{"id":1471,"date":"2026-02-13T13:42:10","date_gmt":"2026-02-13T10:42:10","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/caglart\/?p=1471"},"modified":"2026-02-14T02:57:40","modified_gmt":"2026-02-13T23:57:40","slug":"insanin-en-geliskin-yetenegi-hkk","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/caglart\/2026\/02\/13\/insanin-en-geliskin-yetenegi-hkk\/","title":{"rendered":"\u0130nsan\u0131n en geli\u015fkin yetene\u011fi hkk."},"content":{"rendered":"<p>Varsayal\u0131m ki, d\u0131\u015f d\u00fcnya var! Mesela bkz., \u201cK\u0131rm\u0131z\u0131 daire\u201d. (*) Ama bu varsay\u0131m\u0131 yapabilmek i\u00e7in, \u00f6nce kendi varl\u0131\u011f\u0131m\u0131z\u0131 kan\u0131tlamal\u0131y\u0131z. Mesela bkz., \u201cVarolu\u015f\u201d. (**)<br \/>\nHeyhat! Kendi varl\u0131\u011f\u0131m\u0131z\u0131 kan\u0131tlama yolunda R. Descartes\u2019in o \u00fcnl\u00fc deyi\u015finden \u00f6te gidebilmi\u015f de\u011filiz (hen\u00fcz?). Ho\u015f, o deyi\u015f de hayli \u00e7eli\u015fiktir kendi i\u00e7inde! \u00d6nce var olmu\u015f olmal\u0131y\u0131m ki, d\u00fc\u015f\u00fcn\u00fcp d\u00fc\u015f\u00fcnmedi\u011fimi kavrayabileyim, d\u00fc\u015f\u00fcn\u00fc\u015f\u00fcn ne oldu\u011funu bilebileyim, d\u00fc\u015f\u00fcn\u00fcyor oldu\u011fuma karar verebileyim.<br \/>\nNeyse, kendimizin de var oldu\u011funu varsayabiliriz! G\u00fcne\u015f\u2019in, D\u00fcnya\u2019n\u0131n, Ay\u2019\u0131n ve di\u011fer gezegen ve uydular\u0131n da; h\u00fclasa, G\u00fcne\u015f Sistemi\u2019nin de.<br \/>\nBildi\u011fimiz kadar\u0131yla J. Kepler de \u00f6yle yapm\u0131\u015f olmal\u0131 ki, G\u00fcne\u015f \u00e7evresinde dolanan D\u00fcnya ve di\u011fer gezegenleri G\u00fcne\u015f\u2019e ba\u011flayan hayali \u00e7izgilerin e\u015fit zaman s\u00fcrelerinde e\u015fit alan tarad\u0131\u011f\u0131 yasas\u0131n\u0131 bulmu\u015f. Buna \u201cKepler\u2019in \u0130kinci Yasas\u0131\u201d diyoruz.<br \/>\nAcaba bu bulu\u015f ke\u015fif midir yoksa icat m\u0131? Evet, Keplerden \u00f6nce de ayn\u0131 yasa ge\u00e7erliydi, sonra da ge\u00e7erli oldu. Bu durumda \u201cKe\u015fiftir!\u201d diye yan\u0131tlamak gerekir bu paragraf\u0131n ba\u015f\u0131ndaki soruyu. Dahas\u0131, Kepler\u2019in bu yasay\u0131 T. Brahe\u2019nin g\u00f6zlem notlar\u0131, verisi \u00fcst\u00fcnde yapt\u0131\u011f\u0131 incelemelerden sonra buldu\u011funa bakarak da peki\u015ftirilebilir ayn\u0131 yan\u0131t.<br \/>\nAcaba bilimsel bulu\u015flar t\u00fcm\u00fcyle mi ke\u015fiftir?<br \/>\nHay\u0131r!<br \/>\n\u0130cat m\u0131?<br \/>\nHay\u0131r!<br \/>\n\u0130lk \u201cHay\u0131r!\u201ddan ba\u015flayal\u0131m.<br \/>\nL. E. Boltzmann\u2019\u0131n \u201cEnerji Da\u011f\u0131l\u0131m Form\u00fcl\u00fc\u201d, bu form\u00fcl kullan\u0131larak elde edilen M. Planck\u2019\u0131n \u201cKaracisim Enerji Da\u011f\u0131l\u0131m Form\u00fcl\u00fc\u201d ve yine ayn\u0131 da\u011f\u0131l\u0131m\u0131n kullan\u0131ld\u0131\u011f\u0131 A. Einstein\u2019\u0131n \u201cIs\u0131 S\u0131\u011fas\u0131\u201d form\u00fcl\u00fc ke\u015fif olamaz. \u00c7\u00fcnk\u00fc, bu form\u00fcllerde sonsuz b\u00fcy\u00fckl\u00fckte enerji de\u011ferleri kullan\u0131lmaktad\u0131r ve b\u0131rak\u0131n be\u015f on kilograml\u0131k k\u00fctleleri, t\u00fcm evrenin enerjisi bile sonsuz olmasa gerektir. Demek ki, bu paragrafta an\u0131lan fizik ke\u015fif olamaz. \u00c7\u00fcnk\u00fc, evrende sonsuz enerji yok! Demek ki, bu paragrafta an\u0131lan form\u00fcller ke\u015fif de\u011fil. \u0130cat m\u0131d\u0131r acaba? Bu da de\u011fil. \u00c7\u00fcnk\u00fc, en az\u0131ndan, bulunu\u015flar\u0131ndan sonra de\u011fi\u015fime u\u011framad\u0131lar, geli\u015fmediler. Bulunu\u015flar\u0131ndan bu yana, \u00f6ylece kaskat\u0131 kald\u0131lar.