowledge on how network effects can be shaped to impact outcomes in an intentional manner.

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There are first-order conditions that must be met to gauge whether the subject of the observation is a network. Firstly, networks are all about connectivity within and between systems. Understanding the components that bind the system would be helpful. However, do keep in mind that complexity systems (CPS and CAS) might have emergent properties due to the association and connectivity of the network that might not be fully explained by network theory. All the same, understanding networking theory is a building block to understanding emergent systems and the outcome of its structure on addressing niche and macro challenges in society.

network bible

Networks operates spatially in a different space and that has been intentionally done to allow some simplification and subsequent generalization of principles. The geometry of network is called network topology. It is a 2D perspective of connectivity.

Networks are subject to constraints (physical resources, governance constraint, temporal constraints, channel capacity, absorption and diffusion of information, distribution constraint) that might be internal (originated by the system) or external (originated in the environment that the network operates in).

network phone

Finally, there is an inherent non-linearity impact in networks. As nodes increase linearly, connections will increase exponentially but might be subject to constraints. The constraints might define how the network structure might morph and how information and signals might be processed differently.

 

Graph theory is the most widely used tool to study networks. It consists of four parts: vertices which represent an element in the network, edges refer to relationship between nodes which we call links, directionality which refers to how the information is passed ( is it random and bi-directional or follows specific rules and unidirectional), channels that refer to bandwidth that carry information, and finally the boundary which establishes specificity around network operations. A graph can be weighted – namely, a number can be assigned to each length to reflect the degree of interaction or the strength of resources or the proximity of the nodes or the ordering of discernible clusters.

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The central concept of network theory thus revolves around connectivity between nodes and how non-linear emergence occurs. A node can have multiple connections with other node/nodes and we can weight the node accordingly. In addition, the purpose of networks is to pass information in the most efficient manner possible which relays into the concept of a geodesic which is either the shortest path between two nodes that must work together to achieve a purpose or the least number of leaps through links that information must negotiate between the nodes in the network.

 

Technically, you look for the longest path in the network and that constitutes the diameter while you calculate the average path length by examining the shortest path between nodes, adding all of those paths up and then dividing by the number of pairs. Significance of understanding the geodesic allows an understanding of the size of the network and throughput power that the network is capable of.

 

Nodes are the atomic elements in the network. It is presumed that its degree of significance is related to greater number of connections. There are other factors that are important considerations: how adjacent or close are the nodes to one another, does some nodes have authority or remarkable influence on others, are nodes positioned to be a connector between other nodes, and how capable are the nodes in absorbing, processing and diffusing the information across the links or channels. How difficult is it for the agents or nodes in the network to make connections? It is presumed that if the density of the network is increased, then we create a propensity in the overall network system to increase the potential for increased connectivity.

android network

As discussed previously, our understanding of the network is deeper once we understand the elements well. The structure or network topology is represented by the graph and then we must understand size of network and the patterns that are manifested in the visual depiction of the network. Patterns, for our purposes, might refer to clusters of nodes that are tribal or share geographical proximity that self-organize and thus influence the structure of the network. We will introduce a new term homophily where agents connect with those like themselves. This attribute presumably allows less resources needed to process information and diffuse outcomes within the cluster. Most networks have a cluster bias: in other words, there are areas where there is increased activity or increased homogeneity in attributes or some form of metric that enshrines a group of agents under one specific set of values or activities. Understanding the distribution of cluster and the cluster bias makes it easier to influence how to propagate or even dismantle the network. This leads to an interesting question: Can a network that emerges spontaneously from the informal connectedness between agents be subjected to some high dominance coefficient – namely, could there be nodes or links that might exercise significant weight on the network?

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The network has to align to its environment. The environment can place constraints on the network. In some instances, the agents have to figure out how to overcome or optimize their purpose in the context of the presence of the environmental constraints.  There is literature that suggests the existence of random networks which might be an initial state, but it is widely agreed that these random networks self-organize around their purpose and their interaction with its environment. Network theory assigns a number to the degree of distribution which means that all or most nodes have an equivalent degree of connectivity and there is no skewed influence being weighed on the network by a node or a cluster. Low numbers assigned to the degree of distribution suggest a network that is very democratic versus high number that suggests centralization.  To get a more practical sense, a mid-range number assigned to a network constitutes a decentralized network which has close affinities and not fully random. We have heard of the six degrees of separation and that linkage or affinity is most closely tied to a mid-number assignment to the network.airbnb

We are now getting into discussions on scale and binding this with network theory. Metcalfe’s law states that the value of a network grows as a square of the number of the nodes in the network. More people join the network, the more valuable the network. Essentially, there is a feedback loop that is created, and this feedback loop can kindle a network to grow exponentially. There are two other topics – Contagion and Resilience. Contagion refers to the ability of the agents to diffuse information. This information can grow the network or dismantle it. Resilience refers to how the network is organized to preserve its structure. As you can imagine, they have huge implications that we see.  How do certain ideas proliferate over others, how does it cluster and create sub-networks which might grow to become large independent networks and how it creates natural defense mechanisms against self-immolation and destruction?

