text:
KNX

KNX is an open standard (see EN 50090, ISO/IEC 14543) for commercial and residential building automation. KNX devices can manage lighting, blinds and shutters, HVAC, security systems, energy management, audio video, white goods, displays, remote control, etc. KNX evolved from three earlier standards; the European Home Systems Protocol (EHS), BatiBUS, and the European Installation Bus (EIB or Instabus).

It can use twisted pair (in a tree, line or star topology), powerline, RF, or IP links. On this network, the devices form distributed applications and tight interaction is possible. This is implemented via interworking models with standardised datapoint types and objects, modelling logical device channels.

Standard
The KNX standard has been built on the OSI-based EIB communication stack extended with the physical layers, configuration modes and application experience of BatiBUS and EHS.

KNX installations can use several physical communication media:

 * Twisted pair wiring (TP1 Cable) (inherited from the EIB standard). (The previously inherited BatiBUS communication medium (TP0) is no longer part of the KNX Specifications.)
 * Power-line networking (inherited from EIB standard). (The previously inherited EHS communication medium (PL132) is no longer part of the KNX Specifications.)
 * Radio (KNX-RF)
 * IP (also referred to as EIBnet/IP or KNXnet/IP)

KNX is not based on a specific hardware platform and a network can be controlled by anything from an 8-bit microcontroller to a PC, according to the demands of a particular building. The most common form of installation is over twisted pair medium.

KNX is an approved standard by the following organisations, (inter alia):

 * International standard (ISO/IEC 14543-3)
 * European standard (CENELEC EN 50090 and CEN EN 13321–1)
 * US standard (ANSI/ASHRAE 135)
 * China Guobiao (GB/T 20965)

It is administered by the KNX Association cvba, a non-profit organisation governed by Belgian law which was formed in 1999. The KNX Association had 500 registered hardware and software vendor members from 45 nations as at 1 July 2021. It had partnership agreements with 100,000 installer companies in 172 countries and more than 500 registered training centres. This is a royalty-free open standard and thus access to the KNX specifications is unrestricted.

Architecture
KNX devices are commonly connected by a twisted pair bus and can be modified from a controller. The bus is routed in parallel to the electrical power supply to all devices and systems on the network linking:

 * Sensors (e.g. push buttons, thermostats, anemometers, movement) gather information and send it on the bus as a data telegram;
 * Actuators (dimming units, heating valves, displays) receive data telegrams which are then converted into actions; and
 * Controllers and other logic functions (room temperature controllers, shutter controllers and other)
 * System devices and components (e.g. line couplers, backbone couplers).

Classifying devices as either "sensor" or "actuator" is outdated and simplistic. Many actuators include controller functionality, but also sensor functionality (for instance measuring operating hours, number of switch cycles, current, electrical power consumption, and more).

Application software, together with system topology and commissioning software, is loaded onto the devices via a system interface component. Installed systems can be accessed via LAN, point to point links, or phone networks for central or distributed control of the system via computers, tablets and touch screens, and smartphones.

The key features of the KNX architecture are:

 * Interworking and distributed application models for the building automation various tasks;
 * Schemes for configuration and management of resources on the network, and to permit the binding of parts of a distributed application in different nodes;
 * A communication system with a message protocol and models for the communication stack in each node (capable of hosting distributed applications (KNX Common Kernel); and
 * Models for the realization of these elements when developing actual devices to be mounted and linked in an installation.

Applications, interworking and binding
Central to the KNX architecture concepts are datapoints (inputs, outputs, parameters, and diagnostic data) which represent process and control variables in the system. The standardised containers for these datapoints are group objects and interface object properties. The communication system offers a reduced instruction set to read and write datapoint values. Datapoints have to conform to standardised datapoint types, themselves grouped into functional blocks. These functional blocks and datapoint types are related to applications fields, but some of them are of general use (such as date and time). Datapoints may be accessed through unicast or multicast mechanisms.

To logically link applications' datapoints across the network, KNX has three underlying binding schemes: one for free, one for structured and one for tagged binding:

 * In free binding, links between datapoints are not prescribed - in combination with free addressing, this supports customized multicast grouping at the level of individual datapoints and is central to S-mode configuration (see below);
 * In structured binding, the KNX specification stipulates a precise pattern for linking a whole set of datapoints, usually corresponding to a Functional Block or Channel (push-button modes follow this concept);
 * Tagged binding is also pre-structured by the application models, but the numerical value of address is part of its value.

Kernel and message protocol
The common kernel sits on top of the physical layers and the medium-specific data link layer and is shared by all the devices on the KNX Network. It is OSI 7-layer model compliant:

 * A general data link layer, which sits above the specific data link layers for each medium, provides access control and the logical link control;
 * A network layer (for nodes with routing functionality) provides a segment-wise acknowledged telegram (frame) and controls the hop count of a frame;
 * A transport layer enables four types of communication: one-to-many connectionless (multicast), one-to-all connectionless (broadcast), one-to-one connectionless, one-to-one connection-oriented;
 * (OSI session and presentation layers are empty); and
 * An application layer offers a toolkit of services to the application process.

Configuration modes
An installation has to be configured at the network topology level and at individual nodes or devices. The first level is a precondition or “bootstrap” phase, prior to the configuration of the distributed applications, i.e. binding and parameter setting. Configuration may be achieved through a combination of local activity on the devices (such pushing a button), and active network management communication over the bus (peer-to-peer, or more centralized master-slave).

The KNX configuration mode:

 * picks out a certain scheme for configuration and binding;
 * maps it to a particular choice of address scheme; and
 * completes all this with a choice of management procedures and matching resource realizations.

Some modes require more active management over the bus, whereas some others are mainly oriented towards local configuration. There are three categories of KNX devices:

 * A-mode or "Automatic mode" devices which can configure themselves, and are able to be installed by the end user;
 * E-mode or "Easy mode" devices that require basic training to install: their behaviour is pre-programmed, but configuration parameters need to be tailored to the user's requirements; or
 * S-mode or "System mode" devices that can be used to create sophisticated building automation systems: they have no default behaviour, and must be programmed and installed by specialists.

KNX encompasses tools for project engineering tasks such as linking a series of individual devices into a functioning installation and integrating different media and configuration modes. This is embodied in an Engineering Tool Software (ETS) suite.

Devices
A KNX installation always consists of a set of devices connected to the bus or network. Device models vary according to node roles, capabilities, management features and configuration modes, and are all laid down in the profiles. There are also general-purpose device models, such as for bus coupling units (BCUs) or bus interface modules (BIMs).

Devices may be identified and subsequently accessed throughout the network either by their individual address, or by their unique serial number, depending on the configuration mode. (Unique serial numbers are allocated by the KNX Association Certification Department.) Devices can also disclose both a manufacturer specific reference and functional (manufacturer independent) information when queried.

Topology and addressing
A KNX wired network can be formed with tree, line and star topologies, which can be mixed as needed; ring topologies are not supported. A tree topology is recommended for a large installation.

KNX can link up to 57,375 devices using 16-bit addresses.

 * The lowest eight bits provide up to 256 addresses within one line, which can consist of up to four segments, each having a maximum of 64 (TP1-64) devices, or up to 256 (TP1-256) devices. Each segment requires a local power supply and the maximum length of a segment is 1000 m. (The actual number of devices supported is dependent on the power supply and the power load of the individual devices.) Segments connected with line repeaters can extend to a length of 4000 m and link up to 256 devices.
 * Lines may be grouped together into an area, with up to 15 lines connected to a main line via line couplers. The next four bits of the address are used to identify individual lines.
 * An entire domain can be formed with 15 areas linked by a backbone line using backbone couplers, and the top four bits of the address space identify an area. (Line repeaters may not be used on a backbone or mainline.)

Coupling units allow address filtering which helps to improve performance given the limited bus signal speed. An installation based on KNXnet/IP allows the integration of KNX sub networks via IP as the KNX address structure is similar to an IP address.

TP 1
The TP1 twisted pair bus (inherited from EIB) provides asynchronous, character oriented data transfer and half-duplex bidirectional differential signaling with a signaling speed of 9600 bit/s. Media access control is via CSMA/CA. Every bus user has equal data transmission rights and data is exchanged directly (peer-to-peer) between bus users. SELV power is distributed via the same pair for low-power devices. A deprecated specification, TP0, running at a slower signalling speed of 4800 bit/s, has been retained from the BatiBUS standard but KNX products cannot exchange information with BatiBUS devices.

PL 110
PL 110 power-line transmission is delivered using spread frequency shift keying signalling with asynchronous transmission of data packets and half duplex bi-directional communication. It uses the central frequency 110 kHz (CENELEC B-band) and has a data rate of 1200 bit/s. It also uses CSMA. KNX Powerline is aimed at smart white goods, but the take-up has been low. An alternative variant, PL 132, has a carrier frequency centred on 132.5 kHz (CENELEC C-band).

RF
RF enables communication in the 868.3 MHz band for using frequency shift keying with Manchester data encoding.

IP
KNXnet/IP port 3671 has integration solutions for IP-enabled media like Ethernet (IEEE 802.2), Bluetooth, WiFi/Wireless LAN (IEEE 802.11), FireWire (IEEE 1394) etc.

Frame format
Ignoring any preamble for medium-specific access and collision control, a frame format is generally:

Security
KNX Telegrams can be signed or encrypted thanks to the extension of the protocol that was developed starting in 2013, KNX Data Secure for securing telegrams on the traditional KNX media TP and RF and KNX IP Secure for securing KNX telegrams tunnelled via IP. KNX Data Secure became an EN standard (EN 50090-3-4) in 2018, KNX IP Secure an ISO standard (ISO 22510) in 2019.

