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City of Milton Keynes

The City of Milton Keynes is a unitary authority area with both borough and city status, in Buckinghamshire. It is the northernmost district of the South East England Region. The borough abuts Bedfordshire, Northamptonshire and the remainder of Buckinghamshire.

The principal built-up area in the borough is the Milton Keynes urban area, which accounts for about 20% of its area and 90% of its population. The borough also includes many rural areas surrounding the Milton Keynes urban area (especially to the north), containing several villages and the town of Olney. At the 2021 census, the population of the unitary authority area was just over 287,000.

History
The district was created on 1 April 1974 under the Local Government Act 1972, covering the whole area of four former districts and part of a fifth, which were all abolished at the same time:
 * Bletchley Urban District
 * Newport Pagnell Urban District
 * Newport Pagnell Rural District
 * Winslow Rural District (part within the designated New Town area only, rest went to Aylesbury Vale)
 * Wolverton Urban District

The new district was named Milton Keynes (after its largest settlement). The district was given borough status from its creation, allowing the chair of the council to take the title of mayor.

As established in 1974, the borough of Milton Keynes was one of five non-metropolitan districts of Buckinghamshire, with Buckinghamshire County Council providing county-level services to the area. On 1 April 1997, Milton Keynes became a self-governing unitary authority by being redefined as its own non-metropolitan county, independent from Buckinghamshire County Council. Milton Keynes remains part of the ceremonial county of Buckinghamshire for the purposes of lieutenancy.

On 15 August 2022, letters patent were issued giving the borough the status of a city, allowing the council to change its name to Milton Keynes City Council.

Local government
Arising from the local government elections of May 2024, the borough is governed by a Labour administration. The Liberal Democrat party is the main opposition group.

In the 2024 Labour gained 4 seats to become the majority party, having previously been part of a joint Labour-Lib-Dem run administration.

Economy
According to data from the Office for National Statistics for 2017, the borough was the highest performing NUTS3 region in the UK outside inner London (which takes the first five places), on the basis of gross value added per head.

Education
Further education in the borough is provided by Milton Keynes College. For higher education, the Open University's headquarters are in Milton Keynes – though, as this is a distance education institution, the only students resident on campus are approximately 200 full-time postgraduates. A campus of the University of Bedfordshire located in Central Milton Keynes, provides conventional undergraduate courses.

Cranfield University is the academic partner in project with Milton Keynes City Council to establish a new university, code-named "MK:U",

on a reserved site in the city centre. , the project is stalled pending assurance of government funding.

Population
At the 2021 census, the population of the borough was 287,060. This was an increase of 15.3% from the 2011 census, when the population of the borough was 248,821. By 2050, the City Council projects that the borough's population will reach 410,000.

Education
At the 2021 census, of residents aged 16 and over, 15.8% had no qualifications, 10.9% had a level1 qualification, 14.2% had level2, 4.7% were in apprenticeship, 15.7% had level3, 35.8% had level4 and 2.9% had other qualifications.

Ethnicity
In the 2021 census, almost 71.8% of the population described their ethnic origin as white, 12.3% as Asian, 9.7% as black, 4% as mixed, and 2% as another ethnic group.

Religion
The following table shows the religion of respondents in recent censuses in the city of Milton Keynes.

Housing and home ownership
Household tenure breaks down to 60.8% of dwellings owner-occupied, 21% of homes privately rented and 18% are socially rented. Due to the borough's fast-growing population, the City Council plans for a minimum of 26,500 dwellings across the borough over the period between 2016 and 2031, with development primarily focused on city estates, expansion areas and strategic land locations in the south and east of Milton Keynes, Campbell Park (in CMK) and the three "Key Settlements" outside of the 1967 "designated development area" of Milton Keynes: Newport Pagnell, Woburn Sands and Olney.

Public health
According to Public Health England, "The health of people in Milton Keynes is generally similar to the England average. About 15.1% (8,680) children live in low income families. Life expectancy for both men and women is similar to the England average."

Milton Keynes urban area
''The urban area accounts for about 20% of the borough by area and 90% by population. This is a partial list of the districts of the Milton Keynes urban area.

The City of Milton Keynes is fully parished. These are the parishes, and the districts they contain, that are now elements of the Milton Keynes built-up area as defined by the Office for National Statistics.

Bletchley, Fenny Stratford, Woburn Sands, Central Milton Keynes, Newport Pagnell, Wolverton and Stony Stratford are towns. The civil parishes are:
 * Abbey Hill: Kiln Farm, Two Mile Ash, Wymbush
 * Bletchley and Fenny Stratford: Brickfields, Central Bletchley, Denbigh, Mount Farm, Fenny Lock, Granby, Fenny Stratford, Newton Leys, Water Eaton
 * Bradwell: Bradville, Bradwell, Bradwell Abbey, Bradwell Common, Bradwell village, Heelands, Rooksley
 * Broughton and Milton Keynes – a joint parish council: Atterbury, Brook Furlong, Broughton, Fox Milne, Middleton (includes Milton Keynes Village), Northfield, Oakgrove, Pineham
 * Campbell Park (civil parish): Fishermead, Newlands, Oldbrook, Springfield, Willen and Willen Lake, Winterhill, The Woolstones
 * Central Milton Keynes: Central MK, Campbell Park
 * Fairfields
 * Great Linford: Bolbeck Park, Blakelands, Conniburrow, Downs Barn, Downhead Park, Giffard Park, Great Linford, Neath Hill, Pennyland, Redhouse, Tongwell, Willen Park
 * Kents Hill, Monkston and Brinklow: Brinklow, Kents Hill, Kingston, Monkston
 * Loughton and Great Holm: Loughton, Loughton Lodge, Great Holm, Elfield Park, the Bowl
 * New Bradwell
 * Newport Pagnell
 * Shenley Brook End: Emerson Valley, Furzton, Kingsmead, Shenley Brook End, Shenley Lodge, Snelshall, Tattenhoe, Tattenhoe Park, Westcroft
 * Shenley Church End: Crownhill, Grange Farm, Hazeley, Medbourne, Oakhill, Oxley Park, Shenley Church End, Woodhill
 * Simpson and Ashland: Ashland, Simpson, West Ashland
 * Stantonbury: Bancroft/Bancroft Park, Blue Bridge, Bradville, Linford Wood, Oakridge Park, Stantonbury, Stantonbury Fields
 * Stony Stratford: Fullers Slade, Galley Hill, Stony Stratford
 * Walton: Caldecotte, Old Farm Park, Tilbrook, Tower Gate, Walnut Tree, Walton, Walton Hall, Walton Park, Wavendon Gate
 * Wavendon: Wavendon, Eagle Farm, Glebe Farm
 * West Bletchley: Far Bletchley, Old Bletchley, West Bletchley.
 * Whitehouse
 * Woburn Sands
 * Wolverton and Greenleys: Greenleys, Stacey Bushes, Stonebridge, Wolverton, Old Wolverton
 * Woughton: Beanhill, Bleak Hall, Coffee Hall, Eaglestone, Leadenhall, Netherfield, Peartree Bridge, Redmoor, Tinkers Bridge (part)
 * Old Woughton: Passmore (part of Tinkers Bridge), Woughton on the Green, Woughton Park.

Rest of the borough
The rural area accounts for about 80% of the borough by area and about 10% by population. Olney is a town. These are the extra-urban civil parishes:
 * Astwood and Hardmead
 * Bow Brickhill
 * Caldecote, Calverton, Castlethorpe, Chicheley, Clifton Reynes, Cold Brayfield
 * Emberton
 * Filgrave
 * Gayhurst
 * Hanslope, Haversham-cum-Little Linford
 * Lathbury, Lavendon, Little Brickhill, Long Street
 * Moulsoe
 * Newton Blossomville, North Crawley
 * Olney
 * Ravenstone
 * Sherington, Stoke Goldington
 * Tyringham
 * Warrington, Weston Underwood

Neighbourhood Plans
, the borough has 28 designated Neighbourhood Areas, of which 22 have made/adopted Neighbourhood Development Plans approved by the City Council, spanning both urban and rural parishes.

Freedom of the City
The following people and military units have received the Freedom of the City (from 2022) or Freedom of the Borough (1982–2021).

Individuals

 * Jock Campbell, Baron Campbell of Eskan: 18 March 1982.
 * James Marshall: 2009.
 * Dame Cleo Laine: 2011.
 * Peter Winkelman: 12 November 2015.
 * Leah Williamson: 28 February 2023. (first recipient of the Freedom of the City)

Military Units

 * The Royal Green Jackets: 1998.
 * The Rifles: 2007. (confirmation)
 * 678 (Rifles) Squadron 6 Regiment Army Air Corps: 11 March 2018.

Organisations and businesses

 * Red Bull Racing, 2014

title: City of Milton Keynes


text:
David Gerrold

David Gerrold (born Jerrold David Friedman; January 24, 1944) is an American science fiction screenwriter and novelist. He wrote the script for the original Star Trek episode "The Trouble with Tribbles", created the Sleestak race on the TV series Land of the Lost, and wrote the novelette "The Martian Child", which won both Hugo and Nebula Awards, and was adapted into a 2007 film starring John Cusack.

Early life
Gerrold was born to a Jewish family on January 24, 1944, in Chicago, Illinois. He attended Van Nuys High School and graduated from Ulysses S. Grant High School in its first graduating class, Los Angeles Valley College, and San Fernando Valley State College (now California State University, Northridge).

Star Trek: The Original Series
Within days of seeing the Star Trek series premiere "The Man Trap" on September 8, 1966, 22-year-old Gerrold wrote a 60-page outline for a two-part episode called "Tomorrow Was Yesterday" about the Enterprise discovering a ship launched from Earth centuries earlier. Although Star Trek producer Gene L. Coon rejected the outline, he realized Gerrold was talented and expressed interest in his submitting some story premises. Bearing preliminary titles and, in some cases, preliminary character names, Gerrold submitted five premises.

Two of the submissions of which he later had little recollection involved a spaceship-destroying machine, similar to Norman Spinrad's "The Doomsday Machine", and a situation in which Kirk had to play a chess game with an advanced intelligence using his crew as chess pieces. A third premise, "Bandi", involved a small being running about the Enterprise as someone's pet, and which empathically sways the crew's feelings and emotions to comfort it, even at someone else's expense.

