Infinite regress is a philosophical concept to describe a series of entities. Each entity in the series depends on its predecessor, following a recursive principle. For example, the epistemic regress is a series of beliefs in which the justification of each belief depends on the justification of the belief that comes before it.
An infinite regress argument is an
argument against a theory based on the fact that this theory leads to an
infinite regress. For such an argument to be successful, it must
demonstrate not just that the theory in question entails an infinite
regress but also that this regress is vicious. There are different ways in which a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of metaphysical impossibility.
Other forms occur when the infinite regress is responsible for the
theory in question being implausible or for its failure to solve the
problem it was formulated to solve.
Traditionally, it was often assumed without much argument
that each infinite regress is vicious but this assumption has been put
into question in contemporary philosophy.
While some philosophers have explicitly defended theories with infinite
regresses, the more common strategy has been to reformulate the theory
in question in a way that avoids the regress. One such strategy is foundationalism,
which posits that there is a first element in the series from which all
the other elements arise but which is not itself explained this way.
Another way is coherentism,
which is based on a holistic explanation that usually sees the entities
in question not as a linear series but as an interconnected network.
"why game" redirects here; not to be confused with Why (board game).
An infinite regress is an infinite series
of entities governed by a recursive principle that determines how each
entity in the series depends on or is produced by its predecessor. This principle can often be expressed in the following form: X is F because X stands in R to Y and Y is F. X and Y stand for objects, R stands for a relation and F stands for a property in the widest sense. In the epistemic regress, for example, a belief is justified because it
is based on another belief that is justified. But this other belief is
itself in need of one more justified belief for itself to be justified
and so on. Or in the cosmological argument, an event occurred because it was
caused by another event that occurred before it, which was itself caused
by a previous event, and so on. This principle by itself is not sufficient: it does not lead to a regress if there is no X that is F. This is why an additional triggering condition has to be fulfilled: there has to be an X that is F for the regress to get started. So the regress starts with the fact that X is F. According to the recursive principle, this is only possible if there is a distinct Y that is also F. But in order to account for the fact that Y is F, we need to posit a Z that is F
and so on. Once the regress has started, there is no way of stopping it
since a new entity has to be introduced at each step in order to make
the previous step possible.
An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just
that the theory in question entails an infinite regress but also that
this regress is vicious. The mere existence of an infinite regress by itself is not a proof for anything. So in addition to connecting the theory to a recursive principle paired
with a triggering condition, the argument has to show in which way the
resulting regress is vicious.For example, one form of evidentialism
in epistemology holds that a belief is only justified if it is based on
another belief that is justified. An opponent of this theory could use
an infinite regress argument by demonstrating (1) that this theory leads
to an infinite regress (e.g. by pointing out the recursive principle
and the triggering condition) and (2) that this infinite regress is
vicious (e.g. by showing that it is implausible given the limitations of
the human mind). In this example, the argument has a negative form since it only denies
that another theory is true. But it can also be used in a positive form
to support a theory by showing that its alternative involves a vicious
regress. This is how the cosmological argument
for the existence of God works: it claims that positing God's existence
is necessary in order to avoid an infinite regress of causes.
Viciousness
For an infinite regress argument to be successful, it has to show that the involved regress is vicious. A non-vicious regress is called virtuous or benign. Traditionally, it was often assumed without much argument that each
infinite regress is vicious but this assumption has been put into
question in contemporary philosophy. In most cases, it is not
self-evident whether an infinite regress is vicious or not. The truth regress
constitutes an example of an infinite regress that is not vicious: if
the proposition "P" is true, then the proposition that "It is true that
P" is also true and so on. Infinite regresses pose a problem mostly if the regress concerns concrete objects. Abstract objects,
on the other hand, are often considered to be unproblematic in this
respect. For example, the truth-regress leads to an infinite number of
true propositions or the Peano axioms entail the existence of infinitely many natural numbers. But these regresses are usually not held against the theories that entail them.
There are different ways in which a regress can be vicious. The most serious type of viciousness involves a contradiction in the form of metaphysical impossibility. Other types occur when the infinite regress is responsible for the
theory in question being implausible or for its failure to solve the
problem it was formulated to solve. The vice of an infinite regress can be local if it causes problems only
for certain theories when combined with other assumptions, or global
otherwise. For example, an otherwise virtuous regress is locally vicious
for a theory that posits a finite domain. In some cases, an infinite regress is not itself the source of the problem but merely indicates a different underlying problem.
Impossibility
Infinite regresses that involve metaphysical impossibility are the most serious cases of viciousness. The easiest way to arrive at this result is by accepting the assumption that actual infinities are impossible, thereby directly leading to a contradiction. This anti-infinitists position is opposed to infinity in general, not just specifically to infinite regresses. But it is open to defenders of the theory in question to deny this outright prohibition on actual infinities. For example, it has been argued that only certain types of infinities
are problematic in this way, like infinite intensive magnitudes (e.g.
infinite energy densities). But other types of infinities, like infinite cardinality (e.g.
infinitely many causes) or infinite extensive magnitude (e.g. the
duration of the universe's history) are unproblematic from the point of
view of metaphysical impossibility. While there may be some instances of viciousness due to metaphysical
impossibility, most vicious regresses are problematic because of other
reasons.
