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Necker Cube

Necker Cube

The Necker Cube is an optical illusion first published in 1832 by Swiss crystallographer Louis Albert Necker. The Necker Cube is an ambiguous line drawing. It is a wire-frame drawing of a cube in isometric perspective, which means that parallel edges of the cube are drawn as parallel lines in the picture. When two lines cross, the picture does not show which is in front and which is behind. This makes the picture ambiguous; it can be interpreted two different ways. When a person stares at the picture, it will often seem to flip back and forth between the two valid interpretations (so-called multistable perception). multistable perception The effect is interesting because each part of the picture is ambiguous by itself, yet the human visual system picks an interpretation of each part that makes the whole consistent. The Necker Cube is sometimes used to test computer models of the human visual system to see if they can arrive at consistent interpretations of the image the same way humans do. Humans do not usually see an inconsistent interpretation of the cube. A cube whose edges cross in an inconsistent way is called an impossible object, specifically an impossible cube. With the cube on the left, most people see the lower-left face as being in front most of the time. This is possibly because people view objects from above, with the top side visible, far more often than from below, with the bottom visible, so the brain "prefers" the interpretation that the cube is viewed from above. There is evidence that by focusing on different parts of the figure one can force a more stable perception of the cube. The intersection of the two faces that are parallel to the observer froms a rectange, and the lines that converge on the square form a "y-junction" at the two diagonally opposite sides. If an observer focuses on the upper "y-junction" the lower left face will appear to be in front. The upper right face will appear to be in front if the eyes focus on the lower junction (Einhauser, et al., 2004). The Necker cube can shed light on the human visual system. Sidney Bradford, blind from birth but regaining his sight following an operation at age 52, did not perceive the ambiguity that normally sighted observers do.

External links

- [http://www.cs.ubc.ca/nest/imager/contributions/flinn/Illusions/NC/nc.html history of the cube and a Java applet]
- [http://www.cs.cf.ac.uk/Dave/JAVA/boltzman/Necker.html modelling human perception of the cube]
- [http://www.cut-the-knot.org/Curriculum/Geometry/Necker.shtml Necker Cube: A Visual Illusion] at cut-the-knot
- [http://enane.de/llpol.htm Explanation of the Necker cube and other gestalt phenomena]

References

[http://www.blackwell-synergy.com/links/doi/10.1111/j.1460-9568.2004.03722.x/abs/ Einhäuser, Wolfgang, Martin, Kevan A. C. & König, Peter (2004) Are switches in perception of the Necker cube related to eye position?. European Journal of Neuroscience 20 (10), 2811-2818.]Category:Optical illusions

Optical illusion

An optical illusion is a type of illusion characterized by visually perceived images that are deceptive or misleading [http://www.answers.com/topic/optical-illusion]. Information gathered by the eye is interpreted by the brain to give the perception that something is present when it is not. There are physiological illusions, that occur naturally, and cognitive illusions, that can be demonstrated by specific visual tricks that show particular assumptions in the human perceptual system [http://www.mindfake.com/what.html].

Physiological illusions

Physiological illusions, such as the afterimages following bright lights or adapting stimuli of excessively longer alternating patterns (contingent perceptual aftereffect, CAE), are the effects on the eyes or brain of excessive stimulation of a specific type - brightness, tilt, colour, movement, and so on. The theory is that stimuli have individual dedicated neural paths in the visual outer wall of an organism for the early stages of visual processing; repetitive stimulation of only a few channels misleads the visual system.

Cognitive illusions

Cognitive illusions are often more well-known. Instead of demonstrating a physiological base they interact with different levels of perceptual processing, in-built assumptions or 'knowledge' are misdirected. Cognitive illusions are commonly divided into ambiguous illusions, distorting illusions, paradox illusions, or fiction illusions. They often exploit the predictive hypotheses of early visual processing. Stereograms are based on a cognitive visual illusion. A mirage is an illusion that results from a natural optical phenomenon. The variation in the apparent size of the Moon (smaller when overhead, larger when near the horizon) is another natural illusion; it is not an optical phenomenon, but rather a cognitive or perceptual illusion. Developed illusions include phenomena such as the Necker cube and the Scintillating/Hermann grid. They could also be called discovered illusions. Understanding these phenomena is useful in order to understand the limitations of the human visual system. Ambiguous illusions are pictures or objects that offer significant changes in appearance. Perception will 'switch' between the alternates as they are considered in turn as available data does not confirm a single view. The Necker cube is a well known example, the motion parallax due to movement is being misinterpreted, even in the face of other sensory data. Another popular is the Rubin vase. Distorting illusions are the most common, these illusions offer distortions of size, length, or curvature. They were simple to discover and are easily repeatable. Many are physiological illusions, such as the Café wall illusion which exploits the early visual system encoding for edges. Other distortions, such as converging line illusions, are more difficult to place as physiological or cognitive as the depth-cue challenges they offer are not easily placed. All pictures that have perspective cues are in effect illusions. Visual judgements as to size are controlled by perspective or other depth-cues and can easily be wrongly set. Paradox illusions offer objects that are paradoxical or impossible, such as the Penrose triangle or impossible staircases seen, for example, in the work of M. C. Escher. The triangle is an illusion dependent on a cognitive misunderstanding that adjacent edges must join. They occur as a byproduct of perceptual learning. Fiction illusions are the perception of objects that are genuinely not there to all but a single observer, such as those induced by schizophrenia or hallucinogenic drugs. Known illusions include:
- Ames room illusion
- Ames trapezoidal window illusion
- Benham's top
- Bezold Effect
- Cafe wall illusion
- Converging line distortion illusion
- Craik-O'Brien-Cornsweet illusion
- Ehrenstein illusion
- Fraser spiral illusion
- Hering illusion
- Hermann grid illusion
- Illusory figure
- Impossible trident illusion
- Isometric illusion
- Jastrow illusion
- Kanizsa triangle
- Mach band
- Missing square puzzle
- Moon illusion
- Motion aftereffect
- Muller-Lyer distortion illusion
- Necker cube illusion
- Orbison illusion
- Penrose triangle aka Impossible triangle illusion
- Phi phenomenon
- Poggendorff illusion
- Ponzo illusion
- Pulfrich effect or Pulfrich pendulum illusion
- Rubin vase
- Sander illusion
- Scintillating illusion
- Size-weight illusion
- Stroop effect
- White's illusion
- Wundt illusion
- Zollner illusion Many famous artists have worked extensively with optical illusions, including M.C. Escher, Salvador Dalí, Giuseppe Arcimboldo, Marcel Duchamp, and Oscar Reutersvärd. Optical illusion is also used in film by the technique of forced perspective.

