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Arlington, Massachusetts

Arlington is a town in Middlesex County, Massachusetts, United States. The town is six miles (10 km) northwest of Boston, and its population was 46,308 at the 2020 census.

History
European colonists settled the Town of Arlington in 1635 as a village within the boundaries of Cambridge, Massachusetts, under the name Menotomy, an Algonquian word considered by some to mean "swift running water", though linguistic anthropologists dispute that translation. A larger area was incorporated on February 27, 1807, as West Cambridge, replacing Menotomy. This includes the town of Belmont, and outwards to the shore of the Mystic River, which had previously been part of Charlestown. The town was renamed Arlington on April 30, 1867, in honor of those buried in Arlington National Cemetery.

The Massachusett tribe lived around the Mystic Lakes, the Mystic River, and Alewife Brook. Chief Nanepashemet was killed by a rival tribe in about 1619, and Nanepashemet's widow "Squaw Sachem of Mistick" became the acknowledged leader of the tribe. In 1639, she deeded the land of what was then Cambridge and Watertown to the colonists. She lived her last years on the west side of the Mystic Lakes near Medford, where she died sometime between 1650 and 1667.

A stream called Mill Brook flows through the town, which historically figured largely into Arlington's economy. In 1637, Captain George Cooke built the first mill in this area. Subsequently, seven mills were built along the stream, including the Old Schwamb Mill, which still survives. The Schwamb Mill has been a working mill since 1650, making it the longest working mill in the country.

Paul Revere's midnight ride to alert colonists took him through Menotomy, now known as Arlington. Later on that first day of the American Revolution, more blood was shed in Menotomy than in the battles of Lexington and Concord combined. Minutemen from surrounding towns converged on Menotomy to ambush the British on their retreat from Concord and Lexington. Twenty-five Americans were killed in Menotomy, half of all Americans killed in the day's battles, as well as 40 British troops (more than half their fatalities). Arlington resident Cyrus Dallin would later create an iconic sculpture of the rider; a version can be seen at the town's Cyrus Dallin Art Museum.

The Jason Russell House is a museum which remembers those 12 Americans who were killed in and around this pictured dwelling on April 19, 1775. Bullet holes are visible in the interior walls to this day.

In its early years, Arlington was a thriving farming community and had its own lettuce that was quite popular. Arlington had a large ice industry on Spy Pond from the mid-19th century until the last ice house burned down in 1930; much of its ice was sent to the Caribbean and India by "Ice King" Frederic Tudor.

Arlington's population grew by over 90 percent during the 1920s. In 1979, the first spreadsheet software program VisiCalc was developed by Bob Frankston and Dan Bricklin in the attic of the Arlington apartment rented by Bob Frankston.

Geography and infrastructure
Arlington covers 3,517.5 acres (14 km2), or 5.5 square miles, of which 286.2 acres (1.2 km2), or 0.4 square miles, are covered by water. There are 210.52 acres (0.9 km2) of parkland. Elevation ranges from 4 feet (1.2 m) above sea level (along Alewife Brook) to 377 feet (114.9 m) near Park Avenue and Eastern Avenue.

Arlington borders on the Mystic Lakes, Mystic River, and Alewife Brook. Within its borders are Spy Pond, the Arlington Reservoir, Mill Brook, and Hills Pond.

Neighborhoods

 * Arlington Center
 * Arlington Heights, in the west
 * East Arlington, east of Franklin Street
 * Brattle Square
 * Jason Heights
 * Arlmont Village
 * Morningside
 * North Union
 * Turkey Hill
 * Little Scotland
 * Poets' Corner
 * Kelwyn Manor
 * Quincy Heights, a neighborhood in Arlington Heights

Zip Codes

 * 02474: East Arlington, and most of the rest of the town north of the Minuteman Bikeway
 * 02476: Arlington Heights, and most of the rest of the town south of the Bikeway and west of Spy Pond

Adjacent municipalities
Arlington is located in eastern Massachusetts and is bordered by the cities of Medford to the northeast, Somerville to the east, Cambridge to the southeast, and the towns of Winchester to the north, Lexington to the west, and Belmont to the south.

Transportation
Several MBTA bus routes pass through the town.

The Minuteman Bikeway also runs through the center of town, connecting residents by bike to Bedford, Lexington, the Alewife Red Line station and Boston.

Route 2 is a limited access highway that runs along the southern border of Arlington with Belmont.

Demographics
Historically, Arlington is known for being an Irish, Italian and Greek middle class community but in the last decades has become increasingly expensive, while still retaining its middle class homes with a mixture of double/triple decker homes (multiple family styles homes) and (mostly smaller sized for single family homes) single family homes.

At the 2020 census, there were 46,308 people living in 19,308 households in the town. The population density was 9,004.1 people per square mile. There were 19,974 housing units at an average density of 3,841.2 /sqmi as of the 2010 census. The racial makeup of the town as of the 2020 census was 75.6% White, 3.3% African American, 0.1% Native American, 13.7% Asian and 6.1% from two or more races. Hispanic or Latino of any race were 5.0% of the population.

There were 19,308 households with an average household size of 2.37 According to previous data, 27.0% had children under the age of 18 living with them, 45.1% were married couples living together, 2.0% had a male householder with no wife present, 9.9% had a female householder with no husband present, and 43.0% were non-families. 35.1% of all households were made up of individuals, and 11.2% had someone living alone who was 65 years of age or older.

Of the 46,308 people in the population, 6.5% were under the age of 5, 21.4% were under the age of 18, and 16% were 65 years and over. 53.3% of the population was female. The median household income was $125,701, up from $85,059 in 2010. The per capita income for the town was $69,007, up from $47,571 in 2010. About 4.6% of the population were below the poverty line.

Income
Data is from the 2009–2013 American Community Survey 5-Year Estimates.

Government

Arlington's executive branch consists of an elected five-member select board. The day-to-day operations are handled by a town manager hired by the select board. The legislative branch is a representative town meeting, presided over by the town moderator, and is made up of 252 town meeting members. Twelve town meeting members are elected to staggered three year terms from each of the 21 precincts. Article LXXXIX section 8 of the Massachusetts Constitution permits towns with a population greater than 12,000 to adopt a city form of government. The town of Arlington meets the population requirement to become a city, but has not done so, in part because it would lose its ability to engage citizens in local government under the representative town meeting form of government. Annual town meetings begin in April on the first Monday after Patriots' Day, and are held two nights a week until all items on the town warrant are resolved, and generally last three to four weeks.

In April 2021, Arlington voted to become the third municipality in the United States to recognize polyamorous domestic partnerships, following adjacent cities of Somerville and Cambridge.

Public schools
Arlington has a public school system with ten schools. (seven elementary schools, two middle schools and one high school) The seven elementary schools (K–5) are Brackett, Bishop, Dallin, Hardy, Peirce, Stratton, and Thompson. There are also two middle schools, grade 6 at Gibbs, and grades 7–8 at Ottoson, and Arlington High School, which includes grades 9–12. In addition, Arlington is in the district served by the Minuteman Regional High School, located in Lexington, one of the top vocational-technical schools in Massachusetts.

Private and parochial schools
There are two Parochial schools, Arlington Catholic High School, and an elementary/middle school, St. Agnes School, both affiliated with St. Agnes Parish. In addition, there are two secular elementary schools, Lesley Ellis and the Alivia Elementary School.

Supplementary schools
The Greater Boston Japanese Language School (ボストン補習授業校), a supplementary school for Japanese people, has its weekday office in Arlington, while it holds classes at Medford High School in Medford.

