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Hertfordshire

Hertfordshire ( or  ; often abbreviated Herts) is a ceremonial county in the East of England and one of the home counties. It borders Bedfordshire to the north-west, Cambridgeshire to the north-east, Essex to the east, Greater London to the south and Buckinghamshire to the west. The largest settlement is Watford, and the county town is Hertford.

The county has an area of 634 sqmi and had a population of 1,198,800 at the 2021 census. After Watford (131,325), the largest settlements are Hemel Hempstead (95,985), Stevenage (94,470) and the city of St Albans (75,540). For local government purposes Hertfordshire is a non-metropolitan county with ten districts beneath Hertfordshire County Council.

Elevations are higher in the north and west, reaching more than 800 ft in the Chilterns near Tring. The county centres on the headwaters and upper valleys of the rivers Lea and the Colne; both flow south and each is accompanied by a canal. Hertfordshire's undeveloped land is mainly agricultural and much of the county is covered by the Metropolitan green belt.

Since 1903, Letchworth has served as the prototype garden city while Stevenage became the first town to expand under post-war Britain's New Towns Act 1946 (9 & 10 Geo. 6. c. 68). Services have become the largest sector of the county's economy.

History
The county's landmarks span many centuries, ranging from the Six Hills in Stevenage built by local inhabitants during the Roman period, to Leavesden Film Studios. The volume of intact medieval and Tudor buildings surpasses London, in places in well-preserved conservation areas, especially in St Albans, which includes remains of the Roman town of Verulamium.

In 913, Hertfordshire was the area assigned to a fortress constructed at Hertford under the rule of Edward the Elder. Hertford is derived from the Anglo-Saxon heort ford, meaning deer crossing (of a watercourse). The name Hertfordshire is first recorded in the Anglo-Saxon Chronicle in 1011. Deer feature in many county emblems. Many of the names of the current settlements date back to the Anglo-Saxon period, with many featuring standard placename suffixes attributed to the Anglo-Saxons: "ford", "ton", "den", "bourn", "ley", "stead", "ing", "lett", "wood", and "worth", are represented in this county by Hertford, Royston, Harpenden, Redbourn, Cuffley, Wheathampstead, Tring, Radlett, Borehamwood and Rickmansworth.

There is evidence of human life in Hertfordshire from the Mesolithic period. It was first farmed during the Neolithic period and permanent habitation appeared at the beginning of the Bronze Age. This was followed by tribes settling in the area during the Iron Age.

Following the Roman conquest of Britain in AD 43, the Catuvellauni tribe quickly submitted and adapted to the Roman life; resulting in the development of several new towns, including Verulamium (St Albans) where in c. 293 the first recorded British martyrdom is traditionally believed to have taken place. Saint Alban, a Romano-British soldier, took the place of a Christian priest and was beheaded on Holywell Hill. His martyr's cross of a yellow saltire on a blue field is reflected in the flag and coat of arms of Hertfordshire as the yellow field to the stag or Hart representing the county. He is the Patron Saint of Hertfordshire.

With the departure of the Roman Legions in the early 5th century, the now-unprotected territory was invaded and colonised by the Anglo-Saxons. By the 6th century, the majority of the modern county was part of the East Saxon kingdom. This relatively short-lived kingdom collapsed in the 9th century, ceding the territory of Hertfordshire to the control of the West Anglians of Mercia. The region finally became an English shire in the 10th century, on the merger of the West Saxon and Mercian kingdoms.

In the midst of the Norse invasions, Hertfordshire was on the front lines of much of the fighting. King Edward the Elder, in his reconquest of Norse-held lands in what was to become England, established a "burh" or fort in Hertford, which was to curb Norse activities in the area. His father, King Alfred the Great, established the River Lea as a boundary between his kingdom and that of the Norse lord Guthrum, with the north and eastern parts of the county being within the Danelaw. There is little evidence however of Norse placenames within this region, and many of the Anglo-Saxon features remained intact to this day. The county however suffered from renewed Norse raids in the late 10th to early 11th centuries, as armies led by Danish kings Swein Forkbeard and Cnut the Great harried the country as part of their attempts to undermine and overthrow English king Athelred the Unready.

A century later, William of Normandy received the surrender of the surviving senior English Lords and Clergy at Berkhamsted, resulting in a new Anglicised title of William the Conqueror, before entering London unopposed and being crowned at Westminster. Hertfordshire was used for some of the new Norman castles at Bishop's Stortford, and at King's Langley, a staging post between London and the royal residence of Berkhamsted.

The Domesday Book recorded the county as having nine hundreds. Tring and Danais became one—Dacorum—from Danis Corum or Danish rule harking back to a Viking not Saxon past. The other seven were Braughing, Stevenage, Cashio, Buntingford, Hertford, Hitchin and Odsey.

In the later Plantagenet period, St. Albans Abbey was an initial drafting place of what was to become Magna Carta. And in the later Wars of the Roses, St. Albans was the scene of two major battles between the Lancastrians and the Yorkists.

In Tudor times, Hatfield House was often frequented by Queen Elizabeth I. Stuart King James I used the locale for hunting and facilitated the construction of a waterway, the New River, supplying drinking water to London.

As London grew, Hertfordshire became conveniently close to the English capital; much of the area was owned by the nobility and aristocracy, this patronage helped to boost the local economy. However, the greatest boost to Hertfordshire came during the Industrial Revolution, after which the population rose dramatically. In 1903, Letchworth became the world's first garden city and Stevenage became the first town to redevelop under the New Towns Act 1946 (9 & 10 Geo. 6. c. 68). The first shooting-down of a zeppelin over Great Britain during WW1 happened in Cuffley.

From the 1920s until the late 1980s, the town of Borehamwood was home to one of the major British film studio complexes, including the MGM-British Studios. Many well-known films were made here including the first three Star Wars movies (IV, V, & VI). The studios generally used the name of Elstree. American director Stanley Kubrick not only used to shoot in those studios but also lived in the area until his death. Big Brother UK and Who Wants to Be a Millionaire? have been filmed there. EastEnders is filmed at Elstree. Hertfordshire has seen development at Warner Bros. Studios, Leavesden; the Harry Potter series was filmed here and the 1995 James Bond film GoldenEye.

On 17 October 2000, the Hatfield rail crash killed four people with over 70 injured. The crash exposed the shortcomings of Railtrack, which consequently saw speed restrictions and major track replacement. On 10 May 2002, the fourth of the Potters Bar rail accidents occurred killing seven people; the train was travelling at high speed when it derailed and flipped into the air when one of the carriages slid along the platform where it came to rest.

In early December 2005, the 2005 Hemel Hempstead fuel depot explosions occurred at the Hertfordshire Oil Storage Terminal at Buncefield on the edge of Hemel Hempstead.

Geography
Hertfordshire is located in the south-eastern part of England and is the county immediately north of London. It is officially part of the East of England region, a mainly statistical unit. To the east is Essex, to the west is Buckinghamshire and to the north are Bedfordshire and Cambridgeshire. A significant minority of the population across all districts commute to Central London.

The county's boundaries were roughly fixed by the Counties (Detached Parts) Act 1844 which eliminated exclaves; amended when, in 1965 under the London Government Act 1963, East Barnet Urban District and Barnet Urban District were abolished, their area was transferred to form part of the present-day London Borough of Barnet and the Potters Bar Urban District of Middlesex was transferred to Hertfordshire.

The highest point in the county is at 244 m (AOD) on the Ridgeway long distance national path, on the border of Hastoe near Tring with Drayton Beauchamp, Buckinghamshire.

At the 2011 census, among the county's ten districts, East Hertfordshire had the lowest population density (290 people per km2) and Watford the highest (4210 per km2). Compared with neighbouring Bedfordshire and Buckinghamshire, Hertfordshire lacks large towns or cities on the scale of Luton or Milton Keynes, whose populations exceed 200,000, but its overall population (1.2 million in 2021) is greater than those of the two aforementioned counties.

The River Lea near Harpenden runs through Wheathampstead, Welwyn Garden City, Hertford, Ware, and Broxbourne before reaching Cheshunt and ultimately the River Thames. The far west of the county is the most hilly, with the Chiltern Hills surrounding Tring, Berkhamsted and the Ashridge estate. This Area of Outstanding Natural Beauty runs from near Hitchin in the north to Berkshire and Oxfordshire.

Many of the county's major settlements are in the central, northern and southern areas, such as Watford, Hemel Hempstead, Kings Langley, Rickmansworth, St. Albans, Harpenden, Redbourn, Radlett, Borehamwood, Potters Bar, Stevenage, Hatfield, Welwyn and Welwyn Garden City, Hitchin, Letchworth and Baldock. These are all small to medium-sized locations, featuring a mix of post-WWII new towns and older/more historical locales. The City of St. Albans is an example of a historical settlement, as its cathedral and abbey date to the Norman period, and there are ruins from the Roman settlement of Verulamium nearby the current city centre. Stevenage is a mix of post-WWII new town planning amidst its prior incarnation as a smaller town. The Old Town in Stevenage represents this historic core and has many shops and buildings reflecting its pre-WWII heritage. Hitchin also has a historic centre, with many Tudor and Stuart era buildings interspersed amongst more contemporary structures.

Hertfordshire's eastern regions are predominantly rural and arable, intermixed with villages and small to medium-sized towns. Royston, Buntingford and Bishop's Stortford, along with Ware and the county town of Hertford are major settlements in this regard. The physical geography of eastern Hertfordshire is less elevated than the far west, but with lower rising hills and prominent rivers such as the Stort. This river rises in Essex and terminates via a confluence with the Lea near to Ware. Apart from the Lea and Stort, the River Colne is the major watercourse in the county's west. This runs near Watford and Radlett, and has a complex system/drainage area running south into both Greater London and Buckinghamshire.

