Feedback

There are two kinds of feedback that are important in our study of complex systems: Positive Feedback  and Negative Feedback. Despite the value-laden connotations of these designations, there is no inherent value judgement regarding 'positive' (good) versus 'negative' (bad) feedback. Instead, the terms can more accurately be described as referring to reinforcing deviation (positive) versus suppressing or dampening deviation (negative). Reinforcing feedback thus amplifies slight tendencies in a system's behavior, whereas dampening feedback works to restrain any changes to system behavior.

Negative Feedback

We can think of a thermostat and temperature regulation as a classic example of dampening (negative) feedback at work. The thermostat has a desired state that it wishes to maintain, and it is constantly monitoring an input about whether or not it is achieving that target. If the temperature exceeds the target, then the thermostat activates a cooling mechanism; if the temperature falls short of the target then the thermostat activates a heating mechanism. The thermostat is therefore situated within an environment, (acted upon by outside forces) but is simultaneously helping create this environment (by being one of the environmental activating forces). It is able to respond to the input of the environment by activating and output that suppressed any deviation from the goal state (the goldilocks temperature).

Because of how Negative Feedback helps maintain a particular status quo, it is an important dimension of life, or Homeostasis. Our body's ability to maintain a somewhat steady state is something we often take for granted, but it is worth pausing to reflect upon the amount of constant adjustments that are required in order to keep things like our temperature or glucose levels steady in light of extreme environmental fluctuations. 

Maintaining our own body temperatures within a narrow, healthy range requires three aspects: an input (temperature) a sensor (or brain) and a viable output (shiver to raise temperature if cold; sweat to lower temperature if hot).  While this is somewhat similar to the thermostat example, there are some slight differences: even though the act of sweating or shivering does in fact have a minute impact on the environment we are located within, these outputs do not have a significant enough impact on the environment to alter the input.

Cybernetics 

While homeostasis refers specifically to biological systems able to maintain themselves, in fact for any system where the goal is to avoid deviance - to maintain a steady state or goal for some given target such as temperature - these same three elements - inputs, sensors and outputs - need to be present.

Cybernetics is a field dedicated to understanding a whole host of systems from different disciplines in light of these characteristics, to better understand the means of self regulation in entities that seek to maintain a particular target behavior. The field emerged in the 1940s, and it, (along with general systems theory, which shares many similarities with complexity research but deals with closed rather than open-systems), is in many ways is a pre-cursor to complex adaptive systems thinking.

In many cybernetic systems, the dynamics become quite interesting, in that an output can flow back into the system as an input, in ways that we can think of as more directly 'self-regulating'.  A fly-ball governor is one such self-regulating mechanism (described on the Cybernetics page), where the self-regulating dynamics of the mechanisms cause it to slow down when it exceeds a particular speed. Anther such self-regulating or self-governing dynamics can be observed in eco-systems, where if a population of animals increases beyond the environment's carrying capacity, that environment ceases to sustain those high numbers resulting in a die-off of excess animals.  Similarly, if population numbers drop significantly, then those remaining will have a high availability of food, and any offspring will thrive, leading to population growth. These two competing forces  -population growth and carrying capacity - work in tandem to  dampen the fluctuation of population numbers, preventing them from getting too high or too low. 

Another other classic example is the idea of an oarsman on a boat, trying to reach an island, and constantly adjusting the movement of the oar to compensate for the deviations caused by the environmental factors (water currents, wind, etc. ).

Cybernetic systems differ from complex adaptive systems in that the CAS features such as  Emergence are typically associated as being the result of amplifying or positive feedback  vs Cybernetic systems that work more to maintain a stable state

Positive  Feedback

If negative feedback relied on an input, a sensor, and an output, then positive feedback operates in a equivalent way: the difference being that the output does not counteract the input, but instead builds upon, or reinforces it in some way.

We can observe that in many systems driven by simple rules, such as Fractals that over iterative sequences of graphic generation, become differentiated by more detail, more variation, and more pattern becoming apparent.

But Fractals are a specific class of entity that is limited to the domain of mathematics. Again, these kinds of positive feedback systems can exist in a wide range of non-mathematical domains, with the same principles at work.

Viral Orders:

In discussion the Path Dependency of Complex Systems, we used the example of a cat video going viral, in order to illustrate how a small, early amplification of a system preference can cause a massive shift in system outcome. Using the analogy of the 'rich get richer', cat videos that initially might get a few more clicks are recommended more frequently, leading to more views, leading to more recommendations and so forth. This illustrates the power of  positive feedback to amplify a particular aspect of a system such that it grows in importance in a non-linear way.

