Notes on Positive Feedback and Natural Systems
Notes are from: Donald L. DeAngelis et al., Positive Feedback in Natural Systems, Oak Ridge National Laboratories (1986).
Components of systems may be tangible objects (planets, gears, organisms), or they may be "abstract properties like energy storages or amounts of infomration."
In relation to feedback, there are two types of systems.
1. "open loop systems" -- flow of input is all one direction (sun warming earth)
2. "closed loop systems." -- flow is two ways, interdependent.
"The existence of a flow of information from the system "output" to the "input" that regulates the input to maintain a stable set point, is the commonly accepted emblem of a cybernetic system."
Feedback will not always be information flow. It can be change in biomass, energy, or material that only incidentally conveys information affecting the system.
Negative feedback -- deviation counteracting, or homeostatic (regulatory). Actual negative feedback regulation can fail badly if time delays exist that sufficiently slow down the action of negative feedback. Much of the cyclical phenomena we see in nature and society are the result of this imperfect regulation. Negative feedback is necessary for homeostasis, but not always sufficient.
Feedforward -- a variation of positive feedback, but whereas feedback is the effect, delayed in time and perhaps mediated by other system components, that a change in a given component has on itself as a result of a prior change in that component, feedforward is an effect that a component has on itself, again perhaps mediated by other components, because of expected changes in the component.
Positive feedback -- when mutual causal effects are deviation amplifying. It occurs when the response of the system to an initial deviation of the system acts to reinforce the change in the direction of the deviation. (In evolutionary terms, deviations that are reinforced into a criticality are called "frozen accidents".) This positive feedback can cause instabilities and ultimate transitions from one state to another.
Flannery (1972) described the rise of the centralized political state in terms of deviation amplification caused by positive feedback loops. Bateson (1972) described such feedback in interpersonal relations in tribal societies.
Neither positive nor negative feedbacks manifest themselves individually in a conspicuous way. However, when the system is driven far from equilibrium (by a temporary unusual environmental condition, for example), specific positive or negative feedbacks may become very obvious. The system could be driven into a regime where homeostatic forces no longer operate. Positive feedback loops may act to amplify the deviation, perhaps driving the system to extinction. On the other hand, other positive feedback loops may be activated that rescue the system from extinction and allow it to shift back to the point where homeostatic forces restore it to equilibrium.
Information and complexity is increasing in the biosphere (and human society) through evolutionary time in a mutually reinforcing way.
The problem of entropy for this type of evolution was resolved in the 20th century with the recognition that the earth is an "open" thermodynamic system in which entropy can, in principle, decrease. In fact, the modern theory of nonequilibrium thermodynamics provides a conceptual framework for understanding the emergence of greater and greater complexity through time both in living and nonliving systems.
Nearly every index of human cultural complexity has increased at a growing rate through human history and, as far as can be fathomed, through human prehistory as well. Halle (1977) points out that every increase in complexity in nature makes possible new changes that could nothave occurred before (non-abelian). As a system becomes more complex, the number of possible novelties increases in proportion to this complexity.
A characteristic of cooperative systems is the presence of "thresholds." When a threshold is crossed, presumably during slow changes in some of the system variables or parameter values, the mode of behavior of the system can suddenly change. Part of the reason for catastrophic failures lies in the very nature of structural design, which emphasizes resilience. Design for resilience stablizes a structure under most conditions, but it can engender a vulnerability to positive feedback amplification of small cracks in the structure.
The "law of collapse" has relevance to advanced economic systems. According to Leontief (1966), such economic systems are composed of a set of "basic" commodities (see Notes on Networks, below: core hubs like water and ATP), each of which is dependent on all others. The loss or severe reduction of one commodity will generate a chain reaction, destroying or damaging all others (see network vulnerability to 'attack'). A similar fragility afflicts advanced societies as a whole. Such societies have evolved a high density of tight interactions among various sectors. Disruption of a part of the society may propagate and could even trigger a total collapse, as has occasionally happened.
Complex systems can compensate for the instability resulting from a high degree of interconnectedness. One way is by redundancy; i.e. if one critical pathway is severed another pathway, perhaps existing only latently, can take over for it (see Strategic Implications of BP turn off, comments, Supply redundancy during Gulf War I). The human brain employs a great deal of functional redundancy.
Summary: At least four generalizations.
