{"id":15500,"date":"2016-06-01T13:09:55","date_gmt":"2016-06-01T10:09:55","guid":{"rendered":"http:\/\/109.232.216.219\/~bilimvegelecek\/?p=15500"},"modified":"2018-01-02T13:25:08","modified_gmt":"2018-01-02T10:25:08","slug":"animasyonda-populer-matematik-simpsonlar-ve-matematiksel-sirlari","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2016\/06\/01\/animasyonda-populer-matematik-simpsonlar-ve-matematiksel-sirlari","title":{"rendered":"Animasyonda pop\u00fcler matematik:\u00a0Simpsonlar ve matematiksel s\u0131rlar\u0131"},"content":{"rendered":"

Simon Singh son kitab\u0131, \u201cSimpsonlar ve Matematiksel S\u0131rlar\u0131\u201dnda, yazar ekibinde matematik, fizik ve bilgisayarbilimleri e\u011fitimi alm\u0131\u015f ki\u015filer de bulunan \u201cSimpsonlar\u201d ve \u201cFuturama\u201d adl\u0131 animasyonlar \u00fczerinden <\/em>e\u011flence end\u00fcstrisi ve matematik d\u00fcnyas\u0131n\u0131n bir\u00e7ok ilgin\u00e7 yolla birbirlerini nas\u0131l etkileyebilece\u011fini anlat\u0131yor.<\/em><\/p>\n

Sunu\u015f:<\/strong> Okuyaca\u011f\u0131n\u0131z yaz\u0131 Amerikan Matematik Toplulu\u011fu\u2019nun Notices of the AMS<\/em> adl\u0131 dergisinin, Ocak 2015 tarihli say\u0131s\u0131nda (62. Cilt, Say\u0131: 1, ss.40-44) yay\u0131mlanm\u0131\u015ft\u0131r. Anaba\u015fl\u0131kta de\u011fi\u015fiklik yapt\u0131k, spot ve araba\u015fl\u0131klar ekledik. Yazar:\u00a0Christopher Goff \/ Pasifik \u00dcniversitesi, Matematik Do\u00e7enti<\/p><\/blockquote>\n

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Simon Singh<\/figcaption><\/figure>\n

Matematik\u00e7i olmayanlar Simon Singh taraf\u0131ndan yaz\u0131lan (ayn\u0131 zamanda Fermat\u2019\u0131n Son Teoremi <\/em>kitab\u0131n\u0131n yazar\u0131) bu kitap hakk\u0131nda soru sorabilir: The Simpsons and Their Mathematical Secrets <\/em>(Simpsonlar ve Matematiksel S\u0131rlar\u0131<\/em>), televizyon tarihinin en uzun soluklu program\u0131 Simpsonlar<\/em>\u2019da ge\u00e7en matematiksel g\u00f6ndermelerle ilgili gibi g\u00f6r\u00fcn\u00fcyor; ancak kitap ayn\u0131 zamanda Futurama <\/em>ve her iki program\u0131n yazarlar\u0131n\u0131n matematiksel yeterliliklerine de de\u011finiyor. Singh bu iki program\u0131n merce\u011finden bakarak, matematik ve pop\u00fcler k\u00fclt\u00fcr\u00fcn daha geni\u015f bir alan\u0131n\u0131n, e\u011flence end\u00fcstrisi ve matematik d\u00fcnyas\u0131n\u0131n bir\u00e7ok ilgin\u00e7 yolla birbirlerini nas\u0131l etkileyebileceklerinin tasvirini yap\u0131yor.<\/p>\n

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Simon Singh’in \u201cSimpsonlar ve Matematiksel S\u0131rlar\u0131\u201d kitab\u0131.<\/figcaption><\/figure>\n

Matematik ve pop\u00fcler k\u00fclt\u00fcr<\/strong><\/p>\n

Matematik ve pop\u00fcler k\u00fclt\u00fcrle ilgili su y\u00fcz\u00fcne \u00e7\u0131kan bir konu, g\u00f6r\u00fcn\u00fc\u015fte birbirinden apayr\u0131 duran bu iki alan\u0131n ortakl\u0131klar\u0131yla ilgilidir ve her birinin di\u011ferini nas\u0131l \u015fekillendirdi\u011fi ve di\u011ferinin etkisinde nas\u0131l \u015fekillendi\u011fini \u00e7al\u0131\u015f\u0131r. \u00d6rne\u011fin, matematik modeller animasyonlarda ve filmlerde \u00f6zel efektlerin olu\u015fturulmas\u0131nda kullan\u0131labilir.(1, 2, 18)\u00a0 <\/sup>Matematiksel yetene\u011fe sahip karakterlerin yarat\u0131lmas\u0131yla izleyicilerin matematik\u00e7ilerle ilgili d\u00fc\u015f\u00fcnceleri etkilenebilir,(16)<\/sup> matematik derslerindeki pop\u00fcler k\u00fclt\u00fcr referanslar\u0131 dersle ilgili endi\u015felerin azalmas\u0131n\u0131 ve \u00f6\u011frencilerin derin matematiksel d\u00fc\u015f\u00fcnceye ilgi duymas\u0131na sebep olacak bir ge\u00e7i\u015f noktas\u0131 bulmas\u0131n\u0131 sa\u011flayabilir,(14)<\/sup> yeni teoremler televizyon programlar\u0131ndan gelebilir,(6)<\/sup> ve son olarak, yay\u0131nc\u0131l\u0131k piyasas\u0131 incelemesini yapt\u0131\u011f\u0131m\u0131z kitap gibi pop\u00fcler \u00e7al\u0131\u015fmalar\u0131 destekleyebilir.<\/p>\n

