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.

 

The Law of Unintended Consequences

The Law of Unintended Consequence is that the actions of a central body that might claim omniscient, omnipotent and omnivalent intelligence might, in fact, lead to consequences that are not anticipated or unintended.

The concept of the Invisible Hand as introduced by Adam Smith argued that it is the self-interest of all the market agents that ultimately create a system that maximizes the good for the greatest amount of people.

Robert Merton, a sociologist, studied the law of unintended consequence. In an influential article titled “The Unanticipated Consequences of Purposive Social Action,” Merton identified five sources of unanticipated consequences.

Ignorance makes it difficult and impossible to anticipate the behavior of every element or the system which leads to incomplete analysis.

Errors that might occur when someone uses historical data and applies the context of history into the future. Linear thinking is a great example of an error that we are wrestling with right now – we understand that there are systems, looking back, that emerge exponentially but it is hard to decipher the outcome unless one were to take a leap of faith.

Biases work its way into the study as well. We study a system under the weight of our biases, intentional or unintentional. It is hard to strip that away even if there are different bodies of thought that regard a particular system and how a certain action upon the system would impact it.

Weaved with the element of bias is the element of basic values that may require or prohibit certain actions even if the long-term impact is unfavorable. A good example would be the toll gates established by the FDA to allow drugs to be commercialized. In its aim to provide a safe drug, the policy might be such that the latency of the release of drugs for experiments and commercial purposes are so slow that many patients who might otherwise benefit from the release of the drug lose out.

Finally, he discusses the self-fulfilling prophecy which suggests that tinkering with the elements of a system to avert a catastrophic negative event might in actuality result in the event.

It is important however to acknowledge that unintended consequences do not necessarily lead to a negative outcome. In fact, there are could be unanticipated benefits. A good example is Viagra which started off as a pill to lower blood pressure, but one discovered its potency to solve erectile dysfunctions. The discovery that ships that were sunk became the habitat and formation of very rich coral reefs in shallow waters that led scientists to make new discoveries in the emergence of flora and fauna of these habitats.

unitended con ahead

If there are initiatives exercised that are considered “positive initiative” to influence the system in a manner that contribute to the greatest good, it is often the case that these positive initiatives might prove to be catastrophic in the long term. Merton calls the cause of this unanticipated consequence as something called the product of the “relevance paradox” where decision makers thin they know their areas of ignorance regarding an issue, obtain the necessary information to fill that ignorance gap but intentionally or unintentionally neglect or disregard other areas as its relevance to the final outcome is not clear or not lined up to values. He goes on to argue, in a nutshell, that unintended consequences relate to our hubris – we are hardwired to put our short-term interest over long term interest and thus we tinker with the system to surface an effect which later blow back in unexpected forms. Albert Camus has said that “The evil in the world almost always comes of ignorance, and good intentions may do as much harm as malevolence if they lack understanding.”

An interesting emergent property that is related to the law of unintended consequence is the concept of Moral Hazard. It is a concept that individuals have incentives to alter their behavior when their risk or bad decision making is borne of diffused among others. For example:

If you have an insurance policy, you will take more risks than otherwise. The cost of those risks will impact the total economics of the insurance and might lead to costs being distributed from the high-risk takers to the low risk takers.

Unintended-Consequences cartoon

How do the conditions of the moral hazard arise in the first place? There are two important conditions that must hold. First, one party has more information than another party. The information asymmetry thus creates gaps in information and that creates a condition of moral hazard. For example, during 2006 when sub-prime mortgagors extended loans to individuals who had dubitable income and means to pay. The Banks who were buying these mortgages were not aware of it. Thus, they ended up holding a lot of toxic loans due to information asymmetry. Second, is the existence of an understanding that might affect the behavior of two agents. If a child knows that they are going to get bailed out by the parents, he/she might take some risks that he/she would otherwise might not have taken.

