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Pixel density

Pixels per inch (ppi) and pixels per centimetre (ppcm or pixels/cm) are measurements of the pixel density of an electronic image device, such as a computer monitor or television display, or image digitizing device such as a camera or image scanner. Horizontal and vertical density are usually the same, as most devices have square pixels, but differ on devices that have non-square pixels. Pixel density is not the same as resolution—where the former describes the amount of detail on a physical surface or device, the latter describes the amount of pixel information regardless of its scale. Considered in another way, a pixel has no inherent size or unit (a pixel is actually a sample), but when it is printed, displayed, or scanned, then the pixel has both a physical size (dimension) and a pixel density (ppi).

Basic principles
Since most digital hardware devices use dots or pixels, the size of the media (in inches) and the number of pixels (or dots) are directly related by the 'pixels per inch'. The following formula gives the number of pixels, horizontally or vertically, given the physical size of a format and the pixels per inch of the output:

 * $$\text{Number of Pixels} = \text{Size in Inches} * \text{PPI}$$

Pixels per inch (or pixels per centimetre) describes the detail of an image file when the print size is known. For example, a 100×100 pixel image printed in a 2 inch square has a resolution of 50 pixels per inch. Used this way, the measurement is meaningful when printing an image. In many applications, such as Adobe Photoshop, the program is designed so that one creates new images by specifying the output device and PPI (pixels per inch). Thus the output target is often defined upon creating the image.

Outputting to a different device
When moving images between devices, such as printing an image that was created on a monitor, it is important to understand the pixel density of both devices. Consider a 23″ HD monitor (20″ wide), that has a known, native resolution of 1920 pixels (horizontal). Let us assume an artist created a new image at this monitor resolution of 1920 pixels, possibly intended for the web without regard to printing. Rewriting the formula above can tell us the pixel density (PPI) of the image on the monitor display:
 * $$\text{PPI (monitor)} = \frac{\text{Number of Pixels}}{\text{Size in Inches}} = \frac{1920}{20} = 96\text{ ppi}$$

Now, let us imagine the artist wishes to print a larger banner at 48″ horizontally. We know the number of pixels in the image, and the size of the output, from which we can use the same formula again to give the PPI of the printed poster:
 * $$\text{PPI (poster)} = \frac{\text{Number of Pixels}}{\text{Size in Inches}} = \frac{1920}{48} = 40\text{ ppi}$$

This shows that the output banner will have only 40 pixels per inch. Since a printer device is capable of printing at 300 ppi, the resolution of the original image is well below what would be needed to create a decent quality banner, even if it looked good on a monitor for a website. We would say more directly that a 1920 × 1080 pixel image does not have enough pixels to be printed in a large format.

Printing on paper
Printing on paper is accomplished with different technologies. Newspapers and magazines were traditionally printed using a halftone screen, which would print dots at a given frequency, the screen frequency, in lines per inch (LPI) by using a purely analog process in which a photographic print is converted into variable sized dots through interference patterns passing through a screen. Modern inkjet printers can print microscopic dots at any location, and don't require a screen grid, with the metric dots per inch (DPI). These are both different from pixel density or pixels per inch (PPI) because a pixel is a single sample of any color, whereas an inkjet print can only print a dot of a specific color either on or off. Thus a printer translates the pixels into a series of dots using a process called dithering. The dot pitch, smallest size of each dot, is also determined by the type of paper the image is printed on. An absorbent paper surface, uncoated recycled paper for instance, lets ink droplets spread — so has a larger dot pitch.

Often one wishes to know the image quality in pixels per inch (PPI) that would be suitable for a given output device. If the choice is too low, then the quality will be below what the device is capable of—loss of quality—and if the choice is too high then pixels will be stored unnecessarily—wasted disk space. The ideal pixel density (PPI) depends on the output format, output device, the intended use and artistic choice. For inkjet printers measured in DPI it is generally good practice to use half or less than the DPI to determine the PPI. For example, an image intended for a printer capable of 600 dpi could be created at 300 ppi. When using other technologies such as AM or FM screen printing, there are often published screening charts that indicate the ideal PPI for a printing method.

Using the DPI or LPI of a printer remains useful to determine PPI until one reaches larger formats, such as 36" or higher, as the factor of visual acuity then becomes more important to consider. If a print can be viewed close up, then one may choose the printer device limits. However, if a poster, banner or billboard will be viewed from far away then it is possible to use a much lower PPI.

Computer displays
The PPI/PPCM of a computer display is related to the size of the display in inches/centimetres and the total number of pixels in the horizontal and vertical directions. This measurement is often referred to as dots per inch, though that measurement more accurately refers to the resolution of a computer printer.

For example, a 15-inch (38 cm) display whose dimensions work out to 12 inches (30.48 cm) wide by 9 inches (22.86 cm) high, capable of a maximum 1024×768 (or XGA) pixel resolution, can display around 85 PPI, or 33.46PPCM, in both the horizontal and vertical directions. This figure is determined by dividing the width (or height) of the display area in pixels by the width (or height) of the display area in inches. It is possible for a display to have different horizontal and vertical PPI measurements (e.g., a typical 4:3 ratio CRT monitor showing a 1280×1024 mode computer display at maximum size, which is a 5:4 ratio, not quite the same as 4:3). The apparent PPI of a monitor depends upon the screen resolution (that is, the number of pixels) and the size of the screen in use; a monitor in 800×600 mode has a lower PPI than does the same monitor in a 1024×768 or 1280×960 mode.

