text:
USNS Mercy

USNS Mercy (T-AH-19) is the lead ship of her class of hospital ships in non-commissioned service with the United States Navy. Her sister ship is USNS Comfort (T-AH-20). She is the third US Navy ship to be named for the virtue mercy. In accordance with the Geneva Conventions, Mercy and her crew do not carry any offensive weapons, though defensive weapons are available.

United States Naval Ship (USNS) Mercy was built as a San Clemente-class oil tanker, SS Worth, by National Steel and Shipbuilding Company, San Diego, California, in 1976. Starting in July 1984, she was renamed and converted to a hospital ship by the same company. Launched on 20 July 1985, Mercy was placed in service on 8 November 1986. She has a raised forecastle, a transom stern, a bulbous bow, an extended deckhouse with a forward bridge, and a helicopter-landing deck with a flight-control facility.

The conversions from oil tankers cost $208 million per ship and took 35 months to complete. The Mercy-class hospital ships are the third largest ships in the US Navy Fleet by length, surpassed only by the nuclear-powered Nimitz-class aircraft carrier- and Gerald R. Ford-class aircraft carrier supercarriers.

Her primary mission is to provide medical and surgical services to support Marine Corps Air/Ground Task Forces deployed ashore, Army and Air Force units deployed ashore, and naval amphibious task forces and battle forces afloat. Secondarily, she provides mobile surgical hospital service for use by appropriate US Government agencies in disaster and humanitarian relief, and limited humanitarian care incident to these missions and to peacetime military operations.

Mercy, homeported in San Diego, is normally in reduced operating status. Her crew remains a part of the staff of Naval Medical Center San Diego until ordered to sea, at which time they have five days to fully activate the ship to a NATO Role III Medical Treatment Facility. The only higher level being onshore fixed facilities outside the theater of operations. Like most USNS ships, mariners from the US Navy's Military Sealift Command are responsible for navigation, propulsion, and most deck duties on board. Mercy is as of 2012 part of MSC's Service Support Program. The "Medical Treatment Facility", or hospital on the ship, is commanded by a captain of the Navy Medical Corps or Navy Nurse Corps.

Philippine Training Mission (1987)
On 27 February 1987, Mercy began training while en route on a humanitarian cruise to the Philippines and the South Pacific. The staff included U.S. Navy, Indian Navy, U.S. Army, and U.S. Air Force active duty and reserve personnel; United States Public Health Service; medical providers from the Armed Forces of the Philippines; and MSC civilian mariners. Over 62,000 outpatients and almost 1,000 inpatients were treated at seven Philippine and South Pacific ports. Mercy returned to Oakland, California, on 13 July 1987.

Operation Desert Shield/Desert Storm (1990–91)
On 9 August 1990, Mercy was activated in support of Operation Desert Shield. Departing on 15 August, she arrived in the Persian Gulf on 15 September. For the next six months, Mercy provided support to multinational allied forces. She admitted 690 patients and performed almost 300 surgeries. After treating the 21 American and two Italian repatriated prisoners of war, she departed for home on 16 March 1991, arriving in Oakland on 23 April.

Operation Unified Assistance (2004)
Mercy departed San Diego on 5 January 2005 en route to the tsunami-devastated regions of Southeast Asia, where she provided medical care to the victims of the disaster as part of Operation Unified Assistance, and further care as part of Theater Security Cooperation Program 2005. Combined, she provided over 107,000 patient services, rendered by members of the Department of Defense, Project HOPE, and the United States Public Health Service.

Pacific Partnership (2006)
Mercy departed San Diego in 2006 as the inaugural deployment of Pacific Partnership, an ongoing Civic Assistance mission designed to "Prepare in Calm to Respond in Crisis". She visited several ports in the South Pacific Ocean including the Philippines, Indonesia, and Banda Aceh. The ship's primary mission was to provide humanitarian assistance to these countries, and her staff included several non-governmental organizations, doctors from the armed services of several countries, as well as active-duty and reserve military providers from many branches of the US Armed Forces.

Pacific Partnership (2008)
Mercy departed San Diego on 14 April 2008 for Pacific Partnership 2008, a four-month humanitarian and civic deployment in Southeast Asia and Oceania. Mercy, with 900 officers and sailors, included 300 US health and construction experts. Partners participating in the mission included the nations of Australia, Canada, Chile, Japan, South Korea, New Zealand, and Portugal, as well as several non-governmental organizations. Originally intended to visit the Philippines, Vietnam, the Federated States of Micronesia, East Timor, and Papua New Guinea, Mercy was to be redirected to the Bay of Bengal to provide immediate assistance to victims of the cyclone in Burma, but relief efforts in Burma were called off. On 10 June, the humanitarian mission was temporarily suspended after one of the ship's helicopters was shot at in the strife-torn southern Philippines area of Mindanao. Over the course of the deployment, Mercy would treat 91,000 patients, including performing 1,369 surgeries.

Pacific Partnership (2010)

On 24 February 2010, the Commander of the US Pacific Fleet announced that Mercy will be the lead vessel of Pacific Partnership 2010, a continuation of the recurring humanitarian mission to Southeast Asia and Oceania. For Pacific Partnership 2010 Mercy visited Vietnam, Cambodia, Indonesia, and East Timor; treated 109,754 patients, and performed 1,580 surgeries.

Pacific Partnership (2012)
3 May 2012 saw Mercy depart San Diego once again for Pacific Partnership 2012, the latest deployment of the Pacific Partnership series. In an effort to further expand the scope of the mission of "Preparing in Calm to Respond in Crisis", many more man hours of Subject Matter Expert Exchange (SMEE) with host nations, Veterinary Care, and construction projects were performed compared to past Mercy deployments, building the capacity of host nations to respond to regional disasters in a coordinated manner. The ship visited Indonesia, the Philippines, Vietnam, and Cambodia carrying personnel not only from the Department of Defense, but also 13 partner nations and 28 non-governmental organizations.

The National Conflict Resolution Center honored the master and crew of hospital ship USNS Mercy with its 25th annual Peacemaker Award for her participation in Pacific Partnership (2012).

Aftermath of Typhoon Haiyan (2013)
In mid-November 2013, Mercy was ordered to activate for Operation Damayan, the relief effort in response to the devastation caused by Typhoon Haiyan, which struck the Philippines on 7 November 2013. However, Mercy was deactivated before sailing.

Rim of the Pacific (RIMPAC) (2014)
The US Navy announced that Mercy would be participating in RIMPAC 2014, a large multi-national naval exercise involving ships and personnel from 23 countries. In addition to providing medical and surgical care to personnel injured during the exercise, Mercy participated in multi-lateral Subject Matter Expert Exchanges with other military medical professionals. In addition, Mercy steamed with Peace Ark, the hospital ship from the People's Republic of China during phases of the exercise.

Pacific Partnership (2015)
Ten years after the relief effort for victims of the Indian Ocean tsunami, US Pacific Fleet announced that Mercy would once again participate in Pacific Partnership. Focusing on Subject Matter Expert Exchanges and Community Health Engagements, Pacific Partnership 15 looks to continue the mission of helping nations in the region "Prepare in Calm to Respond in Crisis". Countries hosting Mercy include Fiji, Papua New Guinea, the Philippines and Vietnam.

Pacific Partnership (2016)
Celebrating 10 years of Pacific Partnership, US Pacific Fleet announced that Mercy would continue to participate in the ongoing series of Disaster Preparedness missions. Focusing on local Subject Matter Expert Exchanges, Pacific Partnership 16 continues to "Prepare in Calm to Respond in Crisis". Countries that have invited Mercy include East Timor, Malaysia, Indonesia, the Philippines and Vietnam.

Pacific Partnership (2018)
US Pacific Fleet announced that Mercy would set sail to Sri Lanka for Pacific Partnership 2018.

The United Seamen's Service at its annual Admiral of the Ocean Sea Awards (AOTOS) event honored the masters and crews of hospital ship USNS Mercy with Special Recognition Mariner's Plaque for her participation in Pacific Partnership (2018).

Operational responses during the COVID-19 pandemic (2020)
From March until May 2020, Mercy was deployed to Los Angeles to provide hospital relief in response to COVID-19. The ship arrived and docked at the Port of Los Angeles cruise ship terminal on 27 March 2020, and departed on May 16. The ship's mission was to treat patients other than those with COVID-19, freeing up land-based hospitals to deal with the virus. The deployment mirrors USNS Comfort (T-AH-20)'s simultaneous mission to support New York's COVID-19 response. As of 15 April, Mercy had treated 48 patients, of whom 30 had been discharged. Seven crew members have tested positive for the virus and been removed from the ship for quarantine; 100 other sailors who had contact with them were also removed for quarantine. She arrived back in San Diego on 15 May. This was followed by a seven-month maintenance period during which a flight deck was created between the forecastle and the aftercastle, for two large helicopters, the V-22 Osprey and MH-60 Seahawk. Mercy can also refuel aircraft.

Train derailment
On 31 March 2020, while Mercy was docked, a Pacific Harbor Line freight train was deliberately derailed by its onboard engineer in an attempt to crash into the ship, but the attack was unsuccessful. According to U.S. federal prosecutors, the train's engineer "was suspicious of the Mercy, believing it had an alternate purpose related to COVID-19 or a government takeover". The train came to a stop approximately 750 ft from the ship after destroying several barriers and suffered a substantial fuel oil leak requiring cleanup from fire fighters and hazardous materials personnel. No one was injured and the ship was not harmed; the engineer was charged with train wrecking and terrorism. The engineer later cited Qanon and COVID-19 conspiracy theories as the reasons for his attack.

Awards and decorations

 * Navy Unit Commendation – (Aug 1990–Mar 1991)
 * Navy Meritorious Unit Commendation – (Feb–Jul 1987, Sep 2001–Jun 2005, Apr–Sep 2006, May–Sep 2010)
 * Southwest Asia Service Medal – (Sep 1990–Mar 1991)
 * Humanitarian Service Medal – (Dec 2004–Feb 2005, Operation Unified Assistance; May–Jun 2006)
 * Philippine Republic Presidential Unit Citation – (Feb–Jul 1987)

General characteristics

 * Specifications:
 * Displacement:
 * Full load: 69,390 tons
 * Light: 24,275 tons
 * Length:
 * Overall: 894 feet (272.6 meters)
 * Waterline: 854 5/6 feet (260.6 meters)
 * Beam: 105 3/4 feet (32.25 meters)
 * Draft: 32 5/6 feet (10.0 meters)
 * Propulsion: 1 steam turbine, 2 boilers, 1 shaft, 24,500 shaft horsepower
 * Speed: 17.5 knots
 * Range: 13,400 nautical miles (24,817 kilometers) at 17.5 knots
 * Personnel:
 * Merchant Marine: 16 ROS; 61 active
 * Navy communications & support: 58 (6 officers, 52 enlisted)
 * Medical and dental (active only): 1,156
 * Aviation: helicopter landing platform, 2 spots
 * Patient capacity:
 * Intensive care wards: 80 beds
 * Recovery wards: 20 beds
 * Intermediate care wards: 280 beds
 * Light care wards: 120 beds
 * Limited care wards: 500 beds
 * Total patient capacity: 1000 beds
 * Operating rooms: 12
 * Departments and facilities:
 * Casualty reception
 * Radiological services including CT
 * Main laboratory plus satellite lab
 * Central sterile processing
 * Medical supply/pharmacy
 * Physical therapy and burn care
 * Intensive care unit
 * Dental services
 * Optometry/lens lab
 * Morgue
 * Laundry
 * Burn treatment
 * Angiography
 * Blood bank
 * Oxygen producing plants (two)

title: USNS Mercy


text:
Talk:Carleton Place

Addition of Mississippi River (Ontario)
Is there really a Mississippi River in Ontario? If there is, it should have a page. Should we have a disambiguation page? -- Zoe

Yes it does exist. I believe it was named after a local Indian tribe. I will gather some statistics on it. Since I am a total newbie here, could I leave it to you to set up a link to an empty page?