Conformity
Any product labeled with the KNX trademark must be certified to conform with the standards (and thus interoperable with other devices) by accredited third party test labs. All products bearing the KNX logo are programmed through a common interface using the vendor-independent ETS software.

title: KNX


text:
Talk:Forced perspective

Role of light
A miniature model is CLOSER than it appears to be and so requires LESS light. Also the whole argument is irrelevant if shot with homogenous lighting or outside. An object only appears dimmer when further away if moving into an area of less light.

Forced perspective in architecture that isn't Disney or Vegas?
Does anyone know of an example of f.p. not located at a theme park or in Vegas? Something that isn't merely a replica of an existing building? I personally only know of all the postmodern stuff. Tomsintown 23:51, 29 August 2006 (UTC)

How do they do it?
Okay, you've defined what f.p. is. Now, would you please describe how they do it? --Uncle Ed 23:45 Feb 20, 2003 (UTC)
 * I'm not in film but I'll do my best. Will begin within the hour. -- Goatasaur

There is a famous cathedral that has a painting on its ceiling, that gives the impression of a massive domed structure overhead when one looks up, in fact I believe there are birds in the painting... I have seen pictures of it but cannot recall its name. -- Goatasaur

I've added as much as possible without cluttering, but this might now need cleaning up and wikifying. I think 'The Role of Light' could really do with a good quality diagram to clarify the explanation. Bigpinkthing 14:48, 7 July 2006 (UTC)

Spoiler warning
Spoiler warning needed for 1] end of film, 2] shows resolution of main character's spiritual quest, 3] reveals surprising change of last shot from "character returns to family home" to "character returns to spiritual home". "alyosha" 05:48, 18 December 2005 (UTC)

 * Which film? The article mentions quite a few, and I for one can't see which one this complaint is about.
 * In fact, that section may well have been deleted in the 6 years since that paragraph was written.
 * And anyway, Wikipedia policy is against spoiler warnings.
 * --Thnidu (talk) 05:44, 31 January 2012 (UTC)

Possible content
Is there any mathamatical principles or rules of thumb when it comes to creating the desired perspective effect? I'm thinking for architecture, if there is a ratio that can be applied. Thanks.

Pictures of Leaning Tower of Pisa?
Almost every tourist that visits the tower takes a picture of themselves in various poses trying to push the tower up, carrying it on their back etc... The photos would make a good illustration As a European, I feel aesthetically offended by those ugly US-American tourists in their barbaric clothing standing next to our famous cultural landmarks. Why can't they dress and behave properly? Europe isn't Disneyland! Yanke behave or go home. 217.238.42.61 (talk) 19:53, 23 April 2016 (UTC)

The person "holding up" the Leaning Tower of Pisa is making a White Power symbol (what used to be the 'okay' symbol). Is this suitable for Wikipedia? — Preceding unsigned comment added by 64.229.83.235 (talk) 12:45, 22 February 2020 (UTC)

Subject much too inclusive
Forced perspective means just one thing: the progressive reduction in the size of objects to increase the appearance of depth, usually, but not always, in a two-dimensional image. In some cases, rectangular objects like buildings are built as trapezoids so that their converging lines simulate perspective. (For the seldom-seen Billy Wilder film, Kiss Me, Stupid, the entire town of Climax, Nevada was built on a single soundstage, requiring multiple uses of forced perspective. For example, the entire front of a small house was set to the left of and parallel to the camera position, with the front door at the end of the porch nearest the camera. The door, porch, and steps were full-size, but the facade tapered until the far end of the same porch was only perhaps 5 feet high. On the flat screen, the 10-foot wide trapezoidal facade appears to be a 25 foot rectangle.) In other cases, different elements are made progressively smaller as they recede from the camera. In still others (like the Casablanca example cited) The background objects and people are all uniformly smaller than those in the foreground.

However, an iguana placed in the foreground, far in front of human actors in order to simulate a dinosaur is not "forced" perspective, but simply a different form of trick photography, based on the fact that viewers estimate the size of objects by reference to other, known, objects in the same image. It is not the perspective that is faked but the apparent size. (In the real world, things only appear to diminish in size as they actually recede in three-dimensional space; in the two-dimensional image world, things only appear to recede as they actually diminish on the image plane.)

This article should be re-written. Jim Stinson 21:01, 2 August 2007 (UTC)

NeilCoughlin (talk) I do not believe the story of the filming of Casablanca is accurate. I've just watched the ending of Casablanca on Youtube: http://www.youtube.com/watch?v=-ElIW9pzm4Y and I see no flat painting of an airplane or where dwarves fit in. There was clearly a large plane or working model of a plane used. I shall investigate further, but recommend that paragraph be removed. —Preceding undated comment added 17:07, 2 September 2010 (UTC).

More examples
One of the best examples I've seen is the part in the original Willy Wonka movie with the shrinking hallway. — Preceding unsigned comment added by 203.129.23.146 (talk) 07:56, 17 August 2011 (UTC)

Camel Spiders : snopes.com People scale the spiders by the legs in the background, instead of the hand in the foreground ! --195.137.93.171 (talk) 17:49, 31 January 2016 (UTC)

Nodal point: diagram, please?
The explanation in the last two paragraphs of Nodal point: forced perspective in motion is difficult to follow:
 * The techniques developed center around a nodal point axis, so the camera's panning axis is at the point between the lens and aperture ring where the light travelling through the camera meets its axis. By comparison, the normal panning axis would be at the point at which light would strike the film (or image sensor in a digital camera).

 * The position of this nodal point can be different for every lens. However, on wide angle lenses it is often found between the midpoint of the lens and the aperture ring.

Could someone who understands it possibly add a (link to a) diagram? --Thnidu (talk) 05:35, 31 January 2012 (UTC)

Probably best just to delete it - the explanation Cardinal_point_(optics) is arguably untrue. It's one of those things where the Internet has taken over from science and Wikipedia prefers a commonly-held belief over the truth ! The technique is about camera motion - panning around the nodal point is about eliminating motion of the point of view - precisely the opposite ! I'll be bold ... it's gone

The 'normal panning point' is the centre of gravity of the camera, so it doesn't tilt under its own weight ! Nothing to do with optics at all. If you're both tracking and panning, yes the nodal panning-point might matter slightly, but only if you require a precise distortion. Often they will track for a metre, so a couple of millimetres of nodal error will be no bigger than the variation in the actor's height from morning to evening (we all shrink during the day and grow back at night). No-one will notice it. I tried to link but YouTube is blacklisted - does it work in 'Talk' ? No ! Google it yourself ! (How Lord of the Rings used forced perspective shots with a moving camera VIDEO - YouTube)

--195.137.93.171 (talk) 17:34, 31 January 2016 (UTC)

I fudged it - a bit better ? I guess the pan+tilt but no-tracking situation is notable for those 'indie' film-makers that can't afford computerised camera motion and slaved movable bits of sets. The main point of camera movement is to give the viewer an appreciation of the 3D relationship among the objects in the scene - if you can still fake false perspective, the illusion with a moving camera will be much stronger ! --195.137.93.171 (talk) 16:28, 1 February 2016 (UTC)
 * If the camera's point of view is moved, then parallax would reveal the true relative positions of the characters in space. Even if the camera is just rotated, its point of view may move accidentally if the camera is not rotated about the correct point. This point of view is called the 'zero-parallax-point' (or front nodal point), and is approximated in practice as the centre of the entrance pupil.

Isn't it 'False Perspective' ?
There's one instance in the article ... 'Forced' is just a mis-hearing which has become widespread in an industry that mumbles and an audience that listens to too much loud music on headphones. --195.137.93.171 (talk) 17:04, 31 January 2016 (UTC)

Perhaps I'm just old ! Satire on False Perspective

There is a redirect from False perspective to Diorama --195.137.93.171 (talk) 18:19, 31 January 2016 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 01:45, 18 February 2023 (UTC)
 * Forced perspective gallery by Francesco Borromini.jpg

Needs an Intro
After reading this article, I am still clueless about what "forced perspective" is. I think it would be better if there was, you know, a "forced perspective for dummies" kind of intro. G41rn8 (talk) 03:36, 26 February 2024 (UTC)

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

title: Talk:Forced perspective


text:
Slaughterhouse-Five

Slaughterhouse-Five, or, The Children's Crusade: A Duty-Dance with Death is a 1969 semi-autobiographic science fiction-infused anti-war novel by Kurt Vonnegut. It follows the life experiences of Billy Pilgrim, from his early years, to his time as an American soldier and chaplain's assistant during World War II, to the post-war years. Throughout the novel, Billy frequently travels back and forth through time. The protagonist deals with a temporal crisis as a result of his post-war psychological trauma. The text centers on Billy's capture by the German Army and his survival of the Allied firebombing of Dresden as a prisoner of war, an experience that Vonnegut endured as an American serviceman. The work has been called an example of "unmatched moral clarity" and "one of the most enduring anti-war novels of all time".

Plot
The novel's first chapter begins with "All this happened, more or less"; this introduction implies an unreliable narrator tells the story. Vonnegut utilizes a non-linear, non-chronological description of events to reflect Billy Pilgrim's psychological state. Events become clear through flashbacks and descriptions of time travel experiences. In the first chapter, the narrator describes his writing of the book, his experiences as a University of Chicago anthropology student and a Chicago City News Bureau correspondent, his research on the Children's Crusade and the history of Dresden, and his visit to Cold War–era Europe with his wartime friend Bernard V. O'Hare. In the second chapter, Vonnegut introduces Billy Pilgrim, an American man from the fictional town of Ilium, New York. Billy believes that an extraterrestrial species from the planet Tralfamadore held him captive in an alien zoo and that he has experienced time travel.

