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Talk:Loss of significance

Untitled
The page reads:

'Examples of ill-conditioned calculations are:

 * Subtracting two almost equal numbers
 * Division by almost zero

In these ill-conditioned calculations you get errors which tend to blow up 	dramatically. '

Division by a small non-zero number does not result in loss of significance. It may (depending on the numerator) cause numerical overflow, as may multiplication, addition, or subtraction. This is a very different and separate problem from loss of significance.

Subtraction of almost equal numbers is the sole source of loss of significance.

The formula given for loss of significance gives undefined results for x < y. Is "assuming x > y" missed out, or should it be abs(1 - y / x)?

I think this page is a good place to mention cathastropic cancelation. This is already mentioned once by someone else but might have been unclear and incomplete. 18:44, 13 March 2007 Ehdr (Talk | contribs) m (Mentioned "cancellation") Citations maybe usable from "What Every Computer Scientist Should Know About Floating-Point Arithmetic", by David Goldberg

84.41.135.110 17:25, 4 July 2007 (UTC)

Kahan algorithm
Hi, what about Kahan algorithm.? —Preceding unsigned comment added by 149.156.67.102 (talk) 18:59, 14 October 2009 (UTC)

Sujit Kadam, Ohio University, USA
Hello Everyone,

This is Sujit Kadam, pursuing Masters in Mathematics - Computational track at Ohio University, USA. I would like to propose few changes to this page. I think the section "A better algorithm" is bit confusing and needs some changes regarding examples and formula used. The formula used for 'x1' and 'x2' in this section are correct if the coefficient 'b' is negative in the quadratic equation. In our example, the quadratic equation used has positive coefficient 'b'. Hence, in the formula it gives - b + sqrt(b*b -4ac) = - 200 + sqrt(200*200 - 4*1* − 0.000015)

This actually results into subtraction operation and loss of significant digits.

If 'b' was negative (say -200) in the example then the formula would result into an addition operation. Hence, we would be able to avoid loss of significant digits.

-b + sqrt(b*b - 4ac) = -(-200) + sqrt(-200*-200 - 4*1*− 0.000015)

My proposed changes for this section:
A better algorithm

A better algorithm for solving quadratic equations is based on two observations: that one solution is always accurate when the other is not, and that given one solution of the quadratic, the other is easy to find.

If
 * $$\begin{alignat}{3}

& x_1  && = \frac{-b + \sqrt{b^2 - 4ac}}{2a}               \qquad & \text{(1)} \\ \end{alignat}$$

and
 * $$\begin{alignat}{3}

& x_2  && = \frac{2c}{-b + \sqrt{b^2 - 4ac}}               \qquad & \text{(2)} \\ \end{alignat}$$

then we have the identity (one of Vi%C3%A8te%27s formulas for a second degree polynomial)

 * $$x_1 x_2 = c / a \ $$.

The above formulas (1) and (2) work perfectly for a quadratic equation whose coefficient 'b' is negative (b < 0). If 'b' is negative then '-b' in the formulas get converted to a positive value as -(-b) is equal to 'b'. Hence, we can avoid subtraction and loss of significant digits caused by it. But if the coefficient 'b' is positive then we need to use a different set of formulas. The second set of formulas that are valid for finding roots when coefficient 'b' is positive are mentioned below.

 * $$\begin{alignat}{3}

& x_1  && = \frac{-b - \sqrt{b^2 - 4ac}}{2a}                \qquad & \text{(3)} \\ \end{alignat}$$ and

 * $$\begin{alignat}{3}

& x_2  && = \frac{2c}{-b - \sqrt{b^2 - 4ac}}                \qquad & \text{(4)} \\ \end{alignat}$$

In the above formulas (3) and (4) when 'b' is positive the formula converts it to negative value as -(+b) is equal to -b. Now, as per the formulas '-b' is subtracted by square root of (b*b - 4ac) so basically it's an addition operation. In our example, coefficient 'b' of quadratic equation is positive. Hence, we need to use the second set of formulas i.e. Formula (3) and (4).

The algorithm is as follows. Use the quadratic formula to find the solution of greater magnitude, which does not suffer from loss of precision. Then use this identity to calculate the other root. Since no subtraction is involved, no loss of precision occurs.

Applying this algorithm to our problem, and using 10-digit floating-point arithmetic, the solution of greater magnitude, as before, is $$x_1 = -200.00000005.$$ The other solution is then

 * $$ x_2 = c / (-200.00000005) = 0.000000075,$$

which is accurate.

 * I like the overall idea here...but it's somewhat convoluted. You can get the Viete formula x_1*x_2 = c/a pretty easily (just multiply out the expression (x- x_1)(x-x_2) and equate it to the monic polynomial x^2 + b/a x + c/a).  So you don't need to write out all those formulae above if your intent was simply to use the Viete formula thing.  --DudeOnTheStreet (talk) 07:33, 4 May 2011 (UTC)

More detail in the instability section
I think it would be beneficial to include more detail in the example discussing instability of the quadratic formula. First, the quadratic formula certainly does not always provide an inaccurate root, so it would be useful to include why this formula may not always produce an accurate result, instead of citing just one example. This could be a simple change, for instance, just a statement about how when c is very small, loss of significance can occur in either of the root calculations, depending on the sign of b. In addition, I think the example would be more effective with more explanation. I think it is important to show what is so special about this particular polynomial that causes loss of significance to occur. Simply stating "subtraction" as a reason for loss of significance might be misleading for some readers, as the accurate root was calculated using -b minus a similar number. —Preceding unsigned comment added by Vv148408 (talk • contribs) 07:19, 24 September 2010 (UTC)
 * Done. But is it really any better?  I don't buy the 'explanation', myself, but perhaps others will find it more illuminating than I do!

 * I personally think that the effect is caused by any calculation needing more significant figures than we have available for the computational task; but I have no reference to back me up. My impressions were formed by many years of practical computation, and the need to engineer effective algorithms for arbitrary-precision floating point on a fixed-point computer architecture.  But that is original research, and thus not encyclopaedic.

 * yoyo (talk) 06:05, 5 July 2012 (UTC)

Change in the Example
My name is Kyle D, and I am an undergraduate, also at Ohio University, studying Electrical Engineering. I am proposing a change to the example on the page.

Problems with the example:

1. A machine does not store Floating Point decimal digits, except for Binary Coded Decimal calculations, which is rare.

Decimal works for the purpose of the example, but is not reflective of the actual computation.

If we used a binary number: It would be easier on everyone's eyes. (0.12345678901234567890 is hard to look at.) A reader familiar with binary would get a better understanding of the actual computation. A reader unfamiliar with binary would still understand the example as a decimal example.

2. 10 digits is a lot to think about. It's only an example.

I think a 4 bit FP processor should work for the purposes of this example.

The current decimal example should also be included later in the page, to demonstrate the phenomenon in Decimal numbers, and with more digits.

I think these changes would make the example a lot easier to understand, for both binary and decimal readers. Here is the proposed example:

For the purposes of this example, if the reader is not familiar with binary numbers, bits can be considered as decimal digits.

Consider the real binary number

1.001111111

A floating-point representation of this number on a machine that keeps 4 floating-point bits would be

1.001,

which is fairly close — the difference is very small in comparison with either of the two numbers.

Now perform the calculation

1.001111111 − 1

The real answer, accurate to 7 significant bits, is

0.001111111

However, on the 4-bit floating-point machine, the calculation yields

1.001 − 1.000 = 0.001

Whereas the original numbers are significant in all of the first 4 bits, their floating-point difference is only accurate in its first nonzero bit. This amounts to loss of information.

This phenomenon can be extended to any size Floating Point number. Instead of 4 significant bits, an IEEE standard single precision floating point number has 23 significant bits and 1 sign bit.

Additionally, the phenomenon can also be demonstrated with decimal numbers. The following example demonstrates Loss of Significance for a Decimal floating point data type with 10 significant digits:

Consider the real decimal number

0.1234567891234567890.

A floating-point representation of this number on a machine that keeps 10 floating-point digits would be

0.1234567891,

which is fairly close — the difference is very small in comparison with either of the two numbers.

Now perform the calculation

0.1234567891234567890 − 0.1234567890.

The real answer, accurate to 10 digits, is

0.0000000001234567890.

However, on the 10-digit floating-point machine, the calculation yields

0.1234567891 − 0.1234567890 = 0.0000000001.

Whereas the original numbers are accurate in all of the first (most significant) 10 digits, their floating-point difference is only accurate in its first nonzero digit. This amounts to loss of information.

'Workarounds It is possible to do computations using an exact fractional representation of rational numbers and keep all significant digits, but this is often prohibitively slower than floating-point arithmetic. Furthermore, it usually only postpones the problem: What if the data is accurate to only 10 digits? The same effect will occur.

One of the most important parts of numerical analysis is to avoid or minimize loss of significance in calculations. If the underlying problem is well-posed, there should be a stable algorithm for solving it. The art is in finding a stable algorithm. —Preceding unsigned comment added by Kyle.drerup (talk • contribs) 14:56, 24 September 2010 (UTC)

Possible error
"If the underlying problem is well-posed, there should be a stable algorithm for solving it. The art is in finding it." Why is that? It seems like wishful thinking rather than a mathematical fact. — Preceding unsigned comment added by 181.28.64.87 (talk) 08:19, 12 December 2012 (UTC)

Rump polynomial
... should be added, I suppose? --Cognoscent (talk) 12:34, 1 October 2013 (UTC)

title: Talk:Loss of significance


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La Bruyère, Belgium

La Bruyère ( or ; Les Brouyires) is a municipality of Wallonia located in the province of Namur, Belgium.

The municipality is composed of the following districts: Bovesse, Émines, Meux, Rhisnes, Saint-Denis-Bovesse, Villers-lez-Heest, and Warisoulx. Rhisnes is the administrative seat of the municipality.

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

title: La Bruyère, Belgium


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Mettet

Mettet (Metet) is a municipality of Wallonia located in the province of Namur, Belgium.

On 1 January 2006 Mettet had 11,977 inhabitants. The total area is 116.78 km², giving a population density of 103 inhabitants per km².

The municipality consists of the following districts: Biesme, Biesmerée, Ermeton-sur-Biert, Furnaux, Graux, Mettet, Oret, Saint-Gérard, and Stave.

Circuit Jules Tacheny
In Mettet there is a race track, Circuit Jules Tacheny Mettet, for motorbikes and cars.