I don't know if you have a standard way to to handle the many towns, rivers, lakes, etc. with identical names. -- ACS

What I'll do is create a link on the article page to Mississippi River (Ontario), and you can click on that to create the article. -- Zoe

Short-lived disambiguation page for "Mississippi River"
I have added a disambiguation page, and will slowly begin moving the link pointers from Mississippi River to Mississippi River (United States) and so on. -- Aetas-Nex

The above change and move were promptly undone. See Talk:Mississippi River. There are two articles, Mississippi River and Mississippi River (Ontario). The disambiguation is handled at the top of both articles. The bigger river keeps the title Mississippi River. Whiner01 03:15, 3 May 2006 (UTC)

Pix
I will also take a few more pictures of Carleton Place as well as the Mississippi River and upload them. -- Aetas-Nex

Please everyone sign your comments using the standard ~ -- it inserts your username, the time, and the date. Otherwise your comments end up un-dated. Un-dated comments frustrate all readers. Whiner01 08:33, 3 May 2006 (UTC)

Twin Town
It is twinned with Comrie in Perthshire, Scotland. I'm not sure which section to add this into. 161.12.7.4 13:57, 14 September 2007 (UTC)

Calvary Christian Academy
The link I removed was to the wrong article. It referenced Maryland, this particular CCA is in Canada. The external link at the bottom, however, is correct. -- Endofline (talk) 13:54, 12 September 2010 (UTC)

Leigh Instruments
Hasn't Leigh Instruments been closed for close to 20 years now? — Preceding unsigned comment added by 216.254.135.122 (talk) 14:01, 27 June 2011 (UTC)
 * Actually, that was a direct quote from the citation.IEEE Canada – The Crash Position Indicator =Dhodges (talk) 19:29, 27 June 2011 (UTC)

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

title: Talk:Carleton Place


text:
Talk:Vitalism

NPOV
No scientist believes that biological processes are directly reducible to chemical or physical processes, so the main claim and the way the whole article frames vitalism is unacademic - to say the least. Furthermore, there are no references to the current debate and conspicuously absent are contributions from the fields of biosemiotics or any reference to von Uexküll or Rose. In short, the article is not informative and does not meet Wikipedia standards. 86.6.148.125 (talk) 10:39, 18 March 2024 (UTC)
 * Thank you for pointing thosse things out. Since you seem quite knowledgeable about vitalism why not try to fix some of these things yourself? Thank you.  The Blue  Rider  Postal horn icon.svg 11:14, 18 March 2024 (UTC)

 * IP, please read the information related to pseudo-scientific articles at the top of this page as well as WP:FRINGE. Do you have a source for your statement "No scientist believes that biological processes are directly reducible to chemical or physical processes"? Because it looks to me that the exact opposite is actually true. In any event, since you have not provided a single source to justify the NPOV tag on the article, I will remove it. In the future, please propose specific changes and always provide sources to back them up. --McSly (talk) 14:24, 18 March 2024 (UTC)
 * So I think the OP has a point here but we have to be cautious of how we characterize things. On the one hand, very few scientists (or virtually none) believe that biological processes are not made up of underlying chemical and physical processes. But as far as I am aware, it is very much an open question whether biological organisms are directly reducible to those processes in our best scientific explanations. This is just to make the banal point that biology is not chemistry or physics; it has its own concepts and explanations, many of which incorporate insights from physics and especially chemistry, but are unique to the biological level. An example would be a notion like "homeostasis," which seems to be something that occurs in a full-fledged way only at very high levels of biological organization, not amid isolated chemical or physical processes alone.
 * The article here conflates the open scientific/philosophical questions of reductionism and emergence, as well as the potential limits to mechanical modes of explanation in the biological sphere, with vitalism as positing non-natural entities. That is a problem. AtavisticPillow (talk) 18:55, 11 June 2024 (UTC)

title: Talk:Vitalism


text:
Cheng Man-ch'ing

Cheng Man-ch'ing or Zheng Manqing (29 July 1902 - 26 March 1975) was a Chinese expert of tai chi, Chinese medicine, and the so-called three perfections: calligraphy, painting and poetry. He was born in Yongjia (present-day Wenzhou), Zhejiang Province, during the Qing dynasty. Cheng died March 26, 1975; his grave is near the city of Taipei in Taiwan.

Because of his skills in the 3 Perfections or "Excellences" – considered to be among some of the traditional skills and pastimes of a Confucian scholar – plus medicine and tai chi, he was often referred to as the "Master of Five Excellences." Because he had been a college professor, his students in the USA called him "Professor Cheng."

Early years
Cheng's father died when Cheng was very young. Around the age of nine, Cheng was struck on the head by a falling object, and was in a coma for a short while. He recuperated slowly, and was apprenticed to a well-known artist, Wang Xiangchan 汪香禪, in hopes that simple jobs like grinding ink would help his health. Wang taught Cheng's aunt Zhang Hongwei 張紅薇, as well as fellow townsmen Ma Mengrong and Ma Gongyu, all of whom became quite well-known. Within a few years, Cheng's teacher sent him out to earn his living at painting. During Cheng's childhood, his mother took him out to find medicinal plants and taught him the fundamentals of traditional Chinese herbal medicine.

By the age of eighteen, Cheng was teaching poetry and art in Beijing and within a few years had become a successful artist whose works were in demand. His aunt's friend Cai Yuanpei gave him a letter of introduction that led him to Shanghai, where he became acquainted with influential figures including Wu Changshuo, Zheng Xiaoxu, Xu Beihong, and Zhang Daqian. He took a position as the Dean of the Department of Traditional Painting at the prestigious Shanghai College of Art, which was headed by Liu Haisu. Cheng participated in national and international exhibitions, including one in 1933 organized by Xu Beihong, and was deeply involved with a number of art societies, including the Bee Society. These groups met to socialize, paint, and organize fundraising exhibitions. Around 1930, Cheng left the Shanghai College of Art and with Huang Binhong, and other leading artists, founded the College of Chinese Culture and Art. The school was forced to close upon the Japanese invasion.

In his twenties, Cheng developed lung disease (believed to be tuberculosis partly from exposure to the chalk dust from the school blackboards). Ill to the point of coughing up blood, he began to practice tai chi more diligently to aid his recovery. Cheng retired from teaching and devoted himself for several years to the study of tai chi, traditional Chinese medicine, and literature. His literary studies were with retired scholar Qian Mingshan.

In addition to his childhood instruction, Cheng Man-ch'ing received formal Chinese medical training. While he was teaching art in Shanghai, one of his friends grew ill and was unable to find relief. Cheng Man-ch'ing wrote a complex prescription for his friend, who took the medicine and recovered fully. One story from his memorial book is that a retired traditional doctor named Song You'an 宋幼庵 came across the prescription. He demanded to be put in contact with the person who wrote it, as the sophistication and erudition of the prescription showed exceptional talent and competence. As war was raging across China at that time, it took several years before Cheng Man-ch'ing was able to present himself for study. With Song, Cheng received instruction and became conversant with the Chinese pharmacopoeia. Dr Song was the twelfth generation of physician in his family; his medical school had a formidable collection of traditional medicines.

Around 1928 Cheng met the well-known master Yang Chengfu (1883–1936), with whom he began to study Yang-style tai chi, until Yang died. While the exact dates of Cheng's study with Yang are not clear, one of Yang's top students, scholar Chen Weiming wrote that Cheng studied six years with Yang. Cheng, according to Yang's son Zhenji, ghostwrote Yang's second book Essence and Applications of Tai Chi or The Substance and Application of Tai Chi (Taijiquan tiyong quanshu, 1934), for which Cheng also wrote a preface and most likely arranged for the calligraphic dedications.

Cheng taught tai chi, practiced medicine, and continued his art practice in Sichuan Province during the Sino-Japanese war years. In this period he taught Abraham Liu while at the Central Military Academy, China's equivalent of West Point.[Reference 1 At age 32 he taught tai chi at the Central Military Academy (formerly the Huang-po Military Academy -equivalent to West Point in the United States.)"]By 1946, he had developed a significantly abbreviated 37-move version of Yang's traditional form. He wrote the manuscript for his Thirteen Chapters during this period, and showed them to his elder classmate Chen Weiming, who gave it his imprimatur.

Taiwan
Cheng moved to Taiwan in 1949 with the retreating Republican Chinese government. He continued his career as a physician and as a teacher of his new tai chi form, as well as actively practicing painting, poetry, and calligraphy. He published Cheng's 13 Chapters of Tai Chi Boxing in 1950 which has been translated into English twice. He started the Shih Chung T'ai Chi Association in Taipei, where many now well-known students including (Benjamin Lo, Liu Hsi-heng, Hsu I-chung, Qi Jiang Tao, Robert W. Smith, T. T. Liang, William C. C. Chen, Huang Sheng Shyan and others) trained with him.

Though he tended not to advertise it, Cheng served as one of the painting teachers of Soong Mei-ling, Madame Chiang Kai-shek, whom he taught to paint "birds and flowers" style (his colleague Huang Junbi instructed her in landscape painting. Cheng also continued to be a medical advisor to Chiang Kai-shek.

United States
In 1964, Cheng moved with his wife, two sons, and three daughters to the United States, where he taught at the New York T'ai Chi Association at 211 Canal Street in Manhattan. He then founded and taught at the Shr Jung T'ai Chi school at 87 Bowery in New York City's Chinatown section, with the assistance of his six American senior students, known as the "Big Six": Tam Gibbs, Lou Kleinsmith, Ed Young, Mort Raphael, Maggie Newman, and Stanley Israel. Later students/assistants are known as "the Little Six": Victor Chin, Y Y Chin, Jon Gaines, Natasha Gorky, Wolfe Lowenthal, and Ken VanSickle. Other American students include Frank Wong, Michael and Lora Howard, Herman Kauz, René Houtrides, Patt Benton, Lucjan Shila, Carol Yamasaki, Robert Ante, Judyth Weaver, Patrick Watson, Min Pai, Lawrence Galante, Lisa Marcusson, Saul Krotki, Robert Chuckrow, Robert D. Morningstar, Phillip Carter, and William C. Phillips. In Taiwan, Cheng's students continued running the school in his absence. It operated initially under the direction of Liu Hsi-heng. Hsu I-chung is the current director.

While living in New York City, Cheng often spent several hours in the early afternoons studying or teaching classes of three or four students in the C. V. Starr East Asian Library at Columbia University, usually in a small, mahogany-panelled loft above the main floor. For relaxation, he raised orchids.

Writings
Cheng wrote numerous books and articles on a variety of subjects, including commentaries on the I Ching, the Tao Te Ching, the Analects of Confucius, his original works of poetry, essays, medicine, and several art collections. https://chengmanching.wordpress.com/writings./ In 1967 in collaboration with Robert W. Smith, and T. T. Liang, Cheng published "T'ai Chi, the Supreme Ultimate Exercise for Health, Sport and Self-defense," which was his second tai chi book in English. Translations of his works include: "Master Cheng's New Method of T'ai Chi Ch'uan Self-Cultivation"; "Cheng Man Ch'ing: Essays on Man and Culture"; "Cheng Man Ch'ing: Master of Five Excellences," and "T'ai Chi Ch'uan: A Simplified Method of Calisthenics for Health and Self-Defense."

Cheng also produced several tai chi films, and some of his classes and lectures were recorded and in later years released on DVD.

Tai chi
Cheng Man-ch'ing is best known in the West for his tai chi. The following are some of the characteristics of his "Yang-style short form."