As a chaplain's assistant in the United States Army during World War II, Billy is an ill-trained, disoriented and fatalistic American soldier who discovers that he does not like war and refuses to fight. He is transferred from a base in South Carolina to the front line in Luxembourg during the Battle of the Bulge. He narrowly escapes death as the result of a string of events. He also meets Roland Weary, a patriot, warmonger, and sadistic bully who derides Billy's cowardice. The two of them are captured in 1944 by the Germans, who confiscate all of Weary's belongings and force him to wear wooden clogs that cut painfully into his feet; the resulting wounds become gangrenous, which eventually kills him. While Weary is dying in a rail car full of prisoners, he convinces a fellow soldier, Paul Lazzaro, that Billy is to blame for his death. Lazzaro vows to avenge Weary's death by killing Billy, because revenge is "the sweetest thing in life."

At this exact time, Billy becomes "unstuck in time"; Billy travels through time to moments from his past and future. The novel describes the transportation of Billy and the other prisoners into Germany. The German soldiers held their prisoners in the German city of Dresden; the prisoners had to work in "contract labor" (forced labor); these events occurred in 1945. The Germans detained Billy and his fellow prisoners in an empty slaughterhouse called Schlachthof-fünf ("slaughterhouse five"). During the Allied bombing of Dresden, German guards hid their captives in the partially underground setting of the slaughterhouse; this protected those captives from complete annihilation. As a result, they are among the few survivors of the firestorm that raged in the city between February 13 and 15, 1945. After V-E Day in May 1945, Billy was transferred to the United States and received an honorable discharge in July 1945.

Billy is hospitalized with symptoms similar to post-traumatic stress disorder and placed under psychiatric care at a Veterans Affairs hospital in Lake Placid. During Billy's stay at the hospital, Eliot Rosewater introduces him to the work of an obscure science fiction writer named Kilgore Trout. After his release, Billy marries Valencia Merble, whose father owns the Ilium School of Optometry that Billy later attends. Billy becomes a successful and wealthy optometrist. In 1947, Billy and Valencia conceive their first child, Robert, on their honeymoon in Cape Ann, Massachusetts. Two years later, their second child, Barbara, was born. On Barbara's wedding night, Billy is abducted by a flying saucer and taken to a planet many light-years away from Earth called Tralfamadore. The Tralfamadorians have the power to see in four dimensions; they simultaneously observe all points in the space-time continuum. They universally adopt a fatalistic worldview: death means nothing to them, and their typical response to hearing about death is "so it goes."

The Tralfamadorians transport Billy to Tralfamadore and place him inside a transparent geodesic dome exhibit in a zoo; the inside resembles a house on planet Earth. The Tralfamadorians later abduct a pornographic film star named Montana Wildhack, who had disappeared on Earth and supposedly drowned in San Pedro Bay. The Tralfamadorians intend to have her mate with Billy. Montana and Billy fall in love and have a child together. Billy is instantaneously sent back to Earth in a time warp to re-live past or future moments of his life.

In 1968, Billy and a co-pilot are the only survivors of a plane crash in Vermont. While driving to visit Billy in the hospital, Valencia crashes her car and dies of carbon monoxide poisoning. Billy shares a hospital room with Bertram Rumfoord, a Harvard University history professor researching an official war history of the USAAF in World War II. They discuss the bombing of Dresden, which the professor initially refuses to believe Billy witnessed. Despite the significant loss of civilian life and the destruction of Dresden, they both regard the bombing as a justifiable act.

Billy's daughter takes him home to Ilium. He escapes and flees to New York City. In Times Square he visits a pornographic book store, where he discovers books written by Kilgore Trout and reads them. He discovers a science fiction novel titled The Big Board at the bookstore. The novel is about a couple abducted by extraterrestrials. The aliens trick the abductees into thinking they are managing investments on Earth, which excites the humans and, in turn, sparks interest in the observers. He also finds some magazine covers that mention Montana Wildhack's disappearance. While Billy surveys the bookstore, one of Montana's pornographic films plays in the background. Later in the evening, when he discusses his time travels to Tralfamadore on a radio talk show, he is ejected from the studio. He returns to his hotel room, falls asleep, and time-travels back to 1945 in Dresden. Billy and his fellow prisoners are tasked with locating and burying the dead. After a Maori New Zealand soldier working with Billy dies of dry heaves the Germans begin cremating the bodies en masse with flamethrowers. German soldiers execute Billy's friend Edgar Derby for stealing a teapot. Eventually all of the German soldiers leave to fight on the Eastern Front, leaving Billy and the other prisoners alone with tweeting birds as the war ends.

Through non-chronological storytelling, other parts of Billy's life are told throughout the book. After Billy is evicted from the radio studio, Barbara treats Billy as a child and often monitors him. Robert becomes starkly anti-communist, enlists as a Green Beret and fights in the Vietnam War. Billy is eventually killed in 1976, at which point the United States has been partitioned into twenty separate countries and attacked by China with thermonuclear weapons. He gives a speech in a baseball stadium in Chicago in which he predicts his own death and proclaims that "if you think death is a terrible thing, then you have not understood a word I've said." Billy soon after is shot with a laser gun by an assassin commissioned by the elderly Lazzaro.

Characters

 * Narrator: Recurring as a minor character, the narrator seems anonymous while also clearly identifying himself as Kurt Vonnegut, when he says, "That was I. That was me. That was the author of this book." As noted above, as an American soldier during World War II, Vonnegut was captured by Germans at the Battle of the Bulge and transported to Dresden. He and fellow prisoners-of-war survived the bombing while being held in a deep cellar of Schlachthof Fünf ("Slaughterhouse-Five"). The narrator begins the story by describing his connection to the firebombing of Dresden and his reasons for writing Slaughterhouse-Five.
 * Billy Pilgrim: A fatalistic optometrist ensconced in a dull, safe marriage in Ilium, New York. During World War II, he was held as a prisoner-of-war in Dresden and survived the firebombing, experiences which had a lasting effect on his post-war life. His time travel occurs at desperate times in his life; he relives past and future events and becomes fatalistic (though not a defeatist) because he claims to have seen when, how and why he will die.
 * Roland Weary: A weak man dreaming of grandeur and obsessed with gore and vengeance, who saves Billy several times (despite Billy's protests) in hopes of attaining military glory. He coped with his unpopularity in his home city of Pittsburgh by befriending and then beating people less well-liked than him, and is obsessed with his father's collection of torture equipment. Weary is also a bully who beats Billy and gets them both captured, leading to the loss of his winter uniforms and boots. Weary dies of gangrene on the train en route to the POW camp, and blames Billy in his dying words.
 * Paul Lazzaro: Another POW. A sickly, ill-tempered car thief from Cicero, Illinois who takes Weary's dying words as a revenge commission to kill Billy. He keeps a mental list of his enemies, claiming he can have anyone "killed for a thousand dollars plus traveling expenses." Lazzaro eventually fulfills his promise to Weary and has Billy assassinated by a laser gun in 1976.
 * Kilgore Trout: A failed science fiction writer whose hometown is also Ilium, New York, and who makes money by managing newspaper delivery boys. He has received only one fan letter (from Eliot Rosewater; see below). After Billy meets him in a back alley in Ilium, he invites Trout to his wedding anniversary celebration. There, Kilgore follows Billy, thinking the latter has seen through a "time window." Kilgore Trout is also a main character in Vonnegut's 1973 novel Breakfast of Champions.
 * Edgar Derby: A middle-aged high school teacher who felt that he needed to participate in the war rather than just send off his students to fight. One of his sons is serving with the marines in the Pacific Theatre. Though relatively unimportant, Derby seems to be the only American before the bombing of Dresden to understand what war can do to people. During Campbell's presentation he stands up and castigates him, defending American democracy and the alliance with the Soviet Union. German forces summarily execute him for looting after they catch him taking a teapot from catacombs after the bombing. Vonnegut has said that this death is the climax of the book as a whole.
 * Howard W. Campbell Jr.: An American-born Nazi. Before the war, he lived in Germany where he was a noted German-language playwright recruited by the Nazi Ministry of Propaganda. In an essay, he connects the misery of American poverty to the disheveled appearance and behavior of the American POWs. Edgar Derby confronts him when Campbell tries to recruit American POWs into the American Free Corps to fight the Communist Soviet Union on behalf of the Nazis. He appears wearing swastika-adorned cowboy hat and boots and with a red, white and blue Nazi armband. Campbell is the protagonist of Vonnegut's 1962 novel Mother Night.
 * Valencia Merble: Billy's wife and the mother of their children, Robert and Barbara. Billy is emotionally distant from her. She dies from carbon monoxide poisoning after an automobile accident en route to the hospital to see Billy after his airplane crash.
 * Robert Pilgrim: Son of Billy and Valencia. A troubled, middle-class boy and disappointing son who becomes an alcoholic at age 16, drops out of high school, and is arrested for vandalizing a Catholic cemetery. He later so absorbs the anti-Communist worldview that he metamorphoses from suburban adolescent rebel to Green Beret sergeant. He wins a Purple Heart, Bronze Star and Silver Star in the Vietnam War.
 * Barbara Pilgrim: Daughter of Billy and Valencia. She is a "bitchy flibbertigibbet" from having had to assume the family's leadership at the age of twenty. She has "legs like an Edwardian grand piano," marries an optometrist, and treats her widowed father as a childish invalid.
 * Tralfamadorians: The race of extraterrestrial beings who appear (to humans) like upright toilet plungers with a hand atop, in which is set a single green eye. They abduct Billy and teach him about time's relation to the world (as a fourth dimension), fate, and the nature of death. The Tralfamadorians are featured in several Vonnegut novels. In Slaughterhouse Five, they reveal that the universe will be accidentally destroyed by one of their test pilots, and there is nothing they can do about it.
 * Montana Wildhack: A beautiful young model who is abducted and placed alongside Billy in the zoo on Tralfamadore. She and Billy develop an intimate relationship and they have a child. She apparently remains on Tralfamadore with the child after Billy is sent back to Earth. Billy sees her in a film showing in a pornographic book store when he stops to look at the Kilgore Trout novels sitting in the window. Her unexplained disappearance is featured on the covers of magazines sold in the store.
 * "Wild Bob": A superannuated army officer Billy meets in the war. He tells his fellow POWs to call him "Wild Bob", as he thinks they are the 451st Infantry Regiment and under his command. He explains "If you're ever in Cody, Wyoming, ask for Wild Bob", which is a phrase that Billy repeats to himself throughout the novel. He dies of pneumonia.
 * Eliot Rosewater: Billy befriends him in the veterans' hospital; he introduces Billy to the sci-fi novels of Kilgore Trout. Rosewater wrote the only fan letter Trout ever received. Rosewater had also suffered a terrible event during the war. Billy and Rosewater find the Trout novels helpful in dealing with the trauma of war. Rosewater is featured in other Vonnegut novels, such as God Bless You, Mr. Rosewater (1965).
 * Bertram Copeland Rumfoord: A Harvard history professor, retired U.S. Air Force brigadier general, and millionaire. He shares a hospital room with Billy and is interested in the Dresden bombing. He is in the hospital after breaking his leg on his honeymoon with his fifth wife Lily, a barely literate high school drop-out and go-go girl. He is described as similar in appearance and mannerisms to Theodore Roosevelt. Bertram is likely a relative of Winston Niles Rumfoord, a character in Vonnegut's 1959 novel The Sirens of Titan.
 * The Scouts: Two American infantry scouts trapped behind German lines who find Roland Weary and Billy. Roland refers to himself and the scouts as the "Three Musketeers". The scouts abandon Roland and Billy because the latter are slowing them down. They are revealed to have been shot and killed by Germans in ambush.
 * Bernard V. O'Hare: The narrator's old war friend who was also held in Dresden and accompanies him there after the war. He is the husband of Mary O'Hare, and is a district attorney from Pennsylvania.
 * Mary O'Hare: The wife of Bernard V. O'Hare, to whom Vonnegut promised to name the book The Children's Crusade. She is briefly discussed in the beginning of the book. When the narrator and Bernard try to recollect their war experiences Mary complains that they were just "babies" during the war and that the narrator will portray them as valorous men. The narrator befriends Mary by promising that he will portray them as she said and that in his book "there won't be a part for Frank Sinatra or John Wayne."
 * Werner Gluck: The sixteen-year-old German charged with guarding Billy and Edgar Derby when they are first placed at Slaughterhouse Five in Dresden. He does not know his way around and accidentally leads Billy and Edgar into a communal shower where some German refugee girls from Breslau are bathing. He is described as appearing similar to Billy.

