Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable and/or stochastic environments, as well as due to ignorance, indolence, or both.[1] It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, psychology, sociology, engineering, metrology, meteorology, ecology and information science.

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Situations often arise wherein a decision must be made when the results of each possible choice are uncertain.


Although the terms are used in various ways among the general public, many specialists in decision theory, statistics and other quantitative fields have defined uncertainty, risk, and their measurement as:

The lack of certainty, 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 are assigned to each possible state or outcome – this also includes the application of a probability density function to continuous variables.[2]
Second order uncertainty
In statistics and economics, second-order uncertainty is represented in probability density functions over (first-order) probabilities.[3][4].
Opinions in subjective logic [5] carry this type of uncertainty.
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.[6][7][8][9]
Knightian uncertainty
In economics, in 1921 Frank Knight distinguished uncertainty from risk with uncertainty being lack of knowledge which is immeasurable and impossible to calculate; this is now referred to as Knightian uncertainty:

Uncertainty must be taken in a sense radically distinct from the familiar notion of risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.

— Frank Knight (1885–1972), Risk, Uncertainty, and Profit (1921), University of Chicago.[10]
You cannot be certain about uncertainty.
— Frank Knight

Other taxonomies of uncertainties and decisions include a broader sense of uncertainty and how it should be approached from an ethics perspective:[11]

A taxonomy of uncertainty

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, actuarial science, and information theory. 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. But outside of the more mathematical uses of the term, usage may vary widely. In cognitive psychology, uncertainty can be real, or just a matter of perception, such as expectations, threats, etc.

Vagueness 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 or subjective logic.

Ambiguity 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, the Heisenberg uncertainty principle 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.


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 for Standards and Technology (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, and may be grouped into two categories according to the method used to estimate their numerical values:

By propagating the variances 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 of a repeated observation.

In metereology, physics, and engineering, the uncertainty or margin of error 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 bars on a graph, or by the following notations:

  • measured value ± uncertainty
  • measured value +uncertainty
  • measured value (uncertainty)

In the last notation, parentheses are the concise notation for the ± notation. For example, applying 10 ​12 meters in a scientific or engineering application, it could be written 10.5 m or 10.50 m, 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 10.5±0.05, and 10.50 means 10.50±0.005, also written 10.50(5) and 10.500(5) respectively. But if the accuracy is within two tenths, the uncertainty is ± one tenth, and it is required to be explicit: 10.5±0.1 and 10.50±0.01 or 10.5(1) and 10.50(1). 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, 1.00794(7) stands for 1.00794±0.00007, while 1.00794(72) stands for 1.00794±0.00072.[12] This concise notation is used for example by IUPAC in stating the atomic mass of elements.

The middle notation is used when the error is not symmetrical about the value – for example 3.4+0.3
. 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 of the mean, which is the standard deviation divided by the square root of the number of measurements. This procedure neglects systematic errors, 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"), 95.4% ("two sigma"), or 99.7% ("three sigma") confidence intervals.

In this context, uncertainty depends on both the accuracy and precision of the measurement instrument. The lower the accuracy and precision of an instrument, the larger the measurement uncertainty is. Notice that 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.

Uncertainty and the media

Uncertainty in science, and science in general, may be interpreted differently in the public sphere than in the scientific community.[13] 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.[13] One example is explained by the information deficit model. Also, in the public realm, there are often many scientific voices giving input on a single topic.[13] 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.[13] 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 as an issue of scientific uncertainty, which was a precursor to the conflict frame used by journalists when reporting the issue.[14]

"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."[15] 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.[13] Conversely, uncertainty is often interpreted by the public as ignorance.[16] 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).[17] One way that journalists inflate uncertainty is by describing new research that contradicts past research without providing context for the change.[17] Journalists may give scientists with minority views equal weight as scientists with majority views, without adequately describing or explaining the state of scientific consensus on the issue.[17] In the same vein, journalists may give non-scientists the same amount of attention and importance as scientists.[17]

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".[17] 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.[17] There is often a "product over process" approach to science journalism that aids, too, in the downplaying of uncertainty.[17] 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".[17]

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.[18] 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.[18]

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.[17]