Parks and historical sites

 * The Old Schwamb Mill is the oldest continuously-operating mill site in the United States. Founded by the Schwambs, who immigrated to the U.S. from Germany, the mill currently produces and sells museum-quality, hand-turned wooden oval and circular frames, created much as they were in 1864. Named to the National Register of Historic Places in 1971, the mill-museum is operated by a nonprofit educational trust that maintains the mill's traditions.
 * Menotomy Rocks Park encompasses Hills Pond and has trails through the surrounding forested land.
 * Robbins Farm Park along Eastern Avenue includes a playground, ball fields, a basketball court and a commanding view of the Boston skyline.
 * Robbins Library contains the oldest continuously operated free children's library in the country. A sculpture of the Menotomy Hunter by Cyrus Dallin can be found in an adjacent park.
 * Spy Pond Park provides access to the northeastern shore of Spy Pond.
 * The Arlington Center Historic District, where the Robbins Library and Old Burying Ground are located, is listed in the National Register of Historic Places. It also contains the Town Hall and the Robbins Memorial Flagstaff that contains four sculptures by Cyrus Dallin.
 * The Cyrus E. Dallin Art Museum is a site dedicated to the artwork and sculpture of noted artist Cyrus E. Dallin.
 * The Great Meadow comprises both wet meadow swamp and forest right outside the border of Arlington. While the Great Meadow lies within the borders of Lexington, the park is owned and maintained by the Town of Arlington.
 * The House at 5 Willow Court
 * The Henry Swan House, built in 1888, is a historic house at 418 Massachusetts Avenue. It was added to the National Register of Historic Places in 1985.
 * The Jason Russell House contains a museum that displays, among other items, a mastodon tusk found in Spy Pond in the late 1950s by a fisherman who originally thought he had brought up a tree branch.
 * The Minuteman Bikeway, a popular rail trail built in 1992, passes through various Arlington neighborhoods, including Arlington Center.
 * The Prince Hall Mystic Cemetery, the only black Freemason Cemetery in the country.
 * The Uncle Sam Memorial Statue commemorates native son Samuel Wilson, who was perhaps the original Uncle Sam.
 * The Water tower at Park Circle is an exact copy of the rotunda of the ancient Greek Arsinoeon of the Samothrace temple complex.

Regent Theatre
The Regent Theatre is a historic theater in downtown Arlington. It was built in 1916 for vaudeville acts and is still used for live performances as well as films. It was remodeled in 1926. The theatre, located at 7 Medford Street, has 500 seats. It hosts the Arlington International Film Festival.

Notable people

 * Sven Birkerts (born 1951), essayist and literary critic
 * Paul Boudreau, former NFL offensive line coach for the St. Louis Rams
 * John Quincy Adams Brackett, Former Massachusetts Governor
 * William Stanley Braithwaite, writer, poet and literary critic. Won Spingarn Medal in 1918
 * Noel Buck, professional soccer player for New England Revolution
 * Christopher Castellani, writer
 * Andrew Chaikin, space journalist and author of A Man on the Moon, on which HBO based a miniseries
 * Haroutioun Hovanes Chakmakjian, chemistry professor, Armenian scholar, and father of Alan Hovhaness
 * Pat Connaughton, Player for 2021 NBA Champion Milwaukee Bucks
 * Dane Cook, comedian & actor
 * Robert Creeley (1926–2005), poet
 * Greg Cronin, head coach for the Anaheim Ducks of the National Hockey League (NHL)
 * Cyrus E. Dallin (1861–1944), sculptor; best known for Boston's Equestrian Statue of Paul Revere, Appeal to the Great Spirit sculpture in front of the Museum of Fine Arts, Boston and the Angel Maroni Sculpture atop the Salt Lake Temple in Salt Lake City, Utah
 * Adio diBiccari, sculptor
 * Joshua Eric Dodge, Wisconsin Supreme Court
 * Olympia Dukakis (1931-2021), actress, Academy Award winner
 * Bob Frankston, co-inventor of Visicalc, the first electronic spreadsheet, at 231 Broadway
 * Samuel Garman (1843–1927), explorer, ichthyologist, and herpetologist
 * Roy J. Glauber, Nobel Prize winner (Physics), 2005
 * Katy Grannan, photographer
 * George Franklin Grant, first black graduate of Harvard Dental School and inventor of a type of golf tee
 * Deborah Henson-Conant, Grammy-nominated harpist
 * Susan Hilferty, costume designer, Wicked
 * Winslow Homer, painter (location is now in Belmont)
 * Alan Hovhaness (1911–2000), composer
 * Timothy Hutton, Actor, youngest winner of an Academy Award for Best Supporting Actor
 * Anthony James (1942–2020), actor
 * John A. "Johnny" Kelley, Boston Marathon winner, 1935 and 1945, Olympian athlete
 * Richard Lennon, Roman Catholic Bishop of Cleveland
 * J. C. R. Licklider (1915–1990), computer scientist
 * Elaine J. McCarthy projection designer for Broadway and opera
 * William J. McCarthy, President of the International Brotherhood of Teamsters (IBT)
 * Eugene Francis McGurl, US Army Air Forces 95th Bomb Sq., 17th Bomb Grp Navigator who flew with Crew 5 in General Jimmy Doolittle's "Thirty Seconds over Tokyo" raid in World War II
 * Tom McNeeley, Jr., former heavyweight contender who challenged Floyd Patterson for the heavyweight title in Toronto in 1961
 * John Messuri, Princeton College hockey player
 * Eileen Myles, poet, novelist
 * Jordan Peterson, Canadian clinical psychologist and professor of psychology at the University of Toronto. Lived in Arlington between 1993 and 1998 while teaching at Harvard University
 * David Powers, former Special Assistant to US President John F. Kennedy
 * Hilary Putnam (1926–2016), philosopher, mathematician and computer scientist, professor emeritus at Harvard
 * Warren Winn Rawson, market gardener and seed distributor
 * Herb Reed, vocalist and founding member of The Platters
 * Miles Robinson, current professional soccer player for Atlanta United
 * Dave "Chico" Ryan, bassist of Sha Na Na
 * Whitney Smith, vexillologist and designer of the flag of Guyana
 * Chris Smither, blues guitarist/singer.
 * Bill Squires, American Track & Field Coach
 * Anthony Stacchi, scenarist (Open Season)
 * Mark J. Sullivan, Director of the United States Secret Service
 * John Townsend Trowbridge (1827–1916), writer
 * Samuel Whittemore, elderly soldier in the Battle of Lexington and Concord
 * Alan Wilson (1943–1970), also known as Alan "Blind Owl" Wilson; singer, songwriter, leader of Canned Heat
 * Samuel Wilson (1766–1854), meat-packer, namesake of "Uncle Sam"
 * Brianna Wu, video game developer, primary victim of Gamergate controversy, congressional candidate
 * Tom Yewcic, former quarterback with the Boston Patriots from 1961 to 1966, and former catcher for the Detroit Tigers; only person ever to play two professional sports at Fenway Park

In popular culture

 * Two feature films have been shot partially in Arlington: The Out-of-Towners, starring Steve Martin and Goldie Hawn, and Once Around, starring Richard Dreyfuss and Holly Hunter.
 * Three widely recognized television shows have been filmed in Arlington: This Old House, Trading Spaces, and Made.
 * A History Channel special, Bible Battles, was filmed in Arlington.
 * Arlington is referenced in the movie The Verdict starring Paul Newman. South Boston's K Street takes the place of Arlington in the movie.
 * The music video for "Sing" by The Dresden Dolls was shot at the Regent Theatre in Arlington Center.
 * The Steve Katsos Show is filmed at ACMi Studios in Arlington Heights.
 * Arlington's Little League baseball team won the Massachusetts State Little League championship in 1971.

Sister cities

 * Teosinte, El Salvador
 * Nagaokakyo, Kyoto, Japan

title: Arlington, Massachusetts


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Talk:1925 in music

Untitled
I cut "Bing Crosby's solo career begins"; since he was still a member of Paul Whiteman's Rhythm Boys making records without his own name on the lable as late as 1929, this is misleading if not outright inaccurate. -- Infrogmation 03:30 Feb 12, 2003 (UTC)

"Sweet Georgia Brown" w.m. Ben Bernie, Maceo Pinkard & Kenneth Casey
At least SGB is under the copyrght section, I will add it to Top Records. Ben Bernie, band leader and composer, released instrumental version on Vocalion in June. Trying to get reference, either Isham Jones on Brunswick "I'll See You In My Dreams" was top selling record of year. I will be doing chart.

Below are other 1925 records with sales figures (Victor). However, the number for "All Alone" is either Whiteman or both artists combined. Another problem with all, especially Dalhart, is when did sales occur? (i.e. 1924 to Oct. 1929?) Will provide all details, and be sure not to misrepresent.