Notable people

 * Alain Crépin (1954–), conductor and musician

title: Mettet


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Gembloux

Gembloux (Djiblou; Gembloers, ) is a city and municipality of Wallonia located in the province of Namur, Belgium.

On 1 January 2006, the municipality had 21,964 inhabitants. The total area is 95.86 km2, yielding a population density of 229 inhabitants per km2. The mayor, who was elected on 8 October 2006, is Benoît Dispa.

The municipality consists of the following districts: Beuzet, Bossière, Bothey, Corroy-le-Château, Ernage, Gembloux, Grand-Leez, Grand-Manil, Isnes, Lonzée, Mazy, and Sauvenière.

This city is well known for its Agricultural University and for its cutlery. The university is housed in the historical Abbey of Gembloux, which dates from the tenth century.

Gembloux's belfry is a UNESCO World Heritage Site, as part of the Belfries of Belgium and France site, in recognition of its architecture and testimony to the rise in municipal power in the area.

History
The central city grew around the Gembloux Abbey, founded in the tenth century. In the vicinity of the city, in 1578, the Battle of Gembloux was fought during the Eighty Years' War. In May 1940, the Battle of Hannut and the Battle of the Gembloux Gap took place nearby, tank battles during the larger Battle of France.

Notable inhabitants

 * The Marquess of Trazegnies d'Ittre
 * Christophe Szpajdel, sketch artist (born 1970)

Twin towns
Gembloux is twinned with
 * 🇫🇷 - Épinal, France : since 1974
 * - Loughborough, United Kingdom : since 1993
 * 🇬🇷 - Skyros, Greece : since 1994
 * 🇪🇸 - Aller, Spain : since 2007

title: Gembloux


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Namur

Namur (Namen ; Nameur) is a city and municipality in Wallonia, Belgium. It is the capital both of the province of Namur and of Wallonia, hosting the Parliament of Wallonia, the Government of Wallonia and its administration.

Namur stands at the confluence of the rivers Sambre and Meuse and straddles three different regions – Hesbaye to the north, Condroz to the south-east, and Entre-Sambre-et-Meuse to the south-west. The city of Charleroi is located to the west. The language spoken is French.

The municipality consists of the following sub-municipalities: Beez, Belgrade, Boninne, Bouge, Champion, Cognelée, Daussoulx, Dave, Erpent, Flawinne, Gelbressée, Jambes, Lives-sur-Meuse, Loyers, Malonne, Marche-les-Dames, Namur proper, Naninne, Saint-Servais, Saint-Marc, Suarlée, Temploux, Vedrin, Wépion, and Wierde.

Early history

The town began as an important trading settlement in Celtic times, straddling east–west and north–south trade routes across the Ardennes. The Romans established a presence after Julius Caesar defeated the local Aduatuci tribe.

Namur came to prominence during the early Middle Ages when the Merovingians built a castle or citadel on the rocky spur overlooking the town at the confluence of the two rivers. In the 10th century, it became a county in its own right. The town developed somewhat unevenly, as the counts of Namur could only build on the north bank of the Meuse - the south bank was owned by the bishops of Liège and developed more slowly into the town of Jambes (now effectively a suburb of Namur). In 1262, Namur fell into the hands of the Count of Flanders, and was purchased by Duke Philip the Good of Burgundy in 1421.

After Namur became part of the Spanish Netherlands in the 1640s, its citadel was considerably strengthened. Louis XIV of France invaded in 1692, capturing the town and annexing it to France. His renowned military engineer Vauban rebuilt the citadel. French control was short-lived, as William III of Orange-Nassau captured Namur only three years later in 1695 during the War of the Grand Alliance. Under the Barrier Treaty of 1709, the Dutch gained the right to garrison Namur, although the subsequent Treaty of Utrecht of 1713 gave control of the formerly Spanish Netherlands to the Austrian House of Habsburg. Thus, although the Austrians ruled the town, the citadel was controlled by the Dutch. It was rebuilt again under their tenure.

General Jean-Baptiste Cyrus de Valence's column laid siege to the city on 19 November 1792 during the War of the First Coalition and, after 12 days, the city surrendered on 1 December and its whole garrison of 3,000 men was taken prisoner. France invaded the region again in 1794, annexing Namur and imposing a repressive regime. After the defeat of Napoleon in 1815, the Congress of Vienna incorporated what is now Belgium into the United Kingdom of the Netherlands. Belgium broke away from the Netherlands in 1830 following the Belgian Revolution, and Namur continued to be a major garrison town under the new government. The citadel was rebuilt yet again in 1887.

20th and 21st centuries
In World War I, Namur was a major target of the German invasion of Belgium in 1914, which sought to use the Meuse valley as a route into France. On August 21, 1914, the Germans bombarded the town of Namur without warning. Several people were killed. Despite being billed as virtually impregnable, the citadel fell after only three days' fighting and the town was occupied by the Germans for the rest of the war. Namur fared little better in World War II; it was in the front lines of both the Battle of the Ardennes in 1940 and the Battle of the Bulge in 1944. The town suffered heavy damage in both wars.

Namur continued to host the Belgian Army's paratroopers until their departure in 1977.

After the creation of the Walloon Region, Namur was chosen as the seat of its executive and parliament. In 1986, Namur was officially declared capital of Wallonia. Its position as regional capital was confirmed by the Parliament of Wallonia in 2010.

Economy
Namur is an important commercial and industrial centre, located on the Walloon industrial backbone, the Sambre and Meuse valley. It produces machinery, leather goods, metals and porcelain. Its railway station is also an important junction situated on the north–south line between Brussels and Luxembourg City, and the east–west line between Lille and Liège. River barge traffic passes through the middle of the city along the Meuse.

Culture and sights
Namur has taken on a new role as the capital of the federal region of Wallonia. Its location at the head of the Ardennes has also made it a popular tourist centre, with a casino located in its southern district on the left bank of the Meuse.

The town's most prominent sight is the Citadel of Namur, now demilitarised and open to the public. Namur also has a distinctive 18th-century cathedral dedicated to Saint Aubain and a belfry classified by UNESCO as part of the Belfries of Belgium and France which are listed as a World Heritage Site.

The Couvent des Soeurs de Notre-Dame used to contain masterpieces of Mosan art by Hugo d'Oignies, currently presented in the Musée des Arts Anciens (Rue de Fer). Elsewhere there is an archeological museum and a museum dedicated to Félicien Rops.

An odd Namurois custom is the joust on stilts (dating back to 1411) practiced by the stiltwalkers of Namur. The annual Combat de l'Échasse d'Or (Fight for the Golden Stilt), held on the third Sunday in September, is the most important joust of the year. Two teams, the Mélans and the Avresses, dress in medieval clothes while standing on stilts and do battle in one of the town's principal squares. Since 2021, Namur stilt jousts are registered on the UNESCO Representative List of the Intangible Cultural Heritage of Humanity.

Namur possesses a distinguished university, the University of Namur (previously known as the Facultés universitaires Notre-Dame de la Paix, FUNDP), founded in 1831. The University of Louvain (UCLouvain) also has several facilities in the city through its UCLouvain Namur University Hospital (CHU UCLouvain Namur), the provinces' largest employer.

Since 1986 Namur has been home to the Namur International Festival of French-Speaking Film. A jazz (Nam'in'Jazz) and a rock (Verdur Rock) festival both take place in Namur annually.

The local football team is named Union Royale Namur.

The local baseball team is named Namur Angels.

The annual Namur cyclo-cross race, part of the UCI Cyclo-cross World Cup, takes place on the hills around the citadel. From 1950 to 2007, the Belgian Motocross Grand Prix was held every first weekend in August on a challenging race circuit around the citadel. Between 20,000 and 50,000 spectators gathered to support the Belgian motocross stars such as; Joël Robert, Roger De Coster, Eric Geboers & Stefan Everts. The Namur circuit achieved iconic status and was known as the Monaco of the Motocross World Championships in reference to the prestigious Formula One automobile race.

Sights near Namur include Maredsous Abbey, Floreffe Abbey, and Annevoie Castle with its surrounding Jardins d'Annevoie.

Twin towns — sister cities
Namur is twinned with:

 * 🇮🇩 Bandung, Indonesia
 * 🇨🇦 Quebec City, Quebec, Canada
 * 🇷🇸 Subotica, Serbia
 * 🇫🇷 Bourg-en-Bresse, France
 * 🇯🇵 Ōgaki, Gifu Prefecture, Japan
 * 🇺🇸 Belmont, California, United States
 * 🇺🇸 Lafayette, Louisiana, United States
 * 🇮🇹 Empoli, Toscana, Italy
 * 🇷🇴 Cluj-Napoca, Cluj, Romania
 * 🇸🇪 Tierp, Sweden
 * Pristina, Kosovo

Notable people

 * Rémy Belvaux (1966–2006), actor, film director and screenwriter
 * Julie Billiart Canonized saint and Foundress of the Sisters of Notre Dame de Namur, died in Namur in 1816.
 * Francy Boland (1929–2005), jazz pianist and arranger
 * Cécile de France (born 1975), actress
 * Count Edouard de Woelmont, Belgian Canon.
 * Olivier Gourmet (born 1963), actor
 * Ludivine Henrion (born 1984), cyclist
 * Friedrich Hermann Otto, Prince of Hohenzollern-Hechingen (1776–1838), Prince of Hohenzollern-Hechingen
 * Pierre Jonckheer (born 1951), politician, Member of European Parliament 1999-2009
 * Denzel Jubitana (born 1999), Football Player
 * Philippe Kirsch (born 1947), Canadian jurist and diplomat, former president of the ICC
 * Louis Leloir (1911–1992), Benedictine monk and orientalist
 * Benjamin Lessennes (born 1999), racing driver
 * Jeanne Maubourg (1873-1953), opera singer, radio actress in Canada
 * Henri Michaux (1899–1984), French-speaking poet and painter
 * Benoît Poelvoorde (born 1964), actor and comedian
 * Jacques François Rosart (1714–1777), engraver of metal type
 * Christophe Rochus (born 1978), tennis player
 * Olivier Rochus (born 1981), tennis player
 * Félicien Rops (1833–1898), graphic artist and illustrator (Symbolism)
 * Thierry Zéno (born 1950), director and screenwriter
 * Raphaël Liégeois (born 1988), biomedical engineer and Belgian astronaut

title: Namur


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Ohey

Ohey (Ohè) is a municipality of Wallonia located in the province of Namur, Belgium.

On 1 January 2006 the municipality had 4,283 inhabitants. The total area is 56.62 km2, giving a population density of 76 /km2.