Implausibility
A more common form of viciousness arises from the
implausibility of the infinite regress in question. This category often
applies to theories about human actions, states or capacities. This argument is weaker than the argument from impossibility since it
allows that the regress in question is possible. It only denies that it
is actual. For example, it seems implausible due to the limitations of the human
mind that there are justified beliefs if this entails that the agent
needs to have an infinite amount of them. But this is not metaphysically
impossible, e.g. if it is assumed that the infinite number of beliefs
are only non-occurrent or dispositional while the limitation only applies to the number of beliefs one is actually thinking about at one moment. Another reason for the implausibility of theories involving an infinite regress is due to the principle known as Ockham's razor, which posits that we should avoid ontological extravagance by not multiplying entities without necessity. Considerations of parsimony are complicated by the distinction between
quantitative and qualitative parsimony: concerning how many entities are
posited in contrast to how many kinds of entities are posited. For example, the cosmological argument for the existence of God promises to increase quantitative
parsimony by positing that there is one first cause instead of allowing
an infinite chain of events. But it does so by decreasing qualitative parsimony: it posits God as a new type of entity.
Failure to explain
Another form of viciousness applies not to the infinite
regress by itself but to it in relation to the explanatory goals of a
theory. Theories are often formulated with the goal of solving a specific
problem, e.g. of answering the question why a certain type of entity
exists. One way how such an attempt can fail is if the answer to the
question already assumes in disguised form what it was supposed to
explain. This is akin to the informal fallacy of begging the question. From the perspective of a mythological world view, for example, one way
to explain why the earth seems to be at rest instead of falling down is
to hold that it rests on the back of a giant turtle. In order to
explain why the turtle itself is not in free fall, another even bigger
turtle is posited and so on, resulting in a world that is turtles all the way down.
Despite its shortcomings in clashing with modern physics and due to its
ontological extravagance, this theory seems to be metaphysically
possible assuming that space is infinite. One way to assess the
viciousness of this regress is to distinguish between local and global explanations. A local
explanation is only interested in explaining why one thing has a
certain property through reference to another thing without trying to
explain this other thing as well. A global
explanation, on the other hand, tries to explain why there are any
things with this property at all. So as a local explanation, the regress
in the turtle theory is benign: it succeeds in explaining why the earth
is not falling. But as a global explanation, it fails because it has to
assume rather than explain at each step that there is another thing
that is not falling. It does not explain why nothing at all is falling.
It has been argued that infinite regresses can be benign
under certain circumstances despite aiming at global explanation. This
line of thought rests on the idea of the transmission involved in the vicious cases: it is explained that X is F because Y is F where this F was somehow transmitted from Y to X. The problem is that to transfer something, it first must be possessed,
so the possession is presumed rather than explained. For example, in
trying to explain why one's neighbor has the property of being the owner
of a bag of sugar, it is revealed that this bag was first in someone
else's possession before it was transferred to the neighbor and that the
same is true for this and every other previous owner. This explanation is unsatisfying since ownership is presupposed at every step. In non-transmissive explanations, however, Y is still the reason for X being F and Y is also F but this is just seen as a contingent fact. This line of thought has been used to argue that the epistemic regress is not vicious. From a Bayesian
point of view, for example, justification or evidence can be defined in
terms of one belief raising the probability that another belief is
true.The former belief may also be justified but this is not relevant for explaining why the latter belief is justified.
Responses
Philosophers have responded to infinite regress arguments
in various ways. The criticized theory can be defended, for example, by
denying that an infinite regress is involved. Infinitists, on the other hand, embrace the regress but deny that it is vicious. Another response is to modify the theory in order to avoid the regress. This can be achieved in the form of foundationalism or of coherentism.
Foundationalism
Traditionally, the most common response is foundationalism. It posits that there is a first element in the series from which all
the other elements arise but which is not itself explained this way. So from any given position, the series can be traced back to elements
on the most fundamental level, which the recursive principle fails to
explain. This way an infinite regress is avoided. This position is well-known from its applications in the field of epistemology. Foundationalist theories of epistemic justification state that besides
inferentially justified beliefs, which depend for their justification on
other beliefs, there are also non-inferentially justified beliefs. The non-inferentially justified beliefs constitute the foundation on
which the superstructure consisting of all the inferentially justified
beliefs rests. Acquaintance theories, for example, explain the justification of
non-inferential beliefs through acquaintance with the objects of the
belief. On such a view, an agent is inferentially justified to believe
that it will rain tomorrow based on the belief that the weather forecast
told so. They are non-inferentially justified in believing that they
are in pain because they are directly acquainted with the pain. So a different type of explanation (acquaintance) is used for the foundational elements.
Another example comes from the field of metaphysics concerning the problem of ontological hierarchy.
One position in this debate claims that some entities exist on a more
fundamental level than other entities and that the latter entities
depend on or are grounded in the former entities. Metaphysical foundationalism
is the thesis that these dependence relations do not form an infinite
regress: that there is a most fundamental level that grounds the
existence of the entities from all other levels. This is sometimes expressed by stating that the grounding-relation responsible for this hierarchy is well-founded.
Coherentism
Coherentism, mostly found in the field of epistemology, is another way to avoid infinite regresses. It is based on a holistic explanation that usually sees the entities in
question not as a linear series but as an interconnected network. For
example, coherentist theories of epistemic justification hold that
beliefs are justified because of the way they hang together: they cohere
well with each other. This view can be expressed by stating that justification is primarily a
property of the system of beliefs as a whole. The justification of a
single belief is derivative in the sense that it depends on the fact
that this belief belongs to a coherent whole. Laurence BonJour is a well-known contemporary defender of this position.
