Social physics or sociophysics is a field of science which uses mathematical tools inspired by physics
to understand the behavior of human crowds. In a modern commercial use,
it can also refer to the analysis of social phenomena with big data.
Social physics is closely related to econophysics which uses physics methods to describe economics.
History
The earliest mentions of a concept of social physics began with the English philosopher Thomas Hobbes. In 1636, Hobbes traveled to Florence, Italy, and met the astronomer Galileo Galilei, of whom was well-known for his contributions to the sciences, namely, the ideas of motion.
It was here that Hobbes began to outline the idea of representing the
"physical phenomena" of society in terms of the laws of motion. In his treatise De Corpore, Hobbes sought to relate the movement of "material bodies"
to the mathematical terms of motion outlined by Galileo and similar
scientists of the time period. Although there was no explicit mention of
"social physics", the sentiment of examining society with scientific
methods began before the first written mention of social physics.
Later, French social thinker Henri de Saint-Simon’s first book, the 1803 Lettres d’un Habitant de Geneve, introduced the idea of describing society using laws similar to those of the physical and biological sciences. His student and collaborator was Auguste Comte, a French philosopher widely regarded as the founder of sociology, who first defined the term in an essay appearing in Le Producteur, a journal project by Saint-Simon. Comte defined social physics as
Social
physics is that science which occupies itself with social phenomena,
considered in the same light as astronomical, physical, chemical, and
physiological phenomena, that is to say as being subject to natural and
invariable laws, the discovery of which is the special object of its
researches.
After Saint-Simon and Comte, Belgian statistician Adolphe Quetelet, proposed that society be modeled using mathematical probability and social statistics. Quetelet's 1835 book, Essay on Social Physics: Man and the Development of his Faculties, outlines the project of a social physics characterized by measured variables that follow a normal distribution, and collected data about many such variables.
A frequently repeated anecdote is that when Comte discovered that
Quetelet had appropriated the term 'social physics', he found it
necessary to invent a new term 'sociologie' (sociology) because he
disagreed with Quetelet's collection of statistics.
There have been several “generations” of social physicists. The first generation began with Saint-Simon, Comte, and Quetelet, and ended with the late 1800s with historian Henry Adams. In the middle of the 20th century, researchers such as the American astrophysicist John Q. Stewart and Swedish geographer Reino Ajo, who showed that the spatial distribution of social interactions could be described using gravity models. Physicists such as Arthur Iberall use a homeokinetics approach to study social systems as complex self-organizing systems.
For example, a homeokinetics analysis of society shows that one must
account for flow variables such as the flow of energy, of materials, of
action, reproduction rate, and value-in-exchange. More recently there have been a large number of social science papers that use mathematics broadly similar to that of physics, and described as “computational social science”.
In the late 1800s, Adams separated “human physics” into the
subsets of social physics or social mechanics (sociology of interactions
using physics-like mathematical tools) and social thermodynamics or sociophysics, (sociology described using mathematical invariances similar to those in thermodynamics). This dichotomy is roughly analogous to the difference between microeconomics and macroeconomics.
Examples
Ising model and voter dynamics
A
5x5 representational grid of an Ising model. Each space holds a spin
and the red bars indicate communication between neighbors.
One of the most well-known examples in social physics is the relationship of the Ising model and the voting dynamics of a finite population. The Ising model, as a model of ferromagnetism, is represented by a grid of spaces, each of which is occupied by a spin (physics),
numerically ±1. Mathematically, the final energy state of the system
depends on the interactions of the spaces and their respective spins.
For example, if two adjacent spaces share the same spin, the surrounding
neighbors will begin to align,
and the system will eventually reach a state of consensus. In social
physics, it has been observed that voter dynamics in a finite population
obey the same mathematical properties of the Ising model. In the social
physics model, each spin denotes an opinion, e.g. yes or no, and each
space represents a "voter".
If two adjacent spaces (voters) share the same spin (opinion), their
neighbors begin to align with their spin value; if two adjacent spaces
do not share the same spin, then their neighbors remain the same. Eventually, the remaining voters will reach a state of consensus as the "information flows outward".
Example
of social validation in the Sznajd model. If two neighbors agree (top),
then their neighbors agree with them. If two neighbors disagree
(bottom), their neighbors begin to disagree as well.
The Sznajd model is an extension of the Ising model and is classified as an econophysics model. It emphasizes the alignment of the neighboring spins in a phenomenon called "social validation".
It follows the same properties as the Ising model and is extended to
observe the patterns of opinion dynamics as a whole, rather than
focusing on just voter dynamics.
Potts model and cultural dynamics
The Potts model
is a generalization of the Ising model and has been used to examine the
concept of cultural dissemination as described by American political
scientist Robert Axelrod.
Axelrod's model of cultural dissemination states that individuals who
share cultural characteristics are more likely to interact with each
other, thus increasing the number of overlapping characteristics and
expanding their interaction network. The Potts model has the caveat that each spin can hold multiple values, unlike the Ising model that could only hold one value.
