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Klein four-group

In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces the identity) and in which composing any two of the three non-identity elements produces the third one. It can be described as the symmetry group of a non-square rectangle (with the three non-identity elements being horizontal reflection, vertical reflection and 180-degree rotation), as the group of bitwise exclusive-or operations on two-bit binary values, or more abstractly as $$\mathbb{Z}_2\times\mathbb{Z}_2$$, the direct product of two copies of the cyclic group of order 2 by the Fundamental Theorem of Finitely Generated Abelian Groups. It was named Vierergruppe, meaning four-group) by Felix Klein in 1884. It is also called the Klein group, and is often symbolized by the letter $$V$$ or as $$K_4$$.

The Klein four-group, with four elements, is the smallest group that is not cyclic. Up to isomorphism, there is only one other group of order four: the cyclic group of order 4. Both groups are abelian.

Presentations
The Klein group's Cayley table is given by:

The Klein four-group is also defined by the group presentation
 * $$V = \left\langle a,b \mid a^2 = b^2 = (ab)^2 = e \right\rangle.$$

All non-identity elements of the Klein group have order 2, so any two non-identity elements can serve as generators in the above presentation. The Klein four-group is the smallest non-cyclic group. It is, however, an abelian group, and isomorphic to the dihedral group of order (cardinality) 4, symbolized $$D_4$$ (or $$D_2$$, using the geometric convention); other than the group of order 2, it is the only dihedral group that is abelian.

The Klein four-group is also isomorphic to the direct sum $$\mathbb{Z}_2\oplus\mathbb{Z}_2$$, so that it can be represented as the pairs {(0,0), (0,1), (1,0), (1,1)} under component-wise addition modulo 2 (or equivalently the bit strings {00, 01, 10, 11}under bitwise XOR), with (0,0) being the group's identity element. The Klein four-group is thus an example of an elementary abelian 2-group, which is also called a Boolean group. The Klein four-group is thus also the group generated by the symmetric difference as the binary operation on the subsets of a powerset of a set with two elements—that is, over a field of sets with four elements, such as $$\{\emptyset,\{\alpha\},\{\beta\},\{\alpha,\beta\}\}$$; the empty set is the group's identity element in this case.

Another numerical construction of the Klein four-group is the set $\{ 1, 3, 5, 7 \}$, with the operation being multiplication modulo 8. Here a is 3, b is 5, and c = ab is 3 × 5 = 15 ≡ 7 (mod 8).

The Klein four-group also has a representation as 2 × 2 real matrices with the operation being matrix multiplication:

e =\begin{pmatrix} 1 & 0\\     0 & 1    \end{pmatrix},\quad a = \begin{pmatrix} 1 & 0\\      0 & -1    \end{pmatrix},\quad $$

b = \begin{pmatrix} -1 & 0\\      0 & 1    \end{pmatrix},\quad c = \begin{pmatrix} -1 & 0\\       0 & -1    \end{pmatrix} $$

On a Rubik's Cube, the "4 dots" pattern can be made in three ways, depending on the pair of faces that are left blank; these three positions together with the solved position form an example of the Klein group, with the solved position serving as the identity.

Geometry
In two dimensions, the Klein four-group is the symmetry group of a rhombus and of rectangles that are not squares, the four elements being the identity, the vertical reflection, the horizontal reflection, and a 180° rotation.

In three dimensions, there are three different symmetry groups that are algebraically the Klein four-group:
 * one with three perpendicular 2-fold rotation axes: the dihedral group $$D_2$$
 * one with a 2-fold rotation axis, and a perpendicular plane of reflection: $$C_{2\mathrm{h}}=D_{1\mathrm{d}}$$
 * one with a 2-fold rotation axis in a plane of reflection (and hence also in a perpendicular plane of reflection): $$C_{2\mathrm{v}}=D_{1\mathrm{h}}$$.

Permutation representation
The three elements of order two in the Klein four-group are interchangeable: the automorphism group of V is thus the group of permutations of these three elements, that is, the symmetric group $$S_3$$.

The Klein four-group's permutations of its own elements can be thought of abstractly as its permutation representation on four points:
 * $$V={}$${, (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)}

In this representation, $$V$$ is a normal subgroup of the alternating group $$A_4$$ (and also the symmetric group $$S_4$$) on four letters. In fact, it is the kernel of a surjective group homomorphism from $$S_4$$ to $$S_3$$.

Other representations within S4 are:

They are not normal subgroups of S4.

Algebra
According to Galois theory, the existence of the Klein four-group (and in particular, the permutation representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals, as established by Lodovico Ferrari: the map $$S_4\to S_3$$ corresponds to the resolvent cubic, in terms of Lagrange resolvents.

In the construction of finite rings, eight of the eleven rings with four elements have the Klein four-group as their additive substructure.

If $$\mathbb{R}^{\times}$$ denotes the multiplicative group of non-zero reals and $$\mathbb{R}^+$$ the multiplicative group of positive reals, then $$\mathbb{R}^{\times}\times\mathbb{R}^{\times}$$ is the group of units of the ring $$\mathbb{R}\times\mathbb{R}$$, and $$\mathbb{R}^+\times\mathbb{R}^+$$ is a subgroup of $$\mathbb{R}^{\times}\times\mathbb{R}^{\times}$$ (in fact it is the component of the identity of $$\mathbb{R}^{\times}\times\mathbb{R}^{\times}$$). The quotient group $$(\mathbb{R}^{\times}\times\mathbb{R}^{\times})/(\mathbb{R}^+\times\mathbb{R}^+)$$ is isomorphic to the Klein four-group. In a similar fashion, the group of units of the split-complex number ring, when divided by its identity component, also results in the Klein four-group.

Graph theory
Among the simple connected graph, the simplest (in the sense of having the fewest entities) that admits the Klein four-group as its automorphism group is the diamond graph shown below. It is also the automorphism group of some other graphs that are simpler in the sense of having fewer entities. These include the graph with four vertices and one edge, which remains simple but loses connectivity, and the graph with two vertices connected to each other by two edges, which remains connected but loses simplicity.

Music
In music composition, the four-group is the basic group of permutations in the twelve-tone technique. In that instance, the Cayley table is written

title: Klein four-group


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Dividend

A dividend is a distribution of profits by a corporation to its shareholders. When a corporation earns a profit or surplus, it is able to pay a portion of the profit as a dividend to shareholders. Any amount not distributed is taken to be re-invested in the business (called retained earnings). The current year profit as well as the retained earnings of previous years are available for distribution; a corporation is usually prohibited from paying a dividend out of its capital. Distribution to shareholders may be in cash (usually by bank transfer) or, if the corporation has a dividend reinvestment plan, the amount can be paid by the issue of further shares or by share repurchase. In some cases, the distribution may be of assets.

The dividend received by a shareholder is income of the shareholder and may be subject to income tax (see dividend tax). The tax treatment of this income varies considerably between jurisdictions. The corporation does not receive a tax deduction for the dividends it pays.

A dividend is allocated as a fixed amount per share, with shareholders receiving a dividend in proportion to their shareholding. Dividends can provide at least temporarily stable income and raise morale among shareholders, but are not guaranteed to continue. For the joint-stock company, paying dividends is not an expense; rather, it is the division of after-tax profits among shareholders. Retained earnings (profits that have not been distributed as dividends) are shown in the shareholders' equity section on the company's balance sheet – the same as its issued share capital. Public companies usually pay dividends on a fixed schedule, but may cancel a scheduled dividend, or declare an unscheduled dividend at any time, sometimes called a special dividend to distinguish it from the regular dividends. (more usually a special dividend is paid at the same time as the regular dividend, but for a one-off higher amount). Cooperatives, on the other hand, allocate dividends according to members' activity, so their dividends are often considered to be a pre-tax expense.

The usually fixed payments to holders of preference shares (or preferred stock in American English) are classed as dividends. The word dividend comes from the Latin word dividendum ("thing to be divided").

History
In the financial history of the world, the Dutch East India Company (VOC) was the first recorded (public) company ever to pay regular dividends. The VOC paid annual dividends worth around 18 percent of the value of the shares for almost 200 years of existence (1602–1800).

In common-law jurisdictions, courts have typically refused to intervene in companies' dividend policies, giving directors wide discretion as to the declaration or payment of dividends. The principle of non-interference was established in the Canadian case of Burland v Earle (1902), the British case of Bond v Barrow Haematite Steel Co (1902), and the Australian case of Miles v Sydney Meat-Preserving Co Ltd (1912). However in Sumiseki Materials Co Ltd v Wambo Coal Pty Ltd (2013) the Supreme Court of New South Wales broke with this precedent and recognised a shareholder's contractual right to a dividend.

Forms of payment
Cash dividends are the most common form of payment and are paid out in currency, usually via electronic funds transfer or a printed paper check. Such dividends are a form of investment income of the shareholder, usually treated as earned in the year they are paid (and not necessarily in the year a dividend was declared). For each share owned, a declared amount of money is distributed. Thus, if a person owns 100 shares and the cash dividend is 50 cents per share, the holder of the stock will be paid $50. Dividends paid are not classified as an expense, but rather a deduction of retained earnings. Dividends paid does not appear on an income statement, but does appear on the balance sheet.