References

- [http://www.richardgregory.org/papers/knowl_illusion/knowledge-in-perception.pdf "Knowledge in perception and illusion"] by Richard Gregory, Phil. Trans. R. Soc. Lond. B (1997) 352, 1121–1128 - authorative introduction to optical illusions.

External links

- [http://www.eyetricks.com Optical Illusions & Other Eye Tricks]
- [http://www.lookmind.com/illusions.php Illusion World]
- [http://www.3dnauta.com Anamorphosis 3D multiple]
- [http://www.ritsumei.ac.jp/~akitaoka/index-e.html Illusions by Akiyoshi Kitaoka]
- [http://www.michaelbach.de/ot/index.html Optical Illusions & Visual Phenomena]
- [http://www.scientificpsychic.com/graphics/index.html Visual Paradoxes]
- [http://www.cut-the-knot.org/Curriculum/index.shtml#illusions Visual Illusions: 30 Java applets help see why they happen]
- [http://www.at-bristol.org.uk/Optical/default.htm Optical Illusions: Can you believe your eyes?]
- [http://www.cs.brown.edu/stc/outrea/greenhouse/nursery/optical_illusions/home.html Optical Illusions: Computer Art in the Classroom]
- [http://www.allopticalillusions.com Optical Illusions, Online Illusions]
- [http://www.coolopticalillusions.com Optical Illusions Pictures & Magic Eye Tricks]
- [http://www.grand-illusions.com/ Grand Illusions]
- [http://www.enane.de/empirhyp.htm Explanation of many visual illusions and other gestalt effects]
- [http://illusionsetc.blogspot.com Optical Illusions, and Optical Illusions in real life]
- [http://www.planetperplex.com/en/color_illusions.html Color Optical Illusions] Category:Optical phenomena ja:錯視

Switzerland

The Swiss Confederation or Switzerland (Latin: Confoederatio Helvetica) is a landlocked federal republic in Europe, bordering Germany, France, Italy, Austria and Liechtenstein. The country has a strong tradition of political and military neutrality, but also of international cooperation, and is home to many international organisations. Confoederatio Helvetica is the Latin official name. The use of Latin avoids having to choose one of the four official languages. The abbreviation (CH) is similarly used; for example, it is used as Switzerland's ccTLD, .ch. The Latin title Confoederatio Helvetica means Helvetic Confederation. The titles commonly used in French, Italian and Romansh translate as Swiss Confederation, while the German name of Schweizerische Eidgenossenschaft translates roughly as "Swiss Oath Fellowship" or "Swiss Commonwealth of the Covenant".