The dot pitch of a computer display determines the absolute limit of possible pixel density. Typical circa-2000 cathode ray tube or LCD computer displays range from 67 to 130 PPI, though desktop monitors have exceeded 200 PPI, and certain smartphone manufacturers' flagship mobile device models have been exceeding 500 PPI since 2014.

In January 2008, Kopin Corporation announced a 0.44 inch (1.12 cm) SVGA LCD with a pixel density of 2272 PPI (each pixel only 11.25μm). In 2011 they followed this up with a 3760-DPI 0.21-inch diagonal VGA colour display. The manufacturer says they designed the LCD to be optically magnified, as in high-resolution eyewear devices.

Holography applications demand even greater pixel density, as higher pixel density produces a larger image size and wider viewing angle. Spatial light modulators can reduce pixel pitch to 2.5 μm, giving a pixel density of 10,160 PPI.

Some observations indicate that the unaided human generally can't differentiate detail beyond 300 PPI. However, this figure depends both on the distance between viewer and image, and the viewer’s visual acuity. The human eye also responds in a different way to a bright, evenly lit interactive display from how it does to prints on paper.

High pixel density display technologies would make supersampled antialiasing obsolete, enable true WYSIWYG graphics and, potentially enable a practical “paperless office” era. For perspective, such a device at 15 inch (38 cm) screen size would have to display more than four Full HD screens (or WQUXGA resolution).

The PPI pixel density specification of a display is also useful for calibrating a monitor with a printer. Software can use the PPI measurement to display a document at "actual size" on the screen.

Calculation of monitor PPI
PPI can be calculated from the screen's diagonal size in inches and the resolution in pixels (width and height). This can be done in two steps:

where
 * 1) Calculate diagonal resolution in pixels using the Pythagorean theorem: $$d_p = \sqrt{w_p^2 + h_p^2}$$
 * 2) Calculate the PPI: $$PPI = \frac{d_p}{d_i}$$
 * 1) $$w_p$$ is width resolution in pixels
 * 2) $$h_p$$ is height resolution in pixels
 * 3) $$d_p$$ is diagonal size in pixels.
 * 4) $$d_i$$ is diagonal size in inches (this is the number advertised as the size of the display).

For example: These calculations may not be very precise. Frequently, screens advertised as “X inch screen” can have their real physical dimensions of viewable area differ, for example:
 * 1) For 15.6-inch screen with a 5120×2880 resolution you get $$\frac{\sqrt{5120^2 + 2880^2}}{15.6}$$ = 376.57 PPI.
 * 2) For 50-inch screen with a 8192×4608 resolution you get $$\frac{\sqrt{8192^2 + 4608^2}}{50}$$ = 188 PPI.
 * 3) For 27-inch screen with a 3840×2160 resolution you get $$\frac{\sqrt{3840^2 + 2160^2}}{27}$$ = 163 PPI.
 * 4) For 32-inch screen with a 3840×2160 resolution you get $$\frac{\sqrt{3840^2 + 2160^2}}{32}$$ = 138 PPI.
 * 5) For an old-school 10.1-inch netbook screen with a 1024×600 resolution you get $$\frac{\sqrt{1024^2 + 600^2}}{10.1}$$ = 117.5 PPI.
 * 6) For 27-inch screen with a 2560×1440 resolution you get $$\frac{\sqrt{2560^2 + 1440^2}}{27}$$ = 108.8 PPI.
 * 7) For a 21.5-inch (546.1 mm) screen with a 1920×1080 resolution you get $$\frac{\sqrt{1920^2 + 1080^2}}{21.5}$$ = 102.46 PPI;
 * Apple Inc. advertised their mid-2011 iMac as a "21.5 inch (viewable) [...] display," but its actual viewable area is 545.22 mm or 21.465 inches. The more precise figure increases the calculated PPI from 102.46 (using 21.5) to 102.63.
 * The HP LP2065 20 inch (50.8 cm) monitor has an actual viewable area of 20.1 inch (51 cm).
 * In a more significant case, some monitors such as the Dell UltraSharp UP3216Q (3840×2160 px) are advertised as a 32-inch "class" monitor (137.68 PPI), but the actual viewing area diagonal is 31.5 inches, making the true PPI 139.87.

Calculating PPI of camera view screens
Camera manufacturers often quote view screens in 'number of dots'. This is not the same as the number of pixels, because there are 3 'dots' per pixel – red, green and blue. For example, the Canon 50D is quoted as having 920,000 dots. This translates as 307,200 pixels (×3 = 921,600 dots). Thus the screen is 640×480 pixels.

This must be taken into account when working out the PPI. 'Dots' and 'pixels' are often confused in reviews and specs when viewing information about digital cameras specifically.

Scanners and cameras
"PPI" or "pixel density" may also describe image scanner resolution. In this context, PPI is synonymous with samples per inch. In digital photography, pixel density is the number of pixels divided by the area of the sensor. A typical DSLR, circa 2013, has 1–6.2 MP/cm2; a typical compact has 20–70 MP/cm2.

For example, Sony Alpha SLT-A58 has 20.1 megapixels on an APS-C sensor having 6.2 MP/cm2 since a compact camera like Sony Cyber-shot DSC-HX50V has 20.4 megapixels on an 1/2.3" sensor having 70 MP/cm2. The professional camera has a lower PPI than a compact camera, because it has larger photodiodes due to having far larger sensors.

Smartphones
Smartphones use small displays, but modern smartphone displays have a larger PPI rating, such as the Samsung Galaxy S7 with a quad HD display at 577 PPI, Fujitsu F-02G with a quad HD display at 564 PPI, the LG G6 with quad HD display at 564 PPI or – XHDPI or Oppo Find 7 with 534 PPI on 5.5-inch display – XXHDPI (see section below). Sony's Xperia XZ Premium has a 4K display with a pixel density of 807 PPI, the highest of any smartphone as of 2017.