The municipality is composed of the following districts: Évelette, Goesnes, Haillot, Jallet, Ohey, Perwez.

Also located in Ohey are the villages of Bois-Dame-Agis, Ève, Filée, La Bouchaille, Libois, Résimont, Saint-Mort and Tahier.

title: Ohey


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Profondeville

Profondeville (Parfondveye) is a municipality of Wallonia located in the province of Namur, Belgium.

On January 1, 2016, Profondeville had a total population of 12,117. The total area of the municipality is 50.34 km² and the population density is 240.70 inhabitants per km².

The original municipality of Profondeville was expanded, during the post-1974 fusion of the Belgian municipalities, with the addition of the ancienne communes of Arbre, Bois-de-Villers, Lesve, Lustin, Rivière and the Lakisse area from the southeast of the newly-adjoining municipality of Floreffe.

Twin towns

 * 🇫🇷 Roquebrune-Cap-Martin, France

title: Profondeville


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Sambreville

Sambreville (Sambveye) is a municipality and since March 12, 2024 a Belgian city of Wallonia located in the province of Namur, Belgium.

On January 1, 2006, Sambreville had a total population of 26,949. The total area is 34.20 km2 which gives a population density of 788 pd/km2.

Villages and towns
The municipality was created in 1977, as part of the post-1974 fusion of the Belgian municipalities, bringing together the ancienne communes (now towns and villages) of:
 * Arsimont
 * Auvelais
 * Falisolle
 * Keumiée
 * Moignelée
 * Tamines
 * Velaine

Tamines is associated with the Rape of Belgium during World War I. At least 384 townspeople were massacred, including women and children.

Twin towns

 * 🇮🇹 Gessopalena, Italy

title: Sambreville


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Sombreffe

Sombreffe (Sombrefe) is a municipality of Wallonia located in the province of Namur, Belgium.

On 1 January 2014 the municipality had 8,226 inhabitants. The total area is 35.78 km2, giving a population density of 230 inhabitants per km2.

The municipality is composed of the following districts: Boignée, Ligny, Sombreffe and Tongrinne.

title: Sombreffe


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Cerfontaine

Cerfontaine may refer to:

 * Cerfontaine, Belgium, a municipality located in the province of Namur
 * Cerfontaine, Nord, a commune of the Nord département in northern France
 * Gerlach Cerfontaine, CEO of Schiphol Group, the 100% shareholder of Schiphol Airport in the Netherlands

title: Cerfontaine


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Couvin

Couvin (Couvén) is a city and municipality of Wallonia located in the province of Namur, Belgium.

On 1 January 2018 the municipality had 13,782 inhabitants. Couvin is the second largest municipality of Belgium by surface area, after Tournai. The total area is 206.93 km2, giving a population density of 67 PD/km2.

The municipality consists of the following districts: Aublain, Boussu-en-Fagne, Brûly, Brûly-de-Pesche, Couvin, Cul-des-Sarts, Dailly, Frasnes-lez-Couvin, Gonrieux, Mariembourg, Pesche, Petigny, Petite-Chapelle, and Presgaux.

Transport
Couvin railway station provides the town with a rail link direct to Charleroi. The line terminates here; the next station is Mariembourg.

Tourism
There are a number of sites of interest to tourists in the municipality.

One end of the Chemin de Fer à vapeur des Trois Vallées heritage railway is at Mariembourg. The Brasserie des Fagnes brewery is also situated there.

Caves in the area include the Trou de l’Abîme and the Neptune Caves.

Wolfsschlucht I, known locally as "Hitler's Bunker", is located at Brûly-de-Pesche. It was used as one of Adolf Hitler's military headquarters during the Battle of France.

title: Couvin


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Doische

Doische (Dweche) is a municipality of Wallonia located in the province of Namur, Belgium.

On 1 January 2006 the municipality had 2,846 inhabitants. The total area is 84.02 km2, giving a population density of 34 inhabitants per km2.

The municipality consists of the following districts: Doische, Gimnée, Gochenée, Matagne-la-Grande, Matagne-la-Petite, Niverlée, Romerée, Soulme, Vaucelles, and Vodelée.

Notable residents

 * Philippe Buchez (1796-1865), historian, sociologist, and Utopian socialist politician
 * Daniel Petit (1948- ), Canadian politician for the New Democratic Party

title: Doische


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Florennes

Florennes (Florene) is a municipality of Wallonia located in the province of Namur, Belgium. As of 1 January 2006, Florennes has a total population of 10,754. The total area is 133.55 km2 which gives a population density of 81 inhabitants per km2.

The municipality consists of the following districts: Corenne, Flavion, Florennes, Hanzinelle, Hanzinne, Hemptinne, Morialmé, Morville, Rosée, Saint-Aubin and Thy-le-Bauduin.

Florennes hosts Florennes Air Base, a Belgian military airfield which is the home base for F-16 Fighting Falcon jets.

The first week-end of every July, Florennes is a large festival due to the folk walk with a couple of thousand valorous walkers.

Cyclists Firmin Lambot, who won the Tour de France in 1919 and in 1922 and Léon Scieur, who won the Tour in 1921, were born in Florennes.

The village was formerly the site of Florennes Abbey, dissolved during the French Revolution and since entirely demolished.

title: Florennes


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Philippeville

Philippeville (Flipveye) is a city and municipality of Wallonia located in the province of Namur, Belgium. The Philippeville municipality includes the former municipalities of Fagnolle, Franchimont, Jamagne, Jamiolle, Merlemont, Neuville, Omezée, Roly, Romedenne, Samart, Sart-en-Fagne, Sautour, Surice, Villers-en-Fagne, Villers-le-Gambon, and Vodecée.

The foundation of Philippeville
At the beginning of the 16th century, the Philippeville region was on the boundary between Charles V’s Burgundian Netherlands and Francis I’s France. Fighting around Philippeville did not start, however, until 1554, after Henry II had succeeded his father on the throne. This area was ideal for an attack as it was covered with forests, sparsely populated and divided among the County of Hainaut, that of Namur, by now part of Burgundy, and the Prince-Bishopric of Liège. The medieval forts in the area were taken and pillaged one after the other. The fortress of Mariembourg, close to Couvin, and the town of Givet soon fell to the French. In 1555, Charles V's new commander, William the Silent, established a new fort in the village of Echerennes, a village known since the 9th century. He garrisoned his troops there as soon as the fort was completed, barely four months after the start of construction.

In 1556, Charles V named his new fortress Philippeville in honour of his son, Philip II of Spain, who would succeed him in the Netherlands – and on the city – the following year.

From 1557 to present
In 1659, the Treaty of the Pyrenees stopped the Franco-Spanish War (1635–59) and most frontier cities became French, until Napoleon’s defeat at Waterloo. Philippeville itself was one of the final French fortresses to surrender following Waterloo in 1815. There was then a brief Dutch interlude until the Belgian Revolution in 1830.

A treaty drafted in London on 15 November 1831, which the Netherlands refused to sign, was followed by the Treaty of London (1839), which created the Kingdom of Belgium. Part of the terms of the treaty required the Philippeville's fortifications, along with those of Menin, Ath, Mons and Mariembourg, to be dismantled. Philippeville's defensive walls were dismantled in 1856 under the reign of King Leopold I, in accordance with the terms of the treaty, having been declared superfluous on account of Belgium's enforced neutrality, and have been replaced by the wide boulevards that circle the city today.

Sights

 * Ten kilometres of underground passages dating from the foundation of the city can still be explored under Philippeville. Some sections are open to tourists.

Born in Philippeville

 * Jérôme-Joseph de Momigny, a noted composer and musicologist of the classical/romantic period, was born here on 20 January 1762.

Twin cities

 * 🇫🇷: Saulieu

title: Philippeville


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Viroinval

Viroinval (Virwinvå) is a municipality of Wallonia located in the province of Namur, Belgium.

On January 1, 2006, Viroinval had a total population of 5,680. The total area is 120.90 km2 which gives a population density of 47 inhabitants per km2.

The municipality consists of the following districts: Dourbes, Mazée, Le Mesnil, Nismes, Oignies-en-Thiérache, Olloy-sur-Viroin, Treignes, Vierves-sur-Viroin.

The name Viroinval, Viroin (River) Valley, was chosen for the municipality that was formed by fusing eight villages, in 1977.

Attractions

name="SteamTrainLine"> The latter village has a relevant museum.
 * From 1995 to 2004, Viroinval was the location of the geographical centre of the European Union, at coordinates 50.00917°N, 4.66639°W in Oignies-en-Thiérache, and a monument there records that finding. On May 1, 2004, the EU expanded from fifteen states to twenty-five, and the geographical centre of the union moved eastwards to the village of Kleinmaischeid, Rhineland-Palatinate, Germany. On 1 January 2007 it shifted even further south-eastwards.
 * The tourist steam train line Mariembourg–Treignes has most of its stations in villages of Viroinval: Nismes, Olloy-sur-Viroin, Vierves-sur-Viroin, and Treignes.<ref

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Walcourt

Walcourt (Walcoû) is a city and municipality of Wallonia located in the province of Namur, Belgium.

On 1 January 2006, the municipality had 17,516 inhabitants. The total area is 123.18 km2, giving a population density of 142 inhabitants per km2.

The municipality consists of the following districts: Berzée, Castillon, Chastrès, Clermont, Fontenelle, Fraire, Gourdinne, Laneffe, Pry, Rognée, Somzée, Tarcienne, Thy-le-Château, Vogenée, Walcourt, Yves-Gomezée.

History
The Basilica of Saint Maternus is a Gothic minor basilica, founded in 1026. It contains one of the oldest Madonnas in Western Christianity. In 1689, the Battle of Walcourt was fought here between French troops and the Grand Alliance during the Nine Years' War.

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Like a Virgin (album)

Like a Virgin is the second studio album by American singer and songwriter Madonna, released on November 12, 1984, by Sire Records. Following the success of her 1983 self-titled debut album, Madonna was eager to start working on its follow-up. She selected Nile Rodgers to produce the album due to his work on Let's Dance (1983) by David Bowie, which she was a fan of. To ensure it be exactly as she envisioned it, Madonna chose all the songs for the album: She penned six of her own, five of which were co-written with former boyfriend and collaborator Stephen Bray, and six written by other artists. Recording sessions took place at Power Station Studio in New York City. Rodgers enlisted the help of his former Chic bandmates Bernard Edwards and Tony Thompson.