Different classes of stocks have different priorities when it comes to dividend payments. Preferred stocks have priority claims on a company's income. A company must pay dividends on its preferred shares before distributing income to common share shareholders.

Stock or scrip dividends are those paid out in the form of additional shares of the issuing corporation, or another corporation (such as its subsidiary corporation). They are usually issued in proportion to shares owned (for example, for every 100 shares of stock owned, a 5% stock dividend will yield 5 extra shares).

Nothing tangible will be gained if the stock is split because the total number of shares increases, lowering the price of each share, without changing the market capitalization, or total value, of the shares held. (See also Stock dilution.)

Stock dividend distributions do not affect the market capitalization of a company. Stock dividends are not includable in the gross income of the shareholder for US income tax purposes. Because the shares are issued for proceeds equal to the pre-existing market price of the shares; there is no negative dilution in the amount recoverable.

Property dividends or dividends in specie (Latin for "in kind") are those paid out in the form of assets from the issuing corporation or another corporation, such as a subsidiary corporation. They are relatively rare and most frequently are securities of other companies owned by the issuer, however, they can take other forms, such as products and services.

Interim dividends are dividend payments made before a company's Annual General Meeting (AGM) and final financial statements. This declared dividend usually accompanies the company's interim financial statements.

Other dividends can be used in structured finance. Financial assets with known market value can be distributed as dividends; warrants are sometimes distributed in this way. For large companies with subsidiaries, dividends can take the form of shares in a subsidiary company. A common technique for "spinning off" a company from its parent is to distribute shares in the new company to the old company's shareholders. The new shares can then be traded independently.

Payout ratio
A dividend payout ratio characterizes how much of a company's earnings (or its cash flow) is paid out in the form of dividends.

Most often, the payout ratio is calculated based on dividends per share and earnings per share:

Payout ratio = $dividends per share⁄earnings per share$ × 100

A payout ratio greater than 100% means the company paid out more in dividends for the year than it earned.

Since earnings are an accountancy measure, they do not necessarily closely correspond to the actual cash flow of the company. Hence another way to determine the safety of a dividend is to replace earnings in the payout ratio by free cash flow. Free cash flow is the business's operating cash flow minus its capital expenditures. It's a measure of how much incoming cash is "free" to pay out to stockholders and/or to grow the business.

Free cash flow payout ratio = $dividends per share⁄free cash flow per share$ × 100

A free cash flow payout ratio greater than 100% means the company paid out more cash in dividends for the year than the "free" cash it took in.

Dividend dates
A dividend that is declared must be approved by a company's board of directors before it is paid. For public companies in the US, four dates are relevant regarding dividends: The position in the UK is very similar, except that the expression "in-dividend date" is not used.

Declaration date – the day the board of directors announces its intention to pay a dividend. On that day, a liability is created and the company records that liability on its books; it now owes the money to the shareholders.

In-dividend date – the last day, which is one trading day before the ex-dividend date, where shares are said to be cum dividend ('with [including] dividend'). That is, existing shareholders and anyone who buys the shares on this day will receive the dividend, and any shareholders who have sold the shares lose their right to the dividend. After this date the shares becomes ex dividend.

Ex-dividend date – the day on which shares bought and sold no longer come attached with the right to be paid the most recently declared dividend. In the United States and many European countries, it is typically one trading day before the record date. This is an important date for any company that has many shareholders, including those that trade on exchanges, to enable reconciliation of who is entitled to be paid the dividend. Existing shareholders will receive the dividend even if they sell the shares on or after that date, whereas anyone who bought the shares will not receive the dividend. It is relatively common for a share's price to decrease on the ex-dividend date by an amount roughly equal to the dividend being paid, which reflects the decrease in the company's assets resulting from the payment of the dividend.

Book closure date – when a company announces a dividend, it will also announce the date on which the company will temporarily close its books for share transfers, which is also usually the record date.

Record date – shareholders registered in the company's record as of the record date will be paid the dividend, while shareholders who are not registered as of this date will not receive the dividend. Registration in most countries is essentially automatic for shares purchased before the ex-dividend date.

Payment date – the day on which dividend cheques will actually be mailed to shareholders or the dividend amount credited to their bank account.

Dividend frequency
The dividend frequency is the number of dividend payments within a single business year. The most usual dividend frequencies are yearly, semi-annually, quarterly and monthly. Some common dividend frequencies are quarterly in the US, semi-annually in Japan, UK and Australia and annually in Germany.

Dividend-reinvestment
Some companies have dividend reinvestment plans, or DRIPs, not to be confused with scrips. DRIPs allow shareholders to use dividends to systematically buy small amounts of stock, usually with no commission and sometimes at a slight discount. In some cases, the shareholder might not need to pay taxes on these re-invested dividends, but in most cases they do. Utilizing a DRIP is a powerful investment tool because it takes advantage of both dollar cost averaging and compounding. Dollar cost averaging is the principle of investing a set amount of capital at recurring intervals. In this case, if the dividend is paid quarterly, then every quarter you are investing a set amount (the number of shares you own multiplied by the dividend per share). By doing this, you buy more shares when the price is low and fewer when the price is high. Additionally, the fractional shares that are purchased then begin paying dividends, compounding your investment and increasing the number of shares and total dividend earned each time a dividend distribution is made.

Law and government policy on dividends
Governments may adopt policies on dividend distribution for the protection of shareholders and the preservation of company viability, as well as treating dividends as a potential source of revenue.

Most countries impose a corporate tax on the profits made by a company. Many jurisdictions also impose a tax on dividends paid by a company to its shareholders (stockholders), but the tax treatment of a dividend income varies considerably between jurisdictions. The primary tax liability is that of the shareholder, although a tax obligation may also be imposed on the corporation in the form of a withholding tax. In some cases, the withholding tax may be the extent of the tax liability in relation to the dividend. A dividend tax is in addition to any tax imposed directly on the corporation on its profits.

A dividend paid by a company is not an expense of the company.

Australia and New Zealand
Australia and New Zealand have a dividend imputation system, wherein companies can attach franking credits or imputation credits to dividends. These franking credits represent the tax paid by the company upon its pre-tax profits. One dollar of company tax paid generates one franking credit. Companies can attach any proportion of franking up to a maximum amount that is calculated from the prevailing company tax rate: for each dollar of dividend paid, the maximum level of franking is the company tax rate divided by (1 − company tax rate). At the current 30% rate, this works out at 0.30 of a credit per 70 cents of dividend, or 42.857 cents per dollar of dividend. The shareholders who are able to use them, apply these credits against their income tax bills at a rate of a dollar per credit, thereby effectively eliminating the double taxation of company profits.

India
In India, a company declaring or distributing dividends is required to pay a Corporate Dividend Tax in addition to the tax levied on their income. The dividend received by the shareholders is then exempt in their hands. Dividend-paying firms in India fell from 24 percent in 2001 to almost 19 percent in 2009 before rising to 19 percent in 2010. However, dividend income over and above ₹1,000,000 attracts 10 percent dividend tax in the hands of the shareholder with effect from April 2016. Since the Budget 2020–2021, DDT has been abolished. Now, the Indian government taxes dividend income in the hands of investor according to income tax slab rates.

United States and Canada
The United States and Canada impose a lower tax rate on dividend income than ordinary income, on the assertion that company profits had already been taxed as corporate tax. In the United States, shareholders of corporations face double taxation - taxes on both corporate profits and taxes on distribution of dividends.

United Kingdom
The rules in Part 23 of the Companies Act 2006 (sections 829-853) govern the payment of dividends to shareholders. The Act refers in this section to "distribution", covering any kind of distribution of a company's assets to its members (with some exceptions), "whether in cash or otherwise". A company is only able to make a distribution out of its accumulated, realised profits, "so far as not previously utilised by distribution or capitalisation, less its accumulated, realised losses, so far as not previously written off in a reduction or reorganisation of capital duly made".

The United Kingdom government announced in 2018 that it was considering a review of the existing rules on dividend distribution following a consultation exercise on insolvency and corporate governance. The aim was to address concerns which had emerged where companies in financial distress were still able to distribute "significant dividends" to their shareholders. A requirement has been proposed under which the largest companies would be required to publish a distribution policy statement covering dividend distribution.

The law in England and Wales regarding dividend payment was clarified in 2018 by the England and Wales Court of Appeal in the case of Global Corporate Ltd v Hale [2018] EWCA Civ 2618. Certain payments made to a director/shareholder had been treated by the High Court as quantum meruit payments to Hale in his capacity as a company director but the Appeal Court reversed this judgment and treated the payments as dividends. At the time of payment they had been treated as "dividends" payable from an anticipated profit. The company subsequently went into liquidation; an attempt to recharacterise the payments as payments for services rendered was held to be unlawful.