History

Switzerland is a federation of relatively autonomous cantons, some of which have a history of confederacy that goes back more than 700 years, arguably putting them among the world's oldest surviving republics. According to the popular legend, in 1291, representatives of the three forest cantons of Uri, Schwyz, and Unterwalden signed the Federal Charter. The charter united the involved parties in the struggle against foreign rule by the Habsburgs, who then held the German imperial throne of the Holy Roman Empire. At the Battle of Morgarten on November 15, 1315, the Swiss defeated the Habsburg army and secured quasi-independence as the Swiss Confederation. The authenticity of the Federal Charter is disputed, with many historians agreeing that it is in fact a forgery of the 14th century. By 1353, the three original cantons had been joined by the cantons of Glarus and Zug and the city states of Lucerne, Zürich and Berne, forming the "Old Federation" of eight states that persisted during much of the 15th century (although Zürich was expelled from the confederation during the 1440s due to a territorial conflict) and led to a significant increase of power and wealth of the federation, in particular due to the victories over Charles the Bold of Burgundy during the 1470s, and the success of the Swiss mercenaries. The traditional listing order of the cantons of Switzerland reflects this state, listing the eight "Old Cantons" first, with the city states preceding the founding cantons, followed by cantons that joined the federation after 1481, in historical order. The Swiss victory in a war against the Swabian League in 1499 amounted to de facto independence from the Holy Roman Empire. In 1506, Pope Julius II engaged the Swiss Guard that continues to serve the Vatican to the present day. The expansion of the federation, and the reputation of invincibility acquired during the earlier wars, suffered a first setback in 1515 with the Swiss defeat in the Battle of Marignano. The success of Zwingli's Reformation in some cantons led to inter-cantonal wars in 1529 and 1531 (Kappeler Kriege). The conflict between Catholic and Protestant cantons persisted, erupting in further violence at the battles of Villmergen in 1656 and 1712. 1712] Under the Treaty of Westphalia in 1648, European countries recognised Switzerland's independence from the Holy Roman Empire and its neutrality (ancien régime). In 1798, the armies of the French Revolution conquered Switzerland and imposed a new unified constitution. This centralised the government of the country and effectively abolished the cantons. The new regime was known as the Helvetic Republic and was highly unpopular. It had been imposed by a foreign invading army, had destroyed centuries of tradition, including the right to worship, and had made Switzerland nothing more than a French satellite state. Uprisings were common and only the presence of French troops kept them from succeeding. The brutal French suppression of the Nidwalden revolt in September was especially infamous. When war broke out between France and other countries Switzerland found itself being invaded by other outside forces from Austria and Russia. The Swiss were divided mainly between "Republicans" who were in favour of a centralised government, and "Federalists" who wanted to restore autonomy to the cantons. The violent conflict between both sides was never-ending. In Paris in 1803, Napoleon Bonaparte organised a meeting of the leading Swiss politicians from both sides. The result was the Act of Mediation which largely restored Swiss autonomy and introduced a Confederation of 19 Cantons. From then on much of Swiss politics would be about preserving the cantons' right to self-rule and the need for a central government. The Congress of Vienna in 1815 fully re-established Swiss independence and the European powers agreed to permanently recognise the Swiss neutrality. At this time, the territory of Switzerland was increased for the last time, by the new cantons of Valais, Neuchatel and Geneva. In 1847, a civil war broke out between the Catholic and the Protestant cantons (Sonderbundskrieg). Its immediate cause was a 'special treaty' (Sonderbund) of the Catholic cantons. The war lasted for less than a month, causing fewer than 100 casualties. Apart from small riots, this was the latest armed conflict on Swiss territory. As a consequence of the civil war, Switzerland adopted a federal constitution in 1848, amending it extensively in 1874 and establishing federal responsibility for defence, trade, and legal matters. In 1891, the constitution was revised with unusually strong elements of direct democracy, which remains unique even today. Since then, continued political, economic, and social improvement has characterised Swiss history. In 1920, Switzerland joined the League of Nations, and in 1963 the Council of Europe. Switzerland proclaimed neutrality in World War I and was not involved militarily in the conflict. Neutrality was again proclaimed in World War II, and although a German intervention was both planned and anticipated, it ultimately didn't occur. The massive mobilisation of Swiss armed forces under the leadership of General Henri Guisan is often cited as a decisive factor that the German invasion was never initiated. Modern historical findings, such as the research done by the Bergier commission, indicate that another major factor was the continued trade by Swiss banks with Nazi Germany. Bergier commission Women were granted the right to vote in the first cantons in 1959, at the federal level in 1971, in the last canton, Appenzell Innerrhoden, only in 1990. In 1979, parts of the canton of Berne attained independence, forming the new canton of Jura. On April 18, 1999 the Swiss population and the cantons voted in favour of a completely revised federal constitution. In 2002 Switzerland became a full member of the United Nations, leaving the Vatican as the last widely recognised state without full UN membership. Switzerland is not a member state of the EU but applied for membership therein in May 1992. Switzerland has not advanced this application since the rejection, by referendum, of the European Economic Area in December 1992. However, Swiss law is gradually being adjusted to that of the EU and the government has signed a number of bilateral agreements with the European Union. Switzerland (together with Liechtenstein) has been surrounded by the EU since Austria's membership in 1995. On June 5, 2005, Swiss voters agreed, by a 55% majority, to join the Schengen treaty, a result that was welcomed by EU commentators as a sign of goodwill by a Switzerland that is traditionally perceived as isolationist.