Upon release Like a Virgin received mixed reviews from music critics: Rodgers' production received praise, but Madonna's vocals were criticized. It became Madonna's first number one album on the Billboard 200, as well as the first female album to sell over five million copies in the United States. The Recording Industry Association of America (RIAA) later certified it diamond for shipment of ten million units. Overseas, it reached number one in Germany, the Netherlands, New Zealand, Spain, Italy and the United Kingdom. With sales of over 21 million copies worldwide, Like a Virgin remains one of the best-selling albums of all time. Four official singles were released from the album ―all reached the top five of the Billboard Hot 100, with the title track becoming Madonna's first number one, and "Material Girl" reaching number two.

The album was promoted on Madonna's first concert tour, the Virgin Tour of 1985, which only visited cities in North America. Like a Virgin has been noted as the album that made Madonna a superstar, as well as the one that proved she was not a one-hit wonder. On top of that, the younger female population began emulating the singer's fashion style. In 2023, Like a Virgin was selected for preservation in the United States' National Recording Registry by the Library of Congress due to it being considered "culturally, historically, or aesthetically significant".

Background
Following the release of her 1983 self-titled debut album, and hit singles like "Holiday", "Lucky Star" and "Borderline", Madonna became, according to author Craig Rosen, "one of the most exciting new artists of the 1980s". Despite this, the singer wasn't entirely pleased with how her first album had turned out, and was eager to star working on its follow-up. Of her upcoming second album, she told British magazine NME: "The production won't be so slick, because where Reggie [Lucas] and Mtume come from is a whole different school. I want a sound that's mine", and even hinted at working with a British producer. To ensure the album be exactly as she envisioned it, Madonna requested her label Sire Records that she be allowed to produce herself, a request that was immediately denied.

Angry with the label, the singer would publicly vent during interviews, and refer to her bosses as a "hierarchy of old men [...] a chauvinistic environment to be working in because I’m treated like this sexy little girl". The executives at Sire decided to allow Madonna to work with any producer of her choice. She picked Nile Rodgers, co-founder of American disco band Chic, and main producer of David Bowie's Let's Dance (1983), one of her favorite albums of the time. Rodgers had previously met Madonna after attending one of her gigs at a New York City nightclub, and was impressed with her stage presence; "I kept thinking to myself, 'Damn, is she a star', but she wasn't at that time. I always wanted to work with her and this seemed like the perfect opportunity". However, when the time came he initially hesitated, as he had been warned by several people that Madonna was a "totally self-centered bitch" and a "pain in the ass to work with". When the two actually met, Rodgers quickly changed his mind and said the singer was great and a "true professional". Madonna, by her part, "couldn't believe that the record company actually gave me the money so that I could work with [Rodgers]".

Development
Madonna wanted Like a Virgin to be "stronger" than her debut, hence she chose all the songs herself. She had been penning songs and creating demos with former boyfriend and collaborator Stephen Bray since early 1984. When Madonna first met with Rodgers, she allegedly told him, "if you don’t love these songs we can’t work together", to which the producer responded: "I don’t love them now, but I will when I’ve finished working on them!". Around the time they began working on the album, Billy Steinberg and Tom Kelly were pitching songs to artists. Steinberg had begun a new relationship and came up with the lyrics to "Like a Virgin". He brought the track to Kelly, who created the music and, together, recorded a demo tape. Kelly then met with Warner Bros. A&R executive Michael Ostin and had him listen to the demo; Ostin, who was set to meet Madonna the next day, thought the song was "perfect" for her. Madonna "loved" the song right away, but Rodgers wasn't convinced. He felt it was "really queer", and that the line like a virgin wasn't a "terrific" hook, nor an "all-time catch phrase". Four days later, Rodgers realized that the song was still stuck in his head; "[It] grew on me. I really started to like it. [...] [I] handed [my] apology [to Madonna] and said, 'you know... if it's so catchy, it must be something. So let's do it". Written by Peter Brown and Robert Rans for another Warner Bros. singer, "Material Girl" was also presented to Madonna by Ostin.

Ostin also suggested that the singer covered Rose Royce's "Love Don't Live Here Anymore" (1978). He was driving into work and heard the song on the radio; "I called [Nile and Madonna], they were in the studio. I said, 'I have an idea. You know the old Rose Royce record, 'Love Don't Live Here Anymore'? Why don't you try and record a version of it?". Both Rodgers and Madonna were reluctant, but ultimately decided that a ballad could be a good move to bring "diversity" to the album. The final song to be created for Like a Virgin was "Dress You Up". Rodgers had previously asked songwriters Andrea LaRusso and Peggy Stanziale to write a song for Madonna in the style of Chic but, due to other projects, the composition took time. When the lyrics of the song were submitted, Rodgers turned them down as he felt there was no time to compose a melody and record it for the album; however, Madonna liked them and persuaded the producer to include the track.

"Into the Groove" was written and produced by Madonna and former Bray, and recorded at Sigma Sound Studios. Inspired by the dance floor and a Puerto Rican boy the singer was attracted to, it was used on the Susan Seidelman-directed film Desperately Seeking Susan, which Madonna starred. The song was originally written for Cheyne, the fifteen-year old protégée of Mark Kamins, the man who discovered Madonna's debut single "Everybody" (1982) and took her to Sire Records. Madonna then decided to record the track herself and use it on Desperately Seeking Susan, much to Kamins' dismay.

Recording
Recording sessions took place at New York's Power Station studios on April 1984. Rodgers envisioned a "simpler set-up" and, after hearing Madonna's demos, came to the conclusion they were too similar to what she had done on her debut: Heavily sequenced and synthesizer-led. He decided that the singer needed a "more streetwise sound", and to record with a live band. Rodgers subsequently assembled a rhythm section consisting of himself on guitar, Chic colleagues Bernard Edwards and Tony Thompson on bass and drums, respectively. Sessions took place in the afternoon, as Rodgers would attend late-night parties and wasn't used to work in the morning. It was Jason Corsaro, the album's audio engineer, who persuaded the producer to use digital recording, a new technique he believed was going to be the "future" of recording. He brought in a Sony 3324 24-track digital tape recorder and a Sony F1 two-track, which were used for the mixing.

Madonna's vocals were recorded at the studio's small, wooden, high-ceilinged piano room at the back. Corsaro would place gobos around her while using the top capsule of a stereo AKG C24 tube microphone, with a Schoeps microphone preamplifier and a Pultec equalizer. "That was part of the Power Station way" ―recalled Corsaro― "nothing was subtle and everything had a particular sound". Once the tracks met with everybody's approval, Robert Sabino added the keyboard parts; he did this by playing a Sequential Circuits Prophet-5, as well as some Rhodes and acoustic piano. Rodgers also played the Synclavier on this part. Corsaro remembered that the final songs "adhered very closely" to the Bray-produced demos, which were "quite simple in structure. All we did was get better musicians". Madonna, although not required, was present every minute of the recording and mixing processes; Corsaro commented: "Nile was there most of the time, but she was there all of the time. She never left". After hearing the album, Madonna's then manager Freddy DeMann pressured her to "put a little more bass on it", and make it sound like Michael Jackson's Thriller (1982). All the singer did was write the words "Bass Up" on the record's box without altering a thing.

Composition
Alexis Petridis from The Guardian described Like a Virgin as a "cocktail of post-disco dance music, with a dash of hip-hop and a surprisingly large shot of choppy, angular new wave rock". Noted an "80s teen-pop" take on Marilyn Monroe's "Diamonds Are a Girl's Best Friend", opener "Material Girl" is a synth-pop song with disco and new wave elements. A tongue-in-cheek satire on the superficiality and materialism of the 1980s, Madonna sings in a shrill voice about how she won't accept men who cannot provide her with wealth and luxuries, because we are living in a material world. Throughout the song, a robotic male voice repeats the hook living in a material world. Second track "Angel" begins with the sound of twinkling synths and giggles. It is an "ode to heavenly love" with a new wave overtone, built on an ascending hook consisting of a three chord sequence, which serves for the verse and refrain. One of the lyrics is taken from Public Image Ltd's "Death Disco" (1979), while Rodgers provides pizzicato guitars.

Title track "Like a Virgin" is a "mildly titillating" dance-rock song, in which the singer talks about how true love can make a girl feel shiny and new. The bass-line on the introduction is a reworking of the Four Tops' "I Can't Help Myself (Sugar Pie Honey Bunch)" (1965). Madonna sings in a "little girl lost" voice the opening line I made it through the wilderness/Somehow, I made it through/Didn’t know how lost I was until I found you. The drums, played by Tony Thompson, give the track "far more whallop than a drum machine ever could", according to Rikky Rooksby, author of The Complete Guide to the Music of Madonna. The lyrics to fourth track "Over and Over" talk about determination and picking oneself up from disappointments; I get up again, over and over, Madonna sings in the refrain. Instrumentation and production are sparse, featuring only a "silky" guitar.

"Love Don't live Here Anymore" is the only ballad on the album, as well as the most soulful. The song echoes back to Philadelphia soul, and features acoustic guitar and synth strings on the first half. Lyrically, it's about a woman being abandoned and "emptied of love". Madonna sings in a "tearful, angsty" tone as the track "builds and the strings undulate, belting that last anymore until she’s literally panting for breath". Included only on the 1985 international re-issue of Like a Virgin, Madonna's voice in "Into the Groove" is doubletracked. The track has a "bumping" synth-bass line, while the lyrics celebrate "dancefloor escapism", and juxtapose music, dance, sex and love. "Dress You Up" is a "drum machine-driven" dance song with a nu-disco beat, consisting of a two-chord verse. It features a guitar solo on its bridge, while Madonna sings about clothes she would like to drape over her lover, so that she can cover him with "velvet kisses", and caress his body with her hands.

Seventh track "Shoo-Bee-Doo" begins as a stripped-down piano ballad, before turning into a "deceptively bouncy ditty". The song reminiscences doo-wop and girl groups like the Shirelles and the Ronettes, while the lyrics deal with relationship problems, and Madonna trying to get through to her confused lover. Starting with the refrain followed by an opening verse, eight track "Pretender" is a synth-pop song about seduction and the insecurity felt by Madonna as she "[lets] things happen too fast" with a man who "isn't what he seems". Like a Virgin closes with "Stay", a song that features a fast triple rhythm with synths. The hook consist the phrase stay, darling being repeated over and over. Also present is the noise of someone slapping a microphone and a spoken sequence towards the end.