Effect on stock price
After a stock goes ex-dividend (when a dividend has just been paid, so there is no anticipation of another imminent dividend payment), the stock price should drop.

To calculate the amount of the drop, the traditional method is to view the financial effects of the dividend from the perspective of the company. Since the company has paid say £x in dividends per share out of its cash account on the left hand side of the balance sheet, the equity account on the right side should decrease an equivalent amount. This means that a £x dividend should result in a £x drop in the share price.

A more accurate method of calculating the fall in price is to look at the share price and dividend from the after-tax perspective of a shareholder. The after-tax drop in the share price (or capital gain/loss) should be equivalent to the after-tax dividend. For example, if the tax of capital gains Tcg is 35%, and the tax on dividends Td is 15%, then a £1 dividend is equivalent to £0.85 of after-tax money. To get the same financial benefit from a, the after-tax capital loss value should equal £0.85. The pre-tax capital loss would be $£0.85⁄1 − T_{cg}$ = $£0.85⁄1 − 0.35$ = $£0.85⁄0.65$ = £1.31. In this case, a dividend of £1 has led to a larger drop in the share price of £1.31, because the tax rate on capital losses is higher than the dividend tax rate. However in many countries the stock market is dominated by institutions which pay no additional tax on dividends received (as opposed to tax on overall profits). If that is the case, then the share price should fall by the full amount of the dividend.

Finally, security analysis that does not take dividends into account may mute the decline in share price, for example in the case of a price–earnings ratio target that does not back out cash; or amplify the decline when comparing different periods.

The effect of a dividend payment on share price is an important reason why it can sometimes be desirable to exercise an American option early.

Criticism and analysis
Some believe company profits are best re-invested in the company with actions such as research and development, capital investment or expansion. Proponents of this view (and thus critics of dividends per se) suggest that an eagerness to return profits to shareholders may indicate the management having run out of good ideas for the future of the company. A counter-argument to this position came from Peter Lynch of Fidelity investments, who declared: "One strong argument in favor of companies that pay dividends is that companies that don’t pay dividends have a sorry history of blowing the money on a string of stupid diworseifications"; using his self-created term for diversification that results in worse effects, not better. Additionally, studies have demonstrated that companies that pay dividends have higher earnings growth, suggesting dividend payments may be evidence of confidence in earnings growth and sufficient profitability to fund future expansion. Benjamin Graham and David Dodd wrote in Securities Analysis (1934): "The prime purpose of a business corporation is to pay dividends to its owners. A successful company is one that can pay dividends regularly and presumably increase the rate as time goes on."

Other studies indicate that dividend-paying stocks tend to offer superior long-term performance relative to the overall market at least in developed economies, relative to a stock index such as the S&P 500 or Dow Jones Industrial Average or relative to stocks that do not pay dividends. Several explanations have been proposed for this outperformance such as dividends being associated with value stocks which are themselves associated with long-term outperformance; being more durable in crashes or bear markets;  being associated with profitable companies exhibiting high levels of free cashflow; and being associated with mature, unfashionable companies that are overlooked by many investors and thus an effective contrarian strategy. Assett managers at Tweedy, Browne and Capital Group have suggested dividends are an effective measure of a given company's overall financial status.

Shareholders in companies that pay little or no cash dividends can potentially reap the benefit of the company's profits when they sell their shareholding, or when a company is wound down and all assets liquidated and distributed amongst shareholders. However, data from professor Jeremy Siegel found stocks that do not pay dividends tend to have worse long-term performance, as a group, than the general stock market and also perform worse than dividend-paying stocks.

Tax implications
Taxation of dividends is often used as justification for retaining earnings, or for performing a stock buyback, in which the company buys back stock, thereby increasing the value of the stock left outstanding.

When dividends are paid, individual shareholders in many countries suffer from double taxation of those dividends: In many countries, the tax rate on dividend income is lower than for other forms of income to compensate for tax paid at the corporate level.
 * 1) the company pays income tax to the government when it earns any income, and then
 * 2) when the dividend is paid, the individual shareholder pays income tax on the dividend payment.

A capital gain should not be confused with a dividend. Generally, a capital gain occurs where a capital asset is sold for an amount greater than the amount of its cost at the time the investment was purchased. A dividend is a parsing out a share of the profits, and is taxed at the dividend tax rate. If there is an increase of value of stock, and a shareholder chooses to sell the stock, the shareholder will pay a tax on capital gains (often taxed at a lower rate than ordinary income). If a holder of the stock chooses to not participate in the buyback, the price of the holder's shares could rise (as well as it could fall), but the tax on these gains is delayed until the sale of the shares.

Certain types of specialized investment companies (such as a REIT in the U.S.) allow the shareholder to partially or fully avoid double taxation of dividends.

Cooperatives
Cooperative businesses may retain their earnings, or distribute part or all of them as dividends to their members. They distribute their dividends in proportion to their members' activity, instead of the value of members' shareholding. Therefore, co-op dividends are often treated as pre-tax expenses. In other words, local tax or accounting rules may treat a dividend as a form of customer rebate or a staff bonus to be deducted from turnover before profit (tax profit or operating profit) is calculated.

Consumers' cooperatives allocate dividends according to their members' trade with the co-op. For example, a credit union will pay a dividend to represent interest on a saver's deposit. A retail co-op store chain may return a percentage of a member's purchases from the co-op, in the form of cash, store credit, or equity. This type of dividend is sometimes known as a patronage dividend or patronage refund, as well as being informally named divi or divvy.

Producer cooperatives, such as worker cooperatives, allocate dividends according to their members' contribution, such as the hours they worked or their salary.

Trusts
In real estate investment trusts and royalty trusts, the distributions paid often will be consistently greater than the company earnings. This can be sustainable because the accounting earnings do not recognize any increasing value of real estate holdings and resource reserves. If there is no economic increase in the value of the company's assets then the excess distribution (or dividend) will be a return of capital and the book value of the company will have shrunk by an equal amount. This may result in capital gains which may be taxed differently from dividends representing distribution of earnings.

The distribution of profits by other forms of mutual organization also varies from that of joint-stock companies, though may not take the form of a dividend.

In the case of mutual insurance, for example, in the United States, a distribution of profits to holders of participating life policies is called a dividend. These profits are generated by the investment returns of the insurer's general account, in which premiums are invested and from which claims are paid. The participating dividend may be used to decrease premiums, or to increase the cash value of the policy. Some life policies pay nonparticipating dividends. As a contrasting example, in the United Kingdom, the surrender value of a with-profits policy is increased by a bonus, which also serves the purpose of distributing profits. Life insurance dividends and bonuses, while typical of mutual insurance, are also paid by some joint stock insurers.

Insurance dividend payments are not restricted to life policies. For example, general insurer State Farm Mutual Automobile Insurance Company can distribute dividends to its vehicle insurance policyholders.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Dividend


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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.

Precision is how close the measurements are to each other.

In other words: In the first, more common definition of "accuracy" above, the concept is independent of "precision", so a particular set of data can be said to be accurate, precise, both, or neither.
 * Precision is a description of random errors (a measure of statistical variability).
 * Accuracy has two definitions, per ISO:
 * 1) More commonly, a description of systematic errors (a measure of statistical bias of a given measure of central tendency). Low accuracy causes a difference between a result and a true value. This secondary measure is referred to as trueness by ISO.
 * 2) A combination of both types of observational error (random and systematic), so high accuracy requires both high precision and high trueness.

In simpler terms, given a statistical sample or set of data points from repeated measurements of the same quantity, the sample or set can be said to be accurate if their average is close to the true value of the quantity being measured, while the set can be said to be precise if their standard deviation is relatively small.

Common technical definition
In the fields of science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's true value. The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.

The field of statistics, where the interpretation of measurements plays a central role, prefers to use the terms bias and variability instead of accuracy and precision: bias is the amount of inaccuracy and variability is the amount of imprecision.

A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment. Eliminating the systematic error improves accuracy but does not change precision.

A measurement system is considered valid if it is both accurate and precise. Related terms include bias (non-random or directed effects caused by a factor or factors unrelated to the independent variable) and error (random variability).

The terminology is also applied to indirect measurements—that is, values obtained by a computational procedure from observed data.

In addition to accuracy and precision, measurements may also have a measurement resolution, which is the smallest change in the underlying physical quantity that produces a response in the measurement.

In numerical analysis, accuracy is also the nearness of a calculation to the true value; while precision is the resolution of the representation, typically defined by the number of decimal or binary digits.

In military terms, accuracy refers primarily to the accuracy of fire (justesse de tir), the precision of fire expressed by the closeness of a grouping of shots at and around the centre of the target.

Quantification
In industrial instrumentation, accuracy is the measurement tolerance, or transmission of the instrument and defines the limits of the errors made when the instrument is used in normal operating conditions.

Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the true value. The accuracy and precision of a measurement process is usually established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units (abbreviated SI from French: Système international d'unités) and maintained by national standards organizations such as the National Institute of Standards and Technology in the United States.