Simpsonlar <\/em>Matt Groening taraf\u0131ndan The Tracey Ullman Show<\/em> i\u00e7in bir dizi ske\u00e7 olarak tasarland\u0131.\u00a0 Buradaki ba\u015far\u0131s\u0131 onu 1989-1990 sezonundan itibaren yay\u0131nland\u0131\u011f\u0131 Fox\u2019da d\u00fczenli bir program olmaya g\u00f6t\u00fcrd\u00fc. \u201cEn iyi Animasyon Program\u0131\u201d dal\u0131nda 10\u2019dan fazla Emmy \u00f6d\u00fcl\u00fc sahibi oldu. Simpson ailesi, n\u00fckleer tesis g\u00fcvenlik teknisyeni baba Homer ve onun sevgili mavi sa\u00e7l\u0131 kar\u0131s\u0131 Marge, belal\u0131 o\u011fullar\u0131 Bart, akademik olarak ba\u015far\u0131l\u0131 k\u0131zlar\u0131 Lisa ve bebekleri Maggie\u2019den olu\u015fur.<\/p>\n

Ba\u015far\u0131s\u0131 Fox\u2019un Groening\u2019den ba\u015fka bir animasyon program\u0131 istemesine neden oldu ve 1999\u2019da bilimkurgu temal\u0131 Futurama<\/em>\u2019n\u0131n ilk b\u00f6l\u00fcm\u00fc yay\u0131nland\u0131. Futurama<\/em>\u2019da pizza servisi yapan Fry 1999\u2019\u0131n y\u0131lba\u015f\u0131 gecesi yanl\u0131\u015fl\u0131kla dondurucu hazneye d\u00fc\u015fer ve 1000 y\u0131l boyunca \u00e7\u00f6z\u00fclmez. Gelecekte Fry, Bender isimli robotla arkada\u015f olur ve uzaktan bir akrabas\u0131, ya\u015fl\u0131 Prof. Fanrsworth i\u00e7in kuryelik yapmaya ba\u015flar. Futurama <\/em>d\u00f6rt y\u0131l boyunca yay\u0131nlan\u0131r ve daha sonra bir d\u00f6rt y\u0131lda Cartoon Network\u2019de tekrarlar\u0131 yay\u0131nlan\u0131r. Pop\u00fclerli\u011fi d\u00f6rt filmle program\u0131 tekrar hayata d\u00f6nd\u00fcr\u00fcr ve sonunda Comedy Central\u2019da tekrar dizi olarak devam eder. Program, birisi Fox\u2019da, di\u011feri Comedy Central\u2019da yay\u0131nlan\u0131rken olmak \u00fczere, En \u0130yi Animasyon dal\u0131nda iki Emmy \u00f6d\u00fcl\u00fc al\u0131r.<\/p>\n

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Simpsonlar\u2019\u0131n \u201cHer Dem Ye\u015fil Tara\u00e7an\u0131n B\u00fcy\u00fcc\u00fcs\u00fc\u201d isimli b\u00f6l\u00fcm\u00fcnde karatahtada, Fermat\u2019n\u0131n \u00fcnl\u00fc \u00f6zde\u015fli\u011fini sa\u011flamay\u0131 k\u0131l pay\u0131 ka\u00e7\u0131rm\u0131\u015f 398712 +436512 =447212 ifadesi g\u00f6r\u00fcl\u00fcr.<\/figcaption><\/figure>\n

Hem Simpsonlar<\/em> hem de Futurama <\/em>milyonlarca izleyici taraf\u0131ndan takip edilen olduk\u00e7a pop\u00fcler yap\u0131mlar. Haliyle, b\u00f6l\u00fcmlerinde ge\u00e7en matematiksel g\u00f6ndermeler ve \u015fakalar bir matematik \u00f6\u011fretmeninin ula\u015fmay\u0131 hayal dahi edemeyece\u011fi kadar \u00e7ok insana ula\u015f\u0131yor. Pop\u00fcler k\u00fclt\u00fcr ve matematik aras\u0131ndaki etkile\u015fimle ilgilenen biri olarak, b\u00fcy\u00fck yay\u0131nc\u0131lar\u0131n ve iyi bilinen yazarlar\u0131n bu iki alan\u0131n kar\u015f\u0131l\u0131kl\u0131 etkile\u015fimi ile ilgili baz\u0131 ilgin\u00e7 \u00f6rnekleri ayd\u0131nlatmalar\u0131 konusunda olduk\u00e7a heyecanl\u0131y\u0131m.<\/p>\n

Ancak profesyonel matematik\u00e7iler Simon Singh\u2019in hedef kitlesinde de\u011fil. Ger\u00e7ekten, pop\u00fcler k\u00fclt\u00fcr\u00fc hem g\u00f6zlemleyen hem de ele\u015ftiren matematik\u00e7iler i\u00e7in bu kitapta \u00e7ok az \u015fey yeni olacakt\u0131r, \u00f6zellikle bu alandaki \u00e7al\u0131\u015fmalara a\u015fina olanlar i\u00e7in. Dr. Sarah J. Greenwald ve Dr. Andrew Nestler on y\u0131l\u0131 a\u015fk\u0131n bir s\u00fcredir Simpsonlar <\/em>ve Futurama <\/em>\u00fczerine yaz\u0131yorlar ve olduk\u00e7a kapsaml\u0131 web siteleri tasarl\u0131yorlar.(15, 19, 12) <\/sup>Ben de uzun s\u00fcredir, 2004\u2019te matematik ve filmler ile ilgili sunumlar yapmaya ba\u015flad\u0131\u011f\u0131mdan beri, konuyla ilgiliyim. \u0130lk sunumumdan k\u0131sa bir s\u00fcre sonra, Greenwald ve ben, PRIMUS<\/em> dergisinin matematik ve pop\u00fcler k\u00fclt\u00fcr \u00fczerine yo\u011funla\u015ft\u0131\u011f\u0131 bir say\u0131s\u0131n\u0131n edit\u00f6rl\u00fc\u011f\u00fcn\u00fc yapt\u0131k. Bundan sonra bir ba\u015fka ortak \u00e7al\u0131\u015fmam\u0131z daha oldu.(4)<\/sup><\/p>\n