Artwork and release
Like a Virgin takes its name after the eponymous song. Madonna herself found the phrase "ironic and provocative [...] how can you be like a virgin? I liked the play on words". Author Graham Thompson felt that the title makes a "provocative link" between the singer's own religious name—Madonna as the Catholic title for Jesus' mother Mary—and the Christian concept of the virgin birth. The artwork for Like a Virgin was shot by Steven Meisel at a suite in the St. Regis New York. The sepia-tinted cover shows the singer lying on a satin bed, decked out in a wedding dress, with a tight-fitting bustier, full-length gloves, and a belt buckle that reads "Boy Toy"; she stares directly at the camera with heavy make-up and messy hair.

Stylist and designer Maripol described the singer's look as that of a "bride of Satan". Matthew Rettenmund, author of Encyclopedia Madonnica, wrote: "[The cover] effectively communicates the conflicted views of what a wedding dress should represent (virginity), and what [...] it does represent (sexual knowingness). Thompson added that artwork shows the singer, "not just as an object of desire, but also as a desiring female subject". Colombian music journalist Manolo Bellon pointed out that in the cover, Madonna plays a character for the first time: She portrays a "virgin who doesn't want to be [one]". The singer herself referred to the photograph as a "statement of independence, if you wanna be a virgin, you are welcome. But if you wanna be a whore, it's your fucking right to be so". From Billboard, Joe Lynch named it Madonna's second best album cover.

Even though it was completed by the end of April, the release of Like a Virgin was held back, due to the success of "Borderline" and the continuing sales of Madonna's first album, which at that point exceeded one million copies in the United States. Rodgers himself recalled: "We finished [Like a Virgin], but Madonna (the album) was still the focus [...] then 'Borderline' hit out of the clear blue sky. We didn't expect that". On June 30, 1984, Brian Chin from Billboard announced that the album would be released the following month. On October 6, the release date was reported to be the 29th of that month. Like a Virgin was officially released on November 12, 1984. On August of 1985, it was re-issued outside of North America with additional track "Into the Groove", which at the time had sold over a million copies and reached number one in the UK. On May 22, 2001, Warner Bros. released a remastered edition of Like a Virgin with additional remixes of the title track and "Material Girl". It was reissued on clear vinyl on November 8, 2019.

Live performances and tour
On May 16, 1984, after recording was complete, Madonna sang "Like a Virgin" and "Dress You Up" at a party offered by artist Keith Haring at New York's Paradise Garage. Four months later, on September 14, Madonna opened the inaugural MTV Video Music Awards ceremony with a performance of "Like a Virgin". She emerged from a 17-foot wedding cake donning the same wedding dress from the album cover. During the number, she slithered and writhed across the floor, with her dress going up and her underpants showing. The singer explained that this was not intentional, as one of her shoes had come off at the beginning and she simply had tried to reach for it; "I thought, 'Well, I'll just pretend I meant to do this', and I dove on the floor and I rolled around", she later recalled. MTV's Jessie Peterson opined that the performance put Madonna "on the map as Queen of Pop Music", and established the VMAs as "the place where water-cooler moments happen". It was named one of the best performances in the show's history by Slant Magazine and Billboard. On December 13, Madonna sang "Like a Virgin" on British television program Top of the Pops, decked out in a pink wig and golden metallic jacket. It was named the second best performance on the show's history.

Like a Virgin was further promoted on the Virgin Tour, Madonna's first concert tour, which visited cities in the US and Canada from April to June 1985. The tour received mixed critical reviews but was a commercial success, with Billboard reporting a gross of $3.3 million ($0 million in dollars); all 17,672 tickets for the concert at New York City's Radio City Music Hall sold out in a record-breaking 34 minutes. One of the Detroit concerts was filmed and release in VHS as Madonna Live: The Virgin Tour.

Singles
In the United States, title track "Like a Virgin" was released as lead single on October 31, 1984. In most European countries, it was issued on November 11. Upon release, it received generally positive reviews from critics, who singled out Madonna's vocals and deemed it her first signature song. Additionally, it became her first number-one hit on the Billboard Hot 100. The accompanying music video was directed by Mary Lambert, and shows the singer sailing down the canals of Venice in a gondola, and roaming around a castle in a white wedding dress.

Second single "Material Girl" was first released in the US on November 30, whereas in Europe it was published on February 18, 1985. AllMusic's Stephen Thomas Erlewine said it's one of the songs that made Madonna as an icon, along with "Like a Virgin". Commercially, it was successful, reaching the Hot 100's second spot, and the third spot of the UK Singles Chart. The music video, also directed by Lambert, is a homage to Marilyn Monroe's performance of "Diamonds Are a Girl's Best Friend" from the 1953 film Gentlemen Prefer Blondes.

"Angel" was released as the third single on April 10, 1985. it received generally mixed reviews from critics, with some calling it a "classic" and others deeming it sub-par compared to the singer's previous works. "Angel" became Madonna's fifth consecutive top-five single on the Hot 100. "Into the Groove" was released in the UK on July 15. It wasn't given a release in the US, instead it was issued as B-side to the 12" maxi-single of "Angel", thus was ineligible to enter the Billboard Hot 100. "Angel"/"Into the Groove" reached the first spot of the Dance Club Songs chart. Billboard readers voted "Into the Groove" the best dance single from the 1980s decade.

Final single "Dress You Up" was released on July 24, 1985. Critics reacted positively towards the track, referring to it as irresistible. Despite positive feedback, "Dress You Up" was added to the Parents Music Resource Center's "Filthy Fifteen" list due to perceived sexual innuendo on its lyrics. It fared well commercially, reaching the fifth spot on both the Hot 100 and the UK Singles Chart. A promotional two-sided 7" single of "Love Don't Live Here Anymore" and "Over and Over" was released in Japan on March 1986.

Video compilation
A VHS video compilation titled Madonna was made available in December 1984; it included the videos for "Borderline", "Burning Up", "Like a Virgin", and an extended mix of "Lucky Star". The release topped Billboard's Music Videocassette chart from April 13 to November 9, 1985, and was the year's best selling music videocassette. Additionally, Madonna was certified platinum by the Recording Industry Association of America (RIAA) for shipments of 100,000 units, and was recognized as the "Best Selling Video Cassette Merchandised as Music Video" by the National Association of Recording Merchandisers. According to The Saturday Evening Post, the video has sold over one million copies. To promote the release, a party was held on Chicago's Cabaret Metro on February 9, 1985. Dubbed "The Virgin Party", it drew a crowd of around 1,200 people; attendees were encouraged to wear white, and for $5 admission fees, were able to view the Madonna videocassette and the "Material Girl" music video. The event was organized as a drive to promote music videos, which at that point did not have a large market.

Critical reception
Reviews of Like a Virgin were mixed upon release. From Billboard, Brian Chine called it a "fine" second album, even though Madonna "does no searching whatsoever in her singing [...] [She] hits her notes straight on, and with a pretty enough melody". Also from Billboard, Michael Paoletta praised Rodgers' "sleek but snewy rhythm arrangements". From The New York Times, Stephen Holden was pleased with the "handsomely produced" record and the singer's voice, which he felt echoed the "rock-and-roll girl-group tradition that preceded the Beatles", but while these "worshipfully extolled their boyfriends' cars, haircuts and rebel poses, Madonna's point of view is decidedly more self-interested". "The words 'shiny and new' describe not only the way the love-smitten singer feels in the title song but the sound of the album", concluded Holden. Debby Miller from Rolling Stone opined that, "[d]espite [Madonna's] little-girl voice, there’s an undercurrent of ambition that makes her more than the latest Betty Boop [...] Her light voice bobs over the heavy rhythm and synth tracks like a kid on a carnival ride". Author J. Randy Taraborrelli applauded Madonna's voice for being "reflectively sharper" than on her debut, and felt Like a Virgin reflected her as a "more versatile and artistic performer". From streaming service Tidal, John Murph described the album as "far warmer, fuller and more soulful than the often cold and tinny synth sounds that typified a lot of underground dance music" of the time.

The album was described as "smart, funny, sexy and irresistible" by Q magazine, while for The National's Saeed Saeed, it is a "ruthlessly focused collection of pop songs [...] featuring at least three pop classics". Alexis Petridis referred to Like a Virgin as "provocative, fun, [and] witty [...] [It's also] the last album on which Madonna sounded like a product of the environment that birthed her". It was deemed a "masterpiece" by Joseph Earp from Australian website Junkee. WhatCulture's Reece Shrewsbury felt the songs on Like a Virgin are stronger than those on Madonna. To Matthew Rettenmund, "[Like a Virgin] is not Madonna's strongest album, but its nine tracks feature [her] at her least self-conscious and most cleverly effervescent". Daryl Easlea praised Rodgers' production, but felt the album "tapers off, veering towards filler" on its second half. Despite being home to some of the "catchiest, not to mention most iconic tracks in pop music", Like a Virgin is made up of "mostly fillers", according to the staff of Instinct magazine.

Pete Bishop from The Pittsburgh Press wrote that in Like a Virgin, Madonna "sort of hum-de-dums her way through [...] a lot of simple love lyrics over a lot of lightweight, pop-style fun-rock [...] sometimes sounding like a one-woman Pointer Sisters and sometimes like Cyndi Lauper with her nose pinched shut". Despite naming it "pleasent enough", Bishop concluded that its main "weakness" is that "you could put these [songs] behind any decent-voiced singer. Like a Virgin does not establish Madonna as anyhing special". Taraborrelli added that, when compared to Madonna's subsequent records, Like a Virgin "does come across as a bit repetitious and immature". Both Sal Cinquemani from Slant Magazine and Stephen Thomas Erlewine felt it is not as "innovative" as Madonna's first record, with the former adding: "[On the first album], she stunned with style and a certain joy. Here, the calculation is apparent, and while that's part of [her] essence - even something that makes her fun - it throws [Like a Virgin]'s balance off a little too much for it to be consistent". This sentiment was echoed by Sam Damshenas and Daniel Megarry from Gay Times, who wrote that, like Madonna, Like a Virgin lacks the innovation of the singer's posterior works. The staff of The Advocate concluded that, "this could have been the best EP of the '80s, with generation-defining songs [...] Instead it was a nine-song album with five great singles and four tracks that unbelievably escaped the cutting room floor". In the same vein, Erlewine added that the singles "overshadow" the rest of the album, which "vacillates wildly in terms of quality". To Michael Paoletta from Billboard, Like a Virgin hasn't aged as well as the singer's other works from the 1980s decade. People magazine dismissed the a record as a "tolerable bit of fluff" with "primitive" lyrics.