To counter the possibility of unintended consequences, it is important to raise our thinking to second-order thinking. Most of our thinking is simplistic and is based on opinions and not too well grounded in facts. There are a lot of biases that enter first order thinking and in fact, all of the elements that Merton touches on enters it – namely, ignorance, biases, errors, personal value systems and teleological thinking. Hence, it is important to get into second-order thinking – namely, the reasoning process is surfaced by looking at interactions of elements, temporal impacts and other system dynamics. We had mentioned earlier that it is still difficult to fully wrestle all the elements of emergent systems through the best of second-order thinking simply because the dynamics of a complex adaptive system or complex physical system would deny us that crown of competence. However, this fact suggests that we step away from simple, easy and defendable heuristics to measure and gauge complex systems.

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.

Complex Physical and Adaptive Systems

There are two models in complexity. Complex Physical Systems and Complex Adaptive Systems! For us to grasp the patterns that are evolving, and much of it seemingly out of our control – it is important to understand both these models. One could argue that these models are mutually exclusive. While the existing body of literature might be inclined toward supporting that argument, we also find some degree of overlap that makes our understanding of complexity unstable. And instability is not to be construed as a bad thing! We might operate in a deterministic framework, and often, we might operate in the realms of a gradient understanding of volatility associated with outcomes. Keeping this in mind would be helpful as we deep dive into the two models. What we hope is that our understanding of these models would raise questions and establish mental frameworks for intentional choices that we are led to make by the system or make to influence the evolution of the system.

 

Complex Physical Systems (CPS)

Complex Physical Systems are bounded by certain laws. If there are initial conditions or elements in the system, there is a degree of predictability and determinism associated with the behavior of the elements governing the overarching laws of the system. Despite the tautological nature of the term (Complexity Physical System) which suggests a physical boundary, the late 1900’s surfaced some nuances to this model. In other words, if there is a slight and an arbitrary variation in the initial conditions, the outcome could be significantly different from expectations. The assumption of determinism is put to the sword.  The notion that behaviors will follow established trajectories if rules are established and the laws are defined have been put to test. These discoveries by introspection offers an insight into the developmental block of complex physical systems and how a better understanding of it will enable us to acknowledge such systems when we see it and thereafter allow us to establish certain toll-gates and actions to navigate, to the extent possible, to narrow the region of uncertainty around outcomes.

universe

The universe is designed as a complex physical system. Just imagine! Let this sink in a bit. A complex physical system might be regarded relatively simpler than a complex adaptive system. And with that in mind, once again …the universe is a complex physical system. We are awed by the vastness and scale of the universe, we regard the skies with an illustrious reverence and we wonder and ruminate on what lies beyond the frontiers of a universe, if anything. Really, there is nothing bigger than the universe in the physical realm and yet we regard it as a simple system. A “Simple” Complex Physical System. In fact, the behavior of ants that lead to the sustainability of an ant colony, is significantly more complex: and we mean by orders of magnitude.

ant colony

Complexity behavior in nature reflects the tendency of large systems with many components to evolve into a poised “critical” state where minor disturbances or arbitrary changes in initial conditions can create a seemingly catastrophic impact on the overall system such that system changes significantly. And that happens not by some invisible hand or some uber design. What is fundamental to understanding complex systems is to understand that complexity is defined as the variability of the system. Depending on our lens, the scale of variability could change and that might lead to different apparatus that might be required to understand the system. Thus, determinism is not the measure: Stephen Jay Gould has argued that it is virtually impossible to predict the future. We have hindsight explanatory powers but not predictable powers. Hence, systems that start from the initial state over time might represent an outcome that is distinguishable in form and content from the original state. We see complex physical systems all around us. Snowflakes, patterns on coastlines, waves crashing on a beach, rain, etc.

Complex Adaptive Systems (CAS)

Complex adaptive systems, on the contrary, are learning systems that evolve. They are composed of elements which are called agents that interact with one another and adapt in response to the interactions.

cas

Markets are a good example of complex adaptive systems at work.

