\u00d6N NOT: \u2018Daha kolay bir \u00e7\u00f6z\u00fcm yok mu?\u2019 ba\u015fl\u0131kl\u0131 bir \u00f6nceki konumuzda s\u00f6z\u00fc edilen kolay \u00e7\u00f6z\u00fcme dair \u0130PUCU alttaki yaz\u0131da mevcuttur.<\/p>\n
\u2018Daha kolay bir \u00e7\u00f6z\u00fcm yok mu?\u2019 ba\u015fl\u0131kl\u0131 bir \u00f6nceki konumuzdaki resimde ka\u00e7 tane \u00fc\u00e7gen g\u00f6r\u00fcyorsunuz?
\nYalan, yanl\u0131\u015f veya d\u00fc\u015f\u00fcnmeden s\u00f6ylemeyin!
\nO resimde hi\u00e7, bir tane bile, \u00fc\u00e7gen yok!
\nBa\u015fka herhangi bir yerde de hi\u00e7, bir tane bile, \u00fc\u00e7gen yok!
\nBu evrenin hi\u00e7bir yerinde \u00fc\u00e7gen yok!
\nBu evrenin hi\u00e7bir yerinde \u00fc\u00e7gen \u00fcretemezsiniz!<\/p>\n
Bakal\u0131m! \u00dc\u00e7gen nedir? Yani, \u00fc\u00e7gen tan\u0131m\u0131 nedir? \u015eudur: \u00dc\u00e7 k\u00f6\u015fesi olan ve k\u00f6\u015feleri d\u00fcz \u00e7izgi par\u00e7alar\u0131yla (do\u011fru par\u00e7alar\u0131yla) birle\u015ftirilmi\u015f \u015fekil.
\nB\u00f6yle bir \u015fekil olu\u015fturulamaz ki, \u00e7\u00fcnk\u00fc; d\u00fcz \u00e7izgi yani do\u011fru, olu\u015fturulabilir de\u011fildir! Uzunlu\u011fu olacak, geni\u015fli\u011fi olmayacak! Nas\u0131l olu\u015ftural\u0131m? Noktalar\u0131 hareket ettirerek mi?
\nNokta da olu\u015fturamay\u0131z!
\nNokta var olacak ama uzunlu\u011fu, geni\u015fli\u011fi ve derinli\u011fi olmayacak.
\nAk\u0131llara seza!
\nNokta olu\u015fturamad\u0131\u011f\u0131m\u0131z i\u00e7in \u00fc\u00e7gen de olu\u015fturamay\u0131z!
\n\u00c7izgi olu\u015fturamad\u0131\u011f\u0131m\u0131z i\u00e7in \u00fc\u00e7gen de olu\u015fturamay\u0131z!
\n\u00c7ember de olu\u015fturamay\u0131z, parabol de, hiperbol de, \u2026 .<\/p>\n
Ne var ki, bunlar niyetine \u00e7izdi\u011fimiz \u015fekillere bakarak hepsini de hayal edebiliriz! Zaten b\u00f6yle yap\u0131yoruz. Dahas\u0131, hayallerimize \u00e7ok k\u0131ymet takdir ediyoruz. \u00d6rne\u011fin, kum \u00fcst\u00fcndeki \u00e7iziklerine g\u00f6lgesi d\u00fc\u015fen Romal\u0131 askeri ha\u015flamam\u0131\u015f m\u0131yd\u0131 Ar\u015fimet? Bkz., https:\/\/ruslanismayilov.wordpress.com\/2014\/04\/27\/arsimet\/<\/p>\n
Ortada \u00fc\u00e7gen yokken, o varm\u0131\u015fcas\u0131na, hesap kitap yap\u0131yoruz. Nokta bile olu\u015fturam\u0131yoruz ama koskoca Geometri k\u00fclliyat\u0131 olu\u015fturabiliyoruz.