Logical DPI values on Android
Android supports the following logical DPI values for controlling how large content is displayed:

Metrication
The digital publishing industry primarily uses pixels per inch but sometimes pixels per centimeter is used, or a conversion factor is given.

The PNG image file format only allows the meter as the unit for pixel density.

Image file format support
The following table show how pixel density is supported by popular image file formats. The cell colors used do not indicate how feature-rich a certain image file format is, but what density support can be expected of a certain image file format.

Even though image manipulation software can optionally set density for some image file formats, not many other software uses density information when displaying images. Web browsers, for example, ignore any density information. As the table shows, support for density information in image file formats varies enormously and should be used with great care in a controlled context.

title: Pixel density


text:
Talk:Yuppie

To describe Yuppies
Not all of them are white or of WASP origins, baby-boomer (that can include generation Xers) and urbanites from the east or west coasts. Nor the yuppies are selfish, neo-conservative, social liberal and obsessed with professionalism. I've heard of newer terms of BUPpies (Black Urban Professionals) and HUPs (Hispanic Urban Professionals), plus the Asian American image is usually of a yuppie one esp. in the urban areas of California known for university and hi-tech business operations in the then-launched booming web sites industry. + 71.102.11.193 (talk) 05:03, 22 May 2010 (UTC)

 * Although this article was nominated for deletion, the consensus was strongly in favor of keeping it. Loodog made the nomination, noting that it was a neologism. The arguments to keep, however were not particularly detailed or insightful, amounting basically to "It appears a lot, so it must be important". Unfortunately that conclusion does not assist in molding the article contents. What we're left with is a lot of people expressing their personal experience, backed with references to legitimize their perception. The article should be brief, not the heavy WP:SYNTHESIS that it is now. Also unpalatable, as you point out, is the very fuzzy definition of the word. Not just in identifying or isolating groups, but in the very concept that a particular person, of a particular color, of a particular age, of a particular political bias can be reduced to a label of a single word, where another person objectively cannot. "Yuppie" is highly subjective, politically correct, trendy verbiage. If a typical Wiki biographical article were to include the word, it would probably be struck as WP:PEACOCK or WP:BIAS. Note that in Wiki Advanced Search, it's very infrequently used in biographical articles. I'd be in favor of reducing this article to three or four sentences, including one that emphasizes the fuzzy nature of its usage. Regards, Piano non troppo (talk) 08:56, 22 May 2010 (UTC)

Burning Of Bombay Street
The 2011 BBC documentary "The Burning Of Bombay Street" has been cited by one Wiki user as containing evidence via graffiti on a wall in one scene that "yuppy" was in use in Belfast in 1969. The documentary actually contained much footage more recently filmed, Presenter Lawrence Pitkethly revisited the area with a BBC film crew, and any "yuppy" graffiti is from more recent years. From extensive reading and quoting of late 1960s Belfast newspapers for a study I did on "The Troubles" in 1997, I can say with confidence that the "yuppy" word was entirely absent. A word that was apparently emotive enough to inspire graffiti would surely not have been.

The Wiki user states that the graffiti refers to a desire for more social housing, not yuppy apartments, which is also a concern of more recent years.

(Solidsandie (talk) 02:14, 18 March 2011 (UTC))

Chicago Magazine May 1980
The claim that Chicago Magdazine was first purveyor of the "yuppie" word is unsubstantiated. The Wikipedia link beside the Chicago Magazine claim does not lead to a copy of the article. As an encyclopedia, I think we should remain impartial about this until a hard copy of the article becomes available somewhere. So far it is hearsay. The '80s web historian in the case linked to below is reserving judgement, and I believe that if we are to perform to professional encyclopedia standards, we should do the same. Please see link below:

(Solidsandie (talk) 03:28, 27 April 2011 (UTC))so i let him go

fg

More about the Chicago Magazine 1980 claim
We've already covered the fact that Chicago Magazine claims that Dan Rottenberg had first printed use of the "yuppie" word in that magazine in may 1980. We also know that there is another claim to the coining of the word from Joseph Epstein in 1982. Once again, the Wiki article reverted to backing the Chicago Magazine claim, although the Chicago magazine article is nowhere to be found on-line. The only satisfactory proof would surely be a hard copy of the article from 1980? Until that appears, I request that Wikipedia continues to adopt a neutral stance, simply recording that the first appearance of the word is contested.

What we have at the moment is two sources claiming two different things. It is worth noting my own experience as a writer on all things '80s: I received an e-mail from a lady claiming to have spotted a very early usage of the "yuppie" word in an American soap opera. Close examination of the episode in question by myself revealed that the phrase used was "upwardly mobile", not yuppie! There does seem to be some confusion about these two phrases. "Upwardly mobile", of course, is of somewhat older vintage than Yuppie.

It is also worth noting the view of the Times (UK) newspaper on yuppies at the time of the 1987 stock market crash:

"I've lost my shirt today as well as the money of a lot of other guys," said one stereotype of the Yuppies who swarmed to the financial world to reap the benefits of the Reagan boom -

Yuppies were generally seen as not only being "upwardly mobile", but anxious to take advantage of the opportunities offered them by the Reagan years.

I am actively seeking a genuine May 1980 copy of the Chicago Magazine article so that this controversy can be resolved once and for all. Until then, please can the Wiki article remain neutral? That would be the position of any other encyclopedia.