Examples
Aristotle
Aristotle argued that knowing does not necessitate an infinite regress because some knowledge does not depend on demonstration:
Some hold that
owing to the necessity of knowing the primary premises, there is no
scientific knowledge. Others think there is, but that all truths are
demonstrable. Neither doctrine is either true or a necessary deduction
from the premises. The first school, assuming that there is no way of
knowing other than by demonstration, maintain that an infinite regress
is involved, on the ground that if behind the prior stands no primary,
we could not know the posterior through the prior (wherein they are
right, for one cannot traverse an infinite series): if on the other hand
– they say – the series terminates and there are primary premises, yet
these are unknowable because incapable of demonstration, which according
to them is the only form of knowledge. And since thus one cannot know
the primary premises, knowledge of the conclusions which follow from
them is not pure scientific knowledge nor properly knowing at all, but
rests on the mere supposition that the premises are true. The other
party agrees with them as regards knowing, holding that it is only
possible by demonstration, but they see no difficulty in holding that
all truths are demonstrated, on the ground that demonstration may be
circular and reciprocal.
Our own doctrine is that not all knowledge is demonstrative: on the
contrary, knowledge of the immediate premises is independent of
demonstration. (The necessity of this is obvious; for since we must know
the prior premises from which the demonstration is drawn, and since the
regress must end in immediate truths, those truths must be
indemonstrable.) Such, then, is our doctrine, and in addition, we
maintain that besides scientific knowledge there is its original source
which enables us to recognize the definitions.
Gilbert Ryle argues in the philosophy of mind that mind-body dualism
is implausible because it produces an infinite regress of "inner
observers" when trying to explain how mental states are able to
influence physical states.
A strange loop is a cyclic structure that goes through several levels in a hierarchical system. It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started.
Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.
A tangled hierarchy is a hierarchical system in which a strange loop appears.
Definitions
A strange loop is a hierarchy of levels, each of which is
linked to at least one other by some type of relationship. A strange
loop hierarchy is "tangled" (Hofstadter refers to this as a "heterarchy"),
in that there is no well defined highest or lowest level; moving
through the levels, one eventually returns to the starting point, i.e.,
the original level. Examples of strange loops that Hofstadter offers
include: many of the works of M. C. Escher, the Canon 5. a 2 from J.S. Bach's Musical Offering, the information flow network between DNA and enzymes through protein synthesis and DNA replication, and self-referentialGödelian statements in formal systems.
And yet when I say "strange loop", I
have something else in mind — a less concrete, more elusive notion. What
I mean by "strange loop" is — here goes a first stab, anyway — not a
physical circuit but an abstract loop in which, in the series of stages
that constitute the cycling-around, there is a shift from one level of
abstraction (or structure) to another, which feels like an upwards
movement in an hierarchy, and yet somehow the successive "upward" shifts
turn out to give rise to a closed cycle. That is, despite one's sense
of departing ever further from one's origin, one winds up, to one's
shock, exactly where one had started out. In short, a strange loop is a
paradoxical level-crossing feedback loop. (pp.101–102)
In cognitive science
According to Hofstadter, strange loops take form in human
consciousness as the complexity of active symbols in the brain
inevitably leads to the same kind of self-reference which Gödel proved was inherent in any sufficiently complex logical or arithmetical system (that allows for arithmetic by means of the Peano axioms) in his incompleteness theorem. Gödel showed that mathematics and logic contain strange loops: propositions that not only refer to mathematical and logical truths, but also to the symbol systems expressing those truths. This leads to the sort of paradoxes seen in statements such as "This statement is false," wherein the sentence's basis of truth is found in referring to itself and its assertion, causing a logical paradox.
Hofstadter argues that the psychological self arises out of a similar kind of paradox. The brain is not born with an "I" – the ego
emerges only gradually as experience shapes the brain's dense web of
active symbols into a tapestry rich and complex enough to begin twisting back upon itself.
According to this view, the psychological "I" is a narrative fiction,
something created only from intake of symbolic data and the brain's
ability to create stories about itself from that data. The consequence
is that a self-perspective is a culmination of a unique pattern of
symbolic activity in the brain, which suggests that the pattern of
symbolic activity that makes identity, that constitutes subjectivity,
can be replicated within the brains of others, and likely even in artificial brains.
Strangeness
The "strangeness" of a strange loop comes from the brain's
perception, because the brain categorizes its input in a small number of
"symbols" (by which Hofstadter means groups of neurons standing for
something in the outside world). So the difference between the
video-feedback loop and the brain's strange loops, is that while the
former converts light to the same pattern on a screen, the latter
categorizes a pattern and outputs its "essence", so that as the brain
gets closer and closer to its "essence", it goes further down its
strange loop.
Downward causality
Hofstadter thinks that minds appear to determine the world by way of "downward causality", which refers to effects being viewed in terms of their underlying causes. Hofstadter says this happens in the proof of Gödel's incompleteness theorem:
Merely from knowing the formula's
meaning, one can infer its truth or falsity without any effort to derive
it in the old-fashioned way, which requires one to trudge methodically
"upwards" from the axioms. This is not just peculiar; it is astonishing.
Normally, one cannot merely look at what a mathematical conjecture says and simply appeal to the content of that statement on its own to deduce whether the statement is true or false. (pp. 169–170)
Hofstadter claims a similar "flipping around of causality" appears to happen in minds possessing self-consciousness; the mind perceives itself as the cause of certain feelings.
