Idempotence and Eagle Eye: Difference between pages

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{{otheruses4|the 2008 action thriller}}
'''Idempotence''' {{IPAEng|ˌaɪdɨmˈpoʊtəns}} describes the property of operations in [[mathematics]] and [[computer science]] which means that multiple applications of the operation does not change the result. The concept of idempotence arises in a number of places in [[abstract algebra]] (in particular, in the theory of [[projector (linear algebra)|projector]]s, [[closure operator]]s and [[functional programming]], in which it is connected to the property of [[Referential transparency (computer science)|referential transparency]]).
{{Infobox Film
| name =
| image = Eagle eye poster.jpg
| caption = Theatrical release poster
| director = [[D.J. Caruso]]
| producer = [[Steven Spielberg]]<br/>[[Alex Kurtzman]]<br/>[[Roberto Orci]]<br/>Pat Crowley<br/>Ed McDonnell
| writer = Dan McDermott<br/>John Glenn<br/>Travis Wright<br/>Hillary Seitz
| starring = [[Shia LaBeouf]]<br/>[[Michelle Monaghan]]<br/>[[Rosario Dawson]]<br/>[[Billy Bob Thornton]]<br/>[[Anthony Mackie]]<br/>[[Michael Chiklis]]<br/>[[Cameron Boyce]]
| music = [[Brian Tyler]]
| cinematography = [[Dariusz Wolski]]
| editing = Jim Page
| distributor = [[DreamWorks Pictures]]<br>[[Alliance Films]] (Canada)<br>[[Momentum Pictures]] (North America)
| released = '''Australia:'''<br />September 25, 2008<br /> '''[[North America]]:'''<br />September 26, 2008<br />'''United Kingdom:'''<br />October 17, 2008
| runtime = 118 minutes
| country = [[United States]]
| language = [[English language|English]]
| budget = $80 million <ref name=mojo/>
| gross = $88 million <ref name=mojo/>
| website = http://www.eagleeyemovie.com/
| amg_id = 1:406951
| imdb_id = 1059786
}}
'''''Eagle Eye''''' is a [[2008 in film|2008]] [[political cinema|action]]/[[thriller (genre)|thriller film]] directed by [[D.J. Caruso]] and starring [[Shia LaBeouf]] and [[Michelle Monaghan]]. The two portray a young man and a single mother who are brought together and coerced by an anonymous caller into carrying out a terrorist cell's plot. The film has been rated PG-13 by the MPAA and has been released in regular [[35mm]] theatres and [[IMAX]] theatres.


==Plot==
There are several meanings of idempotence, depending on what the concept is applied to:
The film begins with the armed forces getting a lead on a suspected terrorist. As the man is a recluse, getting a positive ID proves difficult, and the [[Department of Defense|DOD]]'s computer system recommends that the mission be aborted. From continued aerial surveillance of the area, the suspect is apparently attending a funeral but the possibility that it is a facade makes those present all nervous - the system continues to recommend abort. The [[Secretary of Defense]] ([[Michael Chiklis]]) agrees with the abort recommendation, but the President orders the mission be carried out anyway. This turns into a political backlash when all those killed turn out to be civilians, and retaliatory bombings are carried out in response.


The scene abruptly shifts to the life of Jerry Shaw ([[Shia LaBeouf]]), a [[Stanford University]] drop out who not only lacks any real direction in his life, but also faces great financial difficulty. He gets a phone call from his parents telling him that his twin brother, Ethan, is dead. Following the funeral, Jerry gets a $1,000 check from his dad. When Jerry tries to deposit the check and withdraw some money from the [[ATM]], he's surprised to see that his account is filled with a lump sum of money. Soon he returns home to find his apartment filled with a large amount of weapons, explosives, and forged documents. He receives a phone call from an unknown woman, who explains that the [[Federal Bureau of Investigation|FBI]] are about to apprehend him in thirty seconds and that he must escape. Not believing her, he is caught by the FBI, led by Agent Thomas Morgan ([[Billy Bob Thornton]]) and [[Air Force Office of Special Investigations]] Special Agent Zoe Perez ([[Rosario Dawson]]). The unknown woman arranges Jerry's escape and has him join up with single mother Rachel Holloman ([[Michelle Monaghan]]). Holloman is being coerced into helping by the woman, who threatens to kill her son, Sam, a trumpet player on his way to [[Washington, D.C.]] from [[Chicago]] for a band recital.
*A [[unary operation]] (or [[function (mathematics)|function]]) is called '''idempotent''' if, whenever it is applied twice to any value, it gives the same result as if it were applied once. For example, the [[absolute value]] function is idempotent as a function from the set of real numbers to the set of real numbers: {{nowrap|1=abs(abs (''x'')) = abs(''x'')}}.
*A [[binary operation]] is called '''idempotent''' if, whenever it is applied to two equal values, it gives that value as the result. For example, the operation giving the [[maximum]] value of two values is idempotent: {{nowrap|1=max(''x'', ''x'') = ''x''}}.
*Given a binary operation, an '''idempotent element''' (or simply an '''idempotent''') for the operation is a value for which the operation, when given that value for both of its operands, gives the value as the result. For example, the number 1 is an idempotent of [[multiplication]]: {{nowrap|1=1 × 1 = 1}}.


The woman helps the pair to avoid the police and FBI units, demonstrating the ability to remotely control virtually any networked device, such as traffic lights, cell phones, and even automated cranes. While Jerry and Rachel follow her instructions, the woman has a [[crystal]] explosive made into a necklace and its sound-based trigger placed inside Sam's trumpet. Jerry and Rachel are led to Washington, D.C. through various means. Along the way, they are introduced to the woman, who is actually a top secret [[super-computer]] called ARIA tasked with gathering intelligence from all over the world. ARIA, the overtaken computer, can control virtually anything electronic to that end. In light of the mistake made by the President at the beginning of the film, ARIA has decided that the [[executive branch]] is a threat to the public good and must be eliminated. ARIA plans to destroy the President's Cabinet, and calls this Operation Guillotine. It has decided to leave the Secretary of Defense, who agreed with its recommendation to abort, as the [[United States presidential line of succession|successor to the presidency]]. She does not reveal this to Jerry or Rachel, merely explaining that she is trying to help the people of the United States.
== Definitions ==
===Unary operation===


