Hani, A\u015fil \u00f6n\u00fcnde duran kaplumba\u011faya asla eri\u015femez, \u00e7\u00fcnk\u00fc harket bile edemezdi ya. \u00c7\u00fcnk\u00fc o kaplumba\u011faya eri\u015fmezden evvel, o mesafenin yar\u0131s\u0131na gelmeli, bundan evvel de o yar\u0131n\u0131n yar\u0131s\u0131 olan mesafeyi arkada b\u0131rakmas\u0131 gerikir idi. B\u00f6yle b\u00f6yle, yani her yar\u0131n\u0131n mutlaka bir yar\u0131s\u0131 olaca\u011f\u0131 nedeniyle hi\u00e7bir mesafeyi arkada b\u0131rakamaz; s\u00f6z\u00fcn k\u0131sas\u0131, harekete ba\u015flayamazd\u0131 bile. Parmenides ile Zeno ikilisinin A\u015fil ile Kaplumba\u011fa meseli tam\u0131 tam\u0131na \u00f6yle idi. (*)<\/p>\n
\u0130lk olarak, A\u015fil ile kaplumba\u011fam\u0131z aras\u0131ndaki mesafenin ne oldu\u011funu tan\u0131mlayamay\u0131z.<\/p>\n
Yani, o iki canl\u0131n\u0131n birbirine en yak\u0131n noktalar\u0131 aras\u0131ndaki mesafe midir s\u00f6z konusu olan?<\/p>\n
\u0130yi de, o iki canl\u0131n\u0131n birbirine en yak\u0131n noktalar\u0131n\u0131 nas\u0131l tespit edece\u011fiz? \u0130lkin, nokta tespit edilebilir de\u011fildir ki? Evrende nokta olu\u015fturamay\u0131z. (Pek \u00e7ok kez irdeledik bu konuyu.) \u0130kincileyin, aradaki o mesafeyi nas\u0131l saptayaca\u011f\u0131z? Nas\u0131l \u00f6l\u00e7ece\u011fiz?
\nDiyelim ki, tam\u0131 tam\u0131na \u00f6l\u00e7t\u00fck o mesafeyi ve A olarak kaydetmeye yeltendik. Kay\u0131t alt\u0131na alabilecek miyiz? Noktadan sonra ka\u00e7 basamakl\u0131 olacak acaba bu mesafe? Diyelim ki, N basamakl\u0131 olacak s\u00f6z konusu mesafe ve zaman i\u00e7inde r\u00fczgard\u0131 yeldi, Yer hareketiydi gibi herhangi bir etki ile asla de\u011fi\u015fmeyecek.<\/p>\n
Tart\u0131\u015fmam\u0131z\u0131 bir \u00f6rnekle \u015f\u00f6ylece somutla\u015ft\u0131ral\u0131m. Diyelim ki, A mesafesi 10 metreden az k\u0131sa ve \u00f6l\u00e7\u00fcm sonucu 9\u2019dan sonra N basamakl\u0131 bir de\u011fer elde ettik.<\/p>\n
10\u2019un yar\u0131s\u0131 5; 5\u2019in yar\u0131s\u0131 2,5; 2,5\u2019un yar\u0131s\u0131 1,25; diye gitse N+1 kez ard\u0131\u015f\u0131k yar\u0131lama sonras\u0131nda noktadan sonra N basamakl\u0131 bir say\u0131 elde ederiz. Buradan anla\u015f\u0131l\u0131r ki, s\u00fcrekli yar\u0131lama ile noktadan sonra N basamakl\u0131 herhangi bir uzakl\u0131ktan \u00e7ok daha k\u00fc\u00e7\u00fck mesafe \u00f6l\u00e7\u00fcmlerine gere\u011fimiz do\u011far.<\/p>\n
\u015e\u00f6yle d\u00fc\u015f\u00fcnm\u00fc\u015fler de olmu\u015ftur tarih boyunca; \u201cHer ne ise! \u00d6l\u00e7emezsek \u00f6l\u00e7emeyelim. Biz \u00f6l\u00e7emiyor olabiliriz ama A\u015fil ile mal\u00fbm kaplumba\u011fa aras\u0131nda belli bir mesafe vard\u0131r ve biz bu mesafeyi s\u00fcrekli ard\u0131\u015f\u0131k yar\u0131lara b\u00f6lebiliriz.\u201d
\nBu d\u00fc\u015f\u00fcnce t\u00fcmden yanl\u0131\u015f de\u011fildir; elbet b\u00f6lebiliriz ama ger\u00e7eklikte de\u011fil. Sadece hayalde b\u00f6lebiliriz.
