Category Archives: growth

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.

scales

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.

sublinear

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.