1. PF may be essentially involved in processes within systems that bring about increasing complexity.
2. Changes in the system tend ot accelerate, so that rapid transitions from one state to the next can occur.
3. There are frequently thresholds such that small changes in a variable or parameter beyond a certain critical point can trigger large scale change in the system (self-organized criticality).
4. A network of potential PFs, perhaps nont apparent at a given time because held in check, can make a system fragile to certain types of perturbations.
Positive and negative feedbacks have been known to "nest" at specific scales of the system.
An increase in the number of components or interactions in the system increases the number of conditions that must be satisfied for stability; hence, the likelihood of a randomly-connected system being stable decreases as the size of the system increases.
The autocatalysis of atoms in stellar interiors has been called "nuclear evolution", and it is a system of PF (mass to energy taking more mass to energy), and NF (gravity vs. thermal pressure).
Waves in the ocean as PF and NF: At the peak of the developing wave, the air velocity is greater; hence, by Bernoulli's law the air pressure is less than in the trough. The air in the trough circulates in the reverse direction and transfers energy to the water in a manner that increases the wave amplitude. As the wave becomes larger, its structure increases the pressure differential over the water created by the wind and the wave continues to grow (PF) until gravitational forces prevent further growth (NF -- gravitational force as de facto parameter).
The process of dissolution of crystal occurs when the crystal is subjected to increasing temperature. As the temperature increases, defects occur in the structure. The number of defects increases until many are close to each other. "At this point disorder can rise catastrophically because of cooperative effects of the interactions." (Careri, 1984).
Some structures are durable and can provide building blocks on the path to higher levels of organization. Nuclear evolution provided the earth with a variety of stable elements, many of which were able to interact chemically. The stage was set for "chemical evolution." Chemical evolution may be defined as the progressive building up of more complex chemical structures. This can occur when there is an external source of free energy, which can support the sefl-amplifying processes.
These examples show that evolution toward more and more complex organic molecules under primal conditions was not only possible but favored. Each new state, more complex than its predecessor, could have created conditions to make the system more vulnerable to instabilities from new fluctuations. Then the creation of greater and greater molecular complexity can be pictured as a PF loop. The dissipation of energy (along with entropy production) initially increases during each new fluctuation, but then settles down to a lower level as the system adjusts itself to its new constraints. The continued working of this fluctuation-dissipation cycle drives the system further and further from thermal equilibrium (heat death).
Each new level of complexity alters conditions in a way that makes the next level possible.
A species is seldom a passive inhabitant in its environment, but interacts with its surroundings through its behavior. This interaction can result in a second type of positive feedback mechanism that can propel evolutionary change.
The environment (system) itself evolves as its component interactions evolve, creating the possibility for further evolution by organisms discovering and exploiting new opportunities suddenly made available by the new state of the system.
Implications:
As seems clear, terrorism is a deviation that is, for the present, being amplified by certain system components already in existence. Terrorism is experiencing positive feedback (for various reasons). If there is a homeostatic mechanism inherent in our system, it is either nesting at a higher scale of terrorism than we currently inhabit, or the negative feedback mechanism is activating slowly (which might result in the same phenomena as scalar nesting, which would presumably speed it up--or it might be too slow, deleteriously so).
Entropy in the system is currently on the rise. But other components in the system are reacting, too. The race is to the threshold.
Which will be reached first, the higher-complexity threshold, or the system-collapse threshold? I think any serious person would put great confidence in the former. The terrorists operate amidst chaos, thriving in regions of instability and uncertainty. The forces of organization, who can marshal an immense amount of information and power, will surely destroy them.
The Positive-Feedback loop of organizational disaggregation and power atomization stems from the Army of Davids syndrome. The system is changing, and complexity is increasing. In this new system-state, new opportunities are appearing and are being exploited by these various system components -- most notably terrorists. But the forces of organized stability are also expoiting these new realities, as Bobbitt recognizes in his theory of the market-state.
In the end, terrorism will only succeed in bringing about evolved survival mechanisms and an increase in human complexity (right?).
Components of systems may be tangible objects (planets, gears, organisms), or they may be "abstract properties like energy storages or amounts of infomration."
In relation to feedback, there are two types of systems.
1. "open loop systems" -- flow of input is all one direction (sun warming earth)
2. "closed loop systems." -- flow is two ways, interdependent.
"The existence of a flow of information from the system "output" to the "input" that regulates the input to maintain a stable set point, is the commonly accepted emblem of a cybernetic system."
