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Uncertainty refers to
epistemic Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Ep ...
situations involving imperfect or unknown
information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random, ...
. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...
environments, as well as due to
ignorance Ignorance is a lack of knowledge and understanding. The word "ignorant" is an adjective that describes a person in the state of being unaware, or even cognitive dissonance and other cognitive relation, and can describe individuals who are unaware ...
, indolence, or both. It arises in any number of fields, including
insurance Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge ...
,
philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. S ...
,
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which re ...
,
statistics Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
,
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...
,
finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of ...
,
medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care p ...
,
psychology Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries betwe ...
,
sociology Sociology is a social science that focuses on society, human social behavior, patterns of social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of empirical investigation and ...
,
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
,
metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
,
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...
,
ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps ...
and
information science Information science (also known as information studies) is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information. ...
.


Concepts

Although the terms are used in various ways among the general public, many specialists in
decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
,
statistics Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
and other quantitative fields have defined uncertainty, risk, and their measurement as:


Uncertainty

The lack of
certainty Certainty (also known as epistemic certainty or objective certainty) is the epistemic property of beliefs which a person has no rational grounds for doubting. One standard way of defining epistemic certainty is that a belief is certain if and ...
, a state of limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome. ;Measurement of uncertainty: A set of possible states or outcomes where
probabilities Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
are assigned to each possible state or outcome – this also includes the application of a
probability density function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
to continuous variables. ;Second order uncertainty: In statistics and economics, second-order uncertainty is represented in probability density functions over (first-order) probabilities. :Opinions in subjective logic carry this type of uncertainty. ;
Risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environm ...
: A state of uncertainty where some possible outcomes have an undesired effect or significant loss. ;Measurement of risk: A set of measured uncertainties where some possible outcomes are losses, and the magnitudes of those losses – this also includes loss functions over continuous variables.


Uncertainty versus Variability

There is a difference between uncertainty and variability. Uncertainty is quantified by a probability distribution which depends upon our state of information about the likelihood of what the single, true value of the uncertain quantity is. Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data.


Knightian uncertainty

In economics, in 1921
Frank Knight Frank Hyneman Knight (November 7, 1885 – April 15, 1972) was an American economist who spent most of his career at the University of Chicago, where he became one of the founders of the Chicago School. Nobel laureates Milton Friedman, George ...
distinguished uncertainty from risk with uncertainty being lack of knowledge which is immeasurable and impossible to calculate. Because of the absence of clearly defined statistics in most economic decisions where people face uncertainty, he believed that we cannot measure probabilities in such cases; this is now referred to as Knightian uncertainty. Knight pointed out that the unfavorable outcome of known risks can be insured during the decision-making process because it has a clearly defined expected probability distribution. Unknown risks have no known expected probability distribution, which can lead to extremely risky company decisions. Other taxonomies of uncertainties and decisions include a broader sense of uncertainty and how it should be approached from an ethics perspective: For example, if it is unknown whether or not it will rain tomorrow, then there is a state of uncertainty. If probabilities are applied to the possible outcomes using weather forecasts or even just a calibrated probability assessment, the uncertainty has been quantified. Suppose it is quantified as a 90% chance of sunshine. If there is a major, costly, outdoor event planned for tomorrow then there is a risk since there is a 10% chance of rain, and rain would be undesirable. Furthermore, if this is a business event and $100,000 would be lost if it rains, then the risk has been quantified (a 10% chance of losing $100,000). These situations can be made even more realistic by quantifying light rain vs. heavy rain, the cost of delays vs. outright cancellation, etc. Some may represent the risk in this example as the "expected opportunity loss" (EOL) or the chance of the loss multiplied by the amount of the loss (10% × $100,000 = $10,000). That is useful if the organizer of the event is "risk neutral", which most people are not. Most would be willing to pay a premium to avoid the loss. An insurance company, for example, would compute an EOL as a minimum for any insurance coverage, then add onto that other operating costs and profit. Since many people are willing to buy insurance for many reasons, then clearly the EOL alone is not the perceived value of avoiding the risk. Quantitative uses of the terms uncertainty and risk are fairly consistent from fields such as
probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
, actuarial science, and
information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940 ...
. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example, surprisal is a variation on uncertainty sometimes used in
information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940 ...
. But outside of the more mathematical uses of the term, usage may vary widely. In
cognitive psychology Cognitive psychology is the scientific study of mental processes such as attention, language use, memory, perception, problem solving, creativity, and reasoning. Cognitive psychology originated in the 1960s in a break from behaviorism, which ...
, uncertainty can be real, or just a matter of perception, such as expectations, threats, etc.
Vagueness In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word "prime" is ...
is a form of uncertainty where the analyst is unable to clearly differentiate between two different classes, such as 'person of average height.' and 'tall person'. This form of vagueness can be modelled by some variation on Zadeh's
fuzzy logic Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completel ...
or subjective logic.
Ambiguity Ambiguity is the type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement ...
is a form of uncertainty where even the possible outcomes have unclear meanings and interpretations. The statement ''"He returns from the bank"'' is ambiguous because its interpretation depends on whether the word 'bank' is meant as ''"the side of a river"'' or ''"a financial institution"''. Ambiguity typically arises in situations where multiple analysts or observers have different interpretations of the same statements. Uncertainty may be a consequence of a lack of knowledge of obtainable facts. That is, there may be uncertainty about whether a new rocket design will work, but this uncertainty can be removed with further analysis and experimentation. At the subatomic level, uncertainty may be a fundamental and unavoidable property of the universe. In
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, the
Heisenberg uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
puts limits on how much an observer can ever know about the position and velocity of a particle. This may not just be ignorance of potentially obtainable facts but that there is no fact to be found. There is some controversy in physics as to whether such uncertainty is an irreducible property of nature or if there are "hidden variables" that would describe the state of a particle even more exactly than Heisenberg's uncertainty principle allows.