The parallels between downward causality in formal systems and downward causality in brains are explored by Theodor Nenu in 2022, together with other aspects of Hofstadter's metaphysics of mind. Nenu
also questions the correctness of the above quote by focusing on the
sentence which "says about itself" that it is provable (also known as a
Henkin-sentence, named after logician Leon Henkin). It turns out that under suitable meta-mathematical choices (where the Hilbert-Bernays provability conditions
do not obtain), one can construct formally undecidable (or even
formally refutable) Henkin-sentences for the arithmetical system under
investigation. This system might very well be Hofstadter's Typographical Number Theory used in Gödel, Escher, Bach or the more familiar Peano Arithmetic
or some other sufficiently rich formal arithmetic. Thus, there are
examples of sentences "which say about themselves that they are
provable", but they don't exhibit the sort of downward causal powers
described in the displayed quote.
The "chicken or the egg" paradox is perhaps the best-known strange loop problem.
The "ouroboros",
which depicts a dragon eating its own tail, is perhaps one of the most
ancient and universal symbolic representations of the reflexive loop
concept.
A Shepard tone is another illustrative example of a strange loop. Named after Roger Shepard, it is a sound consisting of a superposition of tones separated by octaves. When played with the base pitch of the tone moving upwards or downwards, it is referred to as the Shepard scale. This creates the auditory illusion
of a tone that continually ascends or descends in pitch, yet which
ultimately seems to get no higher or lower. In a similar way a sound
with seemingly ever increasing tempo can be constructed, as was
demonstrated by Jean-Claude Risset.
A quine
in software programming is a program that produces a new version of
itself without any input from the outside. A similar concept is metamorphic code.
Efron's dice are four dice that are intransitive under gambler's preference. I.e., the dice are ordered A > B > C > D > A, where x > y means "a gambler prefers x to y".
Individual preferences are always transitive, excluding preferences when given explicit rules such as in Efron's dice or rock-paper-scissors; however, aggregate preferences of a group may be intransitive. This can result in a Condorcet paradox
wherein following a path from one candidate across a series of majority
preferences may return to the original candidate, leaving no clear
preference by the group. In this case, some candidate beats an
opponent, who in turn beats another opponent, and so forth, until a
candidate is reached who beats the original candidate.
The mathematical phenomenon of polysemy
has been observed to be a strange loop. At the denotational level, the
term refers to situations where a single entity can be seen to mean more than one mathematical object. See Tanenbaum (1999).
The Stonecutter is an old Japanese fairy tale with a story that explains social and natural hierarchies as a strange loop.
Causal loop diagram
that depicts the causes of a stampede as a positive feedback loop.
Alarm or panic can sometimes be spread by positive feedback among a herd
of animals to cause a stampede.
Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop
where the outcome of a process reinforces the inciting process to build
momentum. As such, these forces can exacerbate the effects of a small
disturbance. That is, the effects of a perturbation on a system include
an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback. Both concepts play an important role in science and engineering, including biology, chemistry, and cybernetics.
Mathematically, positive feedback is defined as a positive loop gain around a closed loop of cause and effect. That is, positive feedback is in phase with the input, in the sense that it adds to make the input larger. Positive feedback tends to cause system instability. When the loop gain is positive and above 1, there will typically be exponential growth, increasing oscillations, chaotic behavior or other divergences from equilibrium. System parameters will typically accelerate towards extreme values,
which may damage or destroy the system, or may end with the system latched into a new stable state. Positive feedback may be controlled by signals in the system being filtered, damped, or limited, or it can be cancelled or reduced by adding negative feedback.
Positive feedback is used in digital electronics to force voltages away from intermediate voltages into '0' and '1' states. On the other hand, thermal runaway is a type of positive feedback that can destroy semiconductor junctions. Positive feedback in chemical reactions can increase the rate of reactions, and in some cases can lead to explosions. Positive feedback in mechanical design causes tipping-point, or over-centre, mechanisms to snap into position, for example, in switches and locking pliers. Out of control, it can cause bridges to collapse. Positive feedback in economic systems can cause boom-then-bust cycles. A familiar example of positive feedback is the loud squealing or howling sound produced by audio feedback in public address systems: the microphone picks up sound from its own loudspeakers, amplifies it, and sends it through the speakers again.
Overview
Positive feedback enhances or amplifies an effect by it
having an influence on the process that gave rise to it. For example,
when part of an electronic output signal returns to the input, and is in
phase with it, the system gain is increased. The feedback from the outcome to the originating process can be direct, or it can be via other state variables. Such systems can give rich qualitative behaviors, but whether the
feedback is instantaneously positive or negative in sign has an
extremely important influence on the results. Positive feedback reinforces and negative feedback moderates the original process. Positive and negative in this sense refer to loop gains greater than or less than zero, and do not imply any value judgements as to the desirability of the outcomes or effects. A key feature of positive feedback is thus that small disturbances get
bigger. When a change occurs in a system, positive feedback causes
further change in the same direction.
Basic
A
basic feedback system can be represented by this block diagram. In the
diagram the + symbol is an adder and A and B are arbitrary causal functions.
A simple feedback loop is shown in the diagram. If the loop gain AB is positive, then a condition of positive or regenerative feedback exists.
If the functions A and B are linear and AB is smaller than
unity, then the overall system gain from the input to output is finite
but can be very large as AB approaches unity. In that case, it can be shown that the overall or loop gain from input to output is:
When AB> 1, the system is unstable, so does not have a well-defined gain; the gain may be called infinite.