\nDahas\u0131, hi\u00e7bir Geometri unsurunu \u00f6l\u00e7emiyoruz. Haydi diyelim noktay\u0131 ge\u00e7tik. \u2018Daha kolay bir \u00e7\u00f6z\u00fcm yok mu?\u2019 ba\u015fl\u0131kl\u0131 bir \u00f6nceki konumuzdaki resimdeki \u2018kare\u2019lerin kenar uzunluklar\u0131n\u0131n e\u015fit oldu\u011funu biliyor muyuz? Hay\u0131r! \u00d6l\u00e7meye kalk\u0131\u015fsak, \u00f6l\u00e7emeyiz. Yani hassal\u0131kl\u0131 \u00f6\u00e7emeyiz. \u00d6rne\u011fin, cetvelimizin d\u00fcz oldu\u011fundan emin olabilecek miyiz? \u00d6rne\u011fin, santimetre cinsinden diyelim, noktadan sonra ka\u00e7\u0131nc\u0131 basama\u011fa dek gidebilece\u011fiz?<\/p>\n
Ayn\u0131 nedenle, x a\u00e7\u0131s\u0131n\u0131n 45 derece oldu\u011fundan emin miyiz? Nas\u0131l \u00f6l\u00e7ebiliriz ki? A\u00e7\u0131 kenarlar\u0131n\u0131n d\u00fcz \u00e7izgiler, do\u011fru \u00e7izgiler oldu\u011fundan emin miyiz?
\nAma x a\u00e7\u0131s\u0131n\u0131 45 derece olarak hayal etmekte s\u0131n\u0131rs\u0131z \u00f6zg\u00fcr\u00fcz.<\/p>\n
Dahas\u0131, \u00fc\u00e7gen olu\u015fturamay\u0131z; kare, dikd\u00f6rtgen, yamuk da olu\u015fturamay\u0131z. Ama kare, dikd\u00f6rtgen ve yamuk \u015fekillerinin biti\u015ftirilmi\u015f iki \u00fc\u00e7gene ayr\u0131\u015ft\u0131r\u0131labilece\u011fini \u2018g\u00f6r\u00fcnce\u2019, \u00fc\u00e7genin i\u00e7 a\u00e7\u0131lar\u0131 toplam\u0131 180 derece oldu\u011funa g\u00f6re kare, dikd\u00f6rtgen ve yamuk \u015fekillerinin i\u00e7 a\u00e7\u0131lar\u0131n\u0131n toplam\u0131n\u0131n 360 derece edece\u011fini s\u00f6yleyebiliriz. Burada asl\u0131nda Temel Mant\u0131k \u015f\u00f6yle i\u015fmektedir: \u2018p ise q\u2019 yani p\u2192q.<\/p>\n
Bu bir b\u00fcy\u00fcd\u00fcr elbette. Kendi kendimizi b\u00fcy\u00fcledi\u011fimizin fark\u0131na varmak ise, gayet m\u00fc\u015fk\u00fcl bir i\u015ftir! Yani hem b\u00fcy\u00fclendi\u011fimizin fark\u0131na varmak hem de bu b\u00fcy\u00fcy\u00fc bizzat kendimizin yapt\u0131\u011f\u0131n\u0131 fark etmek m\u00fc\u015fk\u00fcl bir i\u015ftir.<\/p>\n
Kald\u0131 ki, ba\u015fkalar\u0131n\u0131n yapt\u0131\u011f\u0131 b\u00fcy\u00fcy\u00fc bile fark etmekte zorland\u0131\u011f\u0131m\u0131z\u0131n \u00f6rnekleri de hayli \u00e7ok say\u0131dad\u0131r. \u00d6rne\u011fin, Parmenides-Zeno ikilisinin, \u00f6nceki yaz\u0131lar\u0131m\u0131zda \u00e7ok kez konu edindi\u011fimiz, s\u00f6z\u00fcmona paradokslar\u0131 son derece ba\u015far\u0131l\u0131 b\u00fcy\u00fc \u00f6rnekleridir. Sofokles tragedyalar\u0131 da \u00e7ok ba\u015far\u0131l\u0131 b\u00fcy\u00fc \u00f6rneklerindendir. \u2018Once Upon in America\u2019 filmi de, \u2018Godfather\u2019 filmi de. \u2018Seasons In The Sun\u2019 \u015fark\u0131s\u0131 da, \u2018Uzun \u0130nce Bir Yolday\u0131m\u2019 t\u00fcrk\u00fcs\u00fc de, \u2018\u00c7\u00f6kertme’den \u00c7\u0131kt\u0131m da Halil’im\u2019 t\u00fcrk\u00fcs\u00fc de. Daha ba\u015fka onlarcas\u0131, y\u00fczlercesi, binlercesi, milyonlarcas\u0131 da.
\nB\u00fcy\u00fcler deryas\u0131nda y\u00fcz\u00fcp duran bal\u0131klar misaliyiz.<\/p>\n
Madem \u00e7ok kez konu ettik, bir kez fazlas\u0131 zarar etmez; \u015fu 2500 y\u0131ll\u0131k Parmenides-Zeno Paradokslar\u0131 diye bilinen konulardan A\u015fil ve Kaplumba\u011fa ile ilgili olana yeniden bakal\u0131m.