 * I presented top 20 list, but deleted the rank numbers, since none existed at the time. I can modify display and content if there was any interest Tillywilly17 (talk) 20:14, 25 March 2022 (UTC)

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

title: Talk:1925 in music


text:
Talk:Empty product

section break 2
We should say that 00 = 1 and it is an indeterminate form. The two statements are both true. Why would anyone have a problem with that? Michael Hardy (talk) 15:44, 17 June 2008 (UTC)

 * Which article are you talking about, this one or exponentiation? You're right that it makes little difference whether an indeterminate form is "defined" or not. However, I just made a quick survey of three calculus texts from my shelf, and none of them defines 0^0 at all. Do you know of any calculus text that defines 0^0? — Carl (CBM · talk) 16:12, 17 June 2008 (UTC)

At least they implicitly define it when they say that for all x,
 * $$ e^x = \sum_{n=0}^\infty {x^n \over n!}, $$

since when x = 0 then the first term is 00/0 ! . But why should it matter what calculus textbooks say about it? Calculus texts are efforts at pedagogical improvements in ways to present standard material to students who don't want to become experts on it, not authoritative statements on issues on which there's no standard pronouncement. Michael Hardy (talk) 16:02, 18 June 2008 (UTC)
 * The exponentiation in the first term on the right-hand side is the real-to-integer, iterated-product version of exponentiation, not the real-to-real or complex-to-complex version, which as I say is intensionally quite distinct. But the point for WP purposes is that if there "is no standard pronouncement" then it's inappropriate for us to create one. --Trovatore (talk) 17:19, 18 June 2008 (UTC)

...and saying that it's a convention is creating one. It violates NPOV. Michael Hardy (talk) 19:28, 18 June 2008 (UTC)
 * At this writing the article does not use the word convention, except when talking about the intersection of no subsets of a given set. --Trovatore (talk) 19:51, 18 June 2008 (UTC)

If we are talking about fixed exponent 0 in $$x^n$$ then when x tends to 0 the result is 1. So there's no problem with the summation formula of $$e^x$$.Linkato1 (talk) 02:47, 28 November 2018 (UTC)

"Convention"?
This article now says:
 * This justifies the convention that 0m = 0 when m is positive.
 * This justifies the convention that 0m = 0 when m is positive.

Does anyone really regard this as a convention rather than as a fact? I was surprised to find respectable mathematicians saying that the fact that the empty product is 1 is merely a convention, rather than a fact, but even then I didn't think someone would say that the fact stated above is a convention. Michael Hardy (talk) 23:48, 12 June 2008 (UTC)

 * I think that's just badly phrased and should be reworded. I'll go ahead and do it. — Carl (CBM · talk) 00:12, 13 June 2008 (UTC)

It is a reminent from: "This justifies the convention that 0m = 1 when m is zero", which by some editors is considered a convention rather than a fact. Bo Jacoby (talk) 06:44, 13 June 2008 (UTC).

 * That one is a convention. But 0^2 = 0 isn't. — Carl (CBM · talk) 10:45, 13 June 2008 (UTC)
 * I certainly don't agree that 00 = 1 is only a convention. Michael Hardy (talk) 17:30, 13 June 2008 (UTC)

 * That's reasonable enough; but there are many authors who do consider it only a convention. I located a nice quote from one of them for the exponentiation article: "The choice whether to define 0^0 is based on convenience, not on correctness.". Although I risk repeating myself too often: of course many authors do define 0^0 to be 1; especially when 0^0 represents the empty product, this definition is very common. But many other authors leave 0^0 undefined, especially in complex analysis. Regardless of our personal feelings on the matter, we can still write a description of the subtleties that arise in the literature. — Carl (CBM · talk) 22:50, 13 June 2008 (UTC)

There's no problem and there's no convention as if we are talking about $$0^x$$ then it's always 0 as long as x is non-negative and if we are talking about $$x^0$$ it's always 1 regardless of what x is. It's only when we have $$x^y$$ and both x and y tend to 0 that we must be carefull and analyse the situation.Linkato1 (talk) 02:54, 28 November 2018 (UTC)

Intuitive justification
I've altered this section to read as follows:
 * Imagine a calculator that can only multiply. It has an "ENTER" key and a "CLEAR" key. One would wish that, for example, if one presses "CLEAR", 7 "ENTER", 3 "ENTER", 4 "ENTER", then the display reads 84, because 7 × 3 × 4 = 84.  More precisely, we specify:
 * A number is displayed just after "CLEAR" is pressed;
 * When a number is displayed and one enters another number, the product is displayed;
 * When "CLEAR" is pressed and then some numbers are entered, their product is displayed.
 * Then the starting value after pressing "CLEAR" has to be 1. After one has pressed "clear" and done nothing else, the number of factors one has entered is zero.  Therefore the product of zero numbers is 1.
 * When "CLEAR" is pressed and then some numbers are entered, their product is displayed.
 * Then the starting value after pressing "CLEAR" has to be 1. After one has pressed "clear" and done nothing else, the number of factors one has entered is zero.  Therefore the product of zero numbers is 1.
 * Then the starting value after pressing "CLEAR" has to be 1. After one has pressed "clear" and done nothing else, the number of factors one has entered is zero.  Therefore the product of zero numbers is 1.

Someone had changed it so that the third desideratum said that when clear is pressed and then a number is entered, that number is displayed. In some ways that makes this closer to a logically rigorous argument, and in this context I think that in itself may be a mistake. But also it doesn't seem so much like a self-evident desideratum since this whole thing is supposed to be about mutliplying. Michael Hardy (talk) 01:59, 12 October 2008 (UTC)

Need for rewrite
I think this article is badly in need for rewriting to make more mathematical (and common language) sense. Take the opening phrase "an empty product, or nullary product, is the result of multiplying no numbers". No it is not, it is an expression asking for the product of an sequence (or set or multiset) of numbers (could be other things as well though), which sequence (set, etc.) happens to be empty. First, there is no such thing as multiplying no numbers, or even one or three numbers; multiplication takes two arguments (the distinction that should be made is between a multiplication and a product; possibly "multiplying together" can be used but it makes no good sense for 0 arguments). Second, and empty product is not the result of anything, it is something like "0!" whose value is 1, but it is not identical to 1 (or otherwise conversely "1 is an empty product", which seems a bad formulation). In short, one should make distinction between expressions and there values, and an empty product is an expression. But there are many more points that are just not carefully stated (and a lot non encyclopedic wording as well). I agree it takes effort to be clear and precise at the same time, but it is worth the effort. To get an idea look at empty sum, which I think is better. I plan to make changes here soon (but feel free to protest already). Marc van Leeuwen (talk) 08:15, 18 March 2010 (UTC)

 * I cleaned it up a bit. There was too much repetition, and I deleted some things that were copied from other wiki-pages that were somewhat off topic. MvH (talk) 00:19, 28 March 2014 (UTC)MvH

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Convention
I can understand why some might not want to call the value 1 for the empty product a "convention". When you have a unique 2-sided multiplicative identity, it's the only reasonable convention.

But it's still a convention. What if you're in a structure with an associative multiplication, but no multiplicative identity? You can still define repeated products, but now there's nothing to assign to the empty product.