At [[the Pentagon]], where ARIA is housed, Agent Perez discovers that Ethan worked as a technician for the computer and locked it down to prevent ARIA from carrying out her plan. Perez warns the Secretary of Defense and they discuss the situation in a sealed room to prevent ARIA from hearing their conversation. Jerry and Rachel arrive at the Pentagon and are led to the super computer, where ARIA forces Jerry to impersonate Ethan and use an override code allowing her to go ahead with the plan. She then instructs Rachel to eliminate Jerry to prevent the lock from being reinstated, but Rachel cannot bring herself to do it. Rachel is led out of the building by ARIA while Jerry is caught by Agent Morgan. Having been warned by Agent Perez, Morgan believes Jerry's story and takes him to the [[United States Capitol]]. On their way, however, ARIA sends an [[MQ-9 Reaper]] [[UCAV]] after them. Agent Morgan sacrifices himself to destroy the craft and save Jerry.
A [[unary operation]] ''f'' that is a map from some set ''S'' into itself is called idempotent if, for all ''x'' in ''S'',


Meanwhile, Agent Perez returns to the super computer and is successful in destroying it, but not before ARIA uploads roughly a fifth of its memory to another location. Rachel is given the explosive necklace and sent to watch the President's speech. Sam's class, whose recital has been moved from the [[Kennedy Center]] to the Capitol for the President's [[State of the Union Address]], begins to play. The trigger that will set off the explosive necklace is set to activate when Sam plays a high [[F (musical note)|F]] on his trumpet corresponding to the word "free" in the last verse of the [[The Star-Spangled Banner|U.S. national anthem]]. Jerry successfully infiltrates the vicinity and fires Morgan's pistol into the air, stopping the performance and emptying the room, but provoking a [[Secret Service]] agent to shoot him in the shoulder.
:''f''(''f''(''x'')) = ''f''(''x'').


In the aftermath of the chaos ARIA caused, the Secretary of Defense urges that another super computer should not be built. Ethan posthumously receives the [[Medal of Honor]] while Jerry, injured but alive and well, receives the [[Congressional Gold Medal]]. The film ends with Jerry attending Sam's birthday party. Rachel thanks him for attending and kisses him on the cheek. She then tells Jerry that she is glad that he is there. After a second of silence, Jerry tells her, "Me too," and the film ends.
In particular, the [[identity function]] id<sub>''S''</sub>, defined by {{nowrap|1=id<sub>''S''</sub>(''x'') = ''x''}}, is idempotent, as is the [[constant function]] ''K<sub>c</sub>'', where ''c'' is an element of ''S'', defined by {{nowrap|1=''K<sub>c</sub>''(''x'') = ''c''}}.


==Main cast==
An important class of idempotent functions is given by [[projection (linear algebra)|projection]]s in a [[vector space]]. An example of a projection is the function π<sub>''xy''</sub> defined by {{nowrap|1= π<sub>''xy''</sub>(''x'', ''y'', ''z'') = (''x'', ''y'', 0)}}, which projects an arbitrary point in 3D space to a point on the ''x''–''y''-[[plane (mathematics)|plane]], where the third coordinate (''z'') is equal to 0.
* '''[[Shia LaBeouf]]''' as '''Jerry Shaw''': a young slacker who is framed as a terrorist and vows to clear his name with the FBI's help. LaBeouf also plays Ethan Shaw, Jerry's twin brother who is a skilled, intelligent man in the Air Force with a secret occupation.
* '''[[Michelle Monaghan]]''' as '''Rachel Holloman''': a single mother who is also framed as a terrorist and vows to clear her name with her companions.
* '''[[Rosario Dawson]]''' as '''Zoe Perez''': a government agent who is tracking down the terrorist cell.<ref>{{cite news | author=Michael Fleming | url=http://www.variety.com/article/VR1117970168.html?categoryid=13&cs=1 | title=Rosario Dawson joining 'Eagle Eye' | publisher=[[Variety (magazine)|Variety]] | date=[[2007-08-13]] | accessdate=2007-11-13 }}</ref>
* '''[[Billy Bob Thornton]]''' as '''Thomas Morgan''': the patriotic leader of a homeland security team tracking down the cell.<ref>{{cite news | author=Tatiana Siegel | coauthors=Michael Fleming | url=http://www.variety.com/article/VR1117975526.html?categoryid=13&cs=1 | title=Billy Bob Thornton spies 'Eagle Eye' | publisher=[[Variety (magazine)|Variety]] | date=[[2007-11-07]] | accessdate=2007-11-13 }}</ref>
* '''[[Ethan Embry]]''' as '''Toby Grant''': Morgan's companion whom he assists into tracking down the cell.<ref>{{cite news | author=Clint Morris | url=http://www.moviehole.net/news/20071121_embry_joins_eagle_eye_1.html | title=Embry joins Eagle Eye | publisher=Moviehole | date=[[2007-11-21]] | accessdate=2007-11-27 }}</ref>
* '''[[Anthony Mackie]]''' as '''Major Bowman''': A soldier assigned to monitor the super-computer.
* '''[[Michael Chiklis]]''' as '''George Callister''': The U.S. Secretary of Defense.
* '''[[Cameron Boyce]]''' as '''Sam Holloman''': Rachel's Son
* '''[[Julianne Moore]]''' as '''ARIA''': The supercomputer whose machinations form the basis for the film's events.