Measurements

The most commonly used procedure for calculating measurement uncertainty is described in the "Guide to the Expression of Uncertainty in Measurement" (GUM) published by ISO. A derived work is for example the
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...
(NIST) Technical Note 1297, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results", and the Eurachem/Citac publication "Quantifying Uncertainty in Analytical Measurement". The uncertainty of the result of a measurement generally consists of several components. The components are regarded as
random variables A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
, and may be grouped into two categories according to the method used to estimate their numerical values: * Type A, those evaluated by
statistical Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industri ...
methods * Type B, those evaluated by other means, e.g., by assigning a
probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomeno ...
By propagating the
variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...
s of the components through a function relating the components to the measurement result, the combined measurement uncertainty is given as the square root of the resulting variance. The simplest form is the
standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, w ...
of a repeated observation. In
metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
,
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which re ...
, and
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
, the uncertainty or
margin of error The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a census of the en ...
of a measurement, when explicitly stated, is given by a range of values likely to enclose the true value. This may be denoted by
error bar Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the repor ...
s on a graph, or by the following notations: * ''measured value'' ± ''uncertainty'' * ''measured value'' * ''measured value'' (''uncertainty'') In the last notation, parentheses are the concise notation for the ± notation. For example, applying 10 meters in a scientific or engineering application, it could be written or , by convention meaning accurate to ''within'' one tenth of a meter, or one hundredth. The precision is symmetric around the last digit. In this case it's half a tenth up and half a tenth down, so 10.5 means between 10.45 and 10.55. Thus it is ''understood'' that 10.5 means , and 10.50 means , also written and respectively. But if the accuracy is within two tenths, the uncertainty is ± one tenth, and it is ''required'' to be explicit: and or and . The numbers in parentheses ''apply'' to the numeral left of themselves, and are not part of that number, but part of a notation of uncertainty. They apply to the least significant digits. For instance, stands for , while stands for . This concise notation is used for example by
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
in stating the
atomic mass The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&n ...
of
elements Element or elements may refer to: Science * Chemical element, a pure substance of one type of atom * Heating element, a device that generates heat by electrical resistance * Orbital elements, parameters required to identify a specific orbit of o ...
. The middle notation is used when the error is not symmetrical about the value – for example . This can occur when using a logarithmic scale, for example. Uncertainty of a measurement can be determined by repeating a measurement to arrive at an estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged, then the mean measurement value has a much smaller uncertainty, equal to the
standard error The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error ...
of the mean, which is the standard deviation divided by the square root of the number of measurements. This procedure neglects
systematic error Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mista ...
s, however. When the uncertainty represents the standard error of the measurement, then about 68.3% of the time, the true value of the measured quantity falls within the stated uncertainty range. For example, it is likely that for 31.7% of the atomic mass values given on the list of elements by atomic mass, the true value lies outside of the stated range. If the width of the interval is doubled, then probably only 4.6% of the true values lie outside the doubled interval, and if the width is tripled, probably only 0.3% lie outside. These values follow from the properties of the normal distribution, and they apply only if the measurement process produces normally distributed errors. In that case, the quoted standard errors are easily converted to 68.3% ("one
sigma Sigma (; uppercase Σ, lowercase σ, lowercase in word-final position ς; grc-gre, σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as ...
"), 95.4% ("two sigma"), or 99.7% ("three sigma")
confidence interval In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as ...
s. In this context, uncertainty depends on both the
accuracy and precision Accuracy and precision are two measures of ''observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their '' true value'', while ''precision'' is how close the measurements are to each oth ...
of the measurement instrument. The lower the accuracy and precision of an instrument, the larger the measurement uncertainty is. Precision is often determined as the standard deviation of the repeated measures of a given value, namely using the same method described above to assess measurement uncertainty. However, this method is correct only when the instrument is accurate. When it is inaccurate, the uncertainty is larger than the standard deviation of the repeated measures, and it appears evident that the uncertainty does not depend only on instrumental precision.