CAS agents have three levels of activity. As described by Johnson in Complexity Theory: A Short Introduction – the three levels of activity are:

  1. Performance (moment by moment capabilities): This establishes the locus of all behavioral elements that signify the agent at a given point of time and thereafter establishes triggers or responses. For example, if an object is approaching and the response of the agent is to run, that would constitute a performance if-then outcome. Alternatively, it could be signals driven – namely, an ant emits a certain scent when it finds food: other ants will catch on that trail and act, en masse, to follow the trail. Thus, an agent or an actor in an adaptive system has detectors which allows them to capture signals from the environment for internal processing and it also has the effectors that translate the processing to higher order signals that influence other agents to behave in certain ways in the environment. The signal is the scent that creates these interactions and thus the rubric of a complex adaptive system.
  2. Credit assignment (rating the usefulness of available capabilities): When the agent gathers experience over time, the agent will start to rely heavily on certain rules or heuristics that they have found useful. It is also typical that these rules may not be the best rules, but it could be rules that are a result of first discovery and thus these rules stay. Agents would rank these rules in some sequential order and perhaps in an ordinal ranking to determine what is the best rule to fall back on under certain situations. This is the crux of decision making. However, there are also times when it is difficult to assign a rank to a rule especially if an action is setting or laying the groundwork for a future course of other actions. A spider weaving a web might be regarded as an example of an agent expending energy with the hope that she will get some food. This is a stage setting assignment that agents have to undergo as well. One of the common models used to describe this best is called the bucket-brigade algorithm which essentially states that the strength of the rule depends on the success of the overall system and the agents that constitute it. In other words, all the predecessors and successors need to be aware of only the strengths of the previous and following agent and that is done by some sort of number assignment that becomes stronger from the beginning of the origin of the system to the end of the system. If there is a final valuable end-product, then the pathway of the rules reflect success. Once again, it is conceivable that this might not be the optimal pathway but a satisficing pathway to result in a better system.
  3. Rule discovery (generating new capabilities): Performance and credit assignment in agent behavior suggest that the agents are governed by a certain bias. If the agents have been successful following certain rules, they would be inclined toward following those rules all the time. As noted, rules might not be optimal but satisficing. Is improvement a matter of just incremental changes to the process? We do see major leaps in improvement … so how and why does this happen? In other words, someone in the process have decided to take a different rule despite their experiences. It could have been an accident or very intentional.

One of the theories that have been presented is that of building blocks. CAS innovation is a result of reconfiguring the various components in new ways. One quips that if energy is neither created, nor destroyed …then everything that exists today or will exist tomorrow is nothing but a reconfiguration of energy in new ways. All of tomorrow resides in today … just patiently waiting to be discovered. Agents create hypotheses and experiment in the petri dish by reconfiguring their experiences and other agent’s experiences to formulate hypotheses and the runway for discovery. In other words, there is a collaboration element that comes into play where the interaction of the various agents and their assignment as a group to a rule also sets the stepping stone for potential leaps in innovation.

Another key characteristic of CAS is that the elements are constituted in a hierarchical order. Combinations of agents at a lower level result in a set of agents higher up and so on and so forth. Thus, agents in higher hierarchical orders take on some of the properties of the lower orders but it also includes the interaction rules that distinguishes the higher order from the lower order.

Short History of Complexity

Complexity theory began in the 1930’s when natural scientists and mathematicians rallied together to get a deeper understanding of how systems emerge and plays out over time.  However, the groundwork of complexity theory began in the 1850’s with Darwin’s introduction to Natural Selection. It was further extended by Mendel’s genetic algorithms. Darwin’s Theory of Evolution has been posited as a slow gradual process. He says that “Natural selection acts only by taking advantage of slight successive variations; she can never take a great and sudden leap, but must advance by short and sure, though slow steps.” Thus, he concluded that complex systems evolve by leaps and the result is an organic formulation of an irreducibly complex system which is composed of many parts, all of which work together closely for the overall system to function. If any part is missing or does not act as expected, then the system becomes unwieldy and breaks down. So it was an early foray into distinguishing the emergent property of a system from the elements that constitute it. Mendel, on the other hand, laid out the property of inheritance across generations. An organic system inherits certain traits that are reconfigured over time and adapts to the environment, thus leading to the development of an organism which for our purposes fall in the realm of a complex outcome. One would imagine that there is a common thread between Darwin’s Natural Selection and Mendel’s laws of genetic inheritance. But that is not the case and that has wide implications in complexity theory. Mendel focused on how the traits are carried across time: the mechanics which are largely determined by some probabilistic functions. The underlying theory of Mendel hinted at the possibility that a complex system is a result of discrete traits that are passed on while Darwin suggests that complexity arises due continuous random variations.