Each spin, then, represents an individual's "cultural
characteristics... [or] in Axelrod’s words, 'the set of individual
attributes that are subject to social influence'".
It is observed that, using the mathematical properties of the Potts
model, neighbors whose cultural characteristics overlap tend to interact
more frequently than with unlike neighbors, thus leading to a
self-organizing grouping of similar characteristics.
Simulations done on the Potts model both show Axelrod's model of
cultural dissemination agrees with the Potts model as an Ising-class
model.
Recent work
In modern use “social physics” refers to using “big data” analysis and the mathematical laws to understand the behavior of human crowds.
The core idea is that data about human activity (e.g., phone call
records, credit card purchases, taxi rides, web activity) contain
mathematical patterns that are characteristic of how social interactions
spread and converge. These mathematical invariances can then serve as a
filter for analysis of behavior changes and for detecting emerging
behavioral patterns.
Recent books about social physics include MIT Professor Alex Pentland’s book Social Physics or Nature editor Mark Buchanan’s book The Social Atom. Popular reading about sociophysics include English physicist Philip Ball’s Why Society is a Complex Matter, Dirk Helbing's The Automation of Society is next or American physicist Laszlo Barabasi’s book Linked.
Econophysics was started in the mid-1990s by several physicists working in the subfield of statistical mechanics.
Unsatisfied with the traditional explanations and approaches of
economists – which usually prioritized simplified approaches for the
sake of soluble theoretical models over agreement with empirical data –
they applied tools and methods from physics, first to try to match
financial data sets, and then to explain more general economic
phenomena.
One driving force behind econophysics arising at this time was
the sudden availability of large amounts of financial data, starting in
the 1980s. It became apparent that traditional methods of analysis were
insufficient – standard economic methods dealt with homogeneous agents
and equilibrium, while many of the more interesting phenomena in
financial markets fundamentally depended on heterogeneous agents and far-from-equilibrium situations.
The term "econophysics" was coined by H. Eugene Stanley,
to describe the large number of papers written by physicists in the
problems of (stock and other) markets, in a conference on statistical
physics in Kolkata (erstwhile Calcutta) in 1995 and first appeared in its proceedings publication in Physica A 1996. The inaugural meeting on econophysics was organised in 1998 in Budapest by János Kertész and Imre Kondor. The first book on econophysics was by R. N. Mantegna & H. E. Stanley in 2000.
The almost regular meeting series on the topic include: ECONOPHYS-KOLKATA (held in Kolkata & Delhi), Econophysics Colloquium, ESHIA/ WEHIA.
If "econophysics" is taken to denote the principle of applying
statistical mechanics to economic analysis, as opposed to a particular
literature or network, priority of innovation is probably due to
Emmanuel Farjoun and Moshé Machover (1983). Their book Laws of Chaos: A Probabilistic Approach to Political Economy proposes dissolving (their words) the transformation problem in Marx's political economy by re-conceptualising the relevant quantities as random variables.
For potential games,
it has been shown that an emergence-producing equilibrium based on
information via Shannon information entropy produces the same
equilibrium measure (Gibbs measure from statistical mechanics) as a stochastic dynamical equation which represents noisy decisions, both of which are based on bounded rationality models used by economists.
The fluctuation-dissipation theorem connects the two to establish a
concrete correspondence of "temperature", "entropy", "free
potential/energy", and other physics notions to an economics system.
The statistical mechanics model is not constructed a-priori - it is a
result of a boundedly rational assumption and modeling on existing
neoclassical models. It has been used to prove the "inevitability of
collusion" result of Huw Dixon in a case for which the neoclassical version of the model does not predict collusion. Here the demand is increasing, as with Veblen goods, stock buyers with the "hot hand" fallacy preferring to buy more successful stocks and sell those that are less successful, or among short traders during a short squeeze as occurred with the WallStreetBets group's collusion to drive up GameStop stock price in 2021.
Quantifiers derived from information theory were used in several papers by econophysicist Aurelio F. Bariviera and coauthors in order to assess the degree in the informational efficiency of stock markets.
Zunino et al. use an innovative statistical tool in the financial
literature: the complexity-entropy causality plane. This Cartesian
representation establish an efficiency ranking of different markets and
distinguish different bond market dynamics. It was found that more
developed countries have stock markets with higher entropy and lower
complexity, while those markets from emerging countries have lower
entropy and higher complexity. Moreover, the authors conclude that the
classification derived from the complexity-entropy causality plane is
consistent with the qualifications assigned by major rating companies to
the sovereign instruments. A similar study developed by Bariviera et
al.
explore the relationship between credit ratings and informational
efficiency of a sample of corporate bonds of US oil and energy companies
using also the complexity–entropy causality plane. They find that this
classification agrees with the credit ratings assigned by Moody's.
Another good example is random matrix theory,
which can be used to identify the noise in financial correlation
matrices. One paper has argued that this technique can improve the
performance of portfolios, e.g., in applied in portfolio optimization.