An unofficial status, the purple star-shaped flower with yellow stamens, the Pasqueflower is among endemic county flowers.

Geology
The rocks of Hertfordshire belong to the great shallow syncline known as the London Basin. The beds dip in a south-easterly direction towards the syncline's lowest point roughly under the River Thames. The most important formations are the Cretaceous Chalk, exposed as the high ground in the north and west of the county, forming the Chiltern Hills and the younger Palaeocene, Reading Beds and Eocene, London Clay which occupy the remaining southern part. The eastern half of the county was covered by glaciers during the Ice Age and has a superficial layer of glacial boulder clays.

Natural resources and environment
Much of the west – and much more in the east – have richly diverse countryside. These range from beech woods of the Chilterns, clayland buffer zone countryside of Braughing and the Hadhams across to ancient hornbeam coppices west of the upper Lea valley. The county has sweeping panoramas of chalklands near Royston, Baldock, Hexton and Tring.

Large parts of the county are used for agriculture.

Some quarrying of sand and gravel occurs around St Albans. In the past, clay has supplied local brick-making and still does in Bovingdon, just south-west of Hemel Hempstead. The chalk that is the bedrock of much of the county provides an aquifer that feeds streams and is also exploited to provide water supplies for much of the county and beyond. Chalk has also been used as a building material and, once fired, the resultant lime was spread on agricultural land to improve fertility. The mining of chalk since the early 18th century has left unrecorded underground galleries that occasionally collapse unexpectedly and endanger buildings.

Fresh water is supplied to London from Ware, using the New River built by Hugh Myddleton and opened in 1613. Local rivers, although small, supported developing industries such as paper production at Nash Mills.

Hertfordshire affords habitat for a variety of flora and fauna. A bird once common in the shire is the hooded crow, the old name of which is the eponymous name of the regional newspaper, the Royston Crow published in Royston. A product, now largely defunct, was watercress, based in Hemel Hempstead and Berkhamsted supported by reliable, clean chalk rivers.

Economy
This is a table of trends of regional gross value added of Hertfordshire at current basic prices with figures in millions of British Pounds Sterling.

Hertfordshire has the main operational and/or headquarters UK site of some very large employers. Clockwise from north:

In Stevenage (a subsidiary of: BAE Systems, Airbus and Finmeccanica) MBDA, develops missiles. In the same town, Airbus (Defence & Space Division) produces satellites.

Hatfield was where de Havilland developed the first commercial jet liner, the Comet. Now the site is a business park and new campus for the University of Hertfordshire. This major employment site notably hosts EE, Computacenter and Ocado groceries and other goods e-commerce.

Welwyn Garden City hosts Tesco's UK base, hosts the UK Cereal Partners factory and in pharmaceuticals it hosts Roche UK's headquarters (subsidiary of the Swiss Hoffman-La Roche). GlaxoSmithKline has plants in Ware and Stevenage.

Hemel Hempstead has large premises of Dixons Carphone.

The National Pharmacy Association (NPA), the trade association for UK pharmacies, is based in St Albans.

Kings Langley has the plant-office of Pure, making DAB digital radios.

Watford hosts national companies such as J D Wetherspoon, Camelot Group, Bathstore, and Caversham Finance (BrightHouse). It is also the UK base of multi-nationals Hilton Worldwide, TotalEnergies, TK Maxx, Costco, JJ Kavanagh and Sons, Vinci and Beko. The 2006 World Golf Championship and the 2013 Bilderberg Conference, took place at The Grove hotel. Warner Bros. owns and runs its main UK base since the 2000s, Warner Studios, in Leavesden, Watford.

Rickmansworth hosts Skanska.

Television
Local news and television programmes is provided by BBC London & ITV London, however northern parts of the county receive BBC East & ITV Anglia from Norwich.

Radio
Local Radio programmes are provided by BBC Three Counties Radio, Heart Hertfordshire, Greatest Hits Radio Bucks, Beds and Herts (formerly Mix 96), Mix 92.6 (formerly Radio Verulam St. Albans) and Community Radio Dacorum (Hemel Hempstead).

Watersports
Waltham Cross, Broxbourne, is the location of the Lee Valley White Water Centre, a purpose built venue opened in 2010 for the 2012 Summer Olympics. The site consists of two white water courses; one 300m Grade IV "Olympic" run; and one 160m Grade III "legacy" run.

During the games the Center was the venue for the canoe and kayak slalom events.

Lee Valley has since hosted the ICF Canoe Slalom World Championships twice. First in 2015, and most recently in 2023, where Britain topped the medal table with 5 golds.

Football
As of the 2021–22 season, there are four professional football teams in Hertfordshire: Watford F.C., Stevenage F.C., Arsenal W.F.C. and Boreham Wood F.C.

Since 1922, Watford play their home games at Vicarage Road. The club joined the Football League in 1920 as a founding member of the Third Division and first played in the First Division of English football in 1982, finishing as runners-up to champions Liverpool. Watford was promoted to the Premier League at the end of the 2020–2021 season. After spending one season in the Premier League, they were relegated to the Championship again for the 2022-2023 season.

Stevenage F.C. was formed in 1976 as Stevenage Borough and have played at Broadhall Way since 1980. Stevenage was the first club to win a competitive match at the new Wembley Stadium, beating Kidderminster Harriers 3–2 in the 2007 FA Trophy Final. The club currently play in the EFL League Two and have been managed by former player Alex Revell since February 2020.

Arsenal F.C., whilst based at the Emirates Stadium in the London Borough of Islington, has long held a training ground in the county. Until 1999, it held the London Colney University of London facility, until it built a new purpose-built compound adjacent to it. Watford FC currently utilises the old Arsenal training area as its training facility.

Arsenal W.F.C. play at Meadow Park in Borehamwood. The club was formed in 1987 and have played in the FA Women's Super League since its inaugural season in 2011.

Hertfordshire has many semi-professional and amateur clubs. The highest placed are Hemel Hempstead Town and St Albans City, who play in the National League South and Bishop's Stortford F.C. who play in the National League North.

Rugby league
Hemel Stags are a rugby league team based in Hemel Hempstead. Hemel Stags have played at Pennine Way Stadium since the club's founding in 1981. Until 2018, the club played in league 1, the third tier of the British rugby league system, and now compete in the Conference League South.

Rugby union
The Hertfordshire Rugby Football Union is the governing body for rugby union in Hertfordshire and is responsible for any interested parties involved in rugby.

Tring Rugby play matches at Cow Lane, Tring. The first XV currently play in the Regional 1 South East, League. A level 5 league.

GAA
Gaelic Football is played within Hertfordshire, with clubs from Oxfordshire all the way to Cambridge playing in the Hertfordshire League and Championship. Eire Óg, Oxford are the 2022 County Champions. Hurling is played by an amalgamated team, St Declan's CLG, with players contributed from all football teams across Hertfordshire. St Declan's currently play in the Warwickshire League and Championship, having previously played in the London GAA championship. A number of St Declan's players have also played for the Warwickshire Senior Hurling team, playing in the Lory Meagher and Nicky Rackard competitions, including Patrick Lancaster, Eamon Doherty, Alan Hayes, and Alex Hanley.

Landmarks

Below is a list of notable visitor attractions in Hertfordshire:
 * Aldenham Country Park
 * Ashridge – the estate surrounding the neo-Gothic house by James Wyatt (not open to the public) is National Trust land.
 * Bridgewater Monument, built in 1832 in memory of Francis Egerton, 3rd Duke of Bridgewater. 108 ft tall and open to the public to ascend to the top
 * Berkhamsted Castle
 * Cedars Park, Broxbourne – historic park once the site of James I's favourite residence, Theobalds Palace. Maintained by Broxbourne Services and the Friends of Cedars Park.
 * de Havilland Aircraft Heritage Centre, between London Colney and South Mimms
 * Frogmore Paper Mill, Apsley
 * Hatfield
 * Hatfield House – Jacobean house, gardens and park
 * Mill Green Watermill in Hatfield
 * University of Hertfordshire – a public research university based in Hatfield
 * Henry Moore Foundation, Much Hadham – sculpture park on the work of Henry Moore
 * Knebworth House, 250 acre of country park, venue of many rock and pop festivals
 * Leavesden Film Studios, home of the Warner Bros. Making of Harry Potter studio tour
 * Letchworth Garden City – the world's first Garden City. Site of the first planned Green Belt, the UK's first roundabout, and a number of experiments in early town planning and house and factory design
 * Spirella Building
 * Magic Roundabout (Hemel Hempstead) – a complex road junction
 * Royston Cave – in Royston town centre
 * Rye House Gatehouse in Hoddesdon (part of the Rye House Plot to assassinate King Charles II)
 * St Albans
 * Beech Bottom Dyke – large-scale Iron Age defensive or boundary ditch
 * Sopwell Nunnery
 * St Albans Cathedral
 * Verulamium – Roman town remains, including museum of Roman life and the remains of a Roman amphitheatre
 * Scott's Grotto, Ware
 * Shaw's Corner, Ayot St Lawrence – home of George Bernard Shaw
 * Stevenage – the first UK New Town
 * Six Hills Roman barrows site
 * Therfield Heath – a local nature reserve in the north of the county
 * Welwyn Roman Baths
 * Welwyn Viaduct to the north of Welwyn Garden City
 * Walter Rothschild Zoological Museum, Tring – a museum-annotated collection of dead mammals, birds, reptiles and insects
 * Watford Museum, fine art and local artefacts

Main footpaths

 * The Ridgeway
 * Icknield Way
 * Grand Union Canal Walk
 * Harcamlow Way
 * Hertfordshire Way
 * Hertfordshire Chain Walk

Transport
Hertfordshire is a home county with many towns forming part of the London commuter belt and has some of the principal roads in England including the A1, A1(M), A41, A414, M1, M11, and the M25.