 * It eliminates most of the repetitions of certain moves of the Yang long form.
 * It takes around ten minutes to practice instead of the twenty to thirty minutes of the Yang long form
 * The hand and wrist are held open, yet relaxed, in what Cheng called the "Fair Lady's Hand" formation (as opposed to the straighter "Chinese tile" formation of the Yang style)
 * The form postures are not as expansive as Yang Chengfu's form
 * Cheng postures are performed in "middle frame" style, which changes the movement of the feet from the Yang version.
 * Cheng's concept of "swing and return" in which the momentum from one movement initiates the next.

These changes allowed Cheng to teach larger numbers of students in a shorter time. His shortened form became extremely popular in Taiwan and Malaysia, and he was one of the earliest Chinese masters to teach tai chi publicly in the United States. His students have continued to spread his form around the world.

Cheng rejected the appellation "Yang-style Short Form" to characterize his tai chi. When pressed on the issue, he called his form "Yang-style tai chi in 37 Postures." However, the postures in his form are counted differently from those in the Yang Chengfu form. In the older form each movement counts as a posture, whereas in the Cheng form postures are counted only the first time they are performed, and rarely or not at all when they are repeated. These differences in how the postures are counted have led some Cheng practitioners, such as William C. C. Chen, to characterize their own forms as exceeding 70 "movements," and indeed, upon close comparison with the Yang Chengfu form, Cheng's postures, if counted the same way as Yang's are, would number over 70. Moreover, there is nothing in Cheng's teaching to prohibit a practitioner of his style from repeating any number of movements just as many or more times than they are repeated in the Yang Chengfu form.

Cheng's changes to the Yang-style form were not officially recognised by the Yang family and (perhaps partly because of the continued popularity of Cheng's shortened form) his style is still a source of controversy among some tai chi practitioners. From Cheng's own point of view, the approval of his elder brother disciple Chen Weiming was all the recognition he needed, since by that time Yang Chengfu was deceased, and all of the current generation of Yang Chengfu leaders were junior to him.

Legacy
Cheng Man-ch'ing left a legacy mainly in two areas: art and tai chi. In the arts, though he retired in his thirties from teaching, he remained an actively exhibiting artist his whole life, with frequent exhibitions in Taiwan both solo and with his group "Seven Friends of Painting" and solo shows in the United States. After his death, the National Palace Museum in Taiwan held a retrospective exhibit of his works. These were published in Special Exhibition of Painting and Calligraphic Works by Zheng Manqing in 1982. A retrospective exhibit "Zheng Manqing Calligraphy and Painting" was held in his hometown of Wenzhou (Yongjia) in 2017.

Cheng Man-ch'ing's tai chi legacy includes many hundreds of schools around the world that follow his lineage. In Taiwan, a number of his direct students still teach, and the Shih Chung school in Taiwan still operates. Huang Sheng Shyan (Huang Xingxian), one of Cheng's most accomplished disciples, established over 40 schools in South East Asia, through which Cheng's tai chi has continued to reach over 10,000 practitioners. Grandmaster William C. C. Chen continues to teach in New York City.

A little-appreciated dimension of Cheng's legacy was his willingness to teach non-Chinese students. While he was not the first Chinese martial artist to do this in America, his warm embrace of Westerners, who ran the gamut from experienced fighters to long-haired hippies of the day, proved controversial with the Chinese Association that had initially sponsored his move to New York. At one point, when Cheng was out of the country, the Association members locked the Western students out of the Canal Street school. Informed of this, Cheng instructed Ed Young to find a new location. Upon his return to New York, Cheng taught at the new location, 87 Bowery, sending an unmistakable message of inclusiveness and rejecting the insularity that was traditional in the Chinese martial arts community.

In New York City, among Cheng's senior students, Ed Young died September 29, 2023 (aged 91). While Prof. Cheng was teaching in New York, he asked Fred Lehrman to help initiate schools in Milwaukee WI, Minneapolis MN, Gainesville FL, Boulder CO, and Halifax, Nova Scotia. Among these, the ones in Milwaukee and at Naropa Institute in Boulder have continued into the new millennium. The official program at Naropa Institute was initially created by Judyth O. Weaver with the permission of Chögyam Trungpa in 1974. It had over 500 students in the first Tai Chi summer session. From 1975 it included several of the main Shih Jung teachers, including Lehrman, Tam Gibbs, Maggie Newman, Ed Young, and Wolfe Lowenthal as visiting instructors over the next period of years, in addition to resident teachers Jane and Bataan Faigao from 1977. The Faigaos also established Rocky Mountain T'ai Chi Ch'uan in Boulder. The New York School of Tai Chi Chuan, later the T'ai Chi Foundation, was founded by Patrick Watson at the request of Prof. Cheng. William C. Phillips operates Patience T'ai Chi Association in Brooklyn, NY. Don Ahn founded the Ahn T'ai Chi Studio and taught thousands of students form and Taoist techniques. Carol Yamasaki taught hundreds of students in the Detroit area including at the Birmingham Unitarian Church designed by her architect father, Minoru Yamasaki.

Cheng's students carried on his tradition of writing about tai chi, creating tai chi study material, and documenting his teaching. A feature film The Professor: Tai Chi's Journey West documents his years in New York City.

Notes and references

 * Cheng Man-ch'ing. See "Zheng Manqing" entry for selected Chinese titles.
 * Cheng Man-ch'ing. Cheng Man-ch'ing Videos . (2007). Set of 1960s videos on DVD of Cheng teaching in New York City. Chen Man Ching Index.
 * Cheng Man-ch'ing. Cheng-tsu's Thirteen Treatises on T'ai Chi Ch'uan . Translated by Benjamin Lo and Martin Inn. Berkeley: North Atlantic Books (1985).
 * Cheng Man-ch'ing; Master Cheng's New Method of T'ai Chi Self-Cultivation, Translated by Mark Hennessy; Frog, Ltd. Books, Berkeley, CA; ISBN 1-883319-92-7 (1999)
 * Cheng Man-ch'ing, and Robert W. Smith, T'ai Chi Rutland, VT: Tuttle, 1967.
 * Chuckrow, Robert; The Tai Chi Book-Refining and Enjoying a Lifetime of Practice . ISBN 1-886969-64-7. A CMC Shr Jung NYC Student.
 * Davis, Barbara; "In Search of a Unified Dao: Zheng Manqing's Life and Contributions to Taijiquan." In Journal of Asian Martial Arts, v.5, n. 2, p. 36-59.
 * DeMarco, M. & LaFredo, T. G. (Eds). Cheng Man-ch'ing and T'ai Chi: Echos in the Hall of Happiness. Santa Fe, NM: Via Media Publishing, 2014. ISBN 0615967361
 * Kauskas, Jan. Laoshi: Tai Chi, Teachers, and Pursuit of Principle. Santa Fe, NM: Via Media Publishing, 2014. ISBN 9780615967363
 * Kauz, Herman; Tai Chi Handbook . ISBN 0-385-09370-5. A CMC Shr Jung NYC Student.
 * Lowenthal, Wolfe; There Are No Secrets: Professor Cheng Man-Ch'Ing and His Tai Chi Chuan . ISBN 1-55643-112-0. A CMC Shr Jung NYC Student.
 * McFarlane, Stewart The Complete Book of T'ai Chi . DK Publishing, New York (1997). ISBN 0-7894-1476-7, paperback ISBN 0-7894-4259-0. Covers only the 37 Form of Cheng Man-ch'ing's tai chi; illustrated drawings.
 * Phillips, William; In the Presence of Cheng Man-Ch’ing: My Life and Lessons with the Master of Five Excellences, Floating World Press, 2020. ISBN 978-0-6482831-2-6
 * Strugatz, Barry, director. "The Professor: Tai Chi's Journey West" . First Run Features.
 * Wile, Douglas. Zheng Manqing's Uncollected Writings on Taijiquan, Qigong, and Health, with New Biographical Notes. Milwaukee: Sweet Ch'i Press, 2007.
 * Yang Chengfu. Taijiquan tiyong quanshu. 1934. Translated by Louis Swaim as The Essence and Applications of Taijiquan. 2005. ISBN 1-55643-545-2.
 * Yang Zhenji, Yang Chengfu shi taijiquan Guangxi: Guangxi Minzu Chubanshe, 1993.
 * Zheng Manqing. Zhengzi taijiquan shisan pian [Cheng-tzu's Thirteen Treatises on T'ai Chi Ch'uan] . Taiwan (1950).
 * Zheng Manqing. Taijiquan zixiu xinfa [Master cheng's New Method of T'ai chi ch'uan Self-cultivation]
 * Zheng Manqing. Yi quan [The Complete I Ching] . Taipei: Meiya Publishing (1974).
 * Zheng Manqing. Zheng Manran shuhua ji [Collection of Zheng Manran's Calligraphy and Painting]. Taipei: Zhonghua shuju (1971).

title: Cheng Man-ch'ing


text:
Internment

Internment is the imprisonment of people, commonly in large groups, without charges or intent to file charges. The term is especially used for the confinement "of enemy citizens in wartime or of terrorism suspects". Thus, while it can simply mean imprisonment, it tends to refer to preventive confinement rather than confinement after having been convicted of some crime. Use of these terms is subject to debate and political sensitivities. The word internment is also occasionally used to describe a neutral country's practice of detaining belligerent armed forces and equipment on its territory during times of war, under the Hague Convention of 1907.

Interned persons may be held in prisons or in facilities known as internment camps (also known as concentration camps). The term concentration camp originates from the Spanish–Cuban Ten Years' War when Spanish forces detained Cuban civilians in camps in order to more easily combat guerrilla forces. Over the following decades the British during the Second Boer War and the Americans during the Philippine–American War also used concentration camps.

The term "concentration camp" and "internment camp" are used to refer to a variety of systems that greatly differ in their severity, mortality rate, and architecture; their defining characteristic is that inmates are held outside the rule of law. Extermination camps or death camps, whose primary purpose is killing, are also imprecisely referred to as "concentration camps".

The Universal Declaration of Human Rights restricts the use of internment, with Article 9 stating, "No one shall be subjected to arbitrary arrest, detention or exile."

Defining internment and concentration camp

The American Heritage Dictionary defines the term concentration camp as: "A camp where persons are confined, usually without hearings and typically under harsh conditions, often as a result of their membership in a group which the government has identified as dangerous or undesirable."

Although the first example of civilian internment may date as far back as the 1830s, the English term concentration camp was first used in order to refer to the reconcentration camps (Spanish:reconcentrados) which were set up by the Spanish military in Cuba during the Ten Years' War (1868–1878). The label was applied yet again to camps set up by the United States during the Philippine–American War (1899–1902). And expanded usage of the concentration camp label continued, when the British set up camps during the Second Boer War (1899–1902) in South Africa for interning Boers during the same time period.

During the 20th century, the arbitrary internment of civilians by the state reached its most extreme forms in the Soviet Gulag system of concentration camps (1918–1991) and the Nazi concentration camps (1933–1945). The Soviet system was the first applied by a government on its own citizens. The Gulag consisted in over 30,000 camps for most of its existence (1918–1991) and detained some 18 million from 1929 until 1953, which is only a third of its 73-year lifespan. The Nazi concentration camp system was extensive, with as many as 15,000 camps and at least 715,000 simultaneous internees. The total number of casualties in these camps is difficult to determine, but the deliberate policy of extermination through labor in many of the camps was designed to ensure that the inmates would die of starvation, untreated disease and summary executions within set periods of time. Moreover, Nazi Germany established six extermination camps, specifically designed to kill millions of people, primarily by gassing.

As a result, the term "concentration camp" is sometimes conflated with the concept of an "extermination camp" and historians debate whether the term "concentration camp" or the term "internment camp" should be used to describe other examples of civilian internment.