There are also analogies between finance theory and diffusion theory. For instance, the Black–Scholes equation for option pricing is a diffusion-advection equation (see however
for a critique of the Black–Scholes methodology). The Black–Scholes
theory can be extended to provide an analytical theory of main factors
in economic activities.
Influence
Papers
on econophysics have been published primarily in journals devoted to
physics and statistical mechanics, rather than in leading economics
journals. Some Mainstream economists have generally been unimpressed by this work. Other economists, including Mauro Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more interest, but also criticized some trends in econophysics.
Econophysics is having some impacts on the more applied field of quantitative finance,
whose scope and aims significantly differ from those of economic
theory. Various econophysicists have introduced models for price
fluctuations in physics of financial markets or original points of view on established models. Also several scaling laws have been found in various economic data.
Main results
Presently, one of the main results of econophysics comprises the explanation of the "fat tails" in the distribution of many kinds of financial data as a universal self-similar scaling property (i.e. scale invariant over many orders of magnitude in the data),
arising from the tendency of individual market competitors, or of
aggregates of them, to exploit systematically and optimally the
prevailing "microtrends" (e.g., rising or falling prices). These "fat
tails" are not only mathematically important, because they comprise the
risks,
which may be on the one hand, very small such that one may tend to
neglect them, but which - on the other hand - are not negligible at all,
i.e. they can never be made exponentially tiny, but instead follow a
measurable algebraically decreasing power law, for example with a failure probability of only where x
is an increasingly large variable in the tail region of the
distribution considered (i.e. a price statistics with much more than 108
data). I.e., the events considered are not simply "outliers" but must
really be taken into account and cannot be "insured away".
It appears that it also plays a role that near a change of the tendency
(e.g. from falling to rising prices) there are typical "panic
reactions" of the selling or buying agents with algebraically increasing
bargain rapidities and volumes. The "fat tails" are also observed in commodity markets.
As in quantum field theory the "fat tails" can be obtained by complicated "nonperturbative" methods, mainly by numerical ones, since they contain the deviations from the usual Gaussian approximations, e.g. the Black–Scholes
theory. Fat tails can, however, also be due to other phenomena, such
as a random number of terms in the central-limit theorem, or any number
of other, non-econophysics models. Due to the difficulty in testing such
models, they have received less attention in traditional economic
analysis.
Complexity economics is the application of complexity science to the problems of economics. It sees the economy not as a system in equilibrium, but as one in motion, perpetually constructing itself anew.
It uses computational and mathematical analysis to explore how economic
structure is formed and reformed, in continuous interaction with the
adaptive behavior of the 'agents' in the economy.
Models
The "nearly archetypal example" is an artificial stock market model created by the Santa Fe Institute in 1989. The model shows two different outcomes, one where "agents do not search much for predictors
and there is convergence on a homogeneous rational expectations
outcome" and another where "all kinds of technical trading strategies
appearing and remaining and periods of bubbles and crashes occurring".
Another area has studied the prisoner's dilemma,
such as in a network where agents play amongst their nearest neighbors
or a network where the agents can make mistakes from time to time and
"evolve strategies". In these models, the results show a system which displays "a pattern of constantly changing distributions of the strategies".
More generally, complexity economics models are often used to
study how non-intuitive results at the macro-level of a system can
emerge from simple interactions at the micro level. This avoids
assumptions of the representative agent method, which attributes outcomes in collective systems as the simple sum of the rational actions of the individuals.
Measures
Economic complexity index
MIT physicist César Hidalgo and Harvard economist Ricardo Hausmann
introduced a spectral method to measure the complexity of a country's
economy by inferring it from the structure of the network connecting
countries to the products that they export. The measure combines
information of a country's diversity,
which is positively correlated with a country's productive knowledge,
with measures of a product ubiquity (number of countries that produce or
export the product). This concept, known as the "Product Space", has been further developed by MIT's Observatory of Economic Complexity, and in The Atlas of Economic Complexity in 2011.
Relevance
The economic complexity index (ECI) introduced by Hidalgo and Hausmann is highly predictive of future GDP per capita growth. In Hausmann, Hidalgo et al.,
the authors show that the List of countries by future GDP (based on
ECI) estimates ability of the ECI to predict future GDP per capita
growth is between 5 times and 20 times larger than the World Bank's
measure of governance, the World Economic Forum's (WEF) Global
Competitiveness Index (GCI) and standard measures of human capital, such
as years of schooling and cognitive ability.
Metrics for country fitness and product complexity
Pietronero and collaborators have recently proposed a different approach.
These metrics are defined as the fixed point of non-linear iterative
map. Differently from the linear algorithm giving rise to the ECI, this
non-linearity is a key point to properly deal with the nested structure
of the data. The authors of this alternative formula claim it has
several advantages:
Consistency with the empirical evidence from the export
country-product matrix that diversification plays a crucial role in the
assessment of the competitiveness of countries. The metrics for
countries proposed by Pietronero is indeed extensive with respect to the
number of products.
Non-linear coupling between fitness and complexity required by the
nested structure of the country-product matrix. The nested structure
implies that the information on the complexity of a product must be
bounded by the producers with the slowest fitness.