(Solidsandie (talk) 19:16, 5 August 2011 (UTC))

Connotation of the term?
The article briefly visits Yuppie being used as a negative term by people of lower income than the accused yuppies, but does not really clarify whether the term is pejorative or just purely descriptive and biased in that scenario. Can anybody expand on this, and update the article as such? Would anybody ever call themselves yuppies in a neutral or positive light, despite being somewhat self-flattering (describing oneself as upcoming). Any clarification here (or in the article) would be great. Thanks! Dataxpress (talk) 17:14, 15 November 2011 (UTC)

Spelling Mistake
If you actually pick up a dictionary book instead of just guessing you will see in dictionaries from the very early 1980's including the OED that it is actually yupe, meaning young urban professional employee. — Preceding unsigned comment added by 86.128.56.151 (talk) 22:33, 28 October 2013 (UTC)

External links modified
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alternative explaination
I was told it meant if asked were you willing to kiss a lot of ass and lose your self-respect in order to make a lot of money what would you say...yup 75.130.206.121 (talk) 22:41, 14 April 2016 (UTC)

Lists
These lists should be rewritten as paragraph and fully sourced re: WP:TRIVIA. -Classicfilms (talk) 16:09, 20 May 2016 (UTC)

In popular culture

 * Yuppie Drone, The Pheremones' 1985 hit.
 * In Duck Dynasty, Phil Robertson uses the term to describe one who had adapted to the urban lifestyle or a city slicker and could not hold their own if they were to have to go into survival mode. Robertson often calls his sons and daughters-in-law yuppies.
 * The Bonfire of the Vanities, by Tom Wolfe, a "satire of yuppie excess"
 * Bright Lights, Big City by Jay McInerney (McInerney himself has been called "the archetypal yuppie")
 * Family Ties, the TV show, features a young Michael J. Fox as the Republican coat-and-tie-wearing 'yuppie-in-the-making' Alex P. Keaton and his parents (played by Michael Gross and Meredith Baxter-Birney) as former hippies.
 * Fight Club, the 1996 Chuck Palahniuk novel and 1999 film adaptation, follows "a disenchanted yuppie ... numbed by the sterile materialism of modern life."
 * In John Carpenter's They Live, a pair of working class protagonists come into possession of sunglasses that reveal yuppies as predatory aliens.
 * Girl with Curious Hair by David Foster Wallace, a short story about a young Republican enjoying life after prep school with a group of punk rockers.
 * Slaves of New York by Tama Janowitz describes a later (early 1990s) evolution of the Yuppie, in which the upper tier made considerably more than the lower, supporting tier, the "slaves" of the title, who were trapped by rents and insufficient salaries into a struggle merely to stay afloat in Manhattan.
 * American Psycho, the 1991 Bret Easton Ellis novel and 2000 film about yuppie serial killer Patrick Bateman.
 * thirtysomething, U.S. TV series, seen as a representation of "yuppie angst" and midlife crisis.
 * Stuff White People Like, a satirical blog that pokes fun at generalizations and yuppie culture.
 * Wall Street, the 1987 film about stock traders, has been described as "encapsulation of 80s yuppie greed culture", particularly Bud Fox, Charlie Sheen's naive 20-something character.
 * Dr. Snow, the 1988 true-crime novel by Carol Saline tells the story of the FBI's four-year (1982-1986) investigation/manhunt that brought down the cocaine distribution ring engineered by Philadelphia dentist Larry Lavin (a.k.a. "Dr. Snow") and his Ivy League college mates, in what the Bureau recorded in its annals as "The Yuppie Conspiracy".
 * "Yuppy Love", a 1989 Only Fools and Horses episode based on Gordon Gekko from Wall Street, in which Del Boy reinvents himself as a yuppy and hangs out in trendy wine bars. Del's attempts at reinventing himself as a 'Yuppy' were a recurring theme over the next few seasons.
 * National Lampoon's Christmas Vacation, a 1989 comedy, features neighbors Todd and Margo as the quintessential yuppies.
 * Married... with Children, a Fox TV comedy sitcom (1987–97) featured the Bundy's neighbors: A couple led by twice-married Marcy D'Arcy (her two husbands Steve Rhodes and Jefferson D'Arcy are upwardly mobile men), a bipolar paleoliberal-neoconservative feminist banker who loathes their blue-collar neighbors and she bullies Al Bundy, a failed shoe salesman.
 * Jeff Goldblum's character in the 1983 movie The Big Chill is a quintessential yuppie who sold out his 1960s hippie ideals for money.
 * The Last Days of Disco features male characters in the early 1980s who complain that they are referred to as yuppies.
 * King of the Hill features the Hill family's next door neighbors, Kahn Souphanousinphone, Sr. and his wife, Minh. They are stereotypical yuppies based on a stereotype about Asian Americans. Khan and Minh are originally from Laos and moved to the U.S. through Anaheim, California, a known yuppie cultural center in Southern California and ended up in fictional Arlen, Texas.
 * "Yer So Bad" song by rock singer Tom Petty features the verse "My sister got lucky, married a Yuppie"
 * "Paranoid Android", a song from Radiohead's OK Computer album, features the lines "The dust and the screaming/The yuppies networking"
 * "Ghosts of the Overdoses", a song from Damien Dempsey's Seize the Day album, features the line "From the cities, to make way for all the Yuppies"
 * Irish soap opera Fair City had a week-long special in 2005 looking at the murkier side of yuppie life against the backdrop of property speculation reflecting the Celtic Tiger.
 * Alex, a long-running comic strip that features archetypal yuppie characters.
 * An episode of Portlandia titled "Pull Out King" features a sketch in which a character played by Jello Biafra awakes from a 28-year coma to discover that the world has been overrun by Yuppies (who identify themselves as being "Foodies," "Yogies," and one couple clarifying, "It's a Corgi!")