The former label continues to see expanded use for cases post-World War II, for instance in relation to British camps in Kenya during the Mau Mau rebellion (1952–1960), and camps set up in Chile during the military dictatorship of Augusto Pinochet (1973–1990). According to the United States Department of Defense as many as 3 million Uyghurs and members of other Muslim minority groups are being held in China's re-education camps which are located in the Xinjiang region and which American news reports often label as concentration camps. The camps were established in the late 2010s under General Secretary Xi Jinping's administration.

Impact
Scholars have debated the efficacy of internment as a counterinsurgency tactic. A 2023 study found that internment during the Irish war of independence led to greater grievances among Irish rebels and led them to fight longer in the war.

Active

 * North Korean prison camps (1948–present)
 * Guantanamo Bay detention camp (2002–present)
 * Refugee detention centres in Libya (2011–present)
 * Uyghur re-education camps in China (2017–present)
 * Anti-gay detention camps in Chechnya (2017–present)
 * Migrant detentions as part of immigration detention in the United States (2018–present)
 * Internment camps in Ethiopia during the Tigray War and the War in Amhara (2020–present).
 * Russian filtration camps in Ukraine during the Russian invasion of Ukraine (2022–present)
 * Sde Teiman detention camp in Israel during the Israel–Hamas war (2024–present)

Closed

 * Abercorn Barracks, Northern Ireland (sometimes referred to as Ballykinlar Barracks) (1919–1921) (1971)
 * Reconcentration policy during Cuba's War of Independence from Spain (1896–1898)
 * Second Boer War in South Africa (1900–1902)
 * Curragh Camp in Ireland (1939–46 & 1957–59). Curragh Camp was by far the largest, at least 30 other prisons and camps were used throughout the country.
 * Cyprus internment camps (1946–1949)
 * Reconcentrados "Zones of Protection" 1901, Philippine-American War
 * Herero and Namaqua genocide (1904–1907)
 * Concentration of Armenians during the Armenian Genocide (1915–1916)
 * Finnish Civil War (1918)
 * Frongoch internment camp British camp used for WWI and Irish 1916 Easter Rising prisoners
 * Gormanston Camp in the Irish Free State (1922–1923)
 * Malayan New villages as part of the Briggs Plan during the Malayan Emergency (1950–1960)
 * Italian concentration camps in Africa and Europe (1930–1944)
 * HM Prison Maze in Northern Ireland (1971–75), previously known as Long Kesh Detention Centre, and known colloquially as the Maze or H-Blocks)
 * German concentration camps before and during World War II (1933–1945)
 * Japanese internment of prisoners of war and civilians during World War II (ended 1945)
 * Japanese-American internment camps in World War II (1942–1946)
 * Japanese Canadian internment (1942–1949)
 * Deoli internment camp in India (1962–1967)
 * Omarska camp in Bosnia, 1992
 * Dretelj camp (1992–1995)
 * Camp Bucca in Iraq (2003–2009)
 * Abu Ghraib prison in Iraq (1980–2014)

title: Internment


text:
Hölder's inequality

In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of $L^{p}$ spaces.

The numbers $[1, ∞]$ and $f$ above are said to be Hölder conjugates of each other. The special case $(S, Σ, μ)$ gives a form of the Cauchy–Schwarz inequality. Hölder's inequality holds even if $p, q ∈$ is infinite, the right-hand side also being infinite in that case. Conversely, if $g$ is in $1/p + 1/q = 1$ and $S$ is in $p, q ∈$, then the pointwise product $f ∈ L^{p}(μ)$ is in $g ∈ L^{q}(μ)$.

Hölder's inequality is used to prove the Minkowski inequality, which is the triangle inequality in the space $|f |^{p}$, and also to establish that $|g|^{q}$ is the dual space of $L^{1}(μ)$ for $α, β ≥ 0$ $(1, ∞)$.

Hölder's inequality (in a slightly different form) was first found by. Inspired by Rogers' work, gave another proof as part of a work developing the concept of convex and concave functions and introducing Jensen's inequality, which was in turn named for work of Johan Jensen building on Hölder's work.

Conventions
The brief statement of Hölder's inequality uses some conventions.

 * In the definition of Hölder conjugates, $α|f |^{p} = β |g|^{q}$ means zero.
 * If $p = q = 2$ $μ$, then $\|fg\|_{1}$ and $L^{p}(μ)$ stand for the (possibly infinite) expressions
 * $$\begin{align}

&\left(\int_S |f|^p\,\mathrm{d}\mu\right)^{\frac{1}{p}} \\ &\left(\int_S |g|^q\,\mathrm{d}\mu\right)^{\frac{1}{q}} \end{align}$$

 * If $L^{q}(μ)$, then $fg$ stands for the essential supremum of $L^{1}(μ)$, similarly for $L^{p}(μ)$.
 * The notation $L^{q}(μ)$ with $L^{p}(μ)$ is a slight abuse, because in general it is only a norm of $p$ if $p ∈$ is finite and $q$ is considered as equivalence class of $f$-almost everywhere equal functions. If $1/∞$ and $p, q ∈$, then the notation is adequate.
 * On the right-hand side of Hölder's inequality, 0 × ∞ as well as ∞ × 0 means 0. Multiplying $\|f \|_{p}$ with ∞ gives ∞.

Estimates for integrable products
As above, let $g$ and $[1, ∞)$ denote measurable real- or complex-valued functions defined on $[1, ∞)$. If $\|g\|_{q}$ is finite, then the pointwise products of $f$ with $f$ and its complex conjugate function are $μ$-integrable, the estimate

 * $$\biggl|\int_S f\bar g\,\mathrm{d}\mu\biggr|\le\int_S|fg|\,\mathrm{d}\mu =\|fg\|_1$$

and the similar one for $p = ∞$ hold, and Hölder's inequality can be applied to the right-hand side. In particular, if $f$ and $g$ are in the Hilbert space $\|f \|_{∞}$, then Hölder's inequality for $|f |$ implies

 * $$|\langle f,g\rangle| \le \|f\|_2 \|g\|_2,$$

where the angle brackets refer to the inner product of $\|g\|_{∞}$. This is also called Cauchy–Schwarz inequality, but requires for its statement that $\|f \|_{p}$ and $1 ≤ p ≤ ∞$ are finite to make sure that the inner product of $S$ and $f$ is well defined. We may recover the original inequality (for the case $\|f \|_{p}$) by using the functions $f ∈ L^{p}(μ)$ and $g ∈ L^{q}(μ)$ in place of $g$ and $μ$.

Generalization for probability measures
If $a > 0$ is a probability space, then $\|fg\|_{1}$ $f$ just need to satisfy $fg$, rather than being Hölder conjugates. A combination of Hölder's inequality and Jensen's inequality implies that

 * $$\|fg\|_1 \le \|f\|_p \|g\|_q$$

for all measurable real- or complex-valued functions $g$ and $f$ on $g$.

Notable special cases
For the following cases assume that $f$ and $g$ are in the open interval $[1, ∞]$ with $L^{2}(μ)$.

Counting measure
For the $$n$$-dimensional Euclidean space, when the set $$S$$ is $$\{1,\dots,n\}$$ with the counting measure, we have

 * $$\sum_{k=1}^n |x_k\,y_k| \le \biggl( \sum_{k=1}^n |x_k|^p \biggr)^{\frac{1}{p}} \biggl( \sum_{k=1}^n |y_k|^q \biggr)^{\frac{1}{q}}

\text{ for all }(x_1,\ldots,x_n),(y_1,\ldots,y_n)\in\mathbb{R}^n\text{ or }\mathbb{C}^n.$$ Often the following practical form of this is used, for any $$(r,s)\in\mathbb{R}_+$$:
 * $$\biggl(\sum_{k=1}^n |x_k|^r\,|y_k|^s \biggr)^{r+s}\le \biggl( \sum_{k=1}^n |x_k|^{r+s} \biggr)^{r} \biggl( \sum_{k=1}^n |y_k|^{r+s} \biggr)^{s}.$$

For more than two sums, the following generalisation holds, with real positive exponents   $$ \lambda_i $$ and $$ \lambda_a + \lambda_b+ \cdots +\lambda_z =1$$:
 * $$\sum_{k=1}^n |a_k|^{\lambda_a}\,|b_k|^{\lambda_b} \cdots |z_k|^{\lambda_z} \le \biggl(\sum_{k=1}^n |a_k|\biggr)^{\lambda_a} \biggl(\sum_{k=1}^n |b_k|\biggr)^{\lambda_b} \cdots \biggl(\sum_{k=1}^n |z_k|\biggr)^{\lambda_z}.

$$ Equality holds iff $$ |a_1|: |a_2|: \cdots : |a_n| =|b_1|: |b_2|: \cdots : |b_n| = \cdots = |z_1|: |z_2|: \cdots : |z_n| $$.

If $$S=\N$$ with the counting measure, then we get Hölder's inequality for sequence spaces:

 * $$\sum_{k=1}^{\infty} |x_k\,y_k| \le \biggl( \sum_{k=1}^{\infty} |x_k|^p \biggr)^{\frac{1}{p}} \left( \sum_{k=1}^{\infty} |y_k|^q \right)^{\frac{1}{q}}

\text{ for all }(x_k)_{k\in\mathbb N}, (y_k)_{k\in\mathbb N}\in\mathbb{R}^{\mathbb N}\text{ or }\mathbb{C}^{\mathbb N}.$$

Lebesgue measure
If $$S$$ is a measurable subset of $$\R^n$$ with the Lebesgue measure, and $$f$$ and $$g$$ are measurable real- or complex-valued functions on $$S$$, then Hölder's inequality is

 * $$\int_S \bigl| f(x)g(x)\bigr| \,\mathrm{d}x \le\biggl(\int_S |f(x)|^p\,\mathrm{d}x\biggr)^{\frac{1}{p}} \biggl(\int_S |g(x)|^q\,\mathrm{d}x\biggr)^{\frac{1}{q}}.$$

Probability measure
For the probability space $$(\Omega, \mathcal{F}, \mathbb{P}),$$ let $$\mathbb{E}$$ denote the expectation operator. For real- or complex-valued random variables $$X$$ and $$Y$$ on $$\Omega,$$ Hölder's inequality reads

 * $$\mathbb{E}[|XY|] \leqslant \left (\mathbb{E}\bigl[ |X|^p\bigr]\right)^{\frac{1}{p}} \left(\mathbb{E}\bigl[|Y|^q\bigr]\right)^{\frac{1}{q}}.$$

Let $$1 < r < s < \infty$$ and define $$p = \tfrac{s}{r}.$$ Then $$q = \tfrac{p}{p-1}$$ is the Hölder conjugate of $$p.$$ Applying Hölder's inequality to the random variables $$|X|^r$$ and $$1_{\Omega}$$ we obtain

 * $$\mathbb{E}\bigl[|X|^r\bigr]\leqslant \left(\mathbb{E}\bigl[|X|^s\bigr]\right)^{\frac{r}{s}}.$$

In particular, if the $f$th absolute moment is finite, then the $g$th absolute moment is finite, too. (This also follows from Jensen's inequality.)