In the media

Uncertainty in science, and science in general, may be interpreted differently in the public sphere than in the scientific community.Zehr, S. C. (1999)
Scientists' representations of uncertainty
In Friedman, S.M., Dunwoody, S., & Rogers, C. L. (Eds.), Communicating uncertainty: Media coverage of new and controversial science (3–21). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
This is due in part to the diversity of the public audience, and the tendency for scientists to misunderstand lay audiences and therefore not communicate ideas clearly and effectively. One example is explained by the
information deficit model In studies of the public understanding of science, the information deficit model (or simply deficit model) or science literacy/knowledge deficit model attributes public scepticism or hostility to science and technology to a lack of understanding, re ...
. Also, in the public realm, there are often many scientific voices giving input on a single topic. For example, depending on how an issue is reported in the public sphere, discrepancies between outcomes of multiple scientific studies due to methodological differences could be interpreted by the public as a lack of consensus in a situation where a consensus does in fact exist. This interpretation may have even been intentionally promoted, as scientific uncertainty may be managed to reach certain goals. For example, climate change deniers took the advice of Frank Luntz to frame
global warming In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to E ...
as an issue of scientific uncertainty, which was a precursor to the conflict frame used by journalists when reporting the issue. "Indeterminacy can be loosely said to apply to situations in which not all the parameters of the system and their interactions are fully known, whereas ignorance refers to situations in which it is not known what is not known." These unknowns, indeterminacy and ignorance, that exist in science are often "transformed" into uncertainty when reported to the public in order to make issues more manageable, since scientific indeterminacy and ignorance are difficult concepts for scientists to convey without losing credibility. Conversely, uncertainty is often interpreted by the public as ignorance. The transformation of indeterminacy and ignorance into uncertainty may be related to the public's misinterpretation of uncertainty as ignorance. Journalists may inflate uncertainty (making the science seem more uncertain than it really is) or downplay uncertainty (making the science seem more certain than it really is). One way that journalists inflate uncertainty is by describing new research that contradicts past research without providing context for the change. Journalists may give scientists with minority views equal weight as scientists with majority views, without adequately describing or explaining the state of
scientific consensus Scientific consensus is the generally held judgment, position, and opinion of the majority or the supermajority of scientists in a particular field of study at any particular time. Consensus is achieved through scholarly communication at confer ...
on the issue. In the same vein, journalists may give non-scientists the same amount of attention and importance as scientists. Journalists may downplay uncertainty by eliminating "scientists' carefully chosen tentative wording, and by losing these caveats the information is skewed and presented as more certain and conclusive than it really is". Also, stories with a single source or without any context of previous research mean that the subject at hand is presented as more definitive and certain than it is in reality. There is often a "product over process" approach to
science journalism Science journalism conveys reporting about science to the public. The field typically involves interactions between scientists, journalists, and the public. Origins Modern science journalism dates back to '' Digdarshan'' (means showing th ...
that aids, too, in the downplaying of uncertainty. Finally, and most notably for this investigation, when science is framed by journalists as a triumphant quest, uncertainty is erroneously framed as "reducible and resolvable". Some media routines and organizational factors affect the overstatement of uncertainty; other media routines and organizational factors help inflate the certainty of an issue. Because the general public (in the United States) generally trusts scientists, when science stories are covered without alarm-raising cues from special interest organizations (religious groups, environmental organizations, political factions, etc.) they are often covered in a business related sense, in an economic-development frame or a social progress frame. The nature of these frames is to downplay or eliminate uncertainty, so when economic and scientific promise are focused on early in the issue cycle, as has happened with coverage of plant biotechnology and nanotechnology in the United States, the matter in question seems more definitive and certain. Sometimes, stockholders, owners, or advertising will pressure a media organization to promote the business aspects of a scientific issue, and therefore any uncertainty claims which may compromise the business interests are downplayed or eliminated.