A fourth premise, "The Protracted Man", applied science fiction to an effect seen in West Side Story, when Maria twirls in her dancing dress and the colours separate. Gerrold's story involved a man transported from a shuttlecraft trying out a new space warp technology. The man is no longer unified, separating into three visible forms when he moves, separated by a fraction of a second. As efforts are undertaken to correct the condition and move the Enterprise to where corrective action can be taken, the protraction worsens.

The fifth premise, "The Fuzzies", was also initially rejected by Coon, but a while later he changed his mind and called Gerrold's agent to accept it. Gerrold then expanded the story to a full television story outline entitled "A Fuzzy Thing Happened to Me...", and it eventually became "The Trouble with Tribbles". The name "Fuzzy" was changed because H. Beam Piper had written novels about a fictional alien species of the same name (see Little Fuzzy). The script went through numerous rewrites, including, at the insistence of Gerrold's agent, being re-set in a stock frontier town instead of an "expensive" space station. Gerrold later wrote a book, The Trouble with Tribbles, telling the story of producing the episode and his earlier premises.

"The Cloud Minders" from the third season has a story credited to Gerrold and Oliver Crawford.

"I came in with what I thought was a near-perfect Star Trek story, which is we find a culture that isn't working for everybody and fix it. But my original ending was that, as they're flying off, Kirk says, 'Well, we solved another one.' Spock says, 'Well, actually, it'll take years and years and years for all of these changes to be put in place.' And McCoy says, 'I wonder how many children are going to die in the meantime.' So the idea was, 'Let's get gritty. We're not going to change things overnight, but we can put changes in place that will have long-term effects.' There was also more to the story that was about the social issue, and there was no magical zenite gas that was causing the problem. Freddy Freiberger and Margaret Armen came in and changed it to a 'Let's solve it all in the last five minutes with gas masks' (ending). And I thought, 'That's really not a very good story. It doesn't do what Gene Roddenberry or Gene L. Coon would have been willing to do.' So I was disappointed."

The Trouble with Tribbles was one of two books Gerrold wrote about Star Trek in the early 1970s after the original series had been canceled. His other was an analysis of the series, entitled The World of Star Trek, in which he criticized some of the elements of the show, particularly Kirk's habit of placing himself in dangerous situations and leading landing parties himself.

Star Trek: The Animated Series
Gerrold contributed two stories for the Emmy Award-winning Star Trek: The Animated Series which ran from 1973 to 1974: "More Tribbles, More Troubles" and "Bem". "Bem" featured the first use of James T. Kirk's middle name, which was revealed to be Tiberius. This was later entered into live-action canon in the movie Star Trek VI: The Undiscovered Country when Captain Kirk and Doctor McCoy are on trial for the death of the Klingon Chancellor Gorkon.

Star Trek: The Next Generation
Many of the changes Gerrold had advocated in The World of Star Trek were incorporated into Star Trek: The Next Generation when it debuted in 1987. He parted company with the producers at the beginning of the first season.

Gerrold wrote a script for Star Trek: The Next Generation entitled "Blood and Fire", which included an AIDS metaphor and a gay couple in the ship's crew. Gerrold wrote this script in response to being with Roddenberry at a convention in 1987 where he had promised that the upcoming Next Generation series would deal with the issue of sexual orientation in the egalitarian future. The script was purchased by the TNG producers, but eventually shelved. He later reworked the story into the third book in the Star Wolf series (see below) and again as a two-part episode of the fan-produced Star Trek: New Voyages, which he also directed.

Other Trek involvement
Gerrold had wanted to appear onscreen in an episode of Star Trek, particularly "The Trouble with Tribbles". The character of Ensign Freeman, who appears in the bar scene with the Klingons, was originally intended by Gerrold to be a walk-on part for himself, however another actor took the role since Gerrold was deemed too thin at the time. He also had an in-joke cameo of sorts in Star Trek The Animated Series: "More Tribbles, More Troubles" where a very thin Ensign is told to seal off the transporter room area by Kirk. Gerrold also provided the voice for alien Em/3/Green in "The Jihad". While Gerrold appeared as a crewman extra with other Trek fandom notables in Star Trek: The Motion Picture, he did not appear in a Trek series until Star Trek: Deep Space Nine, when he played a security guard in "Trials and Tribble-ations", set during the timeframe of his original episode.

Gerrold wrote a novelization of the Star Trek: The Next Generation series premiere "Encounter at Farpoint", published in 1987, and an original Star Trek novel titled The Galactic Whirlpool, published in 1980, which was based on his story outline "Tomorrow Was Yesterday". In 2006, for the 40th anniversary of Star Trek, he co-edited, with Robert J. Sawyer, an essay collection titled Boarding the "Enterprise".

Gerrold acted as a series consultant for fan-produced series Star Trek: New Voyages and Star Trek: Phase II starting in 2006. In June 2013 he was named showrunner of the series.

Early science fiction novels
His science fiction novels include The Man Who Folded Himself (1973), about a man who inherits a time-travel belt, and When HARLIE Was One (1972), the story of an artificial intelligence's relationship with his creators. When HARLIE Was One was nominated for best novel for both the Hugo Award and the Nebula Award. This novel is notable for being one of the first to describe a computer virus. A revised edition, entitled When HARLIE Was One, Release 2.0, was published in 1988, incorporating new insights and reflecting new developments in computer science.

The War Against the Chtorr
Gerrold is the author of the War Against the Chtorr series of books, about an invasion of Earth by mysterious aliens: A Matter for Men (1983), A Day for Damnation (1985), A Rage for Revenge (1989), and A Season for Slaughter (1993). He eventually announced that what was initially supposed to be a trilogy would in fact require seven books. In approximately 2010 Gerrold was reputed to have a considerable amount of work completed on the remainder of the series, and the fifth book, A Method for Madness, was listed on Amazon with a publication date. The publication date has been updated several times since; the last was January 1, 2014. At that time the remaining books in the series were tentatively titled A Method For Madness, A Time For Treason, and A Case For Courage. In 2017, he announced that the fifth book, now tentatively titled A Nest for Nightmares, and the sixth book, A Method For Madness, are nearing completion, over two decades after the last book came out. Whether a seventh Chtorr book is still planned, or what its title will be if it is, are unknown. Gerrold is considering crowdfunding and other ways to raise money to fund completion of organization of the material and final writing for the two books.

The alien invasion is an ecological one. Instead of Earthlings terraforming another planet, the aliens are "Chtorraforming" Earth. Instead of armies, the unseen aggressors gradually unleash plants and animals from their older, more evolved planet (which is indicated as being perhaps a half billion years older than Earth, and evolved into a higher effective competitiveness). These outcompete and displace their terrestrial counterparts and Earth becomes more and more Chtorr-like as the "war" progresses.

Portions of the remaining books have made it into print, however. Gerrold released to fans a cliffhanger teaser chapter from Method for Madness. In his collection The Involuntary Human (ISBN 978-1-886-77869-6), he included "It Needs Salt" (as a portion of the planned but not formally scheduled Time for Treason). Finally, he also published the story "Enterprise Fish" in a volume of Thrilling Wonder Stories, (ISBN 978-0-9796718-1-4; edited by Winston Engle). "Enterprise Fish" is described as an excerpt from Time for Treason. The Chtorr series and its central character have moved through stages of development with each book in the series, with another layer of the Chtorran ecology explained and understanding of it unveiled with each successive book. Since "It Needs Salt" and "Enterprise Fish" are short stories from planned future layers of plot and character development, fans of the series are forewarned that they contain "spoilers".

Star Wolf
Gerrold is also the author of the Star Wolf series of books, centered on the star ship Star Wolf and its crew: Voyage of the Star Wolf (1990), The Middle of Nowhere (1995), Blood and Fire (2004), and Yesterday's Children (1972) which is actually an earlier novel that features the same main character, later significantly expanded and republished as Starhunt (1985)—it occurs prior to the other novels in the series' main continuity. The initial germ of Yesterday's Children was the "framing" story in his early Star Trek proposal "Tomorrow Was Yesterday", much altered over time. Gerrold had planned to develop this concept into a TV series, as he writes in an introduction to Voyage of the Star Wolf. The Star Wolf series reflects Gerrold's contention that, due to the distances involved, space battles would be more like submarine hunts than the dogfights usually portrayed—in most cases the ships doing battle would not even be able to see each other.

Other works
After his early success with "The Trouble with Tribbles" Gerrold continued writing television scripts (mostly for science fiction series such as Land of the Lost, Babylon 5, Sliders, and The Twilight Zone). He has also made several uncredited appearances on the TV series The Big Bang Theory.

In 1999, he contributed a short piece to Smart Reseller magazine predicting that cell phones could evolve into devices he called "Personal Information Telecommunications Agent", and described a feature set very similar to modern smartphones:

"I've got a cell phone, a pocket organiser, a beeper, a calculator, a digital camera, a pocket tape recorder, a music player, and somewhere around here, I used to have a color television.

Sometime in the next few years, all of those devices are going to meld into one. It will be a box less than an inch thick and smaller than a deck of cards. (The size will be determined by what's convenient to hold, not by the technology inside.)

The box will have a high-res color screen, a microphone, a plug for a headset or earphones, a camera lens, wireless connectivity, cell phone and beeper functions, a television and radio receiver, a digital recorder, and it will have enough processing power and memory to function as a desktop system. It will be able to dock with a keyboard and full size monitor. Oh yes, and it will handle email as well.

Most important of all, it will have both speech recognition and speech synthesis. It will listen and respond in English or whatever language you need, and yes it will be a translator too. It will be an agent, going out and doing cyber errands for you. For instance, I need a Japanese restaurant in Tulsa, near the Ramada Inn. Book a reservation and arrange transportation.

If there's no Japanese restaurant, try for Italian. Or voicemail Bob as follows: 'Bob, we accept your offer, but we'll need a draft of the deal memo by the 15th. Let me know if that's a problem.'

I call this device a Personal Information Telecommunications Agent, or Pita for short. The acronym also can stand for Pain in the Ass, which it is equally likely to be, because having all that connectivity is going to destroy what's left of everyone's privacy."