Product measure
For two σ-finite measure spaces $p = q = 2$ and $L^{2}(μ)$ define the product measure space by

 * $$S=S_1\times S_2,\quad \Sigma=\Sigma_1\otimes\Sigma_2,\quad \mu=\mu_1\otimes\mu_2,$$

where $S$ is the Cartesian product of $\|f \|_{2}$ and $\|g\|_{2}$, the σ-algebra $p = 2$ arises as product σ-algebra of $|f |$ and $|g|$, and $p$ denotes the product measure of $(S, Σ, μ)$ and $p, q ∈$. Then Tonelli's theorem allows us to rewrite Hölder's inequality using iterated integrals: If $q$ and $(1,∞)$ are $1/p + 1/q ≤ 1$-measurable real- or complex-valued functions on the Cartesian product $s$, then

 * $$\int_{S_1}\int_{S_2}|f(x,y)\,g(x,y)|\,\mu_2(\mathrm{d}y)\,\mu_1(\mathrm{d}x) \le\left(\int_{S_1}\int_{S_2}|f(x,y)|^p\,\mu_2(\mathrm{d}y)\,\mu_1(\mathrm{d}x)\right)^{\frac{1}{p}}\left(\int_{S_1}\int_{S_2}|g(x,y)|^q\,\mu_2(\mathrm{d}y)\,\mu_1(\mathrm{d}x)\right)^{\frac{1}{q}}.$$

This can be generalized to more than two σ-finite measure spaces.

Vector-valued functions
Let $1/p + 1/q = 1$ denote a σ-finite measure space and suppose that $(S_{1}, Σ_{1}, μ_{1})$ and $(S_{2}, Σ_{2}, μ_{2})$ are $S_{1}$-measurable functions on $r$, taking values in the $S$-dimensional real- or complex Euclidean space. By taking the product with the counting measure on $S_{2}$, we can rewrite the above product measure version of Hölder's inequality in the form

 * $$ \int_S \sum_{k=1}^n|f_k(x)\,g_k(x)|\,\mu(\mathrm{d}x) \le \left(\int_S\sum_{k=1}^n|f_k(x)|^p\,\mu(\mathrm{d}x)\right)^{\frac{1}{p}}\left(\int_S\sum_{k=1}^n|g_k(x)|^q\,\mu(\mathrm{d}x)\right)^{\frac{1}{q}}.$$

If the two integrals on the right-hand side are finite, then equality holds if and only if there exist real numbers $Σ$, not both of them zero, such that

 * $$\alpha \left (|f_1(x)|^p,\ldots,|f_n(x)|^p \right )= \beta \left (|g_1(x)|^q,\ldots,|g_n(x)|^q \right ),$$

for $μ$-almost all $f$ in $g$.

This finite-dimensional version generalizes to functions $S$ and $S$ taking values in a normed space which could be for example a sequence space or an inner product space.

Proof of Hölder's inequality
There are several proofs of Hölder's inequality; the main idea in the following is Young's inequality for products.

$n$

Alternative proof using Jensen's inequality:

$μ$

We could also bypass use of both Young's and Jensen's inequalities. The proof below also explains why and where the Hölder exponent comes in naturally.

$x$

Statement
Assume that $Σ_{1}$ and let $S$ denote the Hölder conjugate. Then for every $Σ_{2}$,

 * $$\|f\|_p = \max \left \{ \left| \int_S f g \, \mathrm{d}\mu \right | : g\in L^q(\mu), \|g\|_q \le 1 \right\},$$

where max indicates that there actually is a $f$ maximizing the right-hand side. When $μ_{1}$ and if each set $g$ in the σ-field $μ_{2}$ with $Σ$ contains a subset $(S, Σ, μ)$ with $f = (f_{1}, ..., f_{n})$ (which is true in particular when $$ is σ-finite), then

 * $$\|f\|_\infty = \sup \left\{ \left| \int_S f g \,\mathrm{d}\mu \right| : g\in L^1(\mu), \|g\|_1 \le 1 \right \}.$$

Proof of the extremal equality:

$$

Remarks and examples

 * The equality for $$p = \infty$$ fails whenever there exists a set $$A$$ of infinite measure in the $$\sigma$$-field $$\Sigma$$ with that has no subset $$B \in \Sigma$$ that satisfies: $$0 < \mu(B) < \infty.$$ (the simplest example is the $$\sigma$$-field $$\Sigma$$ containing just the empty set and $$S,$$ and the measure $$\mu$$ with $$\mu(S) = \infty.$$) Then the indicator function $$1_A$$ satisfies $$\|1_A\|_{\infty} = 1,$$ but every $$g \in L^1 (\mu)$$ has to be $$\mu$$-almost everywhere constant on $$A,$$ because it is $$\Sigma$$-measurable, and this constant has to be zero, because $$g$$ is $$\mu$$-integrable. Therefore, the above supremum for the indicator function $$1_A$$ is zero and the extremal equality fails.
 * For $$p = \infty,$$ the supremum is in general not attained. As an example, let $$S = \mathbb{N}, \Sigma = \mathcal{P}(\mathbb{N})$$ and $$\mu$$ the counting measure. Define:

 * $$\begin{cases} f: \mathbb{N} \to \mathbb{R} \\ f(n) = \frac{n-1}{n} \end{cases}$$

 * Then $$\|f\|_{\infty} = 1.$$ For $$g \in L^1 (\mu, \mathbb{N})$$ with $$0 < \|g\|_1 \leqslant 1,$$ let $$m$$ denote the smallest natural number with $$g(m) \neq 0.$$ Then

 * $$\left |\int_S fg\,\mathrm{d}\mu\right| \leqslant \frac{m-1}{m}|g(m)|+\sum_{n=m+1}^\infty|g(n)| = \|g\|_1-\frac{|g(m)|}m<1.$$

Applications

 * The extremal equality is one of the ways for proving the triangle inequality $g = (g_{1}, ..., g_{n})$ for all $Σ$ and $\{1, ..., n\}$ in $α, β ≥ 0$, see Minkowski inequality.
 * Hölder's inequality implies that every $\|f \|_{p} = 0$ defines a bounded (or continuous) linear functional $fg$ on $\|g\|_{q} = 0$ by the formula
 * $$\kappa_f(g) = \int_S f g \, \mathrm{d}\mu,\qquad g\in L^q(\mu).$$
 * The extremal equality (when true) shows that the norm of this functional $\|f \|_{p} > 0$ as element of the continuous dual space $\|g\|_{q} > 0$ coincides with the norm of $$ in $\|f \|_{p} = ∞$ (see also the $\|g\|_{q} = ∞$-space article).

Statement
Assume that $\|f \|_{p}$ $q$ and $\|g\|_{q}$ $g$ such that

 * $$\sum_{k=1}^n \frac1{p_k} = \frac1r$$

where 1/∞ is interpreted as 0 in this equation. Then for all measurable real or complex-valued functions $p = ∞$ defined on $A$,

 * $$\left\|\prod_{k=1}^n f_k\right\|_r \le \prod_{k=1}^n \left\|f_k\right\|_{p_k}$$

where we interpret any product with a factor of ∞ as ∞ if all factors are positive, but the product is 0 if any factor is 0.

In particular, if $$f_k \in L^{p_k}(\mu)$$ for all $$k \in \{ 1, \ldots, n \}$$ then $$\prod_{k=1}^n f_k \in L^r(\mu).$$

Note: For $$r \in (0, 1),$$ contrary to the notation, $q = 1$ is in general not a norm because it doesn't satisfy the triangle inequality.

Proof of the generalization: $μ$

Interpolation
Let $|fg| ≤ \|f \|_{∞} |g|$ $$ and let $p = 1$ denote weights with $q = ∞$. Define $$p$$ as the weighted harmonic mean, that is,

 * $$ \frac1p = \sum_{k=1}^n \frac{\theta_k}{p_k}.$$

Given measurable real- or complex-valued functions $$f_k$$ on $f$, then the above generalization of Hölder's inequality gives
 * $$\left\| |f_1|^{\theta_1}\cdots |f_n|^{\theta_n}\right\|_p \le \left\||f_1|^{\theta_1}\right\|_{\frac{p_1}{\theta_1}}\cdots \left\| |f_n|^{\theta_n}\right\|_{\frac{p_n}{\theta_n}} = \|f_1\|_{p_1}^{\theta_1}\cdots \|f_n\|_{p_n}^{\theta_n}.$$

In particular, taking $$f_1 = \cdots = f_n=:f$$ gives
 * $$\|f\|_p \leqslant \prod_{k=1}^n \|f\|_{p_k}^{\theta_k}.$$

Specifying further $p, q ∈$ and $\|f \|_{p}$, in the case $$n = 2,$$ we obtain the interpolation result

An application of Hölder gives

Both Littlewood and Lyapunov imply that if $$f \in L^{p_0}\cap L^{p_1}$$ then $$f \in L^p$$ for all $$p_0 < p < p_1.$$

Two functions
Assume that $\|g\|_{q}$ and that the measure space $(1,∞)$ satisfies $a^{p} = b^{q}$. Then for all measurable real- or complex-valued functions $(0, ∞]$ and $(0, ∞]$ on $S$ such that $p ∈$ for $$-almost all $\|f \|_{p} = \|g\|_{q}$,

 * $$\|fg\|_1\geqslant \|f\|_{\frac{1}{p}}\,\|g\|_{\frac{-1}{p-1}}.$$

If

 * $$\|fg\|_1 < \infty \quad \text{and} \quad \|g\|_{\frac{-1}{p-1}} > 0, $$

then the reverse Hölder inequality is an equality if and only if

 * $$\exists \alpha \geqslant 0 \quad |f| = \alpha|g|^{\frac{-p}{p-1}} \qquad \mu\text{-almost everywhere}.$$

Note: The expressions:

$$ \|f\|_{\frac{1}{p}}$$ and $$\|g\|_{\frac{-1}{p-1}},$$

are not norms, they are just compact notations for

 * $$\left (\int_S|f|^{\frac{1}{p}}\,\mathrm{d}\mu\right)^{p} \quad \text{and} \quad \left (\int_S|g|^{\frac{-1}{p-1}}\,\mathrm{d}\mu\right)^{-(p-1)}.$$

Multiple functions
The Reverse Hölder inequality (above) can be generalized to the case of multiple functions if all but one conjugate is negative. That is,

 * Let $$p_1,..., p_{m-1} < 0$$ and $$p_m \in \mathbb{R}$$ be such that $$\sum_{k=1}^{m} \frac{1}{p_k} = 1$$ (hence $$0 < p_m < 1$$). Let $$f_k$$ be measurable functions for $$k = 1,...,m$$. Then

 * $$\left\|\prod_{k=1}^m f_k\right\|_1 \ge \prod_{k=1}^m \left\|f_k\right\|_{p_k}.$$

This follows from the symmetric form of the Hölder inequality (see below).

Symmetric forms of Hölder inequality
It was observed by Aczél and Beckenbach that Hölder's inequality can be put in a more symmetric form, at the price of introducing an extra vector (or function):

Let $$f = (f(1),\dots,f(m)), g = (g(1),\dots, g(m)), h = (h(1),\dots,h(m))$$ be vectors with positive entries and such that $$f(i) g(i) h(i) = 1$$ for all $$i$$. If $$p,q,r$$ are nonzero real numbers such that $$\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=0$$, then:
 * $$\|f\|_p \|g\|_q \|h\|_r \ge 1$$ if all but one of $$p,q,r$$ are positive;
 * $$\|f\|_p \|g\|_q \|h\|_r \le 1$$ if all but one of $$p,q,r$$ are negative.

The standard Hölder inequality follows immediately from this symmetric form (and in fact is easily seen to be equivalent to it). The symmetric statement also implies the reverse Hölder inequality (see above).

The result can be extended to multiple vectors:

Let $$f_1, \dots, f_n$$ be $$n$$ vectors in $$\mathbb{R}^m$$ with positive entries and such that $$f_1(i) \dots f_n(i) = 1$$ for all $$i$$. If $$p_1,\dots,p_n$$ are nonzero real numbers such that $$\frac{1}{p_1}+\dots+\frac{1}{p_n}=0$$, then:
 * $$\|f_1\|_{p_1} \dots \|f_n\|_{p_n} \ge 1$$ if all but one of the numbers $$p_i$$ are positive;
 * $$\|f_1\|_{p_1} \dots \|f_n\|_{p_n} \le 1$$ if all but one of the numbers $$p_i$$ are negative.