==Production==
A unary operation {{nobreak|''f'' : ''S'' → ''S''}} is idempotent if it maps all elements of ''S'' to [[Fixed point (mathematics)|fixed point]]s. For a set with ''n'' elements there are
Screenwriter Dan McDermott wrote the original script for ''Eagle Eye'' based on an original idea by [[Steven Spielberg]]. The studio [[DreamWorks]] then bought McDermott's script and set up the project to potentially be directed by Spielberg. When the director became busy with ''[[Indiana Jones and the Kingdom of the Crystal Skull]]'', he dropped out of the project. Director [[D.J. Caruso]], who directed the 1996 TV series ''[[High Incident]]'' under Spielberg's executive production, replaced the director in helming ''Eagle Eye''. However, Spielberg remains [[executive producer]].<ref>[http://imdb.com/title/tt1059786/fullcredits Eagle Eye (2008) - Full cast and crew<!-- Bot generated title -->]</ref> In June 2007, actor LaBeouf who was involved in Spielberg's and Caruso's 2007 film ''[[Disturbia]]'' and ''Indiana Jones and the Kingdom of the Crystal Skull'', re-joined the director and executive producer to star as the lead in ''Eagle Eye''. McDermott's script was rewritten by screenwriters John Glenn, Travis Wright and Hillary Seitz in preparation for production.<ref name=duo>{{cite news | author=Michael Fleming | coauthors=Pamela McClintock | url=http://www.variety.com/article/VR1117967613.html?categoryid=13&cs=1 | title='Disturbia' duo set for 'Eagle Eye' | publisher=[[Variety (magazine)|Variety]] | date=[[2007-06-25]] | accessdate=2007-11-13 }}</ref> Filming began on [[November 6]] [[2007]] <ref>{{cite news | author=Nellie Andreeva | coauthors=Borys Kit | url=http://www.hollywoodreporter.com/hr/content_display/film/news/e3ife647aa3f09848617a57d0ad911d18b3 | title=For most part, the shows go on | publisher=[[The Hollywood Reporter]] | date=[[2007-11-06]] | accessdate=2007-11-13 }}</ref> and wrapped in February 2008.<ref name=HR2>{{cite news | author= Carly Mayberry and Borys Kit | url=http://www.hollywoodreporter.com/hr/content_display/film/news/e3i18d831ccf80216b9f4dee1db47cddfe6 | title='Eagle' lands Chiklis in cabinet post | publisher=[[The Hollywood Reporter]] | date=[[2008-01-08]] | accessdate=2008-01-08 }}</ref> The film's [[visual effects]] are being created by [[Sony Pictures Imageworks]].<ref>{{cite news | url=http://www.hollywoodreporter.com/hr/content_display/news/e3ie4014cd99a43c45eb9d280d73cb9236d | title=G-Force' is with Imageworks | author=Carolyn Giardina | work=[[The Hollywood Reporter]] | publisher=[[Nielsen Company|The Nielsen Company]] | date=[[2008-07-01]] | accessdate=2008-07-01 }}</ref> On August 13, the film was rated PG-13 by the [[MPAA]] for intense sequences of action violence and language.


The story was originally conceived in [[1996]], Caruso said by the time the film came to fruition 12 years later, "the technology had finally caught up to the storytelling. ... Everybody has a [[BlackBerry]] or an [[iPhone]] on their [[belt]], and we think we're constantly being tracked. It's less [[science fiction]] than when Steven (Spielberg) conceived it."<ref name="EW Fall Preview">Vary, Adam B. "Fall Movie Summer Preview, September: Eagle Eye." ''[[Entertainment Weekly]]'', Iss. #1007/1008, August 22/29, 2008, pg.52.</ref> Caruso wanted to bring a gritty, [[1970s]]-era sensibility to the film. Accordingly, a key chase scene in a high-tech package-processing hub on [[conveyor belt|conveyor belts]] was shot without the use of [[computer-generated imagery]]. "It was like [[Chutes and Ladders]] for adults. It was pretty dangerous, and a lot of fun.<ref name="EW Fall Preview" /> While filming the scene, Monaghan suffered a welt after a [[cable]] brushed her [[neck]] and Caruso hit his head on a protruding [[bolt]], requiring [[stitch|stitches]].<ref name="EW Fall Preview" />
:<math>\sum_{k=0}^n {n \choose k} k^{n-k}</math>


==Music==
idempotent functions, where
The music to ''Eagle Eye'' was written by composer [[Brian Tyler]], who recorded the score with an 88-piece ensemble of the [[Hollywood Studio Symphony]] at the Sony Scoring Stage. The session was interrupted by the [[2008 Chino Hills earthquake|Chino Hills earthquake]] on July 29, 2008 – and a recording of the quake hitting the scoring stage is online.<ref name=scoring>{{cite news | author=Dan Goldwasser | url=http://www.scoringsessions.com/news/156 | title=Brian Tyler scores ''Eagle Eye'' | publisher=ScoringSessions.com | date=[[2008-09-11]] | accessdate=2008-09-16 }}</ref> The score was released on [[iTunes]] on September 25, 2008 and followed by a CD release on September 30.


==Promotion==
:<math>{n \choose k} k^{n-k}</math>
The official movie website features an [[Alternate reality game|ARG]] type of gameplay system to promote the movie. The voice previewed behind the phone in multiple trailers contacts the player, placing them in unique experiences. This has been called the Eagle Eye Freefall Experience. While official cast listings do not list the name of the actress behind the mysterious voice featured in the film and trailers, Rosario Dawson confirmed at the Hollywood premiere that it belongs to [[Julianne Moore]].<ref>{{cite news|url=http://omg.yahoo.com/news/eagle-eye-star-reveals-identity-of-movies-mayhem-causing-voice/13209|title='Eagle Eye' Star Reveals Identity Of Movie's Mayhem Causing Voic}}</ref>


==Critical reception==
is the number of idempotent functions with exactly ''k'' fixed points. The [[integer sequence]] of the number of idempotent functions as given by the sum above starts with 1, 1, 3, 10, 41, 196, 1057, 6322, 41393,&hellip;<ref>{{SloanesRef|sequencenumber=A000248}}</ref>
''Eagle Eye'' received generally negative reviews from critics. As of [[October 1]], [[2008]], the review aggregator [[Rotten Tomatoes]] reported that 28% of critics gave the film positive reviews based on 118 reviews, with the consensus that the film "is a preposterously plotted thriller that borrows heavily from other superior films."<ref>{{cite web|url=http://www.rottentomatoes.com/m/eagle_eye/ |title=Eagle Eye Movie Reviews, Pictures - Rotten Tomatoes |accessdate=2008-10-01 |publisher=[[Rotten Tomatoes]]}}</ref> [[Metacritic]] reported the film had an average score of 43 out of 100, based on 28 reviews &mdash; indicating mixed or average reviews.<ref>{{cite web|url=http://www.metacritic.com/film/titles/eagleeye |title=Eagle Eye (2008): Reviews |accessdate=2008-09-27 |publisher=[[Metacritic]]}}</ref>