Broad and Pareto-like distribution of the metrics.
Each iteration of the method refines information, does not change
the meaning of the iterated variables and does not shrink information.
The metrics for country fitness and product complexity have been used in a report of the Boston Consulting Group on Sweden growth and development perspectives.
Dispersed interaction—The economy has interaction between
many dispersed, heterogeneous, agents. The action of any given agent
depends upon the anticipated actions of other agents and on the
aggregate state of the economy.
No global controller—Controls are provided by mechanisms of
competition and coordination between agents. Economic actions are
mediated by legal institutions, assigned roles, and shifting
associations. No global entity controls interactions. Traditionally, a
fictitious auctioneer has appeared in some mathematical analyses
of general equilibrium models, although nobody claimed any descriptive
accuracy for such models. Traditionally, many mainstream models have
imposed constraints, such as requiring that budgets be balanced, and such constraints are avoided in complexity economics.
Cross-cutting hierarchical organization—The economy has many
levels of organization and interaction. Units at any given level
behaviors, actions, strategies, products typically serve as "building
blocks" for constructing units at the next higher level. The overall
organization is more than hierarchical, with many sorts of tangling
interactions (associations, channels of communication) across levels.
Ongoing adaptation—Behaviors, actions, strategies, and products are revised frequently as the individual agents accumulate experience.
Novelty niches—Such niches are associated with new markets,
new technologies, new behaviors, and new institutions. The very act of
filling a niche may provide new niches. The result is ongoing novelty.
Out-of-equilibrium dynamics—Because new niches, new
potentials, new possibilities, are continually created, the economy
functions without attaining any optimum or global equilibrium.
Improvements occur regularly.
Contemporary trends in economics
Complexity
economics has a complex relation to previous work in economics and
other sciences, and to contemporary economics. Complexity-theoretic
thinking to understand economic problems has been present since their
inception as academic disciplines. Research has shown that no two separate micro-events are completely isolated, and there is a relationship that forms a macroeconomic
structure. However, the relationship is not always in one direction;
there is a reciprocal influence when feedback is in operation.
Complexity economics has been applied to many fields.
Intellectual predecessors
Complexity economics draws inspiration from behavioral economics, Marxian economics, institutional economics/evolutionary economics, Austrian economics and the work of Adam Smith. It also draws inspiration from other fields, such as statistical mechanics in physics, and evolutionary biology.
Some of the 20th century intellectual background of complexity theory
in economics is examined in Alan Marshall (2002) The Unity of Nature,
Imperial College Press: London. See Douma & Schreuder (2017) for a
non-technical introduction to Complexity Economics and a comparison with
other economic theories (as applied to markets and organizations).
In the
literature, usually chaotic models are proposed but not calibrated on
real data nor tested. However some attempts have been made recently to
fill that gap. For instance, chaos could be found in economics by the
means of recurrence quantification analysis. In fact, Orlando et al.
by the means of the so-called recurrence quantification correlation
index were able detect hidden changes in time series. Then, the same
technique was employed to detect transitions from laminar (i.e. regular)
to turbulent (i.e. chaotic) phases as well as differences between
macroeconomic variables and highlight hidden features of economic
dynamics.
Finally, chaos could help in modeling how economy operate as well as in
embedding shocks due to external events such as COVID-19.
For an updated account on the tools and the results obtained by
empirically calibrating and testing deterministic chaotic models (e.g.
Kaldor-Kalecki, Goodwin, Harrod ), see Orlando et al.
Complexity economics as mainstream, but non-orthodox
Rosser "granted" Horgan "that it is hard to identify a concrete
and surprising discovery (rather than "mere metaphor") that has arisen
due to the emergence of complexity analysis" in the discussion journal
of the American Economic Association, the Journal of Economic Perspectives.
Surveying economic studies based on complexity science, Rosser wrote
that the findings, rather than being surprising, confirmed
"already-observed facts." Rosser wrote that there has been "little work on empirical techniques for testing dispersed agent complexity models."
Nonetheless, Rosser wrote that "there is a strain of common perspective
that has been accumulating as the four C's of cybernetics, catastrophe,
chaos, and complexity emerged, which may now be reaching a critical
mass in terms of influencing the thinking of economists more broadly."
“The
truly creative changes and the big shifts occur right at the edge of
chaos,” said Dr. Robert Bilder, a psychiatry and psychology professor at
UCLA's Semel Institute for Neuroscience and Human Behavior.
The edge of chaos is a transition space between order and disorder
that is hypothesized to exist within a wide variety of systems. This
transition zone is a region of bounded instability that engenders a
constant dynamic interplay between order and disorder.
The phrase edge of chaos was coined in the late 1980s by chaos theory physicist Norman Packard. In the next decade, Packard and mathematicianDoyne Farmer co-authored many papers on understanding how self-organization and order emerges at the edge of chaos. One of the original catalysts that led to the idea of the edge of chaos were the experiments with cellular automata done by computer scientistChristopher Langton where a transition phenomenon was discovered. The phrase refers to an area in the range of a variable, λ (lambda), which was varied while examining the behaviour of a cellular automaton (CA). As λ varied, the behaviour of the CA went through a phase transition of behaviours. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicistJames P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.