This also applies when measurements are repeated and averaged. In that case, the term standard error is properly applied: the precision of the average is equal to the known standard deviation of the process divided by the square root of the number of measurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements.

With regard to accuracy we can distinguish:
 * the difference between the mean of the measurements and the reference value, the bias. Establishing and correcting for bias is necessary for calibration.
 * the combined effect of that and precision.

A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Where not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m (the last significant place is the tenths place), while a recording of 843 m would imply a margin of error of 0.5 m (the last significant digits are the units).

A reading of 8,000 m, with trailing zeros and no decimal point, is ambiguous; the trailing zeros may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: 8.0 × 103 m indicates that the first zero is significant (hence a margin of 50 m) while 8.000 × 103 m indicates that all three zeros are significant, giving a margin of 0.5 m. Similarly, one can use a multiple of the basic measurement unit: 8.0 km is equivalent to 8.0 × 103 m. It indicates a margin of 0.05 km (50 m). However, reliance on this convention can lead to false precision errors when accepting data from sources that do not obey it. For example, a source reporting a number like 153,753 with precision +/- 5,000 looks like it has precision +/- 0.5. Under the convention it would have been rounded to 150,000.

Alternatively, in a scientific context, if it is desired to indicate the margin of error with more precision, one can use a notation such as 7.54398(23) × 10−10 m, meaning a range of between 7.54375 and 7.54421 × 10−10 m.

Precision includes: In engineering, precision is often taken as three times Standard Deviation of measurements taken, representing the range that 99.73% of measurements can occur within. For example, an ergonomist measuring the human body can be confident that 99.73% of their extracted measurements fall within ± 0.7 cm - if using the GRYPHON processing system - or ± 13 cm - if using unprocessed data.
 * repeatability — the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; and
 * reproducibility — the variation arising using the same measurement process among different instruments and operators, and over longer time periods.

A shift in the meaning of these terms appeared with the publication of the ISO 5725 series of standards in 1994, which is also reflected in the 2008 issue of the BIPM International Vocabulary of Metrology (VIM), items 2.13 and 2.14.

According to ISO 5725-1, the general term "accuracy" is used to describe the closeness of a measurement to the true value. When the term is applied to sets of measurements of the same measurand, it involves a component of random error and a component of systematic error. In this case trueness is the closeness of the mean of a set of measurement results to the actual (true) value and precision is the closeness of agreement among a set of results.

ISO 5725-1 and VIM also avoid the use of the term "bias", previously specified in BS 5497-1, because it has different connotations outside the fields of science and engineering, as in medicine and law.

In binary classification
Accuracy is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both true positives and true negatives) among the total number of cases examined. As such, it compares estimates of pre- and post-test probability. To make the context clear by the semantics, it is often referred to as the "Rand accuracy" or "Rand index". It is a parameter of the test. The formula for quantifying binary accuracy is: $$\text{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}$$ where $TP = True positive$; $FP = False positive$; $TN = True negative$; $FN = False negative$

In this context, the concepts of trueness and precision as defined by ISO 5725-1 are not applicable. One reason is that there is not a single “true value” of a quantity, but rather two possible true values for every case, while accuracy is an average across all cases and therefore takes into account both values. However, the term precision is used in this context to mean a different metric originating from the field of information retrieval (see below).

In multiclass classification
When computing accuracy in multiclass classification, accuracy is simply the fraction of correct classifications: $$\text{Accuracy}=\frac{\text{correct classifications}}{\text{all classifications}}$$ This is usually expressed as a percentage. For example, if a classifier makes ten predictions and nine of them are correct, the accuracy is 90%.

Accuracy is also called top-1 accuracy to distinguish it from top-5 accuracy, common in convolutional neural network evaluation. To evaluate top-5 accuracy, the classifier must provide relative likelihoods for each class. When these are sorted, a classification is considered correct if the correct classification falls anywhere within the top 5 predictions made by the network. Top-5 accuracy was popularized by the ImageNet challenge. It is usually higher than top-1 accuracy, as any correct predictions in the 2nd through 5th positions will not improve the top-1 score, but do improve the top-5 score.

In psychometrics and psychophysics
In psychometrics and psychophysics, the term accuracy is interchangeably used with validity and constant error. Precision is a synonym for reliability and variable error. The validity of a measurement instrument or psychological test is established through experiment or correlation with behavior. Reliability is established with a variety of statistical techniques, classically through an internal consistency test like Cronbach's alpha to ensure sets of related questions have related responses, and then comparison of those related question between reference and target population.

In logic simulation
In logic simulation, a common mistake in evaluation of accurate models is to compare a logic simulation model to a transistor circuit simulation model. This is a comparison of differences in precision, not accuracy. Precision is measured with respect to detail and accuracy is measured with respect to reality.

In information systems
Information retrieval systems, such as databases and web search engines, are evaluated by many different metrics, some of which are derived from the confusion matrix, which divides results into true positives (documents correctly retrieved), true negatives (documents correctly not retrieved), false positives (documents incorrectly retrieved), and false negatives (documents incorrectly not retrieved). Commonly used metrics include the notions of precision and recall. In this context, precision is defined as the fraction of retrieved documents which are relevant to the query (true positives divided by true+false positives), using a set of ground truth relevant results selected by humans. Recall is defined as the fraction of relevant documents retrieved compared to the total number of relevant documents (true positives divided by true positives+false negatives). Less commonly, the metric of accuracy is used, is defined as the total number of correct classifications (true positives plus true negatives) divided by the total number of documents.

None of these metrics take into account the ranking of results. Ranking is very important for web search engines because readers seldom go past the first page of results, and there are too many documents on the web to manually classify all of them as to whether they should be included or excluded from a given search. Adding a cutoff at a particular number of results takes ranking into account to some degree. The measure precision at k, for example, is a measure of precision looking only at the top ten (k=10) search results. More sophisticated metrics, such as discounted cumulative gain, take into account each individual ranking, and are more commonly used where this is important.

In cognitive systems
In cognitive systems, accuracy and precision is used to characterize and measure results of a cognitive process performed by biological or artificial entities where a cognitive process is a transformation of data, information, knowledge, or wisdom to a higher-valued form. (DIKW Pyramid) Sometimes, a cognitive process produces exactly the intended or desired output but sometimes produces output far from the intended or desired. Furthermore, repetitions of a cognitive process do not always produce the same output. Cognitive accuracy (CA) is the propensity of a cognitive process to produce the intended or desired output. Cognitive precision (CP) is the propensity of a cognitive process to produce only the intended or desired output. To measure augmented cognition in human/cog ensembles, where one or more humans work collaboratively with one or more cognitive systems (cogs), increases in cognitive accuracy and cognitive precision assist in measuring the degree of cognitive augmentation.

title: Accuracy and precision


text:
Cold-blooded

Cold-blooded is an informal term for one or more of a group of characteristics that determine an animal's thermophysiology. These include:
 * Ectothermy, controlling body temperature through external processes, such as by basking in the sun
 * Poikilothermy, the ability of an organism to function over a wide internal temperature range
 * Bradymetabolism, the ability to greatly alter metabolic rate in response to need; for example, animals that hibernate

Cold blooded and Coldblooded may also refer to:

Music

 * Cold Blooded (Rick James album), 1983
 * "Cold Blooded" (song), the title track from the album
 * "Coldblooded" (James Brown song), a 1974 funk song
 * Coldblooded (album), a 1974 funk album by The Bar-Kays
 * "Cold Blooded", a song by Damageplan from the 2004 album New Found Power
 * Cold Blooded (EP), a 2013 EP by Datsik

Films

 * Coldblooded (film), a 1995 American dark comedy/thriller
 * Cold Blooded (film), a 2012 Canadian crime thriller

Other

 * Cold-blooded, a person or act said to be lacking in conscience
 * Cold-blood (horse), a horse bred for strength and calmness, such as a draft horse
 * "Cold Blooded" (Grimm), an episode of the TV series Grimm

title: Cold-blooded


text:
Oldenburg (city)

Oldenburg (Northern Low Saxon: Ollnborg) is an independent city in the state of Lower Saxony, Germany. The city is officially named Oldenburg (Oldb) (Oldenburg in Oldenburg) to distinguish from Oldenburg in Holstein.

During the French annexation (1811–1813) in the wake of the Napoleonic war against Britain, it was also known as Le Vieux-Bourg in French. The city is at the rivers Hunte and Haaren, in the northwestern region between the cities of Bremen in the east and Groningen (Netherlands) in the west. It has a population of 170,000 (November 2019). Oldenburg is part of the Northwest Metropolitan Region, with 2.37 million people.

The city is the place of origin of the House of Oldenburg. Before the end of the German Empire (1918), it was the administrative centre and residence of the monarchs of Oldenburg.