[[Roger Ebert]] of the ''[[Chicago Sun-Times]]'' gave ''Eagle Eye'' a score of two stars out of four, saying: "The word preposterous is too moderate to describe ''Eagle Eye''. This film contains not a single plausible moment after the opening sequence, and that's borderline. It's not an assault on intelligence. It's an assault on consciousness."<ref>[http://rogerebert.suntimes.com/apps/pbcs.dll/article?AID=/20080925/REVIEWS/809250304 Eagle Eye review], Roger Ebert, Chicago Sun-Times, September 25, 2008</ref> [[James Berardinelli]] of ReelViews gave the film one and a half stars out of four, saying: "This movie tests the viewing public's tolerance for enduring crass stupidity when the payoff is a series of repetitive, ADD-infected chase scenes. Director D.J. Caruso does a moderately good job of hiding how incredibly dumb this screenplay is by keeping things moving at such a whirlwind pace that a lot more seems to be happening than actually is. In reality, the chase scenes don't mean anything because they don't advance the plot—it's mice on a treadmill, running and running and not getting anywhere."<ref>[http://www.reelviews.net/php_review_template.php?identifier=1347 Eagle Eye review], James Berardinelli, ReelViews, September 2008</ref> ''[[The Hollywood Reporter]]'' called it a "slick, silly [[techno thriller]]" and "Even those who surrender all disbelief at the door will be hard pressed not to smirk at some of wildly improbable plotting--"<ref>[http://www.hollywoodreporter.com/hr/film/reviews/article_display.jsp?JSESSIONID=tyyQLghZ4mk5pcJyLH3KbnQTgb7ykTGkjVp6tWB2t2F2DFGfWLLc!1414428201&&rid=11712 Film Review: Eagle Eye], Michael Rechtshaffen, THE HOLLYWOOD REPORTER, September 25 2008</ref>
===Binary operation===


Josh Rosenblatt of ''[[The Austin Chronicle]]'' enjoyed the film, calling it "good, manic fun plus a heavy dose of political intrigue adding up to two hours of clamorous, mind-numbing nonsense."<ref>[http://www.austinchronicle.com/gyrobase/Calendar/Film?Film=oid%3A676050 Eagle Eye review], Josh Rosenblatt, Austin Chronicle, September 2008</ref> William Arnold of the ''[[Seattle Post-Intelligencer]]'' also gave ''Eagle Eye'' a positive review, remarking that it's "engrossing as an intellectual puzzle" and "a solid thriller."<ref>[http://seattlepi.nwsource.com/movies/380574_eagle26q.html Eagle Eye review], William Arnold, Seattle Post-Intelligencer, September 2008</ref> Mark Bell of [[Film Threat]] said: "the film isn't a complete waste of your time [...] but don't expect anything brilliant."<ref>[http://www.filmthreat.com/index.php?section=reviews&Id=11218 Eagle Eye review], Mark Bell, Film Threat, September 2008</ref> Nathan Rabin ''[[The Onion]]'''s [[The A.V. Club|A.V. Club]] called the film "achingly idiotic" and "the unintentional laugh riot of the year."<ref>[http://www.avclub.com/content/cinema/eagle_eye Eagle Eye review], Nathan Rabin, The Onion (A.V. Club), September 26th, 2008</ref> Neely Tucker of ''[[The Washington Post]]'' said that ''Eagle Eye'' is "sometimes entertaining" but "doesn't have much to say."<ref>[http://www.ew.com/ew/article/0,,20228543,00.html Eagle Eye review], Neely Tucker, Washington Post, September 2008</ref> Robert Koehler of ''[[Variety (magazine)|Variety]]'' felt that the film's "first 35 minutes sizzle" but "the story [becomes] near-parody in the final act."<ref>Odessy[http://www.variety.com/review/VE1117938502.html?categoryid=31&cs=1 Eagle Eye review], Robert Koehler, Variety, September 2008</ref>
A [[binary operation]] ★ on a set ''S'' is called idempotent if, for all ''x'' in ''S'',


==Box office performance==
:''x''★''x'' = ''x''.
In its opening weekend, ''Eagle Eye'' grossed $29.1 million in 3,510 theaters in the United States and Canada, ranking (for 1 week) #1 at the box office.<ref>{{cite web|url=http://www.boxofficemojo.com/movies/?page=weekend&id=eagleeye.htm |title=Eagle Eye (2008) - Weekend Box Office Results |accessdate=2008-10-04 |publisher=[[Box Office Mojo]]}}</ref> As of [[October 12]], 2008, it has grossed $88 million worldwide &mdash; $70.5 million in the United States and Canada and $17.5 million in other territories.<ref name=mojo>{{cite web|url=http://www.boxofficemojo.com/movies/?id=eagleeye.htm |title=Eagle Eye (2008) |accessdate=2008-10-12 |publisher=[[Box Office Mojo]]}}</ref>


==Mobile game==
For example, the operations of [[union (set theory)|set union]] and [[intersection (set theory)|set intersection]] are both idempotent, as are [[logical conjunction]] and [[logical disjunction]], and, in general, the [[meet (mathematics)|meet]] and [[join (mathematics)|join]] operations of a [[lattice (order)|lattice]].
A [[Mobile game]] based on the movie was developed and published by Magmic Games. It was released for Blackberry, Windows Mobile, BREW and J2ME devices prior to the movies launch in early September.<ref>{{cite news|url=http://magmic.com/game/EagleEye|title=Eagle Eye: The Game}}</ref><ref>{{cite news|url=http://www.pocketgamer.co.uk/r/Various/Eagle+Eye/product.asp?p=Eagle%20Eye&i=7452&art=9067|title=Movie tie-in}}</ref>


=="Aria" The Giant Computer From The Movie==
An element ''x'' of ''S'' is called idempotent for ★ if, for that element,
The visual design (including the water below) of the computer from the movie came from the [[Super-Kamiokande]],a [[Neutrino detector|neutrino observatory]] in the city of [[Hida, Gifu|Hida]], [[Gifu Prefecture]], [[Japan]]. The observatory was designed to search for [[proton decay]], study [[solar neutrino|solar]] and [[Neutrino#Atmospheric neutrinos|atmospheric neutrino]]s, and keep watch for [[supernova]]s in the [[Milky Way Galaxy]].
[http://www-sk.icrr.u-tokyo.ac.jp/sk/gallery/index-e.html Pictures of Super-K from Japanese website]