Four principal national railway lines pass through the county:
 * the West Coast Main Line from . Avanti West Coast operates high speed intercity services via to the Midlands, North Wales, the North West England and Scotland. West Midlands Trains provides local commuter and regional services.
 * the East Coast Main Line from . Local commuter and regional services are provided by Govia Thameslink Railway. London North Eastern Railway runs high speed intercity services via Stevenage to the east coast of Northern England and Scotland
 * the Midland Main Line which forms part of the Thameslink route between Bedford and Brighton via Central London with services are provided by Govia Thameslink Railway. East Midlands Railway provide intercity services along the line from London St Pancras to the East Midlands and Yorkshire
 * the West Anglia Main Line from London Liverpool Street. Local commuter and regional services are provided by Greater Anglia mainly in the east of the county

A number of other local rail routes also cross Hertfordshire:
 * the London to Aylesbury Line from London Marylebone runs via Rickmansworth and Chorleywood
 * the Abbey Line, a local line from Watford to
 * the Cambridge Line, a branch of the East Coast line which runs via Royston and Letchworth to

Three commuter lines operated by Transport for London enter the county: The distance travelled by buses in Hertfordshire has reduced by 56.5% since 2017.
 * the Lea Valley Lines, a suburban metro line from Liverpool Street to Cheshunt via Seven Sisters
 * the Watford DC Line, a suburban metro line from Euston to Watford Junction
 * five stations on the London Underground Metropolitan line

Stansted Airport and Luton Airport are both within 10 mi of the county's borders in Essex and Bedfordshire, respectively. The commercial airfield at Elstree is for light aircraft.

The Grand Union Canal passes through Rickmansworth, Watford, Hemel Hempstead, Berkhamsted and Tring.

Education

Hertfordshire has 26 independent schools and 73 state secondary schools. The state secondary schools are entirely comprehensive, although 7 schools in the south and southwest of the county are partially selective (see Education in Watford). All state schools have sixth forms, and there are no sixth form colleges. The tertiary colleges, each with multiple campuses, are Hertford Regional College, North Hertfordshire College, Oaklands College and West Herts College. The University of Hertfordshire is a modern university based largely in Hatfield. It has more than 23,000 students.

Literature
Hertfordshire is the location of Jack Worthing's country house in Oscar Wilde's play The Importance of Being Earnest.

Jane Austen's novel Pride and Prejudice is primarily set in Hertfordshire.

The location of Mr Jarndyce's Bleak House in Charles Dickens's Bleak House is near St Albans.

The eponymous residence in E. M. Forster's novel Howards End was based on Rooks Nest House just outside Stevenage.

George Orwell based Animal Farm on Wallington, Hertfordshire, where he lived between 1936 and 1940. Manor Farm and The Great Barn both feature in the novel.

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Helene Kröller-Müller

Helene Kröller-Müller (11 February 1869 – 14 December 1939) was a German art collector. She was one of the first European women to put together a major art collection. She is credited with being one of the first collectors to recognise the genius of Vincent van Gogh. Her entire collection was eventually sold to the Dutch government, along with her and her husband, Anton Kröller's, large forested country estate. Today it is the Kröller-Müller Museum and sculpture garden and Hoge Veluwe National Park, one of the largest national parks in the Netherlands.

Life and career
She was born Helene Emma Laura Juliane Müller at, Essen, Germany, into a wealthy industrialist family. Her father, Wilhelm Müller, owned Wm. H. Müller & Co., a prosperous supplier of raw materials to the mining and steel industries.

She studied under Henk Bremmer in 1906–1907. As she was one of the wealthiest women in the Netherlands at the time, Bremmer recommended that she form an art collection. In 1907, she began her collection with the painting Train in a Landscape by Paul Gabriël. Subsequently, Helene Kröller-Müller became an avid art collector, and one of the first people to recognise the genius of Vincent van Gogh. She eventually amassed more than 90 van Gogh paintings and 185 drawings, one of the world's largest collections of the artist's work, second only to the Van Gogh Museum in Amsterdam. She also bought more than 400 works by Dutch artist Bart van der Leck, but his popularity did not take off like van Gogh's.

Kröller-Müller also collected works by modern artists, such as Picasso, Georges Braque, Jean Metzinger, Albert Gleizes, Fernand Léger, Diego Rivera, Juan Gris, Piet Mondrian, Gino Severini, Joseph Csaky, Auguste Herbin, Georges Valmier, María Blanchard, Léopold Survage and Tobeen. However, Bremmer advised her not to buy A Sunday Afternoon on the Island of La Grande Jatte by Georges Seurat, which turned out to be an important icon of 20th-century art. She did purchase however Le Chahut by Seurat, another icon in the history of modern art. Also, she steered away from artists of her native Germany, whose work she found "insufficiently authoritative."

On a trip to Florence in June 1910, she conceived the idea of creating a museum-house. From 1913 onwards parts of her collection were open to the public; until the mid-1930s her exhibition hall in The Hague was one of the very rare places where one could see more than a few works of modern art. In 1928, Anton and Helene created the Kröller-Müller Foundation to protect the collection and the estates. In 1935, they donated to the Dutch people their entire collection totaling approximately 12,000 objects, on condition that a large museum be built in the gardens of her park. Held in the care of the Dutch government, the Kröller-Müller Museum was opened in 1938.

The Kröller-Müller Museum is nestled in their 75-acre (300,000 m2) forested country estate, today the largest national park in the Netherlands, the Hoge Veluwe National Park near the town of Otterlo and the city of Arnhem. A lavish art gallery was planned near their iconic lakeside Jachthuis Sint Hubertus hunting lodge and landscape statue of their close personal friend, the South African Boer General Christian de Wet on the estate. Due to threat of war the plans were never implemented in their lifetime but once the war was over a large forest sculpture garden and understated open exhibition extension was opened, housing statues by Rodin and the second largest collection of van Gogh paintings in the world, including the famous Sunflowers.

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title: Helene Kröller-Müller


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Hans-Georg Gadamer

Hans-Georg Gadamer (11 February 1900 – 13 March 2002) was a German philosopher of the continental tradition, best known for his 1960 magnum opus on hermeneutics, Truth and Method (Wahrheit und Methode).

Family and early life
Gadamer was born in Marburg, Germany, the son of Johannes Gadamer (1867–1928), a pharmaceutical chemistry professor who later also served as the rector of the University of Marburg. He was raised a Protestant Christian. Gadamer resisted his father's urging to take up the natural sciences and became more and more interested in the humanities. His mother, Emma Karoline Johanna Geiese (1869–1904) died of diabetes while Hans-Georg was four years old, and he later noted that this may have had an effect on his decision not to pursue scientific studies. Jean Grondin describes Gadamer as finding in his mother "a poetic and almost religious counterpart to the iron fist of his father". Gadamer did not serve during World War I for reasons of ill health and similarly was exempted from serving during World War II due to polio.

Education
He later studied classics and philosophy in the University of Breslau under Richard Hönigswald, but soon moved back to the University of Marburg to study with the Neo-Kantian philosophers Paul Natorp (his doctoral thesis advisor) and Nicolai Hartmann. He defended his dissertation The Essence of Pleasure in Plato's Dialogues (Das Wesen der Lust nach den Platonischen Dialogen) in 1922.

Shortly thereafter, Gadamer moved to Freiburg University and began studying with Martin Heidegger, who was then a promising young scholar who had not yet received a professorship. He became close to Heidegger, and when Heidegger received a position at Marburg, Gadamer followed him there, where he became one of a group of students such as Leo Strauss, Karl Löwith, and Hannah Arendt. It was Heidegger's influence that gave Gadamer's thought its distinctive cast and led him away from the earlier neo-Kantian influences of Natorp and Hartmann. Gadamer studied Aristotle both under Edmund Husserl and under Heidegger.

Early career
Gadamer habilitated in 1929 and spent most of the early 1930s lecturing in Marburg. Unlike Heidegger, who joined the Nazi Party in May 1933 and continued as a member until the party was dissolved following World War II, Gadamer was silent on Nazism, and he was not politically active during Nazi rule. Gadamer did not join the Nazis, and he did not serve in the army because of the polio he had contracted in 1922. He joined the National Socialist Teachers League in August 1933.

In 1933 Gadamer signed the Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State.

In April 1937 he became a temporary professor at Marburg, then in 1938 he received a professorship at Leipzig University. From an SS-point of view Gadamer was classified as neither supportive nor disapproving in the "SD-Dossiers über Philosophie-Professoren" (i.e. SD-files concerning philosophy professors) that were set up by the SS-Security-Service (SD). In 1946, he was found by the American occupation forces to be untainted by Nazism and named rector of the university.

The level of Gadamer's involvement with the Nazis has been disputed in the works of Richard Wolin and Teresa Orozco. Orozco alleges, with reference to Gadamer's published works, that Gadamer had supported the Nazis more than scholars had supposed. Gadamer scholars have rejected these assertions: Jean Grondin has said that Orozco is engaged in a "witch-hunt" while Donatella Di Cesare said that "the archival material on which Orozco bases her argument is actually quite negligible". Cesare and Grondin have argued that there is no trace of antisemitism in Gadamer's work, and that Gadamer maintained friendships with Jews and provided shelter for nearly two years for the philosopher Jacob Klein in 1933 and 1934. Gadamer also reduced his contact with Heidegger during the Nazi era.

At Heidelberg
Communist East Germany was less to Gadamer's liking than Nazi Germany, so he left for West Germany, accepting first a position in Goethe University Frankfurt and then the succession of Karl Jaspers in the University of Heidelberg in 1949. He remained in this position, as emeritus, until his death in 2002 at the age of 102. He was also an Editorial Advisor of the journal Dionysius. It was during this time that he completed his magnum opus, Truth and Method (1960), and engaged in his famous debate with Jürgen Habermas over the possibility of transcending history and culture in order to find a truly objective position from which to critique society. The debate was inconclusive, but marked the beginning of warm relations between the two men. It was Gadamer who secured Habermas's first professorship in the University of Heidelberg.