History
Archaeological finds point to a settlement dating back to the 8th century. The first documentary evidence, in 1108, referenced Aldenburg in connection with Elimar I (also known as Egilmar I) who is now commonly seen as the first count of Oldenburg. The town gained importance due to its location at a ford of the navigable Hunte river. Oldenburg became the capital of the County of Oldenburg (later a Duchy (1774–1810), Grand Duchy (1815–1918), and Free State (1918–1946)), a small state in the shadow of the much more powerful Hanseatic city of Bremen.

In the 17th century Oldenburg was a wealthy town in a time of war and turmoil and its population and power grew considerably. In 1667, the town was struck by a disastrous plague epidemic and, shortly after, a fire destroyed Oldenburg. The Danish kings, who were also counts of Oldenburg at the time, had little interest in the condition of the town and it lost most of its former importance. In 1773, Danish rule ended. Only then were the destroyed buildings in the city rebuilt in a neoclassicist style. (German-speakers usually call the "neoclassicist style" of that period klassizistisch, while neoklassizistisch specifically refers to the classicist style of the early 20th century.)

After the German government announced the abdication of Emperor Wilhelm II (9 November 1918) following the exhaustion and defeat of the German Empire in World War I, monarchic rule ended in Oldenburg as well with the abdication of Grand Duke Frederick Augustus II of Oldenburg (Friedrich August II von Oldenburg) on 11 November 1918. The Grand Duchy now became the Free State of Oldenburg (Freistaat Oldenburg), with the city remaining the capital.

In the 1928 city elections, the Nazi Party received 9.8% of the vote, enough for a seat on the Oldenburg city council. In the September 1930 Oldenburg state elections, the Nazi Party's share of the vote rose to 27.3%, and on May 29, 1932, the Nazi Party received 48.4% in the state election, enough to put the Nazi party in charge of forming a state government and, significantly, making Oldenburg the first state in the country to put the Nazis in power based on electoral turnout. By that autumn, a campaign of Aryanization began, forcing the sale of formerly Jewish-owned properties at steep discounts.

In 1945, after World War II, the State of Oldenburg became part of the British zone of occupation. The British military government of the Oldenburg region resided in the city. Several displaced-persons camps were set up in the city that had suffered only 1.4% destruction during the bombing campaigns of World War II. About 42,000 refugees migrated into Oldenburg, which raised the number of residents to over 100,000. In 1946 the Free State of Oldenburg was dissolved and the area became the 'Administrative District' of Oldenburg (Verwaltungsbezirk Oldenburg) within the newly formed federal German state of Lower Saxony (Niedersachsen). The city was now capital of the district. In 1978 the district was dissolved and succeeded by the newly formed Weser-Ems administrative region (Regierungsbezirk Weser-Ems), again with the city as administrative capital. The state of Lower Saxony dissolved all of the Regierungsbezirke by the end of 2004 in the course of administrative reforms.

City government
Local elections take place every five years. The city council (Stadtrat) has 50 seats. The lord mayor (Oberbürgermeister) is elected directly by the citizens.

Transport
The city centre of Oldenburg is surrounded by a ring of freeways (autobahns) consisting of A 28, A 29 and A 293. Because of this, Oldenburg is connected to the nationwide network of federal autobahns, as well as to the international E-road network (German: Europastraßen).

Oldenburg Central Station, Oldenburg (Oldb) Hauptbahnhof, is at the intersection of the railway lines Norddeich Mole—Leer—Oldenburg—Bremen and Wilhelmshaven—Oldenburg—Osnabrück, with Intercity services to Berlin, Leipzig and Dresden and InterCityExpress services to Frankfurt and Munich.

Oldenburg is only about half an hour drive from Bremen Airport (about 50 km | 31 miles). Other international airports nearby are Hamburg Airport (160 km | 100 miles) and Hannover-Langenhagen Airport (170 km | 106 miles).

The small Hatten Airfield, (Flugplatz Oldenburg-Hatten ICAO airport code: EDWH), is located about 17 km south-west of Oldenburg. It serves to small aircraft (private planes, gliders, balloons, and helicopters). A flight training school is also located there, and small planes can be chartered. Scenic flights can be booked as well.

Oldenburg is connected to shipping through the Küstenkanal, a ship canal connecting the rivers Ems and Weser. With 1.6 million tons of goods annually, it is the most important non-coastal harbour in Lower Saxony.

Bicycles play a very important part in personal transport.

Agriculture
The city is surrounded by large agricultural areas, about 80% of which is grassland. There are farms near and even a few within city limits. Predominant agricultural activities of the region are the cultivation of livestock, especially dairy cows and other grazing animals, crops such as grains for food and animal feed, as well as asparagus, corn, and kale.

Industry
Sea salt production in the Oldenburg region has been used since the 15th century to supply the huge salt demand in the Baltic region. Peat extraction in the area continued for many centuries until it was replaced by coal mines.

Demographics
As of 31.12.2019 Oldenburg had 169,960 residents. 24.8% of the population were first or second generation immigrants.

Recurring cultural events

 * Kultursommer (summer of culture), series of free musical and other cultural events in the city centre during summer holiday season in July.
 * CSD Nordwest (Christopher Street Day) parade of the regional Lesbian, Gay, Bisexual, Transgender community in June, with up to 10,000 participants (since 1995).
 * Stadtfest, a three-day festival of the city centre in August/September, comprises gastronomical offerings and rock and pop music performances on various stages.
 * Oldenburg International Film Festival, a privately organised film festival in September, focused on independent film and film makers. The festival is funded through public subsidies and private sponsoring.
 * Kramermarkt, fun fair at the Weser-Ems Halle on ten days in September/October. The tradition of this annual volksfest dates back to the 17th century, when the Kramermarkt was a market event at the end of the harvest.
 * Oldenburger Kinder- und Jugendbuchmesse (KIBUM), an exhibition of new German language children's and youth literature, takes place over 11 days in November. A non-commercial fair organised by the city government in cooperation with the public library and the university library. In the course of the fair, a prize, the Kinder- und Jugendbuchpreis, is awarded to a debuting author or illustrator.

Points of interest

 * Core city centre, large pedestrianized shopping destination for the region.
 * Oldenburg State Theatre, oldest mainstream theatre in Oldenburg, first opened in 1833.
 * Schloss Oldenburg in the city centre, until 1918 residence of the monarchic rulers of Oldenburg, today a museum. A public park, the Schlossgarten, is nearby.
 * Weser-Ems Halle, exhibition and congress centre with outdoor fair area, located in Oldenburg Donnerschwee.
 * Small EWE Arena and Large EWE Arena, two sports and event halls located near the main railway station, opened in 2005 and 2013, and seating up to 4,000 and 6,852 visitors respectively. The large arena is also home to the EWE Baskets Oldenburg basketball club.

Lutheran community
Oldenburg is the seat of administration and bishop of the Evangelical Lutheran Church in Oldenburg, whose preaching venue is the St Lamberti Church.

Jewish community
The history of the Jewish community of Oldenburg dates back to the 14th century. Towards and during the 19th century, the Jews in Oldenburg were always around 1% of the total population, and by that time had acquired their own synagogue, cemetery and school. Most of them were merchants and businessmen. On 1938 Kristallnacht, the town men were led to Sachsenhausen concentration camp, among them Leo Trepp, the community Rabbi who survived and later became an honorary citizen of Oldenburg and honored by a street named after him. Since 1981 an annual commemoration walk (Erinnerungsgang) has been held by Oldenburg citizens in memory of the deportation of the Oldenburg Jews on November 10, 1938. Those who remained after 1938 emigrated to Canada, USA, United Kingdom, Holland or Mandatory Palestine.

After World War II, a group of survivors returned to the city and maintained a small community until it was dissolved during the 1970s. Nevertheless, due to Jewish emigration from the former USSR to Germany in the 1990s, a community of about 340 people is now maintaining its own synagogue, cemetery and other facilities. The old Jewish cemetery, which is no longer active after the opening of a new one, was desecrated twice in 2011 and 2013.

Print

 * Nordwest-Zeitung (NWZ) Oldenburg-based daily newspaper, also provides local editions in neighbouring counties
 * Free weekly newspapers delivered to households, mainly for ads and inserts: Hunte-Report (Wednesdays+Sundays), Sonntagszeitung (Sundays).
 * Diabolo free weekly city magazine / listings magazine
 * Mox free biweekly event listings magazine (from the same publisher as Diabolo)
 * Alhambra-Zeitung bimonthly leftist, anti-fascist magazine
 * Oldenburger Stachel local alternative magazine (discontinued)
 * Oldenburgische Wirtschaft monthly magazine of the Oldenburg Chamber of Industry and Commerce (Industrie- und Handelskammer)

Radio and television

 * Oldenburg Eins non-commercial public-access cable TV and radio station (live streams available online)
 * Norddeutscher Rundfunk (NDR), public TV and radio broadcaster (part of the ARD), maintains a regional studio in Oldenburg.
 * Radio FFN, commercial radio broadcaster, maintains a regional studio located in the NWZ building.