  • Uncertainty is designed into games, most notably in gambling, where chance is central to play.
  • In scientific modelling, in which the prediction of future events should be understood to have a range of expected values
  • In optimization, 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.
  • Uncertainty or error 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. 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.[19]
  • In physics, the Heisenberg uncertainty principle forms the basis of modern quantum mechanics.
  • In metrology, measurement uncertainty 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. 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 (scales, oscilloscopes, force gages, rulers, thermometers, etc.) is often stated in the manufacturers' specifications.
  • In engineering, uncertainty can be used in the context of validation and verification of material modeling.[20]
  • Uncertainty has been a common theme in art, both as a thematic device (see, for example, the indecision of Hamlet), 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. According to economist Frank Knight, it is different from risk, where there is a specific probability assigned to each outcome (as when flipping a fair coin). Knightian uncertainty involves a situation that has unknown probabilities.
    • Investing in financial markets such as the stock market involves Knightian uncertainty when the probabiliy of a rare but catastrophic event is unknown.
    • In entrepreneurship: New products, services, firms and even markets may be created in the absence of probability estimates. According to entrepreneurship research, expert entrepreneurs use experience based heuristics called effectuation (as opposed to causality) to overcome uncertainty.

See also


  1. ^ Peter Norvig; Sebastian Thrun. "Introduction to Artificial Intelligence". Udacity.
  2. ^ Kabir, H. D., Khosravi, A., Hosen, M. A., & Nahavandi, S. (2018). Neural Network-based Uncertainty Quantification: A Survey of Methodologies and Applications. IEEE Access. Vol. 6, Pages 36218 - 36234, doi:10.1109/ACCESS.2018.2836917
  3. ^ Gärdenfors, Peter; Sahlin, Nils-Eric (1982). "Unreliable probabilities, risk taking, and decision making". Synthese. 53 (3): 361–386. doi:10.1007/BF00486156.
  4. ^ David Sundgren and Alexander Karlsson. Uncertainty levels of second-order probability. Polibits, 48:5–11, 2013.
  5. ^ Audun Jøsang. Subjective Logic: A Formalism for Reasoning Under Uncertainty. Springer, Heidelberg, 2016.
  6. ^ Douglas Hubbard (2010). How to Measure Anything: Finding the Value of Intangibles in Business, 2nd ed. John Wiley & Sons. Description Archived 2011-11-22 at the Wayback Machine, contents Archived 2013-04-27 at the Wayback Machine, and preview.
  7. ^ Jean-Jacques Laffont (1989). The Economics of Uncertainty and Information, MIT Press. Description Archived 2012-01-25 at the Wayback Machine and chapter-preview links.
  8. ^ Jean-Jacques Laffont (1980). Essays in the Economics of Uncertainty, Harvard University Press. Chapter-preview links.
  9. ^ Robert G. Chambers and John Quiggin (2000). Uncertainty, Production, Choice, and Agency: The State-Contingent Approach. Cambridge. Description and preview. ISBN 0-521-62244-1
  10. ^ Knight, F. H. (1921). Risk, Uncertainty, and Profit. Boston: Hart, Schaffner & Marx.
  11. ^ Tannert C, Elvers HD, Jandrig B (2007). "The ethics of uncertainty. In the light of possible dangers, research becomes a moral duty". EMBO Rep. 8 (10): 892–6. doi:10.1038/sj.embor.7401072. PMC 2002561. PMID 17906667.
  12. ^ "Standard Uncertainty and Relative Standard Uncertainty". CODATA reference. NIST. Archived from the original on 16 October 2011. Retrieved 26 September 2011.
  13. ^ a b c d e Zehr, S. C. (1999). Scientists' representation 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.
  14. ^ Nisbet, M.; Scheufele, D. A. (2009). "What's next for science communication? Promising directions and lingering distractions". American Journal of Botany. 96 (10): 1767–1778. doi:10.3732/ajb.0900041. PMID 21622297.
  15. ^ Shackley, S.; Wynne, B. (1996). "Representing uncertainty in global climate change science and policy: Boundary-ordering devices and authority". Science, Technology, & Human Values. 21 (3): 275–302. doi:10.1177/016224399602100302.
  16. ^ Somerville, R. C.; Hassol, S. J. (2011). "Communicating the science of climate change". Physics Today. 64 (10): 48–53. Bibcode:2011PhT....64j..48S. doi:10.1063/pt.3.1296.
  17. ^ a b c d e f g h i Stocking, H. (1999). "How journalists deal with scientific uncertainty". In Friedman, S. M.; Dunwoody, S.; Rogers, C. L. (eds.). Communicating Uncertainty: Media Coverage of New and Controversial Science. Mahwah, NJ: Lawrence Erlbaum. pp. 23–41. ISBN 978-0-8058-2727-9.
  18. ^ a b Nisbet, M.; Scheufele, D. A. (2007). "The Future of Public Engagement". The Scientist. 21 (10): 38–44.
  19. ^ Gregory, Kent J.; Bibbo, Giovanni; Pattison, John E. (2005). "A Standard Approach to Measurement Uncertainties for Scientists and Engineers in Medicine". Australasian Physical and Engineering Sciences in Medicine. 28 (2): 131–139. doi:10.1007/BF03178705.
  20. ^ "Archived copy". Archived from the original on 2015-09-26. Retrieved 2016-07-29.CS1 maint: Archived copy as title (link)

