\u2018Say\u0131 Ekseni\u2019 deyimini ilk kez derste i\u015fiten hemen her \u00f6\u011frenci gibi, bu sat\u0131rlar\u0131n yazan\u0131 fakir de edepsiz ve hatta geri zek\u00e2l\u0131ym\u0131\u015f gibi g\u00f6r\u00fcnmemek i\u00e7in parmak kald\u0131r\u0131p Matematik \u00f6\u011fretmenine sor_A_mam\u0131\u015ft\u0131r \u2019say\u0131lar\u0131n ni\u00e7in bir eksen\u2019, yani d\u00fcz \u00e7izgi \u00fcst\u00fcnde yer alabilece\u011fini.
Hani bir d\u00fcz \u00e7izgi \u00e7izilir de bir yerine dik bir kesme konur ve alt\u0131na s\u0131f\u0131r anlam\u0131nda 0 yaz\u0131l\u0131r. Sa\u011f taraf pozitif, sol taraf negatif say\u0131lar i\u00e7indir.
Parmak kald\u0131r\u0131l\u0131p sorulamam\u0131\u015f ikinci soru da pozitif (negatif) say\u0131lar\u0131n ni\u00e7in sa\u011f (sol) tarafa yaz\u0131ld\u0131\u011f\u0131 da ni\u00e7in tersine olmad\u0131\u011f\u0131na ili\u015fkindir.
Ger\u00e7ekten de, negatif say\u0131lar\u0131n sa\u011f tarafta pozitif say\u0131lar\u0131n ise, sol tarafta olmas\u0131 ters geliyor insana. De\u011fil mi?
Demek ki, Matematik birazc\u0131k bile olsa kar\u0131\u015f\u0131k psikoloji ile.
Belki, say\u0131lar\u0131 kondurmak i\u00e7in de titiz \u00f6\u011fretmenlerin iki uca koydu\u011fu ard\u0131\u015f\u0131k \u00fc\u00e7 nokta ile sonsuzluk \u00e7a\u011fr\u0131\u015f\u0131m\u0131 yapt\u0131\u011f\u0131 ama genellikle d\u00fcz bir \u00e7izgi par\u00e7as\u0131 kullan\u0131l\u0131yor olu\u015funun da alt\u0131nda m\u00fchim bir psikolojik \u00f6zellik yat\u0131yor olabilir mi? Olamaz m\u0131?
Peki ya parabol, hiperbol falan veya helezon, spiral filan kullan\u0131lamaz m\u0131 acaba ayn\u0131 ama\u00e7la? Ni\u00e7in olmas\u0131n? Ama, illa da billa da d\u00fcz \u00e7izgi kullan\u0131l\u0131r. Ni\u00e7in acaba?
Demek ki, (her de\u011filse bile) \u00e7o\u011fu insan\u0131n akl\u0131na \u2018say\u0131lar\u2019 denince d\u00fcz bir \u00e7izgi geliyor (otomatikman).
\u00c7izgi \u00fczerindeki iki nokta aras\u0131nda ka\u00e7 tane nokta vard\u0131r? Bilmiyoruz. Say\u0131m yapabilme olana\u011f\u0131m\u0131z yok. Ba\u015fka yoldan tespit etme, saptama olana\u011f\u0131m\u0131z da yok. Ama, olsa olsa y\u00f6ntemiyle, noktan\u0131n par\u00e7as\u0131, eni, boyu, derinli\u011fi, kaplam\u0131 vs. olmad\u0131\u011f\u0131 hasebiyle (\u00d6klid\u2019in \u201cElementler\u201d adl\u0131 kitab\u0131na g\u00f6re), sonsuz nokta oldu\u011funu s\u00f6yl\u00fcyoruz. \u0130nanmayan m\u0131 var? \u201c\u2014Tersini kan\u0131tla madem.\u201d diyerek s\u0131yr\u0131l\u0131veriyoruz i\u015fin i\u00e7inden.
Peki ya iki Ger\u00e7ek Say\u0131\u2019n\u0131n (\u2018Real Number\u2019) aras\u0131nda ka\u00e7 tane Ger\u00e7ek Say\u0131 vard\u0131r? Bunu da bilmiyoruz. Say\u0131m yapabilme olana\u011f\u0131m\u0131z yok. Ba\u015fka yoldan tespit etme, saptama olana\u011f\u0131m\u0131z da yok. Ama, olsa olsa y\u00f6ntemiyle, hi\u00e7bir Ger\u00e7ek Say\u0131\u2019n\u0131n hi\u00e7bir Ger\u00e7ek Say\u0131\u2019ya b\u00f6l\u00fcm\u00fcn\u00fcn s\u0131f\u0131r olmayaca\u011f\u0131 bilgisiyle, her iki Ger\u00e7ek Say\u0131\u2019n\u0131n aras\u0131nda sonsuz Ger\u00e7ek Say\u0131 oldu\u011funu s\u00f6yl\u00fcyoruz. \u0130nanmayan m\u0131 var? \u201c\u2014Tersini kan\u0131tla madem.\u201d diyerek s\u0131yr\u0131l\u0131veriyoruz i\u015fin i\u00e7inden.
