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Barber paradox

The barber paradox is a puzzle derived from Russell's paradox. It was used by Bertrand Russell himself as an illustration of the paradox, though he attributes it to an unnamed person who suggested it to him; the puzzle shows that an plausible scenario is logically impossible. It describes a barber, defined such that he both shaves himself and does not shave himself; the barber is the "one who shaves all those, those only, who do not shave themselves". The question is, does the barber shave himself? Answering this question results in a contradiction; the barber can not shave himself. Thus, if he shaves himself he ceases to be the barber. Conversely, if the barber does not shave himself he fits into the group of people who would be shaved by the barber, thus, as the barber, he must shave himself; this paradox is incorrectly attributed to Bertrand Russell. It was suggested to Gardner as an alternative form of Russell's paradox, which Russell had devised to show that set theory as it was used by Georg Cantor and Gottlob Frege contained contradictions.

However, Russell denied that the Barber's paradox was an instance of his own: That contradiction is interesting. You can modify its form. I once had a form suggested to me, not valid, namely the question whether the barber shaves himself or not. You can define the barber as "one who shaves all those, those only, who do not shave themselves"; the question is, does the barber shave himself? In this form the contradiction is not difficult to solve, but in our previous form I think it is clear that you can only get around it by observing that the whole question whether a class is or is not a member of itself is nonsense, i.e. that no class either is or is not a member of itself, that it is not true to say that, because the whole form of words is just noise without meaning. This point is elaborated further under Applied versions of Russell's paradox; this sentence is unsatisfiable because of the universal quantifier. The universal quantifier y will include every single element in the domain, including our infamous barber x.

So when the value x is assigned to y, the sentence can be rewritten to shaves ↔ ¬ shaves, an instance of the contradiction a ↔ ¬ a. Cantor's theorem Gödel's incompleteness theorems Halting problem List of paradoxes Double bind Proposition of the Barber's Paradox Joyce, Helen. "Mathematical mysteries: The Barber's Paradox". Plus, May 2002. Edsger Dijkstra's take on the problem The Monist, Vol. 29, No. 3, JULY, 1919, THE PHILOSOPHY OF LOGICAL ATOMISM, page 354


In hydrodynamics, a clapotis is a non-breaking standing wave pattern, caused for example, by the reflection of a traveling surface wave train from a near vertical shoreline like a breakwater, seawall or steep cliff. The resulting clapotic wave does not travel horizontally, but has a fixed pattern of nodes and antinodes; these waves promote erosion at the toe of the wall, can cause severe damage to shore structures. The term was coined in 1877 by French mathematician and physicist Joseph Valentin Boussinesq who called these waves'le clapotis' meaning "the lapping". In the idealized case of "full clapotis" where a purely monotonic incoming wave is reflected normal to a solid vertical wall, the standing wave height is twice the height of the incoming waves at a distance of one half wavelength from the wall. In this case, the circular orbits of the water particles in the deep-water wave are converted to purely linear motion, with vertical velocities at the antinodes, horizontal velocities at the nodes.

The standing waves alternately rise and fall in a mirror image pattern, as kinetic energy is converted to potential energy, vice versa. In his 1907 text, Naval Architecture, Cecil Peabody described this phenomenon: At any instant the profile of the water surface is like that of a trochoidal wave, but the profile instead of appearing to run to the right or left, will grow from a horizontal surface, attain a maximum development, flatten out till the surface is again horizontal. If attention is concentrated on a certain crest, it will be seen to grow to its greatest height, die away, be succeeded in the same place by a hollow, the interval of time between the successive formations of crests at a given place will be the same as the time of one of the component waves. True clapotis is rare, because the depth of the water or the precipitousness of the shore are unlikely to satisfy the idealized requirements. In the more realistic case of partial clapotis, where some of the incoming wave energy is dissipated at the shore, the incident wave is less than 100% reflected, only a partial standing wave is formed where the water particle motions are elliptical.