If you don't specify what the empty product means (that is, give a convention), then it simply has no meaning, notwithstanding there's a best choice for the meaning to give it. --Trovatore (talk) 01:41, 28 September 2019 (UTC)

 * That's more than a best choice, that's the unique choice. The word "convention" just means that's from an agreement among several possibilities, not by deduction. So, if the word "convention" is used, let's say at least that the choice is unique. Vincent Lefèvre (talk) 10:05, 28 September 2019 (UTC)
 * Strictly speaking, there is no "deduction" possible here. That's just wrong.  If you don't define it, it's not defined, period; it is not possible to "deduce" what the value is, in any way whatsoever.  And no, the choice is not "unique".  It's the unique good choice, but the notion of goodness is based on values external to the definition. --Trovatore (talk) 19:40, 28 September 2019 (UTC)
 * By deduction, I meant that there is a proof that if a value exists, then the choice is unique. The value is part of the definition of the multiplication binary operation. There is nothing external. Vincent Lefèvre (talk) 20:16, 28 September 2019 (UTC)
 * There is no such proof. Not from the definition of the concept per se.  You could start with the definition of products as iterated multiplication, and then go ahead and specify that the empty product takes the value 17.
 * Of course you lose some desirable properties, but you can do it. Unless those desired properties are taken to be part of the notion of products, which is an external specification, then there is no proof that the value 17 is wrong. --Trovatore (talk) 20:24, 28 September 2019 (UTC)
 * Here's the proof of the uniqueness: Consider the case $$a_1 = 1$$, where 1 denotes the multiplicative identity (which has been assumed to exist in the first paragraph). Then $$P_0 = P_0 \cdot 1 = P_0 \cdot a_1 = P_1 = a_1 = 1$$. Thus necessarily $$P_0 = 1$$. Vincent Lefèvre (talk) 20:41, 28 September 2019 (UTC)
 * The insufficiently justified step is $$P_0 \cdot a_1 = P_1$$. There is simply no way to "prove" that, without adding an external criterion. --Trovatore (talk) 20:47, 28 September 2019 (UTC)
 * $$P_0 \cdot a_1 = P_1$$ is from the recurrence relation stated in the article, which includes $$m = 1$$. No need for another criterion. Vincent Lefèvre (talk) 20:50, 28 September 2019 (UTC)
 * That relation is a desirable property, but is not the only way iterated products could be defined. Therefore it is an external criterion. --Trovatore (talk) 20:58, 28 September 2019 (UTC)
 * This is always how extensions have been made: one first chooses the desirable property, and one deduces which value will satisfy it. And this is the criterion chosen in the article (quite natural, since the iterated product is defined with the recurrence relation). I'm not basing my proof on something that is not in the article. Vincent Lefèvre (talk) 21:06, 28 September 2019 (UTC)
 * I agree it's quite natural. That's not the point.  If you start by defining iterated products, there is no value for the product of no values, or even of one value.  You note that there is a relationship giving the product of iterated products of two or more values each, and you can see that it would make sense to extend the definition in such a way that the relationship also extends.  This is all very natural, but it isn't a proof. --Trovatore (talk) 21:33, 28 September 2019 (UTC)
 * The recurrence relation is the hypothesis. The proof is how the value of $$P_0$$ is obtained from this hypothesis (the case of one value is completely part of the definition of an iterated binary operation and always unambiguously defined, I hope you do not suggest to write an article for this case!). This is not much different than the notion of continuous extension (extension by continuity): the property of continuity is the hypothesis, and then one seeks to extend the function at one point by taking the limit (the value comes from the property), and determining the limit constitutes a proof. Vincent Lefèvre (talk) 21:56, 28 September 2019 (UTC)
 * Who says it's the hypothesis? --Trovatore (talk) 22:29, 28 September 2019 (UTC)
 * I think that all mathematical notation is convention. This convention is one that it would be a tremendous pain to do without, but it is still a convention. Incidentally, starting with multiplication as a binary operation, the multiplication of just one thing also needs to be defined. The recurrence is an extension of multiplication from a binary operation to an m-ary operation, and it has been found that applying it in reverse order to give meaning to P0 and P1 is extremely useful. So we have adopted it for our own benefit, not because we were forced to. McKay (talk) 05:30, 29 September 2019 (UTC)
 * Yes, all mathematical notation and definitions are conventions. Then one may wonder why saying the word "convention" in some cases but not everywhere. This is misleading. And note that P1 is part of the core definition (otherwise, in some semigroups, trying to use the recurrence relation to deduce and define its value would give several solutions). Only for P0, one can use the recurrence relation to unambiguously define its value (when there is one). Vincent Lefèvre (talk) 09:21, 29 September 2019 (UTC)
 * The point is that the obvious idea of repeated products starts with a minimum of two things to multiply together. Anything else is an extension.  It's a very natural extension once you think of it, but the word "convention" is not out of place — and no, you can't "prove" it's the right one. --Trovatore (talk) 17:18, 29 September 2019 (UTC)
 * No, the definition does not say "two". Vincent Lefèvre (talk) 19:50, 29 September 2019 (UTC)
 * You're missing the point. The obvious notion of an iterated product is, you start by multiplying two things, then you multiply more.  You can't multiply fewer than two things.  Can't be done.
 * There is a natural extension, yes. But it's an extension, and a convention. --Trovatore (talk) 21:14, 29 September 2019 (UTC)
 * For 1 element, there are 0 binary products. For 2 elements, there is 1 binary product. For 3 elements, there are 2 binary products. For 4 elements, there are 3 binary products. And so on. This is as simple as that. No need for an extension. And see the formal definition of an iterated binary operation: this starts at 1 element, not at 2. Vincent Lefèvre (talk) 22:07, 29 September 2019 (UTC)
 * You said it yourself: "For 1 element, there are 0 binary products."  Just so.  You can't multiply fewer than two things, exactly as I said.  The fact that someone has made a formal definition does not change that.  You're really off-base here, Vincent.  This is a convention, not the obvious notion per se, notwithstanding (and I agree) that it has a certain naturality to it. --Trovatore (talk) 22:20, 29 September 2019 (UTC)
 * I have never said that I wanted to multiply fewer than two things. The definition of the iterated product does not imply that. If you are going this way, as McKay say, all mathematical notation is convention. So, whether one starts at 1 element, 2 elements, 3 elements or more, this is a convention. Vincent Lefèvre (talk) 22:36, 29 September 2019 (UTC)
 * I think your "the" in "the" definition of iterated product is a bit -- overstated. It isn't "the" definition, it's a definition.  The obvious notion really does start with 2.  You can't multiply fewer than 2 things, period, but you can multiply 3 things, given that multiplication is associative.
 * So sure, they're both conventions, but the one for empty product is more conventional than the one for 2 or more elements. --Trovatore (talk) 22:46, 29 September 2019 (UTC)
 * No, one cannot multiply 3 things. The multiplication is defined on 2 inputs. Then you have an extension called iterated binary operation applied here to multiplication; this extension covers 3 inputs and more, but also 1 input. I suggest you do some effort reading that article instead of wasting my time. Vincent Lefèvre (talk) 23:53, 29 September 2019 (UTC)
 * Sorry, that article does not help your argument. Are you really going to bikeshed over this. This is a convention; it's not a theorem of the axioms of a monoid. Trovatore isn't wasting your time.--Jasper Deng (talk) 00:39, 30 September 2019 (UTC)

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Cornus florida

Cornus florida, the flowering dogwood, is a species of flowering tree in the family Cornaceae native to eastern North America and northern Mexico. An endemic population once spanned from southernmost coastal Maine south to northern Florida and west to the Mississippi River. The tree is commonly planted as an ornamental in residential and public areas because of its showy bracts and interesting bark structure.

Classification
The flowering dogwood is usually included in the dogwood genus Cornus as Cornus florida L., although it is sometimes treated in a separate genus as Benthamidia florida (L.) Spach. Less common names for C. florida include American dogwood, Florida dogwood, Indian arrowwood, Cornelian tree, white cornel, white dogwood, false box, and false boxwood.

Two subspecies are generally recognized:

Description
Flowering dogwood is a small deciduous tree growing to 10 m high, often wider than it is tall when mature, with a trunk diameter of up to 30 cm. A 10-year-old tree will stand about 5 m tall. The leaves are opposite, simple, ovate, 6 – long and 4 – broad, with an apparently entire margin (actually very finely toothed, under a lens); they turn a rich red-brown in fall.

Flowering dogwood attains its greatest size and growth potential in the Upper South, sometimes up to 40 feet in height. At the northern end of its range, heights of 30–33 feet are more typical. Hot, humid summer weather is necessary for new growth to harden off in the fall.

The maximum lifespan of C. florida is about 80 years.

The flowers are individually small, inconspicuous, and hermaphroditic, with four, greenish-yellow petals (not bracts) 4 mm long. Around 20 flowers are produced in a dense, rounded, umbel-shaped inflorescence, or flower-head, 1 – in diameter. The flower-head is surrounded by four conspicuous large white, pink or red bracts (not petals), each bract 3 cm long and 2.5 cm broad, rounded, and often with a distinct notch at the apex.