As in the standard Hölder inequalities, there are corresponding statements for infinite sums and integrals.

Conditional Hölder inequality
Let $|f |^{p} = |g|^{q}$ be a probability space, $\|f \|_{p}$ a sub-σ-algebra, and $\|g\|_{q}$ $(0, ∞]$ Hölder conjugates, meaning that $α, β > 0$. Then for all real- or complex-valued random variables $S$ and $f$ on $\|f \|_{p} = 0$,

 * $$\mathbb{E}\bigl[|XY|\big|\,\mathcal{G}\bigr] \le \bigl(\mathbb{E}\bigl[|X|^p\big|\,\mathcal{G}\bigr]\bigr)^{\frac{1}{p}} \,\bigl(\mathbb{E}\bigl[|Y|^q\big|\,\mathcal{G}\bigr]\bigr)^{\frac{1}{q}}

\qquad\mathbb{P}\text{-almost surely.}$$

Remarks:
 * If a non-negative random variable $g$ has infinite expected value, then its conditional expectation is defined by
 * $$\mathbb{E}[Z|\mathcal{G}] = \sup_{n\in\mathbb{N}}\,\mathbb{E}[\min\{Z,n\}|\mathcal{G}]\quad\text{a.s.}$$

 * On the right-hand side of the conditional Hölder inequality, 0 times ∞ as well as ∞ times 0 means 0. Multiplying $β = 0$ with ∞ gives ∞.

Proof of the conditional Hölder inequality: $S$

Hölder's inequality for increasing seminorms
Let $μ$ be a set and let $$F(S, \mathbb{C})$$ be the space of all complex-valued functions on $p$. Let $p$ be an increasing seminorm on $$F(S, \mathbb{C}),$$ meaning that, for all real-valued functions $$f, g \in F(S, \mathbb{C})$$ we have the following implication (the seminorm is also allowed to attain the value ∞):

 * $$ \forall s \in S \quad f(s) \geqslant g(s) \geqslant 0  \qquad \Rightarrow \qquad  N(f) \geqslant N(g).$$

Then:

 * $$\forall f, g \in F(S, \mathbb{C}) \qquad N(|fg|) \leqslant \bigl(N(|f|^p)\bigr)^{\frac{1}{p}} \bigl(N(|g|^q)\bigr)^{\frac{1}{q}},$$

where the numbers $$p$$ and $$q$$ are Hölder conjugates.

Remark: If $\|g\|_{q} = 0$ is a measure space and $$N(f)$$ is the upper Lebesgue integral of $$|f|$$ then the restriction of $g$ to all $α = 0$-measurable functions gives the usual version of Hölder's inequality.

Distances based on Hölder inequality
Hölder inequality can be used to define statistical dissimilarity measures between probability distributions. Those Hölder divergences are projective: They do not depend on the normalization factor of densities.

title: Hölder's inequality


text:
No Border network

The No Border Network (In the United Kingdom also called "No Borders Network" or "Noborders Network") refers to loose associations of autonomous organisations, groups, and individuals in Western Europe, Central Europe, Eastern Europe and beyond. They support freedom of movement and resist human migration control by coordinating international border camps, demonstrations, direct actions, and anti-deportation campaigns.

The Western European network opposes what it says are increasingly restrictive harmonisation of asylum and immigration policy in Europe, and aims to build alliances among migrant laborers and refugees. Common slogans used by the Network include; "No Border, No Nation, Stop Deportations!" and "No one is illegal."

No Border Network has existed since 1999, and its website since 2000. The No Borders Network in the United Kingdom claims to have local groups in 11 cities.

No Border Camps
Groups from the No Border network have been involved in organising a number of protest camps (called "No Border Camps" or sometimes "Border Camps" or "Transborder Camps"), e.g. in Strasbourg, France (2002), Otranto, Italy (2003), Cologne (2003, 2012), Gatwick Airport (2007), United Kingdom,  at Patras, Greece, Dikili, Turkey (2008), Calais, France (2009, 2015), Lesvos, Greece (2009), Brussels, Belgium (2010), Siva Reka, Bulgaria (2011),  Stockholm, Sweden (2012), Rotterdam, the Netherlands (2013), Ventimiglia, Italy (2015), Thessaloniki, Greece (2016), near Nantes, France (2019) in Wassenaar, Netherlands (2019), near Nantes, France (2022), and in Rotterdam, Netherlands (2022).

Activities
On 18 December 2007, to coincide with the UN International Migrants Day, the network carried out a coordinated blockade of Border and Immigration Agency (now UK Border Agency) offices in Bristol, Portsmouth, Newcastle and Glasgow to prevent dawn raids by immigration officers from taking place. This form of action has been repeated across the UK by the network several times since.

On 24 October 2008, Phil Woolas, UK Minister of State for Borders and Immigration was pied by No Borders activists following his remarks on population control.

On 10 August 2013, No Border groups from The Netherlands squatted a large terrain at Rotterdam to gather and held several demonstrations.

In February 2010 No Borders groups from the UK and France opened a large centre for refugees sleeping rough in Calais, France, under the name "Kronstadt Hangar".

Calais authorities have accused "extremist activists" within to the No Borders network of being "driven by an anarchist ideology of hatred of all laws and frontiers" and engaging in, and encouraging, violence and harassment against French police and social workers at the Calais Jungle migrant camp, as well as "manipulating" and "misleading" the migrants living there.

After the intercultural philosophy journal "polylog" demanded in connection with the book "Global Freedom of Movement: A Philosophical Plea for Open Borders" that the "debate on freedom of migration or restrictions on immigration should be received more strongly in the context of intercultural philosophizing", new local groups such as [http://NoBorder.%20NoProblem NoBorder. NoProblem] oriented themselves to international migration-sensitive contributions - also in connection with Islamic and decolonial feminisms, degrowth, global ecofeminisms, or the "ethnic studies" less known in the German-speaking world. The group is a student-run independent project of the Institute of Philosophy at the University of Hildesheim, which itself conducts research on philosophies in global perspective.

Publications

 * Freedom to Move, Freedom to Stay: a No Borders Reader. London: No Borders, 2007.
 * James A. Chamberlain. Minoritarian Democracy: The Democratic Case for No Borders Constellations: An International Journal of Critical and Democratic Theory (forthcoming)

title: No Border network


text:
Talk:Tensor product

This page is poorly constructed
Well, maybe that's an overstatement, but it appears as though mathematicians have clogged this page up with soggy, pointless math jargon and made it irritatingly difficult to use as a reference for, you know, actually calculating things with tensor products. If all else fails, can somebody actually push the examples to the top as a quick reference and push the frivalous tedium to the bottom, or even better, package the frivalous tedium into a completely separate page? Or give me permission to do so.

 * THIS PAGE IS THE BEST I′VE FOUND ANYWHERE ON THE INTERNET FOR NON-MATHEMATICIANS. PLEASE KEEP IT AVAILABLE AS IS, UNDER ANOTHER NAME IF YOU MUST.  I′m a physicist who has been studying and using tensors and tensor products on and off over several years. I′ve used practically every major site and pdf on the Inet, as well as many texts, to try to break thru mathematicians' jargon and abstraction, and the more limited understanding of others, to get to a clearer understanding of the finer points, and EXAMPLES. After discovering this page it′s replaced Gower′s as the one I go to whenever I need a refresher.  IMHO it starts simply, at the best point, with just 2 vector spaces, and builds logically from there, and has a splendid set of links to further details such as Hilbert spaces TP and topological spaces TP etc. It includes excellent examples, and does include enough of the mathematical concerns in later sections to make you aware of them and where to go for more detail.  If it′s incorrect anywhere then certainly those places should be corrected, but for me it′s far superior pedagogically to anything else available on this subject.  Relabel it ″Tensor Products for Non-mathematicians″ if necessary, but please, please keep it available. JHE-37 (talk) 17:58, 10 October 2021 (UTC)

There is need to define the tensor product of vector spaces $$V \otimes W$$ as there are two interpretations:
 * 1) $$V \otimes W = \{v\otimes w \mid v \in V, w\in W\}$$ which is not a vector space but a set of product states
 * 2) $$V \otimes W = \text{span}(\{v\otimes w \mid v \in V, w\in W\})$$ which is a vector space by taking the span (all linear combinations) of  product states  — Preceding unsigned comment added by 193.171.241.212 (talk) 10:26, 5 February 2022 (UTC)
 * Only the second interpretation is correct. A definition of the tensor product is given somewhere in the article, but it is rather difficult to find it. From the content of this talk page and the tags at the top of the article, it seems that everybody agree thay the article is awfully written. The problem is to find an expert that is willing to find the time for rewriting the article. D.Lazard (talk) 11:23, 5 February 2022 (UTC)

The first three sections seem to be too much
In my opinion, the first three sections of this article are a nice attempt to explain tensor products, but they need to be revised or removed (specifically, "Intuitive motivation and the concrete tensor product", "Baby step towards the abstract tensor product: the free vector space", "Using the free vector space to "forget" about the basis".

The main problem with these sections is that they're too wordy and overcomplicated. In general, writing lengthy, huge explanations in an introductory setting deceives, misguides, and confuses readers into thinking something is more complicated than it actually is.

I think when a reader visits they page, they will want a quick but rigorous, no-nonsense explanation of a tensor product, and they probably don't want to have to parse through dozens of paragraphs to understand a tensor product. There are already many online PDFs a reader can turn to for more in depth explanations. So, does anyone care if I try to revise these paragraphs to make them less wordy, or if I reorganize them (maybe place them somewhere near the bottom so it doesn't scare off readers)? Since it seems like the real discussion begins at "The definition of the abstract tensor product" (which it should in my opinion), I'm also inclined to remove them all together, but anyone can let me know if they have any opposition. Lltrujello (talk) 05:12, 23 November 2020 (UTC)

 * I agree the first three sections are lengthy or too lengthy. I would not altogether remove them though: if the article starts out with
 * $$V \otimes W := F(V \times W)/{\sim}$$
 * then (either before or immediately after that) we need to include at least a brief explanation of the free vector space.
 * As far as these first aspects are concerned, I suggest the following ordering:
 * a brief recollection on the free vector space
 * the definition of the tensor product.
 * Explain (here I suggest that we do spend a bit of ink; currently this fact is just mentioned in §5.2, but not explained) how the choice of a basis for V and W yields a basis for V \otimes W. This explanation should be comprehensible from reading the preceding part about the free vector space. The goal is not to require readers (who know vector spaces) to jump to other articles for understanding this bit of information.
 * Jakob.scholbach (talk) 13:16, 23 November 2020 (UTC)

inconsistent font usage
I made the fonts consistent in this edit https://en.wikipedia.org/w/index.php?title=Tensor_product&type=revision&diff=1111854170&oldid=1111816282 now undone by an editor of the article.