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Network effect is commonly known as externalities in economics. It is an effect that is external to the transaction but influences the transaction. It is the incremental benefit gained by an existing user for each new user that joins the network.  There are two types of network effects: Direct network effects and Indirect network effect. Direct network effects are same side effects. The value of a service goes up as the number of users goes up. For example, if more people have phones, it is useful for you to have a phone. The entire value proposition is one-sided. Indirect networks effects are multi-sided. It lends itself to our current thinking around platforms and why smart platforms can exponentially increase the network. The value of the service increases for one user group when a new user group joins the network. Take for example the relationship between credit card banks, merchants and consumers. There are three user groups, and each gather different value from the network of agents that have different roles. If more consumers use credit cards to buy, more merchants will sign up for the credit cards, and as more merchants sign up – more consumers will sign up with the bank to get more credit cards. This would be an example of a multi-sided platform that inherently has multi-sided network effects. The platform inherently gains significant power such that it becomes more valuable for participants in the system to join the network despite the incremental costs associated with joining the network. Platforms that are built upon effective multi-sided network effects grow quickly and are generally sustainable. Having said that, it could be just as easy that a few dominant bad actors in the network can dismantle and unravel the network completely. We often hear of the tipping point: namely, that once the platform reaches a critical mass of users, it would be difficult to dismantle it. That would certainly be true if the agents and services are, in the aggregate, distributed fairly across the network: but it is also possible that new networks creating even more multi-sided network effects could displace an entrenched network. Hence, it is critical that platform owners manage the quality of content and users and continue to look for more opportunities to introduce more user groups to entrench and yet exponentially grow the network.

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Winner Take All Strategy

Being the first to cross the finish line makes you a winner in only one phase of life. It’s what you do after you cross the line that really counts.
– Ralph Boston

Does winner-take-all strategy apply outside the boundaries of a complex system? Let us put it another way. If one were to pursue a winner-take-all strategy, then does this willful strategic move not bind them to the constraints of complexity theory? Will the net gains accumulate at a pace over time far greater than the corresponding entropy that might be a by-product of such a strategy? Does natural selection exhibit a winner-take-all strategy over time and ought we then to regard that winning combination to spur our decisions around crafting such strategies? Are we fated in the long run to arrive at a world where there will be a very few winners in all niches and what would that mean? How does that surmise with our good intentions of creating equal opportunities and a fair distribution of access to resources to a wider swath of the population? In other words, is a winner take all a deterministic fact and does all our trivial actions to counter that constitute love’s labor lost?

business award

Natural selection is a mechanism for evolution. It explains how populations or species evolve or modify over time in such a manner that it becomes better suited to their environments. Recall the discussion on managing scale in the earlier chapter where we discussed briefly about aligning internal complexity to external complexity. Natural selection is how it plays out at a biological level. Essentially natural selection posits that living organisms have inherited traits that help them to survive and procreate. These organisms will largely leave more offspring than their peers since the presumption is that these organisms will carry key traits that will survive the vagaries of external complexity and environment (predators, resource scarcity, climate change, etc.) Since these traits are passed on to the next generate, these traits will become more common until such time that the traits are dominant over generations, if the environment has not been punctuated with massive changes. These organisms with these dominant traits will have adapted to their environment. Natural selection does not necessarily suggest that what is good for one is good for the collective species.

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An example that was shared by Robert Frank in his book “The Darwin Economy” was the case of large antlers of the bull elk. These antlers developed as an instrument for attracting mates rather than warding off predators. Big antlers would suggest a greater likelihood of the bull elk to marginalize the elks with smaller antlers. Over time, the bull elks with small antlers would die off since they would not be able to produce offspring and pass their traits. Thus, the bull elks would largely comprise of those elks with large antlers. However, the flip side is that large antlers compromise mobility and thus are more likely to be attacked by predators. Although the individual elk with large antler might succeed to stay around over time, it is also true that the compromised mobility associated with large antlers would overall hurt the propagation of the species as a collective group. We will return to this very important concept later. The interests of individual animals were often profoundly in conflict with the broader interests of their own species. Corresponding to the development of the natural selection mechanism is the introduction of the concept of the “survival of the fittest” which was introduced by Herbert Spencer. One often uses natural selection and survival of the fittest interchangeable and that is plain wrong. Natural selection never claims that the species that will emerge is the strongest, the fastest, the largest, etc.: it simply claims that the species will be the fittest, namely it will evolve in a manner best suited for the environment in which it resides. Put it another way: survival of the most sympathetic is perhaps more applicable. Organisms that are more sympathetic and caring and work in harmony with the exigencies of an environment that is largely outside of their control would likely succeed and thrive.

