This blog is part of an online learning platform which includes the Pathways to New Community Paradigms Wiki and a number of other Internet based resources to explore what is termed here 'new community paradigms' which are a transformational change brought about by members of a community.

It is intended to offer resources and explore ideas with the potential of purposefully directing the momentum needed for communities to create their own new community paradigms.

It seeks to help those interested in becoming active participants in the governance of their local communities rather than merely passive consumers of government service output. This blog seeks to assist individuals wanting to redefine their role in producing a more direct democratic form of governance by participating both in defining the political body and establishing the policies that will have an impact their community so that new paradigms for their community can be chosen rather than imposed.

Sunday, November 26, 2017

More Thinking on Mastering Systems Practice, Dealing with Messes

In the last post, the idea of what Russell Ackoff called “messes” as contrasted with difficulties was introduced. The course promised more on Ackoff in week six but additional background was provided in that NCP post. More will also be offered here, including a paper in which the term “messes” is used, Systems, Messes and Interactive Planning - Modern Times Workplace.

The course quoted Ackoff regards to messes:

Managers are not confronted with problems that are independent of each other, but with dynamic situations that consists of complex systems of changing problems that interact with each other. I call such situations messes. Problems are abstractions extracted from messes by analysis; they are to messes as atoms are to tables and charts … Managers do not solve problems, they manage messes.

Russell Ackoff (1979, s. 93)

It has to be admitted that this is the first time being exposed to Ackoff’s idea of messes being more familiar with the concept of wicked problems. This raises the question though, are "messes" qualitatively different from"wicked problems”?

Judith A. Curry, American climatologist and former chair of the School of Earth and Atmospheric Sciences at the Georgia Institute of Technology, wrote about the differences between messes and wicked problems from which I borrow heavily here.

Russell L. Ackoff wrote about complex problems as messes:

“Every problem interacts with other problems and is, therefore, part of a set of interrelated problems, a system of problems…. I choose to call such a system a mess.”

Robert Horn extended the concept:

“a Social Mess is a set of interrelated problems and other messes. Complexity—systems of systems—is among the factors that makes Social Messes so resistant to analysis and, more importantly, to resolution.”

So a system of problems within a complex system of systems?

“Wicked problem” is a phrase originally used in social planning to describe a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize. Moreover, because of complex interdependencies, the effort to solve one aspect of a wicked problem may reveal or create other problems.

Curry goes on to cite the executive summary of New Tools for Resolving Complex Problems, subtitled Mess Mapping and Resolution Mapping Processes.

Wicked Problems (equivalently, Social Messes) are seemingly intractable problems. They are composed of inter-related dilemmas, issues, and other problems at multiple levels society, economy, and governance. These interconnections—systems of systems—make Wicked Problems so resilient to analysis and to resolution.

Messes then seem to be Frankenstein problems while wicked problems are Godzilla. We will stick with just the course’s messes and difficulties from here on with the understanding we may need a bigger army.

The course seems to be breaking down its systematic approach by what I’ll call embedded bifurcations, difficulties with messes, emotional reactions with rational reactions, and systemic thinking with systematic thinking as part of understanding the “perceived complexity within situations”. The first dealt with being differences between difficulties and messes.

I am going to jump though and first consider problems, situations and systems. As suggested in the last post there are two types of problems, difficulties and messes. Problems, according to the course, are taken up by, not given to, decision makers and problems are extracted from unstructured states of confusion or complex situations.

These are my interpretations, so its necessary to take the course to see if one comes to the same conclusions. Problems, it seems are undesired situations. Situations are not systems but interactions between us and systems. I don’t see unstructured states of confusion and complex situations as being equivalent but a complex situation is different from a complex system. Can a complex situation, on its own be adaptive?

Back to the more basic and tangible ideas of difficulties and messes. Difficulties refer to simpler, more limited types of situations. A difficulty is fairly clear cut, easy to put a label on it and to explain to someone else what is the problem. With difficulty, the overall context and purpose of the activity can be taken for granted, determining how it can best be done is a relatively simple matter. A difficulty can be disentangled from the broader context of work and addressed in a more or less discrete matter. What a solution will look like is roughly known with a difficulty. Finally, one knows enough or knows what is needed to be known to be able to tackle a difficulty.