 

darwin statement

In the 1920’s, literature suggested that a complex system has elements of both: continuous adaptation and discrete inheritance that is hierarchical in nature. A group of biologists reconciled the theories into what is commonly known as the Modern Synthesis. The principles guiding Modern Synthesis were: Natural Selection was the major mechanism for evolutionary change. Small random variations of genes and natural selection result in the origin of new species. Furthermore, the new species might have properties different than the elements that constitute. Modern Synthesis thus provided the framework around Complexity theory. What does this great debate mean for our purposes? Once we arrive at determining whether a system is complex, then how does the debate shed more light into our understanding of complexity. Does this debate shed light into how we regard complexity and how we subsequently deal with it? We need to further extend our thinking by looking at a few new developments that occurred in the 20th century that would give us a better perspective. Let us then continue our journey into the evolution of the thinking around complexity.

 

Axioms are statements that are self-evident. It serves to be a premise or starting point for further reasoning and arguments. An axiom thus is not contestable because if it, then all the following reasoning that is extended against axioms would fall apart. Thus, for our purposes and our understanding of complexity theory – A complex system has an initial state that is irreducible physically or mathematically.

 

One of the key elements in Complexity is computation or computability. In the 1930’s, Turing introduced the abstract concept of the Turing machine. There is a lot of literature that goes into the specifics of how the machine works but that is beyond the scope of this book. However, there are key elements that can be gleaned from that concept to better understand complex systems.  A complex system that evolves is a result of a finite number of steps that would solve a specific challenge. Although the concept has been applied in the boundaries of computational science, I am taking the liberty to apply this to emerging complex systems. Complexity classes help scientists categorize the problems based on how much time and space is required to solve problems and verify solutions. The complexity is thus a function of time and memory. This is a very important concept and we have radically simplified the concept to attend to a self-serving purpose: understand complexity and how to solve the grand challenges?  Time complexity refers to the number of steps required to solve a problem. A complex system might not necessarily be the most efficient outcome but is nonetheless an outcome of a series of steps, backward and forward to result in a final state. There are pathways or efficient algorithms that are produced and the mechanical states to produce them are defined and known. Space complexity refers to how much memory that the algorithm depends on to solve the problem.  Let us keep these concepts in mind as we round this all up into a more comprehensive work that we will relay at the end of this chapter.

Around the 1940’s, John von Neumann introduced the concept of self-replicating machines. Like Turing, Von Neumann’s would design an abstract machine which, when run, would replicate itself. The machine consists of three parts: a ‘blueprint’ for itself, a mechanism that can read any blueprint and construct the machine (sans blueprint) specified by that blueprint, and a ‘copy machine’ that can make copies of any blueprint. After the mechanism has been used to construct the machine specified by the blueprint, the copy machine is used to create a copy of that blueprint, and this copy is placed into the new machine, resulting in a working replication of the original machine. Some machines will do this backwards, copying the blueprint and then building a machine. The implications are significant. Can complex systems regenerate? Can they copy themselves and exhibit same behavior and attributes? Are emergent properties equivalent? Does history repeat itself or does it rhyme? How does this thinking move our understanding and operating template forward once we identify complex systems?

complexity-sciences dis

Let us step forward into the late 1960’s when John Conway started doing experiments extending the concept of the cellular automata. He introduced the concept of the Game of Life in 1970 as a result of his experiments. His main theses was simple : The game is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves, or, for advanced players, by creating patterns with properties. The entire formulation was done on a two-dimensional universe in which patterns evolved over time. It is one of the finest examples in science of how a set of few simple non-arbitrary rules can result in an incredibly complex behavior that is fluid and provides a pleasing pattern over time. In other words, if one were an outsider looking in, you would see a pattern emerging from simple initial states and simple rules.  We encourage you to look at several patterns that many people have constructed using different Game of Life parameters.  The main elements are as follows. A square grid contains cells that are alive or dead. The behavior of each cell is dependent on the state of its eight immediate neighbors. Eight is an arbitrary number that Conway established to keep the model simple. These cells will strictly follow the rules.