In 1968, Gadamer invited Tomonobu Imamichi for lectures at Heidelberg, but their relationship became very cool after Imamichi alleged that Heidegger had taken his concept of Dasein out of Okakura Kakuzo's concept of das in-der-Welt-sein (to be in the being in the world) expressed in The Book of Tea, which Imamichi's teacher had offered to Heidegger in 1919, after having followed lessons with him the year before. Imamichi and Gadamer renewed contact four years later during an international congress.

In 1981, Gadamer attempted to engage with Jacques Derrida at a conference in Paris but it proved less enlightening because the two thinkers had little in common. A last meeting between Gadamer and Derrida was held at the Stift of Heidelberg in July 2001, coordinated by Derrida's students Joseph Cohen and Raphael Zagury-Orly. This meeting marked, in many ways, a turn in their philosophical encounter. After Gadamer's death, Derrida called their failure to find common ground one of the worst debacles of his life and expressed, in the main obituary for Gadamer, his great personal and philosophical respect. Richard J. Bernstein said that "[a] genuine dialogue between Gadamer and Derrida has never taken place. This is a shame because there are crucial and consequential issues that arise between hermeneutics and deconstruction".

Honorary doctorates
Gadamer received honorary doctorates from the University of Bamberg, the University of Wrocław, Boston College, Charles University in Prague, Hamilton College, the University of Leipzig, the University of Marburg (1999) the University of Ottawa, Saint Petersburg State University (2001), the University of Tübingen and University of Washington.

Death
On 11 February 2000, the University of Heidelberg celebrated Gadamer's one hundredth birthday with a ceremony and conference. Gadamer's last academic engagement was in the summer of 2001 at an annual symposium on hermeneutics that two of Gadamer's American students had organised. On 13 March 2002, Gadamer died at Heidelberg's University Clinic at the age of 102. He is buried in the Köpfel cemetery in Ziegelhausen.

Philosophical hermeneutics and Truth and Method
Gadamer's philosophical project, as explained in Truth and Method, was to elaborate on the concept of "philosophical hermeneutics", which Heidegger initiated but never dealt with at length. Gadamer's goal was to uncover the nature of human understanding. In Truth and Method, Gadamer argued that "truth" and "method" were at odds with one another. For Gadamer, "the experience of art is exemplary in its provision of truths that are inaccessible by scientific methods, and this experience is projected to the whole domain of human sciences." He was critical of two approaches to the human sciences (Geisteswissenschaften). On the one hand, he was critical of modern approaches to humanities that modeled themselves on the natural sciences, which simply sought to "objectively" observe and analyze texts and art. On the other hand, he took issue with the traditional German approaches to the humanities, represented for instance by Friedrich Schleiermacher and Wilhelm Dilthey, who believed that meaning, as an object, could be found within a text through a particular process that allowed for a connection with the author's thoughts that led to the creation of a text (Schleiermacher), or the situation that led to an expression of human inner life (Dilthey).

However, Gadamer argued meaning and understanding are not objects to be found through certain methods, but are inevitable phenomena. Hermeneutics is not a process in which an interpreter finds a particular meaning, but "a philosophical effort to account for understanding as an ontological—the ontological—process of man." Thus, Gadamer is not giving a prescriptive method on how to understand, but rather he is working to examine how understanding, whether of texts, artwork, or experience, is possible at all. Gadamer intended Truth and Method to be a description of what we always do when we interpret things (even if we do not know it): "My real concern was and is philosophic: not what we do or what we ought to do, but what happens to us over and above our wanting and doing".

As a result of Martin Heidegger's temporal analysis of human existence, Gadamer argued that people have a so-called historically effected consciousness (wirkungsgeschichtliches Bewußtsein), and that they are embedded in the particular history and culture that shaped them. However the historical consciousness is not an object over and against our existence, but "a stream in which we move and participate, in every act of understanding." Therefore, people do not come to any given thing without some form of preunderstanding established by this historical stream. The tradition in which an interpreter stands establishes "prejudices" that affect how he or she will make interpretations. For Gadamer, these prejudices are not something that hinders our ability to make interpretations, but are both integral to the reality of being, and "are the basis of our being able to understand history at all." Gadamer criticized Enlightenment thinkers for harboring a "prejudice against prejudices".

For Gadamer, interpreting a text involves a fusion of horizons (Horizontverschmelzung). Both the text and the interpreter find themselves within a particular historical tradition, or "horizon." Each horizon is expressed through the medium of language, and both text and interpreter belong to and participate in history and language. This "belongingness" to language is the common ground between interpreter and text that makes understanding possible. As an interpreter seeks to understand a text, a common horizon emerges. This fusion of horizons does not mean the interpreter now fully understands some kind of objective meaning, but is "an event in which a world opens itself to him." The result is a deeper understanding of the subject matter.

Gadamer further explains the hermeneutical experience as a dialogue. To justify this, he uses Plato's dialogues as a model for how we are to engage with written texts. To be in conversation, one must take seriously "the truth claim of the person with whom one is conversing." Further, each participant in the conversation relates to one another insofar as they belong to the common goal of understanding one another. Ultimately, for Gadamer, the most important dynamic of conversation as a model for the interpretation of a text is "the give-and-take of question and answer." In other words, the interpretation of a given text will change depending on the questions the interpreter asks of the text. The "meaning" emerges not as an object that lies in the text or in the interpreter, but rather an event that results from the interaction of the two.

Truth and Method was published twice in English, and the revised edition is now considered authoritative. The German-language edition of Gadamer's Collected Works includes a volume in which Gadamer elaborates his argument and discusses the critical response to the book. Finally, Gadamer's essay on Celan (entitled "Who Am I and Who Are You?") has been considered by many—including Heidegger and Gadamer himself—as a "second volume" or continuation of the argument in Truth and Method.

Contributions to communication ethics
Gadamer's Truth and Method has become an authoritative work in the communication ethics field, spawning several prominent ethics theories and guidelines. The most profound of these is the formulation of the dialogic coordinates, a standard set of prerequisite communication elements necessary for inciting dialogue. Adhering to Gadamer's theories regarding bias, communicators can better initiate dialogic transaction, allowing biases to merge and promote mutual understanding and learning.

Other works
Gadamer also added philosophical substance to the notion of human health. In The Enigma of Health, Gadamer explored what it means to heal, as a patient and a provider. In this work the practice and art of medicine are thoroughly examined, as is the inevitability of any cure.

In addition to his work in hermeneutics, Gadamer is also well known for a long list of publications on Greek philosophy. Indeed, while Truth and Method became central to his later career, much of Gadamer's early life centered on studying Greek thinkers, Plato and Aristotle specifically. In the Italian introduction to Truth and Method, Gadamer said that his work on Greek philosophy was "the best and most original part" of his career. His book Plato's Dialectical Ethics looks at the Philebus dialogue through the lens of phenomenology and the philosophy of Martin Heidegger.

Prizes and awards

 * 1971: Pour le Mérite and the Reuchlin Prize
 * 1972: Great Cross of Merit with Star of the Order of Merit of the Federal Republic of Germany
 * 1979: Sigmund Freud Prize for scientific prose and Hegel Prize
 * 1986: Karl Jaspers Prize
 * 1990: Great Cross of Merit with Star and Sash of the Order of Merit of the Federal Republic of Germany
 * 1993: Grand Cross of the Order of Merit of the Federal Republic of Germany
 * 12 January 1996: appointed an honorary member of the Saxon Academy of Sciences in Leipzig

Honorary doctorates

 * 1995: University of Wrocław
 * 1996: University of Leipzig
 * 1999: Philipps-University Marburg

title: Hans-Georg Gadamer


text:
Honeymoon

A honeymoon is a holiday taken by newlyweds after their wedding to celebrate their marriage. Today, honeymoons are often celebrated in destinations considered exotic or romantic. In a similar context, it may also refer to the phase in a couple's relationship—whether they are in matrimony or not—that exists before getting used to everyday life together.

History
The custom in Western culture and some westernized countries' cultures of a newlywed couple going on a holiday together originated in early-19th-century Great Britain. Upper-class couples would take a "bridal tour", sometimes accompanied by friends or family, to visit relatives who had not been able to attend the wedding. The practice soon spread to the European continent and was known in France as a voyage à la façon anglaise ('English-style voyage'), from the 1820s onwards.

Honeymoons in the modern sense—a pure holiday voyage undertaken by the couple—became widespread during the Belle Époque, in the late 1800s as one of the first instances of modern mass tourism.

According to some sources, the honeymoon is a relic of marriage by capture, based on the practice of the husband going into hiding with his wife to avoid reprisals from her relatives, with the intention that the woman would be pregnant by the end of the month.

Etymology
The honeymoon was originally the period following marriage, "characterized by love and happiness," as attested since 1546. The word may allude to "the idea that the first month of marriage is the sweetest.".

According to a different version, of the Oxford English Dictionary:

"The first month after marriage, when there is nothing but tenderness and pleasure (Samuel Johnson); originally having no reference to the period of a month, but comparing the mutual affection of newly married persons to the changing moon which is no sooner full than it begins to wane; now, usually, the holiday spent together by a newly married couple, before settling down at home."

Today, honeymoon has a positive meaning, but originally it may have referred to the inevitable waning of love, like a phase of the moon. In 1552, Richard Huloet wrote:

"Hony mone, a term proverbially applied to such as be newly married, which will not fall out at the first, but th'one loveth the other at the beginning exceedingly, the likelihood of their exceadinge love appearing to aswage, ye which time the vulgar people call the hony mone."

- Abcedarium Anglico-Latinum pro Tyrunculis

In many modern languages, the word for a honeymoon is a calque (e.g., lune de miel) or near-calque. Persian has a similar word,, which translates to 'month of honey' or 'moon of honey'.