Messes aren’t seen as merely being ‘bigger’ than difficulties. They have a number of features that make them qualitatively different. A mess is harder to pin down or even to say what is the actual problem. Having no sure solutions, it usually doesn’t make much sense to talk about ‘an answer’ with a mess. It becomes more a matter of coping as best one can with the circumstances. The aspects of a mess are beyond one’s direct control and what factors are relevant to the situation and what aren’t isn't easily known. A mess is fuzzy. Because its different elements are closely tied to other areas of activity it’s hard to say who and what is involved in the problem and who and what isn’t. With a mess, one never knows enough and is uncertain even what is needed to be known.

Other attributes that distinguish between difficulties and messes concern their scale and the uncertainty associated with them.

The scale of the situation determines the ways in which messes tend to be ‘larger’ and have more serious implications than difficulties. More people are likely to be involved in a mess. Messes usually have a longer time-scale. They are more complicated making them more difficult to tackle. A mess calls into question how much weight to give to different considerations, assumptions and priorities as well as whether particular goals are realistic or not.

The second group of key features comes under the general heading of uncertainty. There is much more about which one is simply unsure with messes. Uncertainty that is inherent in the situation itself, most notably irreducible uncertainty, as suggested by Donella Meadows, or essentially complex stochastic output.

The next level idea best capturing the difference between difficulties and messes is the idea that difficulties are bounded while messes are unbounded in terms of both scale and uncertainty.

A bounded situation implies that it is fairly limited and that one roughly knows where are those limits. Although no single characteristic provides an essential criterion, to describe a situation as messy, rather than just a difficulty, it implies that in some important respects it is unbounded.

An unbounded situation is more extensive, though just how extensive can be hard to determine so it becomes a mess. Knowing that a messy situation may in some important respects be unbounded is useful. It is though ambiguous on an important point.

Elements of rational and emotional complexity must be considered, for practical purposes, as it is essential to remember that both are important in comprehending a messy situation.

What may be hard to pin down is whether this quality of being unbounded is a characteristic of a person’s experience of a particular situation, or is actually of the nature of the situation itself? Is a messy situation one that someone for their own particular reasons can’t see how to disentangle from everything else? Does it only appear to them to be unbounded or is it actually the situation that is unbounded meaning that the circumstances are such that the situation really has very extensive ramifications.

One of the properties of problems with which helpers have found it quite hard to grapple is the extent to which all problems are personal; different persons see different problems in what other people would take to be the same situation. This is an important point in our argument, and is fairly well accepted in everyday ‘common sense’. This point does not seem to raise much difficulty when it is expressed theoretically, but it is often rather more difficult to bear it in mind and act upon in practice.

In summary, difficulties and messes are general terms without clear-cut or categorical distinctions. Instead, they are on a continuum, with most problems lying somewhere in between.

Thursday, November 23, 2017

Approaching a Systems Practice, Yet Again

Before getting started, it seems important to recognize upfront that New Community Paradigms or NCP doesn't have any answers, only possible pathways to answers. The resources or results of explorations and experiments are only road signs or markers that could hopefully prove useful when others create their own pathways.

Another pathway or in this case, online course has been found and started. This one is Mastering Systems Thinking in Practice from the Open University in the UK, taught as far as I can tell by Professor Andy Lane. As usual for this blog, this is not meant to be a substitute for the course. The order here will often be different from the course and differences in perspectives will be noted.

This will be the second systems thinking course, actually third if you count the Systems Practice course but there are still some issues with that course that need to be dealt with which is part of the motivation to take this one. There is also a desire to extend my systems thinking knowledge to better address wicked problems by including a better understanding of the role of complexity.

The course asserts that “complexity becomes frightening when we assume we ought to be able to ‘solve’ it” but then can't. An approach which is deeply entrenched in Western culture. This is in agreement with what has been asserted before on these pages, “Traditional management frameworks and methodologies are based largely on ‘machine" analogies’ taking a reductionist approach to complexity”.

It is an approach that seems natural and obvious to anyone brought up or educated in a Western culture as being the way to tackle complex situations but while the approach is appropriate for many situations, it’s useless for others. Systems thinking according to the course makes complexity manageable by taking a broader perspective instead of breaking down situations into their component parts. The course seems to largely put ‘Systems thinking’ in an organizational setting, though it encourages personal connection as a means of bridging to larger concepts.