Commercial performance
In the United States, Like a Virgin debuted at number 70 on the Billboard 200 on December 1, 1984. The following week, it climbed to number ten. The album reached the chart's first spot on February 9, 1985, where it spent three weeks. Madonna became the third female artist in the 1980s decade ―after Barbra Streisand and Kim Carnes― to score both a number one album and single, as the title track had reached the Hot 100's top spot two weeks prior. Three weeks after its release, Like a Virgin had sold over three million copies. By July 1985, it had become the first album by a female to sell over five million copies in the United States. The record came in at the third spot on the Billboard 200 year-end chart for 1985. It was eventually certified ten times platinum (diamond) by the Recording Industry Association of America (RIAA), for shipment of ten million copies. After the advent of the Nielsen SoundScan era in 1991, the album sold a further 574,000 copies as of August 2010. Another 882,000 units were sold at the BMG Music Club, which are not counted by the Nielsen SoundScan. Along with True Blue (1986) and The Immaculate Collection (1990), Like a Virgin is one of Madonna's best-selling albums in the United States.

In Canada, Like a Virgin debuted on the 78th spot of the RPM Albums Chart on November 10, 1984; it climbed up the chart and eventually reached the third spot on February 16, 1985. The album was present for a total of 74 weeks on the chart, and was certified diamond by the Canadian Recording Industry Association (CRIA), for shipment of one million copies. Like a Virgin reached the fifth position of RPM's 1985 year-end chart. 750,000 copies were sold in Latin America as of June 1986.

In the United Kingdom, Like a Virgin debuted at number 74 on the UK Albums Chart, on November 24, 1984. However, it fluctuated on the chart for the next eight months and it wasn't until September that it finally reached the chart's top. The album was certified three times platinum by the British Phonographic Industry (BPI) and has sold over a million copies there. In France, the album debuted and peaked at number five on the French Albums Chart on October 6, 1985, staying there for eight weeks. Like a Virgin was certified two times platinum by the Syndicat National de l'Édition Phonographique (SNEP) for shipment of 600,000 copies. Like a Virgin reached number the first place on European countries like Germany, the Netherlands, Spain, and Italy. Like a Virgin became Madonna's first number one album on the European Top 100 Albums, reaching the summit on November 18, 1985, and remaining there for two weeks. Over 2 million copies were sold across Europe by the end of 1985.

In Australia, the album debuted and peaked at the second position of the Kent Music Report albums chart, and was certified seven times platinum by the Australian Recording Industry Association (ARIA) for shipment of 490,000 copies. Like a Virgin remained at the top of the New Zealand Albums Chart for three consecutive weeks, and was certified five times platinum by the Recording Industry Association of New Zealand (RIANZ) for the shipping of 75,000 copies. With over 21 million copies sold worldwide, Like a Virgin is one of the best-selling albums of all time.

Legacy
Like a Virgin has been referred to as the album that made Madonna a superstar. Stephen Thomas Erlewine wrote: "Madonna had hits with her first album [...] but she didn't become an icon, until Like a Virgin". Similarly, Sam Damshenas and Daniel Megarry referred to the album as the one that cemented the singer as a "force to be reckoned with in the world of pop". This opinion was shared by John Murph, who added that Like a Virgin allowed Madonna to "create an archetype of pop stardom that the likes of Gwen Stefani, P!nk and Lady Gaga have followed". To Daniel Garrán from Spanish radio station Los 40, "[Like a Virgin] proved [Madonna] was not a one-hit wonder but a versatile artist capable of cementing her place in the music world [...] pop culture gave in to her charms".

Stephen Holden wrote: "No phenomenon illustrates more pointedly how pop music history seems to run in cycles than the overnight success of [...] Madonna. The month before Christmas [...] Teen-agers were lining up in stores to purchase [Like a Virgin] the way their parents had lined up to buy Beatles records in the late 60's". With the album, the singer was able to take charge of her career, according to the staff of Rhino Entertainment. Chris Smith, author of 101 Albums That Changed Popular Music, where Like a Virgin was included, added that it helped Madonna "steal the spotlight towards herself. [Asserting] her sexuality as only male rock stars had done before, moving well beyond the limited confines of being a pop artist, to becoming a focal point for nationwide discussions of power relationships in the areas of sex, race, gender, religion, and other divisive social topics". For The Guardian's Caroline Sullivan, Madonna became the "biggest thing to hit pop" since "a woman in control of her sex life and career was such a new idea".

According to Santiago Fouz-Hernandez, one of the authors of Madonna's Drowned Worlds, following the album's release and Virgin tour, young girls everywhere started emulating Madonna's style. The singer herself recalled that women would show up to the concerts with "flap skirts on and tights cut off below their knees and lace gloves and rosaries and bows in their hair and big hoop earrings. I was like, 'This is insane!'". Madonna look-alike contests were held in shopping malls across the United States, with Andy Warhol allegedly serving as judge in one of them. Nathan Smith from Out magazine wrote that young women idolized the "transformative transgressions of Madonna, a star who wanted to be in control of sexual identity and dictate the terms of her own erotic encounters". Smith ultimately concluded that, "[Like a Virgin] stands today as a polemic for the reborn woman of the 1980s: empowered, sexually demonstrative, financially independent, and drawing on old antiquated traditions to move ahead in the world". Sal Cinquemani placed the record among the "most definitive pop artifacts from the indulgent Reagan Era".

Like a Virgin is considered one of the best albums of 1984 and of the 1980s decade. In 2017, NPR named Like a Virgin one of the greatest albums ever made by a woman, with Alison Fensterstock writing: "All that came with [the album], made it clear that there would never be a pop music landscape without the impact and influence of Madonna again". Consequence of Sound considered Like a Virgin the second best sophomore album of all time, with Michael Roffman saying it "carved out the throne, the crown, and the title that would be Madonna’s forever: The Queen of Pop". Chuck Arnold, writing for Billboard, concluded that, "Madonna has definitely made better albums than Like a Virgin — among them, Like a Prayer [and] Ray of Light — but her second LP changed the course of pop history". According to Taraborrelli, "every important artist has at least one album in his or her career whose critical and commercial success becomes the artist's magic moment; for Madonna, Like a Virgin was just such a defining moment". Finally, In 2023, Like a Virgin was selected for preservation in the United States' National Recording Registry by the Library of Congress due to it being considered "culturally, historically, or aesthetically significant".

Track listing
All tracks produced by Nile Rodgers.

Personnel
Credits adapted from the album's liner notes.

 * Sire Records – record label, U.S. copyright owner (1984, 1985)
 * Warner Bros. Records – U.S. marketing and distributor (all releases), record label, copyright owner (2001)
 * WEA International – international distributor, international copyright owner (all releases)

Musicians

 * Madonna – lead vocals (all tracks), background vocals (1, 2, 7)
 * Nile Rodgers – Roland Juno-60 (1), Synclavier II (1, 9), guitars (1-4, 6-9), acoustic guitar (5), electric guitar (5), string arrangements and conductor (5)
 * Nathaniel S. Hardy, Jr. – keyboards (1, 5)
 * Robert Sabino – synthesizers (2-9), bass synthesizer (2-6, 8, 9), acoustic piano (7), Fender Rhodes electric piano
 * Bernard Edwards – bass (1, 3, 5, 7)
 * Tony Thompson – drums (1, 3, 5, 7)
 * Jimmy Bralower – LinnDrum and Simmons drum machine programming (2, 4, 6, 8, 9)
 * Lenny Pickett – saxophone solo (7)
 * Karen Milne – string contractor  (5)
 * Kermit Moore – string contractor (5)
 * Curtis King – background vocals (1, 2, 4-9)
 * Frank Simms – background vocals (1, 2, 4-9)
 * George Simms – background vocals (1, 2, 4-9)
 * Brenda King – background vocals (7)

Production

 * Madonna – producer ("Into the Groove")
 * Stephen Bray – producer ("Into the Groove")
 * Nile Rodgers – producer (all tracks except "Into the Groove")
 * Jason Corsaro – recording engineer (all tracks), audio mixing (all tracks)
 * Rob "Ace" Eaton – second engineer (all tracks)
 * Gus Skinas – digital editing
 * Eric Mohler – digital editing assistant
 * Malcolm Pollack – assistant engineer
 * Bob Ludwig – audio mastering at Masterdisk (New York City, New York)
 * Budd Tunick – production manager
 * Weisner-DeMann Entertainment – management

Design

 * Jeri McManus – art direction, design
 * Jeffrey Kent Ayeroff – art direction, design
 * Steven Meisel – photography
 * Maripol – stylist

title: Like a Virgin (album)


text:
Electrical element

In electrical engineering, electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electrical elements interconnected by wires. Where the elements roughly correspond to real components, the representation can be in the form of a schematic diagram or circuit diagram. This is called a lumped-element circuit model. In other cases, infinitesimal elements are used to model the network in a distributed-element model.

These ideal electrical elements represent actual, physical electrical or electronic components. Still, they do not exist physically and are assumed to have ideal properties. In contrast, actual electrical components have less than ideal properties, a degree of uncertainty in their values, and some degree of nonlinearity. To model the nonideal behavior of a real circuit component may require a combination of multiple ideal electrical elements to approximate its function. For example, an inductor circuit element is assumed to have inductance but no resistance or capacitance, while a real inductor, a coil of wire, has some resistance in addition to its inductance. This may be modeled by an ideal inductance element in series with a resistance.

Circuit analysis using electric elements is useful for understanding practical networks of electrical components. Analyzing how a network is affected by its individual elements makes it possible to estimate how a real network will behave.

Types
Circuit elements can be classified into different categories. One is how many terminals they have to connect them to other components:
 * One-port elements – represent the simplest components, with only two terminals to connect to. Examples are
 * resistances,
 * capacitances,
 * inductances,
 * and diodes.
 * Two-port elements – are the most common multiport elements with four terminals consisting of two ports.
 * Multiport elements – these have more than two terminals. They connect to the external circuit through multiple pairs of terminals called ports. For example,
 * a transformer with three separate windings has six terminals and could be idealized as a three-port element; the ends of each winding are connected to a pair of terminals representing a port.

Elements can also be divided into active and passive:

 * Passive elements – These elements do not have a source of energy; examples are
 * diodes,
 * resistances,
 * capacitances,
 * and inductances.

 * Active elements or sources – these are elements which can source electrical power. They can be used to represent ideal batteries and power supplies; examples are
 * voltage sources
 * and current sources.
 * Dependent sources – These are two-port elements with a voltage or current source proportional to the voltage or current at a second pair of terminals. These are used in the modelling of amplifying components such as
 * transistors,
 * vacuum tubes,
 * and op-amps.