A 19th-century theory claimed that the word alludes to "the custom of the higher order of the Teutones to drink Mead, or Metheglin, a beverage made with honey, for thirty days after every wedding", but the theory has been challenged.

The first recorded use of the word honeymoon to refer to the vacation after the wedding appeared in 1791, in a translation of German folk stories. The first recorded native-English use of the word appeared in 1804.

Modern practice
The modern purpose of honeymooning varies by culture. For those in an arranged marriage, a honeymoon is a time to get to know one another. For some cultures, it is a time for the couple to become sexually intimate. For other cultures, the purpose of the honeymoon mainly involves spending time to relax, creating a shared memorable experience for the couple, and adjusting to married life.

According to the 2023 Global Wedding Report done by The Knot, among the 15 countries surveyed, an average of 75% of couples took a honeymoon. Honeymoons are most popular in European countries. Fewer than half of couples in India took a honeymoon. Beach resorts were the preferred location for many couples.

The United States
Honeymoons are a $12 billion a year industry. In the United States, an average couple spends an average of $4500 for their honeymoon. The Niagara Falls was a popular honeymoon destination for Americans in the 1980s, but it has since become less favored due to the decreasing costs of air travel.

Solomoon or unimoon
An emerging 21st-century travel trend is the "solomoon" or "unimoon", a separate, solo holiday the newlyweds take without their spouse. The New Zealand Herald cites a report by The New York Times that such alternatives to honeymoons are "particularly suited for couples who just cannot agree on where to go".

Effects
One 2015 scholarly study concluded that going on a honeymoon is associated with a somewhat lower risk of divorce, regardless of how much or little is spent on the honeymoon itself. However, high spending and incurring significant debt on other wedding-related expenses, such as engagement rings and wedding ceremonies, is associated with a high risk of divorce.

title: Honeymoon


text:
Harold Kushner

Harold Samuel Kushner (April 3, 1935 – April 28, 2023) was an American rabbi, author, and lecturer. He was a member of the Rabbinical Assembly of Conservative Judaism and served as the congregational rabbi of Temple Israel of Natick, in Natick, Massachusetts, for 24 years.

Kushner gained widespread recognition for his many popular books that simplify complex theological ideas for both Jewish and non-Jewish readers. He received numerous awards, including the Christopher Award in 1987 and the Jewish Book Council's Lifetime Achievement Award in 2007. His most prominent works include When Bad Things Happen to Good People, delving into human suffering, divine kindness, and theodicy following his son's death, and When All You've Ever Wanted Isn't Enough, exploring existential themes of life's purpose and the pursuit of fulfillment.

Considered to be one of America's most prominent rabbis, Kushner was known for his Reconstructionist views and for his ideological progressiveness within the Conservative movement. He argued against the notion of an omnipotent, interventionist God, and instead focused on God's role in offering comfort and solace to those who suffer.

Early life and education
Harold Samuel Kushner was born to Conservative Jewish parents Julius and Sarah (Hartman) Kushner in Brooklyn, New York City. When he began elementary school, his family relocated to the Crown Heights neighborhood. Kushner was an avid fan of the Brooklyn Dodgers in his early years. While his mother was a homemaker, his father owned Playmore Publishing, a shop at Fifth Avenue and 23rd Street that specialized in selling children's books and toys, primarily Bible stories. Julius had hoped that his son would take over the business someday, but Harold did not believe he possessed the same level of business acumen as his father.

After graduating from Erasmus Hall High School, he attended Columbia University, where he initially intended to major in psychology but later switched to literature after being taught by Mark Van Doren, a Pulitzer Prize-winning poet. At Columbia, Kushner's extracurricular positions included working for Jester of Columbia and WKCR, where he eventually became the director of sports broadcasting, and serving as the president of the student Zionist organization.

Despite having a strong religious upbringing, Kushner had no plans to become a rabbi until he joined an evening program at the Jewish Theological Seminary in New York City. He became certain about his calling to be a rabbi during his junior year at Columbia. He completed his bachelor's degree in religious education in 1955, and after completing his master's degree in the social and philosophical foundations of education in 1960, he enrolled full-time at the seminary, where he was ordained that same year. Kushner received his doctorate in Hebrew literature in 1972. He also completed a year of graduate work at the Hebrew University of Jerusalem and held teaching positions at Clark University and the Rabbinical School of the JTS.

Rabbinical career
Following his rabbinic ordination, Kushner went to court to request the waiver of his military exemption. He served for two years as a first lieutenant in the Army's Chaplain Corps at Fort Sill in Oklahoma. After his discharge from the military, Kushner returned to New York and served as an assistant rabbi at Temple Israel in Great Neck from 1962 to 1966.

In 1966, Kushner assumed the position of rabbi at the 450-family congregation Temple Israel in Natick, Massachusetts. He fulfilled the role of congregational rabbi there for 24 years while also being a member of the Rabbinical Assembly, the "clerical arm" of the Conservative movement. From 1972 to 1974, he served as the president of the New England Region of the Rabbinical Assembly. Initially serving as Temple Israel's full-time rabbi, he shifted to part-time in 1983 to allocate more time for writing and in 1990, he transitioned to full-time writing and lecturing. The synagogue deemed Kushner, who was 55 years old at the time, too young to be appointed as rabbi emeritus, so he was bestowed the title of rabbi laureate in 1983. The title, held by only a few American rabbis, underlined his commitment to maintaining an enduring connection with both his congregants and the rabbinate. He attended the synagogue until his death.

Kushner's presence in the Conservative movement was described as "inescapable". In 2001, he co-authored Etz Hayim: A Torah Commentary, the new official Torah commentary of the Conservative movement, in collaboration with Chaim Potok. The comprehensive work comprises four layers of commentary, encompassing insights on Conservative observance of Jewish law and traditional and contemporary interpretations of scripture (midrash), curated by Kushner.

Kushner spoke at the interfaith prayer service for the second inauguration of Bill Clinton. He was also a eulogist at the state funeral of Ronald Reagan in the Washington National Cathedral in 2004, where offered a reading from the Book of Isaiah.

Writing
With the backing of Rabbi Ira Eisenstein, the founder of the Reconstructionist Rabbinical College, Kushner released his inaugural book in 1971 under the title When Children Ask About God: A Guide for Parents Who Don't Always Have All the Answers. Rather than reinforcing the notion of God as an all-knowing and all-powerful creator, he aimed to foster a healthy skepticism and encourage questioning as a means of developing a meaningful religious faith. The book primarily targeted parents and aimed to address the concerns of people who were seeking a new Jewish belief system more in line with their broader worldview.

Kushner is best known for his international best-selling book on the problem of evil, When Bad Things Happen to Good People, published in 1981. Written following the death of his son, Aaron, from the premature aging disease progeria, it deals with questions about human suffering, God, omnipotence, and theodicy. Kushner aimed to assist individuals in maintaining their belief in God's benevolence despite experiencing personal tragedies. His book offers a fresh interpretation of the Book of Job, suggesting that while God may not have the power to prevent suffering, God provides solace to those who are afflicted. His contemporary interpretation of theodicy in the book laid the groundwork for the modernist theological literature within the Conservative Jewish community, alongside works by Elliott N. Dorff, Neil Gillman, Harold M. Schulweis, and David Wolpe. The book resonated with readers across religions and was translated into at least 12 languages. Its success propelled it to the top of The New York Times Best Seller list, and established Kushner as a well-known author and commentator. In 1991, it tied for the ninth position with four other books in the Book of the Month Club's list of the top ten books that had the most significant impact on American lives, based on a nationwide survey. The book was described as "arguably one of the most widely read books written by a rabbi in centuries" and as "one of the most widely read Jewish books of our generation" by Neil Gillman. Its popularity was partly attributed to Protestant clergy members promoting it in their sermons and distributing copies to their congregations. Four million copies had been sold by the book's 20th anniversary.

In 1986, Kushner published When All You've Ever Wanted Isn't Enough: The Search for a Life That Matters, delving into existential themes of life's meaning and individual pursuit of happiness within the context of Ecclesiastes. Its title was deemed an "apt summary of Ecclesiastes". Kushner's goal was to dissect the unfulfillment experienced even by achievers, asserting that "What we miss in our lives, no matter how much we have, is that sense of meaning." He rejected the notion of a singular answer to life's complexities and contended that such answers are found in daily experiences, relationships, and the quest for integrity. Central to his argument was Ecclesiastes, which he called "the most dangerous book in the Bible" for its call to contemplation over blind worship, as Kushner contended that life's richness emerges from thoughtful engagement, emphasizing that an unfulfilled life is more daunting than death itself. The book earned praise as a "useful spiritual survival manual" from The Washington Post and received the 1987 Christopher Award for its "contribution to the exaltation of the human spirit."

Who Needs God, published in 1989, argued for the ongoing relevance of God in a world characterized by unprecedented human achievements. As with Kushner's previous works, Reconstructionist views were apparent in his attempt to make room for religious life and the notion of God without the belief in an all-powerful creator. He aimed to bridge the gap between religious fundamentalism and atheism, highlighting that organized religion's greatest offering is not theology but rather the comfort and support of a spiritual community. Kushner also asserted that the existence of God endows individuals with the ability to perceive holiness in the world and attain a greater sense of purpose.

Kushner authored several other well-received theological books, such as How Good Do We Have to Be? and To Life!. Works such as When All You've Ever Wanted Isn't Enough, Who Needs God? and How Good Do We Have to Be? reached a wide readership of millions. In 2007, Kushner received a Lifetime Achievement Award from the Jewish Book Council.