dig collab

We will digress into the world of business. A common conception that is widely discussed is that businesses must position toward a winner-take-all strategy – especially, in industries that have very high entry costs. Once these businesses entrench themselves in the space, the next immediate initiative would be to literally launch a full-frontal assault involving huge investments to capture the mind and the wallet of the customer. Peter Thiel says – Competition is for losers. If you want to create and capture lasting value, look to build a monopoly.” Once that is built, it would be hard to displace!

NEffect

Scaling the organization intentionally is key to long-term success. There are a number of factors that contribute toward developing scale and thus establishing a strong footing in the particular markets. We are listing some of the key factors below:

  1. Barriers to entry: Some organizations have natural cost prohibitive barriers to entry like utility companies or automobile plants. They require large investments. On the other hand, organizations can themselves influence and erect huge barriers to entry even though the barriers did not exist. Organizations would massively invest in infrastructure, distribution, customer acquisition and retention, brand and public relations. Organizations that are able to rapidly do this at a massive scale would be the ones that is expected to exercise their leverage over a big consumption base well into the future.
  2. Multi-sided platform impacts: The value of information across multiple subsystems: company, supplier, customer, government increases disproportionately as it expands. We had earlier noted that if cities expand by 100%, then there is increasing innovating and goods that generate 115% -the concept of super-linear scaling. As more nodes are introduced into the system and a better infrastructure is created to support communication and exchange between the nodes, the more entrenched the business becomes. And interestingly, the business grows at a sub-linear scale – namely, it consumes less and less resources in proportion to its growth. Hence, we see the large unicorn valuation among companies where investors and market makers place calculated bets on investments of colossal magnitudes. The magnitude of such investments is relatively a recent event, and this is largely driven by the advances in technology that connect all stakeholders.
  3. Investment in learning: To manage scale is to also be selective of information that a system receives and how the information is processed internally. In addition, how is this information relayed to the external system or environment. This requires massive investment in areas like machine learning, artificial intelligence, big data, enabling increased computational power, development of new learning algorithms, etc. This means that organizations have to align infrastructure and capability while also working with external environments through public relations, lobbying groups and policymakers to chaperone a comprehensive and a very complex hard-to-replicate learning organism.
  4. Investment in brand: Brand personifies the value attributes of an organization. One connects brand to customer experience and perception of the organization’s product. To manage scale and grow, organizations must invest in brand: to capture increased mindshare of the consumer. In complexity science terms, the internal systems are shaped to emit powerful signals to the external environment and urge a response. Brand and learning work together to allow a harmonic growth of an internal system in the context of its immediate environment.

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However, one must revert to the science of complexity to understand the long-term challenges of a winner-take-all mechanism. We have already seen the example that what is good for the individual bull-elk might not be the best for the species in the long-term. We see that super-linear scaling systems also emits significant negative by-products. Thus, the question that we need to ask is whether the organizations are paradoxically cultivating their own seeds of destruction in their ambitions of pursuing scale and market entrenchment.

Internal versus External Scale

This article discusses internal and external complexity before we tee up a more detailed discussion on internal versus external scale. This chapter acknowledges that complex adaptive systems have inherent internal and external complexities which are not additive. The impact of these complexities is exponential. Hence, we have to sift through our understanding and perhaps even review the salient aspects of complexity science which have already been covered in relatively more detail in earlier chapter. However, revisiting complexity science is important, and we will often revisit this across other blog posts to really hit home the fundamental concepts and its practical implications as it relates to management and solving challenges at a business or even a grander social scale.