In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and socialsystems operate in a region between order and either complete randomness or chaos, where the complexity is maximal.
The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others.
The phrase has also been borrowed by the business community and is
sometimes used inappropriately and in contexts that are far from the
original scope of the meaning of the term.
Adaptation
plays a vital role for all living organisms and systems. All of them
are constantly changing their inner properties to better fit in the
current environment. The most important instruments for the adaptation are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".
Adaptation to the edge of chaos refers to the idea that many complex adaptive systems (CAS) seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics has shown that edge of chaos is the optimal settings for control of a system.
It is also an optional setting that can influence the ability of a
physical system to perform primitive functions for computation. In CAS, coevolution
generally occurs near the edge of chaos, and a balance should be
maintained between flexibility and stability to avoid structural
failure. As a response to coping with turbulent environments; CAS bring out flexibility, creativity, agility, and innovation near the edge of chaos; provided the network structures have sufficient decentralized, non-hierarchical network structures.
Because of the importance of adaptation
in many natural systems, adaptation to the edge of the chaos takes a
prominent position in many scientific researches. Physicists
demonstrated that adaptation to state at the boundary of chaos and order
occurs in population of cellular automata rules which optimize the performance evolving with a genetic algorithm. Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.
The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos.
Theoretical analysis allowed prediction of the location of the narrow
parameter regime near the boundary to which the system evolves.
A feedback loop where all outputs of a process are available as causal inputs to that process
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems:
Simple causal reasoning about a
feedback system is difficult because the first system influences the
second and second system influences the first, leading to a circular
argument. This makes reasoning based upon cause and effect tricky, and
it is necessary to analyze the system as a whole.
— Karl Johan Åström and Richard M.Murray, Feedback Systems: An Introduction for Scientists and Engineers
History
Self-regulating mechanisms have existed since antiquity, and the idea of feedback had started to enter economic theory in Britain by the 18th century, but it was not at that time recognized as a universal abstraction and so did not have a name.
The first ever known artificial feedback device was a float valve, for maintaining water at a constant level, invented in 270 BC in Alexandria, Egypt.
This device illustrated the principle of feedback: a low water level
opens the valve, the rising water then provides feedback into the
system, closing the valve when the required level is reached. This then
reoccurs in a circular fashion as the water level fluctuates.
Centrifugal governors were used to regulate the distance and pressure between millstones in windmills since the 17th century. In 1788, James Watt designed his first centrifugal governor following a suggestion from his business partner Matthew Boulton, for use in the steam engines of their production. Early steam engines employed a purely reciprocating motion,
and were used for pumping water – an application that could tolerate
variations in the working speed, but the use of steam engines for other
applications called for more precise control of the speed.
In 1868, James Clerk Maxwell wrote a famous paper, "On governors", that is widely considered a classic in feedback control theory. This was a landmark paper on control theory and the mathematics of feedback.
The verb phrase to feed back, in the sense of returning to an earlier position in a mechanical process, was in use in the US by the 1860s, and in 1909, Nobel laureate Karl Ferdinand Braun used the term "feed-back" as a noun to refer to (undesired) coupling between components of an electronic circuit.
By the end of 1912, researchers using early electronic amplifiers (audions)
had discovered that deliberately coupling part of the output signal
back to the input circuit would boost the amplification (through regeneration), but would also cause the audion to howl or sing.
This action of feeding back of the signal from output to input gave
rise to the use of the term "feedback" as a distinct word by 1920.
The development of cybernetics from the 1940s onwards was centred around the study of circular causal feedback mechanisms.
Over the years there has been some dispute as to the best definition of feedback. According to cybernetician Ashby
(1956), mathematicians and theorists interested in the principles of
feedback mechanisms prefer the definition of "circularity of action",
which keeps the theory simple and consistent. For those with more
practical aims, feedback should be a deliberate effect via some more
tangible connection.
[Practical experimenters] object to
the mathematician's definition, pointing out that this would force them
to say that feedback was present in the ordinary pendulum ... between
its position and its momentum—a "feedback" that, from the practical
point of view, is somewhat mystical. To this the mathematician retorts
that if feedback is to be considered present only when there is an
actual wire or nerve to represent it, then the theory becomes chaotic
and riddled with irrelevancies.
Focusing on uses in management theory, Ramaprasad (1983) defines
feedback generally as "...information about the gap between the actual
level and the reference level of a system parameter" that is used to
"alter the gap in some way". He emphasizes that the information by
itself is not feedback unless translated into action.
Maintaining a desired system performance despite disturbance using negative feedback to reduce system error.
An example of a negative feedback loop with goals.
A positive feedback loop example.
Positive feedback: If the signal feedback from output is in phase
with the input signal, the feedback is called positive feedback.
Negative feedback: If the signal feedback is of opposite polarity
or out of phase by 180° with respect to input signal, the feedback is
called negative feedback.