Style
In keeping with Vonnegut's signature style, the novel's syntax and sentence structure are simple, and irony, sentimentality, black humor, and didacticism are prevalent throughout the work. Like much of his oeuvre, Slaughterhouse-Five is broken into small pieces, and in this case, into brief experiences, each focused on a specific point in time. Vonnegut has noted that his books "are essentially mosaics made up of a whole bunch of tiny little chips...and each chip is a joke." Vonnegut also includes hand-drawn illustrations in Slaughterhouse-Five, and also in his next novel, Breakfast of Champions (1973). Characteristically, Vonnegut makes heavy use of repetition, frequently using the phrase, "So it goes". He uses it as a refrain when events of death, dying, and mortality occur or are mentioned; as a narrative transition to another subject; as a memento mori; as comic relief; and to explain the unexplained. The phrase appears 106 times.

The book has been categorized as a postmodern, meta-fictional novel. The first chapter of Slaughterhouse-Five is written in the style of an author's preface about how he came to write the novel. The narrator introduces the novel's genesis by telling of his connection to the Dresden bombing, and why he is recording it. He provides a description of himself and of the book, saying that it is a desperate attempt at creating a scholarly work. He ends the first chapter by discussing the beginning and end of the novel. He then segues to the story of Billy Pilgrim: "Listen: Billy Pilgrim has come unstuck in time", thus the transition from the writer's perspective to that of the third-person, omniscient narrator. (The use of "Listen" as an opening interjection has been said to mimic the opening "Hwaet!" of the medieval epic poem Beowulf.) The fictional "story" appears to begin in Chapter Two, although there is no reason to presume that the first chapter is not also fiction. This technique is common in postmodern meta-fiction.

The narrator explains that Billy Pilgrim experiences his life discontinuously, so that he randomly lives (and re-lives) his birth, youth, old age and death, rather than experiencing them in the normal linear order. There are two main narrative threads: a description of Billy's World War II experience, which, though interrupted by episodes from other periods and places in his life, is mostly linear; and a description of his discontinuous pre-war and post-war lives. A main idea is that Billy's existential perspective had been compromised by his having witnessed Dresden's destruction (although he had come "unstuck in time" before arriving in Dresden). Slaughterhouse-Five is told in short, declarative sentences, which create the impression that one is reading a factual report.

The first sentence says, "All this happened, more or less." (In 2010 this was ranked No. 38 on the American Book Review's list of "100 Best First Lines from Novels".) The opening sentences of the novel have been said to contain the aesthetic "method statement" of the entire novel.

War and death
In Slaughterhouse-Five, Vonnegut attempts to come to terms with war through the narrator's eyes, Billy Pilgrim. An example within the novel, showing Vonnegut's aim to accept his past war experiences, occurs in chapter one, when he states that "All this happened, more or less. The war parts, anyway, are pretty much true. One guy I knew really was shot in Dresden for taking a teapot that wasn't his. Another guy I knew really did threaten to have his personal enemies killed by hired gunmen after the war. And so on. I've changed all the names." As the novel continues, it is relevant that the reality is death.

Slaughterhouse-Five focuses on human imagination while interrogating the novel's overall theme, which is the catastrophic impact that war leaves behind. Death is something that happens fairly often in Slaughterhouse-Five. When a death occurs in the novel, Vonnegut marks the occasion with the saying "so it goes." Bergenholtz and Clark write about what Vonnegut actually means when he uses that saying: "Presumably, readers who have not embraced Tralfamadorian determinism will be both amused and disturbed by this indiscriminate use of 'So it goes.' Such humor is, of course, black humor."

Christian philosophy
Christian philosophy is present in Vonnegut's Slaughterhouse-Five but it is not very well-regarded. When God and Christianity is brought up in the work, it is mentioned in a bitter or disregarding tone. One only has to look at how the soldiers react to the mention of it. Though Billy Pilgrim had adopted some part of Christianity, he did not ascribe to all of it. JC Justus summarizes it the best when he mentions that, "'Tralfamadorian determinism and passivity' that Pilgrim later adopts as well as Christian fatalism wherein God himself has ordained the atrocities of war...". Following Justus's argument, Pilgrim was a character that had been through war and traveled through time. Having experienced all of these horrors in his lifetime, Pilgrim ended up adopting the Christian ideal that God had everything planned and he had given his approval for the war to happen.

Tralfamadorian philosophy
As Billy Pilgrim becomes "unstuck in time", he is faced with a new type of philosophy. When Pilgrim becomes acquainted with the Tralfamadorians, he learns a different viewpoint concerning fate and free will. While Christianity may state that fate and free will are matters of God's divine choice and human interaction, Tralfamadorianism would disagree. According to Tralfamadorian philosophy, things are and always will be, and there is nothing that can change them. When Billy asks why they had chosen him, the Tralfamadorians reply, "Why you? Why us for that matter? Why anything? Because this moment simply is." The mindset of the Tralfamadorian is not one in which free will exists. Things happen because they were always destined to be happening. The narrator of the story explains that the Tralfamadorians see time all at once. This concept of time is best explained by the Tralfamadorians themselves, as they speak to Billy Pilgrim on the matter stating, "I am a Tralfamadorian, seeing all time as you might see a stretch of the Rocky Mountains. All time is all time. It does not change. It does not lend itself to warnings or explanations. It simply is." After this particular conversation on seeing time, Billy makes the statement that this philosophy does not seem to evoke any sense of free will. To this, the Tralfamadorian reply that free will is a concept that, out of the "visited thirty-one inhabited planets in the universe" and "studied reports on one hundred more," "only on Earth is there any talk of free will."

Using the Tralfamadorian passivity of fate, Billy Pilgrim learns to overlook death and the shock involved with death. Pilgrim claims the Tralfamadorian philosophy on death to be his most important lesson:"The most important thing I learned on Tralfamadore was that when a person dies he only appears to die. He is still very much alive in the past, so it is very silly for people to cry at his funeral. All moments, past, present, and future, always have existed, always will exist. ... When a Tralfamadorian sees a corpse, all he thinks is that the dead person is in bad condition in that particular moment, but that the same person is just fine in plenty of other moments. Now, when I myself hear that somebody is dead, I simply shrug and say what the Tralfamadorians say about dead people, which is 'So it goes.'"

Postmodernism
The significance of postmodernism is a reoccurring theme in Kurt Vonnegut's works. Postmodernism arose as a rejection of modernist narratives and structures. According to one critic, Tralfamadorianism is a restatement of Christian teleology: There is no purpose to life, effects do not have causes; the only reason for anything is that God has ordained it. This juxtaposition is displayed throughout the book, rather directly asking the reader to confront the logical absurdities inherent in both Christian faith and Tralfamadorianism. The rigid and dogmatic approach of Christianity is dismissed, while determinism is critiqued.