Singh, kitab\u0131 i\u00e7in Greenwald ve Nestler ile bir s\u00f6yle\u015fi yapt\u0131; kitab\u0131n 8. B\u00f6l\u00fcm\u00fc boyunca onlardan al\u0131nt\u0131 yap\u0131yor. Ayn\u0131 zamanda bu iki matematik\u00e7inin, matematiksel bir i\u00e7eri\u011fin Simpsonlar<\/em>\u2019\u0131n bir b\u00f6l\u00fcm\u00fcne dahil olmas\u0131nda nas\u0131l dolayl\u0131 rol oynad\u0131klar\u0131yla ilgili ilgin\u00e7 bir anekdot veriyor. Greenwald 2005\u2019de NPR\u2019\u0131n Science Friday<\/em>\u2019i i\u00e7in bir s\u00f6yle\u015fi yapt\u0131ktan sonra, Simpson<\/em>lar<\/em>\u2019\u0131n yazarlar\u0131n\u0131n bir k\u0131sm\u0131 program\u0131 duydu. \u0130lgin\u00e7 bir \u015fekilde matematik\u00e7iler programdan baz\u0131 materyalleri s\u0131n\u0131flar\u0131nda kullan\u0131yordu. Simpsonlar<\/em>\u2019\u0131n yazarlar\u0131 Greenwald ve Nestler\u2019i herhangi bir televizyon metninin geli\u015ftirmesinde anahtar ad\u0131m olan senaryo okumalar\u0131na kat\u0131lmalar\u0131 i\u00e7in Fox St\u00fcdyolar\u0131na davet ettiler. Ancak matematik\u00e7iler ayr\u0131ld\u0131ktan sonra yazarlar, beyzbol temal\u0131 b\u00f6l\u00fcm\u00fcn hi\u00e7bir matematiksel \u015faka i\u00e7ermedi\u011fini fark ettiler. Sonrada bir beyzbol ma\u00e7\u0131n\u0131n olas\u0131 seyirci say\u0131s\u0131 ile ilgili bir donmu\u015f kare \u015fakas\u0131 (\u015faka o kadar h\u0131zl\u0131 ge\u00e7iyor ki, seyircilerin kayd\u0131 dondurup ba\u015fa almas\u0131 gerekiyor anlam\u0131nda) olarak \u00fc\u00e7 say\u0131 eklediler. \u0130zleyicilerin \u00e7o\u011funun habersiz oldu\u011fu bu \u00fc\u00e7 say\u0131, Mersenne asal\u0131 (8191), bir m\u00fckemmel say\u0131 (8128) ve bir narsistik say\u0131yd\u0131 (8208).<\/p>\n

Pek \u00e7ok matematik kitab\u0131nda oldu\u011fu gibi The Simpson and Their Mathematical Secrets\u2019<\/em>da da Singh, i\u00e7eri\u011finde akademiyle program\u0131n etkile\u015fimde olmas\u0131n\u0131n pek \u00e7ok yolundan bir k\u0131sm\u0131n\u0131n \u00f6zetlendi\u011fi bir B\u00f6l\u00fcm S\u0131f\u0131r\u2019la ba\u015fl\u0131yor. Bu b\u00f6l\u00fcmde, felsefe, psikoloji ve ilahiyat profes\u00f6rleri kendi disiplinlerine ait fikirlerin Simpson ailesi etraf\u0131nda d\u00f6nen d\u00fcnyada nas\u0131l ortaya \u00e7\u0131kt\u0131\u011f\u0131n\u0131 anlat\u0131yorlar. Ba\u015fkan George H. W. Bush bile Simpson\u2019\u0131 erdemli Amerikan Waltonlar\u0131n\u0131n(*) antitezi olarak de\u011ferlendirdi. Yazarlar da Bart arac\u0131l\u0131\u011f\u0131yla \u015fu hicivli cevab\u0131 verdiler: \u201cHey, biz ayn\u0131 Waltonlar gibiyiz. Biz de krizin bitmesi i\u00e7in dua ediyoruz.\u201d (Sayfa 2)<\/p>\n

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Simpsonlar\u2019\u0131n \u201cBart, Dahi\u201d b\u00f6l\u00fcm\u00fcnde, d\u00e2hiler s\u0131n\u0131f\u0131 \u00f6\u011fretmeni bir matematik-kelime \u015fakas\u0131 yapar.<\/figcaption><\/figure>\n

Yazarlar\u0131n matematik bilgisi nereden geliyor?<\/strong><\/p>\n

Singh kitapta, Simpsonlar<\/em>\u2019\u0131n baz\u0131 yazarlar\u0131na ve onlar\u0131n matematik becerilerine do\u011frudan \u0131\u015f\u0131k tutuyor. Ben de bu yazarlar\u0131 anarak isimlerini verece\u011fim: J. Stewart Burns (lisans matematik, Harvard; y\u00fcksek lisans matematik, Berkeley); David S. Cohen (lisans fizik, Harvard; lisans bilgisayar bilimleri, Berkeley); Al Jean (lisans matematik, Harvard); Ken Keeler (lisans ve doktora \u00a0uygulamal\u0131 matematik, Harvard) ve Jeff Westbrook (lisans fizik, Harvard ve doktora bilgisayar bilimleri, Princeton). Singh baz\u0131 yazarlar\u0131n matematik ve mizah aras\u0131nda benzerlikler oldu\u011funa dikkat \u00e7ekti\u011fini s\u00f6yl\u00fcyor: Burns matematiksel bir bulmacan\u0131n ve bir \u015fakan\u0131n ortak bir yap\u0131y\u0131 payla\u015ft\u0131\u011f\u0131n\u0131 belirtir ve Cohen de k\u0131sa s\u00fcre i\u00e7inde karma\u015f\u0131k bir hik\u00e2ye anlatma i\u015fi ile b\u00fcy\u00fck bir mant\u0131k bulmacas\u0131n\u0131 \u00e7\u00f6zmeyi birbirine benzetir.<\/p>\n