\n\u00d6nce, s\u0131n\u0131rl\u0131 uzunlukta bir \u00e7izgi hayal ettirip, bunu diledi\u011fimiz kez yar\u0131layabilece\u011fimizi s\u00f6yl\u00fcyorlar. Do\u011frudur, bunu herkes hayal edebilir. Sonra da hemencecik bir ger\u00e7ek konuya, yani ger\u00e7ek D\u00fcnya\u2019da olabilecek bir konuya d\u00f6n\u00fcp A\u015fil\u2019in \u2018sonsuz kez yar\u0131lanabilir bir uzakl\u0131\u011f\u0131\u2019 asla y\u00fcr\u00fcyemeyece\u011fini, ko\u015famayaca\u011f\u0131n\u0131; hatta, harekete bile ba\u015flayamayaca\u011f\u0131n\u0131 ileri s\u00fcr\u00fcyorlar. Bir hayali konudan, ger\u00e7ekli\u011fe dair bir sonu\u00e7 \u00e7\u0131karmam\u0131z\u0131 s\u00f6yl\u00fcyorlar. Mesele a\u00e7\u0131k; biri saf hayal, di\u011feri saf ger\u00e7eklik. Ama, bunlar\u0131n \u2018gayet incelikli \u00f6nerme\u2019 olu\u011funu s\u00f6yleyenler t\u00fcm\u00fcn\u00fc ger\u00e7eklik san\u0131yor ve b\u00fcy\u00fcn\u00fcn ayr\u0131m\u0131na varam\u0131yor. Yani, A\u015fil ile kaplumba\u011fa aras\u0131nda \u00e7izgi(ler) olmad\u0131\u011f\u0131n\u0131, olamayaca\u011f\u0131n\u0131 kavra(ya)m\u0131yorlar. Noktalar, \u00e7izgiler, a\u00e7\u0131lar hayal aleminin unsurlar\u0131d\u0131r, bu D\u00fcnya\u2019n\u0131n de\u011fil!<\/p>\n
Bak\u0131lan ile \u2018g\u00f6r\u00fclen\u2019 yani d\u00fc\u015f\u00fcn\u00fclen ayn\u0131 de\u011fil ise, bu bir b\u00fcy\u00fcleni\u015ftir.
\nT\u0131pk\u0131s\u0131 t\u0131pk\u0131s\u0131na, son noktas\u0131n\u0131 birazdan koyaca\u011f\u0131m\u0131z ve halen okumakta oldu\u011funuz bu yaz\u0131n\u0131n (da) bir b\u00fcy\u00fc oldu\u011fu gibi.
\nBu yaz\u0131y\u0131 okumaya ba\u015flad\u0131\u011f\u0131n\u0131zla \u015fimdiki, hele hele biti\u015ften sonraki ak\u0131l, zihin, anlak haliniz (\u2018state\u2019) ayn\u0131 m\u0131? Ama bu yaz\u0131da, sizin arada \u2018g\u00f6rd\u00fc\u011f\u00fcn\u00fcz\u2019 yani d\u00fc\u015f\u00fcnd\u00fcklerinizin hi\u00e7bir par\u00e7as\u0131 yok. Var olan, sadece harf ve noktalama i\u015fareti denilen 30-40 \u00e7e\u015fit \u015fekildir.<\/p>\n
\u015eimdi bir daha bak\u0131n!<\/p>\n","protected":false},"excerpt":{"rendered":"
\u00d6N NOT: \u2018Daha kolay bir \u00e7\u00f6z\u00fcm yok mu?\u2019 ba\u015fl\u0131kl\u0131 bir \u00f6nceki konumuzda s\u00f6z\u00fc edilen kolay \u00e7\u00f6z\u00fcme dair \u0130PUCU alttaki yaz\u0131da mevcuttur. \u2018Daha kolay bir \u00e7\u00f6z\u00fcm yok mu?\u2019 ba\u015fl\u0131kl\u0131 bir \u00f6nceki konumuzdaki resimde ka\u00e7 tane \u00fc\u00e7gen g\u00f6r\u00fcyorsunuz? Yalan, yanl\u0131\u015f veya d\u00fc\u015f\u00fcnmeden s\u00f6ylemeyin! O resimde hi\u00e7, bir tane bile, \u00fc\u00e7gen yok! Ba\u015fka herhangi bir yerde de hi\u00e7, […]<\/p>\n","protected":false},"author":1425,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-1379","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1379","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/users\/1425"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/comments?post=1379"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1379\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=1379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=1379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=1379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}