When in the wild they can typically be found at the forest edge and frequently on dry ridges. While most of the wild trees have white bracts, some selected cultivars of this tree also have pink bracts, some even almost a true red. They typically flower in early April in the southern part of their range, to late April or early May in northern and high altitude areas. The similar Kousa dogwood (Cornus kousa), native to Asia, flowers about a month later.

The fruit is a cluster of two to ten separate drupes, (fused in Cornus kousa), each 10 – long and about 8 mm wide, which ripen in the late summer and the early fall to a bright red, or occasionally yellow with a rosy blush. They are an important food source for dozens of species of birds, which then distribute the seeds. They are also a larval host plant for several moth varieties, including Eudeilinia herminiata, the dogwood thyatirid moth, Antispila cornifoliella, the stinging rose moth, the grand arches moth, the pecan bark borer,  the dogwood borer, the rosaceous leaf roller, the diamondback epinotia moth, spring azures, cecropia moths, and the Io moth. While not poisonous to humans, the fruit is extremely sour and unpleasant-tasting. Flowering dogwood is monoecious, meaning the tree has both male and female flowers, and all trees will produce fruit.

Cultivation
Flowering dogwood does best horticulturally in moist, acidic soil in a site with some afternoon shade, but good morning sun. It does not do well when exposed to intense heat sources such as adjacent parking lots or air conditioning compressors. It also has a low salinity tolerance. The hardiness zone is 5–9 and the preferred pH is between 6.0 and 7.0. In urban and suburban settings, care should be taken not to inflict mower damage on the trunk or roots, as this increases the tree's susceptibility to disease and pest pressure. The common flowering dogwood has been placed on the endangered species list in Ontario. Sites should be selected for reasonably well-drained, fertile soils; full sun is recommended in high-hazard areas (such as stream or pond banks). New plantings should be mulched to a depth of 2 to 4 in, avoiding the stem. Dead wood and leaves should be pruned and completely removed and destroyed yearly. Plants should be watered weekly during droughts, with watering done in the morning, avoiding wetting the foliage. Registered fungicides can be applied when necessary, according to manufacturers instructions and advice of local Extension Service.

Flowering dogwood is grown widely throughout the temperate world.
 * Selected cultivars

 * 'Amerika Touch-O-Pink' – large bracts, tinged pink; large leaves; good disease resistance.
 * 'Appalachian Spring' – large white bracts; red fall foliage; resistant to dogwood anthracnose.
 * 'Autumn Gold' – white bracts; yellow fall color.
 * 'Barton' – large white bracts; blooms at early age; resistant to stem canker and powdery mildew.
 * 'Bay Beauty' – double white bracts; resists heat and drought; good for Deep South.
 * 'Cherokee Daybreak' – white bract; vigorous grower with variegated leaves.
 * 'Cherokee Chief' – red bracts; red new growth.
 * 'Cherokee Brave' – Even redder than 'Cherokee Chief', smaller bracts but dark red color; consistently resistant to powdery mildew.
 * 'Cherokee Princess' – vigorous white bracts, industry standard for white flowers.
 * 'Cherokee Sunset' – purplish-red bracts; variegated foliage.
 * 'Gulf Coast Pink' – best pink flowering dogwood in Florida – northern part only.
 * 'Hohman's Gold' – white bracts; variegated foliage.
 * 'Jean's Appalachian Snow' – large, overlapping white bracts w/ green flowers; very resistant to powdery mildew.
 * 'Karen's Appalachian Blush' – delicate white bracts edged in pink; some powdery mildew resistance.
 * 'Kay's Appalachian Mist' – stiff, creamy white bracts; red fall foliage; good resistance to powdery mildew.
 * 'Plena' – double white bracts; spot anthracnose-resistant.
 * 'Purple Glory' – red bracts; purple foliage; spot anthracnose-resistant but susceptible to stem canker.
 * 'Weaver White' – large white blooms; large leaves; candelabra shape; good in north-central Florida.

Propagation

Cornus florida is easily propagated by seeds, which are sown in the fall into prepared rows of sawdust or sand, and emerge in the spring. Germination rates for good clean seed should be near 100% if seed dormancy is first overcome by cold stratification treatments for 90 to 120 days at 4 C. Flowering dogwood demonstrates gametophytic self-incompatibility, meaning that the plants can't self-fertilize. This is important for breeding programs as it means that it is not necessary to emasculate (remove the anthers from) C. florida flowers before making controlled cross-pollinations. These pollinations should be repeated every other day, as the flowers must be cross-pollinated within one or two days of opening for pollinations to be effective.

Softwood cuttings taken in late spring or early summer from new growth can be rooted under mist if treated with 8,000 to 10,000 ppm indole-3-butyric acid (IBA). In cold climates, potted cuttings must be kept in heated cold frames or polyhouses the following winter to maintain temperatures between 0 and 7 C. Although rooting success can be as high as 50–85%, this technique is not commonly used by commercial growers. Rather, selected cultivars are generally propagated by T-budding in late summer or by whip grafting in the greenhouse in winter onto seedling rootstock.

Micropropagation of flowering dogwood is now used in breeding programs aiming to incorporate resistance to dogwood anthracnose and powdery mildew into horticulturally and economically important cultivars. Nodal (axillary bud) sections are established in a culture of Woody Plant Medium (WPM) amended with 4.4 μmol/L 6-Benzyladenine (BA) to promote shoot growth. Rooting of up to 83% can be obtained when 5–7 week-old microshoots are then transferred to WPM amended with 4.9 μmol/L IBA.

Diseases
Dogwood anthracnose caused by the fungi Discula destructiva has caused severe mortality of dogwoods. In regions where dogwood anthracnose is a problem, homeowners and public land managers are encouraged to know the symptoms and inspect trees frequently. The selection of healthy, disease-free planting stock is essential and transplanting trees from the forest, particularly from mountain forests, should be avoided. Species of Phytophthora cause root rot.

Historical uses
Native Americans used the bark and roots in a remedy for malaria; a red dye was also extracted from the roots. The species has been used in the production of inks, scarlet dyes, and as a quinine substitute. The hard, dense wood has been used for products such as golf club heads, mallets, wooden rake teeth, tool handles, jeweler's boxes and butcher's blocks. Cornus florida is the state tree and flower of Virginia, the state tree of Missouri, and state flower of North Carolina. It was used to treat dogs with mange, which may be how it got its name. The red berries are not edible, despite some rumors otherwise.

In 1915, 40 dogwood saplings were donated by the U.S. to Japan in the 1912-15 exchange of flowers between Tokyo and Washington, D.C. While the cherry blossom trees survived the ensuing sour relations of these two countries and are the main feature of the National Cherry Blossom Festival, all dogwood trees in Tokyo died except the one that had been planted in an agriculture high school. In 2012, the United States sent 3,000 dogwood saplings to Japan to commemorate the 100th anniversary of the Washington, D.C., cherry trees given as a gift to the U.S. by Japan in 1912.

title: Cornus florida


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M45

M45 or variants may refer to:

Military equipment

 * Carl Gustaf m/45, a 9×19mm Swedish submachine gun
 * M45, a variant of the M26 Pershing heavy/medium tank of the United States Army
 * Madsen M1945, a 9x19mm Danish submachinegun, also referred to as the M45
 * M45 (missile), a French Navy submarine-launched ballistic missile
 * M45 Quadmount, a weapon mounting consisting of four "heavy barrel" .50 caliber M2 Browning machine guns
 * MEU(SOC) pistol (also M45 MEUSOC), a magazine-fed, recoil-operated, single-action, semiautomatic pistol
 * M45, a gas mask currently issued in the United States

Transport

 * Infiniti M45, a rebadged Japanese-spec Nissan Gloria of the Infiniti M line
 * M-45 (Michigan highway), a state trunkline highway in the US state of Michigan
 * M-45 (Spain), a highway bypass built in the Community of Madrid of regional importance
 * M45 (Cape Town), a Metropolitan Route in Cape Town, South Africa
 * M45 (Johannesburg), a Metropolitan Route in Johannesburg, South Africa
 * M45 (Durban), a Metropolitan Route in Durban, South Africa
 * M45 motorway, a motorway in Northamptonshire and Warwickshire, England

Other

 * M 45, an age category of masters athletics
 * M45, a single-nucleotide polymorphism that is a component of Haplogroup P1
 * Pleiades (also M45), an open star cluster containing middle-aged, hot B-type stars
 * Yahoo M45, a computer cluster announced in November 2007 by Yahoo

title: M45


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Talk:1995 in American television

Untitled
Let's move this to "USA Television in 1995". It is completely and deliberately constructed to be just that, so let's name it what it is. -- Infrogmation

NO. See the other page. I've been including non-US information when I find it. You're ignoring all of that apparently. I've included tons of info about the BBC and other non-US television. I have NOT intentionally focused on American television, but its difficult because I am in the US and that info is easier for me to find. Help. Don't destroy the articles. -Jazz77

 * Again, I am certainly not trying to "destroy" any pages or information. See Talk:List of 'years in television' for further discussion. -- Infrogmation

Does anyone know why the "First television program broadcast via the Internet" isn't specified by name? -- Editor B

First TV Show on Internet?
I have reason to believe that Computer Chronicles was not the first TV show on the Internet. I think it was a television series called ROX, which debuted on the Internet on April 15th of 1995.