Mental illness
Some have argued that Vonnegut is speaking out for veterans, many of whose post-war states are untreatable. Pilgrim's symptoms have been identified as what is now called post-traumatic stress disorder, which didn't exist as a term when the novel was written. In the words of one writer, "perhaps due to the fact that PTSD was not officially recognized as a mental disorder yet, the establishment fails Billy by neither providing an accurate diagnosis nor proposing any coping mechanisms." Billy found life meaningless due to his experiences in the war, which desensitized and forever changed him.

Dresden
Vonnegut was in the city of Dresden when it was bombed; he came home traumatized and unable to properly communicate the horror of what happened there. Slaughterhouse-Five is the product of the twenty years of work it took for him to articulate the experience in a way that satisfied him. William Allen says, "Precisely because the story was so hard to tell, and because Vonnegut was willing to take two decades necessary to tell it – to speak the unspeakable – Slaughterhouse-Five is a great novel, a masterpiece sure to remain a permanent part of American literature."

Food
Billy Pilgrim ended up owning "half of three Tastee-Freeze stands. Tastee-Freeze was a sort of frozen custard. It gave all the pleasure that ice cream could give, without the stiffness and bitter coldness of ice cream" (61). Throughout Slaughterhouse-Five, when Billy is eating or near food, he thinks of food in positive terms. This is partly because food is both a status symbol and comforting to people in Billy's situation. "Food may provide nourishment, but its more important function is to soothe... Finally, food also functions as a status symbol, a sign of wealth. For instance, en route to the German prisoner-of-war camp, Billy gets a glimpse of the guards' boxcar and is impressed by its contents... In sharp contrast, the Americans' boxcar proclaims their dependent prisoner-of-war status."

The Bird
Throughout the novel, the bird sings "Poo-tee-weet?" After the Dresden firebombing, the bird breaks out in song. The bird also sings outside of Billy's hospital window. The song has been interpreted as symbolizing a loss of words, or the inadequacy of words to describe traumatic situations.

Allusions to other works
As in other novels by Vonnegut, certain characters cross over from other stories, making cameo appearances and connecting the discrete novels to a greater opus. Fictional novelist Kilgore Trout, often an important character in other Vonnegut novels, is a social commentator and a friend to Billy Pilgrim in Slaughterhouse-Five. In one case, he is the only non-optometrist at a party; therefore, he is the odd man out. He ridicules everything the Ideal American Family holds true, such as Heaven, Hell, and Sin. In Trout's opinion, people do not know if the things they do turn out to be good or bad, and if they turn out to be bad, they go to Hell, where "the burning never stops hurting." Other crossover characters are Eliot Rosewater, from God Bless You, Mr. Rosewater; Howard W. Campbell Jr., from Mother Night; and Bertram Copeland Rumfoord, relative of Winston Niles Rumfoord, from The Sirens of Titan. While Vonnegut re-uses characters, the characters are frequently rebooted and do not necessarily maintain the same biographical details from appearance to appearance. Trout in particular is palpably a different person (although with distinct, consistent character traits) in each of his appearances in Vonnegut's work.

In the Twayne's United States Authors series volume on Kurt Vonnegut, about the protagonist's name, Stanley Schatt says:

By naming the unheroic hero Billy Pilgrim, Vonnegut contrasts John Bunyan's "Pilgrim's Progress" with Billy's story. As Wilfrid Sheed has pointed out, Billy's solution to the problems of the modern world is to "invent a heaven, out of 20th century materials, where Good Technology triumphs over Bad Technology. His scripture is Science Fiction, Man's last, good fantasy".

Cultural and historical allusions
Slaughterhouse-Five makes numerous cultural, historical, geographical, and philosophical allusions. It tells of the bombing of Dresden in World War II, and refers to the Battle of the Bulge, the Vietnam War, and the civil rights protests in American cities during the 1960s. Billy's wife, Valencia, has a "Reagan for President!" bumper sticker on her Cadillac, referring to Ronald Reagan's failed 1968 Republican presidential nomination campaign. Another bumper sticker is mentioned, reading "Impeach Earl Warren," referencing a real-life campaign by the far-right John Birch Society.

The Serenity Prayer appears twice. Critic Tony Tanner suggested that it is employed to illustrate the contrast between Billy Pilgrim's and the Tralfamadorians' views of fatalism. Richard Hinchcliffe contends that Billy Pilgrim could be seen at first as typifying the Protestant work ethic, but he ultimately converts to evangelicalism.

Vonnegut's own experiences
In 1995 Vonnegut said that Billy Pilgrim was modeled on Edward "Joe" Crone, a thin soldier who died in Dresden. Vonnegut had told this to friends earlier, but waited until after he learned that both of Crone's parents were deceased to publicly disclose this information.

Edgar Derby, killed for looting a teapot, was modeled on Vonnegut's fellow prisoner Mike Palaia, who was executed for plundering a jar of food (variously described as beans, fruit, or cherries).

Reception
The reviews of Slaughterhouse-Five have been largely positive since the March 31, 1969 review in the New York Times stated: "you'll either love it, or push it back in the science-fiction corner." It was Vonnegut's first novel to become a bestseller, staying on the New York Times bestseller list for sixteen weeks and peaking at No. 4. In 1970, Slaughterhouse-Five was nominated for best-novel Nebula and Hugo Awards. It lost both to The Left Hand of Darkness by Ursula K. Le Guin. It has since been widely regarded as a classic anti-war novel, and has appeared in Time magazine's list of the 100 best English-language novels written since 1923.

Censorship controversy
Slaughterhouse-Five has been the subject of many attempts at censorship due to its irreverent tone, purportedly obscene content and depictions of sex, American soldiers' use of profanity, and perceived heresy. It was one of the first literary acknowledgments that homosexual men, referred to in the novel as "fairies", were among the victims of the Holocaust.

In the United States it has at times been banned from literature classes, removed from school libraries, and struck from literary curricula. In 1972, following the ruling of Todd v. Rochester Community Schools, it was banned from Rochester Community Schools in Oakland County, Michigan. The circuit judge described the book as "depraved, immoral, psychotic, vulgar and anti-Christian." It was later reinstated.

In 1973, Vonnegut learned of a school district in North Dakota that was antagonistic towards Slaughterhouse-Five. An English teacher at a high school in the district wanted to read the novel with their class. Charles McCarthy, the head of the school board, declared the novel inappropriate because of obscene language. All copies of Vonnegut's novel in the school were burned in a furnace.

In a letter to McCarthy in 1973, Vonnegut defended his credibility, his character, and his work. In the letter, entitled "I Am Very Real", Vonnegut wrote that his books "beg that people be kinder and more responsible than they often are". He contended that his work should not be censored based on the general message in the novel.

The U.S. Supreme Court considered the First Amendment implications of the removal of the book, among others, from public school libraries in the case of Island Trees School District v. Pico, and concluded that "local school boards may not remove books from school library shelves simply because they dislike the ideas contained in those books and seek by their removal to 'prescribe what shall be orthodox in politics, nationalism, religion, or other matters of opinion.'" Slaughterhouse-Five is the sixty-seventh entry to the American Library Association's list of the "Most Frequently Challenged Books of 1990–1999" and number forty-six on the ALA's "Most Frequently Challenged Books of 2000–2009". In August 2011, the novel was banned at the Republic High School in Missouri. The Kurt Vonnegut Memorial Library countered by offering 150 free copies of the novel to Republic High School students on a first-come, first-served basis.

Criticism
Slaughterhouse-Five has been described as a quietist work, because Billy Pilgrim believes that the notion of free will is a quaint Earthling illusion. According to Robert Merrill and Peter A. Scholl, "Vonnegut's critics seem to think that he is saying the same thing [as the Tralfamadorians]." For Anthony Burgess, "Slaughterhouse is a kind of evasion—in a sense, like J. M. Barrie's Peter Pan—in which we're being told to carry the horror of the Dresden bombing, and everything it implies, up to a level of fantasy..." For Charles Harris, "The main idea emerging from Slaughterhouse-Five seems to be that the proper response to life is one of resigned acceptance." For Alfred Kazin, "Vonnegut deprecates any attempt to see tragedy, that day, in Dresden...He likes to say, with arch fatalism, citing one horror after another, 'So it goes.'" For Tanner, "Vonnegut has...total sympathy with such quietistic impulses." The same notion is found throughout The Vonnegut Statement, a book of original essays written and collected by Vonnegut's most loyal academic fans.

When confronted with the question of how the desire to improve the world fits with the notion of time presented in Slaughterhouse-Five, Vonnegut responded "you understand, of course, that everything I say is horseshit."