Live Cells:

  1. A live cell with zero or one live neighbors will die
  2. A live cell with two or three live neighbors will remain alive
  3. A live cell with four or more live neighbors will die.

Dead Cells:

  1. A dead cell with exactly three live neighbors becomes alive
  2. In all other cases a dead cell will stay dead.

Thus, what his simulation led to is the determination that life is an example of emergence and self-organization. Complex patterns can emerge from the implementation of very simple rules. The game of life thus encourages the notion that “design” and “organization” can spontaneously emerge in the absence of a designer.

Stephen Wolfram introduced the concept of a Class 4 cellular automata of which the Rule of 110 is well known and widely studied. The Class 4 automata validates a lot of the thinking grounding complexity theory.  He proves that certain patterns emerge from initial conditions that are not completely random or regular but seems to hint at an order and yet the order is not predictable. Applying a simple rule repetitively to the simplest possible starting point would bode the emergence of a system that is orderly and predictable: but that is far from the truth. The resultant state is that the results exhibit some randomness and yet produce patters with order and some intelligence.

turing

 

Thus, his main conclusion from his discovery is that complexity does not have to beget complexity: simple forms following repetitive and deterministic rules can result in systems that exhibit complexity that is unexpected and unpredictable. However, he sidesteps the discussion around the level of complexity that his Class 4 automata generates. Does this determine or shed light on evolution, how human beings are formed, how cities evolve organically, how climate is impacted and how the universe undergoes change? One would argue that is not the case. However, if you take into account Darwin’s natural selection process, the Mendel’s law of selective genetics and its corresponding propitiation, the definitive steps proscribed by the Turing machine that captures time and memory,  Von Neumann’s theory of machines able to replicate themselves without any guidance, and Conway’s force de tour in proving that initial conditions without any input can create intelligent systems – you essentially can start connecting the dots to arrive at a core conclusion: higher order systems can organically create itself from initial starting conditions naturally. They exhibit a collective intelligence which is outside the boundaries of precise prediction. In the previous chapter we discussed complexity and we introduced an element of subjective assessment to how we regard what is complex and the degree of complexity. Whether complexity falls in the realm of a first-person subjective phenomenon or a scientific third-party objective phenomenon has yet to be ascertained. Yet it is indisputable that the product of a complex system might be considered a live pattern of rules acting upon agents to cause some deterministic but random variation.

Complexity: An Introduction

The past was so simple. Life was so simple and good. Those were the good old days. How often have you heard these ruminations? It is fairly common!  Surprisingly, as we forge a path into the future, these ruminations gather pace. We become nostalgic and we thus rake fear of the future. We attribute a good life to a simple life. But the simple life is measured against the past. In fact, our modus operandi is to chunk up the past into timeboxes and then surface all the positive elements. While that is an endeavor that might give us some respite from what is happening today, the fact is that the nostalgia is largely grounded in fiction. It would be foolish to recall the best elements and compare it to what we see emerging today which conflates good and bad. We are wired for survival: If we have survived into the present, it makes for a good argument perhaps that the conditions that led to our survival today can only be due to a constellation of good factors that far outweighed the bad. But when we look into the future rife with uncertainty, we create this rather dystopian world – a world of gloom and doom and then we wonder: why are we so stressed? Soon we engage in a vicious cycle of thought and our actions are governed by the thought. You have heard – Hope for the best and plan for the worst. Really? I would imagine that when one hopes for the best and the facts do not undermine the trend, would it not be better to hope for the best and plan for the best. It is true that things might not work out as planned but ought we to always build out models and frameworks to counter that possibility. We say that the world is complex and that the complexity forces us to establish certain heuristics to navigate the plenar forces of complexity. So let us understand what complexity is. What does it mean? And with our new understanding of complexity through the course of this chapter, would we perhaps arrive at a different mindset that speaks of optimism and innovation. We will certainly not settle that matter at the end of this chapter, but we hope that we will surface enough questions, so you can reflect upon where we are and where we are going in a more judicious manner – a manner grounded on facts and values. Let us now begin our journey!