Carolyn Hessel, director of the Jewish Book Council, attributed Kushner's success to his ability to appeal to everyone regardless of their background. Burton Cooper, a professor of theology at the Louisville Presbyterian Theological Seminary, argues that Kushner's popularity and significance arise from his skill in reaching individuals with a "modern consciousness", a perspective informed by science, and resonating with their longing for religious faith.

In the fall of 2001, Kushner achieved his sixth best-seller with Living a Life That Matters, focused on Jacob from the Old Testament, the sole figure with a complete biography in the Bible. He examines Jacob's complex moral choices, such as deceiving his father to secure his blessing. He interprets Jacob's encounter with an angel as an internal struggle, symbolizing the conflict within his soul and his progression towards integrity. While Kushner's stance suggests Jacob's victory through loss, the Torah presents an alternate perspective, depicting Jacob as the undisputed winner.

Kushner's response to Simon Wiesenthal's question of forgiveness was included in a revised 1997 edition of the book The Sunflower: On the Possibilities and Limits of Forgiveness, alongside those of 45 other leading intellectuals and commentators. Wiesenthal's inquiry emerged from a real-life scenario during the Holocaust, when he confronted a dying Nazi soldier who sought absolution for his heinous deeds, prompting the question: Can such profound wrongdoing be forgiven? Kushner conveyed the essence of forgiveness as follows:

Forgiving is not something we do for another person, as the Nazi asked Wiesenthal to do for him. Forgiving happens inside us. It represents a letting go of the sense of grievance, and perhaps most importantly a letting go of the role of victim. For a Jew to forgive the Nazis would not mean, God forbid, saying to them "What you did was understandable, I can understand what led you to it and I don't hate you for it." It would mean saying "What you did was thoroughly despicable and puts you outside the category of decent human beings. But I refuse to give you the power to define me as a victim. I refuse to let your blind hatred define the shape and content of my Jewishness. I don't hate you; I reject you." And then the Nazi would remained chained to his past and to his conscience, but the Jew would be free.

Kushner was an editor of the journal Conservative Judaism from 1980 to 1984.

Kushner frequently used examples from TV shows and movies in his teachings and writings to connect with his audience, as he believed many people are more familiar with these cultural references than with the Bible, although he expressed concern over the semi-literacy of the Bible and found it surprising when people were not familiar with biblical stories.

Views
Kushner, affiliated with Conservative Judaism, championed progressive concepts within the movement while deeply influenced by Mordecai Kaplan, his teacher and the founder of Reconstructionist Judaism, whom he regarded as the most influential thinker in American Jewish history. During a speech to the Rabbinical Assembly in 1980, he commented that the Conservative movement had faced an ongoing crisis regarding the authority of halakhah (Jewish law) since its inception. He emphasized that the goal of Conservative rabbis was to demonstrate that leading a religious life in the modern era could be fulfilling, without imposing strict observance on less practicing Jews. Paraphrasing Jewish theologian Martin Buber, Kushner also once stated that "people want less theology and more religion." He rejected the definition of religion "as an individual experience", emphasizing its communal aspect.

Informed by the teachings of Kaplan, Kushner was a proponent of Jewish religious naturalism. Discarding the notion of an omnipotent God, he proposed that God lacks complete dominion over the universe and is not culpable for evil. Within this Reconstructionist framework, he identified two core life forces: the randomness of nature and purposeful divine actions. He rejected the notion of God causing suffering as punishment, advocating instead for a God who shares in human pain, as evidenced by God's name "I am with you" in the Book of Exodus. Viewing God as a source of empathy and love, Kushner once recalled being concerned that during Yom Kippur, his synagogue's congregants focused too much on guilt and did not give themselves the chance to experience God's forgiveness. His aphorism "forgiveness benefits us more than the person we forgive" was one of many adopted by religious leaders of various faiths. Drawing from the Reconstructionist tradition, Kushner asserted that God shouldn't be perceived as a distant entity in space, emphasizing that the question of God's existence doesn't necessarily revolve around the concept of a heavenly population.

Kushner's writing and ideas were popular among Christians, but traditional Jews held mixed opinions. He once expressed, "I always thought Judaism was at its best when it not only looked at text, but when it looked at people." Kushner's approach, rooted in a focus on human needs, occasionally led him to reinterpret Jewish theology for emotional solace. This resulted in some Orthodox Jews feeling defensive of traditional Jewish teachings and accusing him of promoting un-Jewish ideas. In When Bad Things Happen to Good People, Kushner reconciled Jewish beliefs in God's omnipotence and benevolence constraining God's influence over random hazards in life. He likened God to a benevolent watchmaker who created the world and its natural laws. This perspective portrays God as taking pride in his creation while permitting it to operate within these established laws, including the occurrence of random challenges. This implies that God intentionally refrains from complete control over every aspect of life, enabling individuals to navigate and respond to various situations while supporting them only with his presence. This view contradicts traditional Jewish teaching and led to criticism from Orthodox Jews, although Kushner himself acknowledged that he may have been wrong about God. Literary critic and journalist Ron Rosenbaum was not convinced by Kushner's argument in the book, describing Kushner's position as "diminishing God to something less than an Omnipotent Being – to something more like an eager cheerleader for good, but one decidedly on the sidelines in the struggle against evil."

In line with Kaplan's influence and Reconstructionist theology, Kushner perceived the Torah as a fully human creation that, while acknowledging its human origins, serves to commemorate significant religious experiences in life. He sometimes expressed doubt about the reliability of individuals who claim to have heard divine messages, and cited the Binding of Isaac as a problematic narrative that contradicts fundamental religious tenets. The story tells of Abraham going to sacrifice his son, Isaac, as an offering to God in obedience to a divine directive. Although Kushner believed that Abraham heard the message, he was skeptical that God actually said it.

Personal life
In 1960, Kushner married Suzette Estrada and moved to Massachusetts. Estrada died in 2022. The couple had a son named Aaron, who died of progeria at the age of 14, a daughter named Ariel, and two grandchildren. Kushner's brother Paul was a rabbi in Bellmore and Merrick on Long Island, and died in 2019.

In 1995, Christian inspirational group The Christophers included Kushner in their list of "50 individuals who have made a positive impact on the world over the past 50 years." He was the recipient of six honorary doctorates.

Kushner moved into a senior residence in Canton, Massachusetts in 2017. He died on April 28, 2023, at age 88.

title: Harold Kushner


text:
Hotspot

Hotspot, Hot Spot or Hot spot may refer to:

Places

 * Hot Spot, Kentucky, a community in the United States

Fictional entities

 * Hot Spot (comics), a name for the DC Comics character Isaiah Crockett
 * Hot Spot (Transformers), any of several characters

Films

 * Hot Spot (1941 film), later retitled I Wake Up Screaming
 * Hot Spot (1945 film), a Private Snafu film
 * The Hot Spot, a 1990 neo-noir film

Other uses in arts, entertainment, and media

 * Hot Spot (board game), a 1979 board game published by Metagaming Concepts
 * "Hot Spot" (Burn Notice), a television episode
 * Hot Spot (musical), 1963
 * "Hot Spot" (song), by Foxy Brown
 * Hotspot (album), a 2020 album by Pet Shop Boys
 * The Hot Spot (Podcast), a GameSpot podcast

Computing

 * Hot spot (computer programming), a compute-intensive region of a program
 * Hot spot, an area which is customizable by users in software frameworks
 * Wi-Fi hotspot, a wireless network access point or area
 * Connectify Hotspot, a software application for creating a wireless access point
 * Mobile hotspot, also known as Tethering, sharing of a mobile device's Internet connection
 * HotSpot (virtual machine), the Java Virtual Machine originally developed by Sun and the current reference implementation of the Java programming language
 * Screen hotspot, an area enabled for user interactivity on a display

Science and healthcare

 * Hotspot (geology), an area of unusually high volcanic activity
 * Hot spot (veterinary medicine), an irritated skin lesion
 * Hot spot, a location with a high level of radioactive contamination
 * Biodiversity hotspot, a region of significant variety and variability of life
 * Hot spot effect in subatomic physics, regions of high energy density or temperature
 * Recombination hotspot, a region in a genome

Other uses

 * Hot spot (casting), a metal casting defect
 * Hot Spot (cricket), an infrared tracking system
 * Airport hot spots, locations where aircraft collisions with ground equipment may occur
 * Hotspot camp, a refugee camp that serves as an initial reception point
 * Pyotraumatic dermatitis (also known as hot spots), a common skin dog infection

title: Hotspot


text:
Heapsort

In computer science, heapsort is a comparison-based sorting algorithm which can be thought of as "an implementation of selection sort using the right data structure." Like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. Unlike selection sort, heapsort does not waste time with a linear-time scan of the unsorted region; rather, heap sort maintains the unsorted region in a heap data structure to efficiently find the largest element in each step.

Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantages of very simple implementation and a more favorable worst-case $O(n log n)$ runtime. Most real-world quicksort variants include an implementation of heapsort as a fallback should they detect that quicksort is becoming degenerate. Heapsort is an in-place algorithm, but it is not a stable sort.

Heapsort was invented by J. W. J. Williams in 1964. The paper also introduced the binary heap as a useful data structure in its own right. In the same year, Robert W. Floyd published an improved version that could sort an array in-place, continuing his earlier research into the treesort algorithm.

Overview
The heapsort algorithm can be divided into two phases: heap construction, and heap extraction.

The heap is an implicit data structure which takes no space beyond the array of objects to be sorted; the array is interpreted as a complete binary tree where each array element is a node and each node's parent and child links are defined by simple arithmetic on the array indexes. For a zero-based array, the root node is stored at index 0, and the nodes linked to node i are iLeftChild(i) = 2⋅i + 1 iRightChild(i) = 2⋅i + 2 iParent(i)    = floor((i−1) / 2) where the floor function rounds down to the preceding integer. For a more detailed explanation, see.

This binary tree is a max-heap when each node is greater than or equal to both of its children. Equivalently, each node is less than or equal to its parent. This rule, applied throughout the tree, results in the maximum node being located at the root of the tree.