Further reading

External links

Adhesive weight

Adhesive weight is the weight on the driving wheels of a locomotive, which determines the frictional grip between wheels and rail, and hence the drawbar pull which a locomotive can exert.

Birthday Honours

The Birthday Honours, in some Commonwealth realms, mark the reigning monarch's official birthday by granting various individuals appointment into national or dynastic orders or the award of decorations and medals. The honours are presented by the monarch or a viceregal representative. The Birthday Honours are one of two annual honours lists, along with the New Year Honours. All royal honours are published in the relevant gazette.


A chassis (US: , UK: ; plural chassis ) is the framework of an artificial object, which supports the object in its construction and use. An example of a chassis is a vehicle frame, the underpart of a motor vehicle, on which the body is mounted; if the running gear such as wheels and transmission, and sometimes even the driver's seat, are included, then the assembly is described as a rolling chassis.

Decision theory

Decision theory (or the theory of choice not to be confused with choice theory) is the study of an agent's choices. Decision theory can be broken into two branches: normative decision theory, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive decision theory, which analyzes how agents actually make the decisions they do.

Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by economists,

statisticians, psychologists, biologists, political and other social scientists, philosophers, and computer scientists.

Empirical applications of this rich theory are usually done with the help of statistical and econometric methods.

Family (biology)

Family (Latin: familia, plural familiae) is one of the eight major hierarchical taxonomic ranks in Linnaean taxonomy; it is classified between order and genus. A family may be divided into subfamilies, which are intermediate ranks between the ranks of family and genus. The official family names are Latin in origin; however, popular names are often used: for example, walnut trees and hickory trees belong to the family Juglandaceae, but that family is commonly referred to as being the "walnut family".

What does or does not belong to a family—or whether a described family should be recognized at all—are proposed and determined by practicing taxonomists. There are no hard rules for describing or recognizing a family. Taxonomists often take different positions about descriptions, and there may be no broad consensus across the scientific community for some time. The publishing of new data and opinion often enables adjustments and consensus.

Fear, uncertainty, and doubt

Fear, uncertainty, and doubt (often shortened to FUD) is a disinformation strategy used in sales, marketing, public relations, politics, cults, and propaganda. FUD is generally a strategy to influence perception by disseminating negative and dubious or false information and a manifestation of the appeal to fear.

While the phrase dates to at least the early 20th century, the present common usage of disinformation related to software, hardware and technology industries generally appeared in the 1970s to describe disinformation in the computer hardware industry, and has since been used more broadly.

Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor.

The measured value of the constant is known with some certainty to four significant digits. In SI units its value is approximately 6.674×10−11 m3⋅kg−1⋅s−2.The modern notation of Newton's law involving G was introduced in the 1890s by C. V. Boys.

The first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment.


Information is the resolution of uncertainty; it is that which answers the question of "what an entity is" and thus defines both its essence and nature of its characteristics. Information relates to both data and knowledge, as data represents values attributed to parameters, and knowledge signifies understanding of a concept. Information is uncoupled from an observer, which is an entity that can access information and thus discern what it specifies; information may exist beyond an event horizon, for example. In the case of knowledge, the information itself requires a cognitive observer to be obtained.

In terms of communication, information is expressed either as the content of a message or through direct or indirect observation. That which is perceived can be construed as a message in its own right, and in that sense, information is always conveyed as the content of a message.

Information can be encoded into various forms for transmission and interpretation (for example, information may be encoded into a sequence of signs, or transmitted via a signal). It can also be encrypted for safe storage and communication.

Regarding uncertainty, the uncertainty of an event is measured by its probability of occurrence and is inversely proportional to that. The more uncertain an event, the more information is required to resolve uncertainty of that event. The bit is a typical unit of information, but other units such as the nat may be used. For example, the information encoded in one "fair" coin flip is log2(2/1) = 1 bit, and in two fair coin flips is

log2(4/1) = 2 bits.