As an example of negative feedback, the diagram might represent a cruise control
system in a car, for example, that matches a target speed such as the
speed limit. The controlled system is the car; its input includes the
combined torque from the engine and from the changing slope of the road
(the disturbance). The car's speed (status) is measured by a speedometer.
The error signal is the departure of the speed as measured by the
speedometer from the target speed (set point). This measured error is
interpreted by the controller to adjust the accelerator, commanding the
fuel flow to the engine (the effector). The resulting change in engine
torque, the feedback, combines with the torque exerted by the changing
road grade to reduce the error in speed, minimizing the road
disturbance.
The terms "positive" and "negative" were first applied to
feedback prior to WWII. The idea of positive feedback was already
current in the 1920s with the introduction of the regenerative circuit. Friis and Jensen (1924) described regeneration in a set of electronic amplifiers as a case where the "feed-back" action is positive in contrast to negative feed-back action, which they mention only in passing. Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black:
Positive feed-back increases the gain of the amplifier, negative feed-back reduces it.
According to Mindell (2002) confusion in the terms arose shortly after this:
...Friis and Jensen had made the
same distinction Black used between "positive feed-back" and "negative
feed-back", based not on the sign of the feedback itself but rather on
its effect on the amplifier's gain. In contrast, Nyquist and Bode, when
they built on Black's work, referred to negative feedback as that with
the sign reversed. Black had trouble convincing others of the utility of
his invention in part because confusion existed over basic matters of
definition.
Even prior to the terms being applied, James Clerk Maxwell had described several kinds of "component motions" associated with the centrifugal governors used in steam engines, distinguishing between those that lead to a continual increase in a disturbance or the amplitude of an oscillation, and those that lead to a decrease of the same.
Terminology
The terms positive and negative feedback are defined in different ways within different disciplines.
the altering of the gap between reference and actual values of a parameter, based on whether the gap is widening (positive) or narrowing (negative).
the valence of the action or effect that alters the gap, based on whether it has a happy (positive) or unhappy (negative) emotional connotation to the recipient or observer.
The two definitions may cause confusion, such as when an incentive
(reward) is used to boost poor performance (narrow a gap). Referring to
definition 1, some authors use alternative terms, replacing positive/negative with self-reinforcing/self-correcting, reinforcing/balancing, discrepancy-enhancing/discrepancy-reducing or regenerative/degenerative respectively. And for definition 2, some authors advocate describing the action or effect as positive/negative reinforcement or punishment rather than feedback.
Yet even within a single discipline an example of feedback can be called
either positive or negative, depending on how values are measured or
referenced.
This confusion may arise because feedback can be used for either informational or motivational purposes, and often has both a qualitative and a quantitative component. As Connellan and Zemke (1993) put it:
Quantitative feedback tells us how much and how many. Qualitative feedback tells us how good, bad or indifferent.
Limitations of negative and positive feedback
While
simple systems can sometimes be described as one or the other type,
many systems with feedback loops cannot be so easily designated as
simply positive or negative, and this is especially true when multiple
loops are present.
When there are only two parts
joined so that each affects the other, the properties of the feedback
give important and useful information about the properties of the whole.
But when the parts rise to even as few as four, if every one affects
the other three, then twenty circuits can be traced through them; and
knowing the properties of all the twenty circuits does not give complete
information about the system.
Other types of feedback
In
general, feedback systems can have many signals fed back and the
feedback loop frequently contain mixtures of positive and negative
feedback where positive and negative feedback can dominate at different
frequencies or different points in the state space of a system.
The term bipolar feedback has been coined to refer to biological
systems where positive and negative feedback systems can interact, the
output of one affecting the input of another, and vice versa.
Some systems with feedback can have very complex behaviors such as chaotic behaviors
in non-linear systems, while others have much more predictable
behaviors, such as those that are used to make and design digital
systems.
Feedback is used extensively in digital systems. For example,
binary counters and similar devices employ feedback where the current
state and inputs are used to calculate a new state which is then fed
back and clocked back into the device to update it.
Applications
Mathematics and dynamical systems
Feedback can give rise to incredibly complex behaviors. The Mandelbrot set
(black) within a continuously colored environment is plotted by
repeatedly feeding back values through a simple equation and recording
the points on the imaginary plane that fail to diverge
By using feedback properties, the behavior of a system can be altered
to meet the needs of an application; systems can be made stable,
responsive or held constant. It is shown that dynamical systems with a
feedback experience an adaptation to the edge of chaos.
In biological systems such as organisms, ecosystems, or the biosphere,
most parameters must stay under control within a narrow range around a
certain optimal level under certain environmental conditions. The
deviation of the optimal value of the controlled parameter can result
from the changes in internal and external environments. A change of some
of the environmental conditions may also require change of that range
to change for the system to function. The value of the parameter to
maintain is recorded by a reception system and conveyed to a regulation
module via an information channel. An example of this is insulin oscillations.