Politics

Schengen treaty]] The bicameral Swiss parliament, the Federal Assembly, is the primary seat of power, apart from the Federal Council. Both houses, the Council of States and the National Council, have equal powers in all respects, including the right to introduce legislation. Under the 1999 constitution, cantons hold all powers not specifically delegated to the federation. The 46 members of the Council of States (two from each canton and one from former half cantons) are directly elected in each canton, whereas the 200 members of the National Council are elected directly under a system of proportional representation. Members of both houses serve for 4 years. Through referenda citizens may challenge any law voted by federal parliament and through initiatives introduce amendments to the federal constitution, making Switzerland a semi-direct democracy. The top executive body and collective Head of State is the Federal Council, a collegial body of seven members. Although the constitution provides that the Assembly elects and supervises the members of the Council, the latter (and its administration) has gradually assumed a pre-eminent role in directing the legislative process as well as executing federal laws. The President of the Confederation is elected from the seven to assume special representative functions for a one-year term. From 1959 to December 2003, the four major parties were represented in the Federal Council according to the "magic formula", proportional to their representation in federal parliament: 2 Christian Democrats (CVP/PDC), 2 from the Social Democrats (SPS/PSS), 2 Free Democrats (FDP/PRD), and 1 from the Swiss People's Party (SVP/UDC). This traditional distribution of seats, however, is not backed up by any law, and in the 2003 elections to the Federal Council the CVP/PDC lost their second seat to the SVP/UDC. The function of the Federal Supreme Court is to hear appeals of cantonal courts or the administrative rulings of the federal administration. The judges are elected by the Federal Assembly for six-year terms. See also: International relations of Switzerland

Direct democracy

Switzerland features a system of government not seen at the national level on any other place on earth: Direct democracy. Any citizen may challenge a law that has been passed by parliament. If he is able to gather 50,000 signatures against the law within 100 days, a national vote has to be scheduled where voters decide by a simple majority whether to accept or reject the law. Also, any citizen may seek a decision on an amendment they want to make to the constitution. For such an amendment initiative to be organised, the signatures of 100,000 voters must be collected within 18 months. Such a popular initiative may be formulated as a general proposal or - much more often - be put forward as a precise new text whose wording can no longer be changed by parliament and the government. After a successful vote gathering, the federal council may create a counterproposal to the proposed amendment and put it to vote on the same day. Such counterproposals are usually a compromise between the status quo and the wording of the initiative. Voters will again decide in a national vote whether to accept the initiative amendment, the counterproposal put forward by the government or both. If both are accepted, one has to additionally signal a preference. Initiatives have to be accepted by a double majority of both the popular votes and a majority of the states.

Energy politics

The energy generated in Switzerland comprises around 40 percent nuclear power and 60 percent from hydroelectricity. On May 18, 2003, two referenda regarding the future of nuclear power in Switzerland were held. The referendum Electricity without nuclear asked for a decision on a nuclear power phase-out and Moratorium Plus asked about an extension an existing law forbidding the building of new nuclear power plants. Both were turned down: Moratorium Plus by a margin of 41.6% for and 58.4% opposed, and Electricity Without Nuclear by a margin of 33.7% for and 66.3% opposed. The former ten-year moratorium on the construction of new nuclear power plants was the result of a citizens' initiative voted on in 1990 which had passed with 54.5% Yes vs. 45.5% No votes (see Nuclear power phase-out#Switzerland for details).

Cantons (states)

Nuclear power phase-out#Switzerland]] The Swiss Confederation consists of 26 cantons:
- These cantons are represented by only one councillor in the Council of States. Their populations vary between 15,000 (Appenzell Innerrhoden) and 1,253,500 (Zürich), and their area between 37 km² (Basel-Stadt) and 7,105 km² (Grisons). The Cantons comprise a total of 2,889 municipalities. The following are enclaves within Switzerland: Büsingen is territory of Germany, Campione d'Italia is territory of Italy.

Geography

Italy With an area of 41,285 km², Switzerland is a small country. The population is around 7.4 million, resulting in a population density of 184 people per km². Switzerland comprises three basic topographical areas: the Swiss Alps, the Swiss plateau, and the Jura mountains.The Alps are a high mountain range running across the central-south of the country. Among the high peaks of the Swiss Alps, the highest of which is the Dufour Peak at 4,634 m, are found countless valleys, some with glaciers. From these the headwaters of several major European rivers such as the Rhine, the Rhône, the Inn, the Aare or the Ticino, flow down into lakes such as Lake Geneva, Lake Zürich, Lake Neuchâtel, and Lake Constance. Lake Constance The northern, more populous part of the country is more open, but can still be mountainous, for example, in the Jura Mountains, a smaller range in the northwest. The Swiss climate is generally temperate, but can vary greatly between the localities, from harsh conditions on the high mountains to the often pleasant Mediterranean climate at Switzerland's southern tip. A zoomable map of Switzerland is available at either [http://www.swissinfo-geo.org www.swissinfo-geo.org] or [http://www.swissgeo.ch www.swissgeo.ch]; a zoomable satellite picture is at [http://map.search.ch/ map.search.ch].
See also: Swisstopo topographical survey, List of lakes of Switzerland, List of rivers of Switzerland, List of mountain passes in Switzerland.