Thus, depending on the feedback, state changes can be convergent or divergent. The result of positive feedback is to augment changes, so that small perturbations may result in big changes.
A system in equilibrium in which there is positive feedback
to any change from its current state may be unstable, in which case the
system is said to be in an unstable equilibrium. The magnitude of the forces that act to move such a system away from its equilibrium is an increasing function of the distance of the state from the equilibrium.
Positive feedback does not necessarily imply instability of an equilibrium; for example, stable on and off states may exist in positive-feedback architectures.
Hysteresis causes the output value to depend on the history of the input.In a Schmitt trigger
circuit, feedback to the non-inverting input of an amplifier pushes the
output directly away from the applied voltage towards the maximum or
minimum voltage the amplifier can generate.
In the real world, positive feedback loops typically do not
cause ever-increasing growth but are modified by limiting effects of
some sort. According to Donella Meadows:
"Positive
feedback loops are sources of growth, explosion, erosion, and collapse
in systems. A system with an unchecked positive loop ultimately will
destroy itself. That's why there are so few of them. Usually, a negative
loop will kick in sooner or later."
Hysteresis, in which the starting point affects where the
system ends up, can be generated by positive feedback. When the gain of
the feedback loop is above 1, then the output moves away from the input:
if it is above the input, then it moves towards the nearest positive
limit, while if it is below the input then it moves towards the nearest
negative limit.
Once it reaches the limit, it will be stable. However, if the input goes past the limit, then the feedback will change signand the output will move in the opposite direction until it hits the opposite limit. The system therefore shows bistable behaviour.
Terminology
The terms positive and negative were first applied to feedback before World War II. The idea of positive feedback was already current in the 1920s with the introduction of the regenerative circuit.
Friis & 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 feedback 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."
These confusions, along with the everyday associations of positive with good and negative with bad, have led many systems theorists to propose alternative terms. For example, Donella Meadows prefers the terms reinforcing and balancing feedbacks.
Examples and applications
In electronics
A
vintage style regenerative radio receiver. Due to the controlled use of
positive feedback, sufficient amplification can be derived from a
single vacuum tube or valve (centre).
Regenerative circuits were invented and patented in 1914 for the amplification and reception of very weak radio signals. Carefully controlled positive feedback around a single transistor amplifier can multiply its gain by 1,000 or more. Therefore, a signal can be amplified 20,000 or even 100,000 times in
one stage, which would normally have a gain of only 20 to 50. The
problem with regenerative amplifiers working at these very high gains is
that they easily become unstable and start to oscillate. The radio
operator has to be prepared to tweak the amount of feedback fairly
continuously for good reception. Superregenerative receivers use even more gain. Modern radio receivers use the superheterodyne design, with many more amplification stages, but much more stable operation and no positive feedback.
Many electronic circuits, especially amplifiers, incorporate negative feedback. This reduces their gain, but improves their linearity, input impedance, output impedance, and bandwidth,
and stabilises all of these parameters, including the loop gain. These
parameters also become less dependent on the details of the amplifying
device itself, and more dependent on the feedback components, which are
less likely to vary with manufacturing tolerance, age and temperature.
The difference between positive and negative feedback for AC signals is one of phase:
if the signal is fed back out of phase, the feedback is negative, and
if it is in phase, the feedback is positive. One problem for amplifier
designers who use negative feedback is that some of the components of
the circuit will introduce phase shift
in the feedback path. If there is a frequency (usually a high
frequency) where the phase shift reaches 180°, then the designer must
ensure that the amplifier gain at that frequency is very low (usually by
low-pass filtering).
If the loop gain (the product of the amplifier gain and the extent of
the positive feedback) at any frequency is greater than one, then the
amplifier will oscillate at that frequency (Barkhausen stability criterion). Such oscillations are sometimes called parasitic oscillations.
An amplifier that is stable in one set of conditions can break into
parasitic oscillation in another. This may be due to changes in
temperature, supply voltage, adjustment of front-panel controls, or even
the proximity of a person or other conductive item.
Amplifiers may oscillate gently in ways that are hard to detect without an oscilloscope,
or the oscillations may be so extensive that only a very distorted or
no required signal at all gets through, or that damage occurs.
Low-frequency parasitic oscillations have been called 'motorboating' due
to the similarity to the sound of a low-revving exhaust note.
The effect of using a Schmitt trigger (B) instead of a comparator (A)
Many common digital electronic circuits employ positive feedback. While normal, simple logic gates
usually rely simply on gain to push digital signal voltages away from
intermediate values to the values that are meant to represent Boolean 0 and 1, but many more complex gates use feedback. When an input voltage is expected to vary in an analogue way, but sharp thresholds are required for later digital processing, the Schmitt trigger
circuit uses positive feedback to ensure that if the input voltage
creeps gently above the threshold, the output is forced smartly and
rapidly from one logic state to the other. One of the corollaries of the
Schmitt trigger's use of positive feedback is that, should the input
voltage move gently down again past the same threshold, the positive
feedback will hold the output in the same state with no change. This
effect is called hysteresis:
the input voltage has to drop past a different, lower threshold to
'un-latch' the output and reset it to its original digital value. By
reducing the extent of the positive feedback, the hysteresis width can
be reduced, but it can not entirely be eradicated. The Schmitt trigger
is, to some extent, a latching circuit.