Related terms

 * Commentator David Brooks characterized yuppies as bourgeois bohemians, or Bobos, in his book Bobos in Paradise - the term became somewhat popular in the 2000s.
 * A buppie is a black urban professional.
 * A huppie is a Hispanic/Latino urban professional.
 * A guppie is a gay urban professional
 * DINKs (DINKY in the UK) is an acronym is for Dual Income, No Kids [Yet]; at least one authority considers this to be synonymous with "yuppie".
 * A scuppie is a Socially Conscious Upwardly-Mobile Person (the term is not commonly used).
 * A Brazilian playboy: while in first this term had the same usage as in English, from the 1990s to the 2010s it changed its meaning to a local version of yuppie which first appeared in Greater Rio de Janeiro. Stereotypes of the Brazilian playboys include being classist, womanizer and sexist, at least way more than their yuppie counterparts from more developed countries, which in turn is result of social anxieties of the poor and the lower middle class against the upper middle and upper classes, or being great seekers of social status and influence. They also, contrary to yuppies, do not fashionize intellectuality, and can or can not be socially liberal (social divisions between liberals and conservatives, specially in the upper classes, makes much less sense in Brazil than in the Anglosphere). In the 2000s, some lower middle and middle middle class Brazilians from Greater São Paulo formed a new urban subculture also called playboy which is little to not related to the former. Non-urban young professionals in Brazil are called by the slang agroboy. Also in São Paulo, the term coxinha gained more currency in the late-2000s, making playboy fall out in the early 2010s, when the usage spread around Brazil, especially after the 2013 Brazilian protests.
 * A winder is a young individual, uninhibited with regards to its own social success, and willing to comply only to a very soft (and versatile) set of moral standards.
 * Yuppification often replaces the word gentrification; it is the act of making something, someone, or someplace appealing and thus marketable to yuppie tastes.
 * Yuppie flu was a sometimes derisive, and inaccurate, term applied to chronic fatigue syndrome.
 * Yuppie food stamp is a slang term in the United States for a $20 bill, because ATMs there typically dispense only $20 bills.
 * Puppie is a poor urban professional (a.k.a. welfie and cheapie).
 * YURP is a term describing the diverse group of young professionals who are dedicated to rebuilding New Orleans, and many low-income locals accuse them of "carpetbaggery".
 * Yuppie Angst is when a yuppie experiences stress in pursuing a busy work schedule, anxiety attacks over minor fears or challenges, reckless driving on highways and overreacting in panic.
 * Yuppie Puppy, derogatory term, synonymous with Malibu Barbie or Malibu Ken i.e. the vacuous overly spoiled and narcissistic offspring of the aforementioned Yuppies.
 * Yuppiedom, a mockery of the term "kingdom" or a place of yuppies.
 * Yuppie Values, also a mocking of core beliefs, trends and behavioral traits of yuppies as more of upper-income liberalism or an evolution of "Hippie values" about trying new or exotic things while pursuing a money-based life.
 * Yuppie Values, also a mocking of core beliefs, trends and behavioral traits of yuppies as more of upper-income liberalism or an evolution of "Hippie values" about trying new or exotic things while pursuing a money-based life.

Other meanings
In South America, "yupi" or "yuppi" means pretty much the same thing, but stereotyped as being Chilean or Argentinian. In the 1980s and 90s, Chile had an economic growth spurt and even in the 2000s and 10s, their economy is rather strong, perhaps the most in Latin or South America. Argentina, like Italy and Spain in Europe, are viewed as a fertile ground for yuppies. The booms could produce a substantial number of young urban professionals in white-collar careers. 67.49.89.214 (talk) 16:09, 30 September 2016 (UTC)

Die Yuppie Scum
Needs a brief mention of "Die Yuppie Scum" phrase used for anti-gentrification protests and at the 1988 Democratic National Convention.

"Die Yuppie Scum" was also used for anti-gentrification protests in NYC

Yuppie was not without detractors, and at the 1988 Democratic National Convention, "Die Yuppie Scum" was the best selling button

Washington Post: "Maybe a horde of yuppies would sweep down from Buckhead and take over -- survival of the fittest. Janice Dagley of Kansas City was selling a lot of "Die Yuppie Scum" bumper stickers, though. Maybe computers and television could replace the whole thing."

La Times: Everybody has a cause, so it’s no surprise to see people with buttons and signs reading “Die Yuppie Scum.”

— Preceding unsigned comment added by 2600:1700:d591:5f10:316e:b09b:a12a:56ad (talk) 11:23, 17 July 2021 (UTC)

Chicago Magazine "Claim" Is Correct
I am not versed in the rationales for policies of Wikipedia, such as the rule against "original research" that seemingly excludes the most useful information. But, for the benefit of those who are desirous of the truth about the earliest known appearance of the word "yuppie," you should be aware that the 1980 Chicago Magazine occurrence of "yuppie" is not a "claim," it is a fact. I have seen the original article and it is cited by the Oxford English Dictionary, which has researchers who verify every citation. -- Fred Shapiro, Editor, New Yale Book of Quotations — Preceding unsigned comment added by 2601:192:100:3DA0:31E7:1401:7107:D36E (talk) 11:24, 20 December 2021 (UTC)

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

title: Talk:Yuppie


text:
Mirror symmetry (string theory)

In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.

Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathematical predictions have since been proven rigorously.