The course highlights UK entities such as PwC, NESTA, Forum for the Future, Advice UK and Oxfam. Systems thinking has been used in UK policy making at both the local and national government level. Here in the US, there is the Waters Foundation, the Institute for Systemic Leadership, and the Donella Meadows Institute as well as several educational institutions, book publishers and reports such as this one from the World Health Organization. It has influenced the work of the Ellen MacArthur Foundation on the Circular Economy and is thought to be an important facet of the 17th Sustainable Development Goal that deals with bringing the work on all other 16 goals together as part of a global partnership.

A good deal written here will be based on questions asked by the course such as, “How do you see the role of systems thinking?”. I now see systems thinking as analogous to aspects of a global navigation system for understanding our world using one of my favorite PBS shows, How We Got To Now with Steven Johnson / Time (Emmy Winner) as the analogy. Sailing by longitude in straight-line fashion can be seen as a step by step analytical process found say in writing blog posts. Systems thinking allows one to think more broadly sailing by latitude but this takes new ways of thinking. Both together allow though for a far more expansive view of the world.

The course is presumed to be advanced but seems often to assume minimal systems thinking background. The course seems to be following a system of embeddedness in presenting the material, working from smaller concepts to larger. This blog will sometimes follow an opposite path because it will connect with past learning.

Systems thinking, according to the course respects complexity, realizing that understanding is often incomplete and that we don’t always know what is and is not included in an issue. Any view is partial and provisional and others likely have a different one. It means resisting the temptation to simplify issues by breaking them down. It also means there is more than one way of understanding the complexity of an issue.

According to the course, Systems thinking focuses on connections or relationships between things, events and ideas, giving them equal status. Fundamentally, it is about relationships and processes, it is a framework for understanding inter-relationships.

Patterns become important and the nature of the relationships between a given set of elements may be: 

  • Causal (A causes, leads to, or contributes to, B); 
  • Influential (X influences Y and Z); 
  • Temporal (P follows Q); or 
  • Relate to embeddedness (M is part of N) and there are others. 
According to the course, “Thinking systemically about these connections includes being open to recognising that the patterns of connection are more often web-like than linear chains of connection”.

I like that the course explicitly differentiates between causality and influences or what I see for the later as correlation. Relationships between things, events and ideas mean patterns of connection giving rise to larger wholes, and in certain cases, giving rise to emergence.

Some seem to wrongly assume that systems thinking only addresses well-understood problems, with one best answer to that problem and the path to finding that answer being linear. Others believe that systems thinking involves making changes to a system that will lead to the elimination of a problem identified within one of the system components.

Systems thinking does not attempt to model reality. One's mental image of the world is a model, a partial representation of reality based on partial knowledge of the external world. An important facet of systems thinking in practice is context.
Each individual's perspective on the world can take one of three vantage points : 
  1. Ignore the incompleteness of one’s viewpoints and representations. 
  2. Recognize that one’s viewpoint is limited and because it is only partial may be misleading. 
  3. Always carry an awareness that one will never know the world or fully the implications of the world’s unknowability. Therefore we must always be trying to account for our own role in perceptions of the world. 
These are all general concepts concerning systems thinking. The course begins constructing a specific understanding of systems thinking by starting with a simpler concept, accessible to being, if not fully understood at least recognizable, “messes” as defined by Russell L. Ackoff’. More on that in the next post. Russell L. Ackoff was the one who admonished us to Never improve a part of the system unless it also improves the whole. It was also Russell L. Ackoff who considered, Why Few Organizations Adopt Systems Thinking. There are two basic reasons according to Ackoff, one the fault of the organizations and one the fault of systems thinking or more precisely systems thinkers.

This was a typical organization, one in which the principal operating principle was "Cover your ass.” Application of this principle produced a management that tried to minimize its responsibility and accountability. The result was a paralyzed organization, one that almost never initiated change of any kind let alone innovation. It made changes only when a competitor made it necessary for it to do so.

We are an introverted profession. We do most of our writing and speaking to each other. This is apparent on examination of the content of any of our journals or conferences. To be sure, some communication among ourselves is necessary, but it is not sufficient.

The course goes on to cite C.W. Churchman (1971), as one of the first people to write about what systems thinking might mean in practice, who said, ‘there are no experts in a systems approach’.

NCP has recognized that a systems thinking approach can take a significantly different path than one dictated by a command and control management approach. A systems thinking approach can call upon the stakeholders of the system in question to take from an investigation resulting from a preceding exploration, found points of leverage so as to craft a strategy which will address the current situation in a manner that is beneficial to the whole system by changing stakeholder and organizational behaviors and avoiding unintended consequences to the greatest extent possible.