Positive
feedback is a mechanism by which an output, such as protein levels, is
enhanced. However, in order to avoid any fluctuation in the protein
level, the mechanism is inhibited stochastically (I); therefore, when
the concentration of the activated protein (A) is past the threshold
([I]), the loop mechanism is activated and the concentration of A
increases exponentially if d[A]=k [A].Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively.
An electronic flip-flop, or "latch", or "bistable multivibrator",
is a circuit that, due to high positive feedback, is not stable in a
balanced or intermediate state. Such a bistable circuit is the basis of
one bit of electronic memory.
The flip-flop uses a pair of amplifiers, transistors, or logic gates
connected to each other so that positive feedback maintains the state of
the circuit in one of two unbalanced stable states after the input
signal has been removed until a suitable alternative signal is applied
to change the state. Computer random access memory (RAM) can be made in this way, with one latching circuit for each bit of memory.
Thermal runaway
occurs in electronic systems because some aspect of a circuit is
allowed to pass more current when it gets hotter, then the hotter it
gets, the more current it passes, which heats it some more and so it
passes yet more current. The effects are usually catastrophic for the
device in question. If devices have to be used near their maximum
power-handling capacity, and thermal runaway is possible or likely under
certain conditions, improvements can usually be achieved by careful
design.
A phonograph turntable is prone to acoustic feedback.
Audio and video systems can demonstrate positive feedback. If a microphone picks up the amplified sound output of loudspeakers in the same circuit, then howling and screeching sounds of audio feedback (at up to the maximum power capacity of the amplifier) will be heard, as random noise is re-amplified by positive feedback and filtered by the characteristics of the audio system and the room.
Audio and live music
Audio feedback
(also known as acoustic feedback, simply as feedback, or the Larsen
effect) is a special kind of positive feedback which occurs when a sound
loop exists between an audio input (for example, a microphone or guitar pickup) and an audio output (for example, a loudly-amplified loudspeaker). In this example, a signal received by the microphone is amplified
and passed out of the loudspeaker. The sound from the loudspeaker can
then be received by the microphone again, amplified further, and then
passed out through the loudspeaker again. The frequency
of the resulting sound is determined by resonance frequencies in the
microphone, amplifier, and loudspeaker, the acoustics of the room, the
directional pick-up and emission patterns of the microphone and
loudspeaker, and the distance between them. For small PA systems the sound is readily recognized as a loud squeal or screech.
Feedback is almost always considered undesirable when it
occurs with a singer's or public speaker's microphone at an event using a
sound reinforcement system or PA system. Audio engineers
use various electronic devices, such as equalizers and, since the
1990s, automatic feedback detection devices to prevent these unwanted
squeals or screeching sounds, which detract from the audience's
enjoyment of the event. On the other hand, since the 1960s, electric guitar players in rock music bands using loud guitar amplifiers and distortion effects have intentionally created guitar feedback to create a desirable musical effect. "I Feel Fine"
by the Beatles marks one of the earliest examples of the use of
feedback as a recording effect in popular music. It starts with a
single, percussive feedback
note produced by plucking the A string on Lennon's guitar. Artists such
as the Kinks and the Who had already used feedback live, but Lennon
remained proud of the fact that the Beatles were perhaps the first group
to deliberately put it on vinyl. In one of his last interviews, he
said, "I defy anybody to find a record—unless it's some old blues record
in 1922—that uses feedback that way."
The principles of audio feedback were first discovered by Danish scientist Søren Absalon Larsen. Microphones are not the only transducers subject to this effect. Phone cartridges can do the same, usually in the low-frequency range below about 100Hz, manifesting as a low rumble. Jimi Hendrix was an innovator in the intentional use of guitar feedback in his guitar solos to create unique sound effects. He helped develop the controlled and musical use of audio feedback in electric guitar playing, and later Brian May was a famous proponent of the technique.
Similarly, if a video camera is pointed at a monitor
screen that is displaying the camera's own signal, then repeating
patterns can be formed on the screen by positive feedback. This video
feedback effect was used in the opening sequences to the first ten
seasons of the television program Doctor Who.
Switches
In electrical switches, including bimetallic strip
based thermostats, the switch usually has hysteresis in the switching
action. In these cases hysteresis is mechanically achieved via positive
feedback within a tipping point mechanism. The positive feedback action
minimises the length of time arcing occurs for during the switching and
also holds the contacts in an open or closed state.
In biology
In physiology
Positive
feedback is the amplification of a body's response to a stimulus. For
example, in childbirth, when the head of the fetus pushes up against the
cervix (1) it stimulates a nerve impulse from the cervix to the brain
(2). When the brain is notified, it signals the pituitary gland to
release a hormone called oxytocin(3). Oxytocin is then carried via the bloodstream to the uterus (4), causing contractions, pushing the fetus towards the cervix, eventually inducing childbirth.Platelet
clotting demonstrates positive feedback. The damaged blood vessel wall
releases chemicals that initiate the formation of a blood clot through
platelet congregation. As more platelets gather, more chemicals are
released that speed up the process. The process gets faster and faster
until the blood vessel wall is completely sealed and the positive
feedback loop has ended. The exponential form of the graph illustrates
the positive feedback mechanism.
A number of examples of positive feedback systems may be found in physiology.
One example is the onset of contractions in childbirth, known as the Ferguson reflex. When a contraction occurs, the hormone oxytocin causes a nerve stimulus, which stimulates the hypothalamus to produce more oxytocin, which increases uterine contractions. This results in contractions increasing in amplitude and frequency.
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.