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A complex system is a part of a larger environment. It is a safe to say that the larger environment is more complex than the system itself. But for the complex system to work, it needs to depend upon a certain level of predictability and regularity between the impact of initial state and the events associated with it or the interaction of the variables in the system itself. Note that I am covering both – complex physical systems and complex adaptive systems in this discussion. A system within an environment has an important attribute: it serves as a receptor to signals of external variables of the environment that impact the system. The system will either process that signal or discard the signal which is largely based on what the system is trying to achieve. We will dedicate an entire article on system engineering and thinking later, but the uber point is that a system exists to serve a definite purpose. All systems are dependent on resources and exhibits a certain capacity to process information. Hence, a system will try to extract as many regularities as possible to enable a predictable dynamic in an efficient manner to fulfill its higher-level purpose.

compl pro

Let us understand external complexities. We can interchangeably use the word environmental complexity as well.  External complexity represents physical, cultural, social, and technological elements that are intertwined. These environments beleaguered with its own grades of complexity acts as a mold to affect operating systems that are mere artifacts. If operating systems can fit well within the mold, then there is a measure of fitness or harmony that arises between an internal complexity and external complexity. This is the root of dynamic adaptation. When external environments are very complex, that means that there are a lot of variables at play and thus, an internal system has to process more information in order to survive. So how the internal system will react to external systems is important and they key bridge between those two systems is in learning. Does the system learn and improve outcomes on account of continuous learning and does it continually modify its existing form and functional objectives as it learns from external complexity? How is the feedback loop monitored and managed when one deals with internal and external complexities? The environment generates random problems and challenges and the internal system has to accept or discard these problems and then establish a process to distribute the problems among its agents to efficiently solve those problems that it hopes to solve for. There is always a mechanism at work which tries to align the internal complexity with external complexity since it is widely believed that the ability to efficiently align the systems is the key to maintaining a relatively competitive edge or intentionally making progress in solving a set of important challenges.

Internal complexity are sub-elements that interact and are constituents of a system that resides within the larger context of an external complex system or the environment. Internal complexity arises based on the number of variables in the system, the hierarchical complexity of the variables, the internal capabilities of information pass-through between the levels and the variables, and finally how it learns from the external environment. There are five dimensions of complexity: interdependence, diversity of system elements, unpredictability and ambiguity, the rate of dynamic mobility and adaptability, and the capability of the agents to process information and their individual channel capacities.

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If we are discussing scale management, we need to ask a fundamental question. What is scale in the context of complex systems? Why do we manage for scale? How does management for scale advance us toward a meaningful outcome? How does scale compute in internal and external complex systems? What do we expect to see if we have managed for scale well? What does the future bode for us if we assume that we have optimized for scale and that is the key objective function that we have to pursue?

Scaling Considerations in Complex Systems and Organizations: Implications

Scale represents size. In a two-dimensional world, it is a linear measurement that presents a nominal ordering of numbers. In other words, 4 is two times two and 6 would be 3 times two. In other words, the difference between 4 and 6 represents an increase in scale by two. We will discuss various aspects of scale and the learnings that we can draw from it. However, before we go down this path, we would like to touch on resource consumption.

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As living organisms, we consume resources. An average human being requires 2000 calories of food per day to sustain themselves. An average human being, by the way, is largely defined in terms of size. So it would be better put if we say that a 200lb person would require 2000 calories. However, if we were to regard a specimen that is 10X the size or 2000 lbs., would it require 10X the calories to sustain itself? Conversely, if the specimen was 1/100th the size of the average human being, then would it require 1/100th the calories to sustain itself. Thus, will we consume resources linearly to our size? Are we operating in a simple linear world? And if not, what are the ramifications for science, physics, biology, organizations, cities, climate, etc.?

Let us digress a little bit from the above questions and lay out a few interesting facts. Almost half of the population in the world today live in cities. This is compared to less than 15% of the world population that lived in cities a hundred years ago.  It is anticipated that almost 75% of the world population will be living in cities by 2050. The number of cities will increase and so will the size. But for cities to increase in size and numbers, it requires vast amount of resources. In fact, the resource requirements in cities are far more extensive than in agrarian societies. If there is a limit to the resources from a natural standpoint – in other words, if the world is operating on a budget of natural resources – then would this mean that the growth of the cities will be naturally reined in? Will cities collapse because of lack of resources to support its mass?

What about companies? Can companies grow infinitely?  Is there a natural point where companies might hit their limit beyond which growth would not be possible? Could a company collapse because the amount of resources that is required to sustain the size would be compromised? Are there other factors aside from resource consumption that play into what might cap the growth and hence the size of the company? Are there overriding factors that come into play that would superimpose the size-resource usage equation such that our worries could be safely kept aside? Are cities and companies governed by some sort of metabolic rate that governs the sustenance of life?