compl

The sky is blue. We hear this statement. It is a simple statement. There is a noun, a verb and an adjective. In the English-speaking world, we can only agree on what constitutes the “sky”. We might have a hard time defining it – Merriam Webster defines the sky as the upper atmosphere or expanse of space that constitutes an apparent great vault or arch over the earth. A five-year-old would point to the sky to define sky. Now how do we define blue. A primary color between green and violet. Is that how you think about blue or do you just arrive at an understanding of what that color means. Once again, a five-year-old would identify blue: she would not look at green and violet as constituent colors. The statement – The sky is blue – for the sake of argument is fairly simple!

However, if we say that the sky is a shade of blue, we introduce an element of ambiguity, don’t we? Is it dark blue, light blue, sky blue (so we get into recursive thinking), or some other property that is bluish but not quite blue. What has emerged thus is an element of complexity – a new variable that might be considered a slider on a scale. How we slide our understanding is determined by our experience, our perception or even our wishful thinking. The point being that complexity ceases to be purely an objective property. Rather it is an emergent property driven by our interpretation. Protagoras, an ancient Greek philosopher, says that the man is a measure of all things. What he is saying is that our lens of evaluation is purely predicated on our experiences in life. There is nothing that exists outside the boundaries of our experience. Now Socrates arrived at a different view – namely, he proved that certain elements are ordered in a manner that exists outside the boundaries of our experience. We will get back to this in later chapters. The point being that complexity is an emergent phenomenon that occurs due to our interpretation. Natural scientists will argue, like Socrates, that there are complex systems that exist despite our interpretations. And that is true as well. So how do we balance these opposing views at the same time: is that a sign of insanity? Well, that is a very complex question (excuse my pun) and so we need to further expand on the term Complexity.

In order to define complexity, let us now break this up a bit further. Complex systems have multiple variables: these variables interact with each other; these variables might be subject to interpretation in the human condition; if not, these variables interact in a manner to enable emergent properties which might have a life of its own. These complex systems might be decentralized and have information processing pathways outside the lens of science and human perception. The complex systems are malleable and adaptive.

Markets are complex institution. When we try to centralize the market, then we take a position that we feel we understand the complexity and thus can determine the outcomes in a certain way. Socialist governments have long tried to manage markets but have not been successful. Nobel winner, Frederich Hayek, has long argued that the markets are a result of spontaneous order and not design. It has multiple variables, significant information processing is underway at any given time in an active market, and the market adapts to the information processing mechanism. But there are winners and losers in a market as well. Why? Because each of them observes the market dynamics and arrive at different conclusions. Complexity does not follow a deterministic path. Neither does the market and we have lot of success and failures that suggest that to be the case.

complex2

Let us look at another example. Examples will probably give us an appreciation for the concept and this will be very important as we sped through the journey into the future.

Insect behavior is a case in point. Whether we look at bees or ants, it is a common fact that these insects have extremely complex systems despite the lack of sufficient instruments for survival for one bee or one ant. In 1705, Bernard Mandeville wrote a book called: Fable of the Bees. It was a poem. Here is a part of the poem. What Mandeville is clearly hinting at is the fact that there would be an innate failure to centralize complex systems like a bee hive. Rather, the complex systems emerge in a way to create innate systems that stabilize for success and survival in the long run.

A Spacious Hive well stock’d with Bees,

That lived in Luxury and Ease;

And yet as fam’d for Laws and Arms,

As yielding large and early Swarms;

Was counted the great Nursery

Of Sciences and Industry.