Applications

* Uncertainty is designed into
game A game is a structured form of play (activity), play, usually undertaken for enjoyment, entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator s ...
s, most notably in
gambling Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three elem ...
, where chance is central to play. * In
scientific modelling Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted ...
, in which the prediction of future events should be understood to have a range of expected values * In
optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
, uncertainty permits one to describe situations where the user does not have full control on the final outcome of the optimization procedure, see scenario optimization and
stochastic optimization Stochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involves random objective functi ...
. ** In
weather forecasting Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th cent ...
, it is now commonplace to include data on the degree of uncertainty in a
weather forecast Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th centu ...
. * Uncertainty or
error An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistic ...
is used in science and engineering notation. Numerical values should only have to be expressed in those digits that are physically meaningful, which are referred to as
significant figures Significant figures (also known as the significant digits, ''precision'' or ''resolution'') of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expres ...
. Uncertainty is involved in every measurement, such as measuring a distance, a temperature, etc., the degree depending upon the instrument or technique used to make the measurement. Similarly, uncertainty is propagated through calculations so that the calculated value has some degree of uncertainty depending upon the uncertainties of the measured values and the equation used in the calculation. * In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which re ...
, the Heisenberg
uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
forms the basis of modern
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
. * In
metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
,
measurement uncertainty In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by ...
is a central concept quantifying the dispersion one may reasonably attribute to a measurement result. Such an uncertainty can also be referred to as a measurement
error An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistic ...
. In daily life, measurement uncertainty is often implicit ("He is 6 feet tall" give or take a few inches), while for any serious use an explicit statement of the measurement uncertainty is necessary. The expected measurement uncertainty of many
measuring instruments A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Estab ...
(scales, oscilloscopes, force gages, rulers, thermometers, etc.) is often stated in the manufacturers' specifications. * In
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
, uncertainty can be used in the context of validation and verification of material modeling. * Uncertainty has been a common theme in art, both as a thematic device (see, for example, the indecision of
Hamlet ''The Tragedy of Hamlet, Prince of Denmark'', often shortened to ''Hamlet'' (), is a tragedy written by William Shakespeare sometime between 1599 and 1601. It is Shakespeare's longest play, with 29,551 words. Set in Denmark, the play depic ...
), and as a quandary for the artist (such as Martin Creed's difficulty with deciding what artworks to make). * Uncertainty is an important factor in
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...
. According to economist
Frank Knight Frank Hyneman Knight (November 7, 1885 – April 15, 1972) was an American economist who spent most of his career at the University of Chicago, where he became one of the founders of the Chicago School. Nobel laureates Milton Friedman, George ...
, it is different from
risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environm ...
, where there is a specific
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
assigned to each outcome (as when flipping a fair coin). Knightian uncertainty involves a situation that has unknown probabilities. * Investing in
financial market A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial marke ...
s such as the stock market involves Knightian uncertainty when the probability of a rare but catastrophic event is unknown.