<br \/>\nS\u00f6z\u00fc fazla uzatmayay\u0131m: tam\u0131 tam\u0131na do\u011fru herhangi bir bilimsel yasa bulunabilmi\u015f de\u011fil hen\u00fcz. Daha da vahimi, nas\u0131l bulunulabilece\u011fi de bilinmiyor. Yani, bulunabilir olup olmad\u0131klar\u0131 da m\u00fcphem!<br \/>\nHi\u00e7bir gezegeni G\u00fcne\u015f\u2019e ba\u011flayan sanal \u00e7izgi e\u015fit zaman aral\u0131klar\u0131nda e\u015fit alanlar taramaz; yakla\u015f\u0131k olarak (***) e\u015fit alanlar tarar. Daha yak\u0131n\u0131m\u0131zdan \u00f6rnekleyelim; hi\u00e7bir cisim Galileo Denklemi\u2019ne tam olarak uymaz.<br \/>\n\u00c7\u00fcnk\u00fc, G\u00fcne\u015f de gezegenler de yery\u00fcz\u00fc cisimleri de nokta de\u011fildir ama yakla\u015f\u0131k olarak nokta imi\u015f gibi d\u00fc\u015f\u00fcn\u00fclebilir! Zira, bilinen yani ilgili makale ve kitaplarda yaz\u0131l\u0131 olan yani kay\u0131t alt\u0131nda olan Fizik sadece ve sadece noktasal yani eni, boyu ve derinli\u011fi olmayan cisimleri kapsar. Daha da vahimi, sadece ve sadece ikili etkile\u015fimleri kapsar. \u00dc\u00e7 cisim (\u00f6rne\u011fin G\u00fcne\u015f, D\u00fcnya ve Ay) aras\u0131ndaki (\u00f6rne\u011fin k\u00fctle\u00e7ekimsel) etkile\u015fimlere dair analitik, kapal\u0131 bir form\u00fclden mahrumuz hen\u00fcz. Bu nedenle, G\u00fcne\u015f \u00e7evresinde D\u00fcnya\u2019n\u0131n dolan\u0131\u015f\u0131 s\u0131ras\u0131nda eliptik y\u00f6r\u00fcnge izledi\u011fini s\u00f6ylerken de di\u011fer gezegen ve uydular\u0131n olmad\u0131\u011f\u0131 var say\u0131l\u0131r; ayn\u0131 anda G\u00fcne\u015f\u2019in de D\u00fcnya\u2019n\u0131n da nokta oldu\u011fu var say\u0131l\u0131r.<br \/>\nGel de \u015fen kahkaha atma!<\/p>\n<audio class=\"wp-audio-shortcode\" id=\"audio-1471-1\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2025\/05\/Bebe.mp3?_=1\" \/><a href=\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2025\/05\/Bebe.mp3\">https:\/\/blog.metu.edu.tr\/caglart\/files\/2025\/05\/Bebe.mp3<\/a><\/audio>\n<p>Evrende nokta da yoktur. (Olsa bile, nokta saptayacak hi\u00e7bir ayg\u0131t\u0131m\u0131z yoktur.) Nokta yaratacak ayg\u0131t da yoktur. Bu durumda \u00e7izgi nas\u0131l olsun ki? Demek ki, elips de yoktur parabol ve \u00e7ember de!<br \/>\nPeki! Nokta, \u00e7izgi, geometrik \u015fekil dediklerimiz nedir? Hayaldir sadece, ham hayaldir. Ba\u015fka bir deyimle d\u00fc\u015f\u00fcncedir! Hayalimiz, d\u00fc\u015f\u00fcncemiz d\u0131\u015f\u0131nda hi\u00e7bir ger\u00e7ek yerde nokta da olu\u015fturamay\u0131z, \u00e7izgi de, \u00e7ember de, elips de\u2026<br \/>\nGeometri hayal de Aritmetik, Cebir hayal de\u011fil midir? \u00d6rne\u011fin 1 say\u0131s\u0131, 3 bu\u00e7uk say\u0131s\u0131, \u03c0 say\u0131s\u0131, karek\u00f6k i\u00e7inde 2 say\u0131s\u0131, k\u00fcp k\u00f6k i\u00e7inde 3 say\u0131s\u0131 ger\u00e7ek midir? Yani, evrenin neresinde vard\u0131r?