Gerrold wrote the non-fiction book Worlds of Wonder: How to Write Science Fiction & Fantasy, published in 2001.

The Martian Child is a semi-autobiographical novel, expanded from a novelette of the same name, based on the author's own experiences as a single adoptive father, with most of the key moments drawn from actual events. The novelette won both the Hugo and Nebula awards, and a movie version was released in November 2007, with John Cusack playing the adoptive father. There is some controversy surrounding this character, as David Gerrold and his character in the novel are both gay, but in the movie he is a straight widower.

In 2000, his long-time admiration of the works of Robert A. Heinlein led him to create a new series, called The Dingilliad. It follows a resourceful teenager and his family as they try to begin a new life. Although not necessarily canon, there are hints that it ties into the War Against the Chtorr universe, with everything from the plagues to the rumored appearance of a giant purple worm (similar cross-universe tie-ins occur in Gerrold's Trackers books). The Dingilliad trilogy consists of Jumping Off the Planet (2000), Bouncing Off the Moon (2001), and Leaping to the Stars (2002). Jumping Off the Planet received the 2002 Hal Clement (Young Adult Award) for Excellence in Children's Science Fiction Literature.

In 2005, Gerrold was awarded the Telluride Tech Festival Award of Technology in Telluride, Colorado.

In 2013, Gerrold wrote a Starcraft 2 short story titled "In the Dark" for Blizzard Entertainment's series of Starcraft short stories.

As of 2015, he is also a member of the board of directors for the Hollywood Science Fiction Museum.

Gerrold continues to write and publish online on Patreon and other mediums. He is also a proponent of personal development programs such as Lifespring and Landmark, among others. See his post on Patreon, "Why I Believe in Personal Development Courses."

Gerrold was the winner of the Robert A. Heinlein Award for 2022.

Novels

 * The Flying Sorcerers (also known as The Misspelled Magishun, 1971; with Larry Niven)
 * Space Skimmer (1972)
 * Yesterday's Children (1972)
 * When HARLIE Was One (1972; revised as When HARLIE Was One, Release 2.0, 1988)
 * Battle for the Planet of the Apes (1973)
 * The Man Who Folded Himself (1973)
 * Moonstar Odyssey (1977)
 * Deathbeast (1978)
 * Chess with a Dragon (1987)
 * The Martian Child (2002)
 * Child of Earth (2005)
 * Ganny Knits a Spaceship (April 2019), ISBN 978-1948818339. Based upon a 2009 short story of the same name that was first published in Jim Baen's Universe.
 * thirteen fourteen fifteen o'clock (2015)
 * Hella (2020)

 * The Dingilliad

 * 1) Jumping Off the Planet (2000)
 * 2) Bouncing Off the Moon (2001)
 * 3) Leaping to the Stars (2002)
 * 4) Hella (2020)

 * Star Trek
 * 1) The Galactic Whirlpool (1980)
 * 2) Encounter at Farpoint (1987) (a novelization)

 * Star Wolf
 * 1) Yesterday's Children (aka Starhunt) (1972, rv.1980)
 * 2) Voyage of the Star Wolf (1990)
 * 3) The Middle of Nowhere (1995)
 * 4) Blood and Fire (2004)

 * Trackers
 * 1) Under the Eye of God (1993)
 * 2) A Covenant of Justice (1994)

 * The War Against the Chtorr
 * 1) A Matter for Men (1983)
 * 2) A Day for Damnation (1984)
 * 3) A Rage for Revenge (1989)
 * 4) A Season for Slaughter (1992)
 * 5) A Nest for Nightmares (in progress)
 * 6) A Method for Madness (in progress)
 * 7) A Time for Treason (projected)
 * 8) A Case for Courage (projected)

Short fiction

 * Collections
 * With a Finger in My I (1972)
 * The Far Side of the Sky (2002)
 * Alternate Gerrolds (2005)
 * The Involuntary Human (2007)

 * Stories

 * "The Impeachment of Adlai Stevenson" (1992) (collected in Mike Resnick's alternate history anthology Alternate Presidents)
 * "The Kennedy Enterprise" (1992) (collected in Mike Resnick's alternate history anthology Alternate Kennedys)
 * "The Firebringers" (1993) (collected in Mike Resnick's alternate history anthology Alternate Warriors)
 * "What Goes Around" (1994) (collected in Mike Resnick's alternate history anthology Alternate Outlaws)
 * "Satan Claus" (1994) (also collected in Alternate Outlaws)
 * "The Fabulous Marble" (2017) (in Baker Street Irregulars edited by Michael A. Ventrella & Jonathan Maberry)
 * "Dangerous Virgins" (2018) (in Release the Virgins edited by Michael A. Ventrella)
 * "The Man Who Broke Time" (2022) (in Three Time Travelers Walk Into... edited by Michael A. Ventrella)
 * "The Four Course Men" (2023) (in The Four ???? of the Apocalypse edited by Keith R.A. DeCandido & Wrenn Simms)

Anthologies edited

 * Protostars (1971) (with Stephen Goldin)
 * Generation (1972)
 * Science Fiction Emphasis 1 (1974)
 * Alternities (1974)
 * Ascents of Wonder (1977)

Plays

 * Uncle Daddy Will Not Be Invited (2013)

Nonfiction
———————
 * The Trouble with Tribbles (1973)
 * The World of Star Trek (1973, rv. 1984)
 * Worlds of Wonder: How to Write Science Fiction & Fantasy (2001)
 * Taking the Red Pill: Science, Philosophy and Religion in The Matrix (2003) (with Glenn Yeffeth)
 * Boarding the Enterprise: Transporters, Tribbles, and the Vulcan Death Grip in Gene Roddenberry's Star Trek (2006) (with Robert J. Sawyer)
 * Notes

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

title: David Gerrold


text:
Borough of Swindon

The Borough of Swindon is a unitary authority area with borough status in Wiltshire, England. Centred on Swindon, it is the most north-easterly district of South West England.

History
The first borough of Swindon was a municipal borough, created in 1900 as a merger of the two urban districts of Old Swindon and New Swindon.

In 1974 the borough of Thamesdown was created under the Local Government Act 1972. Thamesdown covered the areas of the municipal borough of Swindon and the neighbouring Highworth Rural District (which had been created in 1894), which were both abolished at the same time. Thamesdown was a lower-tier non-metropolitan district, with Wiltshire County Council being the higher-tier authority for the area. Thamesdown was given borough status from its creation, allowing the chair of the council to take the title of mayor.

On 1 April 1997 Thamesdown was made a unitary authority, making it administratively independent from Wiltshire County Council. In June 1996, during the transition period to becoming a unitary authority, the council passed an order that the area would be renamed Swindon with effect from 1 April 1997 as well. The former Thamesdown name and logo continued to be used by the municipal bus operator, Thamesdown Transport, until 2017 when it was sold and renamed to "Swindon's Bus Company". Swindon remains part of the ceremonial county of Wiltshire for the purposes of lieutenancy.

Geography
The borough of Swindon occupies an area forming the north east corner of Wiltshire and is bordered by two other counties, Gloucestershire (to the north) and Oxfordshire (to the east). West Berkshire is also only a short distance from the borough's south eastern tip. The generally hilly landscape is sculpted by the upper Thames guiding the northern border, small tributaries draining into the Thames, and the Marlborough Downs rising toward the south.

The borough encompasses the Swindon urban area and surrounding countryside to the north, east and south, including the town of Highworth. It comprises the former Swindon Municipal Borough and a further 18 civil parishes:

 * Bishopstone (with Hinton Parva)
 * Blunsdon
 * Castle Eaton
 * Chiseldon
 * Covingham
 * Hannington
 * Haydon Wick
 * Highworth (town and surrounding district, including Sevenhampton)
 * Inglesham
 * Liddington
 * Nythe, Eldene and Liden
 * St Andrews
 * South Marston
 * Stanton Fitzwarren
 * Stratton St Margaret
 * Wanborough
 * West Swindon
 * Wroughton

Since 1 April 2017 the entire Borough has been parished, following the establishment of West Swindon parish and the creation of Central Swindon North and Central Swindon South (styled by its parish council as South Swindon). The two Central parishes fall within the boundaries of the town and former municipal borough, divided along the Great Western Main Line railway.

At the same time:

 * the part of Chiseldon parish north of the M4, including the former hamlet of Coate, was transferred to Central Swindon South;
 * the parish of Blunsdon St Andrew was divided into St Andrews and Blunsdon, the A419 forming the boundary between them;
 * the parish of Nythe was expanded to form Nythe, Eldene and Liden.

Swindon Borough Council
The council follows a leader and cabinet model and has 57 members elected by 20 wards. Elections are held in three out of every four years, with one-third of the seats being elected at each election. From the first election in 1996 to the 2000 election, Labour had a majority on the council. Following a period where no party had a majority, the Conservatives gained a majority at the 2003 election and had control until the 2023 election, when Labour took control.

Other elections
The borough is divided into two Parliamentary constituencies: North Swindon and South Swindon. Both are seen as key marginal seats at general elections, having been bellwether seats since 1997 when they were created. Currently both seats are held by the Conservative Party.

The borough was one of the first areas to declare in the 2016 European Union membership referendum. 61,745 (54.3%) voters supported leaving the European Union, whilst 51,220 (45.7%) wished to remain.

title: Borough of Swindon


text:
Polish Brethren

The Polish Brethren (Polish: Bracia Polscy) were members of the Minor Reformed Church of Poland, a Nontrinitarian Protestant church that existed in Poland from 1565 to 1658. By those on the outside, they were called "Arians" or "Socinians" (arianie, socynianie), but themselves preferred simply to be called "Brethren" or "Christians", and, after their expulsion from Poland, "Unitarians".

History
The Ecclesia Minor or Minor Reformed Church of Poland, better known today as the Polish Brethren, was started on January 22, 1556, when Piotr of Goniądz (Peter Gonesius), a Polish student, spoke out against the doctrine of the Trinity during the general synod of the Reformed (Calvinist) churches of Poland held in the village of Secemin.

1565: Split with the Calvinists

A theological debate called by the Polish king Sigismund II Augustus himself in 1565 did not succeed in bringing both Protestant factions together again. Finally, the faction that had supported Piotr of Goniądz's arguments broke all ties with the Calvinists and organised its own synod in the town of Brzeziny on June 10, 1565.