This may occur at sea between two different wave trains of near equal wavelength moving in opposite directions, but with unequal amplitudes. In partial clapotis the wave envelope contains some vertical motion at the nodes; when a wave train strikes a wall at an oblique angle, the reflected wave train departs at the supplementary angle causing a cross-hatched wave interference pattern known as the clapotis gaufré. In this situation, the individual crests formed at the intersection of the incident and reflected wave train crests move parallel to the structure; this wave motion, when combined with the resultant vortices, can erode material from the seabed and transport it along the wall, undermining the structure until it fails. Clapotic waves on the sea surface radiate infrasonic microbaroms into the atmosphere, seismic signals called microseisms coupled through the ocean floor to the solid Earth. Clapotis has been called the pleasure of sea kayaking. Rogue wave Seiche Boussinesq, J.. "Théorie des ondes liquides périodiques".

Mémoires Présentés Par Divers Savants à l'Académie des Sciences. 20: 509–616. Boussinesq, J.. "Essai sur la théorie des eaux courantes". Mémoires Présentés Par Divers Savants à l'Académie des Sciences. 23: 1–660. Hires, G.. "Étude du clapotis". La Houille Blanche. 15: 153–63. Doi:10.1051/lhb/1960032. Leméhauté, B.. I.. Clapotis and Wave Reflection: With an Application to Vertical Breakwater Design. Civil Engineering Dept. Queen's University at Kingston, Ontario. Willi Water. "Clapotis Wave Action" – via YouTube

Open and affirming

Open and Affirming is an official designation of congregations and other settings in the United Church of Christ affirming the full inclusion of gays, bisexuals and non-binary persons in the church's life and ministry. The Open and Affirming program is administered by the UCC Open and Affirming Coalition, which supports congregations and other church settings as they consider the adoption of an ONA "covenant" and maintains the official registry of ONA congregations and ministries; the Coalition encourages UCC congregations, campus ministries, regional bodies and other settings of the church to engage their members in serious study of sexual orientation and gender identity and to declare publicly their full welcome and inclusion of LGBTQ people. With more than 1,600 congregations, the UCC's ONA program is the largest of several LGBT-welcoming church movements in U. S. and Canadian churches. There is a similar "Affirming" program in the Christian Church. In 1985 the United Church of Christ's General Synod adopted a resolution encouraging UCC congregations to welcome gay and bisexual people after a time of dialogue and prayer.

Following General Synod resolutions affirming transgender members of the church, the welcome was extended so that, today, an ONA covenant welcomes members of any sexual orientation or gender identity and expression. An ONA church is expected to commit to the inclusion of LGBTQ members in the sacraments and ministries of the church, including marriage; the 1985 resolution had no legislative authority over individual congregations, which are autonomous, but set in motion a movement that spread throughout the church. The resolution allocated no funds to support an ONA program in the UCC's national office; as a result, the UCC Coalition for LGBT Concerns launched an ONA program in 1987, led by the Rev. Ann B. Day and Donna Enberg, which raised funds from individual contributors, sympathetic congregations and private foundations. To this day, the official registry of ONA congregations is managed by the Coalition, a voluntary non-profit organization independent from the church's national office, although it works in close partnership with the UCC's national ministries.

The Coalition publishes a wide range of resources to support congregations considering an ONA commitment and to help existing ONA churches build relationships with the LGBTQ community. New York City's Riverside Church, under the pastoral leadership of the late Rev. William Sloane Coffin, was the first in the UCC to be listed as Open and Affirming in 1987. According to the Coalition, more than 1,600 UCC congregations with 370,000 members are listed as Open and Affirming as of December 2019. Twenty-one of the UCC's 38 regional conferences, most new church starts, all seven seminaries affiliated with the UCC and several UCC-related campus ministries have adopted ONA statements, or "covenants." Other ministries in the UCC, like the Council for Health and Human Service Ministries and the Order of Corpus Christi have adopted ONA covenants. In response to the perceived promotion of the ONA movement by denominational officials, 75 UCC congregations have identified themselves as "Faithful and Welcoming" by affirming the Lexington Confession, which affirms marriage as an relationship between a man and woman.