Singh, \u201cHomer\u2019\u0131n Son Teoremi\u201d isimli 3. b\u00f6l\u00fcmde bu yazarlar ve Andrew Wiles\u2019\u0131n Fermat\u2019\u0131n Son Teoremi\u2019nin ispat\u0131n\u0131n hik\u00e2yesi aras\u0131ndaki ili\u015fkiden bahseder. \u00d6zellikle, Wiles\u2019\u0131n Harvard\u2019da ge\u00e7irdi\u011fi k\u0131sa s\u00fcrede Jean onun birka\u00e7 dersini takip etmi\u015f ve Cohen Berkeley\u2019de \u00f6\u011frenci oldu\u011fu zamanlarda Ken Ripet\u2019\u0131n derslerine devam etmi\u015ftir. Singh bu ili\u015fkilerden, \u201cHer Dem Ye\u015fil Tara\u00e7an\u0131n B\u00fcy\u00fcc\u00fcs\u00fc\u201d isimli b\u00f6l\u00fcmde, bir donmu\u015f kare \u015fakas\u0131 olarak karatahtada g\u00f6r\u00fclen Fermat\u2019n\u0131n \u00f6zde\u015fli\u011fini sa\u011flamay\u0131 k\u0131l pay\u0131 ka\u00e7\u0131rm\u0131\u015f 398712<\/sup> +436512<\/sup> =447212<\/sup> ifadesini tart\u0131\u015ft\u0131\u011f\u0131nda bahseder. Cohen kasten bu kadarc\u0131k matemati\u011fi muziplik olarak araya soku\u015fturmu\u015f ve ilk bak\u0131\u015fta yanl\u0131\u015fl\u0131\u011f\u0131 anla\u015f\u0131lmayan bu karenin online ortamda yarat\u0131\u011f\u0131 tart\u0131\u015fmalar\u0131 heyecanla takip etmi\u015ftir. Cohen\u2019in kitapta s\u00f6yledi\u011fi gibi \u201c… -\u00f6zellikle matemati\u011fi onurland\u0131ran- bir tart\u0131\u015fmay\u0131 k\u0131z\u0131\u015ft\u0131racak bir f\u0131rsat elde etti\u011fimizde, bununla ilgili i\u015flevsel \u015fakalar yapt\u0131\u011f\u0131mda, kendimi i\u015fimle ilgili daha iyi hissediyorum.\u201d \u0130lgin\u00e7 olan, bu yanl\u0131\u015f \u00f6rne\u011fin yay\u0131nlanmas\u0131ndan birka\u00e7 sene sonra, Noam Elkies\u2019in yeni bir hesapsal algoritma vererek daha genel bir sonu\u00e7 elde etmi\u015f olmas\u0131d\u0131r.<\/p>\n

Erd\u00f6s-Bacon say\u0131s\u0131<\/strong><\/p>\n

Baz\u0131lar\u0131 matematik camias\u0131 ile e\u011flence end\u00fcstrisi aras\u0131ndaki bu g\u00f6rece yak\u0131n ba\u011flant\u0131lar\u0131 \u015fa\u015f\u0131rt\u0131c\u0131 bulabilir. B\u00f6l\u00fcm 5\u2019te Singh, okurlara birisinin ortak yazarl\u0131k grafi\u011finde matematik\u00e7i Paul Erd\u00f6s\u2019den ne kadar uzakta oldu\u011funu s\u00f6yleyen Erd\u00f6s say\u0131s\u0131ndan bahsediyor. Yazarlardan Westbrook\u2019un Erd\u00f6s say\u0131s\u0131 3, Cohen\u2019inki de \u00f6yle. Benzer bir \u00f6l\u00e7\u00fcm e\u011flencesi, sinema fanlar\u0131 taraf\u0131ndan da kullan\u0131l\u0131yor. Bir akt\u00f6r\u2019\u00fcn \u201cBacon say\u0131s\u0131\u201d ortak bir filmde oynama grafi\u011finde Kevin Bacon\u2019a olan uzakl\u0131\u011f\u0131n\u0131 g\u00f6steriyor ve Westbrook\u2019un bir de Bacon say\u0131s\u0131 var, 3. Birisinin matematik camias\u0131yla ba\u011flant\u0131s\u0131n\u0131 g\u00f6steren Erd\u00f6s say\u0131s\u0131n\u0131n kullan\u0131lmas\u0131yla ayn\u0131 bi\u00e7imde, Bacon say\u0131s\u0131 da birisinin Hollywood\u2019da sahip oldu\u011fu \u00fcn\u00fc g\u00f6steriyor. B\u00f6ylece \u015faka yollu \u201cErd\u00f6s-Bacon\u201d say\u0131s\u0131 (her iki say\u0131n\u0131n toplam\u0131) da, birisinin hem Hollywood hem de matematik d\u00fcnyas\u0131 ile ba\u011flant\u0131s\u0131n\u0131n bir \u00f6l\u00e7\u00fcs\u00fcn\u00fc verebilir. Daha \u00f6nce de g\u00f6rd\u00fc\u011f\u00fcm\u00fcz gibi Westbrook\u2019un Erd\u00f6s-Bacon say\u0131s\u0131 6. Singh\u2019in kitab\u0131nda beni \u015fa\u015f\u0131rtan g\u00f6rece d\u00fc\u015f\u00fck Erd\u00f6s-Bacon say\u0131s\u0131na sahip Hollywood y\u0131ld\u0131zlar\u0131 var: Akademi \u00f6d\u00fcll\u00fc Colin Firth\u2019\u00fcn Erd\u00f6s-Bacon say\u0131s\u0131 7, yine Akademi \u00f6d\u00fcll\u00fc Natalie Portman\u2019n\u0131nki ise 6. Singh\u2019in listesinde yer almasa da Danica Mckellar de 6 Erd\u00f6s- Bacon say\u0131s\u0131na sahip. Singh, Erd\u00f6s\u2019\u00fcn kendisinin de 4 Erd\u00f6s- Bacon say\u0131s\u0131na sahip oldu\u011funu s\u00f6yl\u00fcyor, ama bu en k\u00fc\u00e7\u00fck rakam de\u011fil. G\u00f6r\u00fcn\u00fc\u015fe bak\u0131l\u0131rsa en k\u00fc\u00e7\u00fck say\u0131 Illinois \u00dcniversitesi\u2019nden Bruce Reznick\u2019 e ait, 3.<\/p>\n