<br \/>\n\u015eu say\u0131lar\u0131n de\u011feri bile bilinmiyor: \u03c0 say\u0131s\u0131, karek\u00f6k i\u00e7inde 2 say\u0131s\u0131, k\u00fcp k\u00f6k i\u00e7inde 3 say\u0131s\u0131. Bu de\u011ferlerin nas\u0131l bulunaca\u011f\u0131 da bilinmiyor. \u00d6rne\u011fin \u03c0 say\u0131s\u0131n\u0131 verece\u011fi iddia edilen pek \u00e7ok algoritma mevcut. Ama bunlar\u0131n herhangi bir ad\u0131m\u0131nda elde edilen say\u0131 noktadan sonra ka\u00e7 basamakl\u0131 olacakt\u0131r? S\u0131n\u0131rl\u0131 say\u0131da m\u0131, s\u0131n\u0131rs\u0131z m\u0131? Komputerle hesaplamaya kalk\u0131nca da ayn\u0131 sorunla kar\u015f\u0131la\u015fmamak m\u00fcmk\u00fcn de\u011fil; bir! \u0130kincisi de, sonsuz tekrar (\u2018iteration\u2019) i\u00e7eren bir algoritmay\u0131 sonuna dek g\u00f6t\u00fcrecek komp\u00fcter icat olmad\u0131 ki. Olsa da ka\u00e7 yazar? O say\u0131y\u0131 nereye yazarak kay\u0131t alt\u0131na alaca\u011f\u0131z da gerekti\u011fi zaman yeniden hesaplamaya gerek kalmaks\u0131z\u0131n kullanabilece\u011fiz?<br \/>\n\u0130\u015fbu ke\u00e7iboynuzunun nektar\u0131 \u015fudur: hemen bir \u00f6nceki \u201cA\u015fil ile Kaplumba\u011fa ve Zamanda Yolculuk B\u00f6l\u00fcm 2 hkk.\u201d ba\u015fl\u0131kl\u0131 yaz\u0131da (****) tan\u0131ml\u0131 Bilim de Matematik de yine oradaki anlam\u0131yla uyduruktur. Uydurmak yani hayal kurmak da insan\u0131n en geli\u015fkin yetene\u011fi de\u011fil midir?<br \/>\nBuyurun size Bilim ile Sanat\u2019\u0131n ortak \u00f6zelli\u011fi!<\/p>\n<p>(*) https:\/\/blog.metu.edu.tr\/caglart\/2025\/01\/01\/kirmizi-daire\/<br \/>\n(**) https:\/\/blog.metu.edu.tr\/caglart\/2024\/12\/05\/varolus\/<br \/>\n(***) Yakla\u015f\u0131k olarak da ne kadar yakla\u015f\u0131k? 1 de, 10 da, 100 de, \u2026 sonsuza yak\u0131n say\u0131lard\u0131r. \u00c7\u00fcnk\u00fc, en az\u0131ndan, \u00f6te yandaki eksili say\u0131lara k\u0131yasla.<br \/>\n(****) https:\/\/blog.metu.edu.tr\/caglart\/2026\/02\/11\/asil-ile-kaplumbaga-ve-zamanda-yolculuk-bolum-2-hkk\/<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Varsayal\u0131m ki, d\u0131\u015f d\u00fcnya var! Mesela bkz., \u201cK\u0131rm\u0131z\u0131 daire\u201d. (*) Ama bu varsay\u0131m\u0131 yapabilmek i\u00e7in, \u00f6nce kendi varl\u0131\u011f\u0131m\u0131z\u0131 kan\u0131tlamal\u0131y\u0131z. Mesela bkz., \u201cVarolu\u015f\u201d. (**) Heyhat! Kendi varl\u0131\u011f\u0131m\u0131z\u0131 kan\u0131tlama yolunda R. Descartes\u2019in o \u00fcnl\u00fc deyi\u015finden \u00f6te gidebilmi\u015f de\u011filiz (hen\u00fcz?). Ho\u015f, o deyi\u015f de hayli \u00e7eli\u015fiktir kendi i\u00e7inde! \u00d6nce var olmu\u015f olmal\u0131y\u0131m ki, d\u00fc\u015f\u00fcn\u00fcp d\u00fc\u015f\u00fcnmedi\u011fimi kavrayabileyim, d\u00fc\u015f\u00fcn\u00fc\u015f\u00fcn ne [&hellip;]<\/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-1471","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1471","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=1471"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1471\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=1471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=1471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=1471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}