LGBT-affirming religious groups UCC Open and Affirming Coalition website UCC LGBT Ministries Open & Affirming website for Christian Church

Quimsachata (Canchis)

Quimsachata is an extinct volcano in the Andes of Peru. It is located in the Cusco Region, Canchis Province at about 24 kilometres northwest of the town of Sicuani; this volcano is constructed from two separate centres, one active 11,500 years ago which formed a scoria cone and a lava field and another active 4450 BCE which formed two lava flows and a lava dome. Volcanism in southern Peru occurs as part of two distinct volcanic systems, the stratovolcanoes of the Western Cordillera and the Altiplano volcanoes which are small systems with surface areas of less than 50 square kilometres. Of these Altiplano volcanoes, a number of them are potassium enriched or ultrapotassic rocks and are arranged along various lineaments. One of these lineaments is associated with the Cusco and Vilcanota faults which separate the Altiplano into a western and eastern portion. Quimsachata is located along this central and still active lineament, whereas the other two lineaments on each side of the fault system were active in the Oligocene and Miocene.

A variety of rock types occur in association with these lineaments. The Quimsachata group consists of Quimsachata itself and Oroscocha. Situated along the foot of the Eastern Cordillera, they are the northernmost young Peruvian volcanoes and lie far away from the principal volcanic arc. Local Inka myths may refer to volcanic activity at Quimsachata, they may have included the event into their creation myths and religious practices despite the eruption occurring long before their civilization. Quimsachata was formed by a lava field, next to the Vilcanota valley, it erupted about 11,500 years ago. Oroscocha is a dome with two associated lava flows; the volcano covers a surface area of 1.5 square kilometres. Oroscocha was erupted from a fissure about 4450 BCE, the flow modified the course of the Vilcanota river. Oroscocha is formed by phenocryst-rich, felsic porphyritic rocks with a composition of peraluminous rhyolite in the flows and trachydacite in the dome, of which the dome is darker than the lava flows.

Mafic inclusions with sizes larger in the lava flows than in the dome are found. The magma that gave rise to the rocks was modified by the injection of lamprophyres while still in the magma chamber. Quimsachata is formed by K-rich andesite

Getty Conservation Institute

The Getty Conservation Institute, located in Los Angeles, California, is a program of the J. Paul Getty Trust, it is headquartered at the Getty Center but has facilities at the Getty Villa, commenced operation in 1985. The GCI is a private international research institution dedicated to advancing conservation practice through the creation and delivery of knowledge, it "serves the conservation community through scientific research and training, model field projects, the dissemination of the results of both its own work and the work of others in the field" and "adheres to the principles that guide the work of the Getty Trust: service, philanthropy and access." GCI has activities in architectural conservation. GCI conducts scientific research related to art conservation, it offers formal education and training programs, it has published a number of scholarly books. GCI has supported field projects around the world to preserve cultural heritage. GCI scientists study the deterioration of objects and buildings, how to prevent or stop such deterioration.

One of many projects in this area involved the effect of outdoor and indoor air pollutants on museum collections. Another project analyzed the cause of deterioration of the sandstone in the original National Capitol Columns now at the United States National Arboretum. In addition, GCI "conducts scientific research on materials' composition." For example, a project on the conservation of photographs has as one of its objectives the creation of an "Atlas of Analytical Signatures of Photographic Processes" which will provide "a precise chemical fingerprint of all the 150 or so ways pictures have been developed." As a part of that project, Getty scientists once examined the world's first photograph from nature by Nicéphore Niépce. Using X-ray fluorescence spectroscopy, reflectance Fourier transform infrared spectroscopy, other techniques during the 2002-2003 project, they found that bitumen of Judea was present in the image. Scientists at GCI viewed the CheMin instrument aboard the Curiosity rover exploring the Gale crater on Mars, as a valuable means to examine ancient works of art without damaging them.