==References==
:''x''★''x'' = ''x''.
{{reflist|2}}


==External links==
In particular, an [[identity element]] of ★ is idempotent for the operation.
*[http://www.7trailers.com/eagle-eye Eagle Eye Trailer]
*[http://www.eagleeyemovie.com Official website]
*[http://www.eagleeyefreefall.com Freefall Experience]
*{{imdb title|id=1059786|title=Eagle Eye}}


*{{rotten-tomatoes|id=eagle_eye|title=Eagle Eye}}
===Connections===
*{{metacritic film|id=eagleeye|title=Eagle Eye}}
*{{mojo title|id=eagleeye|title=Eagle Eye}}
*{{amg movie|id=1:406951|title=Eagle Eye}}
*[http://www.scoringsessions.com/sessions/29816 Scoring Session Photo Gallery at ScoringSessions.com]
*[http://razzmatz.com/eagle-eye-movie-review/ Eagle Eye Movie Review] Razzmatz.com.


{{Box Office Leaders USA
The connections between the three notions are as follows.
|before= [[Lakeview Terrace]]
|date= September 28
|date2=
|date3=
|year= 2008
|after= [[Beverly Hills Chihuahua]]
}}


{{D.J. Caruso}}
*The statement that the binary operation ★ on a set ''S'' is idempotent, is equivalent to the statement that every element of ''S'' is idempotent for ★.
{{Steven Spielberg productions}}

*The defining property of unary idempotence, {{nowrap|1=''f''(''f''(''x'')) = ''f''(''x'')}} for ''x'' in the domain of ''f'', can equivalently be rewritten as {{nowrap|1=''f''&nbsp;<small>o</small>&nbsp;''f'' = ''f''}}, using the binary operation of [[function composition]] denoted by "<small>o</small>". Thus, the statement that ''f'' is an idempotent unary operation on ''S'' is equivalent to the statement that ''f'' is an idempotent element for the operation <small>o</small> on functions from ''S'' to ''S''.

==Common examples==

=== Functions ===

As mentioned above, the identity map and the constant maps are always idempotent maps. Less trivial examples are the [[absolute value]] function of a [[real number|real]] or [[complex number|complex]] argument, and the [[floor function]] of a real argument.

The function which assigns to every subset ''U'' of some [[topological space]] ''X'' the [[closure (topology)|closure]] of ''U'' is idempotent on the [[power set]] of ''X''. It is an example of a [[closure operator]]; all closure operators are idempotent functions.

=== Idempotent ring elements ===

An idempotent element of a [[ring (mathematics)|ring]] is, by definition, an element which is idempotent with respect to the ring's multiplication. One may define a [[partial order]] on the idempotents of a ring as follows: if ''a'' and ''b'' are idempotents, we write ''a'' ≤ ''b'' [[iff]] ''ab'' = ''ba'' = ''a''. With respect to this order, 0 is the smallest and 1 the largest idempotent.

Two idempotents ''a'' and ''b'' are called ''orthogonal'' if ''ab'' = ''ba'' = 0. In this case, ''a'' + ''b'' is also idempotent, and we have ''a'' ≤ ''a'' + ''b'' and ''b'' ≤ ''a'' + ''b''.

If ''a'' is idempotent in the ring ''R'', then so is ''b'' = 1 &minus; ''a''; ''a'' and ''b'' are orthogonal.

If ''a'' is idempotent in the ring ''R'', then ''aRa'' is again a ring, with multiplicative identity ''a''.

An idempotent ''a'' in ''R'' is called ''central'' if ''ax'' = ''xa'' for all ''x'' in ''R''. In this case, ''Ra'' is a ring with multiplicative identity ''a''. The central idempotents of ''R'' are closely related to the decompositions of ''R'' as a [[direct sum]] of rings. If ''R'' is the direct sum of the rings ''R''<sub>1</sub>,...,''R''<sub>''n''</sub>, then the identity elements of the rings ''R''<sub>''i''</sub> are central idempotents in ''R'', pairwise orthogonal, and their sum is 1. Conversely, given central idempotents ''a''<sub>1</sub>,...,''a''<sub>''n''</sub> in ''R'' which are pairwise orthogonal and have sum 1, then ''R'' is the direct sum of the rings ''Ra''<sub>1</sub>,...,''Ra''<sub>''n''</sub>. So in particular, every central idempotent ''a'' in ''R'' gives rise to a decomposition of ''R'' as a direct sum of ''Ra'' and ''R''(1 &minus; ''a'').

Any idempotent ''a'' which is different from 0 and 1 is a [[zero divisor]] (because ''a''(1 &minus; ''a'') = 0). This shows that [[integral domain]]s and [[division ring]]s don't have such idempotents. [[Local ring]]s also don't have such idempotents, but for a different reason. The only idempotent contained in the [[Jacobson radical]] of a ring is 0. There is a [[catenoid]] of idempotents in the [[coquaternion]] ring.

A ring in which ''all'' elements are idempotent is called a [[boolean ring]]. It can be shown that in every such ring, multiplication is commutative, and every element is its own [[additive inverse]].

====Relation with involutions====
If ''a'' is an idempotent, then <math>1-2a</math> is an [[involution]].

If ''b'' is an involution, then <math>\frac{1}{2}(1-b)</math> is an idempotent,
and these are inverse: thus if 2 is invertible in a ring, idempotents and involutions are equivalent.

Further, if ''b'' is an involution, then <math>\frac{1}{2}(1-b)</math> and <math>\frac{1}{2}(1+b)</math> are orthogonal idempotents, corresponding to ''a'' and <math>1-a</math>.

====Numerical examples====

One may consider the ring of integers mod n, where n is [[Square-free integer|squarefree]]. By the [[Chinese Remainder Theorem]], this ring factors into the direct product of rings of integers mod p. Now each of these factors is a field, so it's clear that the only idempotents will be 0 and 1. That is, each factor has 2 idempotents. So if there are m factors, there will be <math>2^m</math> idempotents.