Online

 * Nordwest-Zeitung TV Local video news clips published by the Nordwest-Zeitung

Tertiary education
There are two public universities in Oldenburg:

 * The Carl von Ossietzky University of Oldenburg was founded in 1973 based on a previous college for teacher training, the Pädagogische Hochschule Oldenburg, which had a history in Oldenburg dating back to 1793. The university was officially named after Carl von Ossietzky in 1991. As of 2014, it has almost 13,746 students, a scientific staff of 1,130, as well as 964 technical and administrative staff. A new faculty of medicine and health sciences was established in 2012 as part of the newly founded European Medical School Oldenburg-Groningen, a cooperation with the University of Groningen (Netherlands) and local hospitals.
 * The Jade University of Applied Sciences (Jade-Hochschule) The former Fachhochschule Oldenburg (until 1999) was founded in 1971, a merger of the previous engineering academy with the nautical college in Elsfleth. Oldenburg already had a history of construction engineering training dating back to 1882. Starting in 2000, the Fachhochschule had been part of multiple re-organisations involving several UAS (Fachhochschule) in the northwestern region. A relaunch under the name Jade-Hochschule took place in 2009 (previously: Fachhochschule Oldenburg/Ostfriesland/Wilhelmshaven). The Jade-Hochschule now comprises branches in three towns: Oldenburg, Elsfleth, and Wilhelmshaven. Based in Oldenburg are the departments of architecture, construction engineering and construction management, geodesy, as well as the institute of hearing aid technology and audiology. There are about 2,000 students in the Oldenburg branch. (The Elsfleth branch offers bachelor's degree courses in nautical science, international logistics, and harbour management. The Wilhelmshaven branch offers courses in engineering, business management, and media management.)

Privately managed institutions of higher education:

 * Founded in 2004, the IBS IT & Business School Oldenburg (former Berufsakademie Oldenburg), a college of cooperative education, offers a B.Sc. degree course in business informatics and a B.A. degree course in business studies. The dual-system course combines practical vocational training at one of the partnering local companies with periods of academic studies.
 * The Private Fachhochschule für Wirtschaft und Technik, a regional college of cooperative education, maintains a branch in Oldenburg offering bachelor's degree courses with integrated vocational training in electrical engineering and mechatronics.

Other:

 * The Oldenburg branch of the Lower Saxony police academy (Polizeiakademie Niedersachsen) maintains a study facility in Oldenburg preparing candidates for a career in higher-middle-level or higher-level police service.

Primary and secondary education

 * Gymnasium Graf-Anton-Guenther School
 * Wirtschaftsgymnasium Oldenburg
 * Cäcilienschule Oldenburg
 * Liebfrauenschule Oldenburg
 * Herbartgymnasium Oldenburg
 * Altes Gymnasium Oldenburg
 * Neues Gymnasium Oldenburg
 * Gymnasium Eversten
 * IGS Flötenteich
 * Helene Lange Schule Oldenburg (IGS)
 * Realschule Hochheider Weg
 * Real- und Hauptschule Osternburg
 * Realschule Ofenerdiek
 * Kath. Grundschule Lerigauweg

Sports
Oldenburg hosted the 2007 Fistball World Championship.

It has two football teams, VfB Oldenburg and VfL Oldenburg, who also have a handball section of the same name.

Moreover, Oldenburg is home to the basketball team EWE Baskets Oldenburg.

Twin towns – sister cities
Oldenburg is twinned with:

 * Høje-Taastrup, Denmark (1978)
 * 🇫🇷 Cholet, France (1985)
 * Groningen, Netherlands (1989)
 * 🇷🇺 Makhachkala, Russia (1989)
 * 🇩🇪 Rügen (district), Germany (1990)
 * 🇮🇱 Mateh Asher, Israel (1996)
 * Kingston upon Thames, England, United Kingdom (2010)
 * Buffalo City, South Africa (2012)
 * 🇨🇳 Qingdao, China (2014)
 * 🇨🇳 Xi'an, China (2017)

Public servants and public thinking

 * Anna of Oldenburg (1501–1575), a Countess consort of East Frisia, spouse of Count Enno II of East Frisia.
 * Princess Cecilia of Sweden (1807–1844), Princess of Sweden, died locally
 * Amalia of Oldenburg (1818–1875), a Bavarian princess and Queen of Greece from 1836 to 1862.
 * Karl von Wedel (1842–1919), a Prussian general and diplomat
 * Helene Lange (1848–1930), politician, educator and suffragist
 * Rudolf Heinze (1865–1928), jurist and politician; vice-chancellor of Germany, 1920/21
 * Karl Jaspers (1883–1969), philosopher, psychiatrist and writer
 * Otto Schultze (1884–1966), Generaladmiral with the Kriegsmarine during World War II
 * Peter Suhrkamp (1891–1959), publisher and founder of the Suhrkamp Verlag
 * Otto Suhr (1894–1957), politician and Governing Mayor of Berlin 1955/57
 * Wilhelm Gideon (1898–1977), Nazi SS commandant of the Gross-Rosen concentration camp
 * Hermann Ehlers (1904–1954), politician (CDU), Bundestag President, was a local landlord and died locally
 * Hermann Behrends (1907–1948), Nazi SS officer executed for war crimes
 * Heinz Rökker (1920–2018), WWII fighter pilot
 * Ulrike Meinhof (1934–1976), journalist, far-left activist and co-founder of the Red Army Faction
 * Bernd Althusmann (born 1966), politician (CDU)
 * Thyra von Westernhagen (born 1973), Hanoverian princess by marriage
 * Hasnain Kazim (born 1974), journalist

Arts

 * Martin Zaagmolen (buried 1669), Dutch painter
 * Sophie Löwe (1815–1866), opera soprano.
 * Christian Griepenkerl (1839–1916), painter and professor at the Academy of Fine Arts Vienna
 * August Jerndorff (1846–1906), a Danish painter, known for his portraits.
 * Ellen Plessow (1891 – 1967), a German actress in films from 1922 to 1957
 * Erna Schlüter (1904–1969), operatic dramatic soprano
 * Jürgen Goslar (born 1927), actor and director
 * Thomas Schmidt-Kowalski (1949–2013), composer
 * Klaus Modick (born 1951), author and literary translator
 * Rena Niehaus (born 1954), film actress
 * Thomas Schütte (born 1954), sculptor and draftsman
 * Heiko Daxl (1957–2012), media artist and curator
 * Andrea Clausen (born 1959), stage actress, member of the Burgtheater ensemble
 * Sarah Nemtsov (née Reuter, born 1980), composer
 * Klaas Heufer-Umlauf (born 1983), TV host, producer, actor and singer.

Science & business

 * Otto Mencke (1644–1707), philosopher and scientist.
 * Arp Schnitger (1648–1719), organ builder
 * Wilhelm Heinrich Schüßler (1821–1898), medical doctor and naturopath
 * Isaac Friedlander (1823–1878), American wheat broker and California land speculator
 * Lothar Meyer (1830–1895), chemist, studied here
 * Reinhard Schlichting (1835–1897), American manufacturer and politician in Wisconsin
 * August Brauer (1863–1917), zoologist, studied deep-sea ichthyology
 * Carl Ramsauer (1879–1955), professor and research physicist, discovered the Ramsauer–Townsend effect.
 * Walter Behrmann (1882–1955), geographer; introduced a cylindrical map projection "Behrmann projection"
 * Hans Günther Aach (1919–1999), botanist
 * Manfred Milinski (born 1950), biologist and formerly a director of the Max Planck Institute
 * Thomas Reiter (born 1958), retired European astronaut, Air Force Brigadier General, lives locally

Sport

 * Uta Frommater (born 1948), swimmer, team bronze medallist at the 1968 Summer Olympics
 * Karsten Baumann (born 1969), football player and manager, played 389 games
 * Hans-Jörg Butt (born 1974), footballer, played 479 games and 4 for Germany
 * Oliver Köhrmann (born 1976), handball player
 * Florian Bruns (born 1979), football coach and former player who played 369 games
 * Johannes Bitter (born 1982), handball player, goalkeeper for Germany
 * Thomas Plößel (born 1988), sailor, twice team bronze medallist at the 2016 and 2020 Summer Olympics.

title: Oldenburg (city)


text:
Talk:History of the Church of Jesus Christ of Latter-day Saints

Add a "Post-Modern Era" section? (1995 to present)
The "Modern" section appears very clunky and I believe it should be split. Covering world events, policies, politics, etc. from 1890 through the 20th century seems over-eager. Recommend a new section be created starting with President Hinckley (1995 to present) to represent the Post-Modern Era. Further, the LDS Church seems to be undergoing significant flux, beginning 10 or so years ago, which needs separate attention from, say, LDS multiculturalism. Deaddebate (talk) 00:02, 15 November 2016 (UTC)