Economy

Switzerland is a prosperous and stable modern market economy, with a per capita GDP that is higher than those of the big western European economies. For much of the 20th century Switzerland was the wealthiest country in Europe by a considerable margin. However since the early 1990s it has suffered from slow growth, and as of 2005 it had fallen to fourth among European states with populations above one million in terms of Gross Domestic Product per capita at purchasing power parity, behind Ireland, Denmark and Norway (see list). Switzerland is a member of the European Free Trade Association. In recent years, the Swiss have brought their economic practices largely into conformity with those of the European Union, in an effort to enhance their international competitiveness, but this has not produced strong growth. Full EU membership is a long-term objective of the Swiss government, but there is considerable popular sentiment against this. To this end, it has established an [http://www.europa.admin.ch/e/index.htm Integration Office] under the Department of Foreign and Economic Affairs. To minimise the negative consequences of Switzerland's isolation from the rest of Europe, Bern and Brussels signed seven agreements, called Bilateral Agreements I, to further liberalise trade ties in 1999 and entering into force in 2001. This first series of bilateral agreements included the free movement of persons. A second series covering nine areas was signed in 2004 and awaits ratification. The second series includes the Schengen treaty and the Dublin Convention. They continue to discuss further areas for cooperation. Preparatory discussions are being opened on four new areas: opening up the electricity market, participation in the European GPS system Galileo, cooperating with the European centre for disease prevention and recognising certificates of origin for food products. Switzerland voted against membership in the European Economic Area in December 1992 and has since maintained and developed its relationships with the European Union and European countries through bilateral agreements.
- List of Swiss companies
- Swiss bank

Demographics

Swiss bank (19.2%),
Italian (7.6%),
Romansh (0.6%)]] Switzerland sits at the crossroads of several major European cultures that have heavily influenced the country's languages and culture. Switzerland has three nationwide official languages (German (64%) in the north and centre, French (19%) to the west, and Italian (8%) in the south), plus a fourth national language that is considered official locally (Romansh, a Romance language spoken by a small minority (< 1%) in the southeastern canton of Graubünden and in parts of Ticino). The federal government is obliged to communicate in the three official languages. In the federal parliament, German, French and Italian are the official languages and simultaneous translation is provided. The German spoken in Switzerland is predominantly a group of dialects that are almost unintelligible to Germans and are collectively known as Swiss German, but written communication and broadcasts typically use standard German. Swiss French and Swiss Italian differ far less from their counterparts in France and Italy, respectively. Learning one of the other national languages at school is obligatory for all Swiss, so most Swiss are at least bilingual. English is considered by some as a Swiss lingua franca, and most Swiss people have some command of English; many Swiss documents and websites are available in English. Resident foreigners and temporary foreign workers make up about 20% of the population. The most popular religion in Switzerland is Roman Catholicism (43% of the population). There are various Protestant denominations (35%), while immigration has brought Islam (4%) and Eastern Orthodoxy (2%) as sizeable minority religions. The stability and prosperity of Switzerland, combined with a linguistically diverse population, has led some to describe the country as a consensus, or consociational state.
- List of Swiss people

Culture

List of Swiss people] The culture of Switzerland is influenced by its neighbours, but over the years a distinctive culture with strong regional differences has developed. Traditionally Switzerland is not considered one of the centres of European culture, but this conception might be deceptive. A number of culturally active Swiss have chosen to move abroad, probably given the limited opportunities in their homeland. At the same time, the neutrality of Switzerland has attracted many creative people from all over the world. In war times the tradition of political asylum helped to attract artists, whilst recently low taxes seem predominant. Strong regionalism in Switzerland makes it difficult to speak of a homogeneous Swiss culture. The influence of German, French and Italian culture on their neighbouring parts and the influence of Anglo-American culture cannot be denied. The Rhaeto-Romanic culture in the eastern mountains of Switzerland is robust. The Swiss are noted for their banks, their chocolate, their cheese, their pocket knives, their watches (particularly the famous Rolex), their private boarding schools and their strengths in engineering and the sciences. The tallest building in Switzerland is the Basler Messeturm.
- Music of Switzerland
- Culture of Switzerland
- Swiss cuisine
- SRG SSR idée suisse

External links

- Governmental websites
- [http://www.admin.ch/ch/index.en.html The Federal Authorities]
- [http://www.parlament.ch/e/homepage.htm The Swiss Parliament]
- [http://www.bger.ch/ Federal Supreme Court] - (in German, French and Italian)
- [http://www.bfs.admin.ch/bfs/portal/en/ Swiss Federal Statistical Office]
- [http://www.swissinfo.org/ Switzerland's news and information platform] - maintained by the public Swiss Broadcasting Corporation (in 9 languages)
- Historical Dictionary of Switzerland: [http://www.dhs.ch www.dhs.ch] - Country encyclopedia (in German, French and Italian)
- [http://www.swissworld.org/ Swissworld] - an encyclopedic presentation of the country by the Swiss Confederation
- [http://www.about.ch/ About.ch] - another presentation of the country
- [http://www.myswitzerland.com/ Switzerland Tourism] National tourist office
- [http://www.culturelinks.ch/ Culturelinks.ch] - a portal giving access to Swiss culture websites
- [http://www.are.ch/ Spatial Planning in Switzerland] Website of Swiss Federal Office for Spatial Development (land-use planning, transportation, sustainable development)
- [http://map.search.ch/ Map.Search.ch] Maps of Switzerland
- [http://www.justlanded.com/english/switzerland/ Just Landed Switzerland] - Useful info for moving to Switzerland
- Alemannic Wikipedia
- Category:Landlocked countries als:Schweiz zh-min-nan:Sūi-se ko:스위스 ms:Switzerland ja:スイス simple:Switzerland th:ประเทศสวิตเซอร์แลนด์