Lactation
also involves positive feedback in that as the baby suckles on the
nipple, there is a nerve response into the spinal cord and up into the
hypothalamus of the brain, which then stimulates the pituitary gland to produce more prolactin to produce more milk.
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 (Hodgkin cycle). So a slight initial leakage results in an explosion of sodium leakage, which creates the nerve action potential.
In excitation–contraction coupling
of the heart, an increase in intracellular calcium ions to the cardiac
myocyte is detected by ryanodine receptors in the membrane of the
sarcoplasmic reticulum, which transport calcium out into the cytosol in a
positive feedback physiological response.
In most cases, such feedback loops culminate in
counter-signals being released that suppress or break 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.
In gene regulation
Positive feedback is a well-studied phenomenon in gene regulation, where it is most often associated with bistability.
Positive feedback occurs when a gene activates itself directly or
indirectly via a double negative feedback loop. Genetic engineers have
constructed and tested simple positive feedback networks in bacteria to
demonstrate the concept of bistability. A classic example of positive feedback is the lac operon in E. coli.
Positive feedback plays an integral role in cellular differentiation,
development, and cancer progression, and therefore, positive feedback in
gene regulation can have significant physiological consequences. Random
motions in molecular dynamics
coupled with positive feedback can trigger interesting effects, such as
creating a population of phenotypically different cells from the same
parent cell. This happens because noise can become amplified by positive feedback. Positive feedback can also occur in other forms of cell signaling, such as enzyme kinetics or metabolic pathways.
In evolutionary biology
Positive feedback loops have been used to describe aspects of the dynamics of change in biological evolution. 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. At the human level, Richard D. 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. Crespi (2004) discussed several other examples of positive feedback loops in evolution. The analogy of evolutionary arms races provides further examples of positive feedback in biological systems.
During the Phanerozoic, the biodiversity shows a steady but not monotonic increase from near zero to several thousands of genera.
It has been shown that changes in biodiversity through the Phanerozoic correlate much better with hyperbolic model (widely used in demography and macrosociology) than with exponential and logistic models (traditionally used in population biology and extensively applied to fossilbiodiversity
as well). The latter models imply that changes in diversity are guided
by first-order positive feedback (more ancestors, more descendants) or a
negative feedback arising from resource limitation. The hyperbolic model implies a second-order positive feedback. The hyperbolic pattern of the world population growth has been demonstrated (see below) to arise from second-order positive feedback between the population size and the rate of technological growth.
The hyperbolic character of biodiversity growth can be similarly
accounted for by a positive feedback between the diversity and community
structure complexity. It has been suggested that the similarity between
the curves of biodiversity
and human population probably comes from the fact that both are derived
from the interference of the hyperbolic trend (produced by the positive
feedback) with cyclical and stochastic dynamics.
Immune system
A cytokine storm, or hypercytokinemia is a potentially fatal immune reaction consisting of a positive feedback loop between cytokines and immune cells, with highly elevated levels of various cytokines. In normal immune function, positive feedback loops can be utilized to
enhance the action of B lymphocytes. When a B cell binds its antibodies
to an antigen and becomes activated, it begins releasing antibodies and
secreting a complement protein called C3. Both C3 and a B cell's
antibodies can bind to a pathogen, and when a B cell has its antibodies
bind to a pathogen with C3, it speeds up that B cell's secretion of more
antibodies and more C3, thus creating a positive feedback loop.
Cell death
Apoptosis is a caspase-mediated
process of cellular death, whose aim is the removal of long-lived or
damaged cells. A failure of this process has been implicated in
prominent conditions such as cancer or Parkinson's disease.
The very core of the apoptotic process is the auto-activation of
caspases, which may be modelled via a positive-feedback loop. This
positive feedback exerts an auto-activation of the effector caspase
by means of intermediate caspases. When isolated from the rest of the
apoptotic pathway, this positive feedback presents only one stable
steady state, regardless of the number of intermediate activation steps
of the effector caspase. When this core process is complemented with inhibitors and enhancers of
caspase effects, this process presents bistability, thereby modelling
the alive and dying states of a cell.
In psychology
Winner (1996) described gifted children 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. Winner termed this positive feedback loop as a rage to master. Vandervert (2009a, 2009b) proposed that the child prodigy 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. Vandervert also argued that this working memory/cerebellar positive feedback loop was responsible for language evolution in working memory.
In economics
Markets with social influence
Product recommendations and information about past
purchases have been shown to influence consumers' choices significantly,
whether it is for music, movies, books, technological, and other types
of products. Social influence often induces a rich-get-richer phenomenon
(Matthew effect) where popular products tend to become even more popular.
Market dynamics
According to the theory of reflexivity advanced by George Soros,
price changes are driven by a positive feedback process whereby
investors' expectations are influenced by price movements so their
behaviour acts to reinforce movement in that direction until it becomes
unsustainable, whereupon the feedback drives prices in the opposite
direction.
In social media
Programs such as Facebook and Twitter depend on positive feedback to create interest in topics and drive the take-up of the media. In the age of smartphones and social media, the feedback loop has
created a craze for virtual validation in the form of likes, shares, and
FOMO (fear of missing out). This is intensified by the use of bots which are designed to respond to
particular words or themes and transmit posts more widely.
What is called negative feedback in social media should
often be regarded as positive feedback in this context. Outrageous
statements and negative comments often produce much more feedback than
positive comments.