Philosophy

In
Western philosophy Western philosophy encompasses the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word ...
the first philosopher to embrace uncertainty was
Pyrrho Pyrrho of Elis (; grc, Πύρρων ὁ Ἠλεῖος, Pyrrhо̄n ho Ēleios; ), born in Elis, Greece, was a Greek philosopher of Classical antiquity, credited as being the first Greek skeptic philosopher and founder of Pyrrhonism. Life ...
''Pyrrho'', Internet Encyclopedia of Philosophy https://www.iep.utm.edu/pyrrho/ resulting in the Hellenistic philosophies of
Pyrrhonism Pyrrhonism is a school of philosophical skepticism founded by Pyrrho in the fourth century BCE. It is best known through the surviving works of Sextus Empiricus, writing in the late second century or early third century CE. History Pyrrho of ...
and
Academic Skepticism Academic skepticism refers to the skeptical period of ancient Platonism dating from around 266 BCE, when Arcesilaus became scholarch of the Platonic Academy, until around 90 BCE, when Antiochus of Ascalon rejected skepticism, although individua ...
, the first schools of
philosophical skepticism Philosophical skepticism ( UK spelling: scepticism; from Greek σκέψις ''skepsis'', "inquiry") is a family of philosophical views that question the possibility of knowledge. It differs from other forms of skepticism in that it even rejec ...
.
Aporia In philosophy, an aporia ( grc, ᾰ̓πορῐ́ᾱ, aporíā, literally: "lacking passage", also: "impasse", "difficulty in passage", "puzzlement") is a conundrum or state of puzzlement. In rhetoric, it is a declaration of doubt, made for ...
and acatalepsy represent key concepts in ancient Greek philosophy regarding uncertainty.


See also

*
Certainty Certainty (also known as epistemic certainty or objective certainty) is the epistemic property of beliefs which a person has no rational grounds for doubting. One standard way of defining epistemic certainty is that a belief is certain if and ...
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Dempster–Shafer theory The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and ...
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Further research is needed The phrases "further research is needed" (FRIN), "more research is needed" and other variants are commonly used in research papers. The cliché is so common that it has attracted research, regulation and cultural commentary. Meaning Some res ...
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Fuzzy set theory In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined ...
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Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applic ...
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Information entropy In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable X, which takes values in the alphabet ...
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Interval finite element In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be applied in situations where it is not possible to get reliable probabilistic characteristics of ...
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Measurement uncertainty In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by ...
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Morphological analysis (problem-solving) Morphological analysis is the analysis of morphology in various fields * Morphological analysis (problem-solving) or general morphological analysis, a method for exploring all possible solutions to a multi-dimensional, non-quantified problem * An ...
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Propagation of uncertainty In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of ex ...
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Randomness In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ran ...
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Schrödinger's cat In quantum mechanics, Schrödinger's cat is a thought experiment that illustrates a paradox of quantum superposition. In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead, while it is unobserved in ...
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Scientific consensus Scientific consensus is the generally held judgment, position, and opinion of the majority or the supermajority of scientists in a particular field of study at any particular time. Consensus is achieved through scholarly communication at confer ...
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Statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic b ...
* Subjective logic *
Uncertainty quantification Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system a ...
* Uncertainty tolerance * Volatility, uncertainty, complexity and ambiguity


References


Further reading

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External links


Measurement Uncertainties in Science and Technology, Springer 2005

Proposal for a New Error Calculus Estimation of Measurement Uncertainties — an Alternative to the ISO Guide


* ttp://strategic.mit.edu Strategic Engineering: Designing Systems and Products under Uncertainty (MIT Research Group)br>Understanding Uncertainty site
from Cambridge's Winton programme * {{Authority control Cognition Concepts in epistemology Doubt Experimental physics Measurement Probability Probability interpretations Prospect theory