In the first phase, a heap is built out of the data (see ).

In the second phase, the heap is converted to a sorted array by repeatedly removing the largest element from the heap (the root of the heap), and placing it at the end of the array. The heap is updated after each removal to maintain the heap property. Once all objects have been removed from the heap, the result is a sorted array.

Heapsort is normally performed in place. During the first phase, the array is divided into an unsorted prefix and a heap-ordered suffix (initially empty). Each step shrinks the prefix and expands the suffix. When the prefix is empty, this phase is complete. During the second phase, the array is divided into a heap-ordered prefix and a sorted suffix (initially empty). Each step shrinks the prefix and expands the suffix. When the prefix is empty, the array is sorted.

Algorithm
The heapsort algorithm begins by rearranging the array into a binary max-heap. The algorithm then repeatedly swaps the root of the heap (the greatest element remaining in the heap) with its last element, which is then declared to be part of the sorted suffix. Then the heap, which was damaged by replacing the root, is repaired so that the greatest element is again at the root. This repeats until only one value remains in the heap.

The steps are: The heapify operation is run once, and is $O(n)$ in performance. The siftDown function is called $n$ times and requires $O(n)$ work each time, due to its traversal starting from the root node. Therefore, the performance of this algorithm is $O(log n)$.
 * 1) Call the heapify function on the array. This builds a heap from an array in $O(n + n log n) = O(n log n)$ operations.
 * 2) Swap the first element of the array (the largest element in the heap) with the final element of the heap.  Decrease the considered range of the heap by one.
 * 3) Call the siftDown function on the array to move the new first element to its correct place in the heap.
 * 4) Go back to step (2) until the remaining array is a single element.

The heart of the algorithm is the siftDown function. This constructs binary heaps out of smaller heaps, and may be thought of in two equivalent ways:
 * given two binary heaps, and a shared parent node which is not part of either heap, merge them into a single larger binary heap; or
 * given a "damaged" binary heap, where the max-heap property (no child is greater than its parent) holds everywhere except possibly between the root node and its children, repair it to produce an undamaged heap.

To establish the max-heap property at the root, up to three nodes must be compared (the root and its two children), and the greatest must be made the root. This is most easily done by finding the greatest child, then comparing that child to the root. There are three cases:
 * 1) If there are no children (the two original heaps are empty), the heap property trivially holds, and no further action is required.
 * 2) If root is greater than or equal to the greatest child, the heap property holds and likewise, no further action is required.
 * 3) If the root is less than the greatest child, exchange the two nodes.  The heap property now holds at the newly-promoted node (it is greater than or equal to both of its children, and in fact greater than any descendant), but may be violated between the newly-demoted ex-root and its new children.  To correct this, repeat the siftDown operation on the subtree rooted at the newly-demoted ex-root.

The number of iterations in any one siftdown call is bounded by the height of the tree, which is $\floor{log2 n} = O(log n)$.

Pseudocode
The following is a simple way to implement the algorithm in pseudocode. Arrays are zero-based and swap is used to exchange two elements of the array. Movement 'down' means from the root towards the leaves, or from lower indices to higher. Note that during the sort, the largest element is at the root of the heap at a[0], while at the end of the sort, the largest element is in a[end].

procedure heapsort(a, count) is input: an unordered array a of length count (Build the heap in array a so that largest value is at the root) heapify(a, count) (The following loop maintains the invariants that a[0:end−1] is a heap, and    every element a[end:count−1] beyond end is greater than everything before it,     i.e. a[end:count−1] is in sorted order.) end ← count while end > 1 do (the heap size is reduced by one) end ← end − 1 (a[0] is the root and largest value. The swap moves it in front of the sorted elements.) swap(a[end], a[0]) (the swap ruined the heap property, so restore it) siftDown(a, 0, end)

The sorting routine uses two subroutines, heapify and siftDown. The former is the common in-place heap construction routine, while the latter is a common subroutine for implementing heapify. (Put elements of 'a' in heap order, in-place) procedure heapify(a, count) is (start is initialized to the first leaf node) (the last element in a 0-based array is at index count-1; find the parent of that element) start ← iParent(count-1) + 1 while start > 0 do (go to the last non-heap node) start ← start − 1 (sift down the node at index 'start' to the proper place such that all nodes below         the start index are in heap order) siftDown(a, start, count) (after sifting down the root all nodes/elements are in heap order) (Repair the heap whose root element is at index 'start', assuming the heaps rooted at its children are valid) procedure siftDown(a, root, end) is while iLeftChild(root) < end do   (While the root has at least one child) child ← iLeftChild(root)      (Left child of root) (If there is a right child and that child is greater) if child+1 < end and a[child] < a[child+1] then child ← child + 1 if a[root] < a[child] then swap(a[root], a[child]) root ← child        (repeat to continue sifting down the child now) else (The root holds the largest element. Since we may assume the heaps rooted             at the children are valid, this means that we are done.) return

The heapify procedure operates by building small heaps and repeatedly merging them using siftDown. It starts with the leaves, observing that the they are trivial but valid heaps by themselves, and then adds parents. Starting with element $n/2$ and working backwards, each internal node is made the root of a valid heap by sifting down. The last step is sifting down the first element, after which the entire array obeys the heap property.

To see that this takes $O(n)$ time, count the worst-case number of siftDown iterations. The last half of the array requires zero iterations, the preceding quarter requires at most one iteration, the eighth before that requires at most two iterations, the sixteenth before that requires at most three, and so on.

Looked at a different way, if we assume every siftDown call requires the maximum number of iterations, the first half of the array requires one iteration, the first quarter requires one more (total 2), the first eighth requires yet another (total 3), and so on.

This totals $n/2 + n/4 + n/8 + ⋯ = n⋅(1/2 + 1/4 + 1/8 + ⋯)$, where the infinite sum is a well-known geometric series whose sum is $1$, thus the product is simply $n$.

The above is an approximation. The exact worst-case number of comparisons during the heap-construction phase of heapsort is known to be equal to $2n − 2s_{2}(n) − e_{2}(n)$, where $s_{2}(n)$ is the number of 1 bits in the binary representation of $n$ and $e_{2}(n)$ is the number of trailing 0 bits.

Standard implementation
Although it is convenient to think of the two phases separately, most implementations combine the two, allowing a single instance of siftDownto be expanded inline. Two variables (here, start and end) keep track of the bounds of the heap area. The portion of the array before start is unsorted, while the portion beginning at end is sorted. Heap construction decreases start until it is zero, after which heap extraction decreases end until it is 1 and the array is entirely sorted.

procedure heapsort(a, count) is input: an unordered array a of length count start ← floor(count/2) end ← count while end > 1 do if start > 0 then   (Heap construction) start ← start − 1 else                (Heap extraction) end ← end − 1 swap(a[end], a[0]) (The following is siftDown(a, start, end)) root ← start while iLeftChild(root) < end do child ← iLeftChild(root) (If there is a right child and that child is greater) if child+1 < end and a[child] < a[child+1] then child ← child + 1 if a[root] < a[child] then swap(a[root], a[child]) root ← child        (repeat to continue sifting down the child now) else break               (return to outer loop)

Williams' heap construction
The description above uses Floyd's improved heap-construction algorithm, which operates in $O(n)$ time and uses the same siftDown primitive as the heap-extraction phase. Although this algorithm, being both faster and simpler to program, is used by all practical heapsort implementations, Williams' original algorithm may be easier to understand, and is needed to implement a more general binary heap priority queue.

Rather than merging many small heaps, Williams' algorithm maintains one single heap at the front of the array and repeatedly appends an additional element using a siftUp primitive. Being at the end of the array, the new element is a leaf and has no children to worry about, but may violate the heap property by being greater than its parent. In this case, exchange it with its parent and repeat the test until the parent is greater or there is no parent (we have reached the root). In pseudocode, this is: procedure siftUp(a, end) is input: a is the array, which heap-ordered up to end-1. end is the node to sift up. while end > 0 parent := iParent(end) if a[parent] < a[end] then (out of max-heap order) swap(a[parent], a[end]) end := parent         (continue sifting up) else return procedure heapify(a, count) is (start with a trivial single-element heap) end := 1 while end < count (sift up the node at index end to the proper place such that          all nodes above the end index are in heap order) siftUp(a, end) end := end + 1 (after sifting up the last node all nodes are in heap order)

To understand why this algorithm can take asymptotically more time to build a heap ($O(n log n)$ vs. $O(n)$ worst case), note that in Floyd's algorithm, almost all the calls to siftDown operations apply to very small heaps. Half the heaps are height-1 trivial heaps and can be skipped entirely, half of the remainder are height-2, and so on. Only two calls are on heaps of size $n/2$, and only one siftDown operation is done on the full $n$-element heap. The overall average siftDown operation takes $O(1)$ time.

In contrast, Williams' algorithm most of the calls to siftUp are made on large heaps of height $O(log n)$. Half of the calls are made with a heap size of $n/2$ or more, three-quarters are made with a heap size of $n/4$ or more, and so on. Although the average number of steps is similar to Floyd's technique, pre-sorted input will cause the worst case: each added node is sifted up to the root, so the average call to siftUp will require approximately $(log2n − 1)/2 + (log2n − 2)/4 + (log2n − 3)/8 + ⋯$ $= log2n − (1 + 1/2 + 1/4 + ⋯)$ $= log2n − 2$ iterations.

Because it is dominated by the second heap-extraction phase, the heapsort algorithm itself has $O(n log n)$ time complexity using either version of heapify.

Bottom-up heapsort
Bottom-up heapsort is a variant which reduces the number of comparisons required by a significant factor. While ordinary "top-down" heapsort requires $2n log_{2} n + O(n)$ comparisons worst-case and on average, the bottom-up variant requires $n log_{2}n + O(1)$ comparisons on average, and $1.5n log_{2}n + O(n)$ in the worst case.