Adaptations

 * A film adaptation of the book was released in 1972. Although critically praised, the film was a box office flop. It won the Prix du Jury at the 1972 Cannes Film Festival, as well as a Hugo Award and Saturn Award. Vonnegut commended the film greatly. In 2013, Guillermo del Toro announced his intention to remake the 1972 film and work with a script by Charlie Kaufman.
 * In 1989, a theatrical adaptation was performed at the Everyman Theatre, in Liverpool, England.
 * In 1996, another theatrical adaptation of the novel premiered at the Steppenwolf Theatre Company in Chicago. The adaptation was written and directed by Eric Simonson and featured actors Rick Snyder, Robert Breuler and Deanna Dunagan. The play has subsequently been performed in several other theaters, including a New York premiere production in January 2008, by the Godlight Theatre Company. An operatic adaptation by Hans-Jürgen von Bose premiered in July 1996 at the Bavarian State Opera in Munich, Germany. Billy Pilgrim II was sung by Uwe Schonbeck.
 * In September 2009, BBC Radio 3 broadcast a feature-length radio drama based on the book, which was dramatised by Dave Sheasby, featured Andrew Scott as Billy Pilgrim and was scored by the group 65daysofstatic.
 * In September 2020, a graphic novel adaptation of the book, written by Ryan North and drawn by Albert Monteys, was published by BOOM! Studios, through their Archaia Entertainment imprint. It was the first time the book has been adapted into the comics medium.

title: Slaughterhouse-Five


text:
Talk:Complete metric space

Removed Link
I removed this link:
 * Cech completeness, absolute G_delta spaces

from the discussion of topologically complete spaces, since it's malformed and didn't fit into the sentence. If anybody knows what it's about, please put it back in as a legible sentence and with a link that might be the title of an article (perhaps it should be two).

I also moved the definition of Cauchy net to its own page.

-- Toby 23:40 Feb 20, 2003 (UTC)

Inner Product Spaces
What's all this about inner product spaces? There's nothing in Inner product space about completeness -- except completeness in a metric! If anything's wrong, then it's that this article should have something to say about how the ideas are applied to certain types of metric spaces -- such as inner product spaces. -- Toby 00:50 Feb 21, 2003 (UTC)

OK ... I think I was hasty and actually had in mind the idea of "complete" orthonormal set in an inner product space. Such an "orthonormal basis" is not always a "basis" in the sense of "Hamel basis", i.e., not every vector in such a space is a finite linear combination of basis vectors. And in infinite linear combinations, there are various different notions of convergence, and the one that matters in this case is the one defined by the metric. Michael Hardy 01:05 Feb 21, 2003 (UTC)

Yes, and there's a link to Completeness from Hermitian that's about this. So we should add it to Completeness (I just did). But this is complete orthonormal set, not complete space. -- Toby 03:46 Feb 21, 2003 (UTC)

complete spaces vs. closed set
from this article i don't really understand what is the difference between a closed set and a complete space. maybe someone can give an example of a closed space which ins't complete? —The preceding unsigned comment was added by 217.132.104.254 (talk) 09:38, 8 February 2007 (UTC).

Spaces aren't closed or open; subspaces are/aren't. Consider the rational numbers, Q, thought of as a topological space with the topology induced from the usual Borel topology on the real line R. Q is a closed subset of itself, since the empty set is an open subset of any topological space. However, Q is not complete; consider the sequence of successive decimal approximations to the square root of 2, which is Cauchy but not convergent. Sullivan.t.j 14:14, 8 February 2007 (UTC)

-

Other formulations of the completeness axiom
Is there a reason this specific formulation of the Completeness axiom was chosen over, say, the Supremum formulation, or that of Monotonic Convergence? Should these not at least be mentioned with a discussion of the benefits / downfalls of different formulations? I ask this specifically as the Supremum (or Infimum) formulation is often easier for the non-mathematician to understand. In a sense the most complex formulation is that represented here, and the question is whether this is where Wikipedia articles should be aimed.

-Jdr [13/3/2007 - 10:06pm GMT]

 * "Supremum" makes sense when there is an ordering, but in metric spaces generally there is no supremum. Which "monotic convergence" formultation are you talking about?  Does it work in metric spaces generally?  "Monotonic" seems to connote an ordering. Michael Hardy 22:54, 13 March 2007 (UTC)

Strange Example
In the text there is the example "The topological vector space R^ω of sequences of real numbers which have finitely many nonzero terms (the topology of this space can alternatively be defined as the limit topology of the Rn or as the coproduct of infinitely many copies of R) is not complete (even though its underlying field is). The completion of this space is the product ΠR of infinitely many copies of R. If instead we endow the space with the lp norm, its completion is the space lp(N)."

This contains many false statements, like

1.) The beginning "The topological vector space R^ω of sequences of real numbers which have finitely many nonzero terms" is already a bit strange, since so far no topology is given and therefore R^ω is just a vector space and not yet a topological one. There are many totally different topologies on this vector space.

2.) "the topology of this space can alternatively be defined as the limit topology of the Rn or as the coproduct of infinitely many copies of R" Yes, it is possible to endow this vector space with this particular topology, but then is not metrizable (and therefore not at all a good example for a "Complete Metric Space"). By the way, the space R^ω endowed with this topology is complete but not with respect to a metric (since there is none defining this topology) but with respect to the uniform strucutre as a topological vector space.

3.) The completion of this coproduct in number (2.) is NOT the product ΠR, since the coproduct is already complete as mentioned above. It is true that the product can be the completion of R^ω, but with another topology (which that in fact will be again metrizable)

4.) I admit that the last sentence is correct. "If instead we endow the space with the lp norm, its completion is the space lp(N)."

I would suggest that we remove this example or at least restrict it to the case where we put an lp-norm on it. --130.83.2.27 08:09, 7 August 2007 (UTC)
 * I cut out the example per your item 1 (I am not competent enough to judge items 2 and 3. :) There are many good examples in the text that we can get by without this very technical example, especially that it is not well-written and possibly incorrect. Oleg Alexandrov (talk) 19:43, 7 August 2007 (UTC)

Small correction is needed
The article says, in the section Some theorems:

 * If X is a set and M is a complete metric space, then the set B(X,M) of all bounded functions f from X to M is a complete metric space

I don't think one can make sense of "bounded functions" to a metric space. Either one takes all functions and equip M with a bounded metric, or take M a Banach space. --Bdmy (talk) 18:11, 12 January 2009 (UTC)

 * This looks fine to me, with perhaps one minor clarification. Take F to be the space of all functions from X to M and equip it with the uniform structure of uniform convergence. This uniform structure can be defined with a single pseudometric d(f,g) = sup d(f(x),g'(x)) where x ranges over X. (This is in general not a finite pseudometric.) As the uniform space F is clearly Hausdorff, it is also metrizable. And if M is complete, the the uniform space F'' is complete.

 * Now call a function f from X to M bounded if the image of X by f is bounded.

 * I don't remember of any interesting application of the notion of bounded set in a general metric space (not even sure that it is defined in books, although I agree that there's no much choice), and in my opinion a definition of bounded function should be given. Other than that, I agree with your preceding paragraph: taking this uniform structure with infinite values, you will define a complete space of all functions, without this rather awkward restriction of bounded.  Of course I understand that one wants a finite metric, but this could be achieved by replacing  d  by min(d, 1) without changing much of the interesting properties. --Bdmy (talk) 22:39, 12 January 2009 (UTC)
 * I didn't look your page before, otherwise I had said: Bonsoir, et amitiés de Paris. --Bdmy (talk) 22:43, 12 January 2009 (UTC)

 * Bonjour. Agree, bounded functions should be defined in the article before the statement. And exactly as you write, the min(d,1) is a metric that produces the same uniform structure. As for these concepts being defined in books, they certainly found their way into Topologie Générale of Bourbaki (Ch. X). In fact, Bourbaki treats the somewhat more general set-up: let S be a set of subsets of X. Then one defines in the obvious way the uniformity and topology of uniform convergence in the sets of S (or simply S-convergence). If S consists of just X we're back to uniform convergence, of course, and we can produce the uniformities of compact convergece (for X a topological space), of simple convergence etc. this way. Now carry out all of the above in this more general set-up: the set F equipped with the uniformity of S convergence is a complete uniform space for any choice of S if just M is complete (M does not have to be even metric for this). Also, with M metric, define BS as the set of functions which are bounded in each of the sets in S. Equip also BS with the uniformity of S-convergence, and it is true that it is a complete uniform space; indeed, it is again closed in F equipped with the topology of S-convergence. Amitiés, Stca74 (talk) 07:35, 13 January 2009 (UTC)

 * The set B of these bounded functions is a subset of F and the restriction of the supremum pseudometric above to B is by construction finite, hence a metric. It defines on B the topology of uniform convergence (making B a uniform subspace of F). Now clearly a uniform limit of functions in B is bounded, and hence B is closed inside F. But then as a closed subset of a complete (metrizable) uniform space B is itself complete. So to be fully explicit the article should make it explicit that it is the sup metric defining the topology and uniformity of uniform convergence with respect to which B is a complete metric space. Stca74 (talk) 22:20, 12 January 2009 (UTC)

Characterization of complete spaces through nested balls
I think the following fact (from A. A. Kolmogorov, S. V. Fomin "Introductory real analysis") should be added in the section "Some Theorems" (or even under a new title „A Completeness Criterion of a Metric Space“) or in the as of now poor article "Nested intervals":

Page 60 THEOREM 2 (Nested sphere theorem). A metric space R is complete if and only if every nested sequence $$ \{S_n\} = \{S[x_n, r_n]\} $$ of closed spheres in R such that $$ r_n \rightarrow 0 $$ as $$n \rightarrow \infty $$ has a nonempty intersection.

Matumba (talk) 00:06, 23 February 2009 (UTC)

 * I think this has to do with expansion constants, so I added a bit. -- Taku (talk) 21:57, 23 February 2009 (UTC)

complete space is called when every cauchy sequence converget. —Preceding unsigned comment added by 116.71.184.123 (talk) 21:49, 5 March 2010 (UTC)

“Cauchy space”
Who uses this term for complete metric spaces? Usually it refers to something completely different. --Chricho ∀ (talk) 16:01, 16 June 2014 (UTC)

Universal Property of Completion

 * It has the following universal property: if N is any complete metric space and f is any uniformly continuous function from M to N, then there exists a unique uniformly continuous function f′ from M′ to N, which extends f. The space M' is determined up to isometry by this property, and is called the completion of M''.