Feedback will not always be information flow. It can be change in biomass, energy, or material that only incidentally conveys information affecting the system.
Negative feedback -- deviation counteracting, or homeostatic (regulatory). Actual negative feedback regulation can fail badly if time delays exist that sufficiently slow down the action of negative feedback. Much of the cyclical phenomena we see in nature and society are the result of this imperfect regulation. Negative feedback is necessary for homeostasis, but not always sufficient.
Feedforward -- a variation of positive feedback, but whereas feedback is the effect, delayed in time and perhaps mediated by other system components, that a change in a given component has on itself as a result of a prior change in that component, feedforward is an effect that a component has on itself, again perhaps mediated by other components, because of expected changes in the component.
Positive feedback -- when mutual causal effects are deviation amplifying. It occurs when the response of the system to an initial deviation of the system acts to reinforce the change in the direction of the deviation. (In evolutionary terms, deviations that are reinforced into a criticality are called "frozen accidents".) This positive feedback can cause instabilities and ultimate transitions from one state to another.
Flannery (1972) described the rise of the centralized political state in terms of deviation amplification caused by positive feedback loops. Bateson (1972) described such feedback in interpersonal relations in tribal societies.
Neither positive nor negative feedbacks manifest themselves individually in a conspicuous way. However, when the system is driven far from equilibrium (by a temporary unusual environmental condition, for example), specific positive or negative feedbacks may become very obvious. The system could be driven into a regime where homeostatic forces no longer operate. Positive feedback loops may act to amplify the deviation, perhaps driving the system to extinction. On the other hand, other positive feedback loops may be activated that rescue the system from extinction and allow it to shift back to the point where homeostatic forces restore it to equilibrium.
Information and complexity is increasing in the biosphere (and human society) through evolutionary time in a mutually reinforcing way.
The problem of entropy for this type of evolution was resolved in the 20th century with the recognition that the earth is an "open" thermodynamic system in which entropy can, in principle, decrease. In fact, the modern theory of nonequilibrium thermodynamics provides a conceptual framework for understanding the emergence of greater and greater complexity through time both in living and nonliving systems.
Nearly every index of human cultural complexity has increased at a growing rate through human history and, as far as can be fathomed, through human prehistory as well. Halle (1977) points out that every increase in complexity in nature makes possible new changes that could nothave occurred before (non-abelian). As a system becomes more complex, the number of possible novelties increases in proportion to this complexity.
A characteristic of cooperative systems is the presence of "thresholds." When a threshold is crossed, presumably during slow changes in some of the system variables or parameter values, the mode of behavior of the system can suddenly change. Part of the reason for catastrophic failures lies in the very nature of structural design, which emphasizes resilience. Design for resilience stablizes a structure under most conditions, but it can engender a vulnerability to positive feedback amplification of small cracks in the structure.
The "law of collapse" has relevance to advanced economic systems. According to Leontief (1966), such economic systems are composed of a set of "basic" commodities (see Notes on Networks, below: core hubs like water and ATP), each of which is dependent on all others. The loss or severe reduction of one commodity will generate a chain reaction, destroying or damaging all others (see network vulnerability to 'attack'). A similar fragility afflicts advanced societies as a whole. Such societies have evolved a high density of tight interactions among various sectors. Disruption of a part of the society may propagate and could even trigger a total collapse, as has occasionally happened.
Complex systems can compensate for the instability resulting from a high degree of interconnectedness. One way is by redundancy; i.e. if one critical pathway is severed another pathway, perhaps existing only latently, can take over for it (see Strategic Implications of BP turn off, comments, Supply redundancy during Gulf War I). The human brain employs a great deal of functional redundancy.
Summary: At least four generalizations.
1. PF may be essentially involved in processes within systems that bring about increasing complexity.
2. Changes in the system tend ot accelerate, so that rapid transitions from one state to the next can occur.
3. There are frequently thresholds such that small changes in a variable or parameter beyond a certain critical point can trigger large scale change in the system (self-organized criticality).
4. A network of potential PFs, perhaps nont apparent at a given time because held in check, can make a system fragile to certain types of perturbations.
Positive and negative feedbacks have been known to "nest" at specific scales of the system.
An increase in the number of components or interactions in the system increases the number of conditions that must be satisfied for stability; hence, the likelihood of a randomly-connected system being stable decreases as the size of the system increases.
