Positive feedback

Positive feedback, sometimes referred to as "cumulative causation", refers to situations where some effect causes more of itself. Under strong positive feedback, most systems quickly move to a limit state, where the limit is provided by external factors, or into some other new stable state where the positive feedback is somehow negated. Positive feedback can also lead to oscillation.

A system exhibiting positive feedback, in response to perturbation, acts to increase the magnitude of the perturbation. That is, "A produces more of B which in turn produces more of A".^[1] In contrast, a system that responds to the perturbation in the opposite direction is said to exhibit negative feedback. These concepts were first recognized as broadly applicable by Norbert Wiener in his 1948 work on cybernetics.^[2]

The effect of a positive feedback loop may not be "positive" in the sense of being desirable. Positive refers to the direction of change rather than the desirability of the outcome. A negative feedback loop tends to reduce or inhibit or stabilize a process, while a positive feedback loop tends to expand or promote it and will often ultimately destabilize it.

Overview

Why is positive feedback important? The key feature of positive feedback is that small disturbances are amplified. When positive feedback is present, there is some causal loop where a small change creates an effect that causes an even bigger change -- like a ball rolling down an increasingly steep hill.

When a change in a variable occurs in a system which exhibits positive feedback, the system responds by changing that variable even more in the same direction.

The end result of a positive feedback is often amplifying and "explosive," i.e. a small perturbation results in big changes. Indeed, chemical- and nuclear fission-based explosives offer an excellent physical demonstration of positive feedback. Bombarding a single atom of Uranium 235 with a neutron causes it to emit on average slightly over two neutrons, which (if losses do not overcome this) can hit two or more atoms, which in turn can hit four or more atoms, etc. The number of atoms involved increases exponentially and very soon the entire mass of uranium is involved.

Formally, a system in equilibrium in which there is positive feedback to any change from its current state is said to be in an unstable equilibrium. The magnitude of the forces which act to move such a system away from its set point are an increasing function of the "distance" from the set point.

In the real world, positive feedback loops are always controlled eventually by negative feedback of some sort; a microphone will break or a beaker will crack or a nuclear accident will result in meltdown. This outcome need not be so dramatic, however. A variety of negative feedback loops in the same system can modulate the effect. Embedded in a system of positive and negative feedback loops, positive feedback does not necessarily imply a runaway process. Combined with other processes, it may just have an amplifying effect.

Examples and Applications

In biology

In biology, a number of examples of positive feedback systems may be found in physiology, some of which are well described in works such as Arthur Guyton's 'Textbook of Medical Physiology'.^[3]

One example is the onset of contractions in childbirth. When a contraction occurs, the hormone oxytocin is released into the body, which stimulates further contractions. This results in contractions increasing in amplitude and frequency.^[4]

Another example is the process of blood clotting. The loop is initiated when injured tissue releases signal chemicals that activate platelets in the blood. An activated platelet releases chemicals to activate more platelets, causing a rapid cascade and the formation of a blood clot.^[5]

Lactation also involves positive feedback in that the more the baby suckles, the more milk is produced, via a surge in prolactin secretion.^[6]

Estrogen that functions during the follicular phase of menstruation is also an example of positive feedback.^[7]

The generation of nerve signals is another example, in which the membrane of a nerve fibre causes slight leakage of sodium ions through sodium channels, resulting in a change in the membrane potential, which in turn causes more opening of channels, and so on. So a slight initial leakage results in an explosion of sodium leakage which creates the nerve action potential.^[8]

In most cases, such feedback loops culminate in counter-signals being released that suppress or breaks the loop. Childbirth contractions stop when the baby is out of the mother's body. Chemicals break down the blood clot. Lactation stops when the baby no longer nurses.^[3]

The analogy of Evolutionary arms races provide further examples of positive feedback in biological systems.^[9] While analogies used to describe, theorise, or explicate evolutionary positive feedback are considered by some as an adaptive process, the essential feature of positive feedback is that of the process itself, namely cumulative causation and amplification, as outlined further above. This is unrelated to what people want to believe about it (for example that it must be progressive), or whether they like the outcome which can be favourable or unfavourable. Thus it is "a means of conceptualising the adaptive or maladaptive consequences of given processes or actions".^[10]