 * I agree with separating out a section beginning sometime in the late 20th century. But I'd like to have a discussion about (1) what it should be called, and (2) where the dividing line should be.
 * On the first point, although the church is certainly postmodern in the sense that it has become fully integrated into the institutions of late capitalism, I'm wondering if this way of looking at it is a bit too academic for the average reader. I don't really have a good alternative in mind, though.
 * On the second point, I'm wondering if a better dividing line separating the two eras might be 1978 rather than 1995. The hear 1978, of course, was when the church ended its official segregationist policies. Soon thereafter, the church began redefining itself in terms of the culture wars, beginning with opposition to the ERA and then, in the 1990s, opposition to marriage equality. I also think that certain other events in the 1980s and 1990s fit more in the current era than in the former, such as
 * in 1981 and 1982 when it began focusing on the Book of Mormon as its main holy book, the 1990 revisions to the temple ceremony, the crackdown on dissidents culminating in the 1993 September Six trials, and various structural reforms such as the elimination of state seventies in 1986, the Second Quorum of the Seventy in 1984, the use of emeritus status, etc. CO GDEN  00:25, 8 February 2023 (UTC)

Capital on The in the title
By itself, it is "The Church of", but when something else is prefixed "the" is no longer the first word and orthographically it loses the capital. Anyone have a problem with me changing it? deisenbe (talk) 23:49, 15 March 2020 (UTC)
 * I do. A big problem. The common name of the Church is "The Church of Jesus Christ of Latter-day Saints." So whenever referring to the full name thereof, "The" is always capitalized, per this policy, and this policy, among others. If there are references to what "the church" does in articles where the full name is not being used, then neither of the two words in such references should be capitalized. And all of that is further detailed in the relevant manual of style that Wikipedia uses for all such articles. If I am minsunderstanding your question, please feel free to clarify your question. Thanks. --Jgstokes (talk) 21:36, 16 March 2020 (UTC)

Title capitalization
The title of this article, along with a provision at MOS:LDS, violates MOS:THEINST, a site-wide guideline which trumps WP:LOCALCONSENSUS. Please participate in the discussion at. Thanks. InfiniteNexus (talk) 04:56, 27 September 2022 (UTC)

Is editing this article part of a student assignment?
I've noticed many edits by brand new Wikipedia users lately. Is editing this article part of a student assignment? If so, it might be helpful to read the information at WP:Student assignments. Bahooka (talk) 19:14, 27 November 2023 (UTC)

 * I don't think this is part of a student assignment. Based on the automated tags on the edits, it looks like this page landed on the "Newcomer task: copyedit" list auto-generated by some algorithm. It likely happened when the "Tone" tag got added here. I am finding the signal-to-noise ratio on these edits to be extremely low. Removing the tag would probably get the article off that list, if the low SNR has become problematic. FAQ #2 at might also indicate another route. --FyzixFighter (talk) 20:36, 27 November 2023 (UTC)
 * yeah, I don't think FAQ #2 would actually lead to anything useful unfortunately. Adding Template:No newcomer task might be the appropriate action, given the low SNR. Would anyone disagree with this template being added? --FyzixFighter (talk) 20:44, 27 November 2023 (UTC)
 * @FyzixFighter, no objections here. User:Jgstokes (talk)—We can disagree without becoming disagreeable. 22:17, 27 November 2023 (UTC)
 * @FyzixFighter, thanks for adding the template. Bahooka (talk) 06:20, 28 November 2023 (UTC)


text:
Bloomsbury Group

The Bloomsbury Group or Bloomsbury Set was a group of associated English writers, intellectuals, philosophers and artists in the early 20th century. Among the people involved in the group were Virginia Woolf, John Maynard Keynes, E. M. Forster, Vanessa Bell, and Lytton Strachey. Their works and outlook deeply influenced literature, aesthetics, criticism, and economics, as well as modern attitudes towards feminism, pacifism, and sexuality.

Although popularly thought of as a formal group, it was a loose collective of friends and relatives closely associated with the University of Cambridge for the men and King's College London for the women, who at one point lived, worked or studied together near Bloomsbury, London. According to Ian Ousby, "although its members denied being a group in any formal sense, they were united by an abiding belief in the importance of the arts." The historian C. J. Coventry, resurrecting an older argument by Raymond Williams, disputes the existence of the group and the extent of its impact, describing it as "curio" for those interested in Keynes and Woolf.

Origins

All male members of the Bloomsbury Group, except Duncan Grant, were educated at Cambridge (either at Trinity or King's College). Most of them, except Clive Bell and the Stephen brothers, were members of "the exclusive Cambridge society, the 'Apostles'". At Trinity in 1899 Lytton Strachey, Leonard Woolf, Saxon Sydney-Turner and Clive Bell became good friends with Thoby Stephen, and it was through Thoby and Adrian Stephen's sisters Vanessa and Virginia that the men met the women of Bloomsbury when they came down to London.

In 1905 Vanessa began the "Friday Club" and Thoby ran "Thursday Evenings", which became the basis for the Bloomsbury Group, which to some was really "Cambridge in London". Thoby's premature death in 1906 brought them more firmly together and they became what is now known as the "Old Bloomsbury" group who met in earnest beginning in 1912. In the 1920s and 1930s the group shifted when the original members died and the next generation had reached adulthood.

The Bloomsbury Group, mostly from upper middle-class professional families, formed part of "an intellectual aristocracy which could trace itself back to the Clapham Sect". It was an informal network of an influential group of artists, art critics, writers and an economist, many of whom lived in the West Central 1 district of London known as Bloomsbury. They were "spiritually" similar to the Clapham group who supported its members' careers: "The Bloomsberries promoted one another's work and careers just as the original Claphamites did, as well as the intervening generations of their grandparents and parents."

A historical feature of these friends and relations is that their close relationships all pre-dated their fame as writers, artists, and thinkers.

Members
The group had ten core members:

 * Clive Bell, art critic
 * Vanessa Bell, post-impressionist painter
 * E. M. Forster, fiction writer
 * Roger Fry, art critic and post-impressionist painter
 * Duncan Grant, post-impressionist painter
 * John Maynard Keynes, economist
 * Desmond MacCarthy, literary journalist
 * Lytton Strachey, biographer
 * Leonard Woolf, essayist and non-fiction writer
 * Virginia Woolf, fiction writer and essayist

In addition to these ten, Leonard Woolf, in the 1960s, listed as 'Old Bloomsbury' Adrian and Karin Stephen, Saxon Sydney-Turner, and Molly MacCarthy, with Julian Bell, Quentin Bell and Angelica Bell, and David Garnett as later additions". Except for Forster, who published three novels before the highly successful Howards End in 1910, the group were late developers.

There were stable marriages and varied and complicated affairs among the individual members. Lytton Strachey and his cousin and lover Duncan Grant became close friends of the Stephen sisters, Vanessa Bell and Virginia Woolf. Duncan Grant had affairs with siblings Vanessa Bell and Adrian Stephen, as well as David Garnett, Maynard Keynes, and James Strachey. Clive Bell married Vanessa in 1907, and Leonard Woolf returned from the Ceylon Civil Service to marry Virginia in 1912. Cambridge Apostle friendships brought into the group Desmond MacCarthy, his wife Molly, and E. M. Forster.

The group met not only in their homes in Bloomsbury, central London, but also at countryside retreats. There are two significant ones near Lewes in Sussex: Charleston Farmhouse, where Vanessa Bell and Duncan Grant moved in 1916, and Monk's House (now owned by the National Trust), in Rodmell, owned by Virginia and Leonard Woolf from 1919.

Others
Much about Bloomsbury appears to be controversial, including its membership and name: indeed, some would maintain that "the three words 'the Bloomsbury group' have been so much used as to have become almost unusable".

Close friends, brothers, sisters, and even sometimes partners of the friends were not necessarily members of Bloomsbury: Keynes's wife Lydia Lopokova was only reluctantly accepted into the group, and there were certainly "writers who were at some time close friends of Virginia Woolf, but who were distinctly not 'Bloomsbury': T. S. Eliot, Katherine Mansfield, Hugh Walpole". Another is Vita Sackville-West, who became "Hogarth Press's best-selling author". Members cited in "other lists might include Ottoline Morrell, or Dora Carrington, or James and Alix Strachey".

Shared ideas
The lives and works of the group members show an overlapping, interconnected similarity of ideas and attitudes that helped to keep the friends and relatives together, reflecting in large part the influence of G. E. Moore: "the essence of what Bloomsbury drew from Moore is contained in his statement that 'one's prime objects in life were love, the creation and enjoyment of aesthetic experience and the pursuit of knowledge'".

Philosophy and ethics
Through the Apostles they also encountered the analytic philosophers G. E. Moore and Bertrand Russell who were revolutionizing British philosophy at the start of the 20th century. Distinguishing between ends and means was a commonplace of ethics, but what made Moore's Principia Ethica (1903) so important for the philosophical basis of Bloomsbury thought was Moore's conception of intrinsic worth as distinct from instrumental value. As with the distinction between love (an intrinsic state) and monogamy (a behavior, i.e. instrumental), Moore's differentiation between intrinsic and instrumental value allowed the Bloomsburies to maintain an ethical high-ground based on intrinsic merit, independent of, and without reference to, the consequences of their actions. For Moore, intrinsic value depended on an indeterminable intuition of good and a concept of complex states of mind whose worth as a whole was not proportionate to the sum of its parts. For both Moore and Bloomsbury, the greatest ethic goods were "the importance of personal relationships and the private life", as well as aesthetic appreciation: "art for art's sake".