I am reluctant to make that change to the timeline myself, though, because I was and am involved in the production of ROX. I am very obviously biased! I don't think it would be contrary to the spirit of Wikipedia for me to make to make such a change. I respect the Wikipedia project too much to engage in self-aggrandizement. I hope my comments are not perceived as such.

Nevertheless, I would like to offer the following evidence. Below I am pasting the text of an article which appeared in Time magazine on May 1st, 1995.

Joe Nickell and Bart Everson, a couple of goofy, twentysomething guys from Bloomington, Indiana, are sick of small fame. For three years their satirical public-access TV show has played to critical acclaim in the greater Bloomington area, but it has never attracted the kind of national attention that would capture a slot on network TV. Though local sponsors chip in enough to keep Everson clothed, housed and fed, Nickell still has to support himself as a waiter. So the pair set their sights beyond broadcast TV, beyond cable TV, to the computer networks. Last week, as their 85th episode, Global Village Idiots, was flickering across Bloomington televisions, it was simultaneously stored on the Internet, where millions of people worldwide could retrieve it -- the first television show broadcast in cyberspace.

[Emphasis added]

Although the "satirical public-access TV show" is not mentioned by name, it is in fact ROX, as my second piece of evidence makes clear: This article from Wired Magazine, dated December 1995.

As for Computer Chronicles, I see that they are cited on a number of web pages as the first show on the Internet, but I can't find a precise date (only the year 1995) or any documentation that seems authoritative. I do know that I have researched this topic several times over the past 12 years and that I'd never seen this claim for Computer Chronicles until recently.

If anyone else out there -- Ezhiki? -- finds this evidence compelling, please make a change to the timeline. I won't do it myself for the reasons cited above. If I can answer any questions regarding this I will be happy to do so. I can provide more evidence to support this claim in the form of USENET posts and personal journal entries.

I hope that I am pursuing this matter in the right way. I'm new enough to Wikipedia that I'm not sure of myself. I would welcome any advice.

--Editor B 17:38, Oct 28, 2004 (UTC)

 * Hi, Editor B! I added Computer Chronicles merely per results of the Google search.  Your evidence seems compeling enough for me to accept it, and I do not have any particular reasons not to believe you, but since I am not all that knowledgeable about the subject, I'd prefer to maybe mention both ROX and the Chronicles, and then wait for someone more informed to come along and clarify the issue.  Sorry for not being of much help here.—Ëzhiki (erinaceus europeaus) 18:08, Oct 28, 2004 (UTC)

 * That seems eminently reasonable, especially given the absence of a precise date for Computer Chronicles' debut. I contacted them for clarification last week but haven't heard anything yet.--Editor B 18:14, Oct 28, 2004 (UTC)

 * Here's the Usenet post to which I referred. It is dated April 18, 1995. --Editor B 20:00, Oct 29, 2004 (UTC)

I've edited the article to include both ROX and the Chronicles. Please feel free to edit it if/when you have more information.

I also have a question—the Time article says that ROX was was simultaneously stored on the Internet, where millions of people worldwide could retrieve it. To me, this does not seem to be a broadcast; it sounds more like sharing a show on a P2P network or uploading it to an FTP server today. Of course, it would still be a big deal in 1995, and I am not trying to belittle the merit of this event. I am, however, wondering, if the Chronicles was actually the first show that had been streamed, not just stored somewhere where it would be accessible to public.—Ëzhiki (erinaceus europeaus) 16:46, Nov 2, 2004 (UTC)

 * Thanks. I do appreciate your attention to this historical detail. I still haven't heard from the producers of Chronicles, but I do know that video streaming as we think of it today simply did not exist in early 1995. The Time article about ROX dwelt mostly on Rob Glaser's RealAudio, which was considered revolutionary because it made streaming audio possible. Perhaps Chronicles was on the Mbone. The Mbone might seem closer to traditional broadcasting. The band Severe Tire Damage was on the Mbone in 1993; they appeared on the Chronicles in 1995, and I suspect that this may have been the first Chronicles on the Internet, but I can't find anything conclusive. Even more frustrating: one source indicates this appearance took place in March -- others say May! I will keep looking.--Editor B 03:35, Nov 5, 2004 (UTC)

title: Talk:1995 in American television


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Gentile

Gentile is a word that today usually means someone who is not Jewish. Other groups that claim Israelite heritage, notably Mormons, have historically used the term gentile to describe outsiders. More rarely, the term is used as a synonym for heathen, pagan or any non-circumcised person, regardless of ancestry. As a term used to describe non-members of a religious/ethnic group, gentile is sometimes compared to other words used to describe the "outgroup" in other cultures (see List of terms for ethnic out-groups).

In some translations of the Quran, gentile is used to translate an Arabic word that refers to non-Jews and/or people not versed in or not able to read scripture.

The English word gentile derives from the Latin word, meaning "of or belonging to the same people or nation". Archaic and specialist uses of the word gentile in English (particularly in linguistics) still carry this meaning of "relating to a people or nation." The development of the word to principally mean "non-Jew" in English is entwined with the history of Bible translations from Hebrew and Greek into Latin and English. Its meaning has also been shaped by Rabbinical Jewish thought and Christian theology which, from the 1st century, have often set a binary distinction between "Jew" and "non-Jew."

Etymology
"Gentile" derives from Latin gentilis, which itself derives from the Latin gens, meaning clan or tribe. Gens derives from the Proto-Indo-European *ǵénh₁tis, meaning birth or production. The original meaning of "clan" or "family" was extended in post-Augustan Latin to acquire the wider meaning of belonging to a distinct nation or ethnicity. Later still, the word came to refer to other nations, 'not a Roman citizen'.

In Saint Jerome's Latin version of the Bible, the Vulgate, gentilis was used along with gentes, to translate Greek and Hebrew words with similar meanings when the text referred to the non-Israelite peoples. The most important of such Hebrew words was goy (, plural, goyim), a term with the broad meaning of "people" or "nation" which was sometimes used to refer to Israelites, but with the plural form goyim tending to be used in the Bible to refer to non-Israelite nations. Other words translated in some contexts to mean "gentile/s" in the modern sense were the Biblical Hebrew word nokhri ( – often otherwise translated as 'stranger') and for the New Testament Greek word éthnē (ἔθνη). The first English translators followed this approach, using the word "gentile" to refer to the non-Israelite nations (and principally using the word "nation(s)" to translate goy/goyim in other contexts). See the "Christianity" section.

These developments in Bible translation practice were related to developments in Jewish Rabbinical and Christian thinking which – in the centuries after the Old and New Testament were written – created an increasingly clear binary opposition between "Jew" and "non-Jew". The Hebrew word "goy" went through a change in meaning which parallels the journey of "gentilis/gentile" – both words moving from meaning "nation" to "non-Jew" today. The word "Goy" is now also used in English, principally by Jewish people – see goy.

The Hebrew Bible
In 2006, the academic David Novak wrote, with limited exceptions, "The Bible can be seen as one long discussion of what differentiates Israel from all the other peoples of the world."