Today, mirror symmetry is a major research topic in pure mathematics, and mathematicians are working to develop a mathematical understanding of the relationship based on physicists' intuition. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theory, the formalism that physicists use to describe elementary particles. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.

Strings and compactification
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. These strings look like small segments or loops of ordinary string. String theory describes how strings propagate through space and interact with each other. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles.

There are notable differences between the world described by string theory and the everyday world. In everyday life, there are three familiar dimensions of space (up/down, left/right, and forward/backward), and there is one dimension of time (later/earlier). Thus, in the language of modern physics, one says that spacetime is four-dimensional. One of the peculiar features of string theory is that it requires extra dimensions of spacetime for its mathematical consistency. In superstring theory, the version of the theory that incorporates a theoretical idea called supersymmetry, there are six extra dimensions of spacetime in addition to the four that are familiar from everyday experience.

One of the goals of current research in string theory is to develop models in which the strings represent particles observed in high energy physics experiments. For such a model to be consistent with observations, its spacetime must be four-dimensional at the relevant distance scales, so one must look for ways to restrict the extra dimensions to smaller scales. In most realistic models of physics based on string theory, this is accomplished by a process called compactification, in which the extra dimensions are assumed to "close up" on themselves to form circles. In the limit where these curled up dimensions become very small, one obtains a theory in which spacetime has effectively a lower number of dimensions. A standard analogy for this is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling on the surface of the hose would move in two dimensions.

Calabi–Yau manifolds
Compactification can be used to construct models in which spacetime is effectively four-dimensional. However, not every way of compactifying the extra dimensions produces a model with the right properties to describe nature. In a viable model of particle physics, the compact extra dimensions must be shaped like a Calabi–Yau manifold. A Calabi–Yau manifold is a special space which is typically taken to be six-dimensional in applications to string theory. It is named after mathematicians Eugenio Calabi and Shing-Tung Yau.

After Calabi–Yau manifolds had entered physics as a way to compactify extra dimensions, many physicists began studying these manifolds. In the late 1980s, Lance Dixon, Wolfgang Lerche, Cumrun Vafa, and Nick Warner noticed that given such a compactification of string theory, it is not possible to reconstruct uniquely a corresponding Calabi–Yau manifold. Instead, two different versions of string theory called type IIA string theory and type IIB can be compactified on completely different Calabi–Yau manifolds giving rise to the same physics. In this situation, the manifolds are called mirror manifolds, and the relationship between the two physical theories is called mirror symmetry.

The mirror symmetry relationship is a particular example of what physicists call a physical duality. In general, the term physical duality refers to a situation where two seemingly different physical theories turn out to be equivalent in a nontrivial way. If one theory can be transformed so it looks just like another theory, the two are said to be dual under that transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena. Such dualities play an important role in modern physics, especially in string theory.

Regardless of whether Calabi–Yau compactifications of string theory provide a correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences. The Calabi–Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve problems in enumerative algebraic geometry, a branch of mathematics concerned with counting the numbers of solutions to geometric questions. A classical problem of enumerative geometry is to enumerate the rational curves on a Calabi–Yau manifold such as the one illustrated above. By applying mirror symmetry, mathematicians have translated this problem into an equivalent problem for the mirror Calabi–Yau, which turns out to be easier to solve.

In physics, mirror symmetry is justified on physical grounds. However, mathematicians generally require rigorous proofs that do not require an appeal to physical intuition. From a mathematical point of view, the version of mirror symmetry described above is still only a conjecture, but there is another version of mirror symmetry in the context of topological string theory, a simplified version of string theory introduced by Edward Witten, which has been rigorously proven by mathematicians. In the context of topological string theory, mirror symmetry states that two theories called the A-model and B-model are equivalent in the sense that there is a duality relating them. Today mirror symmetry is an active area of research in mathematics, and mathematicians are working to develop a more complete mathematical understanding of mirror symmetry based on physicists' intuition.

History
The idea of mirror symmetry can be traced back to the mid-1980s when it was noticed that a string propagating on a circle of radius $$R$$ is physically equivalent to a string propagating on a circle of radius $$1/R$$ in appropriate units. This phenomenon is now known as T-duality and is understood to be closely related to mirror symmetry. In a paper from 1985, Philip Candelas, Gary Horowitz, Andrew Strominger, and Edward Witten showed that by compactifying string theory on a Calabi–Yau manifold, one obtains a theory roughly similar to the standard model of particle physics that also consistently incorporates an idea called supersymmetry. Following this development, many physicists began studying Calabi–Yau compactifications, hoping to construct realistic models of particle physics based on string theory. Cumrun Vafa and others noticed that given such a physical model, it is not possible to reconstruct uniquely a corresponding Calabi–Yau manifold. Instead, there are two Calabi–Yau manifolds that give rise to the same physics.

By studying the relationship between Calabi–Yau manifolds and certain conformal field theories called Gepner models, Brian Greene and Ronen Plesser found nontrivial examples of the mirror relationship. Further evidence for this relationship came from the work of Philip Candelas, Monika Lynker, and Rolf Schimmrigk, who surveyed a large number of Calabi–Yau manifolds by computer and found that they came in mirror pairs.

Mathematicians became interested in mirror symmetry around 1990 when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that mirror symmetry could be used to solve problems in enumerative geometry that had resisted solution for decades or more. These results were presented to mathematicians at a conference at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California in May 1991. During this conference, it was noticed that one of the numbers Candelas had computed for the counting of rational curves disagreed with the number obtained by Norwegian mathematicians Geir Ellingsrud and Stein Arild Strømme using ostensibly more rigorous techniques. Many mathematicians at the conference assumed that Candelas's work contained a mistake since it was not based on rigorous mathematical arguments. However, after examining their solution, Ellingsrud and Strømme discovered an error in their computer code and, upon fixing the code, they got an answer that agreed with the one obtained by Candelas and his collaborators.