NCP sees volunteering through civil society as important to a community because the political institutions and market institutions cannot be expected to be able or to be trusted to fulfill all the needs of the community, especially in addressing Wicked Problems. Our challenges are increasingly complex. Our responses to these challenges cannot be merely simplistic but need to be coherently complex which requires systems thinking.

For the course then at the heart of systems thinking: Essentially it is about using practical frameworks for engaging with multiple perspectives.

The first step in doing this, according to the course, is understanding the difference between dealing with difficulties and dealing with messes.

Monday, November 6, 2017

Some Complex Questions for ABCD about Carrying Capacity

In the accompanying NCP post, Cormac Russell’s post on Nurturing the Carrying Capacity of Communities is credited with being an inspiration and here a primary source for attempting to bridge ABCD with dynamic complexity. One premise for this is that communities of all types are dynamic complex systems, another is the concept of carrying capacity which refers to a system's resilience and receptivity before it begins to degrade or the equilibrium population or the number of members a system can support, particularly as it can be applied to communities. The previous post is from more of a complex dynamics perspective while this one will be based more on questions asked of Asset Based Community Development.

Cormac has said before that community should be thought of as a verb rather than as a noun but for this purpose, we need to categorize types. Most geographically placed, politically defined by government type communities such as cities or towns are usually composed of a number of diverse socially and often demographically defined place-based communities, neighborhoods, of differing levels of influence. These neighborhoods have experienced years of working with different public and private institutional agencies which have provided services of one kind or another under the auspices of a governmentally defined entity but not at equal levels. In addition to these but not necessarily separate are other types of community that can extend beyond geographic boundaries. From here on, when speaking of communities, it means the later or neighborhoods and smaller social based communities. 

The carrying capacity of a local community depends upon good stewardship of that community’s welfare which ideally requires nurturing at three levels with correct sequencing that discovers the underpinning capacities and which functions in a way that does not harm the social capital of the community. The result of good stewardship in times of crisis should be sufficiency and abundance, not scarcity and abandonment.

There are things for which communities have adequate carrying capacity to do best on their own. Outside agencies then should ideally facilitate such activities so that the carrying capacity of the community goes as far as possible. Instead, communities are often asked to scale these efforts to extend them beyond the community's boundaries. 

The warning that “Scale is Important but Who’s Scale Are We Talking About?” so as not to scale or grow beyond a community's own carrying capacity for the benefit of outside agencies becomes especially relevant as the community's carrying capacity and established predictable processes (the way it works) will likely be diminished and won't work the same way elsewhere. 

As suggested in the last post, complex dynamics can study a system from a boat on a river level, differential equation, or from an airplane level, iterated logistic map. One aspect of the iterated logistic function noted by the complex dynamics course is that chaos is not determined by a change in population nor in the annihilation (carrying capacity) number nor as a factor of how close the population is to the annihilation number but by the rate of growth. More precisely the rate of growth of a population system at a high enough level that is both bounded and subject to sensitivity to initial conditions.

A call for needing to remove barriers seems though to argue against a community having sufficient carrying capacity on is own taking us to the next level. That level which is beyond the carrying capacity of what communities can do on their own but could do perhaps with some help from outside institutions.  Part of the carrying capacity then has to come from outside the community but the agencies, working on behalf of those responsible for this, may be competing for resources which are then being distributed to competing communities. 

Outside agencies, institutional or otherwise, should then seek to be in a right relationship with these smaller social, demographic, cultural communities. However, it has been many of these very same agencies who have failed, are still failing and are now looking to systematize their failure as the new normal. The role of ABCD is separate from the provision of services and not meant to save institutional systems money and an imposed scaling from a base of community carrying capacity has been demonstrated to be unwise. Outside agencies though have different pressures from budgetary committees and such for imposing scaling on their efforts. These pressures not only can’t be discounted, they should be optimized to provide the best possible service with limited resources to the greatest number. There have been some successes in these partnerships, particularly with healthcare but while empirically verifiable as to what works, are theoretically less clear to me as to how they work.

There are then those things that communities need to have done for them by outside agencies.  They do not have the carrying capacity to do it on their own even with help or that help is never offered so that the agency maintains control. Agencies should seek to do those things in as transparent and accountable a manner as possible but they very often don’t. 