The concept of information has different meanings in different contexts. Thus the concept becomes related to notions of constraint, communication, control, data, form, education, knowledge, meaning, understanding, mental stimuli, pattern, perception, representation, and entropy.

John Maguire (archbishop of Glasgow)

John Aloysius Maguire (1851–1920) was a Roman Catholic bishop who served as the Archbishop of Glasgow from 1902 to 1920.

Keeper of the Register

The Keeper of the Register (more formally known as the Keeper of the National Register of Historic Places) is a National Park Service (NPS) official, responsible for deciding on the eligibility of historic properties for inclusion on the U.S. National Register of Historic Places (NRHP). The Keeper's authority may be delegated as they see fit. The State historic preservation officer for each state submits nominations to the Keeper. Upon receipt, the Keeper has 45 days to decide whether to add the property to the NRHP.


The metre (Commonwealth spelling and BIPM spelling) or meter (American spelling) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m. The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second.The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole – as a result the Earth's circumference is approximately 40,000 km today. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted.

The imperial inch is defined as 0.0254 metres (2.54 centimetres or 25.4 millimetres). One metre is about ​3 3⁄8 inches longer than a yard, i.e. about ​39 3⁄8 inches.

Municipal corporation

A municipal corporation is the legal term for a local governing body, including (but not necessarily limited to) cities, counties, towns, townships, charter townships, villages, and boroughs. The term can also be used to describe municipally owned corporations.

Patron saint

A patron saint, patroness saint, patron hallow or heavenly protector is a saint who in Roman Catholicism, Anglicanism or Eastern Orthodoxy, is regarded as the heavenly advocate of a nation, place, craft, activity, class, clan, family or person.

Planck constant

The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum. He assumed that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, and that constant is named in his honor. In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".

Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to the project of replacing the International Prototype of the Kilogram, a metal cylinder that had defined the kilogram since 1889. The new definition was unanimously approved at the General Conference on Weights and Measures (CGPM) on 16 November 2018 as part of the 2019 redefinition of SI base units. For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.62607015×10−34 J⋅s exactly. The kilogram was the last SI base unit to be re-defined by a fundamental physical property to replace a physical artifact.

Pope Model L

The Pope Model L was a motorcycle produced by Pope Manufacturing Company in Westfield, Massachusetts, between 1914 and 1920.

The Model L was, at 70 miles per hour (110 km/h), the fastest motorcycle in the world when it was introduced.It was technologically advanced for its time, with features not found on other motorcycles, such as overhead valves, chain drive (from 1918) and multi-speed transmission. It was also expensive at $250, as much then as a Model T automobile. (Another source of competition were cyclecars)

Port and starboard

Port and starboard are nautical and aeronautical terms of orientation that deal unambiguously with the structure of vessels and aircraft. Their structures are largely bilaterally symmetrical, meaning they have mirror-image left and right halves if divided sagitally.

One asymmetric feature is that on aircraft and ships where access is at the side, this access is usually only provided on the port side.


Risk is the possibility of losing something of value. Values (such as physical health, social status, emotional well-being, or financial wealth) can be gained or lost when taking risk resulting from a given action or inaction, foreseen or unforeseen (planned or not planned). Risk can also be defined as the intentional interaction with uncertainty. Uncertainty is a potential, unpredictable, and uncontrollable outcome; risk is an aspect of action taken in spite of uncertainty.

Risk perception is the subjective judgment people make about the severity and probability of a risk, and may vary person to person. Any human endeavour carries some risk, but some are much riskier than others.

Uncertainty parameter

The uncertainty parameter U is a parameter introduced by the Minor Planet Center (MPC) to quantify concisely the uncertainty of a perturbed orbital solution for a minor planet. The parameter is a logarithmic scale from 0 to 9 that measures the anticipated longitudinal uncertainty in the minor planet's mean anomaly after 10 years. The uncertainty parameter is also known as condition code in JPL's Small-Body Database Browser. The U value should not be used as a predictor for the uncertainty in the future motion of near-Earth objects.

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 precision with which certain pairs of physical properties of a particle, known as complementary variables or canonically conjugate variables such as position x and momentum p, can be known.

Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928:

where ħ is the reduced Planck constant, h/(2π).

Historically, the uncertainty principle has been confused with a related effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems, that is, without changing something in a system. Heisenberg utilized such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty. It has since become clearer, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program. These include, for example, tests of number–phase uncertainty relations in superconducting or quantum optics systems. Applications dependent on the uncertainty principle for their operation include extremely low-noise technology such as that required in gravitational wave interferometers.

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