In 1990, Edward Witten introduced topological string theory, a simplified version of string theory, and physicists showed that there is a version of mirror symmetry for topological string theory. This statement about topological string theory is usually taken as the definition of mirror symmetry in the mathematical literature. In an address at the International Congress of Mathematicians in 1994, mathematician Maxim Kontsevich presented a new mathematical conjecture based on the physical idea of mirror symmetry in topological string theory. Known as homological mirror symmetry, this conjecture formalizes mirror symmetry as an equivalence of two mathematical structures: the derived category of coherent sheaves on a Calabi–Yau manifold and the Fukaya category of its mirror.

Also around 1995, Kontsevich analyzed the results of Candelas, which gave a general formula for the problem of counting rational curves on a quintic threefold, and he reformulated these results as a precise mathematical conjecture. In 1996, Alexander Givental posted a paper that claimed to prove this conjecture of Kontsevich. Initially, many mathematicians found this paper hard to understand, so there were doubts about its correctness. Subsequently, Bong Lian, Kefeng Liu, and Shing-Tung Yau published an independent proof in a series of papers. Despite controversy over who had published the first proof, these papers are now collectively seen as providing a mathematical proof of the results originally obtained by physicists using mirror symmetry. In 2000, Kentaro Hori and Cumrun Vafa gave another physical proof of mirror symmetry based on T-duality.

Work on mirror symmetry continues today with major developments in the context of strings on surfaces with boundaries. In addition, mirror symmetry has been related to many active areas of mathematics research, such as the McKay correspondence, topological quantum field theory, and the theory of stability conditions. At the same time, basic questions continue to vex. For example, mathematicians still lack an understanding of how to construct examples of mirror Calabi–Yau pairs though there has been progress in understanding this issue.

Enumerative geometry

Many of the important mathematical applications of mirror symmetry belong to the branch of mathematics called enumerative geometry. In enumerative geometry, one is interested in counting the number of solutions to geometric questions, typically using the techniques of algebraic geometry. One of the earliest problems of enumerative geometry was posed around the year 200 BCE by the ancient Greek mathematician Apollonius, who asked how many circles in the plane are tangent to three given circles. In general, the solution to the problem of Apollonius is that there are eight such circles.

Enumerative problems in mathematics often concern a class of geometric objects called algebraic varieties which are defined by the vanishing of polynomials. For example, the Clebsch cubic (see the illustration) is defined using a certain polynomial of degree three in four variables. A celebrated result of nineteenth-century mathematicians Arthur Cayley and George Salmon states that there are exactly 27 straight lines that lie entirely on such a surface.

Generalizing this problem, one can ask how many lines can be drawn on a quintic Calabi–Yau manifold, such as the one illustrated above, which is defined by a polynomial of degree five. This problem was solved by the nineteenth-century German mathematician Hermann Schubert, who found that there are exactly 2,875 such lines. In 1986, geometer Sheldon Katz proved that the number of curves, such as circles, that are defined by polynomials of degree two and lie entirely in the quintic is 609,250.

By the year 1991, most of the classical problems of enumerative geometry had been solved and interest in enumerative geometry had begun to diminish. According to mathematician Mark Gross, "As the old problems had been solved, people went back to check Schubert's numbers with modern techniques, but that was getting pretty stale." The field was reinvigorated in May 1991 when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that mirror symmetry could be used to count the number of degree three curves on a quintic Calabi–Yau. Candelas and his collaborators found that these six-dimensional Calabi–Yau manifolds can contain exactly 317,206,375 curves of degree three.

In addition to counting degree-three curves on a quintic three-fold, Candelas and his collaborators obtained a number of more general results for counting rational curves which went far beyond the results obtained by mathematicians. Although the methods used in this work were based on physical intuition, mathematicians have gone on to prove rigorously some of the predictions of mirror symmetry. In particular, the enumerative predictions of mirror symmetry have now been rigorously proven.

Theoretical physics
In addition to its applications in enumerative geometry, mirror symmetry is a fundamental tool for doing calculations in string theory. In the A-model of topological string theory, physically interesting quantities are expressed in terms of infinitely many numbers called Gromov–Witten invariants, which are extremely difficult to compute. In the B-model, the calculations can be reduced to classical integrals and are much easier. By applying mirror symmetry, theorists can translate difficult calculations in the A-model into equivalent but technically easier calculations in the B-model. These calculations are then used to determine the probabilities of various physical processes in string theory. Mirror symmetry can be combined with other dualities to translate calculations in one theory into equivalent calculations in a different theory. By outsourcing calculations to different theories in this way, theorists can calculate quantities that are impossible to calculate without the use of dualities.

Outside of string theory, mirror symmetry is used to understand aspects of quantum field theory, the formalism that physicists use to describe elementary particles. For example, gauge theories are a class of highly symmetric physical theories appearing in the standard model of particle physics and other parts of theoretical physics. Some gauge theories which are not part of the standard model, but which are nevertheless important for theoretical reasons, arise from strings propagating on a nearly singular background. For such theories, mirror symmetry is a useful computational tool. Indeed, mirror symmetry can be used to perform calculations in an important gauge theory in four spacetime dimensions that was studied by Nathan Seiberg and Edward Witten and is also familiar in mathematics in the context of Donaldson invariants. There is also a generalization of mirror symmetry called 3D mirror symmetry which relates pairs of quantum field theories in three spacetime dimensions.