Yazarlarla ilgili bana ilgin\u00e7 gelen bir ba\u015fka konu da, bir taraftan televizyon i\u00e7in yazarken bir taraftan da matematik \u00e7al\u0131\u015fmaya devam etmeleri. B\u00f6l\u00fcm 9\u2019da Singh okuyucuya yazarlar\u0131n bir \u201cmatematik kul\u00fcb\u00fc\u201d kurmalar\u0131n\u0131n ve ilgili izleyicilere konu\u015fmalar vermelerinin veya Ron Graham, Greenwald ve Nestler gibi di\u011ferlerini konu\u015fma yapmalar\u0131 i\u00e7in davet etmelerinin hik\u00e2yesini anlat\u0131yor. Cohen matematik kul\u00fcb\u00fcndeki bir konu\u015fmas\u0131 s\u0131ras\u0131nda, \u00f6\u011frenciyken yazd\u0131\u011f\u0131 bir makalenin konusu olan krep say\u0131lar\u0131ndan bahsediyor, daha sonra Fox\u2019da yazmaya ba\u015flamas\u0131n\u0131 da i\u00e7eren uzun bir s\u00fcreden sonra makalesi Discrete Applied Mathmematics<\/em>\u2019de bas\u0131l\u0131yor.<\/p>\n

Simpsonlar ve Futurama\u2019dan kimi matematiksel \u00f6rnekler<\/strong><\/p>\n

Yazarlar\u0131n ve onlar\u0131n matematik yeterliliklerinin hik\u00e2yelerinin aras\u0131na Singh, Simpsonlar<\/em> ve Futurama<\/em>\u2019dan bir\u00e7ok matematiksel \u00f6rne\u011fi serpi\u015ftirmi\u015f ve onlar\u0131 genel okuyucu i\u00e7in a\u00e7\u0131klam\u0131\u015f. Bu \u00f6rneklerin pek \u00e7o\u011fu basit matematik veya istatistik bilgisi i\u00e7eriyor. Bu \u00f6rneklerden matematik ve pop\u00fcler k\u00fclt\u00fcr\u00fcn nas\u0131l potansiyel olarak etkile\u015fim halinde olaca\u011f\u0131n\u0131n yollar\u0131n\u0131 g\u00f6steren en \u00f6nemli birka\u00e7 tanesine odaklanaca\u011f\u0131m. \u00d6rnekler, Greenwald ve Nestler\u2019in ilk \u00e7al\u0131\u015fmas\u0131n\u0131 ate\u015fleyen 1990\u2019daki ilk \u015fakadan ba\u015flayarak 2014\u2019teki \u201cFuturama Teorem\u201dle bitiyor.<\/p>\n

Birinci B\u00f6l\u00fcmde, Singh Simpsonlar<\/em>\u0131n ilk resmi b\u00f6l\u00fcm\u00fcn\u00fc anlat\u0131yor, \u201cBart, Dahi (1990)\u201d. B\u00f6l\u00fcmde Bart tamamlad\u0131\u011f\u0131 dahiler s\u0131n\u0131f\u0131n\u0131n giri\u015f testinin \u00fczerine ismini yazar, Martin Prince. Dahi oldu\u011fu fark edilen Bart okulda yerini al\u0131r. \u00d6\u011fretmen tahtaya y= r3<\/sup>\/3 yazar ve \u201cDe\u011fi\u015fim h\u0131z\u0131n\u0131 do\u011fru bir \u015fekilde bulursan\u0131z, olduk\u00e7a \u015fa\u015f\u0131raca\u011f\u0131n\u0131z\u0131 d\u00fc\u015f\u00fcn\u00fcyorum\u201d der. Bart d\u0131\u015f\u0131nda t\u00fcm \u00f6\u011frenciler soruyu \u00e7\u00f6zer ve k\u0131k\u0131rdarlar. \u00d6\u011fretmen tahtada soruyu \u00e7\u00f6zer ve\u00a0 dy=r2<\/sup>dr <\/em>olan cevab\u0131 \u201cr dr r\u201d<\/em> olarak yazar ve \u201char-de-har-har\u201d diye okur.(**)<\/p>\n

Di\u011fer \u00f6rneklerden farkl\u0131 olarak Singh buradaki matemati\u011fi a\u00e7\u0131klamaktan sak\u0131n\u0131r, k\u00fc\u00e7\u00fck bir hat\u0131rlatmayla okuyucu rn<\/sup><\/em>\u2019in r<\/em>\u2019ye g\u00f6re t\u00fcrevini nas\u0131l hesaplayaca\u011f\u0131n\u0131 s\u00f6yler.<\/p>\n

2004\u2019te bir makalede(14)<\/sup> Greenwald ve Nestler bu sahneyi ilk d\u00f6nem kalkulus derslerinde nas\u0131l kulland\u0131klar\u0131n\u0131 anlat\u0131rlar. Bunun \u00f6\u011frencilerin s\u0131navdan \u00f6nce \u00e7al\u0131\u015fmalar\u0131na ve hatta matematik kayg\u0131lar\u0131n\u0131 yenmelerine nas\u0131l yard\u0131mc\u0131 oldu\u011funu a\u00e7\u0131klarlar.<\/p>\n

Ayn\u0131 sayfada Greenwald ve Nestler, Homer\u2019\u0131n bir ak\u015fam bald\u0131zlar\u0131ndan ka\u00e7arken f\u00fct\u00fcristik \u00fc\u00e7 boyutlu d\u00fcnyaya (daha d\u00fc\u015f\u00fck boyutlu Simpson evreninden) ge\u00e7ti\u011fi b\u00f6l\u00fcm\u00fc tart\u0131\u015f\u0131rlar. \u201cAlacakaranl\u0131k Ku\u015fa\u011f\u0131\u201d isimli bu b\u00f6l\u00fcm, s\u0131n\u0131f\u0131n 2 ve 3 boyutlu uzaylar\u0131n geometrileri hakk\u0131nda d\u00fc\u015f\u00fcnmesi sa\u011flar ve hatta \u00f6\u011frencileri 4 boyutlu uzay\u0131n cisimlerini d\u00fc\u015f\u00fcnmeye itebilir. Singh \u201cHomer3<\/sup>\u201d ad\u0131n\u0131 ta\u015f\u0131yan B\u00f6l\u00fcm 13\u2019\u00fc, bir\u00e7ok donmu\u015f kare \u015fakas\u0131nda ge\u00e7en ve yazarlar\u0131n \u201cP=NP\u201d ya da \u201ce\u03c0i <\/sup>= -1\u201d Euler \u00f6zde\u015fli\u011fi gibi arka planda ilgilendikleri ifadelere adar.<\/p>\n