In the 1570s a split was developing between the pacifist and Arian group, led by Marcin Czechowic and Grzegorz Paweł z Brzezin, and the non-pacifist and Ebionite group, led by the Belarusian Symon Budny. In 1579, the Italian exile Fausto Sozzini arrived in Poland and applied for admission to the Ecclesia Minor, which was refused because of his rather unusual personal objection to water baptism, but they saw in the Italian an able advocate and Sozzini's capable answering of Budny, followed by his marriage to the daughter of Krzysztof Morsztyn Sr. in 1586 cemented his place among the Polish Brethren. The calling of the group "Socinian" in England is more a result of the place given to Sozzini's writings in the publishing of his grandson Andrzej Wiszowaty Sr. in Amsterdam a century later than any role of active leadership in Sozzini's life, especially given that without submitting to baptism, he could never formally join the church that later bore his name abroad.

1602–1638: Racovian Academy
Their biggest cultural centres were Pińczów and Raków, site of the main Arian printing press and the university Racovian Academy (Gymnasium Bonarum Artium) founded in 1602 and closed in 1638, which trained over 1000 students.

1658: Expulsion
The Brethren never participated in the Sandomierz Agreement of 1570 between different Polish Protestants. The Minor Church in Poland was dissolved on July 20, 1658, when the Sejm expelled the Socinians from Poland after a series of 17th-century wars known as the Deluge in which Protestant Sweden invaded Poland since the Brethren (like almost all other non-Catholic Christians) were commonly seen as Swedish collaborators.

The Brethren were exiled in three directions and found asylum in the following regions:
 * Duchy of Prussia, where Christopher Crell and his sons founded new congregations.
 * Netherlands, where Andrzej Wiszowaty Sr. published the Bibliotheca Fratrum Polonorum quos Unitarios vocant (1668) and Christopher Sand published the Bibliotheca antitrinitariorum (1684).
 * Transylvania, where the Unitarian Church of Transylvania enjoyed freedom. This was the destination of Andrzej Wiszowaty Jr. who became a teacher at the Unitarian College in Kolozsvár (today Cluj, Romania).

Theology
Originally, the Minor Church followed a non-trinitarian doctrine, inspired by the writings of Michael Servetus. Later on, Socinianism, named for the Italian theologian Fausto Sozzini, became its main theological approach. They were against capital punishment and did not believe in the traditional Christian doctrines of Hell or the Trinity.

Church and state
They advocated the separation of church and state and taught the equality and brotherhood of all people. They opposed social privileges based on religious affiliation, and their adherents refused military service (they were known for carrying wooden swords, instead of the real almost obligatory szablas), and they declined to serve in political office.

Influence
Although never numerous, they had a significant impact on political thought in Poland. After being expelled from Poland, they emigrated to England, East Prussia and the Netherlands, where their works were widely published and influenced much of the thinking of later philosophers such as John Locke and Pierre Bayle.

Their main ideologues were Piotr z Goniadza ("Gonesius"), Grzegorz Paweł z Brzezin, Marcin Czechowic, although Johannes Crellius (from Germany), and Johann Ludwig von Wolzogen (who came to Poland from Austria) were far better known outside Poland. Among the best known adherents of this fellowship are Mikołaj Sienicki, Jan Niemojewski, and writers and poets Zbigniew Morsztyn, Olbrycht Karmanowski and Wacław Potocki.

This expulsion is sometimes taken as the beginning of decline of famous Polish religious freedom, although the decline started earlier and ended later: the last non-Catholic deputy was removed from parliament in the beginning of the 18th century. Most of Polish Brethren moved to the Netherlands, where they greatly influenced European opinion, becoming precursors to Enlightenment.

Influence in Britain
John Locke was preceded by a few decades by Samuel Przypkowski on tolerance and by Andrzej Wiszowaty on 'rational religion'. Isaac Newton had met Samuel Crell, son of Johannes Crellius, of the Spinowski family. Newton was well informed about the developments in Poland and collected many books from the Racovian Academy.

The Englishman John Biddle had translated two works by Przypkowski, as well as the Racovian Catechism and a work by Joachim Stegmann, a "Polish Brother" from Germany. Biddle's followers had very close relations with the Polish Socinian family of Crellius (aka Spinowski).

Influence in the United States
Subsequently, the Unitarian strain of Christianity was continued by, most notably, Joseph Priestley, who had emigrated to the United States and was a friend of both James Madison and Thomas Jefferson, the latter of whom sometimes attended services at Priestley's congregation in Philadelphia. Notably, Priestley was very well informed on the earlier developments in Poland, especially by his mentions of Socinus and Szymon Budny (translator of Bible, author of many pamphlets against the Trinity).

In the modern era
During the Second Polish Republic, the priest Karol Grycz-Śmiałowski recreated what he considered was a revival of the Church of Polish Brethren in Kraków in 1937. During the People's Republic of Poland, it was registered in 1967 as the Unity of Polish Brethren (Jednota Braci Polskich).

Modern groups that look to the Polish Brethren include the Christadelphians and Church of God General Conference. Although Christadelphians had since their origins in the 1840s always looked for historical precedents, the group was unaware of closer precedents in Socinianism. That changed with a series of articles in the community magazine during the early 1970 that was subsequently published. The Polish arm of the Christadelphians use the name Bracia w Chrystusie in a conscious echo of Socinian precedents. The Atlanta Bible College of the Church of God General Conference also publishes a Journal continuing research into the Polish Brethren and related groups.

title: Polish Brethren


text:
Albert Smith

Albert Smith may refer to:

Entertainment

 * Albert Richard Smith (1816–1860), English author and entertainer
 * Albert E. Smith (producer) (1875–1958), English stage magician, film director, and producer
 * Albert J. Smith (actor) (1894–1939), American actor

Politics

 * Albert Smith (Maine politician) (1793–1867), member of U.S. House of Representatives from Maine
 * Albert Smith (New York politician) (1805–1870), member of U.S. House of Representatives from New York
 * Albert E. Smith (Wisconsin politician) (1839–?), Wisconsin state assemblyman
 * Albert L. Smith Jr. (1931–1997), member of U.S. House of Representatives from Alabama
 * Albert James Smith (1822–1883), premier of New Brunswick, Canada 1865–1866
 * Albert Edward Smith (1871–1947), Canadian religious leader and politician
 * Albert Smith (British politician) (1867–1942), British MP and trade unionist
 * Albert Smith (South Australian politician) (1881–1965), member of the Australian House of Representatives
 * Albert Smith (New South Wales politician) (1885–1975), member of the New South Wales Legislative Assembly

Sports

 * Albert Smith (cricketer) (1863–?), English cricketer
 * Albert Smith (footballer, born 1869) (1869–1921), England international
 * Albert Smith (footballer, born 1887) (1887–1929), English football winger
 * Albert Smith (footballer, born 1900) (1900–?), English footballer
 * Albert Smith (footballer, born 1905) (1905–?), Scottish footballer
 * A. J. Smith (Albert J. Smith), American football player, coach, scout, and executive

Other

 * Albert Charles Smith (1906–1999), American botanist
 * Albert Daniel Smith (1887–1970), American pioneer aviator
 * Albert Eugene Smith (1907–1973), American computing pioneer
 * Albert Hugh Smith (1903–1967), English scholar of Old English and Scandinavian languages
 * Albert Joseph Smith (1898–1973), U.S. Marine Corps Medal of Honor recipient
 * Albert C. Smith (United States Army officer) (1894–1974), United States Army general
 * Albert Alexander Smith (1896–1940), African-American artist
 * Albert Smith, a fictional character from Power Rangers Dino Charge

title: Albert Smith


text:
Cataluña (Albéniz)

 * Cataluña is the Spanish name for Catalonia

Cataluña, Op. 47, No. 2, is a composition by Isaac Albéniz. It premiered as a piano performance in Paris in January 1899. Since it has been transcribed for classical guitar by Miguel Llobet, it has become one of the staples of classical guitar music. It has been performed and recorded by guitarists such as Julian Bream, John Williams, Milos Janjic, Charles Mokotoff and many others. It is usually played in the key of G minor.

title: Cataluña (Albéniz)


text:
Aleksandr Prokhorov

Aleksandr Prokhorov (Алекса́ндр Про́хоров) is a male personal name of Russian origin may refer to:
 * Alexander Prokhorov (1916–2002), Soviet physicist
 * Aleksandr Prokhorov (footballer) (1946–2005), Soviet international footballer
 * Aleksandr Prokhorov (politician) (born 1953), Russian politician, governor of Smolensk Oblast
 * Aleksandr Prokhorov (racewalker) (born 1986), Russian racewalking athlete and runner-up at the 2003 European Race Walking Cup

title: Aleksandr Prokhorov


text:
Talk:Medicine Hat

General information
Much of the information in this article has no business to be here, it should be an article about Medicine Hat, not about Alberta. The general information about Alberta should be removed or moved to Alberta (if something is missing there). -- —Preceding unsigned comment added by Nyh (talk • contribs) 03:32, 6 November 2003

 * Can you be more specific? I see very little on here that does not relate to Medicine Hat. --Kmsiever 21:08, 24 July 2006 (UTC)

Some Medicine Hat pics?
I added a pic to the Lethbridge page..anyone have some medicine hat pictures?-- —Preceding unsigned comment added by Dre08 (talk • contribs) 21:07, 21 April 2005

Re Picture of head - inserted as it so clearly related to the medicine man and lost headress in the legend around the town's name. Picture and details were removed by somebody today as "loosely related trivia". I have restored it making clear the association. If it be removed again I shall not restore it but for the record the head is 25 miles east of the town clearly visible in Google Earth, 1000 ft wide. An image of an Indian with a headress facing the town which is likely to have inspired the legend. The photo is in Wikimedia under the name medecine_hat.jpg. I hope encyclopedia readers will not be deprived again of this information, though I would welcome improvements to the layout - perhaps the image could be made smaller, and the entry moved to the Attractions section :-) — Preceding unsigned comment added by 172.209.6.73 (talk) 18:26, 29 October 2006 (UTC)

prisoner of war camp
I found the section about executions of POW camp inmates to be a non-sequitur from the rest of the section. I've edited it for style, and integrated the fact that there was a large camp into the History section. If we want to document all of the pow executions, I think that is valuable, and deserves it's own entry, or at the very least, it's own subsection. The detailed previous accounting does not belong in the main "History" section.