Biological systems contain many types of regulatory circuits, both positive and negative. As in other contexts, positive and negative do not imply that the feedback causes good or bad
effects. A negative feedback loop is one that tends to slow down a
process, whereas the positive feedback loop tends to accelerate it. The mirror neurons are part of a social feedback system, when an observed action is "mirrored" by the brain—like a self-performed action.
Normal tissue integrity is preserved by feedback interactions
between diverse cell types mediated by adhesion molecules and secreted
molecules that act as mediators; failure of key feedback mechanisms in
cancer disrupts tissue function.
In an injured or infected tissue, inflammatory mediators elicit feedback
responses in cells, which alter gene expression, and change the groups
of molecules expressed and secreted, including molecules that induce
diverse cells to cooperate and restore tissue structure and function.
This type of feedback is important because it enables coordination of
immune responses and recovery from infections and injuries. During
cancer, key elements of this feedback fail. This disrupts tissue
function and immunity.
Mechanisms of feedback were first elucidated in bacteria, where a nutrient elicits changes in some of their metabolic functions.
Feedback is also central to the operations of genes and gene regulatory networks. Repressor (see Lac repressor) and activatorproteins are used to create genetic operons, which were identified by François Jacob and Jacques Monod in 1961 as feedback loops.
These feedback loops may be positive (as in the case of the coupling
between a sugar molecule and the proteins that import sugar into a
bacterial cell), or negative (as is often the case in metabolic consumption).
On a larger scale, feedback can have a stabilizing effect on
animal populations even when profoundly affected by external changes,
although time lags in feedback response can give rise to predator-prey cycles.
In zymology,
feedback serves as regulation of activity of an enzyme by its direct
product(s) or downstream metabolite(s) in the metabolic pathway (see Allosteric regulation).
In psychology, the body receives a stimulus from the environment or internally that causes the release of hormones.
Release of hormones then may cause more of those hormones to be
released, causing a positive feedback loop. This cycle is also found in
certain behaviour. For example, "shame loops" occur in people who blush
easily. When they realize that they are blushing, they become even more
embarrassed, which leads to further blushing, and so on.
The climate system is characterized by strong positive and negative
feedback loops between processes that affect the state of the
atmosphere, ocean, and land. A simple example is the ice–albedo positive feedback loop whereby melting snow exposes more dark ground (of lower albedo), which in turn absorbs heat and causes more snow to melt.
Feedback is extensively used in control theory, using a variety of methods including state space (controls), full state feedback, and so forth. In the context of control theory, "feedback" is traditionally assumed to specify "negative feedback".
The most common general-purpose controller using a control-loop feedback mechanism is a proportional-integral-derivative
(PID) controller. Heuristically, the terms of a PID controller can be
interpreted as corresponding to time: the proportional term depends on
the present error, the integral term on the accumulation of past errors, and the derivative term is a prediction of future error, based on current rate of change.
In ancient times, the float valve was used to regulate the flow of water in Greek and Roman water clocks; similar float valves are used to regulate fuel in a carburettor and also used to regulate tank water level in the flush toilet.
The Dutch inventor Cornelius Drebbel
(1572-1633) built thermostats (c1620) to control the temperature of
chicken incubators and chemical furnaces. In 1745, the windmill was
improved by blacksmith Edmund Lee, who added a fantail to keep the face of the windmill pointing into the wind. In 1787, Tom Mead regulated the rotation speed of a windmill by using a centrifugal pendulum to adjust the distance between the bedstone and the runner stone (i.e., to adjust the load).
Internal combustion engines of the late 20th century employed mechanical feedback mechanisms such as the vacuum timing advance but mechanical feedback was replaced by electronic engine management systems once small, robust and powerful single-chip microcontrollers became affordable.
Electronic engineering
The simplest form of a feedback amplifier can be represented by the ideal block diagram made up of unilateral elements.
The use of feedback is widespread in the design of electronic components such as amplifiers, oscillators, and stateful logic circuit elements such as flip-flops and counters. Electronic feedback systems are also very commonly used to control mechanical, thermal and other physical processes.
If the signal is inverted on its way round the control loop, the system is said to have negative feedback; otherwise, the feedback is said to be positive. Negative feedback is often deliberately introduced to increase the stability
and accuracy of a system by correcting or reducing the influence of
unwanted changes. This scheme can fail if the input changes faster than
the system can respond to it. When this happens, the lag in arrival of
the correcting signal can result in over-correction, causing the output
to oscillate or "hunt". While often an unwanted consequence of system behaviour, this effect is used deliberately in electronic oscillators.
Electronic feedback loops are used to control the output of electronic devices, such as amplifiers. A feedback loop is created when all or some portion of the output is fed back to the input. A device is said to be operating open loop if no output feedback is being employed and closed loop if feedback is being used.