Systemic risk
Systemic risk
is the risk that an amplification or leverage or positive feedback
process presents to a system. This is usually unknown, and under certain
conditions, this process can amplify exponentially and rapidly lead to
destructive or chaotic behaviour. A Ponzi scheme
is a good example of a positive-feedback system: funds from new
investors are used to pay out unusually high returns, which in turn
attract more 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). Hyman Minsky
proposed a theory that certain credit expansion practices could make a
market economy into "a deviation amplifying system" that could suddenly
collapse, sometimes called a Minsky moment.
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 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.
The 2010 Flash Crash incident was blamed on the practice of high-frequency trading (HFT), although whether HFT really increases systemic risk remains controversial.
Agriculture and human population can be considered to be in a positive feedback mode, 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.
Technological innovation and human population can be
similarly considered, and this has been offered as an explanation for
the apparent hyperbolic growth of the human population in the past, instead of a simpler exponential growth. It is proposed that the growth rate is accelerating because of second-order positive feedback between population and technology. Technological growth increases the carrying capacity of land for people, which leads to a growing population, and this in turn drives further technological growth.
James Moody, Assistant Professor at Ohio State University, states that students who self-segregate
or grow up in segregated environments have "little meaningful exposure
to other races because they never form relationships with students of
another race...[; as a result,...] they are viewing other racial groups
at a social distance, which can bolster stereotypes," which ultimately
causes a positive feedback loop in which segregated groups become more
prejudiced, polarized, and segregated against each other, similar to
that of political polarization.
In meteorology
Drought
intensifies through positive feedback. A lack of rain decreases soil
moisture, which kills plants or causes them to release less water
through transpiration. Both factors limit evapotranspiration,
the process by which water vapour is added to the atmosphere from the
surface, and add dry dust to the atmosphere, which absorbs water. Less
water vapour means both low dew point
temperatures and more efficient daytime heating, decreasing the chances
of humidity in the atmosphere leading to cloud formation. Lastly,
without clouds, there cannot be rain, and the loop is complete.
Some effects of global warming can either enhance (positive feedbacks) or inhibit (negative feedbacks) warming.
Globally, wildfires and deforestation have reduced forests' net absorption of greenhouse gases, reducing their effectiveness at mitigating climate change. Global warming increases forest fires that release more greenhouse
gases, creating a positive feedback loop that causes more warming.
Over recent decades, "forest disturbance" (damage) by fire has increased in most of the planet's forest zones. The increase in area, frequency, and severity of forest fires creates a positive feedback that increases global warming.
Climate forcings may push a climate system in the direction of warming or cooling, for example, increased atmospheric concentrations of greenhouse gases
cause warming at the surface. Forcings are external to the climate
system and feedbacks are internal processes of the system. Some feedback
mechanisms act in relative isolation to the rest of the climate system
while others are tightly coupled. Forcings, feedbacks and the dynamics of the climate system determine
how much and how fast the climate changes. The main positive feedback in
global warming is the tendency of warming to increase the amount of water vapour in the atmosphere, which in turn leads to further warming. The main negative feedback comes from the Stefan–Boltzmann law,
the amount of heat radiated from the Earth into space is proportional
to the fourth power of the temperature of Earth's surface and
atmosphere.
Other examples of positive feedback subsystems in climatology include:
A warmer atmosphere melts ice, changing the albedo (surface reflectivity), 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.
Peat, occurring naturally in peat bogs, contains carbon. When peat dries it decomposes, and may additionally burn. Peat also releases nitrous oxide.
Global warming affects the cloud distribution. Clouds at
higher altitudes enhance the greenhouse effect, while low clouds mainly
reflect back sunlight, having opposite effects on temperature.
A self-fulfilling prophecy
is a social positive feedback loop between beliefs and behaviour: if
enough people believe that something is true, their behaviour can make
it true, and observations of their behaviour may in turn increase
belief. A classic example is a bank run.
Another sociological example of positive feedback is the network effect.
When more people are encouraged to join a network, this increases the
reach of the network, therefore the network expands ever more quickly. A
viral video is an example of the network effect in which links
to a popular video are shared and redistributed, ensuring that more
people see the video and then re-publish the links. This is the basis
for many social phenomena, including Ponzi schemes and chain letters. In many cases, population size is the limiting factor to the feedback effect.
In political science
In politics, institutions can reinforce norms, which can
subsequently be a source of positive feedback. This rationale is
frequently utilized to comprehend public policy processes, which may be
dissected into a sequence of events. Self-reinforcing processes are
understood to be affected by positive feedback mechanisms (e.g.,
supportive policy constituencies). Conversely, unsuccessful policy processes encounter negative feedback mechanisms (e.g., veto points with veto power).
A comparative illustration of policy feedback can be
observed in the economic foreign policies of Brazil and China,
particularly in their execution of state capitalism tactics during the
1990s and 2000s. Although both nations initially embraced similar state capitalist
ideas, their paths in executing economic policies diverged over time due
to distinct incentives. In China, a positive feedback mechanism
reinforced previous policies, whereas in Brazil, negative feedback
mechanisms compelled the country to abandon state capitalism policies
and dynamics.
In chemistry
If a chemical reaction causes the release of heat, and the reaction itself happens faster
at higher temperatures, then there is a high likelihood of positive
feedback. If the heat produced is not removed from the reactants fast
enough, thermal runaway can occur and very quickly lead to a chemical explosion.
In conservation
Many wildlife are hunted for their parts, which can be
quite valuable. The closer to extinction that targeted species become,
the higher the price there is on their parts.
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