gw scale title

Geoffrey West, a theoretical physicist, has touched on a lot of the questions in his book: Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies.     He says that a person requires about 90W (watts) of energy to survive. That is a light bulb burning in your living room in one day.  That is our metabolic rate. However, just like man does not live by bread alone, an average man has to depend on a number of other artifacts that have agglomerated in bits and pieces to provide a quality of life to maximize sustenance. The person has to have laws, electricity, fuel, automobile, plumbing and water, markets, banks, clothes, phones and engage with other folks in a complex social network to collaborate and compete to achieve their goals. Geoffrey West says that the average person requires almost 11000W or the equivalent of almost 125 90W light bulbs. To put things in greater perspective, the social metabolic rate of 11,000W is almost equivalent to a dozen elephants.  (An elephant requires 10X more energy than humans even though they might be 60X the size of the physical human being). Thus, a major portion of our energy is diverted to maintain the social and physical network that closely interplay to maintain our sustenance.  And while we consume massive amounts of energy, we also create a massive amount of waste – and that is an inevitable outcome. This is called the entropy impact and we will touch on this in greater detail in later articles. Hence, our growth is not only constrained by our metabolic rate: it is further dampened by entropy that exists as the Second Law of Thermodynamics.   And as a system ages, the impact of entropy increases manifold. Yes, it is true: once we get old, we are racing toward our death at a faster pace than when we were young. Our bodies are exhibiting fatigue faster than normal.

Scaling refers to how a system responds when its size changes. As mentioned  earlier, does scaling follow a linear model? Do we need to consume 2X resources if we increase the size by 2X? How does scaling impact a Complex Physical System versus a Complex Adaptive System? Will a 2X impact on the initial state create perturbations in a CPS model which is equivalent to 2X? How would this work on a CAS model where the complexity is far from defined and understood because these systems are continuously evolving? Does half as big requires half as much or conversely twice as big requires twice as much? Once again, I have liberally dipped into this fantastic work by Geoffrey West to summarize, as best as possible, the definitions and implications. He proves that we cannot linearly extrapolate energy consumption and size: the world is smattered with evidence that undermines the linear extrapolation model. In fact, as you grow, you become more efficient with respect to energy consumption. The savings of energy due to growth in size is commonly called the economy of scale. His research also suggests two interesting results. When cities or social systems grow, they require an infrastructure to help with the growth. He discovered that it takes 85% resource consumption to grow the systems by 100%. Thus, there is a savings of 15% which is slightly lower than what has been studied on the biological front wherein organisms save 25% as they grow. He calls this sub linear scaling. In contrast, he also introduces the concept of super linear scaling wherein there is a 15% increasing returns to scale when the city or a social system grows. In other words, if the system grows by 100%, the positive returns with respect to such elements like patents, innovation, etc.   will grow by 115%. In addition, the negative elements also grow in an equivalent manner – crime, disease, social unrest, etc. Thus, the growth in cities are supported by an efficient infrastructure that generates increasing returns of good and bad elements.

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Max Kleiber, a Swiss chemist, in the 1930’s proposed the Kleiber’s law which sheds a lot of light on metabolic rates as energy consumption per unit of time. As mass increases so does the overall metabolic rate but it is not a linear relation – it obeys the power law. It stays that a living organism’s metabolic rate scales to the ¾ power of its mass. If the cat has a mass 100 times that of a mouse, the cat will metabolize about 100 ¾ = 31.63 times more energy per day rather than 100 times more energy per day.  Kleiber’s law has led to the metabolic theory of energy and posits that the metabolic rate of organisms is the fundamental biological rate that governs most observed patters in our immediate ecology. There is some ongoing debate on the mechanism that allows metabolic rate to differ based on size. One mechanism is that smaller organisms have higher surface area to volume and thus needs relatively higher energy versus large organisms that have lower surface area to volume. This assumes that energy consumption occurs across surface areas. However, there is another mechanism that argues that energy consumption happens when energy needs are distributed through a transport network that delivers and synthesizes energy. Thus, smaller organisms do not have as a rich a network as large organisms and thus there is greater energy efficiency usage among smaller organisms than larger organisms. Either way, the implications are that body size and temperature (which is a result of internal activity) provide fundamental and natural constraints by which our ecological processes are governed. This leads to another concept called finite time singularity which predicts that unbounded growth cannot be sustained because it would need infinite resources or some K factor that would allow it to increase. The K factor could be innovation, a structural shift in how humans and objects cooperate, or even a matter of jumping on a spaceship and relocating to Mars.