Positive feedback loops have been utilised in several adaptive theories and explanations pertaining to human evolution and performance. For example, beginning at the macro level, Alfred J. Lotka (1945) argued that the evolution of the species was most essentially a matter of selection that fed back energy flows to capture more and more energy for use by living systems.^[11] At the human level, Richard Alexander (1989) proposed that social competition between and within human groups fed back to the selection of intelligence thus constantly producing more and more refined human intelligence.^[12] Since humans have collectively evolved to be capable of capturing and using more energy that any other species, Lotka’s rigorous energy model of positive feedback and Alexander’s social model of positive feedback appear to be in mutually supportive agreement. Crespi (2004) discussed several other examples of positive feedback loops in evolution.^[13] In psychology, Winner (1996) described gifted children, perhaps representative of the highest class of human intelligence, as driven by positive feedback loops involving setting their own learning course, this feeding back satisfaction, thus further setting their learning goals to higher levels and so on.^[14] Winner termed this positive feedback loop as a “rage to master.” Vandervert (2009a, 2009b) proposed that the child prodigy (a gifted child who reaches adult status in a particular domain of learning, for example, mathematics, music or art by age 10) can be explained in terms of a positive feedback loop between the output of thinking/performing in working memory, which then is fed to the cerebellum where it is streamlined, and then fed back to working memory thus steadily increasing the quantitative and qualitative output of working memory.^[15]^[16] Vandervert also argued that this working memory/cerebellar positive feedback loop was responsible for language evolution in working memory.

In electronics

Feedback is a process of sampling a part of the output signal, compounding it with some derived part of the source signal, and applying the compound to the input of the active feed-forward element of the feedback loop. The input to the system as a whole comes from outside the system; it is energy derived from an external signal source, which is subject to leakage and noise on its way to and within the system, and within the system can be compounded with a sample from the output by way of the feedback element. The notion of feedback relies on the presence of a well defined loop around which signal power propagates, with a well-defined feed-forward pathway inside the feedback loop, and in electronics this is achieved by use of active devices such as transistors or thermionic valves, which have access to a reservoir of power that they can tap to provide power gain for amplification. Feedback implies also the occurrence of a loop delay because that signal power propagation is causal. Negative feedback (patented by H.S. Black in 1934) is useful to set the parameters of an amplifier like voltage gain, input and output impedance, stability and bandwidth. On the other hand, positive feedback is rarely useful in amplifiers; it is useful only in very exceptional circumstances, one of which is to control the input impedance of the amplifier, and even then the amplifier is at serious risk of likely destructive instability.

Feedback is said to be positive if any increase in the output signal results in a feedback signal which on being compounded with a derivative of the source signal causes further increase in the magnitude of the output signal. Hence it is also called regenerative feedback. Positive feedback is in the same phase as the input signal, therefore the 'internal gain' of the amplifier (A_i) increases.

If the circuit elements are practically linear, the 'internal gain', A_i , of the feedback loop is given by A_i = (output voltage/input voltage) = A/ (1 − Aβ). Here A is the gain of the feed-forward active part of the amplifier without feedback, and β is the gain of the feedback element. The 'loop gain' is Aβ. Final or amplifier gain refers to the relation between source signal and load quantity; as well as depending on the 'internal gain' of the feedback loop, the final amplifier gain depends also on the presence of leakage or parasitic pathways, at the input, at the output, and as feed-forward in parallel with the feedback loop, and it depends also on the load, which may be reactive.

An advantage here is the Swing-up control of an inverted pendulum on a cart. Disadvantages are:

Gain can tend to be unstable
Higher distortion
Bandwidth decreases
Stability is difficult or impossible to guarantee

Positive feedback is used extensively in oscillators and in regenerative radio receivers and Q multipliers.

The schmitt trigger circuit uses positive feedback to generate hysteresis and thus provide noise immunity on digital input.

Audio feedback or acoustic feedback is a common example of positive feedback. It is the familiar squeal that results when sound from loudspeakers enters a closely-placed microphone and gets amplified, and as a result the sound gets louder and louder. To avoid this condition, the microphone must be prevented from "hearing" its own loudspeaker.

In economics

In the World System development

The exponential growth of the world population observed until the 1970s has recently been correlated to a non-linear second order positive feedback between the demographic growth and technological development that can be spelled out as follows: technological growth - increase in the carrying capacity of land for people - demographic growth - more people - more potential inventors - acceleration of technological growth - accelerating growth of the carrying capacity - the faster population growth - accelerating growth of the number of potential inventors - faster technological growth - hence, the faster growth of the Earth's carrying capacity for people, and so on (see, e.g., Introduction to Social Macrodynamics by Andrey Korotayev et al.).