Crystallographer

Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals. Before the development of X-ray diffraction crystallography (see below), the study of crystals was based on the geometry of the crystals. This involves measuring the angles of crystal faces relative to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The former is carried out using a goniometer. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wolff net or Lambert net. In fact, the pole to each face is plotted on the net. Each point is labelled with its Miller Index. The final plot allows the symmetry of the crystal to be established. Crystallographic methods now rely on the analysis of the diffraction patterns that emerge from a sample that is targeted by a beam of some type. The beam is not always electromagnetic radiation, even though X-rays are the most common choice. For some purposes electrons or neutrons are used, which is possible due to the wave properties of the particles. Crystallographers often explicitly state the type of illumination used when referring to a method, as with the terms X-ray diffraction, neutron diffraction and electron diffraction. X-rays are useful for visualizing the electron clouds around atoms, whereas neutron diffraction methods will reveal the atomic nuclei. Thus far, electron diffraction has not been widely used. Crystallography by itself typically implies X-rays.

Theory

In many cases, an image of a microscopic object is generated by focusing the rays of the visible spectrum using a lens as in light microscopy. However, because the wavelength of visible light is long compared to atomic bond lengths and atoms themselves, it is necessary to use radiation with shorter wavelengths, such as X-rays. Employing shorter wavelengths implies abandoning microscopy and true imaging, however, because there exists no material from which a lens capable of focusing this type of radiation can be created. (That said, scientists have had some success focusing X-rays with microscopic Fresnel zone plates made from gold). Generally, in diffraction-based imaging, the only wavelengths used are those that are too short to be focused. This difficulty is the reason that crystals must be used. Because of their highly ordered and repetitive structure, crystals are an ideal material for analyzing the structure of solids. To use X-ray diffraction as an example, a single X-ray photon diffracting off of one electron cloud will not generate a strong enough signal for the equipment to detect. However, many X-rays diffracting off many electron clouds in approximately the same relative position and orientation throughout the crystal will result in constructive interference and hence a detectable signal.

Notation

See Miller index for a full treatment of this topic.
- Coordinates in square brackets such as [100] denote a direction (in real space).
- Coordinates in angle brackets or chevrons such as <100> denote a family of directions which are equivalent due to symmetry operations. If it refers to a cubic system, this example could mean [100], [010], [001] or the negative of any of those directions.
- Coordinates in parentheses such as (100) denote the direction of a plane normal.
- Coordinates in curly brackets or braces such as denote a family of plane normals which are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.

Technique

Some materials studied using crystallography, DNA for example, do not occur naturally as crystals. Typically, such molecules are placed in solution and allowed to crystallize over days, weeks, or months through vapor diffusion. A drop of solution containing the molecule, buffer, and precipitants is sealed in a container with a reservoir containing a hygroscopic solution. Water in the drop diffuses to the reservoir, slowly increasing the concentration and allowing a crystal to form. If the concentration were to rise more quickly, the molecule would simply precipitate out of solution, resulting in disorderly granules rather than an orderly and hence usable crystal. Once a crystal is obtained, data can be collected using a beam of radiation. Although many universities that engage in crystallographic research have their own X-ray producing equipment, Synchrotrons are often used as X-ray sources, because of the purer and more complete patterns such sources can generate. Synchrotron sources also have a much higher intensity of x-ray beams, so data collection takes a fraction of the time normally necessary at weaker sources. Producing an image from a diffraction pattern requires sophisticated mathematics and often an iterative process of modelling and refinement. In this process, the mathematically predicted diffraction patterns of an hypothesized or "model" structure are compared to the actual pattern generated by the crystalline sample. Ideally, researchers make several initial guesses, which through refinement all converge on the same answer. Models are refined until their predicted patterns match to as great a degree as can be achieved without radical revision of the model. This is a painstaking process, made much easier today by computers. The mathematical methods for the analysis of diffraction data only apply to patterns, which in turn result only when waves diffract from orderly arrays. Hence crystallography applies for the most part only to crystals, or to molecules which can be coaxed to crystalize for the sake of measurement. In spite of this, a certain amount of molecular information can be deduced from the patterns that are generated by fibers and powders, which while not as perfect as a solid crystal, may exhibit a degree of order. This level of order can be sufficient to deduce the structure of simple molecules, or to determine the coarse features of more complicated molecules (the double-helical structure of DNA, for example, was deduced from an X-ray diffraction pattern that had been generated by a fibrous sample).