The autocatalysis of atoms in stellar interiors has been called "nuclear evolution", and it is a system of PF (mass to energy taking more mass to energy), and NF (gravity vs. thermal pressure).
Waves in the ocean as PF and NF: At the peak of the developing wave, the air velocity is greater; hence, by Bernoulli's law the air pressure is less than in the trough. The air in the trough circulates in the reverse direction and transfers energy to the water in a manner that increases the wave amplitude. As the wave becomes larger, its structure increases the pressure differential over the water created by the wind and the wave continues to grow (PF) until gravitational forces prevent further growth (NF -- gravitational force as de facto parameter).
The process of dissolution of crystal occurs when the crystal is subjected to increasing temperature. As the temperature increases, defects occur in the structure. The number of defects increases until many are close to each other. "At this point disorder can rise catastrophically because of cooperative effects of the interactions." (Careri, 1984).
Some structures are durable and can provide building blocks on the path to higher levels of organization. Nuclear evolution provided the earth with a variety of stable elements, many of which were able to interact chemically. The stage was set for "chemical evolution." Chemical evolution may be defined as the progressive building up of more complex chemical structures. This can occur when there is an external source of free energy, which can support the sefl-amplifying processes.
These examples show that evolution toward more and more complex organic molecules under primal conditions was not only possible but favored. Each new state, more complex than its predecessor, could have created conditions to make the system more vulnerable to instabilities from new fluctuations. Then the creation of greater and greater molecular complexity can be pictured as a PF loop. The dissipation of energy (along with entropy production) initially increases during each new fluctuation, but then settles down to a lower level as the system adjusts itself to its new constraints. The continued working of this fluctuation-dissipation cycle drives the system further and further from thermal equilibrium (heat death).
Each new level of complexity alters conditions in a way that makes the next level possible.
A species is seldom a passive inhabitant in its environment, but interacts with its surroundings through its behavior. This interaction can result in a second type of positive feedback mechanism that can propel evolutionary change.
The environment (system) itself evolves as its component interactions evolve, creating the possibility for further evolution by organisms discovering and exploiting new opportunities suddenly made available by the new state of the system.
Implications:
As seems clear, terrorism is a deviation that is, for the present, being amplified by certain system components already in existence. Terrorism is experiencing positive feedback (for various reasons). If there is a homeostatic mechanism inherent in our system, it is either nesting at a higher scale of terrorism than we currently inhabit, or the negative feedback mechanism is activating slowly (which might result in the same phenomena as scalar nesting, which would presumably speed it up--or it might be too slow, deleteriously so).
Entropy in the system is currently on the rise. But other components in the system are reacting, too. The race is to the threshold.
Which will be reached first, the higher-complexity threshold, or the system-collapse threshold? I think any serious person would put great confidence in the former. The terrorists operate amidst chaos, thriving in regions of instability and uncertainty. The forces of organization, who can marshal an immense amount of information and power, will surely destroy them.
The Positive-Feedback loop of organizational disaggregation and power atomization stems from the Army of Davids syndrome. The system is changing, and complexity is increasing. In this new system-state, new opportunities are appearing and are being exploited by these various system components -- most notably terrorists. But the forces of organized stability are also expoiting these new realities, as Bobbitt recognizes in his theory of the market-state.
In the end, terrorism will only succeed in bringing about evolved survival mechanisms and an increase in human complexity (right?).
posted by John Aristides at 8/08/2006 12:43:00 PM
4 Comments:
Re: Nesting.
Nesting of PF and NF loops takes place when these phenomena alternate frequencies of time.
For instance, on the historical frequency of years, certain positive feedback loops can thrive, but, on the frequency of decades, some negative feedback mechanisms can be dispositive. And vice-versa.
After a certain level of deviation amplification, other system components will activate. When this happens, the original system components that caused the PF are causally overtaken by the latent forces of the NF. Like the gravitational effect on a wave, these NF always existed in the deviation's environment; it's just that they're predominate only after a certain threshold.
In other words, it might be a characteristic of our system to reinforce deviations in the short term, and counterbalance them in the long. In the Terrorist War, the enablers of the threat are the forces of Positive Feedback, the components of the system that were in place before Islamic terrorism appeared. They can only amplify this deviation to a certain point. After that, the "regulatory forces" that are lying latent in the system will be activated, and it's onto the breach -- the rough way back to equilibrium.