My reason was that the inconsistent font uses that have been restored by that undoing editor of the page are confusing. The weak point is where the Latin lower case letter vee in the undoing editor's inconsistently preferred math markup $·$ looks like the Greek lower case letter nu in fonts that are clearer, such as that of $$·$$. This is evident in this snip from the article: "An element of the form $$v \otimes w$$ is called the tensor product of $v$ and $w$." The problem is that the two different math markup formats, $$·$$ and $·$, use different fonts. It is true that, often enough, the font usage that is inconsistently preferred by the undoing editor is slightly quicker to type. My experience is that the LaTeX format $$·$$ is to be preferred as it often is in the article. Chjoaygame (talk) 11:22, 23 September 2022 (UTC)

Definition
In the definition from bases, it says:

The tensor product $$V \otimes W$$ of $V$ and $W$ is a vector space which has as a basis the set of all $$v\otimes w$$ with $$v\in B_V$$ and $$w \in B_W.$$

Out of the blue appears the tensorproduct $$v\otimes w$$, just the thing that should be defined. Madyno (talk) 12:33, 25 November 2022 (UTC)

 * One usage of the symbol $$\otimes$$ is for vector spaces; the other is for vectors. For basis vectors $$ v\in B_V $$ and $$ w\in B_W $$ the expression $$v\otimes w$$, which is a basis vector for $$ V\otimes W $$, should be thought of as a primitive symbol that doesn't reduce to anything simpler. Elements of $$ V\otimes W $$ are sums of such symbols with numerical coefficients. You can of course take the tensor product of non-basis vectors—the result will be written in terms of tensor products of basis vectors, as described in the paragraphs following the one containing the passage you quoted. I think it would be helpful to many readers if some elementary examples could be added to the article showing how the notation works and what it is useful for. Will Orrick (talk) 03:48, 26 November 2022 (UTC)

Tensor product of n vector spaces for n>2
The article defines tensor products of a finite nonnegative integer $$n$$ vector spaces for only the case $$n=2$$. However, the "General tensors" section uses tensor products for general $$n$$, so we need to define somewhere tensor products in general (finite nonnegative integer). Thatsme314 (talk) 19:31, 17 October 2023 (UTC)

 * The case n > 2 is defined in section . D.Lazard (talk) 20:48, 17 October 2023 (UTC)
 * Good catch! Now, we just need to define it for $$n=0$$. Also, it might be nice to re-organize the article to emphasize the general definition. Thatsme314 (talk) 01:00, 18 October 2023 (UTC)

title: Talk:Tensor product


text:
Talk:Staff of office

This article doesn't make any sense due to the lack of context. Can someone put a nice intro? I will appreciate. -- Taku 04:17 Mar 4, 2003 (UTC)

Carrying a stick or a symbolic staff of office can often denote social rank or prestige. Whats wrong? Susan Mason

Because the article doesn't explain what is staff of office. It may be a new computer produced by Apple computer or whatever. If it is a typical staff like one wizard carries, the article first says it. -- Taku 04:31 Mar 4, 2003 (UTC)

Move proposal: section from Walking stick to here
I propose moving Walking stick contents into this article.

As far as I am aware, the term "walking stick" is not used for the various ecclesiastical staffs: the term is not mentioned here. I will try to find a few references as well. Please discuss at Talk:Walking stick where I have also left a message. Mirokado (talk) 20:58, 26 September 2010 (UTC)

Dodsmen?
This word doesn't show up in the dictionary. If it's ok, can someone find the meaning of this word? Komitsuki (talk) 08:05, 16 February 2014 (UTC)

title: Talk:Staff of office


text:
Talk:Wellie Wanging

"welly wanging" comes up with more Google matches than "wellie wanging". Do you know which is more commonly used in Real Life...? -- Oliver P. 04:34 Mar 4, 2003 (UTC)

I went with 'wellie wanging' because that's how the people at the Yorkshire Games (see link) spell it. And they're definite authorities in the matter, I'm sure. Birchtree

 * Okay. I've made redirects, though. (Do you think I'm taking this too seriously...? ;) -- Oliver P. 06:02 Mar 4, 2003 (UTC)

Not as seriously as some. ;) Birchtree 06:08 Mar 4, 2003 (UTC)

Forgive a clueless question, but is the second "w" really capitalized? -- Zoe

You know, she's got a point; it does look odd... Birchtree, do you know of any other reference works which mention this esteemed sport? Does it get a write-up in Britannica, perchance? ;) -- Oliver P. 07:45 Mar 4, 2003 (UTC)

Well, Oliver and Zoe, I don't have the W volume of Britannica to hand unfortunately, but having just checked the entry for American football, it has a redirect from American Football; I've similarly set up Wellie Wanging to do the same. Isn't that great? :) Birchtree 20:49 Mar 4, 2003 (UTC)

title: Talk:Wellie Wanging


text:
Talk:Grape

Pictures overlap
The pictures overlap the list of grape species in my browser (Mozilla 1.3B for Mac OS 10.2) Tuf-Kat
 * Mine, too, in IE 6.0 for Windows. -- [[User:Zoe|
 * Changed it so the table is only two pictures wide instead of three. Does that work for you? Thanks. Wnissen 23:26 May 9, 2003 (UTC)

Semi-protect this page
I realize that this page isn't controversial, but it isn't often improved either. Given the persistent vandalism by the children of Thames Valley District Schools (to whom it's become a running joke), and the fact that these IP users cannot be blocked because it would affect innocent parties, might I suggest that we semi-protect this page so that only registered users can edit it. — Preceding unsigned comment added by 2Nagualdesign (talk • contribs) 22:07, 5 May, 2012 (UTC)

Religion section
Why is the religion section only about Christianity? Wine plays a prominent role in many other religions, such as Judaism. This section needs to be updated. 174.34.196.106 (talk) 08:45, 22 November 2021 (UTC)

 * Do you have a source for this? CheeseInTea (talk) 17:32, 19 May 2022 (UTC)

Semi-protected edit request on 24 November 2022
Smitesh jadhav (talk) 00:09, 24 November 2022 (UTC) grapes calories per one grape = 2 calories
 * Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made. - FlightTime  ( open channel ) 00:20, 24 November 2022 (UTC)

Top producing countries for wine making
It's stated that Iran is the 6th country in the world for producing grapes for wine making, while wine making is illegal in Iran. Aminabzz (talk) 20:06, 12 August 2023 (UTC)

title: Talk:Grape


text:
Juliette Gordon Low

Juliette Gordon Low ( Gordon; October 31, 1860 – January 17, 1927) was the American founder of Girl Scouts of the USA. Inspired by the work of Lord Baden-Powell, founder of Scout Movement, she joined the Girl Guide movement in England, forming her own group of Girl Guides there in 1911.

In 1912 she returned to the States, and the same year established the first U.S. Girl Guide troop in Savannah, Georgia. In 1915, the United States' Girl Guides became known as the Girl Scouts, and Juliette Gordon Low was the first ever leader. She remained active until the time of her death.

Her birthday, October 31, is celebrated each year by the Girl Scouts as "Founder's Day".

Early life
Juliette Magill Kinzie Gordon was born on October 31, 1860, in Savannah, Georgia. She was named after her grandmother, Juliette Augusta Magill Kinzie, and nicknamed Daisy, a common sobriquet at the time, by her uncle. She was the second of six children born to William Washington Gordon II, a cotton broker with the firm Tison & Gordon, which was later renamed to W. W. Gordon & Company, and Eleanor "Nellie" Lytle Kinzie, a writer whose family played a role in the founding of Chicago.

When she was six months old, her father joined the Confederate States Army to fight in the American Civil War. In 1864, due to the close proximity of Union troops to Savannah, she moved with her mother and two sisters to Thunderbolt, Georgia. After the Union victory in Savannah the same year, her family received many visits from General William T. Sherman, who was a friend of her uncle. Sherman arranged an escort to take her family to Chicago in March 1865. Upon arriving in Chicago, Gordon Low became sick with brain fever, although she recovered without severe complications. A few months later, after President Andrew Johnson issued the amnesty proclamation, her father reunited with the family to move back to Savannah.

As a young child, she was accident-prone and had numerous injuries and illnesses. In 1866, her mother mentioned in a letter that "Daisy fell out of bed – on her head, as usual...." That same year, she broke two of her fingers so severely that her parents considered having them amputated. She also had frequent earaches and recurring bouts of malaria.

Juliette developed partial hearing loss as a child. At her wedding, a grain of rice thrown in celebration landed in her left ear and led to an infection. Its removal punctured her ear drum, leading to permanent deafness in that ear.

Hobbies
As a child, she spent more time on art and poetry than on school work. In addition to writing and performing plays, she started a newspaper with her cousins, called The Malbone Bouquet, which featured some of her early poetry. She also formed The Helpful Hands Club with her cousins, with the goal of helping others. The members learned to sew and tried to make clothes for the children of Italian immigrants. She was dubbed "Crazy Daisy" by her family and friends, due to her eccentricities. As her cousin Caroline described her, "While you never knew what she would do next, she always did what she made up her mind to do."

Education
Juliette's parents raised her with traditional Southern values, emphasizing the importance of duty, obedience, loyalty, and respect. By the age of 12, she had begun boarding school, attending several different ones during her teen years, including Miss Emmett's School in New Jersey, the Virginia Female Institute, the Edgehill School, and Mesdemoiselles Charbonniers, a French finishing school in New York. While studying at Edgehill, she joined the secret group Theta Tau (based on the sorority of the same name), whose members held meetings and earned badges. In 1880, after finishing boarding school, Juliette took painting lessons in New York, with teachers including Robert Walter Weir, a prominent landscape painter.

Marriage
After the death of her sister Alice, in 1880, Juliette relocated to Savannah to take over household duties while her mother grieved. During this period, she met William Mackay Low, the son of a family friend, and they began courting in secret. William left Savannah to study at the University of Oxford, and they didn't meet again until almost three years later, in 1884. Juliette had traveled to Europe in the interim and learned several new skills, including shorthand, bareback riding, and hunting partridge. In late 1885, William proposed marriage.

The Lows' wedding in Savannah on December 21, 1886, coincided with her parents' wedding anniversary. The couple honeymooned at St. Catherines Island near Savannah. Then they leased property in London and Scotland, spending the social season in London and the hunting season in Scotland. They spent much of their first two years of marriage apart, due to her medical problems and his long hunting trips and gambling. The long separations, combined with her inability to bear children strained their relationship.

Juliette Gordon Low often painted, but also learned woodworking and metalworking. She even designed and built iron gates for her home in Warwickshire. As a host, she held parties and events at the house and also received visits from such illustrious guests as her husband's friend Albert Edward, the Prince of Wales and the writer Rudyard Kipling, whose wife was related to her mother. Despite her husband's opposition, she devoted time to charity work, including regular visits to a woman with leprosy; she also fed and cared for the poor in a nearby village, and joined the local nursing association.

Separation
By 1895, Gordon Low was growing increasingly unhappy in her marriage. She rarely spent time alone with her husband, who had grown distant and began having affairs and drinking heavily.

In 1901, Anna Bridges Bateman, the widow of Sir Hugh Alleyne Sacheverell-Bateman, stayed as a guest at the Lows' home in Scotland. Upon discovering her husband's affair with Bateman, Gordon Low left to stay with friends and family. She worried that he planned to divorce her, so she sent him a telegram asking for a year before making any final decisions. Although he didn't initially favor divorce or separation, he wrote Juliette a year later to ask that they live apart permanently, and she agreed.

William soon began withholding money from Juliette unless she agreed to a divorce. After consulting a lawyer, she learned that for a divorce to be granted, she would need to prove adultery and desertion, or adultery and cruelty. In the case of adultery, Bateman would need to be named, which would have social repercussions for all parties involved. This slowed the divorce proceedings.

In late 1902, Gordon Low received money from her husband for the first time in two years. She used it and her savings to rent a house in London. William committed to a support agreement in 1903, which was to award her 2,500 pounds a year, the Low home in Savannah, and stocks and securities. Later that year, she purchased her own home in London, along with the house next door, which she rented out for income.

After her husband had what may have been a stroke, Gordon Low temporarily called off the dissolution of their marriage. She considered it wrong to divorce him when he could not defend himself. The proceedings resumed in January 1905 once his condition improved. William died from a seizure in Wales on June 8, 1905, before the divorce was finalized. After the funeral, it was revealed that he had left almost everything to Bateman, and that he had revoked his 1903 support deal with Juliette. William's sisters contested the will, with the support of Gordon Low, who ultimately received a sum of money, the Low house in Savannah with its surrounding land, and stocks and securities.