Materials science

Crystallography is a tool that is often employed by materials scientists. In single crystals, the effects of the crystalline arrangement of atoms is often easy to see macroscopically, because the natural shapes of crystals reflect the atomic structure. In addition, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understanding crystallographic defects. A number of other physical properties are linked to crystallography. For example, the minerals in clay form small, flat, platelike structures. Clay can be easily deformed because the platelike particles can slip along each other in the plane of the plates, yet remain strongly connected in the direction perpendicular to the plates. In another example, iron transforms from a body-centered cubic (bcc) structure to a face-centered cubic (fcc) structure called austenite when it is heated. The fcc structure is a close-packed structure, and the bcc structure is not, which explains why the volume of the iron decreases when this transformation occurs. Crystallography is useful in phase identification: That is, when performing some kind of processing on a material, it is often desired to find out what compounds and what phases are present in the material. Each phase has a characteristic arrangement of atoms. Techniques like X-ray diffraction can be used to identify which patterns are present in the material, and thus which compounds are present (note: the determination of the "phases" within a material should not be confused with the more general problem of "phase determination," which refers to the phase of waves as they diffract from planes within a crystal, and which is a necessary step in the interpretation of complicated diffraction patterns). Crystallography covers the enumeration of the symmetry patterns which can be formed by atoms in a crystal and for this reason has a relation to group theory and geometry. See Symmetry group.

Biology

X-ray crystallography is the primary method for determining the molecular conformations of biological macromolecules, particularly protein and nucleic acids such as DNA and RNA. In fact, the double-helical structure of DNA was deduced from crystallographic data. The first crystal structure of a macromolecule was solved in 1958 (Kendrew, J.C. et al. (1958) A three-dimensional model of the myoglobin molecule obtained by X-ray analysis. Nature 181, 662-666.). The Protein Data Bank (PDB) at http://www.rcsb.org is a freely accessible repository for the structures of proteins and other biological macromolecules. RasMol can be used to visualize biological molecular structures. Electron crystallography has been used to determine some protein structures, most notably membrane proteins and viral capsids.

External links

- [http://www.rockhounds.com/rockshop/xtal/index.html Introduction to Crystallography and Mineral Crystal Systems]
- [http://www.iucr.ac.uk/iucr-top/comm/cteach/pamphlets.html Crystallographic Teaching Pamphlets]
- [http://cst-www.nrl.navy.mil/lattice/spcgrp/ Crystal Lattice Structures]
- [http://www.ccp14.ac.uk/ Freely Available Crystallographic Software for Academia] ja:結晶学

Multistable perception

Multistable perceptual phenomena are a rare form of visual perception, characterized by an unpredictable sequence of spontaneous subjective changes.

Classification

Perceptual multistability can be evoked by a large number of visual patterns that are too ambiguous for the visual system to settle down on a unique interpretation. Famous examples include the Necker cube, Structure from motion, Monocular rivalry and Binocular rivalry, but many more visually ambiguous patterns are known. Because most of these images lead to an alternation between two mutually exclusive perceptual states, they are sometimes also referred to as bistable perception.

Characterization

Transitions from one percept to its alternative are called perceptual reversals. They are spontaneous and stochastic events which cannot be eliminated by intentional efforts (although some control over the alternation process is learnable). Reversal rates vary drastically between stimuli and observers.

Cultural history

Human interest in these phenomena can be traced back to antiquity. The fascination of multistable perception probably comes from the active nature of endogenous perceptual changes or from the dissociation of dynamic perception from constant sensory stimulation. In the 1980s, multistable visual patterns caught the attention of philosophers, psychologists, and neuroscientists.

Bibliography

# Alais, D & Blake, R (eds.), Binocular Rivalry, MIT Press, 2005, ISBN 026201212X # Kruse, P & Stalder, M (eds.), Ambiguity in Mind and Nature: Multistable Cognitive Phenomena, Springer, 1995, ISBN 0387570829

External links

- [http://eluzions.com/Illusions/Ambiguous/ A collection of visually ambiguous patterns]
- [http://www.sandlotscience.com/Ambiguous/Ambiguous_frm.htm Another large collection of multistable images] category:perception

Impossible object

An impossible object is an object that cannot exist according to the known laws of nature, but has a description or representation suggesting, at first sight, that it can. Drawings of objects that cannot exist are called "undecidable figures". The undecidability of these figures invariably rests on them being interpreted as two-dimensional projections of what would be an impossible higher-dimensional object. Artist M. C. Escher is notable for many drawings that feature undecidable figures, sometimes with the entire drawing being an undecidable figure.

Notable examples

Notable undecidable figures include:
- impossible cube
- Penrose stairs
- Penrose triangle
- blivet (or devil's pitchfork)

In fiction

- In the Star Trek: The Next Generation episode "I, Borg", a plan was made to destroy the entire race of Borg – malevolent cybernetic aliens whose minds were interconnected – by showing one of the borg a picture of a highly-complex impossible object. This image would be transmitted back to the Borg hive, overloading its consciousness in larger and larger attempts to understand the image. This plan was dismissed as being genocide, so its potential results were never seen.

