Category Archives: scale

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?

line chaos

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.

embrace chaos

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?


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.


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.


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.

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.


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.


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.


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.


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.