Systemic risk

Systemic risk is the risk that an amplification or leverage or positive feedback process is built into a system, this is usually unknown, and under certain conditions this process can amplify exponentially and rapidly lead to destructive or chaotic behavior. A Ponzi scheme is a good example of a positive-feedback system, because its output (profit) is fed back to the input (new investors), causing rapid growth toward collapse. W. Brian Arthur has also studied and written on positive feedback in the economy (e.g. W. Brian Arthur, 1990)^[17]

Simple systems that clearly separate the inputs from the outputs are not prone to systemic risk. This risk is more likely as the complexity of the system increases, because it becomes more difficult to see or analyze all the possible combinations of variables in the system even under careful stress testing conditions. The more efficient a complex system is, the more likely it is to be prone to systemic risks,(just like playing online poker) because it takes only a small amount of deviation to disrupt the system. Therefore well-designed complex systems generally have built-in features to avoid this condition, such as a small amount of friction, or resistance, or inertia, or time delay to decouple the outputs from the inputs within the system. These factors amount to an inefficiency, but they are necessary to avoid instabilities.

Population and agriculture

Agriculture and human population can be considered to be in a positive feedback mode^[18], which means that one drives the other with increasing intensity. It is suggested that this positive feedback system will end sometime with a catastrophe, as modern agriculture is using up all of the easily available phosphate and is resorting to highly-efficient monocultures which are more susceptible to systemic risk.

In climatology

Within climate, it is important to remember that a positive feedback subsystem never acts in isolation, but is always embedded within the overall climate system, which itself is always subject to one very powerful negative feedback, the Stefan–Boltzmann law: that emitted radiation rises with the fourth power of temperature. Hence, on earth the gain of the overall system is always less than one, stopping the system from suffering runaway effects. While there may have been periods of time such as the exit from an ice age where the gain was greater than one, this has not lasted long enough for extreme effects such as the evaporation of the oceans as is believed to have happened on Venus.

Examples of positive feedback subsystems in climatology include:

A warmer atmosphere will, due to increased evaporation and decreased condensation, contain more water vapour, which is a greenhouse gas, so it will warm the atmosphere further.
A warmer atmosphere will melt ice and this changes the albedo which further warms the atmosphere.
Methane hydrates can be unstable so that a warming ocean could release more methane, which is also a greenhouse gas.

In sociology

In sociology, a self-fulfilling prophecy is a positive feedback loop between beliefs and behavior: if enough people believe that something is true, their behavior makes it true, and observations of their behavior in turn increase belief. A classic example is a bank run.

Another sociological example of positive feedback is the network effect, where more people are encouraged to join a network the larger that network becomes. The result is that the network grows more and more quickly over time. This is the basis for many social phenomena, including the infamous Ponzi scheme. In this case the population size is the limiting factor.

References

^ Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc.
^ Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.
^ ^a ^b Guyton, Arthur C. (1991) Textbook of Medical Physiology. (8th ed). Philadelphia: W.B. Saunders. ISBN 0-7216-3994-1
^ Guyton, Arthur C. (1991), pp.924-925.
^ Guyton, Arthur C. (1991), pp.392-394.
^ Guyton, Arthur C. (1991), p.926.
^ Guyton, Arthur C. (1991), p.907.
^ Guyton, Arthur C. (1991), p.59.
^ Dawkins, R. 1991. The Blind Watchmaker London: Penguin. Note: W.W. Norton also published this book, and some citations may refer to that publication. However, the text is identical, so it depends on which book is at hand
^ Seymour-Smith, Charlotte (1990). Macmillan Dictionary of Anthropology. London: Macmillan Press. p. 114. ISBN 0-333-39334-1.
^ Lotka, A. (1945). The law of evolution as a maximal principle. Human Biology, 17, 168-194.
^ Alexander, R. (1989). Evolution of the human psyche. In P. Millar & C. Stringer (Eds.), The human revolution: Behavioral and biological perspectives on the origins of modern humans (pp. 455-513). Princeton: Princeton University Press.
^ Crespi B. J. (2004) Vicious circles: positive feedback in major evolutionary and ecological transitions. Trends in Ecology and Evolution, 19, 627-633.
^ Winner, E. (1996). Gifted children: Myths and Realities. New York: Basic Books.
^ Vandervert, L. (2009a). Working memory, the cognitive functions of the cerebellum and the child prodigy. In L.V. Shavinina (Ed.), International handbook on giftedness (pp. 295-316). The Netherlands: Springer Science.
^ Vandervert, L. (2009b). The emergence of the child prodigy 10,000 years ago: An evolutionary and developmental explanation. The Journal of Mind and Behavior, 30, 15-32.
^ W. Brian Arthur (February 1990). "Positive Feedbacks in the Economy". Scientific American, Vol 262. No.2, p.80
^ Brown, A. Duncan. (2003) [1] Feed or Feedback. Publisher: International Books.