References

- Mathematical Circus, Martin Gardner 1979 ISBN 0-14-02-2355-X (Chapter 1 – Optical Illusions)
- [http://www.worldofescher.com/gallery/Belvedere.html Escher's Belvedere]

External links

- [http://www.cut-the-knot.org/impossible/index.shtml Things Impossible] at cut-the-knot
- [http://haegar.fh-swf.de/spielwiese/unmoeglicheObjekte/english/Reality.html Impossible Objects] Category:Optical illusions

Sidney Bradford

Sidney Bradford, (1906 - 1960), went blind at 10 months of age but regained sight after a cornea transplant at the age 52. He was the subject of many scientific studies of perception by neuropsychologist Richard Gregory [http://www.richardgregory.org/papers/recovery_blind/recovery-from-early-blindness.pdf]. Just after the restoration of his sight, Bradford was able to read (visually) the time on the ward clock. He could thus see by analogy with earlier touch experience. Bradford did not perceive the ambiguity of the Necker cube and was unable to interpret the perspective of two dimensional art. Nevertheless, he could accurately judge the distance to objects in the same room (being familiar with these distances prevision by virtue of walking to them).

Cut-the-knot

cut-the-knot is an educational website maintained by Alexander Bogomolny devoted to popular exposition of a great variety of topics in mathematics. Its "Manifesto" states:

Judging Mathematics by its pragmatic value is like judging symphonia by the weight of its score.
...
I hope to create a resource that would help learn, if not math itself, then, at least, ways to appreciate its beauty.
...
Learning starts from wondering, and another purpose of this site is to serve as a resource for things, simple but curious, related to Mathematics.
...
This site is a Miscellany.

External links

- http://www.cut-the-knot.org
- [http://www.cut-the-knot.org/manifesto/index.shtml Manifesto] Category:Educational websites Category:Online encyclopedias

Saint-Denis basilica

The Basilica of Saint Denis (French: Basilique de Saint-Denis, or simply Basilique Saint-Denis) is the famous burial site of the French monarchs, comparable to Westminster Abbey in England. Almost all the kings of France were buried in the Basilica, but unlike Westminster Abbey it was not used for coronations (a role devoted to the Cathedral of Reims). The basilica is located in Saint Denis, now a northern suburb of Paris. Saint Denis is a patron saint of France and, according to legend, was the first bishop of Paris. A simple shrine was erected at his burial place. There Dagobert I, king of the Franks, who reigned from 628 to 637, founded the Abbey of Saint Denis, attached to a Benedictine monastery.

Architecture

The church is an architectural landmark, part of which is considered to be the first major structure built in the Gothic style. Saint Denis' Gothic structure that we know and see today was begun in 1136 by the Abbot Suger (1081-1155), but the major construction was not completed until the end of the 13th century. 13th century

Burial site

The abbey is where the kings of France were buried for centuries and is therefore often referred to as the "royal necropolis of France". All but three of the monarchs of France from the 10th century until 1789 have their remains here. The abbey church contains some fine examples of cadaver tombs. The effigies of many of the kings and queens are on their tombs, but during the French Revolution, these tombs were opened by workers under orders from revolutionary officials. The bodies were removed and dumped in two large pits nearby. Archaeologist Alexandre Lenoir saved many of the monuments from the same revolutionary officials by claiming them as artworks for his Museum of French Monuments. Napoleon Bonaparte reopened the church in 1806, but the royal remains were left in their mass-graves. Following Napoleon's first exile to Elba, the Bourbons briefly returned to power. They ordered a search for the corpses of Louis XVI and Marie Antoinette, which were found on January 21, 1815 and brought to St. Denis and buried in the crypt. In 1817, the mass-graves containing all the other remains were opened but it was impossible to distinguish any one from the collection of bones. As such, the remains were placed in an ossuary in St. Denis' crypt, behind two marble plates with the name of each monarch duly recorded. King Louis XVIII, on his death in 1824, was buried in the center of the crypt, near the graves of Louis XVI and Marie Antoinette. Under the direction of architect Viollet-le-Duc, famous for his work on Notre-Dame de Paris, the monuments that were taken to the Museum of French Monuments were returned to the church. The corpse of King Louis VII, who had been buried at the Abbey at Saint-Pont and whose tomb had not been touched by the revolutionaries, was brought to St. Denis and buried in the crypt.

Tombs

Some of the members of the royal families of France buried in the Saint Denis Basilica are:
- Childebert I (496-558)
- Fredegonde (Wife of Chilperic I of Neustria)
- Clovis I (465 - 511)
- Dagobert I (603-639)
- Clovis II (635-657)
- Charles Martel
- Carloman (866-884)
- Pippin the Younger (714-768) and his wife Berthe (726-783)
- Philip III the Bold (1245 - 1285)
- Philip IV the Fair (1268 - 1315) and Isabella of Aragon
- Leo VI of Armenia (1342-1393)
- Francis I of France
- Henry II of France and Catherine de' Medici
- Francis II of France
- Louis XVI of France and Marie Antoinette

External links

- [http://www.findagrave.com/php/famous.php?page=cem&FScemeteryid=1974848 Detailed list of members of the French Royal families buried in Saint Denis Basilica]
- [http://maps.google.com/maps?q=saint-denis,+france&ll=48.935455,2.359765&spn=0.003000,0.010274&t=h&hl=en Satellite image from Google Maps] Category:Basilica churches in France Category:Gothic architecture Category:Cemeteries in France Category:Abbeys in France Category:Seine-Saint-Denis Category:Churches in Paris simple:Saint Denis Basilica

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