This property has any space M′ which contains M as a dense subspace. So, what means that this property determinates M′ up to isometry? 109.105.162.103 (talk) 06:24, 22 February 2019 (UTC)

title: Talk:Complete metric space


text:
Wireless

Wireless communication (or just wireless, when the context allows) is the transfer of information (telecommunication) between two or more points without the use of an electrical conductor, optical fiber or other continuous guided medium for the transfer. The most common wireless technologies use radio waves. With radio waves, intended distances can be short, such as a few meters for Bluetooth or as far as millions of kilometers for deep-space radio communications. It encompasses various types of fixed, mobile, and portable applications, including two-way radios, cellular telephones, personal digital assistants (PDAs), and wireless networking. Other examples of applications of radio wireless technology include GPS units, garage door openers, wireless computer mouse, keyboards and headsets, headphones, radio receivers, satellite television, broadcast television and cordless telephones. Somewhat less common methods of achieving wireless communications involve other electromagnetic phenomena, such as light and magnetic or electric fields, or the use of sound.

The term wireless has been used twice in communications history, with slightly different meanings. It was initially used from about 1890 for the first radio transmitting and receiving technology, as in wireless telegraphy, until the new word radio replaced it around 1920. Radio sets in the UK and the English-speaking world that were not portable continued to be referred to as wireless sets into the 1960s. The term wireless was revived in the 1980s and 1990s mainly to distinguish digital devices that communicate without wires, such as the examples listed in the previous paragraph, from those that require wires or cables. This became its primary usage in the 2000s, due to the advent of technologies such as mobile broadband, Wi-Fi, and Bluetooth.

Wireless operations permit services, such as mobile and interplanetary communications, that are impossible or impractical to implement with the use of wires. The term is commonly used in the telecommunications industry to refer to telecommunications systems (e.g. radio transmitters and receivers, remote controls, etc.) that use some form of energy (e.g. radio waves and acoustic energy) to transfer information without the use of wires. Information is transferred in this manner over both short and long distances.

Photophone
The first wireless telephone conversation occurred in 1880 when Alexander Graham Bell and Charles Sumner Tainter invented the photophone, the telephone that sent audio over a beam of light. The photophone required sunlight to operate, and a clear line of sight between the transmitter and receiver, which greatly decreased the viability of the photophone in any practical use. It would be several decades before the photophone's principles found their first practical applications in military communications and later in fiber-optic communications.

Early wireless
A number of wireless electrical signaling schemes including sending electric currents through water and the ground using electrostatic and electromagnetic induction were investigated for telegraphy in the late 19th century before practical radio systems became available. These included a patented induction system by Thomas Edison allowing a telegraph on a running train to connect with telegraph wires running parallel to the tracks, a William Preece induction telegraph system for sending messages across bodies of water, and several operational and proposed telegraphy and voice earth conduction systems.

The Edison system was used by stranded trains during the Great Blizzard of 1888 and earth conductive systems found limited use between trenches during World War I but these systems were never successful economically.

Radio waves

In 1894, Guglielmo Marconi began developing a wireless telegraph system using radio waves, which had been known about since proof of their existence in 1888 by Heinrich Hertz, but discounted as a communication format since they seemed, at the time, to be a short-range phenomenon. Marconi soon developed a system that was transmitting signals way beyond distances anyone could have predicted (due in part to the signals bouncing off the then unknown ionosphere). Marconi and Karl Ferdinand Braun were awarded the 1909 Nobel Prize for Physics for their contribution to this form of wireless telegraphy.

Millimetre wave communication was first investigated by Jagadish Chandra Bose during 1894–1896, when he reached an extremely high frequency of up to 60GHz in his experiments. He also introduced the use of semiconductor junctions to detect radio waves, when he patented the radio crystal detector in 1901.

Wireless revolution

The wireless revolution began in the 1990s, with the advent of digital wireless networks leading to a social revolution, and a paradigm shift from wired to wireless technology, including the proliferation of commercial wireless technologies such as cell phones, mobile telephony, pagers, wireless computer networks, cellular networks, the wireless Internet, and laptop and handheld computers with wireless connections. The wireless revolution has been driven by advances in radio frequency (RF), microelectronics, and microwave engineering, and the transition from analog to digital RF technology, which enabled a substantial increase in voice traffic along with the delivery of digital data such as text messaging, images and streaming media.

Modes
Wireless communications can be via:

Radio
Radio and microwave communication carry information by modulating properties of electromagnetic waves transmitted through space. Specifically, the transmitter generates artificial electromagnetic waves by applying time-varying electric currents to its antenna. The waves travel away from the antenna until they eventually reach the antenna of a receiver, which induces an electric current in the receiving antenna. This current can be detected and demodulated to recreate the information sent by the transmitter.

Free-space optical
Free-space optical communication (FSO) is an optical communication technology that uses light propagating in free space to transmit wireless data for telecommunications or computer networking. "Free space" means the light beams travel through the open air or outer space. This contrasts with other communication technologies that use light beams traveling through transmission lines such as optical fiber or dielectric "light pipes".

The technology is useful where physical connections are impractical due to high costs or other considerations. For example, free space optical links are used in cities between office buildings that are not wired for networking, where the cost of running cable through the building and under the street would be prohibitive. Another widely used example is consumer IR devices such as remote controls and IrDA (Infrared Data Association) networking, which is used as an alternative to WiFi networking to allow laptops, PDAs, printers, and digital cameras to exchange data.

Sonic
Sonic, especially ultrasonic short-range communication involves the transmission and reception of sound.

Electromagnetic induction
Electromagnetic induction only allows short-range communication and power transmission. It has been used in biomedical situations such as pacemakers, as well as for short-range RFID tags.

Services
Common examples of wireless equipment include:
 * Infrared and ultrasonic remote control devices
 * Professional LMR (Land Mobile Radio) and SMR (Specialized Mobile Radio) are typically used by business, industrial, and Public Safety entities.
 * Consumer Two-way radio including FRS Family Radio Service, GMRS (General Mobile Radio Service), and Citizens band ("CB") radios.
 * The Amateur Radio Service (Ham radio).
 * Consumer and professional Marine VHF radios.
 * Airband and radio navigation equipment used by aviators and air traffic control
 * Cellular telephones and pagers: provide connectivity for portable and mobile applications, both personal and business.
 * Global Positioning System (GPS): allows drivers of cars and trucks, captains of boats and ships, and pilots of aircraft to ascertain their location anywhere on earth.
 * Cordless computer peripherals: the cordless mouse is a common example; wireless headphones, keyboards, and printers can also be linked to a computer via wireless using technology such as Wireless USB or Bluetooth.
 * Cordless telephone sets: these are limited-range devices, not to be confused with cell phones.
 * Satellite television: Is broadcast from satellites in geostationary orbit. Typical services use direct broadcast satellite to provide multiple television channels to viewers.

Electromagnetic spectrum
AM and FM radios and other electronic devices make use of the electromagnetic spectrum. The frequencies of the radio spectrum that are available for use for communication are treated as a public resource and are regulated by organizations such as the American Federal Communications Commission, Ofcom in the United Kingdom, the international ITU-R or the European ETSI. Their regulations determine which frequency ranges can be used for what purpose and by whom. In the absence of such control or alternative arrangements such as a privatized electromagnetic spectrum, chaos might result if, for example, airlines did not have specific frequencies to work under and an amateur radio operator was interfering with a pilot's ability to land an aircraft. Wireless communication spans the spectrum from 9 kHz to 300 GHz.

Mobile telephones
One of the best-known examples of wireless technology is the mobile phone, also known as a cellular phone, with more than 6.6 billion mobile cellular subscriptions worldwide as of the end of 2010. These wireless phones use radio waves from signal-transmission towers to enable their users to make phone calls from many locations worldwide. They can be used within the range of the mobile telephone site used to house the equipment required to transmit and receive the radio signals from these instruments.

Data communications
Wireless data communications allow wireless networking between desktop computers, laptops, tablet computers, cell phones, and other related devices. The various available technologies differ in local availability, coverage range, and performance, and in some circumstances, users employ multiple connection types and switch between them using connection manager software or a mobile VPN to handle the multiple connections as a secure, single virtual network. Supporting technologies include:

 * Wi-Fi is a wireless local area network that enables portable computing devices to connect easily with other devices, peripherals, and the Internet. Standardized as IEEE 802.11 a, b, g, n, ac, ax, Wi-Fi has link speeds similar to older standards of wired Ethernet. Wi-Fi has become the de facto standard for access in private homes, within offices, and at public hotspots. Some businesses charge customers a monthly fee for service, while others have begun offering it free in an effort to increase the sales of their goods.

 * Cellular data service offers coverage within a range of 10-15 miles from the nearest cell site. Speeds have increased as technologies have evolved, from earlier technologies such as GSM, CDMA and GPRS, through 3G, to 4G networks such as W-CDMA, EDGE or CDMA2000. As of 2018, the proposed next generation is 5G.

 * Low-power wide-area networks (LPWAN) bridge the gap between Wi-Fi and Cellular for low-bitrate Internet of things (IoT) applications.
 * Mobile-satellite communications may be used where other wireless connections are unavailable, such as in largely rural areas or remote locations. Satellite communications are especially important for transportation, aviation, maritime and military use.

 * Wireless sensor networks are responsible for sensing noise, interference, and activity in data collection networks. This allows us to detect relevant quantities, monitor and collect data, formulate clear user displays, and to perform decision-making functions

Wireless data communications are used to span a distance beyond the capabilities of typical cabling in point-to-point communication and point-to-multipoint communication, to provide a backup communications link in case of normal network failure, to link portable or temporary workstations, to overcome situations where normal cabling is difficult or financially impractical, or to remotely connect mobile users or networks.