Rejection of bourgeois habits
Bloomsbury reacted against current upper class English social rituals, "the bourgeois habits ... the conventions of Victorian life" with their emphasis on public achievement, in favour of a more informal and private focus on personal relationships and individual pleasure. E. M. Forster for example approved of "the decay of smartness and fashion as factors, and the growth of the idea of enjoyment", and asserted that "if I had to choose between betraying my country and betraying my friend, I hope I should have the guts to betray my country".

The Group "believed in pleasure ... They tried to get the maximum of pleasure out of their personal relations. If this meant triangles or more complicated geometric figures, well then, one accepted that too". Yet at the same time, they shared a sophisticated, civilized, and highly articulated ideal of pleasure. As Virginia Woolf put it, their "triumph is in having worked out a view of life which was not by any means corrupt or sinister or merely intellectual; rather ascetic and austere indeed; which still holds, and keeps them dining together, and staying together, after 20 years".

Politics
Politically, Bloomsbury held mainly left-liberal stances (opposed to militarism, for example); but its "clubs and meetings were not activist, like the political organisations to which many of Bloomsbury's members also belonged", and they would be criticised for that by their 1930s successors, who by contrast were "heavily touched by the politics which Bloomsbury had rejected".

The campaign for women's suffrage added to the controversial nature of Bloomsbury, as Virginia Woolf represented the group in the fictional The Years and Night and Day works about the suffrage movement.

Art
Roger Fry joined the group in 1910. His post-impressionist exhibitions of 1910 and 1912 involved Bloomsbury in a second revolution following on the Cambridge philosophical one. This time the Bloomsbury painters were much involved and influenced. Fry and other Bloomsbury artists rejected the traditional distinction between fine and decorative art.

These "Bloomsbury assumptions" are reflected in members' criticisms of materialistic realism in painting and fiction, influenced above all by Clive Bell's "concept of 'Significant Form', which separated and elevated the concept of form above content in works of art": it has been suggested that, with their "focus on form ...Bell's ideas have come to stand in for, perhaps too much so, the aesthetic principles of the Bloomsbury Group".

The establishment's hostility to post-impressionism made Bloomsbury controversial, and controversial they have remained. Clive Bell polemicized post-impressionism in his widely read book Art (1914), basing his aesthetics partly on Roger Fry's art criticism and G. E. Moore's moral philosophy; and as the war came he argued that "in these days of storm and darkness, it seemed right that at the shrine of civilization - in Bloomsbury, I mean - the lamp should be tended assiduously".

World War I
Old Bloomsbury's development was affected, along with much of modernist culture, by the First World War: "the small world of Bloomsbury was later said by some on its outskirts to have been irretrievably shattered", though in fact its friendships "survived the upheavals and dislocations of war, in many ways were even strengthened by them". Most but not all of them were conscientious objectors. Politically, the members of Bloomsbury had liberal and socialist leanings.

Though the war dispersed Old Bloomsbury, the individuals continued to develop their careers. E. M. Forster followed his successful novels with Maurice which he could not publish because it treated homosexuality untragically. In 1915, Virginia Woolf brought out her first novel, The Voyage Out; and in 1917 the Woolfs founded their Hogarth Press, which would publish T. S. Eliot, Katherine Mansfield, and many others including Virginia herself along with the standard English translations of Freud. Then in 1918 Lytton Strachey published his critique of Victorianism in the shape of four ironic biographies in Eminent Victorians, which added to the arguments about Bloomsbury that continue to this day, and "brought him the triumph he had always longed for ... The book was a sensation".

The following year came J. M. Keynes's influential attack on the Versailles Peace Treaty: The Economic Consequences of the Peace established Maynard as a Neo-Classical economist and political economist of international eminence.

Later Bloomsbury
The 1920s were in a number of ways the blooming of Bloomsbury. Virginia Woolf was writing and publishing her most widely read modernist novels and essays, and E. M. Forster completed A Passage to India, a highly regarded novel on British imperialism in India. Forster wrote no more novels but he became one of England's most influential essayists. Duncan Grant, and then Vanessa Bell, had single-artist exhibitions. Lytton Strachey wrote his biographies of two queens, Queen Victoria (1921) and Elizabeth and Essex: A Tragic History (1928). Desmond MacCarthy and Leonard Woolf engaged in friendly rivalry as literary editors, respectively of the New Statesman and The Nation and Athenaeum, thus fuelling animosities that saw Bloomsbury dominating the cultural scene. Roger Fry wrote and lectured widely on art; meanwhile, Clive Bell applied Bloomsbury values to his book Civilization (1928), which Leonard Woolf saw as limited and elitist, describing Bell as a "wonderful organiser of intellectual greyhound racing tracks".

In the darkening 1930s, Bloomsbury began to die: "Bloomsbury itself was hardly any longer a focus". A year after publishing a collection of brief lives, Portraits in Miniature (1931), Lytton Strachey died; shortly afterwards Carrington shot herself. Roger Fry died in 1934. Vanessa and Clive's eldest son, Julian Bell, was killed in 1937 during the Spanish Civil War. Virginia Woolf wrote Fry's biography, but with the coming of war again her mental instability recurred, and she drowned herself in 1941. In the previous decade she had become one of the century's most famous feminist writers with three more novels, and a series of essays including the moving late memoir "A Sketch of the Past". It was also in the 1930s that Desmond MacCarthy became perhaps the most widely read—and heard—literary critic with his columns in The Sunday Times and his broadcasts for the BBC. John Maynard Keynes's The General Theory of Employment, Interest, and Money (1936) made him one of the century's most influential economists. He died in 1946 after being much involved in monetary negotiations with the United States.

The diversity yet collectivity of Later Bloomsbury's ideas and achievements can be summed up in a series of credos that were made in 1938, the year of the Munich Agreement. Virginia Woolf published her radical feminist polemic Three Guineas that shocked some of her fellow members, including Keynes who had enjoyed the gentler A Room of One's Own (1929). Keynes read his My Early Beliefs to The Memoir Club. Clive Bell published an appeasement pamphlet (he later supported the war), and E. M. Forster wrote an early version of his famous essay "What I Believe" with its choice of personal relations over patriotism: his quiet assertion in the face of the increasingly totalitarian claims of both left and right that "personal relations ... love and loyalty to an individual can run counter to the claims of the State".

Memoir Club
In March 1920 Molly MacCarthy began the Memoir Club to help Desmond and herself write their memoirs; and also "for their friends to regroup after the war (with the proviso that they should always tell the truth)". It met until 1956 or 1964.

Criticism
Early complaints focused on a perceived cliquiness: "on personal mannerisms—the favourite phrases ('ex-quisitely civilized', and 'How simply too extraordinary!'), the incredulous, weirdly emphasised Strachey voice". After World War I, as the members of the Group "began to be famous, the execration increased, and the caricature of an idle, snobbish and self-congratulatory rentier class, promoting its own brand of high culture began to take shape": as Forster self-mockingly put it, "In came the nice fat dividends, up rose the lofty thoughts".

The growing threats of the 1930s brought new criticism from younger writers of "what the last lot had done (Bloomsbury, Modernism, Eliot) in favour of what they thought of as urgent hard-hitting realism"; while "Wyndham Lewis's The Apes of God, which called Bloomsbury élitist, corrupt and talentless, caused a stir" of its own. The most telling criticism, however, came perhaps from within the Group's own ranks, when on the eve of war Keynes gave a "nostalgic and disillusioned account of the pure sweet air of G. E. Moore, that belief in undisturbed individualism, that Utopianism based on a belief in human reasonableness and decency, that refusal to accept the idea of civilisation as 'a thin and precarious crust' ... Keynes's fond, elegiac repudiation of his "early beliefs", in the light of current affairs ("We completely misunderstood human nature, including our own")".

In his book on the background of the Cambridge spies, Andrew Sinclair wrote about the Bloomsbury group: "rarely in the field of human endeavour has so much been written about so few who achieved so little". American philosopher Martha Nussbaum was quoted in 1999 as saying "I don't like anything that sets itself up as an in-group or an elite, whether it is the Bloomsbury group or Derrida".

Raymond Williams saw Bloomsbury as the invention of an ageing and lonely Leonard Woolf, seeking to lift himself and his friends from obscurity. To Williams, the only two so-called "members" of any significance in their respective fields were Keynes and Virginia Woolf. Williams unfavourably compared the Bloomsbury Group to the Pre-Raphaelite Brotherhood and Arts and Crafts movement, finding that the older groups were more radical and consequential.

title: Bloomsbury Group