Until only a few instruments were available to determine the composition without cutting out physical samples large enough to damage the artifacts. The CheMin on Curiosity directs a beam of X-rays at particles as small as 400 µm and reads the radiation scattered back to determine the composition of an object in minutes. Engineers created a smaller, portable version, named the X-Duetto. Fitting into a few briefcase-sized boxes, it can examine objects on site, while preserving their physical integrity, it is now being used by Getty scientists to analyze a large collection of museum antiques and the Roman ruins of Herculaneum, Italy. Training of interested parties around the world is important for the sustainability of GCI's work. For example, GCI collaborated with other organizations to create a course "to assist museum personnel in safeguarding their collections from the effects of natural and human-made emergencies." GCI developed a course on the "Fundamentals of the Conservation of Photographs", now taught in eastern Europe by the Academy of Fine Arts and Design in Bratislava and the Slovak National Library.

Besides courses and workshops, GCI has been involved with long-term education programs, such as establishing a Master's degree program in Archaeological and Ethnographic Conservation in collaboration with the University of California, Los Angeles. GCI's field projects are "selected based on how they fit the institute's goals of raising public awareness, contributing new, broadly applicable information to the field, supporting cultural heritage" and "must be executed in collaboration with partners… who must be serious about their efforts… so that projects are assured of continuing after the Getty's involvement ceases." Among other completed GCI field projects were efforts to preserve the Mogao Caves and Yungang Grottoes in China. It has been stated that "perhaps the institute's most profound contribution to conservation is the dissemination of information and methods learned in the field." Methods of information dissemination include conferences. The following are selected books published by GCI: Ward, Philip R.

The nature of conservation: a race against time. Marina del Rey, CA: Getty Conservation Institute, 1986. ISBN 0-941103-00-5 The conservation of tapestries and embroideries: proceedings of meetings at the Institut royal du patrimoine artistique, Belgium, September 21–24, 1987. Los Angeles: Getty Conservation Institute, 1989. ISBN 0-89236-154-9 Cather, Sharon; the conservation of wall paintings: proceedings of a symposium organized by the Courtauld Institute of Art and the Getty Conservation Institute, July 13–16, 1987. Marina del Rey, CA: Getty Conservation Institute, 1991. ISBN 0-89236-162-X Beley and Jeffrey Levin. Picture LA: landmarks of a new generation. Marina del Rey, CA: Getty Conservation Institute, 1994. ISBN 0-89236-305-3 Klein, Kathryn; the unbroken thread: conserving the textile traditions of Oaxaca. Los Angeles: Getty Conservation Institute, 1997. ISBN 0-89236-380-0 Corzo, Miguel Angel. Mortality immortality?: the legacy of 20th-century art. Los Angeles: Getty Conservation Institute, 1999.

ISBN 0-89236-528-5 Dorge and Sharon L. Jones. Building an emergency plan: a guide for museums and other cultural institutions. Los Angeles: Getty Co

Wang Junfeng

Wang Junfeng is a Chinese lawyer and politician. He is the Global Chairman of multinational law firm King & Wood Mallesons. Wang obtained his LLM from Jilin University, he received his second LLM and a JSD from the University of California, Boalt Hall School of Law. He was the principal founding partner of King & Wood PRC Lawyers, one of China's largest law firms before its 2012 combination with Australian firm Mallesons Stephens Jacques. Before founding King & Wood, Wang headed the Commercial Law Department of the China Global Law Office, which a section of the China Council for Promotion of International Trade; when private law firms were first permitted in China, Wang was among the first to launch a private firm. Wang has advised on many of China's landmark legal matters. Wang was a Communist Party of China delegate to the 11th and 12th National Committee of the Chinese People's Political Consultative Conference. In 2015, Wang courted controversy during the annual national conference because the proposed resolution he brought to the conference advocated official status for the Chinese calendar, rather than issues relating to the welfare of lawyers or the rule of law in China.

Wang was the President of the All China Lawyers Association. In 2014, a petition campaign was mounted by Chinese lawyers to seek Wang's dismissal over draft professional rules for lawyers proposed by the All China Lawyers Association under Wang's leadership which would restrict lawyers' rights to comment on legal issues on the internet or to generate publicity for cases, rules which were seen as aimed at restricting civil rights lawyers' ability to generate public support for their cases. Wang was selected as one of China's Outstanding Lawyers by the Ministry of Justice of China, he was the director of the Chamber of Commerce 2005 Committee. He was a member of the Sixth Share Issue Audit Committee of the China Securities Regulatory Commission