We can check this for the integers mod 6. Since 6 has 2 factors (2 and 3) it should have <math>2^2</math> idempotents.

0 = 0^2 = 0^3 = etc (mod 6)
1 = 1^2 = 1^3 = etc (mod 6)
3 = 3^2 = 3^3 = etc (mod 6)
4 = 4^2 = 4^3 = etc (mod 6)

=== Other examples ===

Idempotent operations can be found in [[Boolean algebra (logic)|Boolean algebra]] as well.
<!--
[[logical conjunction|Logical and]] and [[logical disjunction|logical or]] are both idempotent operations over the elements of the Boolean algebra.
THIS NEEDS EXPLANATION : "AND" as 2-ARY OPERATION DOES NOT FIT IN EITHER OF THE DEFINITIONS
-->

In [[linear algebra]], [[projection (linear algebra)|projection]]s are idempotent. In fact, they are ''defined'' as idempotent [[linear map]]s. By choosing a [[basis (linear algebra)|basis]], any projection gives an idempotent matrix.

An [[idempotent semiring]] is a semiring whose ''addition'' (not multiplication) is idempotent.

==In computing==
{{see also|Referential transparency (computer science)|Reentrant (subroutine)}}
In [[Computer science|computer science]], the term '''idempotent''' is used to describe [[Method (computer science)|method]]s or [[Subroutine|subroutine]] calls that can safely be called multiple times, as invoking the procedure a single time or multiple times results in the system maintaining the same state; i.e., after the method call all variables have the same value as they did before.

Example:
Looking up some customer's name and address in a [[database]] are typically idempotent, since this will not cause the database to change. Placing an order for a car for the customer is not idempotent, since running the method/call several times will lead to several orders being placed, and therefore the state of the database being changed to reflect this.

In [[Event Stream Processing]], idempotence refers to the ability of a system to produce the same outcome, even if an event or message is received more than once.

==See also==
*[[Closure operator]]
*[[Fixed point (mathematics)]]
*[[Idempotent of a code]]
*[[Nilpotent]]
*[[List of matrices]]
*Referential transparency
*[[Superidempotency]]
*[[Subidempotency]]

==Notes==
{{reflist}}

==References==
{{refimprove|date=October 2008}}
* {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | page=443 }}


[[Category:Abstract algebra]]
[[Category:2008 films]]
[[Category:Closure operators]]
[[Category:American films]]
[[Category:Mathematical relations]]
[[Category:English-language films]]
[[Category:Theoretical computer science]]
[[Category:Chase films]]
[[Category:Thriller films]]
[[Category:DreamWorks films]]


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Revision as of 17:24, 12 October 2008

This article is about the 2008 action thriller. For other uses, see Eagle Eye (disambiguation).
Eagle Eye
Theatrical release poster
Directed byD.J. Caruso
Written byDan McDermott
John Glenn
Travis Wright
Hillary Seitz
Produced bySteven Spielberg
Alex Kurtzman
Roberto Orci
Pat Crowley
Ed McDonnell
StarringShia LaBeouf
Michelle Monaghan
Rosario Dawson
Billy Bob Thornton
Anthony Mackie
Michael Chiklis
Cameron Boyce
CinematographyDariusz Wolski
Edited byJim Page
Music byBrian Tyler
Distributed byDreamWorks Pictures
Alliance Films (Canada)
Momentum Pictures (North America)
Release dates
Australia:
September 25, 2008
North America:
September 26, 2008
United Kingdom:
October 17, 2008
Running time
118 minutes
CountryUnited States
LanguageEnglish
Budget$80 million [1]
Box office$88 million [1]

Eagle Eye is a 2008 action/thriller film directed by D.J. Caruso and starring Shia LaBeouf and Michelle Monaghan. The two portray a young man and a single mother who are brought together and coerced by an anonymous caller into carrying out a terrorist cell's plot. The film has been rated PG-13 by the MPAA and has been released in regular 35mm theatres and IMAX theatres.

Plot

The film begins with the armed forces getting a lead on a suspected terrorist. As the man is a recluse, getting a positive ID proves difficult, and the DOD's computer system recommends that the mission be aborted. From continued aerial surveillance of the area, the suspect is apparently attending a funeral but the possibility that it is a facade makes those present all nervous - the system continues to recommend abort. The Secretary of Defense (Michael Chiklis) agrees with the abort recommendation, but the President orders the mission be carried out anyway. This turns into a political backlash when all those killed turn out to be civilians, and retaliatory bombings are carried out in response.

The scene abruptly shifts to the life of Jerry Shaw (Shia LaBeouf), a Stanford University drop out who not only lacks any real direction in his life, but also faces great financial difficulty. He gets a phone call from his parents telling him that his twin brother, Ethan, is dead. Following the funeral, Jerry gets a $1,000 check from his dad. When Jerry tries to deposit the check and withdraw some money from the ATM, he's surprised to see that his account is filled with a lump sum of money. Soon he returns home to find his apartment filled with a large amount of weapons, explosives, and forged documents. He receives a phone call from an unknown woman, who explains that the FBI are about to apprehend him in thirty seconds and that he must escape. Not believing her, he is caught by the FBI, led by Agent Thomas Morgan (Billy Bob Thornton) and Air Force Office of Special Investigations Special Agent Zoe Perez (Rosario Dawson). The unknown woman arranges Jerry's escape and has him join up with single mother Rachel Holloman (Michelle Monaghan). Holloman is being coerced into helping by the woman, who threatens to kill her son, Sam, a trumpet player on his way to Washington, D.C. from Chicago for a band recital.

The woman helps the pair to avoid the police and FBI units, demonstrating the ability to remotely control virtually any networked device, such as traffic lights, cell phones, and even automated cranes. While Jerry and Rachel follow her instructions, the woman has a crystal explosive made into a necklace and its sound-based trigger placed inside Sam's trumpet. Jerry and Rachel are led to Washington, D.C. through various means. Along the way, they are introduced to the woman, who is actually a top secret super-computer called ARIA tasked with gathering intelligence from all over the world. ARIA, the overtaken computer, can control virtually anything electronic to that end. In light of the mistake made by the President at the beginning of the film, ARIA has decided that the executive branch is a threat to the public good and must be eliminated. ARIA plans to destroy the President's Cabinet, and calls this Operation Guillotine. It has decided to leave the Secretary of Defense, who agreed with its recommendation to abort, as the successor to the presidency. She does not reveal this to Jerry or Rachel, merely explaining that she is trying to help the people of the United States.