The Hebrew Bible does not have a word which directly corresponds to the modern concept of a gentile (see etymology above). Instead, the Bible views different groups of gentiles in different ways. Novak states that, "The biblical categories of Gentiles, beginning with those farthest removed from a relationship with Israel and moving up to those closest to a relationship with Israel, seem to be: (1) the Amalekites; (2) the seven Canaanite nations; (3) the nations of the world; (4) the Samaritans; (5) slaves; (6) resident aliens; (7) proselytes."

The Hebrew Bible does not show much concern for non-Israelites except insofar as they interact with the people of Israel. Nonetheless, because the God of Israel is a universal God, there must be some relationship between gentiles and God. Accordingly, Novak observes, gentiles as well as Israelites are enjoined in the book of Psalms to "ascribe to the Lord glory and strength".

Christine E. Hayes states that gentiles in the Hebrew Bible were generally gerim (resident aliens). They were not necessarily converts, whether in the modern or rabbinic sense, but were still given many rights and privileges. They were also allowed to keep their distinct ethnic identities. But after Ezra-Nehemiah, many Israelites believed there was an impermeable ritual and genealogical boundary between themselves and gentiles. However, other scholars argue that the boundary is rooted in religious factors.

Saul Oylan argues that gentiles automatically became Israelite when they lived in one of their tribal territories, which was believed to reflect 'early practices'.

Troy W. Martin believes Jewishness is defined by adherence to covenantal circumcision, regardless of ancestry. Thus, even an uncircumcised Jew could be a gentile despite his biological descent from Abraham. He believes this view was extended to the New Testament, where membership in God's chosen people was based on religious adherence rather than ancestry.

Tannaim
Tannaim were the rabbinic sages whose views are recorded in the Mishnah, from approximately 10–220 CE.

It was this rabbinic literature of the first centuries CE that developed the concept of the gentile as we understand it today - as "any individual who is not a Jew, erasing all ethnic and social differences among different others". "'Mishnah-Tosefta makes no clear distinction among the various types of non-Israelites. Romans, Greeks, Syrians, Egyptians, and the like are classified merely as gentiles, goyim or nokrim' 'The rabbis... had one term for all non-Israelites, whether idolaters or farmers, liars or trustworthy, Greek or Roman.'"

However, the attitudes of the Rabbis to gentiles were not simple or uniform. Porton argues that the Mishnah-Tosefta discusses gentiles for two quite different reasons: firstly, practically, to guide the relations between Israelites and gentiles who were living alongside each other in Palestine. Secondly, at a theoretical level, gentiles are discussed because, in order to define the people of Israel and its symbols and institutions, it was necessary to define who lay outside that group.

Some Tannaim show a positive attitude towards the gentiles. Joshua ben Hananiah believed that there are righteous men amongst the gentiles who will enter the world to come. He believed that except for the descendants of the Amaleks, the rest of the gentiles will adopt monotheism and the righteous among them will escape Gehenna.

Other rabbinical writings show more hostility towards gentiles which needs to be understood in the context of frequent persecution of the Jews in this period. The most famous and extreme of the anti-gentile teachers is Simeon bar Yochai. He is often quoted by antisemites in his sayings: "The best among the Gentiles deserves to be killed", "The most pious woman is addicted to sorcery" and "The best of snakes ought to have its head crushed". Such extreme views can be explained by the sage's life experience: he witnessed his teacher being tortured to death, and became a fugitive after speaking out against Roman oppression.

Eliezer ben Hurcanus writes that the mind of every gentile is always intent upon idolatry. He believed that gentiles only perform animal sacrifice to make a name for themselves. He further believed that gentiles have no share in the world to come.

Eleazar of Modi'im wrote that Jews, when guilty of the same sin as gentiles, will not enter hell whereas the gentiles will. Eleazar ben Azariah believed that the rulings performed by a gentile court are not valid for Jews. Rabbi Akiva believed that Israel's monotheism is far superior to the ever-changing beliefs of the gentiles. Jose the Galilean criticizes Israel for inconsistency compared to the faithfulness of the gentiles to their ancestral beliefs. He believed the good deeds of the gentiles will be rewarded as well.

Later sages
Rav Ashi believed that a Jew who sells a gentile property adjacent to a Jewish property should be excommunicated. The violation of Jewish women by gentile men was so frequent that the rabbis declared that a woman raped by a gentile should not be divorced from her husband, as Torah says: "The Torah outlawed the issue of a gentile as that of a beast." A gentile midwife was not to be employed for fear of the poisoning of the baby. The gentiles should be dealt with caution in cases of using them as witness in a criminal or civil suit. The gentile does not honor his promises like that of a Jew. The laws of the Torah were not to be revealed to the gentiles, for the knowledge of these laws might give gentiles an advantage in dealing with Jews. Shimon ben Lakish wrote that "A gentile who observes Sabbath deserves death".

In modern times
Under rabbinic law, a modern-day gentile is only required to observe the Seven Laws of Noah, but Jews are required to observe Mosaic law. During periods of decreased animosity between Jews and gentiles, some of the rabbinic laws against fellowship and fraternization were relaxed; for example, Maimonides was the personal physician of Saladin. Even though most contemporary rabbinic schools are not as hostile to Gentiles as Medieval rabbinic schools were, some Orthodox rabbinic schools hold extremely xenophobic views. For example, scholars from the Zionist HaRav Kook yeshiva are schooled in the doctrine that Jews and gentiles have different kinds of souls. One of the yeshiva's scholars, David Bar-Hayim, published a paper in 1989 in which he explained the doctrine, entitled "Yisrael Nikraim Adam" (Jews Are Called 'Men'). In his conclusion, Bar-Hayim writes: "There is no escaping the facts: the Torah of Israel makes a clear distinction between a Jew, who is defined as "Man," and a Gentile. This distinction is expressed in a long list of Halachic laws, be they monetary laws, the laws of the Temple, capital laws or others. Even one who is not an erudite Torah scholar is obligated to recognize this simple fact; it cannot be erased or obscured ... One who carefully studies the sources cited previously will realize the abysmal difference between the concepts "Jew" and "Gentile" -- and consequently, he will understand why Halacha differentiates between them."

Bar-Chayim further quotes Abraham Isaac Kook (1865–1935), founder of the yeshiva and the first Ashkenazi chief rabbi of British Mandatory Palestine: "The difference between the Jewish soul, in all its independence, inner desires, longings, character and standing, and the soul of all the Gentiles, on all of their levels, is greater and deeper than the difference between the soul of a man and the soul of an animal, for the difference in the latter case is one of quantity, while the difference in the first case is one of essential quality."

Similar anti-gentile remarks have been expressed by the late chief Sephardi Rabbi Ovadia Yosef, in which he stated in a sermon in 2010 that "The sole purpose of Gentiles is to serve Jews". He said that gentiles served a divine purpose: "Why are Gentiles needed? They will work, they will plow, they will reap. We will sit like an effendi and eat. That is why Gentiles were created. These remarks by Yosef were sharply criticized by many Jewish organizations such as the Anti-Defamation League (ADL) and American Jewish Committee.

Jewish philosopher and professor Menachem Kellner criticizes the assumption of some Orthodox Jews that there is an "ontological divide between Jews and Gentiles", which he believes is contrary to what the Torah teaches.

In Kabbalah
Some Kabbalistic writings suggest a distinction between the souls of the gentiles and the souls of the Jews. These writings describe three levels, elements, or qualities of soul:
 * Nefesh (נפש): the lower part, or "animal part", of the soul. It is linked to instincts and bodily cravings. This part of the soul is provided at birth.
 * Ruach (רוח): the middle soul, the "spirit". It contains the moral virtues and the ability to distinguish between good and evil.
 * Neshamah (נשמה): the higher soul, or "super-soul". This separates man from all other life-forms. It is related to the intellect and allows man to enjoy and benefit from the afterlife. It allows one to have some awareness of the existence and presence of God.

Other descriptions of the soul add two more levels Chaya and Yechida.