Wuapinmon 17:39, 27 July 2007 (UTC)

I love it!
I have been to Med Hat many times with the British Army. I must say the local girls are very...welcoming. —Preceding unsigned comment added by 81.152.170.116 (talk) 21:54, 19 December 2007 (UTC)

Requested Move
This article has been renamed from Medicine Hat, Alberta to Medicine Hat as the result of a move request. - unopposed move. Keith D (talk) 10:58, 9 January 2008 (UTC)

Medicine Hat, Alberta → Medicine Hat The city in Alberta is, apparently, the only place called Medicine Hat in the world. A google search indicates that this city is the overwhelmingly primary use of the term "Medicine Hat". Medicine Hat already redirects to this article. The proposed move is consistent with the naming convention for Canadian cities, and is in keeping with other articles for smaller Canadian places that no longer have disambiguated titles (e.g. Gatineau, Lethbridge, Flin Flon, Penticton, Charlottetown, etc.). Skeezix1000 (talk) 19:37, 4 January 2008 (UTC)

 * Support - agree with nom. The city is the most common use of the term by far. EJF (talk) 15:34, 5 January 2008 (UTC)
 * Support if there is no other entity called "Medicine Hat" or if the city is the primary usage of the term. --Polaron | Talk 15:51, 6 January 2008 (UTC)
 * Support per nom. Mind you, Gatineau is far bigger than Medicine Hat by population, and Lethbridge is quite a bit bigger too. Snocrates 07:33, 9 January 2008 (UTC)

Notable residents
I suggest we remove this section. A exhaustive list of people with articles doesn't belong here. Category:People from Medicine Hat gives the reader the same info, in a more complete manner. Having this section, seems to invite promotional descriptions, such as "prolific artist and exhibitor" or " internationally famed puppeteer". --Rob (talk) 06:09, 12 July 2009 (UTC)

 * I agree that there is perhaps some content in this section that is not entirely appropriate. I don't agree that we should remove the section entirely but at least it should be cleaned up to reflect actual "residents" of the city. Some of those on this list are not residents and thus should certainly be moved to Category:People from Medicine Hat. 174.0.218.154 (talk) 00:53, 9 June 2011 (UTC)

 * I've renamed the section to "Notable people" so that it can be inclusive of both existing and former residents. I'm going to trim some of the promotional descriptions. Hwy43 (talk) 04:29, 9 June 2011 (UTC)

Population
I reverted an edit that changed the population in the article but not the info box only to realize that the figures still don't match. Will try to reconcile figures later but feel free to fix it. --Daffydavid (talk) 08:43, 6 August 2012 (UTC)
 * Per WP:CANSTYLE, "the population figure from the last official Statistics Canada census is the primary and definitive source for population data in articles." This is why the infobox remains unchanged. The Demographics presents both the results of the 2011 StatCan census and the 2012 municipal census in greater detail. Meanwhile, WikiProject Canadian communities/Structure guideline states that the lead section can indicate total population. The former 2009 municipal census result was previously presented here, hence the update with the 2012 figure now that it is available. Per CANSTYLE, there should be no change to the population in the infobox. It should reflect the primary and definitive source. If anything, change the population in the lead section to the 2011 StatCan census population, not the now dated 2009 municipal census. Hwy43 (talk) 16:21, 6 August 2012 (UTC)

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 * https://cypress.civicweb.net/Documents/DocumentDisplay.aspx?Id=367
 * http://www12.statcan.ca/english/census06/data/profiles/community/Details/Page.cfm?Lang=E&Geo1=CSD&Code1=4801006&Geo2=PR&Code2=48&Data=Count&SearchText=Medicine%20Hat&SearchType=Begins&SearchPR=01&B1=All&GeoLevel=&GeoCode=4801006
 * http://www12.statcan.ca/english/census06/data/topics/RetrieveProductTable.cfm?ALEVEL=3&APATH=3&CATNO=&DETAIL=0&DIM=&DS=99&FL=0&FREE=0&GAL=0&GC=99&GK=NA&GRP=1&IPS=&METH=0&ORDER=1&PID=89201&PTYPE=88971&RL=0&S=1&ShowAll=No&StartRow=1&SUB=701&Temporal=2006&Theme=70&VID=0&VNAMEE=&VNAMEF=&GID=838046
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 * http://www.medicinehat.ca/City%20Government/Organizational%20Chart.pdf
 * http://www.gg.ca/honour.aspx?id=8962&t=12
 * http://gonebutnotforgotten.ca/index.php?option=com_content&task=view&id=3975&Itemid=81

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All hell for a basement
all hell for a basement is also a song--Skyandotterwritestuff (talk) 07:55, 11 November 2020 (UTC)

What are people from Medicine Hat called
We are called “Hatters” 2604:3D09:227A:A200:A586:6D31:E90D:DB08 (talk) 20:46, 4 May 2024 (UTC)

title: Talk:Medicine Hat


text:
Timeline of Portuguese history

This is a timeline of Portuguese history, comprising important legal and territorial changes and political events in Portugal and its predecessor states. To read about the background to these events, see History of Portugal.

Centuries: 3rd BC·2nd BC·1st BC·3rd·5th·6th·8th·9th·10th·11th·12th·13th·14th·15th·16th·17th· 18th·19th·20th·21st

title: Timeline of Portuguese history


text:
When HARLIE Was One

When HARLIE Was One is a 1972 science fiction novel by American writer David Gerrold. It was nominated for the Nebula Award for Best Novel in 1972 and the Hugo Award for Best Novel in 1973. The novel, a "fix-up" of previously published short stories, was published as an original paperback by Ballantine Books in 1972, with an accompanying Science Fiction Book Club release. A revised version, subtitled "Release 2.0", was published in 1988 by Bantam Books.

Plot introduction
Central to the story is an artificial intelligence named H.A.R.L.I.E., also referred to by the proper name "HARLIE"—an acronym for Human Analog Replication, Lethetic Intelligence Engine (originally Human Analog Robot Life Input Equivalents).

HARLIE's story revolves around his relationship with David Auberson, the psychologist who is responsible for guiding HARLIE from childhood into adulthood. It is also the story of HARLIE's fight against being turned off, and the philosophical question of whether or not HARLIE is human; for that matter, what it means to be human.

When HARLIE Was One contains one of the first fictional representations of a computer virus (preceded by Gregory Benford in 1970), and one of the first uses of the term "virus" to describe a program that infects another computer.

Reception
Theodore Sturgeon reported that the novel "carries a good freight of social and psychological insight".

In other works
The HARLIE intelligence engine appears in a number of Gerrold's other works:
 * In the Star Wolf series, HARLIE is routinely installed as the administrating AI of Terran warships.
 * The Dingilliad series, Jumping Off the Planet, Bouncing Off the Moon, and Leaping to the Stars.
 * A Nest for Nightmares, the fifth book of The War Against the Chtorr.
 * HARLIE is a major character in Hella .

title: When HARLIE Was One


text:
John Bartram

John Bartram (March 23, 1699 – September 22, 1777) was an American botanist, horticulturist, and explorer, based in Philadelphia, Pennsylvania, for most of his career. Swedish botanist and taxonomist Carl Linnaeus said he was the "greatest natural botanist in the world." Bartram corresponded with and shared North American plants and seeds with a variety of scientists in England and Europe.

He started what is known as Bartram's Garden in 1728 at his farm in Kingsessing (now part of Philadelphia). It was considered the first botanic garden in the United States. His sons and descendants operated it until 1850. Still operating in a partnership between the city of Philadelphia and a non-profit foundation, it was designated a National Historic Landmark in 1960.

Early life
Bartram was born into a Quaker farm family in colonial Marple, Pennsylvania near Philadelphia, on March 23, 1699. He considered himself a plain farmer, with no formal education beyond the local school. He had a lifelong interest in medicine and medicinal plants, and read widely. He started his botanical career by devoting a small area of his farm to growing plants he found interesting. Later, he made contact with European botanists and gardeners interested in North American plants, and developed his hobby into a thriving business.

Plant collecting activities, Correspondence with London, and 1737/1738 Travels through the Mid-Atlantic Colonies
Bartram began to travel extensively in the eastern American colonies in order to study and collect plants.

Bartram maintained a frienship with Peter Collinson, Alexander Catcot, and others through letter writing between London and the colonies, and he regularly collected specimens for Collinson and others in Europe who were interested in obtaining unfamiliar species from the New World for their gardens and scientific study.

In 1737 Bartram travelled by horseback through modern day Delaware and the Eastern Shore of Maryland to Northampton County, Virginia. In the fall of 1738, he made another excurion from his home in Philadelphia through Virginia, visiting the Gover family in Anne Arundel County, to Port Tobacco on the Potomac Cedar Point, Maryland opposite Hooe's Ferry in King George County, Virginia, and then went to Fredericksburg. He proceeded to visit John Clayton in Gloucester County, Virginia, crossed the York River to visit John Custis in Williamsburg, Virginia, and then journeyed up the James River to visit William Byrd II's plantation at Westover. He continued westware to visit Isham Randolph's Dungeness estate, and then continued west to the Blue Ridge Mountains and the Shenandoah Valley.

In 1743, he visited western parts of New York and the northern shores of Lake Ontario, and wrote Observations on the Inhabitants, Climate, Soil, Rivers, Productions, Animals, and other Matters Worthy of Notice, made by Mr. John Bartram in his Travels from Pennsylvania to Onondaga, Oswego, and the Lake Ontario, in Canada (London, 1751). During the winter of 1765/66, he visited East Florida in the south, which was a British colony, and published an account of this trip with his journal (London, 1766). He also visited areas along the Ohio River west of the Appalachian Mountains. Many of his plant acquisitions were shipped to collectors in Europe. In return, they supplied him with books and apparatus.

Bartram, sometimes called the "father of American botany", was one of the first practicing Linnaean botanists in North America. He forwarded plant specimens to Carl Linnaeus, Dillenius, and Gronovius. He also assisted Linnaeus's student Pehr Kalm during his extended collecting trip to North America in 1748–1750.