Another example of this comes from Network Theory dynamics, that examines how networks characterized by Power Laws can be generated when the network is constantly growing, and when new nodes of the network can be added anywhere at random, but will affix preferentially to nodes in the network that are already highly linked. This, phenomena of "growth and preferential attachment" is again an example of positive feedback, and such dynamics are thought to explain things like scaling patterns seen in different cities within a given region.

Network examples are of interest because while behaviors are initially random, because of the nature of positive feedback, these random intensities come to be reinforced over time: leading to an increase in structure and pattern. The situation is almost the opposite of that of fractals: in fractal growth a very simple formula ultimately leads to greater and greater visual complexity: in complex systems steered by positive feedback, an initially random distribution of entities (human habitations, websites, cat videos, cricket chirping), gradually become more ordered and organized, with a few dominant entities emerging and thereafter constraining the performance, behaviors, or success of other entities in the system. We can say that the system, after a time, moves into Enslaved States with only a few behavioral regimes succeeding following feedback. 

In these instances, an initially random situation has small variations amplified, to the extent that  an initially random factor or actor becomes dominant, now steering the system. I do wish to point out that this would seem to muddy our earlier contrast of 'amplifying' vs 'restraining': once a particular behavior is amplified, it in turn winds up constraining the system, as deviance from that behavior is now more difficult. To illustrate: Wikipedia has become the default encyclopedic website due to positive feedback: now that it exists, it is in fact stabilized and resists being disrupted. Its amplified strength as a website is part of what now gives it stability, dampening further disruptions. This is a characteristic of Emergence, in that emergent systems like schools of fish or flocks of birds are driven into being through positive feedback, but then exert a kind of top down resistance to future change.

Dynamics of systems subject to both Positive & Negative Feedback:

Some very interesting complex systems are governed by a combination of both positive and negative feedback. 

For instance, in the example of governing animal population fluctuations described above, we can imagine that rather than settling into one steady-state population, a particular species might oscillate between two regimes - booms and busts in population as the carrying capacity environment undergoes stress and then recovery. When we examine the system more closely, we realize that there are actually both kinds of feedback at play: reproduction rate is an example of amplifying feedback - if every two rabbits that reproduces make four rabbits and those four rabbits go on to make 8 rabbits (and so forth), then we have the kind of accelerating growth associated with positive feedback. What then happens is that this drive towards amplification, is suppressed by resistance (the carrying capacity), which works to counter balance the growth. So if we start with 8 garden rows of carrots and at every generation of new rabbits the rate of carrot row consumption proceeds faster and faster, pretty quickly all the carrots are done (and by extension, all the unfed hungry rabbit are done too). In a way, the  terminology can be muddy in that our definitions of positive and negative can rely on what is considered to be "amplifying" feedback. If we shift the lens, we could think of carrots as the agent in the system (rather than rabbits), and we could state that, due to the positive feedback in their environment (rabbit reproduction), the rate at which carrots are being consumed is increasing (even as the number of carrots is diminishing). Accordingly, what we mean by 'positive' and 'negative' are often context dependent, and can shift depending on how we describe the features of 'amplification' or 'suppression'.

What is nonetheless very interesting is that we can have systems that involve competing forces of feedback - one that drives the system forward, the other that resists or suppresses this drive (as in the case of rabbit reproduction and dwindling carrot supplies). Depending on the extent to which these co-evolving system features are out of sync in terms of these respective rates (rate of rabbit reproduction vs rate of carrot growth), the system can begin to oscillate in irregular ways. These kinds of irregular oscillations can be observed in the logistic map (also called bifurcation diagram), which illustrate how systems can cycle between many different behavioral states - with extremes arising, being dampened and then arising again (to greater and lesser degrees). Many interesting complex systems are therefore neither being entirely steered towards stability (like cybernetic systems), nor steered towards unified amplification (like crickets chirping in sync), but instead ride cascading waves between different states.

The characteristics of how feedback is moving through the system, and whether or not the system is subject to one or more interdependent feedback loops is therefore at the heart of some of the most complex dynamics we observe in complex system, and why systems composed of seemingly simple agents can nonetheless produce very complex dynamics (the complexity is in the nature of the feedback, rather than the inherent characteristics of the system.

As a final thought on this, we can observe the double pendulum experiment, where we see the irregular motion of a pendulum, the motion of which is subject to interwoven feedback from competing sources - while a simple system, the patterns traced exhibit complex dynamics:

source, wikipedia

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