Another distinction is between linear and nonlinear:
 * Linear elements – these are elements in which the constituent relation, the relation between voltage and current, is a linear function. They obey the superposition principle. Examples of linear elements are resistances, capacitances, inductances, and linear-dependent sources. Circuits with only linear elements, linear circuits, do not cause intermodulation distortion and can be easily analysed with powerful mathematical techniques such as the Laplace transform.
 * Nonlinear elements – these are elements in which the relation between voltage and current is a nonlinear function. An example is a diode, where the current is an exponential function of the voltage. Circuits with nonlinear elements are harder to analyse and design, often requiring circuit simulation computer programs such as SPICE.

One-port elements
Only nine types of element (memristor not included), five passive and four active, are required to model any electrical component or circuit. Each element is defined by a relation between the state variables of the network: current, $$I$$; voltage, $$V$$; charge, $$Q$$; and magnetic flux, $$\Phi$$.
 * Two sources:
 * Current source, measured in amperes – produces a current in a conductor. Affects charge according to the relation $$dQ = -I\,dt$$.
 * Voltage source, measured in volts – produces a potential difference between two points. Affects magnetic flux according to the relation $$d\Phi = V\,dt$$.
 * $$\Phi$$ in this relationship does not necessarily represent anything physically meaningful. In the case of the current generator, $$Q$$, the time integral of current represents the quantity of electric charge physically delivered by the generator. Here $$\Phi$$ is the time integral of voltage, but whether or not that represents a physical quantity depends on the nature of the voltage source. For a voltage generated by magnetic induction, it is meaningful, but for an electrochemical source, or a voltage that is the output of another circuit, no physical meaning is attached to it.
 * Both these elements are necessarily non-linear elements. See below.

 * Three passive elements:
 * Resistance $$R$$, measured in ohms – produces a voltage proportional to the current flowing through the element. Relates voltage and current according to the relation $$dV = R\,dI$$.
 * Capacitance $$C$$, measured in farads – produces a current proportional to the rate of change of voltage across the element. Relates charge and voltage according to the relation $$dQ = C\,dV$$.
 * Inductance $$L$$, measured in henries – produces the magnetic flux proportional to the rate of change of current through the element. Relates flux and current according to the relation $$d\Phi = L\,dI$$.
 * Four abstract active elements:
 * Voltage-controlled voltage source (VCVS) Generates a voltage based on another voltage with respect to a specified gain. (has infinite input impedance and zero output impedance).
 * Voltage-controlled current source (VCCS) Generates a current based on a voltage elsewhere in the circuit, with respect to a specified gain, used to model field-effect transistors and vacuum tubes (has infinite input impedance and infinite output impedance). The gain is characterised by a transfer conductance which will have units of siemens.
 * Current-controlled voltage source (CCVS) Generates a voltage based on an input current elsewhere in the circuit with respect to a specified gain. (has zero input impedance and zero output impedance). Used to model trancitors. The gain is characterised by a transfer impedance which will have units of ohms.
 * Current-controlled current source (CCCS) Generates a current based on an input current and a specified gain. Used to model bipolar junction transistors. (Has zero input impedance and infinite output impedance).
 * These four elements are examples of two-port elements.

Non-linear elements
In reality, all circuit components are non-linear and can only be approximated as linear over a certain range. To describe the passive elements more precisely, their constitutive relation is used instead of simple proportionality. Six constitutive relations can be formed from any two of the circuit variables. From this, there is supposed to be a theoretical fourth passive element since there are only five elements in total (not including the various dependent sources) found in linear network analysis. This additional element is called memristor. It only has any meaning as a time-dependent non-linear element; as a time-independent linear element, it reduces to a regular resistor. Hence, it is not included in linear time-invariant (LTI) circuit models. The constitutive relations of the passive elements are given by;
 * Resistance: constitutive relation defined as $$f(V, I)=0$$.
 * Capacitance: constitutive relation defined as $$f(V, Q)=0$$.
 * Inductance: constitutive relation defined as $$f(\Phi, I)=0$$.
 * Memristance: constitutive relation defined as $$f(\Phi, Q)=0$$.

 * where $$f(x,y)$$ is an arbitrary function of two variables.

In some special cases, the constitutive relation simplifies to a function of one variable. This is the case for all linear elements, but also, for example, an ideal diode, which in circuit theory terms is a non-linear resistor, has a constitutive relation of the form $$ V = f(I)$$. Both independent voltage and independent current sources can be considered non-linear resistors under this definition.

The fourth passive element, the memristor, was proposed by Leon Chua in a 1971 paper, but a physical component demonstrating memristance was not created until thirty-seven years later. It was reported on April 30, 2008, that a working memristor had been developed by a team at HP Labs led by scientist R. Stanley Williams. With the advent of the memristor, each pairing of the four variables can now be related.

Two special non-linear elements are sometimes used in analysis but are not the ideal counterpart of any real component:
 * Nullator: defined as $$ V = I = 0 $$
 * Norator: defined as an element that places no restrictions on voltage and current whatsoever.

These are sometimes used in models of components with more than two terminals: transistors, for instance.

Two-port elements
All the above are two-terminal, or one-port, elements except the dependent sources. Two lossless, passive, linear two-port elements are typically introduced into network analysis. Their constitutive relations in matrix notation are;

 * Transformer:

 * $$ \begin{bmatrix} V_1  \\ I_2  \end{bmatrix} = \begin{bmatrix} 0 & n \\ -n & 0 \end{bmatrix}\begin{bmatrix} I_1  \\ V_2 \end{bmatrix}$$

 * Gyrator:

 * $$ \begin{bmatrix} V_1  \\ V_2  \end{bmatrix} = \begin{bmatrix} 0 & -r \\ r & 0 \end{bmatrix}\begin{bmatrix} I_1  \\ I_2 \end{bmatrix}$$

The transformer maps a voltage at one port to a voltage at the other in a ratio of n. The current between the same two ports is mapped by 1/n. On the other hand, the gyrator maps a voltage at one port to a current at the other. Likewise, currents are mapped to voltages. The quantity r in the matrix is in units of resistance. The gyrator is a necessary element in analysis because it is not reciprocal. Networks built from just the basic linear elements are necessarily reciprocal, so they cannot be used by themselves to represent a non-reciprocal system. It is not essential, however, to have both the transformer and gyrator. Two gyrators in cascade are equivalent to a transformer, but the transformer is usually retained for convenience. The introduction of the gyrator also makes either capacitance or inductance non-essential since a gyrator terminated with one of these at port 2 will be equivalent to the other at port 1. However, transformer, capacitance, and inductance are normally retained in analysis because they are the ideal properties of the basic physical components transformer, inductor, and capacitor, whereas a practical gyrator must be constructed as an active circuit.

Examples
The following are examples of representations of components by way of electrical elements.
 * On a first degree of approximation, a battery is represented by a voltage source. A more refined model also includes a resistance in series with the voltage source to represent the battery's internal resistance (which results in the battery heating and the voltage dropping when in use). A current source in parallel may be added to represent its leakage (which discharges the battery over a long period).
 * On a first degree of approximation, a resistor is represented by a resistance. A more refined model also includes a series inductance to represent the effects of its lead inductance (resistors constructed as a spiral have more significant inductance). A capacitance in parallel may be added to represent the capacitive effect of the proximity of the resistor leads to each other. A wire can be represented as a low-value resistor.
 * Current sources are often used when representing semiconductors. For example, on a first degree of approximation, a bipolar transistor may be represented by a variable current source controlled by the input current.

title: Electrical element


text:
Fantasy world

A fantasy world or fictional world is a world created for fictional media, such as literature, film or games. Typical fantasy worlds feature magical abilities. Some worlds may be a parallel world connected to Earth via magical portals or items (like Narnia); an imaginary universe hidden within ours (like Wizarding World); a fictional Earth set in the remote past (like Middle-earth) or future (like Dying Earth); an alternative version of our History (like Lyra's world); or an entirely independent world set in another part of the universe (like the Star Wars Galaxy).

Many fantasy worlds draw heavily on real world history, geography, sociology, mythology, and folklore.

Plot function
The setting of a fantasy work is often of great importance to the plot and characters of the story. The setting itself can be imperiled by the evil of the story, suffer a calamity, and be restored by the transformation the story brings about. Stories that use the setting as merely a backdrop for the story have been criticized for their failure to use it fully.

Even when the land itself is not in danger, it is often used symbolically, for thematic purposes, and to underscore moods. For readers, fantasy worlds offer a "place...[where] assumptions and desires [about the genre] are confirmed" and emotional satisfaction that comes from various elements of the world fulfill readers' expectations for quality.

History
Early fantasy worlds appeared as fantasy lands, part of the same planet but separated by geographical barriers. For example, Oz, though a fantasy world in every way, is described as part of this world.

Although medieval peasants who seldom if ever traveled far from their villages could not conclusively say that it was impossible that, for example, an ogre could live a day's travel away, distant continents were necessary from the Renaissance onwards for such fantastic speculation to be plausible, until finally, further exploration rendered all such terrestrial fantasy lands implausible.

Even within the span of mere decades, Oz, which had been situated in a desert in the United States when first written about in 1900, was relocated to a spot in the Pacific Ocean.

An early example of the fantasy land/world concept can be seen in the One Thousand and One Nights (Arabian Nights), where places of which little was known, but where the occurrence of marvels was thus more credible, had to be set "long ago" or "far away". This is a process that continues and finally culminates in the fantasy world having little connection, if any, to actual times and places. A more recent example of a fantasy land with definite connections to the actual world is Austin Tappan Wright's Islandia. Islandia's remoteness and aura of mystery, as well as its preservation of an arcadian society, are explained by means of a law that allows only limited contact with foreigners.

Dream frames were also once common for encasing the fantasy world with an explanation of its marvels. Such a dream frame was added to the story of The Wonderful Wizard of Oz for the movie version; in the book, Oz is clearly defined as an actual place. H.P. Lovecraft made active use of the dream frame, creating elaborate geographies accessible to humans only when they were asleep and dreaming. These dream settings have been criticized, and are far less frequent today.

This change is part of a general trend toward more self-consistent and substantive fantasy worlds. This has also altered the nature of the plots; earlier works often feature a solitary individual whose adventures in the fantasy world are of personal significance, and where the world clearly exists to give scope to these adventures, and later works more often feature characters in a social web, where their actions are to save the world and those in it from peril.