Bartram was aided in his collecting efforts by other British colonists. In Bartram's Diary of a Journey through the Carolinas, Georgia and Florida, a trip taken from July 1, 1765, to April 10, 1766, Bartram wrote of specimens he had collected. In the colony of British East Florida, he was helped by Dr. David Yeats, secretary of the colony.

About 1728, he established an 8 acre botanic garden in Kingsessing, on the west bank of the Schuylkill, about 3 miles (5 km) from the center of Philadelphia, Pennsylvania. Known as Bartram's Garden, it is frequently cited as the first true botanic collection in North America. It was designated in 1960 as a National Historic Landmark.

In 1743, Bartram was one of the co-founders, along with Benjamin Franklin, of the American Philosophical Society in Philadelphia. It supported scientific studies as well as philosophy.

Contact with other botanists
Bartram was particularly instrumental in sending seeds from the New World to European gardeners; many North American trees and flowers were first introduced into cultivation in Europe by this route. Beginning around 1733, Bartram's work was assisted by his association with the English merchant Peter Collinson. Collinson, also a lover of plants, was a fellow Quaker and a member of the Royal Society, with a familiar relationship with its president, Sir Hans Sloane. Collinson shared Bartram's new plants with friends and fellow gardeners. Early Bartram collections went to Lord Petre, Philip Miller at the Chelsea Physic Garden, Mark Catesby, the Duke of Richmond, and the Duke of Norfolk. In the 1730s, Robert James Petre, 8th Baron Petre of Thorndon Hall, Essex, was the foremost collector in Europe of North American trees and shrubs. Earl Petre's death in 1743 resulted in his American tree collection being auctioned off to Woburn, Goodwood, and other large English country estates. Thereafter, Collinson became Bartram's chief London agent.

"Bartram's Boxes", as they became known, were shipped regularly to Peter Collinson every fall for distribution in England to a wide list of clients, including the Duke of Argyll, James Gordon, James Lee, and John Busch, progenitor of the exotic Loddiges nursery in London. The boxes generally contained 100 or more varieties of seeds, and sometimes included dried plant specimens and natural history curiosities, as well. Live plants were more difficult and expensive to send and were reserved for Collinson and a few special correspondents.

In 1765, after lobbying by Collinson and Benjamin Franklin in London, George III rewarded Bartram a pension of £50 per year as King's Botanist for North America, a post he held until his death. With this position, Bartram shipped his seeds and plants also to the royal collection at Kew Gardens. Bartram also contributed seeds to the Oxford and Edinburgh botanic gardens. In 1769 he was elected a foreign member of the Royal Swedish Academy of Sciences in Stockholm.

Bartram died on September 22, 1777. He was buried at the Darby Friends Cemetery in Darby, Pennsylvania.

Legacy and honors
Most of Bartram's many plant discoveries were named by botanists in Europe. He is best known today for the discovery and introduction of a wide range of North American flowering trees and shrubs, including kalmia, rhododendron, and magnolia species; for introducing the Dionaea muscipula or Venus flytrap to cultivation; and for discovering the Franklin tree, Franklinia alatamaha in southeastern Georgia in 1765, later named by his son William Bartram.

A genus of mosses, Bartramia, was named for him, as were such plants as the North American serviceberry, Amelanchier bartramiana, as well as the subtropical tree Commersonia bartramia (brown kurrajong). This grows in an area from the Bellinger River in coastal eastern Australia to Cape York, Vanuatu, and Malaysia.

John Bartram High School in Philadelphia is named after him.

Bartram's Garden has been designated as a National Historic Landmark.

Family
Bartram married twice, first in 1723 to Mary Maris (d. 1727), with whom he had two sons, Richard and Isaac. After her death, in 1729 he married Ann Mendenhall (1703–1789). They had five boys and four girls together.

His third son, William Bartram (1739–1823), became a noted botanist, natural history artist, and ornithologist in his own right. He wrote Travels Through North & South Carolina, Georgia, East & West Florida,... which was published in Philadelphia by James & Johnson in 1791.

The family business in North American plants was continued after the American Revolution by Bartram's sons John Bartram, Jr., and William Bartram. A total of three generations of the Bartram family continued to operate and expand the botanic garden. Bartram's Garden was known as the major botanic garden in Philadelphia until the last Bartram heirs sold out in 1850.

title: John Bartram


text:
William Bartram

William Bartram (April 20, 1739 – July 22, 1823) was an American naturalist, writer and explorer. Bartram was the author of an acclaimed book, now known by the shortened title Bartram's Travels, which chronicled his explorations of the Southern Colonies of British North America from 1773 to 1777. Bartram has been described as "the first naturalist who penetrated the dense tropical forests of Florida".

Bartram was one of the first ornithologists born in America. In 1756, at the age of 17, he collected the type specimens of 14 species of American birds, which were illustrated and described by the English naturalist George Edwards in Gleanings of Natural History vol. 2 (1760). These accounts formed the basis of the scientific descriptions of Linnaeus (1707–1778), Johann Friedrich Gmelin (1748–1804) and John Latham (1740–1837). Bartram also made significant contributions to botanical literature. Like his father, he was a member of the American Philosophical Society, elected in 1768.

Early life and family
The son of Ann (née Mendenhall) and the naturalist John Bartram, William and his twin sister Elizabeth were born in Kingsessing, Philadelphia, Pennsylvania. As a boy, he accompanied his father on many of his travels to the Catskill Mountains, the New Jersey Pine Barrens, New England, and Florida. From his mid-teens, Bartram was noted for the quality of his botanic and ornithological drawings. He also had an increasing role in the maintenance of his father's botanic garden, and added many rare species to it.

On "may ye 30th 1756", his father John wrote the following passage in a letter to the English naturalist Peter Collinson: "Billy is much obliged to thee for his drawing paper...he hath drawn many rare birds in order to send to thee & dryed ye birds to send to his friend edwards to whome he is much obliged for those two curious bookes...he spent his time this spring in shooting & drawing ye rare birds of quick passage..."

Travels in Georgia
William Bartram arrived in Charleston on March 31, 1773. He learned that a Native American congress was to take place in Augusta, Georgia in June and was invited by Superintendent of Indian affairs, John Stuart, to join the party that would survey a new land cession. After attending to some business Bartram traveled on to Savannah, arriving in that city on either April 11 or 12. While he awaited the beginning of the Native American congress he traveled to the coast of Georgia. He first visited some rice plantations in Midway then traveled on to Darien where he was the guest of Lachlan McIntosh.

In Travels, Bartram related an incident at this point that most probably took place in 1776. As he traveled through the sparsely populated country of South Georgia, he encountered an "intrepid Siminole" who had resolved upon killing the next white man he met but was disarmed by Bartram's unexpected friendliness.

During his trip along the coast, Bartram revisited the region of Fort Barrington on the Altamaha River. John and William Bartram had discovered two new trees there in 1765, but they had no flowers for the season was late. William described these trees in Travels, the Franklin tree (Franklinia alatamaha) and fevertree (Pinkneya pubens). The Franklin tree no longer exists in the wild and all living trees are descended from seeds collected by William Bartram.

Bartram then traveled to Augusta and explored the area while he awaited the conclusion of the Native American congress. The conference ended on June 3, 1773 with the Treaty of Augusta. In return for dissolving their debts to the traders in Augusta, the Creeks and Cherokees gave up 674,000 acres of land in northeast Georgia. Bartram joined the survey party as it marked the boundary. An incident occurred at a place known as the Great Buffalo Lick when the Native Americans questioned the accuracy of the surveyor's course. When the surveyor said it was right because the compass told him so the chief, Young Warrior, said that,

"... the little wicked instrument was a liar; and he would not acquiesce in its decisions, since it would wrong the Indians out of their land. This mistake (the surveyor proving to be in the wrong) displeased the Indians; the dispute arose to that height, that the Chief and his party had determined to break up the business, and return the shortest way home, and forbad the surveyors to proceed any farther: however, after some delay, the complaisance and prudent conduct of the Colonel made them change their resolution; the Chief became reconciled, upon condition that the compass should be discarded, and rendered incapable of serving on this business; that the Chief himself should lead the survey; and, moreover, receive an order for a very considerable quantity of goods."

Bartram returned to Savannah in mid-July and spent the fall and winter on the coast of Georgia, exploring the Altamaha River, writing his report, and preparing his seeds for shipment to England.

Travels in Florida
In March 1774, Bartram began his much-anticipated trip to East Florida. He landed on the north end of Amelia Island and traveled through Old Fernandina to Lord Egmont's plantation where modern Fernandina now stands. Bartram was entertained by Stephen Egan, Egmont's agent, who rode with him around the entire island observing the plantation and Indian mounds. Bartram and Egan sailed from Amelia Island through the Intracoastal Waterway to the St. Johns River and to the Cow Ford (Jacksonville) where Bartram purchased a little sailboat. In three days Bartram landed at the plantation of Francis Philip Fatio at Switzerland. There he received information concerning the recent disturbances at Spalding's Stores. He paused the next day at Fort Picolata where he had failed as a planter seven years earlier. Bartram then kept to the west bank, or Indian shore, the river being the division between Indian country on the west bank and English land on the east. He observed a Seminole village on the bluff where Palatka now stands and where he was invited to a watermelon feast that summer. Just south of Palatka, at Stokes Landing, James Spalding built his Lower Store where Bartram made his headquarters while in Florida. One day while working at his desk Bartram heard a disturbance in the adjacent Indian camp. Stepping outside he discovered his Seminole neighbors were alarmed by a large rattlesnake that had entered their camp. They entreated "Puc Puggy" to come kill the snake, which Bartram reluctantly agreed to do. Later he saw three young men approaching. He wrote:

"I observed one of them was a young prince who had, on my first interview with him, declared himself my friend and protector, when he told me that if ever occasion should offer in his presence, he would risk his life to defend mine or my property. This young champion stood by his two associates, one on each side of him, the two affecting a countenance and air of displeasure and importance, instantly presenting their scratching instruments, and flourishing them, spoke boldly, and said that I was too heroic and violent, that it would be good for me to loose some of my blood to make me more mild and tame, and for that purpose they were come to scratch me; they gave me no time to expostulate or reply, but attempted to lay hold on me, which I resisted, and my friend, the young prince, interposed and pushed them off, saying that I was a brave warrior and his friend, that they should not insult me, when instantly they altered their countenance and behaviour; they all whooped in chorus, took me friendly by the hand, clapped me on the shoulder and laid their hands on their breasts in token of sincere friendship, and laughing aloud, said I was a sincere friend to the Siminoles,..."