\"\"
Matematikte kad\u0131nlara y\u00f6nelik ayr\u0131mc\u0131l\u0131\u011fa de\u011finen bir Simpsonlar b\u00f6l\u00fcm\u00fcnde, Lisa Simpson erkek k\u0131l\u0131\u011f\u0131na girerek Matematikte \u00dcst\u00fcn Ba\u015far\u0131 \u00d6d\u00fcl\u00fc alacakt\u0131r.<\/figcaption><\/figure>\n

Ayr\u0131mc\u0131l\u0131k ele\u015ftirisi: Kad\u0131nlar da matematik yapabilir!<\/strong><\/p>\n

\u00c7e\u015fitli matematiksel e\u011flenceliklerin a\u00e7\u0131klamalar\u0131n\u0131 yapmaya ek olarak, Singh pop\u00fcler k\u00fclt\u00fcr\u00fcn matematik camias\u0131n\u0131 \u00fczerine ele\u015ftiri yapabilme potansiyeline sahip olabilmesinin di\u011fer yollar\u0131n\u0131 a\u00e7\u0131klar. \u00d6rne\u011fin Lisa Simpson karakteri, matematik ve bilimin dahil oldu\u011fu t\u00fcm entelekt\u00fcel alanlarda olduk\u00e7a parlak gen\u00e7 bir k\u0131zd\u0131r. Ne var ki s\u0131kl\u0131kla kad\u0131n olmak veya ak\u0131ll\u0131 olmakla ilgili \u00f6nyarg\u0131lara maruz kal\u0131r. Singh\u2019in B\u00f6l\u00fcm 7\u2019de odakland\u0131\u011f\u0131 \u201cK\u0131zlar Sadece Toplamlara Sahip Olmak \u0130ster\u201d (2006) isimli b\u00f6l\u00fcmde, iki ayr\u0131mc\u0131l\u0131k (kad\u0131n ve zeki olmak) birlikte i\u015flenir. Bu b\u00f6l\u00fcmde kad\u0131n ve matematik konular\u0131 merkeze konulur ve yazarlar\u0131n\u0131n bilindik hicviyle i\u015flenir. M\u00fcd\u00fcr Skinner\u2019\u0131n k\u0131zlar\u0131n matematikte k\u00f6t\u00fc oldu\u011fu y\u00f6n\u00fcndeki yorumu onu yerinden eder ve okul cinsiyetlere g\u00f6re ikiye ayr\u0131l\u0131r. Matemati\u011fe (Say\u0131lar sizi nas\u0131l hissettiriyor?) \u015feklinde yakla\u015fan basmakal\u0131p \u201ckad\u0131n\u201d \u00f6\u011fretmeni, Lisa\u2019y\u0131 h\u00fcsrana u\u011frat\u0131r. Lisa erkek k\u0131l\u0131\u011f\u0131nda erkekler s\u0131n\u0131f\u0131n\u0131n i\u00e7ine s\u0131zar, sonunda \u201cMatematik Dal\u0131nda \u00dcst\u00fcn Ba\u015far\u0131\u201d \u00f6d\u00fcl\u00fcn\u00fc al\u0131ncaya kadar kendini geli\u015ftirir. K\u0131zlar\u0131n da matematik yapabilece\u011fini kan\u0131tlamak i\u00e7in ger\u00e7ek kimli\u011fini a\u00e7\u0131klad\u0131\u011f\u0131nda, Bart onun sadece erkek taklidi yapt\u0131\u011f\u0131 i\u00e7in ba\u015far\u0131l\u0131 oldu\u011funu iddia eder.<\/p>\n

Bu b\u00f6l\u00fcm, k\u00fc\u00e7\u00fck g\u00f6ndermeler ve donmu\u015f karede ge\u00e7en \u015fakalar d\u0131\u015f\u0131nda, matemati\u011fin ana tema olarak kullan\u0131ld\u0131\u011f\u0131 ilk b\u00f6l\u00fcmd\u00fcr. B\u00f6l\u00fcm sonunda yazarlar Lisa\u2019n\u0131n laf\u0131n\u0131 yar\u0131da keserek ve onu Martin Prince\u2019\u0131n fl\u00fct dersindeki yeriyle yer de\u011fi\u015ftirerek, neden kad\u0131nlar\u0131n matematik alan\u0131nda pek yer almad\u0131\u011f\u0131n\u0131n \u00fcst\u00fc kapal\u0131 bir savunmas\u0131n\u0131 yaparlar. Singh, Lisa Simpson ile yeni a\u00e7\u0131lan \u00c9cole Polytechnique\u2019den Lagrange\u2019\u0131n ders notlar\u0131n\u0131 alabilmek i\u00e7in erkek ismi kullanan Sophia Germain (1776-1831) aras\u0131ndaki benzerlik \u00fcst\u00fcnde durur. Greenwald da bu b\u00f6l\u00fcm hakk\u0131nda yay\u0131nlanmadan hemen \u00f6nce yazar. A\u011fustos 2005\u2019te bir s\u00f6yle\u015fi s\u0131ras\u0131nda o ve Nestler, yazarlardan Westbrook ile g\u00f6r\u00fc\u015f\u00fcr, Westbrook onlara gelecek b\u00f6l\u00fcm\u00fc ve yazarlar\u0131n nas\u0131l \u201cherhangi bir ideolojik kurala veya yola uymak istemedi\u011fini\u201d anlat\u0131r. B\u00f6ylece yazarlar cinsiyet ve matematik ile ilgili bu \u015f\u00fcpheye yo\u011funla\u015f\u0131rken sonunda onun etraf\u0131ndan dolanm\u0131\u015flard\u0131r.<\/p>\n

\"\"Futurama i\u00e7in yaz\u0131lan teorem, akademik d\u00fcnyada kabul g\u00f6r\u00fcyor<\/strong><\/p>\n

