Systems Science 6 — Networks, Structure, and Function
Now that we have some idea of what exists in the universe and how the stuffs interact with one another we can take a closer look at how these stuffs form systems, how systems give rise to meta-systems and new levels of organization. In short, we can begin to understand how our world came to be from the interplay of matter, energy, information, and knowledge.
Literally, all matter and energy in the Universe form a weave of networks within networks. Aggregations of matter form nodes within a larger network. The connections between nodes, formed from energies, are the pathways along which information travels. And the inner network of components forming the aggregate hold a structure that represents the knowledge of that node.
Energy, and perhaps a bit of matter now and then, flow through the larger system from subsystem to subsystem via sparse links between those subsystems. Energy flows into and out of subsystems affecting the internal organizations of those subsystems depending on the constituents of each. We have seen that the pre-existing rules of interaction between components determine the kinds of self-organizing structures that obtain from this energy flow. At the simplest, and lowest level of organization, energy flow largely acts to jostle components about (raises their thermal modes of energy) so that they have opportunities to interact with larger numbers of other components. Some interactions result in tighter coupling between components and a stable organization. Such configurations are energetically favored and persist, possibly giving rise to new possibilities for coupling with additional components.
Every once in a while, a configuration may emerge that autocatalyzes, that is, it promotes the development of more of itself. In a sense it becomes self-replicating, competing with non-autocatalytic configurations that would otherwise use the same components.
Such an event is important for the further evolution of organization within the larger system. Given sufficiently many degrees of freedom (number of kinds of components, number of kinds of interactions of components, etc.) and energy flow to move things around, systems can undergo self organization. This pattern is evident in every level of organization in nature. It holds for the Earth as a whole system with sunlight providing the input of energy and deep space acting as the sink for heat radiation. Biological evolution is a special case of the organization and reorganization of complex sub-networks. Living systems from bacteria to humans are, themselves, networks of networks, organized to use energy to self replicate. Fortunately the sun has supplied an adequate flow of energy to drive this process through the development of humanity. Our societies are networks of networks of people and food stuffs and artifacts through which energy flows.
Figure 1. Systems are networks of networks. Here three sub-nets with tight coupling between multiple components also have weak coupling between them. The tightly coupled sub-nets form entities that are components at a higher level of organization. This pattern of networks of components forming higher order nets is found at all levels of organization in nature.
As mentioned, a network of tightly coupled components tends to settle into a few 'comfortable' configurations. Comfortable means that they are all energetically stable over an extended time. Some configurations are so comfortable that they take more energy to disrupt than they would give up if the couplings were broken. Others can be broken more easily and tend to relinquish larger amounts of energy as the configuration falls apart. In the chemistry world this is known as endothermic and exothermic bonds, respectively.
The way networks of components form and create whole structures is largely an historical process. That is, the specific compendium of components (numbers of kinds incorporated and numbers of interactions possible) and the ordering in which they are brought into the mix determines the specific form and function of the structure. Depending then on the history of any specific sub-net, what components were in its immediate vicinity as it condensed, etc. these network/entities will have differing details. Some may be at the low end of complexity and have very few, rigidly determined forms, such as molecules of gases or simple hydrocarbons. More complex entities can take on high degrees of variability based on their history of formation, like DNA or RNA condensates (without templates to form on). Still other, even more complex entities, like the neural nets of brains, are highly variable as a result of the environments in which they form.
The more successful entities in the living world, however, have found the right mix of pre-determined structural form and developmental adaptiveness to variable conditions. The core form (e.g. morphology and physiology) is necessary for producing core behaviors (functions) that provide long-term stability to the entity. But there is enough room for variation due to chance encounters along the way with environmental factors to provide variation in the organization. Variations on a theme is the modus operandi of living systems.
A necessary condition for networks that form entities to maintain stability in a world of fluctuating energy flows is that they must be able to use the energy to maintain internal organization and then dissipate the waste heat and 'left over' energies. They pass the former to the environment via radiation and convection (where unattached components are free to absorb the energy as an elevated thermal mode). The latter may be transferred to another entity with a lower potential in that specific energy form and where a channel (a weak coupling) exists.
When entities absorb energy or incorporate new material components they can undergo a conformational change in structure. For most simple entities this will result in disruption unless the original structure was particularly 'comfortable'. Such latter structures will simply dissipate the energy or kick out the new component(s). But for more complex entities another possibility exists. They can incorporate the material or internally channel the energy such that their structure is changed such that they again are able to dissipate waste heat. Such systems can grow and evolve in form. They become better suited to their environmental conditions.
A change of structure resulting from incorporating some new component(s) or adjusting to a new energy flow that persists over time is a memory of the events that drove the adaptation. The entity has 'learned' something about its environment. This is what it means to convert information (the NEW component or energy) into knowledge (new structural arrangement that does not degrade dissipation).