Bartram joined Spalding's traders in mid-April on a trip to Cuscowilla (Micanopy) and Alachua Savannah, now Paynes Prairie Preserve State Park. In late May, Bartram traveled up the St. Johns River to Spalding's Upper Store at present-day Astor and to Blue Spring. Some of the most memorable events in Travels occurred during this trip upriver when a wolf stole his fish as Bartram slept, he was jostled and threatened by alligators while fishing from his boat, and he was witness to a territorial battle between two of the monsters. He wrote:

"Behold him rushing forth from the flags and reeds. His enormous body swells. His plaited tail brandished high floats upon the lake. The waters like a cataract descend from his opening jaws. Clouds of smoke issue from his dilated nostrils. The earth trembles with his thunder. When immediately from the opposite coast of the lagoon, emerges from the deep his rival champion. They suddenly dart upon each other. The boiling surface of the lake marks their rapid course, and a terrific conflict commences. They now sink to the bottom folded together in horrid wreaths. The water becomes thick and discolored. Again they rise, their jaws clap together, re-echoing through the deep surrounding forests. Again they sink, when the contest ends at the muddy bottom of the lake, and the vanquished makes a hazardous escape, hiding himself in the muddy turbulent waters and sedge on a distant shore. The proud victor exulting returns to the place of action. The shores and forests resound his dreadful roar, together with the triumphing shouts of the plaited tribes around, witnesses of the horrid combat."

During the summer Bartram made another excursion to Alachua Savannah and on to the Suwannee River. He traveled one last time up the St. Johns River in September and left Florida forever in November 1774.

Exploration of the Cherokee Nation
On April 22, 1775 Bartram left Charleston, South Carolina on horseback to explore the Cherokee Nation. After passing through Augusta May 10, Dartmouth on May 15 (35.328°N, -82.87457°W), a few days later he left Fort Prince George and Keowee (34.86362°N, -82.90157°W) after not being able to procure a guide.

In addition to his botanizing, Bartram aptly described the journey:

"...all alone in a wild Indian country, a thousand miles from my native land, and a vast distance from any settlements of white people."

"It was now after noon; I approached a charming vale, amidst sublimely high forests, awful shades! Darkness gathers around, far distant thunder rolls over the trembling hills; the black clouds with august majesty and power, moves slowly forwards, shading regions of towering hills, and threatening all the destructions of a thunderstorm; all around is now still as death, not a whisper is heard, but a total inactivity and silence seems to pervade the earth; the birds afraid to utter a chirrup, and in low tremulous voices take leave of each other, seeking covert and safety; every insect is silenced, and nothing heard but the roaring of the approaching hurricane; the mighty cloud now expands its sable wings, extending from North to South, and is driven irresistibly on by the tumultuous winds, spreading his livid wings around the gloomy concave, armed with terrors of thunder and fiery shafts of lightning; now the lofty forests bend low beneath its fury, their limbs and wavy boughs are tossed about and catch hold of each other; the mountains tremble and seem to reel about, and the ancient hills to be shaken to their foundations: the furious storm sweeps along, smoaking through the vale and over the resounding hills; the face of the earth is obscured by the deluge descending from the firmament, and I am deafened by the din of thunder; the tempestuous scene damps my spirits, and my horse sinks under me at the tremendous peals, as I hasten for the plain."

"I began to ascend the Jore Mountains, which I at length accomplished, and rested on the most elevated peak; from whence I beheld with rapture and astonishment, a sublimely awful scene of power and magnificence, a world of mountains piled upon mountains. Having contemplated this amazing prospect of grandeur, I descended the pinnacles... (probably Wayah Bald 35.18037°N, -83.56044°W)"

Return to Philadelphia
Bartram returned to Philadelphia in January 1777 and assisted his brother John in all aspects of running Bartram's Garden. In the late 1780s, he completed the book for which he became most famous, Travels through North and South Carolina, Georgia, East and West Florida, the Cherokee Country, etc. It was considered at the time one of the foremost books on American natural history. Many of Bartram's accounts of historical sites were the earliest records, including the Georgia mound site of Ocmulgee. In addition to its contributions to scientific knowledge, Travels is noted for its original descriptions of the American countryside. Bartram's writing influenced many of the Romantic writers of the day. William Wordsworth, Samuel Taylor Coleridge, and François-René de Chateaubriand are known to have read the book, and its influence can be seen in many of their works.

Although Bartram has often been characterized as a recluse, all evidence shows that he remained active in commercial, scientific, and intellectual pursuits well into the nineteenth century. He tutored nieces and nephews, penned a number of essays, contributed to several works anonymously, and helped run the family horticultural business. In 1802, Bartram met the school teacher Alexander Wilson and began to teach him the rudiments of ornithology and natural history illustration. Wilson's American Ornithology includes many references to Bartram and the area around Bartram's Garden. Among Bartram's more significant later contributions were the illustrations for his friend Benjamin Smith Barton's explanation of the Linnaean system, Elements of Botany (1803–04).

After the War of 1812, when many of his colleagues, contacts, and friends had died, Bartram settled into a long period of work, observation, and study at the family's garden in Kingsessing. He maintained a "Diary" that records bird migrations, plant life, and the weather. He refused a request to teach botany at the University of Pennsylvania, and in his sixties, declined an invitation from President Thomas Jefferson to accompany an expedition up the Red River in the Louisiana Territory, in 1806.

Death
Bartram died at his home in 1823, at the age of 84. According to a short biography penned by Robert Carr, "He wrote an article on the natural history of a plant a few minutes before his death." Details of the event were described in a letter by Thomas L. McKenney to Dolley Madison, dated July 28, 1835:"'My Dear Madam, / You once did me the favor to send me some lines on the traveller & Botanist Bartram. I send with this a likeness of that excellent man ... On a visit receently [sic] to Bartram's garden Mr. Car pointed out the spot where the old man died. You will doubtless remember it. It is under a pear tree that grewe at the south corner of the house. You have doubtless seen it. The old man, then in his 86th year, rose from the Table, taking with him a bit of bread & cheese, saying - 'I will do as the boys do.' In going out, he reached the pear tree - where he was shortly after discovered throwing up blood from his lungs. A crumb, it supposed, choaking him, he ruptured, in his efforts to dislodge it, a blood vessel. He walked [to] another pear tree near the west corner of the house, & returning, aided by the family, he reached the first, under which he was discovered, were he died.'"

Namesakes
Numerous places and sites are named in his honor:
 * The Bartram Trail, a hiking trail in North Carolina, Georgia, and South Carolina that commemorates his journeys through the area.
 * The Bartram Canoe Trail system of canoe and kayak trails in the Mobile-Tensaw River Delta.
 * William Bartram Scenic & Historic Highway, part of Florida State Road 13 that runs along the east side of the St. Johns River from Jacksonville, Florida south into northwestern St. Johns County.
 * Bartram Trail High School (St. Johns County School District) in St. Johns, Florida.
 * Bartram Trail Elementary School and Bartram Springs Elementary School (Duval County Public Schools) in Jacksonville, Florida.
 * The William Bartram Arboretum, located within Fort Toulouse Park, near Wetumpka, Alabama.
 * Bartram Hall on the University of Florida campus in Gainesville, Florida.
 * Bartram Trail Regional Library System in east Georgia
 * Bartram's bass, or redeye bass (Micropterus coosae), a fish species found only in the Savannah River drainage in Georgia.
 * The Upland Sandpiper (Bartramia longicauda) takes its genus name from William Bartram.

Bartram died on July 22, 1823, at Bartram's Garden.

In popular culture

 * In the film Cold Mountain (2003), Ada gives Inman a copy of Bartram's book and her photograph on the day he leaves to fight in the Civil War, and he treasures both even as they become tattered.
 * In Lauren Groff's short story, "Flower Hunters", from her collection, Florida, the unnamed female protagonist has immersed herself in the chronicles of William Bartram: "Like Bartram, she was once a Northerner, dazzled by the frenzied flora and fauna here." The narrator concludes, "She's most definitely in love with that dead Quaker." The story is set in present-day Florida with flashbacks to Bartram and his travels and observations, which form a backdrop to the plot.

Literature

 * Bartram Trail Conference, Bartram Heritage: A Study of the Life of William Bartram. Montgomery, Alabama, 1979
 * Bell, Whitfield J., Jr., Patriot-Improvers: Biographical Sketches of Members of the American Philosophical Society, vol. 1, 1743–1768. American Philosophical Society, Philadelphia, 1997, "WIlliam Bartram (1739–1823), pp. 414–24.
 * Borland, Hal. The Memorable Bartrams. American Heritage Magazine. April, 1975. Volume 26, Issue 3. Accessed March 2, 2007.
 * Cashin, Edward J. William Bartram in Georgia. New Georgia Encyclopedia. Accessed March 2, 2007.
 * Dallmeyer, Dorinda. 2020. Bartram's Living Legacy: The Travels and the Nature of the South. Macon, GA: Mercer University Press.
 * Ewan, Joseph,ed., William Bartram Botanical and Zoological Drawings, 1756-1788. American Philosophical Society, Philadelphia, 1968.
 * Fagin, N. Bryllion, William Bartram: Interpreter of the American Landscape. The Johns Hopkins Press, Baltimore, 1933.
 * Fishman, Gail. (2001) Journeys Through Paradise, University Press of Florida. ISBN 0-8130-1874-9
 * Hallock, Thomas. From the Fallen Tree: Frontier Narratives, Environmental Politics, and the Roots of a National Pastoral. University of North Carolina Press, 2003.
 * Hallock, Thomas and Nancy E. Hoffmann, eds. William Bartram, The Search for Nature's Design: Selected Art, Letters, and Unpublished Writings. University of Georgia Press, Athens, GA, 2010.
 * Harper, Francis, "Travels in Georgia and Florida, 1773-74. A Report to Dr. John Fothergill." Edited by Francis Harper. Trans. of the American Philosophical Society, n. s. vol. 33, part 2 (November 1943), p. 121-242.
 * Braund, Kathryn E. Holland and Charlotte M. Porter, eds. Fields of Vision: Essays on the "Travels" of William Bartram (University of Alabama Press; 2010; 273 pages), essays by scholars
 * Lowes, John Livingston, The Road to Xanadu: A Study in the Ways of Imagination. Houghton Mifflin, New York, 1927.
 * Magee, Judith, The Art and Science of William Bartram. The Pennsylvania State University Press, University Park, PA, in association with the Natural History Museum, London, 2007.
 * Savage, Henry Jr. Discovering America, 1700-1875. p. 63-70. Harper & Row, 1979.
 * "William Bartram" Dictionary of Literary Biography, Volume 37: American Writers of the Early Republic. Emory Elliot, ed. The Gale Group, 1985, pp. 31–38.
 * "William Bartram 1739-1823" Dictionary of American Biography. American Council of Learned Societies, 1928–1936.
 * Schafer, Daniel L., William Bartram and the Ghost Plantations of British East Florida, University Press of Florida, 2010.

title: William Bartram


text:
Proof by infinite descent

In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. It is a method which relies on the well-ordering principle, and is often used to show that a given equation, such as a Diophantine equation, has no solutions.