Homological mirror symmetry

In string theory and related theories in physics, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.

In string theory, a string may be open (forming a segment with two endpoints) or closed (forming a closed loop). D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to a condition that it satisfies, the Dirichlet boundary condition.

Mathematically, branes can be described using the notion of a category. This is a mathematical structure consisting of objects, and for any pair of objects, a set of morphisms between them. In most examples, the objects are mathematical structures (such as sets, vector spaces, or topological spaces) and the morphisms are functions between these structures. One can also consider categories where the objects are D-branes and the morphisms between two branes $$\alpha$$ and $$\beta$$ are states of open strings stretched between $$\alpha$$ and $$\beta$$.

In the B-model of topological string theory, the D-branes are complex submanifolds of a Calabi–Yau together with additional data that arise physically from having charges at the endpoints of strings. Intuitively, one can think of a submanifold as a surface embedded inside the Calabi–Yau, although submanifolds can also exist in dimensions different from two. In mathematical language, the category having these branes as its objects is known as the derived category of coherent sheaves on the Calabi–Yau. In the A-model, the D-branes can again be viewed as submanifolds of a Calabi–Yau manifold. Roughly speaking, they are what mathematicians call special Lagrangian submanifolds. This means among other things that they have half the dimension of the space in which they sit, and they are length-, area-, or volume-minimizing. The category having these branes as its objects is called the Fukaya category.

The derived category of coherent sheaves is constructed using tools from complex geometry, a branch of mathematics that describes geometric curves in algebraic terms and solves geometric problems using algebraic equations. On the other hand, the Fukaya category is constructed using symplectic geometry, a branch of mathematics that arose from studies of classical physics. Symplectic geometry studies spaces equipped with a symplectic form, a mathematical tool that can be used to compute area in two-dimensional examples.

The homological mirror symmetry conjecture of Maxim Kontsevich states that the derived category of coherent sheaves on one Calabi–Yau manifold is equivalent in a certain sense to the Fukaya category of its mirror. This equivalence provides a precise mathematical formulation of mirror symmetry in topological string theory. In addition, it provides an unexpected bridge between two branches of geometry, namely complex and symplectic geometry.

Strominger–Yau–Zaslow conjecture
Another approach to understanding mirror symmetry was suggested by Andrew Strominger, Shing-Tung Yau, and Eric Zaslow in 1996. According to their conjecture, now known as the SYZ conjecture, mirror symmetry can be understood by dividing a Calabi–Yau manifold into simpler pieces and then transforming them to get the mirror Calabi–Yau.

The simplest example of a Calabi–Yau manifold is a two-dimensional torus or donut shape. Consider a circle on this surface that goes once through the hole of the donut. An example is the red circle in the figure. There are infinitely many circles like it on a torus; in fact, the entire surface is a union of such circles.

One can choose an auxiliary circle $$B$$ (the pink circle in the figure) such that each of the infinitely many circles decomposing the torus passes through a point of $$B$$. This auxiliary circle is said to parametrize the circles of the decomposition, meaning there is a correspondence between them and points of $$B$$. The circle $$B$$ is more than just a list, however, because it also determines how these circles are arranged on the torus. This auxiliary space plays an important role in the SYZ conjecture.

The idea of dividing a torus into pieces parametrized by an auxiliary space can be generalized. Increasing the dimension from two to four real dimensions, the Calabi–Yau becomes a K3 surface. Just as the torus was decomposed into circles, a four-dimensional K3 surface can be decomposed into two-dimensional tori. In this case the space $$B$$ is an ordinary sphere. Each point on the sphere corresponds to one of the two-dimensional tori, except for twenty-four "bad" points corresponding to "pinched" or singular tori.

The Calabi–Yau manifolds of primary interest in string theory have six dimensions. One can divide such a manifold into 3-tori (three-dimensional objects that generalize the notion of a torus) parametrized by a 3-sphere $$B$$ (a three-dimensional generalization of a sphere). Each point of $$B$$ corresponds to a 3-torus, except for infinitely many "bad" points which form a grid-like pattern of segments on the Calabi–Yau and correspond to singular tori.

Once the Calabi–Yau manifold has been decomposed into simpler parts, mirror symmetry can be understood in an intuitive geometric way. As an example, consider the torus described above. Imagine that this torus represents the "spacetime" for a physical theory. The fundamental objects of this theory will be strings propagating through the spacetime according to the rules of quantum mechanics. One of the basic dualities of string theory is T-duality, which states that a string propagating around a circle of radius $$R$$ is equivalent to a string propagating around a circle of radius $$1/R$$ in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, a string has momentum as it propagates around a circle, and it can also wind around the circle one or more times. The number of times the string winds around a circle is called the winding number. If a string has momentum $$p$$ and winding number $$n$$ in one description, it will have momentum $$n$$ and winding number $$p$$ in the dual description. By applying T-duality simultaneously to all of the circles that decompose the torus, the radii of these circles become inverted, and one is left with a new torus which is "fatter" or "skinnier" than the original. This torus is the mirror of the original Calabi–Yau.

T-duality can be extended from circles to the two-dimensional tori appearing in the decomposition of a K3 surface or to the three-dimensional tori appearing in the decomposition of a six-dimensional Calabi–Yau manifold. In general, the SYZ conjecture states that mirror symmetry is equivalent to the simultaneous application of T-duality to these tori. In each case, the space $$B$$ provides a kind of blueprint that describes how these tori are assembled into a Calabi–Yau manifold.

title: Mirror symmetry (string theory)


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IHOP (disambiguation)

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title: IHOP (disambiguation)