If comparisons are cheap (e.g. integer keys) then the difference is unimportant, as top-down heapsort compares values that have already been loaded from memory. If, however, comparisons require a function call or other complex logic, then bottom-up heapsort is advantageous.

This is accomplished by using a more elaborate siftDown procedure. The change improves the linear-time heap-building phase slightly, but is more significant in the second phase. Like top-down heapsort, each iteration of the second phase extracts the top of the heap, a[0], and fills the gap it leaves with a[end], then sifts this latter element down the heap. But this element came from the lowest level of the heap, meaning it is one of the smallest elements in the heap, so the sift-down will likely take many steps to move it back down. In top-down heapsort, each step of siftDown requires two comparisons, to find the minimum of three elements: the new node and its two children.

Bottom-up heapsort conceptually replaces the root with a value of −∞ and sifts it down using only one comparison per level (since no child can possibly be less than −∞) until the leaves are reached, then replaces the −∞ with the correct value and sifts it up (again, using one comparison per level) until the correct position is found.

This places the root in the same location as top-down siftDown, but fewer comparisons are required to find that location. For any single siftDown operation, the bottom-up technique is advantageous if the number of downward movements is at least $2/3$ of the height of the tree (when the number of comparisons is $4/3$ times the height for both techniques), and it turns out that this is more than true on average, even for worst-case inputs.

A naïve implementation of this conceptual algorithm would cause some redundant data copying, as the sift-up potion undoes part of the sifting down. A practical implementation searches downward for a leaf where −∞ would be placed, then upward for where the root should be placed. Finally, the upward traversal continues to the root's starting position, performing no more comparisons but exchanging nodes to complete the necessary rearrangement. This optimized form performs the same number of exchanges as top-down siftDown.

Because it goes all the way to the bottom and then comes back up, it is called heapsort with bounce by some authors.

function leafSearch(a, i, end) is j ← i    while iRightChild(j) < end do (Determine which of j's two children is the greater) if a[iRightChild(j)] > a[iLeftChild(j)] then j ← iRightChild(j) else j ← iLeftChild(j) (At the last level, there might be only one child) if iLeftChild(j) < end then j ← iLeftChild(j) return j

The return value of the  is used in the modified   routine:

procedure siftDown(a, i, end) is j ← leafSearch(a, i, end) while a[i] > a[j] do j ← iParent(j) while j > i do swap(a[i], a[j]) j ← iParent(j)

Bottom-up heapsort was announced as beating quicksort (with median-of-three pivot selection) on arrays of size ≥16000.

A 2008 re-evaluation of this algorithm showed it to be no faster than top-down heapsort for integer keys, presumably because modern branch prediction nullifies the cost of the predictable comparisons which bottom-up heapsort manages to avoid.

A further refinement does a binary search in the upward search, and sorts in a worst case of $(n+1)(log_{2}(n+1) + log_{2} log_{2}(n+1) + 1.82) + O(log_{2}n)$ comparisons, approaching the information-theoretic lower bound of $n log_{2}n − 1.4427n$ comparisons.

A variant which uses two extra bits per internal node (n−1 bits total for an n-element heap) to cache information about which child is greater (two bits are required to store three cases: left, right, and unknown) uses less than $n log_{2}n + 1.1n$ compares.

Other variations

 * Ternary heapsort uses a ternary heap instead of a binary heap; that is, each element in the heap has three children. It is more complicated to program, but does a constant number of times fewer swap and comparison operations. This is because each sift-down step in a ternary heap requires three comparisons and one swap, whereas in a binary heap two comparisons and one swap are required. Two levels in a ternary heap cover 32 = 9 elements, doing more work with the same number of comparisons as three levels in the binary heap, which only cover 23 = 8. This is primarily of academic interest, or as a student exercise, as the additional complexity is not worth the minor savings, and bottom-up heapsort beats both.
 * Memory-optimized heapsort improves heapsort's locality of reference by increasing the number of children even more. This increases the number of comparisons, but because all children are stored consecutively in memory, reduces the number of cache lines accessed during heap traversal, a net performance improvement.
 * The standard implementation of Floyd's heap-construction algorithm causes a large number of cache misses once the size of the data exceeds that of the CPU cache. Better performance on large data sets can be obtained by merging in depth-first order, combining subheaps as soon as possible, rather than combining all subheaps on one level before proceeding to the one above.
 * Out-of-place heapsort  improves on bottom-up heapsort by eliminating the worst case, guaranteeing $n log_{2}n + O(n)$ comparisons. When the maximum is taken, rather than fill the vacated space with an unsorted data value, fill it with a $−∞$ sentinel value, which never "bounces" back up. It turns out that this can be used as a primitive in an in-place (and non-recursive) "QuickHeapsort" algorithm. First, you perform a quicksort-like partitioning pass, but reversing the order of the partitioned data in the array. Suppose (without loss of generality) that the smaller partition is the one greater than the pivot, which should go at the end of the array, but our reversed partitioning step places it at the beginning. Form a heap out of the smaller partition and do out-of-place heapsort on it, exchanging the extracted maxima with values from the end of the array. These are less than the pivot, meaning less than any value in the heap, so serve as $−∞$ sentinel values. Once the heapsort is complete (and the pivot moved to just before the now-sorted end of the array), the order of the partitions has been reversed, and the larger partition at the beginning of the array may be sorted in the same way. (Because there is no non-tail recursion, this also eliminates quicksort's $O(log n)$ stack usage.)
 * The smoothsort algorithm is a variation of heapsort developed by Edsger W. Dijkstra in 1981. Like heapsort, smoothsort's upper bound is $O(n log n)$. The advantage of smoothsort is that it comes closer to $O(n)$ time if the input is already sorted to some degree, whereas heapsort averages $O(n log n)$ regardless of the initial sorted state. Due to its complexity, smoothsort is rarely used.
 * Levcopoulos and Petersson describe a variation of heapsort based on a heap of Cartesian trees. First, a Cartesian tree is built from the input in $O(n)$ time, and its root is placed in a 1-element binary heap. Then we repeatedly extract the minimum from the binary heap, output the tree's root element, and add its left and right children (if any) which are themselves Cartesian trees, to the binary heap. As they show, if the input is already nearly sorted, the Cartesian trees will be very unbalanced, with few nodes having left and right children, resulting in the binary heap remaining small, and allowing the algorithm to sort more quickly than $O(n log n)$ for inputs that are already nearly sorted.
 * Several variants such as weak heapsort require $n log_{2} n+O(1)$ comparisons in the worst case, close to the theoretical minimum, using one extra bit of state per node. While this extra bit makes the algorithms not truly in-place, if space for it can be found inside the element, these algorithms are simple and efficient, but still slower than binary heaps if key comparisons are cheap enough (e.g. integer keys) that a constant factor does not matter.
 * Katajainen's "ultimate heapsort" requires no extra storage, performs $n log_{2} n+O(1)$ comparisons, and a similar number of element moves. It is, however, even more complex and not justified unless comparisons are very expensive.

Comparison with other sorts
Heapsort primarily competes with quicksort, another very efficient general purpose in-place unstable comparison-based sort algorithm.

Heapsort's primary advantages are its simple, non-recursive code, minimal auxiliary storage requirement, and reliably good performance: its best and worst cases are within a small constant factor of each other, and of the theoretical lower bound on comparison sorts. While it cannot do better than $O(n log n)$ for pre-sorted inputs, it does not suffer from quicksort's $O(n^{2})$ worst case, either.

Real-world quicksort implementations use a variety of heuristics to avoid the worst case, but that makes their implementation far more complex, and implementations such as introsort and pattern-defeating quicksort use heapsort as a last-resort fallback if they detect degenerate behaviour. Thus, their worst-case performance is slightly worse than if heapsort had been used from the beginning.

Heapsort's primary disadvantages are its poor locality of reference and its inherently serial nature; the accesses to the implicit tree are widely scattered and mostly random, and there is no straightforward way to convert it to a parallel algorithm.

The worst-case performance guarantees make heapsort popular in real-time computing, and systems concerned with maliciously chosen inputs such as the Linux kernel. The combination of small implementation and dependably "good enough" performance make it popular in embedded systems, and generally any application where sorting is not a performance bottleneck. E.g. heapsort is ideal for sorting a list of filenames for display, but a database management system would probably want a more aggressively optimized sorting algorithm.

A well-implemented quicksort is usually 2–3 times faster than heapsort. Although quicksort requires fewer comparisons, this is a minor factor. (Results claiming twice as many comparisons are measuring the top-down version; see .) The main advantage of quicksort is its much better locality of reference: partitioning is a linear scan with good spatial locality, and the recursive subdivision has good temporal locality. With additional effort, quicksort can also be implemented in mostly branch-free code, and multiple CPUs can be used to sort subpartitions in parallel. Thus, quicksort is preferred when the additional performance justifies the implementation effort.

The other major $O(n log n)$ sorting algorithm is merge sort, but that rarely competes directly with heapsort because it is not in-place. Merge sort's requirement for $Ω(n)$ extra space (roughly half the size of the input) is usually prohibitive except in the situations where merge sort has a clear advantage:
 * When a stable sort is required
 * When taking advantage of (partially) pre-sorted input
 * Sorting linked lists (in which case merge sort requires minimal extra space)
 * Parallel sorting; merge sort parallelizes even better than quicksort and can easily achieve close to linear speedup
 * External sorting; merge sort has excellent locality of reference

Example
The examples sort the values { 6, 5, 3, 1, 8, 7, 2, 4 } in increasing order using both heap-construction algorithms. The elements being compared are shown in a bold font. There are typically two when sifting up, and three when sifting down, although there may be fewer when the top or bottom of the tree is reached.

title: Heapsort