Peripherals
Peripheral devices in computing can also be connected wirelessly, as part of a Wi-Fi network or directly via an optical or radio-frequency (RF) peripheral interface. Originally these units used bulky, highly local transceivers to mediate between a computer and a keyboard and mouse; however, more recent generations have used smaller, higher-performance devices. Radio-frequency interfaces, such as Bluetooth or Wireless USB, provide greater ranges of efficient use, usually up to 10 feet, but distance, physical obstacles, competing signals, and even human bodies can all degrade the signal quality. Concerns about the security of wireless keyboards arose at the end of 2007 when it was revealed that Microsoft's implementation of encryption in some of its 27 MHz models were highly insecure.

Energy transfer
Wireless energy transfer is a process whereby electrical energy is transmitted from a power source to an electrical load that does not have a built-in power source, without the use of interconnecting wires. There are two different fundamental methods for wireless energy transfer. Energy can be transferred using either far-field methods that involve beaming power/lasers, radio or microwave transmissions, or near-field using electromagnetic induction. Wireless energy transfer may be combined with wireless information transmission in what is known as Wireless Powered Communication. In 2015, researchers at the University of Washington demonstrated far-field energy transfer using Wi-Fi signals to power cameras.

Medical technologies
New wireless technologies, such as mobile body area networks (MBAN), have the capability to monitor blood pressure, heart rate, oxygen level, and body temperature. The MBAN works by sending low-powered wireless signals to receivers that feed into nursing stations or monitoring sites. This technology helps with the intentional and unintentional risk of infection or disconnection that arise from wired connections.

Categories of implementations, devices, and standards

 * Cellular networks: 0G, 1G, 2G, 3G, 4G, 5G, 6G
 * Cordless telephony: DECT (Digital Enhanced Cordless Telecommunications)
 * Land Mobile Radio or Professional Mobile Radio: TETRA, P25, OpenSky, EDACS, DMR, dPMR
 * List of emerging technologies
 * Radio station in accordance with ITU RR (article 1.61)
 * Radiocommunication service in accordance with ITU RR (article 1.19)
 * Radio communication system
 * Short-range point-to-point communication: Wireless microphones, Remote controls, IrDA, RFID (Radio Frequency Identification), TransferJet, Wireless USB, DSRC (Dedicated Short Range Communications), EnOcean, Near Field Communication
 * Wireless sensor networks: Zigbee, EnOcean; Personal area networks, Bluetooth, TransferJet, Ultra-wideband (UWB from WiMedia Alliance).
 * Wireless networks: Wireless LAN (WLAN), (IEEE 802.11 branded as Wi-Fi and HiperLAN), Wireless Metropolitan Area Networks (WMAN) and (LMDS, WiMAX, and HiperMAN)

title: Wireless


text:
Sean O'Hagan

Sean O'Hagan (born 1959) is an Irish singer and songwriter who leads the avant-pop band the High Llamas, which he founded in 1992. He is also known for being one half of the songwriting duo (with Cathal Coughlan) in Microdisney and for his work during the early 1990s with the English-French band Stereolab.

Life and career
O'Hagan was born in England to Irish parents, moving to Cork as a teenager.

He is a founding member of the Irish indie band Microdisney, alongside Cathal Coughlan; the band initially formed in Cork but was based in London from 1982 until their split in 1988.

He released a solo album titled High Llamas in 1990, which would become the name of a band he subsequently formed. The High Llamas were influenced by the Beach Boys, Ennio Morricone, Antonio Carlos Jobim and avant-garde electronica. He has also collaborated extensively with Stereolab, he was an official member from 1993 to 1994, and is credited as a guest musician on later releases.

In 1996, O'Hagan collaborated with Tim Gane of Stereolab as Turn On, releasing an album of the same name on Drag City Records. They also worked together on the soundtrack to the film La Vie d'Artiste.

On 27 November 2017, it was announced that O'Hagan and Coughlan would reform Microdisney for a one-off concert in the National Concert Hall, Dublin on 2 June 2018. The concert sold out, and was followed by gigs in Cork and London. Coughlan died in 2022.

Unrealised Beach Boys collaboration
In the mid 1990s, Brian Wilson was attempting to organize a comeback album with the Beach Boys and his collaborator Andy Paley. After Wilson's bandmate Bruce Johnston heard the High Llamas' 1996 album Hawaii, an unsuccessful attempt was made to instead coordinate a collaboration between O'Hagan and Wilson. Some of the songs that later appeared on the High Llamas' 1998 album Cold and Bouncy were then briefly under consideration to be recorded by the Beach Boys.

One of the reasons that the collaboration never happened, by O'Hagan's account, was interference from Wilson's wife Melinda and former wrestler Joe Thomas, who was ultimately chosen to produce Wilson's 1998 solo album, Imagination. O'Hagan, who thought Wilson's musical talents were best served at reclaiming his title as a "20th-century avant-garde pop genius", had voiced objections to Thomas' desire to instead break Wilson into the adult contemporary market. According to O'Hagan, he attended one meeting with Wilson and two with the Beach Boys, but Wilson's "camp" was unable to reach an agreement with the other Beach Boys. He said of Wilson in a 2001 interview,

"I didn't go out of my way to meet Brian, and I wouldn't have wanted to. I'm happy enough to have been influenced by [him] [...] He's not mad, but [...] I asked him what sort of record he wanted to make and told him he could have strings and brass, and I was witness to him running around his house shouting "Too much!" and "You're blowing my mind!" over and over."

A post attributed to Wilson on his website wrote that O'Hagan was "a real sweet guy, but I didn't think I needed him to show me how to do the things I had already done 30 years earlier". Johnston surmised that "Brian was a little intimidated by Sean, in the same way that Gershwin may have been intimidated by Oscar Levant."

Discography
Studio albums and soundtracks
 * High Llamas (1990)
 * La Vie d'artiste (2007) (with Tim Gane)
 * The Musical Paintings Volume 1 (2008) (with Jean Pierre Muller)
 *  Copacabana (2010) (with Tim Gane)
 * Radum Calls, Radum Calls (2019)
 *  Hey Panda  (2024)

Stereolab appearances • Space Age Bachelor Pad Music (1993)

• Ping Pong (1994)

• Mars Audiac Quintet (1994)

• Fluorescences (1996)

• Cybele's Reverie (1996)

• Emperor Tomato Ketchup (1996)

• Miss Modular (1997)

• Dots and Loops (1997)

• The Free Design (1999)

• The First of the Microbe Hunters (2000)

• Sound-Dust (2000)

• ''Chemical Chords (2007)

• Not Music (2010) Other appearances
 * Cornelius – Fantasma (1998)
 * Cornelius – FM (1999)
 * The Heavy Blinkers – Health (2013)

title: Sean O'Hagan


text:
Horst von Möllendorff

Horst von Möllendorff (26 April 1906 – 17 December 1992 ) was a German cartoonist who was "drafted" to work for the Nazis' animated short industry. He was hired as a result of former commercial animator Hans Fischerkoesen not being able to come up with adequate story ideas for his short films. Horst was pulled from his job as a popular Berlin newspaper cartoonist to become a gagman for the animation industry.

Möllendorff received authorship for at least three films:
 * Verwitterte Melodie (Weather-beaten Melody), 1942
 * Der Schneemann (The Snowman), 1943
 * Hochzeit im Korallenmeer (Wedding in the Coral Sea), 1945

title: Horst von Möllendorff


text:
Der Schneemann

Der Schneemann, also known as The Snowman, Snowman in July or The Magic Snowman, is a 1944 animated short film, created in Nazi Germany. It was written by cartoonist Horst von Möllendorff and animated by Hans Fischerkoesen. It was animated in Potsdam, Germany, near UFA's Neubabelsberg Studios.

Plot
Snow falls on the snowman to form a heart shape on him. The snowman wakes and begins juggling with the snow. A dog begins chasing him and takes a bite out of him. The dog then throws snow at the snowman but this only fills the missing part of the snowman. Eventually the dog leaves.

The snowman starts skating on ice but falls through and staggers away largely melted. However, by falling down a hill and rolling in the snow the snowman reforms himself.

The snowman now falls to sleep at night. A rabbit tries to steal his carrot nose but the snowman prevents this. The snowman gets up and enters a house and finds a calendar. He finds the month July on it and then puts himself in a refrigerator so that he may see this month.

During this time, the sun makes the snow melt and gives colour to the botanical species. Meanwhile, the snowman sleeps in the refrigerator.

The snowman wakes in July. His back is stuck in the fridge. He adjusts the thermostat and waits. He leaves the refrigerator and looks for the signs of summer through the window. He embraces the summer and breathes in the perfume of the flowers. He puts a pink rose in his lapel and rolls in the fields.

The snowman melts under the heat of the sun. He begin to sing "Da ist der Sommer meines Lebens..." ("that's the summer of my life") and turns into water. These are the only spoken words in the film. The rabbit from earlier mourns his loss whilst the children of the rabbit jump into the snowman's hat. He picks up the snowman's carrot and takes a bite from it.

title: Der Schneemann


text:
Verwitterte Melodie

Verwitterte Melodie, or Weather-beaten Melody, is a 1942 animated short, made in Nazi Germany. It was written mainly by cartoonist Hans Fischerkoesen, although the sole credits often went to Horst von Möllendorff. It was animated by Jiří Brdečka in Prague.

Plot
The general outline of the plot is of a bee that finds an abandoned phonograph in a meadow and uses her stinger as a stylus to play the record on it.

title: Verwitterte Melodie