Living systems are, of course, the paradigmatic example of adaptive structures. Simple life, like bacteria and single celled eukaryotes, are minimally adaptive in that they have little behavioral control over their environment and must rely on various forms of taxes to find food or escape destructive environments. Life subsystems have to stay within a relatively narrow range of values for characteristic physical and chemical aspects of their environments, such as temperature, salinity, and pH (acidity). In the next post I will be exploring the methods of control (cybernetics) of these subsystems that further refines the roles of information and knowledge in managing the flows of energy and materials.
Multicellular systems, networks of cells, have increased degrees of freedom as well as built-in redundancies. Some of these cells can be altered by genetic mutation such that they form a new sub-network that performs a slightly different function. It specializes in some new capability that increases the fitness of the whole organism. The difference between somatic cells and germ cells may have been one of the earliest differentiations to take place in multicellular evolution.
In all cases living systems must continually import low entropy material and raw energy while exporting waste heat and high entropy material. A living structure has achieved a steady-state condition when the structure has achieved a stable flow through of material and energy while maintaining a a stable network of components internally. The attainment of such a state not only depends on low level operational control, but on multiple levels of control — hierarchical control systems — that organize the internal flows of energy and materials (logistics), the obtaining of those resources while avoiding threats (tactics), and overall planning of future behaviors based on the current and anticipated future state of the environment (strategic). Look for another expication of the importance of hierarchical control in a future post in this series.
When a highly organized adaptive network is able to absorb material, incorporate energy to maintain the structure, and dissipate wastes, as a living system does, then it can be said to be functional. That is the outputs (wastes as far as the entity is concerned) are a function of the processing of the inputs by the network. Such a network could be, in principle, decomposed to find its sub-networks and each of these might be shown to have their own specific functionality with respect to channeling matter and energy fluxes internally. The function of the whole is a result of the functioning of all of its sub-networks (components) along with the overall structure coupling these sub-nets into the whole.
As it turns out frequently in the living world, the output wastes from one entity can become a resource for another entity, especially if the latter has an independent source of energy to synthesize those resources into lower entropy form (new networks). Thus a coupling is formed between entities as part of a yet larger web of organization (see figure below).
The notion of functions of entities or processes supports much of what we think of as organization. When each entity (strongly coupled network, component, process) in a larger network processes inputs to produce outputs that are either used by other entities in the network as inputs or are expelled into the environment, we observe them as performing useful functions.
Figure 2. Multiple cooperating processes each perform a function, turning inputs into outputs. Several processes (P1 and P2) receive inputs of energy, matter, and messages from the environment. They process these in some fashion passing their own outputs on to other processes as inputs to them. P3 is completely 'embedded' in this network. P4 and P5 produce outputs that are emitted to the environment. Note, messages can be passed back and forth between processes, hence the bi-directional arrows.
In the above figure these processes must produce exactly the kinds and quality of outputs needed by the other, downstream processes. This means there must be a stable set of inputs from the environment to begin with. Outputs to the environment (from P4 and P5) are just outputs. There is no implied obligation that this entity (all of the cooperating processes together) produces outputs needed by some other entity. However, should those outputs turn out to be useful to another entity then we have the basis for a higher yet level of organization.
This figure shows a stationary view of an entity. That is, even though materials and energies and messages flow through the entity, it remains the same over time. Sufficiently complex entities, operating in a more dynamic and non-stationary environment, where the inputs are not stable and, indeed, can vary in kind and quality over time, may be able to change their internal structure. Processes may be able to adapt to these changing conditions and still meet their obligations to the other processes. This, in fact, is what we mean by adaptation.
Also not shown is the case where some of the internal processes act as copiers of the structure itself. These processes take in matter and energy, having knowledge (e.g. DNA) of the entire structure of all processes, and use their inputs to replicate the entire entity, or enough of a seed such that the new entity can develop under its interactions with the same environment. Once again, life and beyond.
That the entire universe can be seen as this network of networks (of networks, etc.) suggests some powerful tools for analyzing structure and function that might help us better understand. A basic mathematical tool is graph theory. A graph, in this sense, is just what we have been describing as a network. It is composed of nodes (components) and edges or links (couplings). Some of those links might be represented with arrows indicating a causal relation. An even more useful version of graph theory used to study the flows of stuffs through networks is called flow network theory. This is a form of directed graph where the arrows point in the direction of flows from node to node. This version can be used to study such things as traffic flows and network traffic in the Internet.
Another useful tool, one that can be used with graph theory, is systems dynamics modeling. A system represented as flows and stocks (couplings and components) can be simulated to discover aspects of its behavior that do not show up just by looking at a static diagram of the network.These tools are increasingly being used to explicate the nature of systems. An especially important analysis of the world system called Limits to Growth by Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III. This model demonstrated quite graphically that the Earth system stands in danger of disruption owing to the growth of human populations and consumption. The latter was made physically possible by the advent of easy to acquire fossil fuel energy. The human economy is a network of networks, etc. in which energy flow has allowed the construction of more complex forms of organization (our cultures). The model suggests that this system reaches a point of maladaptive restructuring in which the human built world cannot grow further without destroying itself and much of the natural environment.
It is clear that the analysis and understanding of complex networks is essential to our coming to grips with our place in the Ecos. This alone makes systems science a critical endeavor.