There has been debate among the kabbalists on whether gentiles access the mystical knowledge (Daat). Isaac Luria, prominent kabbalist, wrote:"Israel possesses the three levels of soul, nefesh, ruah, neshamah,—from holiness... the gentiles possess only the level of nefesh from the feminine side of the shells... for the souls of the nations (gentiles), come from the Qlippoth, are called evil and not good' since they are created without knowledge (Daat). The animal soul of man is the good and evil inclination. The soul of the gentiles comes from the three shells: wind, cloud and fire, all of them evil."

Moses de León, presumed author of the main kabbalistic work Sefer Ha-Zohar, agrees with this assumption:"You know that all of the gentiles (goyim) and all of their matters are in the category of the impure... you must know and discern that the gentiles come from the side of impurity, for the souls of the gentiles derive from the side of impurity"

The following passage in the Zohar reaffirms this idea:"Said Rabbi Hiyya: If this is true (that neshamah is acquired through following the Torah) is it so that gentiles have no neshamah, only the living nefesh? Rabbi Yohannan said: That is correct."

The view that gentiles only possess bestial souls was more popularized by the main kabbalistic text of hasidic movement, the Tanya (or Likkutei Amarim). Rabbi Shneur Zalman of Liadi, the founder of the Chabad hasidic dynasty, claims that Jews like gentiles possess a vital animal soul, but the animal soul of the Jew comes from the fourth husk (Qlippoth nogah), while the animal soul of the gentiles comes from the three lower impure husks (Qlippoth Tumaot). Thus nothing gentiles do can elevate them to the level of holiness, their soul remains trapped in the unholy world of the impure Qlippoth.

However, other Kabbalists like Abraham Abulafia believed that higher levels of soul are to some extent accessible to gentiles.

Christianity
The Greek ethnos where translated as "gentile" in the context of early Christianity implies non-Israelite. In the years after the ministry of Jesus, there were questions over the inclusion of non-Jews and the applicability of the Law of Moses, including circumcision. Over a few centuries, this led to a split between Jewish Christians, who followed Jesus but also Mosaic Law, and Pauline Christianity (also known as Gentile Christianity) which abandoned Mosaic Law and eventually became the official religion of the Roman Empire. Jewish Christian beliefs died out around the fifth century, after being rejected by both orthodox Judaism and orthodox Christianity.

With the ministry of Paul the Apostle the gospel began to be spread among the non-Jewish subjects of the Roman empire. A question existed among the disciples whether receiving the Holy Spirit through proselytization would be restricted to Israelites or whether it would include the gentiles as in : "And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?"

Within a few centuries, some Christians used the word "gentiles" to mean non-Christians. The alternative pagani was felt to be less elegant.

Christian Bibles
In the King James Version, "gentile" is only one of several words used to translate goy or goyim. It is translated as "nation" 374 times, "heathen" 143 times, "gentiles" 30 times, and "people" 11 times. Some of these verses, such as Genesis 12:2 ("I will make of thee a great nation") and Genesis 25:23 ("Two nations are in thy womb") refer to Israelites or descendants of Abraham. Other verses, such as Isaiah 2:4 and Deuteronomy 11:23 are generic references to any nation. Typically, the KJV restricts the translation to "gentile" when the text is specifically referring to non-Jewish people. For example, the only use of the word in Genesis is in chapter 10, verse 5, referring to the peopling of the world by descendants of Japheth, "By these were the isles of the Gentiles divided in their lands; every one after his tongue, after their families, in their nations."

In the New Testament, the Greek word ethnos is used for peoples or nations in general, and is typically translated by the word "people", as in John 11:50. ("Nor consider that it is expedient for us, that one man should die for the people, and that the whole nation perish not.") The translation "gentiles" is used in some instances, as in Matthew 10:5–6 to indicate non-Israelite peoples: "These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: But go rather to the lost sheep of the house of Israel."

Altogether, the word is used 123 times in the King James Version of the Bible, and 168 times in the New Revised Standard Version.

The Church of Jesus Christ of Latter-day Saints
In the terminology of the Church of Jesus Christ of Latter-day Saints (LDS Church), the word "gentile" can be used to refer to people who are not members of the LDS Church, since members regard themselves as regathered Israelites. The LDS Church's website states this about the meaning of gentile in Scripture (including the Book of Mormon), "As used in the scriptures, gentiles has several meanings. Sometimes it designates people of non-Israelite lineage, sometimes people of non-Jewish lineage, and sometimes nations that are without the gospel, even though there may be some Israelite blood among the people. This latter usage is especially characteristic of the word as used in the Book of Mormon and Doctrine and Covenants."

Thus, in such usage, Jewish people may be gentiles because they are not members of the LDS Church.

Beyond this Scriptural usage, gentile was widely used by Mormons in day-to-day life in the nineteenth century, with such usage declining through the twentieth century. As with the binary jew/gentile distinction, the mormon/gentile distinction arose as Mormons were socially excluded and ostracised: according to John L. Needham of Utah State University: "'Nineteenth century Mormons in the American West applied 'gentile', as an adjective as much as a slur, to nearly everyone and everything that did not adhere to their faith or desert kingdom. Their xenophobia stood to reason: they were victims of religious discrimination, from ridicule in the press to acts of mob violence. They had been driven from a half dozen eastern states and were denied asylum in all others. Gentile thus served as a call to circle the wagons socially and politically around the fold - a means of naming the other'" Needham goes on to say that today Mormons have "outgrown the term."

Islam
Some translations of the Quran, such as the famous Pickthall translation, employed the word "gentile" in some instances of the translation of the Arabic word الْأُمِّيِّينَ (al-ʼummiyyīn), the definite non-nominative masculine plural of أُمِّيّ (ʼummiyy), as in, for example, the following verse: "Among the People of the Scripture there is he who, if thou trust him with a weight of treasure, will return it to thee. And among them there is he who, if thou trust him with a piece of gold, will not return it to thee unless thou keep standing over him. That is because they say: We have no duty to the Gentiles. They speak a lie concerning Allah knowingly. -"

The word ummi occurs six times in the Quran. Pickthall only uses the word gentile once in the above passage and translates other occurrences as illiterate. However many other western scholars of the Quran came to similar conclusion that the word ummi is equal to the hebrew word Goyim. Edward Henry Palmer used the word gentile in his translation of the Quran several times including in the following verse:"He is who sent unto the Gentiles a prophet amongst themselves to recite to them his signs and to purify them the book and wisdom although they were before in obvious error. -Quran 62:2" Palmer like Pickthall did not translate all instances of the word ummi as Gentiles, but his comment on chapter 3 verse 19 shows his opinion :"Mohammad seems to have borrowed the expression from the Jews, ummiyyun having the same significance as Hebrew Goyim." Edward William Lane similarly believed that the word ummi is identical to the Hebrew Goyim as demonstrated in the following quote :"Ummi probably means gentile- in a secondary sense a heathen; one not having revealed a scripture; or belonging to the nation of the Arabs, who did not write nor read, and therefore metaphorically applied to anyone not knowing the art of writing nor that of reading. Mohammad was termed ummi, meaning a gentile, as distinguished from an Israelite." John Medows Rodwell in his translation of the Quran comments similarly in a note on chapter 52 verse 157 that the word ummi is equivalent to the Greek ethnos and the Hebrew goyim, and was applied by Jews to those who did not know scripture. Elwood Morris Wherry wrote that almost certainly "this appellation came originally from the Jews who used it in expressing their contempt for the Gentile prophet." Some Muslim scholars also agreed with this idea: a French translation of the Quran by Muhammad Hamidullah uses the expression 'gentile prophet' in Sura 7 verse 157-8. Muhammad Shahrur also believed that ummi prophet means gentile prophet in his book Al-Kitab wa-L-Quran (The Book and the Quran). Abul A'la Maududi similarly translated the following instance as gentile. "He it is who has sent to the gentiles a Messenger from among themselves, one who rehearses to them his verses, purifies their lives, and imparts to them the book and the wisdom although before that they were in utter error. -Quran 62:2" Maududi clarifies in notes on this verse that the reason this verse has been sent is because Jews looked down on Arabs as gentiles and did not believe that a prophet can rise from their kind. However vast majority of Islamic scholars and translations made by Muslims are of the idea that ummi means illiterate.

title: Gentile