power law

We are getting bigger faster. That is real. The specter of a dystopian future hangs upon us like the sword of Damocles. The thinking is that this rate of growth and scale is not sustainable since it is impossible to marshal the resources to feed the beast in an adequate and timely manner. But interestingly, if we were to dig deeper into history – these thoughts prevailed in earlier times as well but perhaps at different scale. In 1798 Thomas Robert Malthus famously predicted that short-term gains in living standards would inevitably be undermined as human population growth outstripped food production, and thereby drive living standards back toward subsistence. Humanity thus was checkmated into an inevitable conclusion: a veritable collapse spurred by the tendency of population to grow geometrically while food production would increase only arithmetically. Almost two hundred years later, a group of scientists contributed to the 1972 book called Limits to Growth which had similar refrains like Malthus: the population is growing and there are not enough resources to support the growth and that would lead to the collapse of our civilization. However, humanity has negotiated those dark thoughts and we continue to prosper. If indeed, we are governed by this finite time singularity, we are aware that human ingenuity has largely won the day. Technology advancements, policy and institutional changes, new ways of collaboration, etc. have emerged to further delay this “inevitable collapse” that could be result of more mouths to feed than possible.  What is true is that the need for new innovative models and new ways of doing things to solve the global challenges wrought by increased population and their correspondent demands will continue to increase at a quicker pace. Once could thus argue that the increased pace of life would not be sustainable. However, that is not a plausible hypothesis based on our assessment of where we are and where we have been.

Let us turn our attention to a business. We want the business to grow or do we want the business to scale? What is the difference? To grow means that your company is adding resources or infrastructure to handle increased demand, at a cost which is equivalent to the level of increased revenue coming in. Scaling occurs when the business is growing faster than the resources that are being consumed. We have already explored that outlier when you grow so big that you are crushed by your weight. It is that fact which limits the growth of organism regardless of issues related to scale. Similarly, one could conceivably argue that there are limits to growth of a company and might even turn to history and show that a lot of large companies of yesteryears have collapsed. However, it is also safe to say that large organizations today are by several factors larger than the largest organizations in the past, and that is largely on account of accumulated knowledge and new forms of innovation and collaboration that have allowed that to happen. In other words, the future bodes well for even larger organizations and if those organizations indeed reach those gargantuan size, it is also safe to draw the conclusion that they will be consuming far less resources relative to current organizations, thus saving more energy and distributing more wealth to the consumers.

Thus, scaling laws limit growth when it assumes that everything else is constant. However, if there is innovation that leads to structural changes of a system, then the limits to growth becomes variable. So how do we effect structural changes? What is the basis? What is the starting point? We look at modeling as a means to arrive at new structures that might allow the systems to be shaped in a manner such that the growth in the systems are not limited by its own constraints of size and motion and temperature (in physics parlance).  Thus, a system is modeled at a presumably small scale but with the understanding that as the system is increases in size, the inner workings of emergent complexity could be a problem. Hence, it would be prudent to not linearly extrapolate the model of a small system to that of a large one but rather to exponential extrapolate the complexity of the new system that would emerge. We will discuss this in later articles, but it would be wise to keep this as a mental note as we forge ahead and refine our understanding of scale and its practical implications for our daily consumption.

Model Thinking

Model Framework

The fundamental tenet of theory is the concept of “empiria“. Empiria refers to our observations. Based on observations, scientists and researchers posit a theory – it is part of scientific realism.

A scientific model is a causal explanation of how variables interact to produce a phenomenon, usually linearly organized.  A model is a simplified map consisting of a few, primary variables that is gauged to have the most explanatory powers for the phenomenon being observed.  We discussed Complex Physical Systems and Complex Adaptive Systems early on this chapter. It is relatively easier to map CPS to models than CAS, largely because models become very unwieldy as it starts to internalize more variables and if those variables have volumes of interaction between them. A simple analogy would be the use of multiple regression models: when you have a number of independent variables that interact strongly between each other, autocorrelation errors occur, and the model is not stable or does not have predictive value.

thinking

Research projects generally tend to either look at a case study or alternatively, they might describe a number of similar cases that are logically grouped together. Constructing a simple model that can be general and applied to many instances is difficult, if not impossible. Variables are subject to a researcher’s lack of understanding of the variable or the volatility of the variable. What further accentuates the problem is that the researcher misses on the interaction of how the variables play against one another and the resultant impact on the system. Thus, our understanding of our system can be done through some sort of model mechanics but, yet we share the common belief that the task of building out a model to provide all of the explanatory answers are difficult, if not impossible. Despite our understanding of our limitations of modeling, we still develop frameworks and artifact models because we sense in it a tool or set of indispensable tools to transmit the results of research to practical use cases. We boldly generalize our findings from empiria into general models that we hope will explain empiria best. And let us be mindful that it is possible – more so in the CAS systems than CPS that we might have multiple models that would fight over their explanatory powers simply because of the vagaries of uncertainty and stochastic variations.