Typically, one shows that if a solution to a problem existed, which in some sense was related to one or more natural numbers, it would necessarily imply that a second solution existed, which was related to one or more 'smaller' natural numbers. This in turn would imply a third solution related to smaller natural numbers, implying a fourth solution, therefore a fifth solution, and so on. However, there cannot be an infinity of ever-smaller natural numbers, and therefore by mathematical induction, the original premise—that any solution exists—is incorrect: its correctness produces a contradiction.

An alternative way to express this is to assume one or more solutions or examples exists, from which a smallest solution or example—a minimal counterexample—can then be inferred. Once there, one would try to prove that if a smallest solution exists, then it must imply the existence of a smaller solution (in some sense), which again proves that the existence of any solution would lead to a contradiction.

The earliest uses of the method of infinite descent appear in Euclid's Elements. A typical example is Proposition 31 of Book 7, in which Euclid proves that every composite integer is divided (in Euclid's terminology "measured") by some prime number.

The method was much later developed by Fermat, who coined the term and often used it for Diophantine equations. Two typical examples are showing the non-solvability of the Diophantine equation $$r^2+s^4=t^4$$ and proving Fermat's theorem on sums of two squares, which states that an odd prime p can be expressed as a sum of two squares when $$p\equiv1\pmod{4}$$ (see Modular arithmetic and proof by infinite descent). In this way Fermat was able to show the non-existence of solutions in many cases of Diophantine equations of classical interest (for example, the problem of four perfect squares in arithmetic progression).

In some cases, to the modern eye, his "method of infinite descent" is an exploitation of the inversion of the doubling function for rational points on an elliptic curve E. The context is of a hypothetical non-trivial rational point on E. Doubling a point on E roughly doubles the length of the numbers required to write it (as number of digits), so that a "halving" a point gives a rational with smaller terms. Since the terms are positive, they cannot decrease forever.

Number theory
In the number theory of the twentieth century, the infinite descent method was taken up again, and pushed to a point where it connected with the main thrust of algebraic number theory and the study of L-functions. The structural result of Mordell, that the rational points on an elliptic curve E form a finitely-generated abelian group, used an infinite descent argument based on E/2E in Fermat's style.

To extend this to the case of an abelian variety A, André Weil had to make more explicit the way of quantifying the size of a solution, by means of a height function – a concept that became foundational. To show that A(Q)/2A(Q) is finite, which is certainly a necessary condition for the finite generation of the group A(Q) of rational points of A, one must do calculations in what later was recognised as Galois cohomology. In this way, abstractly-defined cohomology groups in the theory become identified with descents in the tradition of Fermat. The Mordell–Weil theorem was at the start of what later became a very extensive theory.

Irrationality of $\sqrt{2}$
The proof that the square root of 2 ($\sqrt{2}$) is irrational (i.e. cannot be expressed as a fraction of two whole numbers) was discovered by the ancient Greeks, and is perhaps the earliest known example of a proof by infinite descent. Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. Little is known with certainty about the time or circumstances of this discovery, but the name of Hippasus of Metapontum is often mentioned. For a while, the Pythagoreans treated as an official secret the discovery that the square root of two is irrational, and, according to legend, Hippasus was murdered for divulging it. The square root of two is occasionally called "Pythagoras' number" or "Pythagoras' Constant", for example.

The ancient Greeks, not having algebra, worked out a geometric proof by infinite descent (John Horton Conway presented another geometric proof by infinite descent that may be more accessible ). The following is an algebraic proof along similar lines:

Suppose that $\sqrt{2}$ were rational. Then it could be written as

 * $$\sqrt{2} = \frac{p}{q}$$

for two natural numbers, $p$ and $q$. Then squaring would give

 * $$2 = \frac{p^2}{q^2}, $$
 * $$2q^2 = p^2, $$

so 2 must divide p2. Because 2 is a prime number, it must also divide p, by Euclid's lemma. So p = 2r, for some integer r.

But then,

 * $$2q^2 = (2r)^2 = 4r^2, $$
 * $$q^2 = 2r^2, $$

which shows that 2 must divide q as well. So q = 2s for some integer s.

This gives

 * $$\frac{p}{q}=\frac{2r}{2s}=\frac{r}{s}$$.

Therefore, if $\sqrt{2}$ could be written as a rational number, then it could always be written as a rational number with smaller parts, which itself could be written with yet-smaller parts, ad infinitum. But this is impossible in the set of natural numbers. Since $\sqrt{2}$ is a real number, which can be either rational or irrational, the only option left is for $\sqrt{2}$ to be irrational.

(Alternatively, this proves that if $\sqrt{2}$ were rational, no "smallest" representation as a fraction could exist, as any attempt to find a "smallest" representation p/q would imply that a smaller one existed, which is a similar contradiction.)

Irrationality of $\sqrt{k}$ if it is not an integer
For positive integer k, suppose that $\sqrt{k}$ is not an integer, but is rational and can be expressed as $m⁄n$ for natural numbers m and n, and let q be the largest integer less than $\sqrt{k}$ (that is, q is the floor of $\sqrt{k}$). Then

 * $$\begin{align}

\sqrt k &=\frac mn\\ [6pt] &=\frac{m\left(\sqrt k-q\right)}{n\left(\sqrt k-q\right)}\\ [6pt] &=\frac{m\sqrt k-mq}{n\sqrt k-nq}\\ [6pt] &=\frac{\left(n \sqrt k\right)\sqrt k-mq}{n \left(\frac{m}{n}\right) -nq}\\ [6pt] &=\frac{nk-mq}{m-nq} \end{align}$$

The numerator and denominator were each multiplied by the expression ($\sqrt{k}$ − q)—which is positive but less than 1—and then simplified independently. So, the resulting products, say m′ and n′, are themselves integers, and are less than m and n respectively. Therefore, no matter what natural numbers m and n are used to express $\sqrt{k}$, there exist smaller natural numbers m′ < m and n′ < n that have the same ratio. But infinite descent on the natural numbers is impossible, so this disproves the original assumption that $\sqrt{k}$ could be expressed as a ratio of natural numbers.

Non-solvability of r2 + s4 = t4 and its permutations
The non-solvability of $$r^2 + s^4 =t^4$$ in integers is sufficient to show the non-solvability of $$q^4 + s^4 =t^4$$ in integers, which is a special case of Fermat's Last Theorem, and the historical proofs of the latter proceeded by more broadly proving the former using infinite descent. The following more recent proof demonstrates both of these impossibilities by proving still more broadly that a Pythagorean triangle cannot have any two of its sides each either a square or twice a square, since there is no smallest such triangle:

Suppose there exists such a Pythagorean triangle. Then it can be scaled down to give a primitive (i.e., with no common factors other than 1) Pythagorean triangle with the same property. Primitive Pythagorean triangles' sides can be written as $$x=2ab,$$ $$y=a^2-b^2,$$ $$z=a^2+b^2$$, with a and b relatively prime and with a+b odd and hence y and z both odd. The property that y and z are each odd means that neither y nor z can be twice a square. Furthermore, if x is a square or twice a square, then each of a and b is a square or twice a square. There are three cases, depending on which two sides are postulated to each be a square or twice a square:

 * y and z: In this case y and z are both squares. But then the right triangle with legs $$\sqrt{yz}$$ and $$b^2$$ and hypotenuse $$a^2$$ also would have integer sides including a square leg ($$b^2$$) and a square hypotenuse ($$a^2$$), and would have a smaller hypotenuse ($$a^2$$ compared to $$z=a^2+b^2$$).
 * z and x: z is a square. The integer right triangle with legs $$a$$ and $$b$$ and hypotenuse $$\sqrt{z}$$ also would have two sides ($$a$$ and $$b$$) each of which is a square or twice a square, and a smaller hypotenuse ($$\sqrt{z}$$ compared to $z$).
 * y and x: y is a square. The integer right triangle with legs $$b$$ and $$\sqrt{y}$$ and hypotenuse $$a$$ would have two sides (b and a) each of which is a square or twice a square, with a smaller hypotenuse than the original triangle ($$a$$ compared to $$z=a^2+b^2$$).

In any of these cases, one Pythagorean triangle with two sides each of which is a square or twice a square has led to a smaller one, which in turn would lead to a smaller one, etc.; since such a sequence cannot go on infinitely, the original premise that such a triangle exists must be wrong.

This implies that the equations
 * $$r^2 + s^4 = t^4,$$
 * $$r^4 + s^2 =t^4,$$ and
 * $$r^4 + s^4 =t^2$$

cannot have non-trivial solutions, since non-trivial solutions would give Pythagorean triangles with two sides being squares.

For other similar proofs by infinite descent for the n = 4 case of Fermat's Theorem, see the articles by Grant and Perella and Barbara.

title: Proof by infinite descent


text:
Greek Church

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title: Greek Church


text:
Richard Sheridan

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 * Richard Bingham Sheridan (1822–1897), Australian civil servant
 * Richard Brinsley Sheridan (1751–1816), Irish playwright
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title: Richard Sheridan