At the Pentagon, where ARIA is housed, Agent Perez discovers that Ethan worked as a technician for the computer and locked it down to prevent ARIA from carrying out her plan. Perez warns the Secretary of Defense and they discuss the situation in a sealed room to prevent ARIA from hearing their conversation. Jerry and Rachel arrive at the Pentagon and are led to the super computer, where ARIA forces Jerry to impersonate Ethan and use an override code allowing her to go ahead with the plan. She then instructs Rachel to eliminate Jerry to prevent the lock from being reinstated, but Rachel cannot bring herself to do it. Rachel is led out of the building by ARIA while Jerry is caught by Agent Morgan. Having been warned by Agent Perez, Morgan believes Jerry's story and takes him to the United States Capitol. On their way, however, ARIA sends an MQ-9 Reaper UCAV after them. Agent Morgan sacrifices himself to destroy the craft and save Jerry.

Meanwhile, Agent Perez returns to the super computer and is successful in destroying it, but not before ARIA uploads roughly a fifth of its memory to another location. Rachel is given the explosive necklace and sent to watch the President's speech. Sam's class, whose recital has been moved from the Kennedy Center to the Capitol for the President's State of the Union Address, begins to play. The trigger that will set off the explosive necklace is set to activate when Sam plays a high F on his trumpet corresponding to the word "free" in the last verse of the U.S. national anthem. Jerry successfully infiltrates the vicinity and fires Morgan's pistol into the air, stopping the performance and emptying the room, but provoking a Secret Service agent to shoot him in the shoulder.

In the aftermath of the chaos ARIA caused, the Secretary of Defense urges that another super computer should not be built. Ethan posthumously receives the Medal of Honor while Jerry, injured but alive and well, receives the Congressional Gold Medal. The film ends with Jerry attending Sam's birthday party. Rachel thanks him for attending and kisses him on the cheek. She then tells Jerry that she is glad that he is there. After a second of silence, Jerry tells her, "Me too," and the film ends.

Main cast

  • Shia LaBeouf as Jerry Shaw: a young slacker who is framed as a terrorist and vows to clear his name with the FBI's help. LaBeouf also plays Ethan Shaw, Jerry's twin brother who is a skilled, intelligent man in the Air Force with a secret occupation.
  • Michelle Monaghan as Rachel Holloman: a single mother who is also framed as a terrorist and vows to clear her name with her companions.
  • Rosario Dawson as Zoe Perez: a government agent who is tracking down the terrorist cell.[2]
  • Billy Bob Thornton as Thomas Morgan: the patriotic leader of a homeland security team tracking down the cell.[3]
  • Ethan Embry as Toby Grant: Morgan's companion whom he assists into tracking down the cell.[4]
  • Anthony Mackie as Major Bowman: A soldier assigned to monitor the super-computer.
  • Michael Chiklis as George Callister: The U.S. Secretary of Defense.
  • Cameron Boyce as Sam Holloman: Rachel's Son
  • Julianne Moore as ARIA: The supercomputer whose machinations form the basis for the film's events.

Production

Screenwriter Dan McDermott wrote the original script for Eagle Eye based on an original idea by Steven Spielberg. The studio DreamWorks then bought McDermott's script and set up the project to potentially be directed by Spielberg. When the director became busy with Indiana Jones and the Kingdom of the Crystal Skull, he dropped out of the project. Director D.J. Caruso, who directed the 1996 TV series High Incident under Spielberg's executive production, replaced the director in helming Eagle Eye. However, Spielberg remains executive producer.[5] In June 2007, actor LaBeouf who was involved in Spielberg's and Caruso's 2007 film Disturbia and Indiana Jones and the Kingdom of the Crystal Skull, re-joined the director and executive producer to star as the lead in Eagle Eye. McDermott's script was rewritten by screenwriters John Glenn, Travis Wright and Hillary Seitz in preparation for production.[6] Filming began on November 6 2007 [7] and wrapped in February 2008.[8] The film's visual effects are being created by Sony Pictures Imageworks.[9] On August 13, the film was rated PG-13 by the MPAA for intense sequences of action violence and language.

The story was originally conceived in 1996, Caruso said by the time the film came to fruition 12 years later, "the technology had finally caught up to the storytelling. ... Everybody has a BlackBerry or an iPhone on their belt, and we think we're constantly being tracked. It's less science fiction than when Steven (Spielberg) conceived it."[10] Caruso wanted to bring a gritty, 1970s-era sensibility to the film. Accordingly, a key chase scene in a high-tech package-processing hub on conveyor belts was shot without the use of computer-generated imagery. "It was like Chutes and Ladders for adults. It was pretty dangerous, and a lot of fun.[10] While filming the scene, Monaghan suffered a welt after a cable brushed her neck and Caruso hit his head on a protruding bolt, requiring stitches.[10]

Music

The music to Eagle Eye was written by composer Brian Tyler, who recorded the score with an 88-piece ensemble of the Hollywood Studio Symphony at the Sony Scoring Stage. The session was interrupted by the Chino Hills earthquake on July 29, 2008 – and a recording of the quake hitting the scoring stage is online.[11] The score was released on iTunes on September 25, 2008 and followed by a CD release on September 30.

