This post and the next are going to attempt to bridge dynamic complex systems and Asset Based Community Development (ABCD). One can start with the former in this post or one can start with the later with this post.
There might seem a sizable distance to span as understanding dynamic complex systems can be rather abstract and conceptual at a system-wide level while ABCD seeks practical real impact on the ground and in the streets at a neighborhood level. It is believed though that transversing this span will help with understanding both, well at least my understanding. ABCD has been explored in the past, though I will again assert that I have limited understanding, and that I am still trying to improve my understanding of it.
The specific link was inspired by a term that Cormac Russell utilized in his post, Nurturing the Carrying Capacity of Communities. The concept of “carrying or bearing capacity” refers to a system's resilience and receptivity before it begins to degrade. This term was also used in the Introduction to Dynamical Systems and Chaos course, that I recently completed, in understanding changes in populations over time. Communities, like populations, can be said to have a carrying capacity which is not unlimited. Communities, however, are defined and differentiated by more than elements and number and we have a more personal interest that they should not be exploited.
The two previous posts provided some thoughts and more thoughts on dynamic complex systems generally with a bit more on systems thinking, complexity, chaos and new community paradigms all from the perspective of the logistic equation as an iterated function.
Dynamic complexity takes a mathematical perspective which tends to make it abstract and a disconnect with ABCD which has a preference for stories over data. In a previous post, the logistic equation as a means of understanding populations was considered as an iterative function in the form
f(p) = rp(1-p/a)
It needs to be said again that these posts aren’t intended to be a substitute for the course, merely an attempt to apply some lessons learned to other areas and in doing so learn more. Sometimes this means returning to a previous post to make updates to communicate newly attained and relatively better understanding which was done with including this version of the logistic equation. The course provides far better explanations, often repeated in far greater detail. This post only hopes to give a sense of the concepts and perhaps encourage taking the course.
This form of the equation can be seen to be similar to the logistic differential equation below.
dp/dt = rp(1-p/k)
Both of these equations are deterministic giving rise though to very different ranges of possible behaviors that can be discerned. P is again population such as some animal. How fast the population grows still depends on the current population. The r remains a measure of the growth rate, when the growth rate is positive the population is increasing so the larger r, the larger the population will be.
The carrying capacity in a differential logistic equation is the parameter (1-p/k). The quantity k is in a sense the equilibrium population or the number of creatures a system can support. With the previously considered iterated Logistic function, it was the annihilation parameter or (1-p/a).
Although the carrying capacity and annihilation parameter appear mathematically in the same form in the equation, they have different meanings doing different things as defined by the left side of each of the equations. They can be applied to the exact same reality yet giving very different perspectives. Both are limited but both are useful. The concept of carrying capacity seems for me more intuitively understandable as opposed to the annihilation population.
The most noticeable difference between the two equations is on the left side of the equations. The dp/dt on the left side of the differential equation describes the function p in terms of its rate of change.
For differential equations, the solution is population as a function of time, both time and population are continuous. The curve of the function changes continuously, increasing smoothly, passing through all intermediate values defined at all times. Knowing the rate of change of p means knowing what p is, population growth depends on the population value. The derivative is a function of only the p-value and any given p-value has only one derivative associated with it.
The logistic equation in the form of the iterated function also describes population growth, but f(p) is the population at the next time cycle, given the population p this year determines next year p resulting from iterating this function in a series of population values. For iterated functions, the solution is a time series plot or map with the value of the population moving in jumps past any intermediate values connecting the dots, sliding past all values with an initial value at time 0, then by time 1, time 2, etc.
This means that cycles or periodic orbits of different numbers and chaos or aperiodic behavior subject to sensitivity to initial conditions are not possible for a differential equation. With the differential equation, there are then only two fixed points, one an unstable fixed point at zero, as a repeller pushing away towards the other fixed point at k or the carrying capacity.
The carrying capacity or k is then a stable fixed point or an attractor. Any population number between zero and k the carrying capacity gets pulled toward k, anything larger than k also gets pulled decreasing until reaching k. The range of real-world behaviors for one-dimensional differential equations is limited then to increasing to a fixed point or decreasing to a fixed point. A population that is a little larger than zero or less than a k of 100 will increase up to 100. If that population is larger than 100 then the growth rate will be negative and the population decreases.
The iterated function is capable of producing both periodic orbits and chaos and while not all iterated functions will reveal chaos, iterated functions can, therefore, display a much richer array of behaviors because determinism doesn't forbid them.
Chaos, it should be remembered, is the technical term for what is popularly known as the butterfly effect in which the flap of a wing produces a hurricane somewhere. This is not actually true. The totality of a system with a butterfly flapping its wings could end up at a substantially different outcome than a system without the butterfly but it is impossible to say whether the butterfly created or stopped the formation of the hurricane and where it be formed.
Imagine exploring with a boat an unknown but long and exceedingly winding river on which numerous bends in the river hide what is ahead. One might have an idea of the general shape of the river but more specific knowledge of what lay ahead would be limited. It would still be necessary to closely navigate the waters one was sailing for rocks or to obtain resources from the shore but major changes in the landscape, such as giant waterfalls or whirlpools would not be apparent until one came upon them.
An airplane flying the same basic route would not be able to gather any detailed information about the river, except general shape, or about the fauna and flora but it could notice larger aspects of the landscape, useful information far ahead that could prove helpful to the boat.
There was a conjectural attempt made to apply this thinking to some NCP elements used in a Causal Loop Diagram involving Community Advocacy. Systems thinking can be quite good at making elements that can impact a system but which are separated by time or causal steps of more than one or two degrees more apparent. The course on dynamic complexity provided another perspective though in which a deterministic system could potentially result in essentially stochastic or random behavior without outside intervention, not necessarily chaotic but unexpected based on past behavior. While any one of the connections would be highly unlikely to produce this effect, multiple interactions of numerous unique elements over time potentially could. This supposes that the metrics that are often used in measuring systems are in truth not particularly precise, often being more on the level of ordinal numbers, and that through the finer tuned interaction over time of actual true values could have different and surprisingly unpredictable results or unintended consequences. It doesn’t have to produce a hurricane merely take an unexpected turn. How we navigate our world depends on both the interaction of current events and our best attempts at predicting how the future will unfold. Still, it can be readily recognized how abstract and disconnected from everyday reality the perspective being presented here can be.
An ABCD approach would likely be to go to live in a village along the river and learn from the stories of the people. One question could then be whether the village both needed and wanted help or should be left alone but we’ll leave that for next post.
The limitation of this analogy, from the complex dynamics perspective, is that distantly future events on the river of time can only be predicted through model again echoing the George Box aphorism, “All models are wrong, some models are useful” now further constrained by the potential unpredictability of internal dynamics. The limitation with ABCD is that the river can change it flows towards a village or community in unexpected ways.
The yet still strong affinity and resulting confidence with the mathematics of complexity is admittedly based on a personal bias but not necessarily subject to being overly impressed with numbers per se but with the mathematical relations that have been shown to be rooted in the fabric of reality. ABCD also endeavors to reach the fabric of reality of communities, saying subjectively has an arguably negative connotation, which would be misapplied. Instead, it should be recognized as an essential part of the whole truth of understanding communities. The next post will endeavor to obtain a better understanding of ABCD.
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