When two or more amplifiers are cross-coupled using positive feedback, complex behaviors can be created. These multivibrators are widely used and include:
astable circuits, which act as oscillators
monostable circuits, which can be pushed into a state, and will return to the stable state after some time
bistable circuits, which have two stable states that the circuit can be switched between
Negative feedback
A
Negative feedback occurs when the fed-back output signal has a relative
phase of 180° with respect to the input signal (upside down). This
situation is sometimes referred to as being out of phase, but
that term also is used to indicate other phase separations, as in "90°
out of phase". Negative feedback can be used to correct output errors or
to desensitize a system to unwanted fluctuations. In feedback amplifiers, this correction is generally for waveform distortion reduction or to establish a specified gain level. A general expression for the gain of a negative feedback amplifier is the asymptotic gain model.
Positive feedback
Positive
feedback occurs when the fed-back signal is in phase with the input
signal. Under certain gain conditions, positive feedback reinforces the
input signal to the point where the output of the device oscillates between its maximum and minimum possible states. Positive feedback may also introduce hysteresis
into a circuit. This can cause the circuit to ignore small signals and
respond only to large ones. It is sometimes used to eliminate noise from
a digital signal. Under some circumstances, positive feedback may cause
a device to latch, i.e., to reach a condition in which the output is
locked to its maximum or minimum state. This fact is very widely used in
digital electronics to make bistable circuits for volatile storage of information.
The loud squeals that sometimes occurs in audio systems, PA systems, and rock music are known as audio feedback.
If a microphone is in front of a loudspeaker that it is connected to,
sound that the microphone picks up comes out of the speaker, and is
picked up by the microphone and re-amplified. If the loop gain is sufficient, howling or squealing at the maximum power of the amplifier is possible.
Oscillators are often characterized by the frequency of their output signal:
A low-frequency oscillator (LFO) is an electronic oscillator that generates a frequency below ≈20 Hz. This term is typically used in the field of audio synthesizers, to distinguish it from an audio frequency oscillator.
An audio oscillator produces frequencies in the audio range, about 16 Hz to 20 kHz.
An RF oscillator produces signals in the radio frequency (RF) range of about 100 kHz to 100 GHz.
Oscillators designed to produce a high-power AC output from a DC supply are usually called inverters.
There are two main types of electronic oscillator: the linear or harmonic oscillator and the nonlinear or relaxation oscillator.
A latch or a flip-flop is a circuit
that has two stable states and can be used to store state information.
They typically constructed using feedback that crosses over between two
arms of the circuit, to provide the circuit with a state. The circuit
can be made to change state by signals applied to one or more control
inputs and will have one or two outputs. It is the basic storage element
in sequential logic. Latches and flip-flops are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems.
Latches and flip-flops are used as data storage elements. Such data storage can be used for storage of state, and such a circuit is described as sequential logic. When used in a finite-state machine,
the output and next state depend not only on its current input, but
also on its current state (and hence, previous inputs). It can also be
used for counting of pulses, and for synchronizing variably-timed input
signals to some reference timing signal.
Flip-flops can be either simple (transparent or opaque) or clocked
(synchronous or edge-triggered). Although the term flip-flop has
historically referred generically to both simple and clocked circuits,
in modern usage it is common to reserve the term flip-flop exclusively for discussing clocked circuits; the simple ones are commonly called latches.
Using this terminology, a latch is level-sensitive, whereas a
flip-flop is edge-sensitive. That is, when a latch is enabled it becomes
transparent, while a flip flop's output only changes on a single type
(positive going or negative going) of clock edge.
Software
Feedback
loops provide generic mechanisms for controlling the running,
maintenance, and evolution of software and computing systems.
Feedback-loops are important models in the engineering of adaptive
software, as they define the behaviour of the interactions among the
control elements over the adaptation process, to guarantee system
properties at run-time. Feedback loops and foundations of control theory
have been successfully applied to computing systems. In particular, they have been applied to the development of products such as IBM's Universal Database server and IBM Tivoli. From a software perspective, the autonomic
(MAPE, monitor analyze plan execute) loop proposed by researchers of
IBM is another valuable contribution to the application of feedback
loops to the control of dynamic properties and the design and evolution
of autonomic software systems.
The stock market is an example of a system prone to oscillatory "hunting", governed by positive and negative feedback resulting from cognitive and emotional factors among market participants. For example:
When stocks are rising (a bull market),
the belief that further rises are probable gives investors an incentive
to buy (positive feedback—reinforcing the rise, see also stock market bubble and momentum investing); but the increased price of the shares, and the knowledge that there must be a peak after which the market falls, ends up deterring buyers (negative feedback—stabilizing the rise).
Once the market begins to fall regularly (a bear market),
some investors may expect further losing days and refrain from buying
(positive feedback—reinforcing the fall), but others may buy because
stocks become more and more of a bargain (negative feedback—stabilizing
the fall, see also contrarian investing).
George Soros used the word reflexivity, to describe feedback in the financial markets and developed an investment theory based on this principle.
The conventional economic equilibrium model of supply and demand supports only ideal linear negative feedback and was heavily criticized by Paul Ormerod in his book The Death of Economics,
which, in turn, was criticized by traditional economists. This book was
part of a change of perspective as economists started to recognise that
chaos theory applied to nonlinear feedback systems including financial markets.