Common elements
The most common fantasy world is one based on medieval Europe, and has been since William Morris used it in his early fantasy works, such as The Well at the World's End. and particularly since the 1954 publication of J.R.R. Tolkien's The Lord of the Rings. Such a world is often called "pseudo-medieval"—particularly when the writer has snatched up random elements from the era, which covered a thousand years and a continent, and thrown them together without consideration for their compatibility, or even introduced ideas not so much based on the medieval era as on romanticized views of it. When these worlds are copied not so much from history as from other fantasy works, there is a heavy tendency to uniformity and lack of realism. The full width and breadth of the medieval era is seldom drawn upon. Governments, for instance, tend to be uncompromisingly feudal-based, or evil empires or oligarchies, usually corrupt, while there was far more variety of rule in the actual Middle Ages. Fantasy worlds also tend to be economically medieval, and disproportionately pastoral.

Careful world-building plus meticulous attention to detail is often cited as the reason why certain fantasy works are deeply convincing and contain a magical sense of place. Heavy and faithful use of real-world setting for inspiration, as in Barry Hughart's Bridge of Birds, clearly derived from China, or Lloyd Alexander's use of real-world cultures such as Welsh for The Chronicles of Prydain or Indian for The Iron Ring, make the line between fantasy worlds and alternate histories fuzzy. The use of cultural elements, and still more history and geography, from actual settings, pushes a work toward alternative history.

Conversely, the creation by an author of an imaginary country—such as Ruritania or Graustark—does not automatically transform that imaginary country into a fantasy world, even if the location would be impossible in reality owing to a lack of land to contain it; but such Ruritanian romances may be pushed toward the category of fantasy worlds by the introduction of figures such as witches and wise women, where it is not clear if their magic is effectual.

According to Lin Carter in Imaginary Worlds: the Art of Fantasy, fantasy worlds, by their nature, contain some element of magic (paranormal). This element may be the creatures in it (dragons, unicorns, genies and so on) or the magical abilities of the people inhabiting the world. These are often drawn from mythology and folklore, frequently that of the historical country also used for inspiration.

Constructed worlds
Fantasy worlds created through a process called world building are known as a constructed world. Constructed worlds elaborate and make self-consistent the setting of fantasy work. Worldbuilding often relies on materials and concepts taken from the real world.

Despite the use of magic or other fantastic elements such as dragons, the world is normally presented as one that would function normally, one in which people could actually live, making economic, historical, and ecological sense. It is considered a flaw to have, for example, pirates living in lands far from trade routes, or to assign prices for a night's stay in an inn that would equate to several years’ income.

Furthermore, the fantastic elements should ideally operate according to self-consistent rules of their own; for example, if wizards' spells sap their strength, a wizard who does not appear to suffer this must either be putting up a facade or have an alternative explanation. This distinguishes fantasy worlds from Surrealism and even from such dream worlds as are found in Alice's Adventures in Wonderland and Through the Looking-Glass.

Examples
Due to the fuzzy boundary between fantasy and science fiction, it is sometimes difficult to make a hard-and-fast distinction between "fantasy worlds" and planets in science fiction. For example, the worlds of Barsoom, Darkover, Gor, and the Witch World combine elements of both genres and fantasy worlds may have nonexistent, powerful technology.
 * L. Frank Baum created the Land of Oz for his novel The Wonderful Wizard of Oz and its original sequels. He was one of the few authors before Tolkien to use consistent internal geographies and histories to enrich his world.
 * C. S. Lewis, author of The Chronicles of Narnia, set that series' novels mostly in a magical land called Narnia. Lewis was a colleague of Tolkien, and their fictional worlds share several key elements.
 * Terry Pratchett created Discworld, a large disc resting on the backs of four huge elephants, which are in turn standing on the back of an enormous turtle, as it slowly swims through space.
 * J. R. R. Tolkien created Middle-earth, a famous fantasy world. He introduced several revolutionary concepts to fantasy fiction and popularized the idea of intricately detailed fantasy worlds. He wrote at some length about the process, which he called "sub-creation". Middle-earth is intended to be Earth's Old World in a fictional ancient era.
 * George R. R. Martin created a fictional world for his novel series A Song of Ice and Fire. Martin said in 2003 that complete world maps were deliberately not made available so that readers may better identify with people of the real Middle Ages who were unilluminated about distant places. Most of the story is set in the western continent of Westeros, though some are set in the Eastern continent Essos. The Southern continent of Sothoryos is also shown on maps, with a possible fourth continent, Ulthos, to its East. A map of the world is shown in the title sequence of the HBO TV adaptation, Game of Thrones.
 * Robert Jordan created unnamed fictional world for his opus magnum The Wheel of Time.

Fairytale and comic fantasy
Fairytale fantasy may ignore the normal world-building in order to present a world operating by the same logic as the fairytales from which they are derived, though other works in this subgenre develop their worlds fully. Comic fantasy may ignore all possible logic in search of humor, particularly if it is parodying other fantasies' faulty world-building, as in Diana Wynne Jones's Dark Lord of Derkholm, or the illogic of the setting is integral to the comedy, as in L. Sprague de Camp's Solomon's Stone, where the fantasy world is populated by the heroic and glamorous figures that people daydream about being, resulting in a severe shortage of workers in the more mundane, day-to-day industries. Most other subgenres of fantasy suffer if the world-building is neglected.

Retreat of magic
Rather than creating their own fantasy world, many authors choose to set their novels in Earth's past. In order to explain the absence of miraculous elements, authors may introduce "a retreat of magic" (sometimes called "thinning") that explains why the magic and other fantastic elements no longer appear: For example, in The Lord of the Rings, the destruction of the One Ring defeated Sauron, but also destroyed the power of the Three Rings of the elves, resulting in them sailing to the West at the end of the story. A contemporary fantasy necessarily takes place in what purports to be the real world, and not a fantasy world. It may, however, include references to such a retreat. J. K. Rowling's Fantastic Beasts and Where to Find Them explains that wizards eventually decided to conceal all magical creatures and artifacts from non-magic users.

Role-playing games
Dungeons & Dragons, the first major role-playing game, has created several detailed and commercially successful fantasy worlds (called "campaign settings"), with established characters, locations, histories, and sociologies. The Forgotten Realms is perhaps the most extensively developed of these worlds.

title: Fantasy world


text:
Fictional country

A fictional country is a country that is made up for fictional stories, and does not exist in real life, or one that people believe in without proof. Sailors have always mistaken low clouds for land masses, and in later times this was given the name Dutch capes. Other fictional lands appear most commonly as settings or subjects of myth, literature, film, or video games. They may also be used for technical reasons in actual reality for use in the development of specifications, such as the fictional country of Bookland, which is used to allow European Article Number "country" codes 978 and 979 to be used for ISBNs assigned to books, and code 977 to be assigned for use for ISSN numbers on magazines and other periodicals. Also, the ISO 3166 country code "ZZ" is reserved as a fictional country code.

Fictional countries appear commonly in stories of early science fiction (or scientific romance). Such countries supposedly form part of the normal Earth landscape, although not located in a normal atlas. Later similar tales often took place on fictional planets.

In Gulliver's Travels by Jonathan Swift, the protagonist, Lemuel Gulliver, visited various strange places. Edgar Rice Burroughs placed the adventures of Tarzan in areas in Africa that, at the time, remained mostly unknown to the West and to the East. Isolated islands with strange creatures and/or customs enjoyed great popularity in these authors' times. By the 19th century, when Western explorers had surveyed most of the Earth's surface, this option was lost to Western culture. Thereafter, fictional utopian and dystopian societies tended to spring up on other planets or in space, whether in human colonies or in alien societies originating elsewhere. Fictional countries can also be used in stories set in a distant future, with other political borders than today.

Superhero and secret agent comics and some thrillers also use fictional countries on Earth as backdrops. Most of these countries exist only for a single story, a TV-series episode or an issue of a comic book. There are notable exceptions where fictional countries appear as recurring plot elements, such as: Qumar and Equatorial Kundu (The West Wing); Latveria (Marvel Comics); and Qurac and Bialya (DC Comics).

Purposes
Fictional countries often deliberately resemble or even represent some real-world country or present a utopia or dystopia for commentary. Variants of the country's name sometimes make it clear what country they really have in mind. By using a fictional country instead of a real one, authors can exercise greater freedom in creating characters, events, and settings, while at the same time presenting a vaguely familiar locale that readers can recognize. A fictional country leaves the author unburdened by the restraints of a real nation's actual history, politics, and culture, and can thus allow for greater scope in plot construction and be exempt from criticism for vilifying an actual nation, political party, or people. The fictional Tomania (a parody of Nazi Germany named after ptomaine) serves as a setting for Charlie Chaplin's The Great Dictator and skewers a régime infamous for religious bigotry, militarism, racism, diplomatic bullying, and violations of civil liberties.

Fictional countries are also invented for the purpose of military training scenarios, e.g. the group of islands around Hawaii were assigned the names Blueland and Orangeland in the international maritime exercise, RIMPAC 98.

In survey research
Fictional countries have been created for polling purposes. When polled in April 2004, 8% of British people believed that the [fictional] country of Luvania would soon join the European Union. In the 1989 General Social Survey, U.S. respondents were asked to rate the social status of people of "Wisian" background, a fictional national heritage. While a majority of respondents said they could not place the Wisians in the U.S. social hierarchy, those who did ranked their status as quite low, giving an average of 4.12 on a 9-point scale, where 9 was the highest social standing. "Once you let the Wisians in, the neighborhood goes to pot", quipped Time magazine.

Legendary countries
Countries from stories, myths, legends, that some believe to exist, or to have existed at some point:
 * Atlantis
 * Aztlán
 * El Dorado
 * Lemuria (continent)
 * Lyonesse
 * Mu (continent)
 * Ophir (In 1946 an inscribed pottery shard was found at Tell Qasile (in modern-day Tel Aviv) dating to the eighth century BC. It bears, in Paleo-Hebrew script the text "gold of Ophir to/for Beth-Horon ... 30 shekels". The find confirms that Ophir was a place where gold was imported from, although its location remains unknown.)
 * Shangri-La or Shambhala

Books

 * Alberto Manguel & Gianni Guadalupi: The Dictionary of Imaginary Places. ISBN 0-15-626054-9
 * Brian Stableford: The Dictionary of Science Fiction Places. Simon & Schuster, 1999. ISBN 978-0684849584

title: Fictional country