Popper says: “Science does not rest upon rock-bottom. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or ‘given’ base; and when we cease our attempts to drive our piles into a deeper layer, it is not because we have reached firm ground. We simply stop when we are satisfied that they are firm enough to carry the structure, at least for the time being”. This leads to the satisficing solution: if a model can choose the least number of variables to explain the greatest amount of variations, the model is relatively better than other models that would select more variables to explain the same. In addition, there is always a cost-benefit analysis to be taken into consideration: if we add x number of variables to explain variation in the outcome but it is not meaningfully different than variables less than x, then one would want to fall back on the less-variable model because it is less costly to maintain.

problemsol

Researchers must address three key elements in the model: time, variation and uncertainty. How do we craft a model which reflects the impact of time on the variables and the outcome? How to present variations in the model? Different variables might vary differently independent of one another. How do we present the deviation of the data in a parlance that allows us to make meaningful conclusions regarding the impact of the variations on the outcome? Finally, does the data that is being considered are actual or proxy data? Are the observations approximate? How do we thus draw the model to incorporate the fuzziness: would confidence intervals on the findings be good enough?

Two other equally other concepts in model design is important: Descriptive Modeling and Normative Modeling.

Descriptive models aim to explain the phenomenon. It is bounded by that goal and that goal only.

There are certain types of explanations that they fall back on: explain by looking at data from the past and attempting to draw a cause and effect relationship. If the researcher is able to draw a complete cause and effect relationship that meets the test of time and independent tests to replicate the results, then the causality turns into law for the limited use-case or the phenomenon being explained. Another explanation method is to draw upon context: explaining a phenomenon by looking at the function that the activity fulfills in its context. For example, a dog barks at a stranger to secure its territory and protect the home. The third and more interesting type of explanation is generally called intentional explanation: the variables work together to serve a specific purpose and the researcher determines that purpose and thus, reverse engineers the understanding of the phenomenon by understanding the purpose and how the variables conform to achieve that purpose.

This last element also leads us to thinking through the other method of modeling – namely, normative modeling. Normative modeling differs from descriptive modeling because the target is not to simply just gather facts to explain a phenomenon, but rather to figure out how to improve or change the phenomenon toward a desirable state. The challenge, as you might have already perceived, is that the subjective shadow looms high and long and the ultimate finding in what would be a normative model could essentially be a teleological representation or self-fulfilling prophecy of the researcher in action. While this is relatively more welcome in a descriptive world since subjectivism is diffused among a larger group that yields one solution, it is not the best in a normative world since variation of opinions that reflect biases can pose a problem.

How do we create a representative model of a phenomenon? First, we weigh if the phenomenon is to be understood as a mere explanation or to extend it to incorporate our normative spin on the phenomenon itself. It is often the case that we might have to craft different models and then weigh one against the other that best represents how the model can be explained. Some of the methods are fairly simple as in bringing diverse opinions to a table and then agreeing upon one specific model. The advantage of such an approach is that it provides a degree of objectivism in the model – at least in so far as it removes the divergent subjectivity that weaves into the various models. Other alternative is to do value analysis which is a mathematical method where the selection of the model is carried out in stages. You define the criteria of the selection and then the importance of the goal (if that be a normative model). Once all of the participants have a general agreement, then you have the makings of a model. The final method is to incorporate all all of the outliers and the data points in the phenomenon that the model seeks to explain and then offer a shared belief into those salient features in the model that would be best to apply to gain information of the phenomenon in a predictable manner.

business model

There are various languages that are used for modeling:

Written Language refers to the natural language description of the model. If price of butter goes up, the quantity demanded of the butter will go down. Written language models can be used effectively to inform all of the other types of models that follow below. It often goes by the name of “qualitative” research, although we find that a bit limiting.  Just a simple statement like – This model approximately reflects the behavior of people living in a dense environment …” could qualify as a written language model that seeks to shed light on the object being studied.

Icon Models refer to a pictorial representation and probably the earliest form of model making. It seeks to only qualify those contours or shapes or colors that are most interesting and relevant to the object being studied. The idea of icon models is to pictorially abstract the main elements to provide a working understanding of the object being studied.

Topological Models refer to how the variables are placed with respect to one another and thus helps in creating a classification or taxonomy of the model. Once can have logical trees, class trees, Venn diagrams, and other imaginative pictorial representation of fields to further shed light on the object being studied. In fact, pictorial representations must abide by constant scale, direction and placements. In other words, if the variables are placed on a different scale on different maps, it would be hard to draw logical conclusions by sight alone. In addition, if the placements are at different axis in different maps or have different vectors, it is hard to make comparisons and arrive at a shared consensus and a logical end result.

Arithmetic Models are what we generally fall back on most. The data is measured with an arithmetic scale. It is done via tables, equations or flow diagrams. The nice thing about arithmetic models is that you can show multiple dimensions which is not possible with other modeling languages. Hence, the robustness and the general applicability of such models are huge and thus is widely used as a key language to modeling.