\nAyn\u0131 ba\u011flamda \u015f\u00f6yle de sorulabilir; A\u015fil ile o kaplumba\u011fa aras\u0131ndaki mesafe en k\u0131sa ne kadar olabilir? Yani, bir iki paragraf yukar\u0131daki gibi A de\u011feri en k\u00fc\u00e7\u00fck ka\u00e7 olabilir?<\/p>\n
Tabii ki, o canl\u0131lar da atomlardan yap\u0131lmad\u0131r ve atomlar birbirine temas edemez; \u00e7\u00fcnk\u00fc ayn\u0131 y\u00fckl\u00fc kabuk elektronlar\u0131 aras\u0131ndaki Coulomb Kuvveti, aradaki mesafe k\u00fc\u00e7\u00fcld\u00fck\u00e7e b\u00fcy\u00fcr. (**)<\/p>\n
Demek ki, en k\u00fc\u00e7\u00fck A de\u011feri s\u0131f\u0131r olamaz! Peki, en k\u00fc\u00e7\u00fck A de\u011feri ka\u00e7 olabilir?<\/p>\n
(*) https:\/\/www.google.com\/search?q=A%C5%9Fil+ile+Kaplumba%C4%9Fa&rlz=1C1CHBF_enTR866TR866&oq=A%C5%9Fil+ile+Kaplumba%C4%9Fa&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIKCAEQABgTGBYYHjIKCAIQABgTGBYYHjIHCAMQABjvBTIKCAQQABiABBiiBDIHCAUQABjvBTIHCAYQABjvBdIBCDEyMzZqMGo3qAIAsAIA&sourceid=chrome&ie=UTF-8<\/p>\n
https:\/\/cse.google.com\/cse?cx=001101905209118093242%3Arsrjvdp2op4&ie=UTF-8&q=+A%C5%9Fil+ile+Kaplumba%C4%9Fa&sa=Search<\/p>\n
https:\/\/plato.stanford.edu\/search\/searcher.py?query=zeno<\/p>\n
(**) https:\/\/tr.wikipedia.org\/wiki\/Coulomb_kanunu<\/p>\n","protected":false},"excerpt":{"rendered":"
Hani, A\u015fil \u00f6n\u00fcnde duran kaplumba\u011faya asla eri\u015femez, \u00e7\u00fcnk\u00fc harket bile edemezdi ya. \u00c7\u00fcnk\u00fc o kaplumba\u011faya eri\u015fmezden evvel, o mesafenin yar\u0131s\u0131na gelmeli, bundan evvel de o yar\u0131n\u0131n yar\u0131s\u0131 olan mesafeyi arkada b\u0131rakmas\u0131 gerikir idi. B\u00f6yle b\u00f6yle, yani her yar\u0131n\u0131n mutlaka bir yar\u0131s\u0131 olaca\u011f\u0131 nedeniyle hi\u00e7bir mesafeyi arkada b\u0131rakamaz; s\u00f6z\u00fcn k\u0131sas\u0131, harekete ba\u015flayamazd\u0131 bile. Parmenides ile Zeno […]<\/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-1402","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1402","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=1402"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1402\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=1402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=1402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=1402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}