Singh son d\u00f6rt b\u00f6l\u00fcm\u00fc, yine Matt Groening taraf\u0131ndan yarat\u0131lan Futurama<\/em>\u2019ya ay\u0131r\u0131r. David S. Cohen \u201cDavid X. Cohen\u201d ad\u0131yla ba\u015fyazar olur ve matematik, fizik ve bilgisayar programlama ile ilgili \u015fakalar say\u0131ca ve kalite bak\u0131m\u0131ndan \u015fahlan\u0131r. Madison Cube\u2019\u00fcn alt\u0131gen kesitleri ya da Bender\u2019in seri numaras\u0131n\u0131n Hardy-Ramanujan say\u0131s\u0131 1792 olmas\u0131 gibi. Singh bunu Hardy-Ramanujan\u2019\u0131n hik\u00e2yesini de i\u00e7eren bir bi\u00e7imde detayl\u0131ca i\u015fler. M\u00f6bius \u015feridi ve Klein \u015fi\u015fesi de Futurama<\/em>\u2019da ekranlara ta\u015f\u0131n\u0131r.<\/p>\n

Son b\u00f6l\u00fcmde, Singh e\u015fsiz bir \u015feyden bahseder: \u201cFuturama Teoremi\u201d. \u201cBenda\u2019n\u0131n Mahk\u00fbmu\u201d(2010)\u00a0 isimli b\u00f6l\u00fcmde pek \u00e7ok karakter, beyinlerini ba\u015fka bir karakterin v\u00fccuduna aktarmak i\u00e7in Prof. Farnsworth\u2019un bir bulu\u015funu kullanmaktad\u0131r: zihin-de\u011fi\u015ftirici. Ne yaz\u0131k ki, makine bir kere iki zihni yer de\u011fi\u015ftirdi mi, o ikisi aras\u0131nda bir daha de\u011fi\u015fim yapamamaktad\u0131r. Bir\u00e7ok farkl\u0131 de\u011fi\u015fimden sonra, karakterler kendi beyinlerinin kendi bedenlerine tekrar nas\u0131l ula\u015fabilece\u011fini merak etmeye ba\u015flarlar.<\/p>\n

Keeler b\u00f6l\u00fcm\u00fc yazmay\u0131 tamamlamaya u\u011fra\u015f\u0131rken herkesin kendi bedenine d\u00f6nmesini garantileyen bir yolu ispatlam\u0131\u015ft\u0131r. B\u00f6l\u00fcmde ise \u201cSweet\u201d Clyde Dixon ve Ethan \u201cBubblegum\u201d isimli karakterler, Keeler\u2019in ispat\u0131n\u0131 o anda Bender\u2019in v\u00fccudunda olan profes\u00f6re anlat\u0131r.<\/p>\n

\"\"
Futurama\u2019n\u0131n \u201cBenda\u2019n\u0131n Mahk\u00fbmu\u201d(2010) b\u00f6l\u00fcm\u00fcnde, zihin de\u011fi\u015ftirici makineyle zihinleri de\u011fi\u015ftirilen ki\u015filerin, birbirleriyle zihni de\u011fi\u015ftirilen insanlar aras\u0131nda tekrar bir de\u011fi\u015fim yap\u0131lamad\u0131\u011f\u0131 durumda, tekrar kendi bedenlerine nas\u0131l d\u00f6nebilecekleri matematiksel olarak ispatlan\u0131r. Senaryo yazar\u0131n\u0131n ispat\u0131, matematik\u00e7iler taraf\u0131ndan optimize edilir ve hakemli bir dergide bas\u0131l\u0131r.<\/figcaption><\/figure>\n

Evans, Huang ve Nguyen(6)<\/sup> Keeler\u2019in orijinal sonucunu geni\u015fletip optimize ederler ve bu muhtemelen televizyon program\u0131 i\u00e7in yarat\u0131lan bir teoremin akademinin h\u00e2kemli dergi d\u00fcnyas\u0131na ilk giri\u015fi olur. Matematik\u00e7iler uzun bir s\u00fcredir di\u011fer alanlarda do\u011fan problemlerden ilham al\u0131yorlar; ancak bir televizyon program\u0131ndaki muamman\u0131n yeni matematiksel \u00e7al\u0131\u015fmalara y\u00f6n vermesi yine de olduk\u00e7a ilgin\u00e7 duruyor. Belki de matematik\u00e7iler e\u011flence d\u00fcnyas\u0131ndan faydalanabilir.\u00a0 Evans ve arkada\u015flar\u0131n\u0131n makalesi 16.000 ki\u015fiden az\u0131na ula\u015f\u0131rken, \u201cBenda\u2019n\u0131n Mahk\u00fbmu\u201dnda Keeler\u2019in ispat\u0131 muhtemelen 2,6 milyon izleyiciye ula\u015fm\u0131\u015ft\u0131r.(20)<\/sup><\/p>\n

\u00d6zetle Singh, genel okuyucu i\u00e7in e\u011flenceli, a\u00e7\u0131klay\u0131c\u0131 ilgin\u00e7 matemati\u011fi yaz\u0131yor. Ayn\u0131 zamanda matematik d\u00fcnyas\u0131 ve Hollywood aras\u0131ndaki diyalo\u011fu s\u00fcrd\u00fcrmekte de olduk\u00e7a ba\u015far\u0131l\u0131 oluyor. Futurama <\/em>2013\u2019te bir kez daha yay\u0131ndan kald\u0131r\u0131ld\u0131, umudumuz Simpsonlar<\/em>\u2019\u0131n y\u00fcksek kalite matematiksel e\u011flence i\u00e7eren bir d\u00fcnya sunmaya devam etmesi.<\/p>\n

Dipnotlar<\/strong><\/p>\n

* Waltsonlar, 1972-1981 y\u0131llar\u0131 aras\u0131nda Amerika\u2019da yay\u0131nlanan aile dizisi.<\/p>\n

** Kar\u015f\u0131s\u0131ndakini a\u015fa\u011f\u0131lamak i\u00e7in yap\u0131lan bir \u015fakaya verilen tepki.<\/p>\n

Kaynaklar<\/strong><\/p>\n

1) Timothy P. Chartier, \u201cUsing the Force: Star Wars in the classroom, Problems, Resources, and Issues in Mathematics Undergraduate Studies\u201d, (PRIMUS<\/em>) XVII (2007), No. 1 (January\u2013March), 8-23.<\/p>\n