Girl Guides
After her husband's death, Gordon Low traveled, took sculpting classes, and did charity work while looking for a project on which focus her time and skills. In May 1911, she met Sir Robert Baden-Powell at a party, and was inspired by the Boy Scouts, a program that he had organized. With 40,000 members throughout Europe and the United States, at the time, it stressed the importance of both military preparedness and having fun, two values she appreciated. Juliette and Baden-Powell became close friends and spent a lot of time together over the next year.

In August 1911, Gordon Low became involved with the Girl Guides, an girl-serving offshoot of the Boy Scouts, headed by Agnes Baden-Powell, Sir Robert Baden Powell's sister. She formed a Girl Guides patrol near her home in Scotland, where she encouraged the members to become self-sufficient by learning how to spin wool and care for livestock. She also taught them knot tying, map reading, knitting, cooking, and first aid, while her friends in the military instructed them in drilling, signaling, and camping. She organized two new Girl Guides patrols in London when she visited for the winter of 1911.

Start of the American Girl Guides
In 1912, Gordon Low and Baden-Powell took a trip to the United States to spread the scouting movement. She hoped to bring it to her hometown, Savannah, to help girls learn practical skills and build character. When she arrived, she called her cousin Nina Pape, a local educator, saying, "I've got something for the girls of Savannah, and all America, and all the world, and we're going to start it tonight." Soon after, in March 1912, Juliette formed the first two American Girl Guides patrols, registering 18 girls.

The early growth of the movement in the United States was due to Gordon Low's extensive social connections and early work to recruit new members and leaders, among them her family and friends. She also advertised in newspapers and magazines. Baden-Powell put her in touch with people interested in Girl Guiding, including Louise Carnegie. After forming the first American troops, Juliette described herself as "deep in Girl Guides," and, by the next year, she had released the first American Girl Guides manual, entitled How Girls Can Help Their Country, based on Scouting for Boys by Robert Baden-Powell and How Girls Can Help to Build Up the Empire by Agnes Baden-Powell.

Gordon Low established the first headquarters in a remodeled carriage house, behind the Savannah home she had inherited from her husband. The headquarters contained meeting rooms for the local Girl Guide patrols, while the lot outside provided space for marching or signaling drills and sports, including basketball. Edmund Strudwick Nash, who rented the main house from Gordon Low, offered to pay rent on the carriage house as his contribution to the organization, becoming one of the American Girl Guide's first benefactors. Nash's son, Ogden Nash, immortalized "Mrs Low's House" in one of his poems.

Gordon Low traveled along the East Coast, spreading Girl Guiding to other communities, before returning to Savannah to speak with President Taft, who would be visiting her home. She hoped to convince him that his daughter, Helen, should become a patron for the Girl Guides, but was unsuccessful.

American Girl Scouts
Many competing organizations for girls that claimed to be the closest model to Boy Scouting were forming, and Gordon Low believed that gaining support from prominent people would help legitimize her organization as the official sister organization to the Boy Scouts. Her biggest competition was the Camp Fire Girls, which was formed in part by James E. West, the Chief executive of the Boy Scouts of America, and a strong proponent of strict gender roles. In March 1912, Gordon Low wrote to the Camp Fire Girls, inviting them to merge into the Girl Guides, but they declined even after Baden-Powell suggested that they reconsider. West considered many of the Girl Guides activities to be gender-inappropriate, and he was concerned that the public would question the masculinity of the Boy Scouts if the girls participated in similar activities.

Renaming the organization
Although the Girl Guides were growing, the Camp Fire Girls were doing so at a faster rate, so Gordon Low traveled to England to seek counsel from the British Girl Guides. By the time she returned to America, in 1913, she had a plan to spread Girl Guiding nationwide by changing the name from Girl Guides to Girl Scouts, establishing a national headquarters, and recruiting patrons outside Georgia. Upon returning to Savannah, she learned that the Savannah Girl Guides had already renamed themselves to Girl Scouts because "Scout" reminded them of America's pioneer ancestry. West objected to the name change, saying that it trivialized the name of scout and would cause older Boy Scouts to quit. Baden-Powell supported Gordon Low's use of the term "scout," although he preferred the term "guide" for the British Girl Guides.

In 1913, Gordon Low set up the Girl Scouts national headquarters in Washington, D.C., and hired her friend Edith Johnston as National Executive Secretary. The national headquarters served as the "central information dispenser" for Girl Scouting, as well as the place where girls could purchase their badges and the newly published handbook, How Girls Can Help Their Country.

Gordon Low recruited leaders and members in various states and spoke with every group that she could. Around the same time, she designed and patented the trefoil badge, although West claimed that the trefoil belonged to the Boy Scouts and the Girl Scouts had no right using it. She traveled back to London in the summer, where she met King George V and Queen Mary of Teck, and received the Girl Guide Thanks Badge from Princess Louise for promoting Guiding.

Gordon Low also formed the Honorary Committee of Girl Scouts and elected her family and friends to the committee. By using her connections, she was able to convince Susan Ludlow Parish, Eleanor Roosevelt's godmother, Mina Miller Edison, the wife of Thomas Edison, and Bertha Woodward, the wife of the House of Representatives majority leader, to become patrons. Although she had received support from many patrons, Gordon still funded most Girl Scout expenses herself.

World War I
At the start of World War I, Gordon Low rented Castle Menzies, in Scotland, and let a family of Belgian refugees move in temporarily.

On February 13, 1915, she sailed back to the United States on the RMS Lusitania. When she arrived, she continued her work for the Girl Scouts. At the time, the organization had 73 patrons and 2,400 registered members. Gordon Low decided to build a stronger central organization for the Girl Scouts by writing a new constitution that formed an executive committee and a National Council. She held the first National Council meeting under the new name, Girl Scouts, Inc. on June 10, 1915, and was elected the organization's founding president.

The Girl Scouts expanded after the United States entered World War I. Gordon Low publicized the Girl Scouts through newspapers, magazines, events, and film. In 1916, she relocated Girl Scout headquarters from Washington, DC, to New York City. The same year, she returned to England to fundraise and open a home for relatives of wounded soldiers, where she volunteered three nights per week. By November, she was back in the United States, continuing her work with the Girl Scouts.

In response to the thrift program, enacted by the United States Food Administration with the goal of teaching women how to conserve food, Girl Scouts in Washington, DC began growing and harvesting their own food and canning perishable goods. Herbert Hoover wrote to Gordon Low, thanking her for the contributions of the Girl Scouts and expressing hope that others would follow suit. She responded by organizing Girl Scouts to help the Red Cross by making surgical dressings and knitting clothing for soldiers. They also picked oakum, swept workrooms, created scrapbooks for wounded soldiers, and made smokeless trench candles for soldiers to heat their food.

By the end of 1917, Gordon Low convinced Lou Henry Hoover to become the Girl Scouts' National Vice President and Edith Bolling Galt Wilson, President Woodrow Wilson's second wife, to become its Honorary President.

Expanding internationally
Following World War I, interest in the Girl Guides began to increase in many different countries. In response, Olave Baden-Powell, the Chief Guide, created the International Council of Girl Guides and Girl Scouts as a way to bring together the different communities of Guides and Scouts across the world. The first meeting took place at the Girl Guide headquarters in London, which Gordon Low attended as the United States representative.

Gordon Low stepped down as the National President of the Girl Scouts in 1920 to devote more of her time to promoting Guiding and Scouting internationally. She attended as many meetings of the International Council as she could, and underwrote the travel of foreign delegates, so that they could also attend. And she assisted Olave Baden-Powell in converting 65 acres of land into a campsite for the Girl Guides. Gordon Low furnished a bungalow near the main house and named it "The Link" to signify the bond between the British Girl Guides and the American Girl Scouts.

While no longer the President, Gordon Low remained an active presence in the organization. She worked on and appeared in The Golden Eaglet, the first Girl Scout movie. At a fundraising campaign in New York during Girl Scout Week, she dropped pamphlets onto a crowd of people from an airplane. On October 31 that same week, the Girl Scouts celebrated the first Founder's Day, a day to honor Gordon Low and her accomplishments. In 1922, the Girl Scout convention took place in Savannah, her hometown. She helped plan and organize the convention by renting an auditorium, arranging for appearances by professional athletes, the mayor, and the school superintendent, and hiring a film company. After the 1922 convention, she began planning Cloudlands, a camping facility in Cloudland, Georgia, designed to train leaders and girls together. Cloudlands was later renamed Camp Juliette Low.

Breast cancer death
Gordon Low developed breast cancer in 1923 but kept it a secret. She caught the flu after an operation to remove the malignant lumps, leaving her bed-ridden until February 1924. When she recovered, she resumed her work with the American Girl Scouts and the International Council. She secretly had two more operations to try to cure her breast cancer, but was informed in 1925 that she had about six months to live. She continued to do work for the Girl Scouts, and even sneaked away during her recovery from surgery to make a speech at the organization's regional conference in Richmond.

Gordon Low traveled to Liverpool, where Dr. William Blair-Bell was developing a treatment for cancer. She tried it, an IV containing a solution of colloidal lead. The treatment was unsuccessful, and she spent her 66th birthday fighting off lead poisoning. She traveled back to the United States to meet with her doctor, who informed her that she did not have much longer to live. She went to the Low home in Savannah, where she spent her last few months. Gordon Low died in Savannah on January 17, 1927, at the age of 66. An honor guard of Girl Scouts escorted her casket to her funeral at Christ Church the next day. 250 Girl Scouts left school early that day to attend her funeral and burial at Laurel Grove Cemetery. Gordon Low was buried in her Girl Scout uniform with a note in her pocket stating "You are not only the first Girl Scout, but the best Girl Scout of them all." Her tombstone read, "Now abideth faith, hope, and love, but the greatest of these is love."

Legacy
In 1948, a postage stamp honoring Gordon Low, Scott catalogue number 974, was issued by the United States. Over 63 million were printed, making it a common issue. At the time, the Post Office had a policy of not honoring civic organizations. It took a joint resolution of Congress, with the approval of President Harry S. Truman, to produce the stamp for her. (The National Postal Museum suggests that it may have helped that Bess Truman was honorary president of the Girl Scouts.)

Gordon Low's home in Savannah is visited by Girl Scouts from all over the world. In 1965, her birthplace was listed as a National Historic Landmark.

Gordon Low also donated a seven-acre park in Savannah, which bears her name. The park (originally part of her family homestead, the remainder of which was developed into the Gordonston neighborhood, which includes a road named Kinzie Avenue after Low's family) has been the center of long-running disputes between Gordonston residents and non-residents as to whether the park was donated to the residents of Gordonston, or to the residents of Savannah at large, even to the point of disagreement over the park's name. The park figures prominently in Karen Kingsbury's 2013 novel The Chance.

In 1979, she was inducted into the National Women's Hall of Fame.

On May 29, 2012, the Girl Scouts' centennial anniversary was commemorated, with Gordon Low receiving the Presidential Medal of Freedom.

She was inducted into the Savannah Women of Vision investiture in 2016.

Camp Juliette Low in Cloudland, Georgia, bears the name of its founder.

Her birthday, October 31, is commemorated by the Girl Scouts each year as Founder's Day.

She was also awarded two patents, a utility patent for a "Liquid Container for Use with Garbage Cans or the Like", Patent 1,124,925, and a design patent, D45234, for the trefoil Girl Scout Badge.

In 1999, the city of Savannah named its ferry service the Savannah Belles Ferry after four of Savannah's notable women, including Low.

In 2016, the first official Girl Scout trail honoring Juliette Gordon Low was created by a Girl Scout for her Gold Award project. The trail is located in Westwinds Metropark in Holland, Ohio.

Low will be honored on a U.S. quarter in 2025 as part of the final year of the American Women quarters program.

title: Juliette Gordon Low