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Complex systems exhibit important scalar dynamics from two perspectives. First, they are often built up from nested sub-systems, which themselves may be complex systems. Second, at a given scale of inquiry within the system, there will be a tendency for the system to exhibit Power Laws (or scale-free) dynamics in terms of how the system operates. This simply means that there will be a tendency in the system for a small number of elements within the system to dominate: this system domination can manifest in different ways, such as intensity (earthquakes) frequency (citations) or physical size (road networks). In all cases a small ratio of system components (earthquakes, citations, or roads) carry a large ratio of system impact. Understanding how and why this operates is important to the study of complexity.
To understand what we mean by 'nested', we can think of the human body. At one level of magnification we can regard it as a collection of cells, at another as a collection of organs, at another as a complete body. Further, each body is itself part of a larger collection - perhaps a family, a clan or a tribe - and these in turn, may be part of other, even larger wholes: cities or nations. In complex systems we constantly think of both parts and wholes, with the whole (at one level of magnification) becoming just a part (at another level of magnification). While we always need to select a scale to focus upon, it is important to note that complex systems are open - so they are affected by what occurs at other scales of inquiry. When trying to understand any given system within this hierarchy, the impact of subsystems typically occurs near adjacent scales. Thus, while a society can be understood as being composed of humans, composed of bodies, composed of organs, composed of cells, we do not tend to consider the role that cells play in affecting societies. Instead, we attune to understanding interactions between the relevant scales of whatever system we are examining. Depending on the level of enquiry we choose, we may look at the same entity (for example a single human being) and consider it be an emergent 'whole', or simply a component part (or agent) within a larger emergent entity (one being within a complex society).
Various definitions of complexity try to capture this shifting nature of agent versus whole, and how this alters depending on the scale of inquiry. Definitions thus point to complex adaptive systems as being hierarchical, or operating at micro, meso, and macro level. In his seminal article The Architecture of Complexity, Herbert Simon describes such systems as 'composed of interrelated sub-systems, each of the latter being, in turn, hierarchic in structure until we reach some lowest level of elementary subsystem'.
Simon argues that, by partitioning systems into nested hierarchies, wholes are more apt to remain robust. They maintain their integrity even if parts of the system are compromised. He provides the example of two watch-makers, each of whom build watches made up of one thousand parts. One watchmaker organizes the watch's components as independently entities - each of which needs to be integrated into the whole in order for the watch to hold together as a stable entity. If one piece is disturbed in the course of the watchmaking, the whole disintegrates, and the watchmaking process needs to start anew. The second watchmaker organizes the watch parts into hierarchical sub-assemblies: ten individual parts make one unit, ten units make one component, and ten components make one watch. For the second watchmaker, each sub-assembly holds together as a stable, integrated entity, so if work is disrupted in the course of making an assembly, the disruption affects only that component (meaning a maximum of ten assembly steps are lost). The remainder of the assembled components remain intact.
If Simon is correct, then natural systems may preserve robustness by creating sub-assemblies that each operate as wholes. Accordingly, it is worth considering how human systems might benefit from similar strategies.
Simon's watchmaker is a top-down operator who organizes his work flow into parts and wholes to keep the watch components partitioned and robust, creating a more efficient watch-making process. What is noteworthy is that self-organizing, bottom-up systems also seem to have inherent dynamics that appear to push systems towards such partitioning, and that this partitioning holds specific structural properties related to mathematical regularities.
A host of complex systems thus exhibit what is known as Self Similarity - meaning that we can 'zoom in' at any level of magnification and find repeated, nested scales. These scale-free hierarchies follow the mathematical regularities of Power Laws distributions. These distributions are so common in complex systems, that they are often referred to as 'the fingerprint of self-organization" (see Ricardo Solé). We find power-law distributions in systems as diverse as the frequency and magnitude of earthquakes, the structure of academic citation networks, the prices of stocks, and the structure of the World Wide Web.