Promotion

The official movie website features an ARG type of gameplay system to promote the movie. The voice previewed behind the phone in multiple trailers contacts the player, placing them in unique experiences. This has been called the Eagle Eye Freefall Experience. While official cast listings do not list the name of the actress behind the mysterious voice featured in the film and trailers, Rosario Dawson confirmed at the Hollywood premiere that it belongs to Julianne Moore.[12]

Critical reception

Eagle Eye received generally negative reviews from critics. As of October 1, 2008, the review aggregator Rotten Tomatoes reported that 28% of critics gave the film positive reviews based on 118 reviews, with the consensus that the film "is a preposterously plotted thriller that borrows heavily from other superior films."[13] Metacritic reported the film had an average score of 43 out of 100, based on 28 reviews — indicating mixed or average reviews.[14]

Roger Ebert of the Chicago Sun-Times gave Eagle Eye a score of two stars out of four, saying: "The word preposterous is too moderate to describe Eagle Eye. This film contains not a single plausible moment after the opening sequence, and that's borderline. It's not an assault on intelligence. It's an assault on consciousness."[15] James Berardinelli of ReelViews gave the film one and a half stars out of four, saying: "This movie tests the viewing public's tolerance for enduring crass stupidity when the payoff is a series of repetitive, ADD-infected chase scenes. Director D.J. Caruso does a moderately good job of hiding how incredibly dumb this screenplay is by keeping things moving at such a whirlwind pace that a lot more seems to be happening than actually is. In reality, the chase scenes don't mean anything because they don't advance the plot—it's mice on a treadmill, running and running and not getting anywhere."[16] The Hollywood Reporter called it a "slick, silly techno thriller" and "Even those who surrender all disbelief at the door will be hard pressed not to smirk at some of wildly improbable plotting--"[17]

Josh Rosenblatt of The Austin Chronicle enjoyed the film, calling it "good, manic fun plus a heavy dose of political intrigue adding up to two hours of clamorous, mind-numbing nonsense."[18] William Arnold of the Seattle Post-Intelligencer also gave Eagle Eye a positive review, remarking that it's "engrossing as an intellectual puzzle" and "a solid thriller."[19] Mark Bell of Film Threat said: "the film isn't a complete waste of your time [...] but don't expect anything brilliant."[20] Nathan Rabin The Onion's A.V. Club called the film "achingly idiotic" and "the unintentional laugh riot of the year."[21] Neely Tucker of The Washington Post said that Eagle Eye is "sometimes entertaining" but "doesn't have much to say."[22] Robert Koehler of Variety felt that the film's "first 35 minutes sizzle" but "the story [becomes] near-parody in the final act."[23]

Box office performance

In its opening weekend, Eagle Eye grossed $29.1 million in 3,510 theaters in the United States and Canada, ranking (for 1 week) #1 at the box office.[24] As of October 12, 2008, it has grossed $88 million worldwide — $70.5 million in the United States and Canada and $17.5 million in other territories.[1]

Mobile game

A Mobile game based on the movie was developed and published by Magmic Games. It was released for Blackberry, Windows Mobile, BREW and J2ME devices prior to the movies launch in early September.[25][26]

"Aria" The Giant Computer From The Movie

The visual design (including the water below) of the computer from the movie came from the Super-Kamiokande,a neutrino observatory in the city of Hida, Gifu Prefecture, Japan. The observatory was designed to search for proton decay, study solar and atmospheric neutrinos, and keep watch for supernovas in the Milky Way Galaxy. Pictures of Super-K from Japanese website

References

  1. ^ a b c "Eagle Eye (2008)". Box Office Mojo. Retrieved 2008-10-12.
  2. ^ Michael Fleming (2007-08-13). "Rosario Dawson joining 'Eagle Eye'". Variety. Retrieved 2007-11-13. {{cite news}}: Check date values in: |date= (help)
  3. ^ Tatiana Siegel (2007-11-07). "Billy Bob Thornton spies 'Eagle Eye'". Variety. Retrieved 2007-11-13. {{cite news}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  4. ^ Clint Morris (2007-11-21). "Embry joins Eagle Eye". Moviehole. Retrieved 2007-11-27. {{cite news}}: Check date values in: |date= (help)
  5. ^ Eagle Eye (2008) - Full cast and crew
  6. ^ Michael Fleming (2007-06-25). "'Disturbia' duo set for 'Eagle Eye'". Variety. Retrieved 2007-11-13. {{cite news}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  7. ^ Nellie Andreeva (2007-11-06). "For most part, the shows go on". The Hollywood Reporter. Retrieved 2007-11-13. {{cite news}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  8. ^ Carly Mayberry and Borys Kit (2008-01-08). "'Eagle' lands Chiklis in cabinet post". The Hollywood Reporter. Retrieved 2008-01-08. {{cite news}}: Check date values in: |date= (help)
  9. ^ Carolyn Giardina (2008-07-01). "G-Force' is with Imageworks". The Hollywood Reporter. The Nielsen Company. Retrieved 2008-07-01. {{cite news}}: Check date values in: |date= (help)
  10. ^ a b c Vary, Adam B. "Fall Movie Summer Preview, September: Eagle Eye." Entertainment Weekly, Iss. #1007/1008, August 22/29, 2008, pg.52.
  11. ^ Dan Goldwasser (2008-09-11). "Brian Tyler scores Eagle Eye". ScoringSessions.com. Retrieved 2008-09-16. {{cite news}}: Check date values in: |date= (help)
  12. ^ "'Eagle Eye' Star Reveals Identity Of Movie's Mayhem Causing Voic".
  13. ^ "Eagle Eye Movie Reviews, Pictures - Rotten Tomatoes". Rotten Tomatoes. Retrieved 2008-10-01.
  14. ^ "Eagle Eye (2008): Reviews". Metacritic. Retrieved 2008-09-27.
  15. ^ Eagle Eye review, Roger Ebert, Chicago Sun-Times, September 25, 2008
  16. ^ Eagle Eye review, James Berardinelli, ReelViews, September 2008
  17. ^ Film Review: Eagle Eye, Michael Rechtshaffen, THE HOLLYWOOD REPORTER, September 25 2008
  18. ^ Eagle Eye review, Josh Rosenblatt, Austin Chronicle, September 2008
  19. ^ Eagle Eye review, William Arnold, Seattle Post-Intelligencer, September 2008
  20. ^ Eagle Eye review, Mark Bell, Film Threat, September 2008
  21. ^ Eagle Eye review, Nathan Rabin, The Onion (A.V. Club), September 26th, 2008
  22. ^ Eagle Eye review, Neely Tucker, Washington Post, September 2008
  23. ^ OdessyEagle Eye review, Robert Koehler, Variety, September 2008
  24. ^ "Eagle Eye (2008) - Weekend Box Office Results". Box Office Mojo. Retrieved 2008-10-04.
  25. ^ "Eagle Eye: The Game".
  26. ^ "Movie tie-in".

External links

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