That is just beautiful. Thinking beyond materialism how do the properties of the "real" such as truth, beauty, LIBERTY, understanding, wisdom fit into your thought? Aren't these products of evolution too? Doesn't their emergence from a material base indicate a devine plan? I think so. Isn't the fact that the terrorists operate in "chaos" a proof that they operate in the service of existential evil where the above attributes are negated?
Your blog is the most provocotive work I have run across on the web since http://onecosmos.blogspot.com/
[H]ow do the properties of the "real" such as truth, beauty, LIBERTY, understanding, wisdom fit into your thought? Aren't these products of evolution too? Doesn't their emergence from a material base indicate a devine plan?
It certainly indicates something. It is indisputable that history has a direction.
And yes, those are surely products of evolution, in that beauty (for instance) disaggregated from the concept "humanity" would be largely devoid of meaning. The speculation is tripartite:
1. The capacity to appreciate beauty is a gift from the Divine.
2. The capacity to appreciate beauty holds an evolutionary advantage and therefore was selected for.
3. The capacity to appreciate beauty is a pleasant byproduct of other, more functional evolutionary advances.
Whichever it is, it has played an intregral part in human history, and therefore human complexity.
Its cause may not be divine, I'm sure its effects are.
Hawk, over at Belmont Club, brought up the work of William Strauss and Neil Howe.
This is my response:
The archetypal analysis is too limited, for instance. They identify four generational archetypes that, as you wrote, repeat in sequence. Each is a response mechanism to the one before, and, after this plays out over several cycles, we get this topological pattern in Anglo history called the Four Turnings.
The problem with talking about cycles is that it ignores any sense of direction, in both America the organism, and in the ecosystem in which she lives. Both America and her environment evolve; they are, in fact, evolving. A series of four cycles doesn't explain how this mutual evolution occurs, nor does it explain why there are only four turnings instead of, say, five or six. Also, why are some of the ekpyroses (or saecular crises) instigated from without (World War II), while others come from within (Civil War), while others are both within and without (Great Depression). They do a good job investigating all these events, but their categorizations are fuzzy, and I didn't think they analyzed the underlying structure nearly as rigorously as they could have.
Futhermore, they don't really go into the influence of institutional memory on the archetypal plasticity of each generation. They don't really question why generational values lie latent until a triggering event.
Anyway, I'm very interested in this subject because it is what I'm working on. I've found their data to be helpful, and even their questionable conclusions are useful springboards. Glad someone else out there is reading them.
[The rest is pure exposition]
There is a more scientific way to approach this subject matter. For instance, the pattern frequencies that Strauss and Howe observe could be the scalar "nesting" of positive and negative feedback loops in the complex internal and external environments of America.
This has several implications. Close to homeostasis, a particular matrix of components, itself a matrix of P and N feedback, will predominate the evolution of the system. Outside a certain threshold, however, other components will kick in, and the response mechanisms of the society will change. Katrina dramatically changed New Orleans, so the National Guard was activated. Before 9/11, nobody thought much about killing a vast amount of Muslims. Both the National Guard and our Willingess to Kill were latent potentialities in the system, already existing before the triggering events, but they were only activated after the information in the system crossed a certain threshold.
The corruption of New Orleans was also already in existence before Katrina hit. Whereas the National Guard was a limiting agent on the the event's destructive potential, this corruption acted as an amplifier. It added to the system's entropy, and delayed or blocked the system's regulatory response.
Like the corruption of New Orleans, the intellectual decadence of the West existed before the rise of Radical Islam. This decadence, like the above corruption did in New Orleans, acts as an amplifier on Islamism's destructive potential by delaying or blocking the system's natural regulatory responses. In simile, our cultural response to 9/11 was like turning on a firehose only to have the whole thing fall apart five minutes later due to decay (and we can thank Bush for even having a five minute burst).
The positive feedback given to the terrorist threat by our decadence is currently nesting in the 'now', but sooner or later a threshold will be crossed and the response matrix of the West will "move on." When that happens, potential will turn kinetic, and energy in the system will dissipate in the form of war. "Onto the Breach" is a tough way back to equilibrium, but it too is a response mechanism built into the system.
One must pay attention to how we got here in the first place, why we are so successful, and what has made us so fit. The answer is, of course, multi-dimensional. In fact, our multi-dimensionality, and the relationships between our plasticities and our hardnesses, is something our enemies never figure out. Until it's too late.
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