Further, complex systems tend to 'tune' themselves to what is referred to as Self-Organized Criticality: a state at which the scale or scope of a system's response to any given input will follow power-law distribution, regardless of the intensity (or scope) of the input. Imagine a pile of sand, to which one grain is added to the top, then another, then another. There is a moment when the pile reaches a certain threshold, that if we add a grain the pile will endure a kind of small 'collapse': an added grain will dislodge an existing one, which cascades downwards off the pile. When sand piles (or other complex systems), are in the 'critical' state, we cannot predict the impact of that singular grain of sand: whether it will dislodge one or two grains, or whether it will set off an avalanche of several hundred grains. If the addition of one grain causes a massive avalanche, we might think that the avalanche was the 'result' of a major 'cause'. But this is an error (see Non-Linearity ). That single grain could just as easily have set off any size of avalanche, and the frequency of which these avalanches of different sizes occur follows a power law (see also Per Bak).
While not fully understood, it is believed that systems gravitate towards these critical states because, it is within these regimes that systems are able to maximize performance while simultaneously using the minimum amount of available energy. When system are poised at this state they also have maximum connectivity with the minimum amount of redundancy. It is also believed that they are the most effective information processors when poised within this critical regime.
The attentive surfer of this website may notice that in the various definitions of complexity being circulated, the term 'hierarchical' is used to describe what we call here 'nested orders'. We have avoided using this term as it holds several connotations that appear unhelpful. First, a hierarchy generally assumes a kind of priority, with 'upper' levels being more significant than lower. Second, it implies control emanating from the top down. Neither of these connotations are appropriate when speaking about complex systems. Each level of nested orders is both a part and a whole, and causality flows both ways as the emergent order is generated by its constituent parts, and steered by those parts as much as it steers (or constrains) its parts once present. We hope that the idea of 'nested orders' is more neutral vis-a-vis notions of primacy and control, but still captures the idea of systems embedded within systems of different scales.
When considering the design of a system for which we are hoping to achieve complex dynamic unfolding, it is therefore important to think about two aspects.
The first is to consider how we might partition systems into different sub-units of similar components, that can operate as a unit without doing damage to units operating either at a higher or lower level. To take an urban example, we might think about the furnishings that operate together to form the unit of a room, rooms that together form the unit of a building, and buildings that operate together to form the unit of a block. Each level operates with respect to the levels above and below, but can be thought of as systems on their own.
But this is not all - there is a dialogue between levels, such that it is not simply a hierarchy that runs from the block down through the building and into the furniture. Instead, each level emerges from the level below, is stabilized over time, and in turn constrains what happens at the scale below. Units emerging from units then constraining these same units, while also forming the Building Blocks of what happens above.
The second is to be careful about how we interpret extreme events: if we look at large sand pile avalanches as somehow fundamentally different from small sand pile cascades, we are unlikely to understand that the same cause tripped off both effects. The same dynamics may be at play for many phenomena, so we should be aware of how much emphasis we place on causal factors in 'extreme' events, if the event is one taking place within a complex system that may be in the critical regime.
To put another way, if we wish to know why a particular cat video went viral, it might not be that productive to look into the details of the cat, its actions, or the quality of the video. That particular video might simply be the sand grain of cat videos - setting of a chain of viewing that would have eventually cascaded simply due to the number of cat videos poised to go viral at any given moment. While it is true that this example does not exactly parallel the sand-pile case, it expresses the same basic premise, that extreme events may simply be one scale of event in a system that is poised to unfold at all potential scales.
Photo Credit and Caption: Image Credit: David Clode via Unsplash
Cite this page:
Wohl, S. (2022, 9 June). Nested Orders. Retrieved from https://kapalicarsi.wittmeyer.io/taxonomy/nested-orders
Nested Orders was updated June 9th, 2022.
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power law distributions + Pareto optimality
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This is a list of Key Concepts that Nested Orders is related to.
CAS tend to organize to a 'critical state' where, regardless of the scale of a given input, the scale of corresponding output observes of a power-law distribution.
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'Scale-free' networks are ones in which identical system structure is observed for any level of network magnification.
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