The power relationships of communities with outside institutional agencies has taken a new turn with agencies claiming that service delivery is neither sustainable nor ironically empowering. Austerity, defined by the agencies, means the communities have fewer outside resources available so have to carry more of the responsibility, including taking over care of those previously highly service dependent, a form of harvesting of the community's carrying capacity. The added incongruity is that these are the same agencies that eroded the carrying capacity of communities for decades, and are failing to do enough now to provide communities with the necessary support to build back up the needed carrying capacity. 

ABCD is based on the simple logic that communities can’t know what external supports they need until they first know what internal capacities or what social capital they have in defining their carrying capacity. A question for many communities then is whether they are even asking the question? ABCD seeks to change this by committing to re-seeding associational life at a hyper-local level (i.e. street level?). ABCD is about the strengthening of social capital within a community so as to save people from a life of institutionalization by creating community alternative to the (institutional) systems world.  The reach of ABCD though is arguably restricted by Dunbar's Number.

What leverage then is afforded to local communities or even those working in support of local communities to ensure that this is done properly? Even if this were accomplished, providing the proportionate support that does not displace or diminish local community power is a difficult balancing act with the best of intentions. We are beginning to attain the level of cities at this point and cities, as Professor Geoffrey West has asserted, naturally scale in terms of economies at a sub-linear rate in a sigmoidal curve for infrastructure having an analog to biology but scale at a superlinear fashion with socio-economic network factors  with each at a rate of about 15% in savings for the former and in growth for the later though not through the equitable distribution of benefits. Detriments are paid for in the form of socio-economic entropy which is also not equitably distributed. The catch is that the entire system is destined to collapse from the stress being generated without a major intervention or transformation of some type. These ideas are expanded upon here. It should be noted here that even though we have been using logistical equations to explain certain phenomena they are still considered qualitative explanations in the sense of being caricatures and not deeper quantitive analysis. 

Agency interactions or what Cormac refers to as conversations, unfortunately, start and remain stuck on the third level, and without proper investment in community building they will remain there but there is little incentive to make that extended investment.  At the third level, the system being generated becomes entrenched leading to a form of top-down service delivery engendering an erosion of social capital and a high level of dependence on external resources that are now disappearing. The system is persistent and resilient even while failing to address the needs of its supposed beneficiaries. 

Many of the institutional agencies operate from a reductionistic top-down management framework,  segmenting members by age and condition, narrowing their foci to create a siloed management approaches,  youth agencies working only with the young, older people’s services working with only seniors; disability services serving only the disabled treating, as Cormac says, treating the community like a tangerine, emphasizing efficiency, through financial metrics, as equal or more important than effectiveness. 

Inadvertently, which is another way of saying with the unintended consequence of, having people being redefined or commodified as service users and patients and thereby defined out of community resulting in the consequent depletion of carrying capacity by the community that was supposedly being helped. Saying inadvertently is giving the benefit of the doubt for the initial intention and could imply responsibility on both sides of the issues. The continued maintenance or manipulation of institutional systems for the benefit of some at the cost of others is a different matter. 

This raises the question though whether ABCD actually addresses issues between different competing communities through democratic principles or simply focuses through relational consensus on the maximum carrying capacity of each community with special attention towards challenged ones? My question is who specifically is the "We" whom Cormac speaks of that needs to learn from communities what they can do and care enough about to do without outside help. Who is the “We” that not only helps communities determine what they can do with some support, and only then helps determine what external resources are needed but also helps in negotiating for them or enhances the carrying capacity of the community to do such on their own? 

It isn't the communities themselves, at least not initially and it is doubtful that it is the institutional agencies so there is presumedly a third sector or movement outside of these communities that is being appealed to beyond the already converted and serving and the interested, morally supporting but uninvolved readers. Is this unformed but more complex network of relationships addressed or is it left to other efforts such as Participatory Budgeting, Placemaking or other forms of direct democratic governance of community?

Cormac sees all of this as causing further atomisation (Irish) to people’s sense of community in what I interpreted as ending up being as a system of disorganized complexity. I am going to suggest though that ABCD also potentially features an atomization (USA) of a community but to the level of independent agents connecting in a complex fashion though in a system of organized complexity as defined by both Jane Jacobs and Warren Weaver. ABCD then becomes a necessary and even primary component of New Community Paradigms but not necessarily a sufficient one. Another bridge to be explored is how Asset Based Community Development could be utilized as a means of Disruptive Innovation. 

Bridging ABCD and Dynamic Complexity

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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