Analogous Models refer to crafting explanations using the power of analogy. For example, when we talk about waves – we could be talking of light waves, radio waves, historical waves, etc.  These metaphoric representations can be used to explain phenomenon, but at best, the explanatory power is nebulous, and it would be difficult to explain the variations and uncertainties between two analogous models.  However, it still is used to transmit information quickly through verbal expressions like – “Similarly”, “Equivalently”, “Looks like ..” etc. In fact, extrapolation is a widely used method in modeling and we would ascertain this as part of the analogous model to a great extent. That is because we time-box the variables in the analogous model to one instance and the extrapolated model to another instance and we tie them up with mathematical equations.

 

Emergent Systems: Introduction

The whole is greater than the sum of its parts. “Emergent properties” refer to those properties that emerge that might be entirely unexpected. As discussed in CAS, they arise from the collaborative functioning of a system. In other words, emergent properties are properties of a group of items, but it would be erroneous for us to reduce such systems into properties of atomic elements and use those properties as binding elements to understand emergence Some common examples of emergent properties include cities, bee hives, ant colonies and market systems. Out thinking attributes causal effects – namely, that behavior of elements would cause certain behaviors in other hierarchies and thus an entity emerges at a certain state. However, we observe that a process of emergence is the observation of an effect without an apparent cause. Yet it is important to step back and regard the relationships and draw lines of attribution such that one can concur that there is an impact of elements at the lowest level that surfaces, in some manner, at the highest level which is the subject of our observation.

emergent

Jochenn Fromm in his paper “Types and Forms of Emergence” has laid this out best. He says that emergent properties are “amazing and paradox: fundamental but familiar.” In other words, emergent properties are changeless and changing, constant and fluctuating, persistent and shifting, inevitable and unpredictable. The most important note that he makes is that the emergent property is part of the system and at the same time it might not always be a part of the system. There is an undercurrent of novelty or punctuated gaps that might arise that is inexplicable, and it is this fact that renders true emergence virtually irreducible. Thus, failure is embodied in all emergent systems – failure being that the system does not behave according to expectation. Despite all rules being followed and quality thresholds are established at every toll gate at the highest level, there is still a possibility of failure which suggests that there is some missing information in the links. It is also possible that the missing information is dynamic – you do not step in the same water twice – which makes the study to predict emergent systems to be a rather difficult exercise. Depending on the lens through which we look at, the system might appear or disappear.

emergent cas

There are two types of emergence: Descriptive and Explanatory emergence. Descriptive emergence means that properties of wholes cannot be necessarily defined through the properties of the pasts. Explanatory emergence means laws of complex systems cannot be deduced from the laws of interaction of simpler elements that constitute it. Thus the emergence is a result of the amount of variety embodied in the system, the amount of external influence that weights and shapes the overall property and direction of the system, the type of resources that the system consumes, the type of constraints that the system is operating under and the number of levels of sub-systems that work together to build out the final system. Thus, systems can be benign as in the system is relatively more predictable whereas a radical system is a material departure of a system from expectation. If the parts that constitute a system is independent of its workings from other parts and can be boxed within boundaries, emergent systems become more predictable. A watch is an example of a system that follows the different mechanical elements in a watch that are geared for reading the time as it ultimate purpose. It is a good example of a complex physical system. However, these systems are very brittle – a failure in one point can cascade into a failure of the entire system. Systems that are more resilient are those where the elements interact and learn from one another. In other words, the behavior of the elements excites other elements – all of which work together to create a dance toward a more stable state. They deploy what is often called the flocking trick and the pheromone trick. Flocking trick is largely the emulation of the particles that are close to each other – very similar to the cellular automata as introduced by Neumann and discussed in the earlier chapter. The Pheromone trick reflects how the elements leave marks that are acted upon as signals by other elements and thus they all work together around these signal trails to behave and thus act as a forcing function to create the systems.

emerg strategy

There are systems that have properties of extremely strong emergence. What does Consciousness, Life, and Culture have in common? How do we look at Climate? What about the organic development of cities? These are just some examples of system where determinism is nigh impossible. We might be able to tunnel through the various and diverse elements that embody the system, but it would be difficult to coherently and tangibly draw all set of relationships, signals, effectors and detectors, etc. to grapple with a complete understanding of the system. Wrestling a strong emergent system would be a task that might even be outside the purview of the highest level of computational power available. And yet, these systems exist, and they emerge and evolve. Yet we try to plan for these systems or plan to direct policies to influence the system, not fully knowing the impact. This is also where the unintended consequences of our action might take free rein.