2) Timothy P. Chartier and Dan B. Goldman, \u201cMathematical movie magic\u201d, Math Horizons<\/em> (April 2004).<\/p>\n

3) David S. Cohen and Manuel Blum, \u201cOn the problem of sorting burnt pancakes\u201d, Discrete Applied Mathematics<\/em> 61 (July 28, 1995), No.2, 105-120.<\/p>\n

4) Leigh H. Edwards, Christopher D. Goff, Sarah J. Greenwald, and Jill E. Thomley, \u201cMathematics and Television\u201d, Encyclopedia of Mathematics and Society<\/em> (October 2011).<\/p>\n

5) Noam Elkies, \u201cRational points near curves and small nonzero|x3\u2212y2|vialatticereduction\u201d, 4th International Symposium, ANTS-IV (Leiden, The Netherlands, July 2000), Lecture Notes in Computer Science<\/em>, Vol. 1838, (Wieb Bosma, ed.), Springer, Berlin-Heidelberg, 2000, pp. 33-63.<\/p>\n

6) Ron Evans, Lihua Huang and Tuan Nguyen, \u201cKeeler\u2019s theorem and products of distinct transpositions\u201d, The American Mathematical Monthly<\/em> 121(2014), No.2, 136-144.<\/p>\n

7) Futurama \u2013 Series, Comedy Central Offcial Site, ComedyCentral.com.<\/p>\n

8) Tom Georgoulias, Sarah J. Greenwald and Mark Wichterich, \u201cFuturama \u03c0k: Mathematics in the year 3000\u201d, Math Horizons<\/em> (April 2004).<\/p>\n

9) Christopher D. Goff and Sarah J. Greenwald (eds.), PRIMUS Special Issue<\/em>: \u201cCurrent Work and Future Directions in Mathematics and Popular Culture\u201d, Vol. XVII (1) January-March, Taylor & Francis, 2007.<\/p>\n

10) Sarah J. Greenwald, \u201cGirls just want to have sums\u201d, The Newsletter of the Association for Women in Mathematics<\/em> 36 (2006), No.2, 22-23.<\/p>\n

11) \u201cKlein\u2019s beer: Futurama comedy and writers in the classroom\u201d, PRIMUS<\/em> XVII (2007), No.1, 52-66.<\/p>\n

12) \u201cDr. Sarah\u2019s Mathematical Backgrounds of the Simpsons\u2019 Writers\u201d, mathsci2.appstate.edu\/~sjg\/ simpsonsmath\/degrees.html (May 31, 2014).<\/p>\n

13) \u201cDr. Sarah\u2019s Mathematical Morsels from The Simpsons&Futurama\u201d, www.mathsci.appstate.edu\/~ sjg\/SimpsonsFuturamamath\/MathClub (June 3, 2014).<\/p>\n

14) Sarah J. Greenwald and Andrew Nestler, \u201cr dr r: Engaging students with signi\ufb01cant mathematical content from The Simpsons\u201d, PRIMUS<\/em> XIV (2004), No.1, 29-39.<\/p>\n

15) \u201cMathematics and Mathematicians on The Simpsons\u201d, SimpsonsMath.com, mathsci2.appstate. edu\/~sjg\/simpsonsmath\/ (May 31, 2014).<\/p>\n

16) Sarah J. Greenwald and Jill E. Thomley, \u201cMathematically talented women in Hollywood: Fred in Angel\u201d, PRIMUS<\/em> XVII (2007), No.1, 103-116.<\/p>\n

17) Kenneth Keeler and Jeffery Westbrook, \u201cShort encodings of planar graphs and maps\u201d, Discrete Applied Mathematics<\/em> 58 (1995), No.3, 239-252.<\/p>\n

18) \u201cMath in the Movies\u201d, Mathematical Association of America<\/em>, www.maa.org\/meetings\/calendarevents\/math-in-the-movies (June 4, 2014).<\/p>\n

19) Andrew Nestler, \u201cAndrew Nestler\u2019s Guide to Mathematics and Mathematicians on The Simpsons\u201d, homepage.smc.edu\/nestler_andrew\/SimpsonsMath. htm (May 31, 2014).<\/p>\n

20) Bonnie Ponce, personal communication, June 1, 2014. (Bonnie Ponce is the editorial assistant to The American Mathematical Monthly).<\/p>\n

21) The Simpsons on FOX Official Site. www. thesimpsons.com (June 4, 2014).<\/p>\n

22) Simon Singh, Fermat\u2019s Enigma: The Epic Quest to Solve the World\u2019s Greatest Mathematical Problem<\/em>, Walker and Company, New York, 1997.<\/p>\n","protected":false},"excerpt":{"rendered":"

Simon Singh son kitab\u0131, \u201cSimpsonlar ve Matematiksel S\u0131rlar\u0131\u201dnda, yazar ekibinde matematik, fizik ve bilgisayarbilimleri e\u011fitimi alm\u0131\u015f ki\u015filer de bulunan \u201cSimpsonlar\u201d ve \u201cFuturama\u201d adl\u0131 animasyonlar \u00fczerinden e\u011flence end\u00fcstrisi ve matematik d\u00fcnyas\u0131n\u0131n bir\u00e7ok ilgin\u00e7 yolla birbirlerini nas\u0131l etkileyebilece\u011fini anlat\u0131yor. Sunu\u015f: Okuyaca\u011f\u0131n\u0131z yaz\u0131 Amerikan Matematik Toplulu\u011fu\u2019nun Notices of the AMS adl\u0131 dergisinin, Ocak 2015 tarihli say\u0131s\u0131nda (62. Cilt, […]<\/p>\n","protected":false},"author":224,"featured_media":15504,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[185,25],"tags":[1793,208,1792,1794],"class_list":["post-15500","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-148-sayi","category-matematik","tag-animasyon","tag-matematik","tag-populer-kultur","tag-simpsonlar"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/15500","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/users\/224"}],"replies":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/comments?post=15500"}],"version-history":[{"count":0,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/15500\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media\/15504"}],"wp:attachment":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media?parent=15500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/categories?post=15500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/tags?post=15500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}