No Bees had better Government,

More Fickleness, or less Content.

They were not Slaves to Tyranny,

Nor ruled by wild Democracy;

But Kings, that could not wrong, because

Their Power was circumscrib’d by Laws.

 

Then we have the ant colonies. An ant is blind. Yet a colony has collective intelligence. The ants work together, despite individual shortcomings that challenge an individual survival, to figure out how to exist and propagate as group. How does a simple living organism that is subject to the whims and fancies of nature survive and seed every corner of the earth in great volumes? Entomologists and social scientists and biologists have tried to figure this out and have posited a lot of theories. The point is that complex systems are not bounded by our reason alone. The whole is greater than the sum of the parts.

 

Key Takeaway

A complex system is the result of the interaction of a network of variables that gives rise to collective behavior, information processing and self-learning and adaptive system that does not completely lie in the purview of human explanation.

 

Books to Read – 2017

It has been a while since I posted on this blog. It just so happens that life is what happens to you when you have other plans. Having said that, I decided early this year to ready 42 books this year across a wide range of genres. I have been trying to keep pace, and have succeeded so far.

Here are the books that I have read and plan to read:

  1. Song of Solomon by Toni Morrison  ( Read)
  2. The Better Angels of Our Nature by Steven Pinker ( Read)
  3. Black Dogs by Ian McEwan ( Read)
  4. Nutshell: A Novel by Ian McEwan ( Read)
  5. Dr. Jekyl and Mr. Hyde by Robert Louis Stevenson ( Read)
  6. Moby Dick by Herman Melville
  7. The Plot Against America by Phil Roth
  8. Humboldt’s Gift by Saul Bellow
  9. The Innovators by Walter Isaacson
  10. Sapiens: A Brief History of Mankind by Yuval Harari
  11. The House of Morgan by Ron Chernow
  12. American Political Rhetoric: Essential Speeches and Writings by Peter Augustine Lawler and Robert Schaefer
  13. Keynes Hayek: The Clash that defined Modern Economics by Nicholas Wapshott
  14. The Year of Magical Thinking by Joan Didion
  15. Small Great Things by Jodi Picoult
  16. The Conscience of a Liberal by Paul Krugman
  17. Globalization and its Discontents by Joseph Stiglitz
  18. Twilight of the  Elites: America after Meritocracy by Chris Hayes
  19. What is Mathematics: An Elementary Approach to Idea and Methods by Robbins & Stewart
  20. Algorithms to live by: Computer Science of Human Decisions by Christian & Griffiths
  21. Andrew Carnegie by David Nasaw
  22. Just Mercy: A Story of Justice and Redemption by Bryan Stevenson
  23. The Evolution of Everything: How New Ideas Emerge by Matt Ridley
  24.  The Only Game in Town: Central Banks, Instability and Avoiding the Next Collapse by Mohammed El-Arian
  25. The Relentless Revolution: A History of Capitalism by Joyce Appleby
  26. The Industries of the Future by Alec Ross
  27. Where Good Ideas come from by Steven Johnson
  28. Original: How Non-Conformists move the world by Adam Grant
  29. Start with Why by Simon Sinek
  30. The Discreet Hero by Mario Vargas Llosa
  31. Istanbul by Orhan Pamuk
  32. Jefferson and Hamilton: The Rivalry that Forged a Nation by John Ferling
  33. The Orphan Master’s Son: A Novel by Adam Johnson
  34. Between the World and Me: Ta Nehisi-Coates
  35. Active Liberty: Interpreting our Democratic Constitution
  36. The Blue Guitar by John Banville
  37. The Euro Crisis and its Aftermath by Jean Pisani-Fery
  38. Africa: Why Economists get it wrong by Morten Jerven
  39. The Snowball: Warren Buffett and the Business of Life
  40. To Explain the World: The Discovery of Modern Science by Steven Weinberg
  41. The Meursalt Investigation by Daoud and Cullen
  42. The Stranger by Albert Camus