Dahas\u0131, \u201cHer d\u00fcz \u00e7izgiyi s\u00fcnd\u00fcrsek veya b\u00fczsek bile her hangi iki nokta aras\u0131ndaki noktalar\u0131n say\u0131s\u0131n\u0131 demeyelim de s\u0131kl\u0131\u011f\u0131n\u0131 de\u011fi\u015ftiremiyoruz.\u201d diyen de \u00e7ok. Ama, \u00f6rne\u011fin 1 santimetre uzunlu\u011fundaki d\u00fcz \u00e7izgi par\u00e7as\u0131nda m\u0131 yoksa 2 santimetre uzunlu\u011fundaki d\u00fcz \u00e7izgi par\u00e7as\u0131nda m\u0131 daha \u00e7ok nokta oldu\u011funu da bilmiyoruz. \u00d6\u011fretmenlere sorman\u0131n da \u00e2lemi yok do\u011frusu. Ama, daha \u00f6nceki baz\u0131 sat\u0131rlar\u0131m\u0131zda irdeledi\u011fimiz gibi, bu \u00e7izgi par\u00e7alar\u0131n\u0131n u\u00e7lar\u0131n\u0131 birle\u015ftiren d\u00fcz \u00e7izgilerin kesi\u015fti\u011fi noktadan bu iki \u00e7izgiyi de kesecek \u00e7izgilerin, \u00f6nceki iki d\u00fcz \u00e7izgi par\u00e7alar\u0131n\u0131n her ikisinin de her noktas\u0131ndan ge\u00e7mesi gerekti\u011fini d\u00fc\u015f\u00fcn\u00fcyoruz. (*) Daha k\u0131sa bir \u00f6rnek \u015fudur: E\u015f merkezli iki (diyelim ki, 1 santimetre ve 2 santimetre \u00e7apl\u0131) \u00e7emberin hangisi daha \u00e7ok (s\u0131k) nokta bar\u0131nd\u0131r\u0131r acaba?
Bu gibi konular Nick Huggett\u2019\u0131n \u2018Stanford Encyclopedia of Philosophy\u2019 platformundaki bir makalesinin 6 Mart 2024 tarihi \u00f6ncesindeki versiyonunda da tart\u0131\u015f\u0131lmaktayd\u0131. (**) Bu makalenin sonundaki adrese yaz\u0131p ilk versiyonu talep ediniz ve b\u00f6ylelikle iki versiyon aras\u0131ndaki fark\u0131 inceleme f\u0131rsat\u0131 bulabilirsiniz. Bu iki metni de inceleme f\u0131rsat\u0131 bulan \u015fansl\u0131lardan biri, bu sat\u0131rlar\u0131n fakir yazan\u0131d\u0131r. (***)
![\"\"](\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/12\/NH.png\")
<\/a><\/p>\nYine \u00f6nceki yaz\u0131lar\u0131m\u0131zda irdelemi\u015f idik; 1, 3, 5, \u2026 gibi Tek Do\u011fal Say\u0131lar, a\u00e7\u0131kt\u0131r ki, Tek say\u0131lmas\u0131 gereken \u221e\u2019a b\u00fcy\u00fcrken 2, 4, 6 gibi \u00c7ift Do\u011fal Say\u0131lar da \u00c7ift say\u0131lmas\u0131 gereken \u221e\u2019a b\u00fcy\u00fcr. Bu durumda, 1 santimetre uzunlu\u011fundaki do\u011fru par\u00e7as\u0131nda bar\u0131nan noktalar ile 2 santimetre uzunlu\u011fundaki do\u011fru par\u00e7as\u0131nda bar\u0131nan noktalar ayn\u0131 Tek say\u0131lmas\u0131 gereken \u221e\u2019a m\u0131 b\u00fcy\u00fcr yoksa \u00c7ift say\u0131lmas\u0131 gereken \u221e\u2019a m\u0131? Ayn\u0131 soru \u00e7ap\u0131 1 santimetre ve 2 santimetre olan e\u015f merkezli \u00e7emberlerin bar\u0131nd\u0131rd\u0131\u011f\u0131 noktalar i\u00e7in de sorulabilir. Keza, bir kare i\u00e7indeki noktalar\u0131n kenar ay\u0131rtlar\u0131 \u00fczerindekiler ile k\u0131yaslanmas\u0131 da t\u00fcrl\u00fc \u00e7e\u015fitli tart\u0131\u015fmaya a\u00e7\u0131kt\u0131r. Belki de, bu gibi sorulara kafa patlatmak yerine pirin\u00e7 ta\u015f\u0131 ay\u0131klamak veya p\u00f6stekinin k\u0131llar\u0131n\u0131 saymak yahut da samanl\u0131kta i\u011fne aramak ye\u011flenebilir.<\/p>\n
Yine de konuyu kapatmazdan evvel, N. Hugget\u2019\u0131n s\u0131k\u00e7a and\u0131\u011f\u0131 Wesley C. Salmon\u2019un \u2018Space, Time, and Motion\u2019 adl\u0131 kitab\u0131ndan s\u00f6z etmeye de\u011fer. (****) Konumuzla ilgili olarak \u015fu PDF belge de incelenebilir: STM<\/a> (<–T\u0131klay\u0131n\u0131z)<\/p>\n Bahsetmek istedi\u011fim bir ba\u015fka an\u0131m da, \u015fimdikine k\u0131yasla (!) daha gen\u00e7 oldu\u011fum g\u00fcnlerden. O zamanki e\u011fitim sisteminde orta 3\u2019den lise 1\u2019e ge\u00e7ti\u011fim yaz birden boy atm\u0131\u015ft\u0131m. Bu nedenle de giysilerimin hepsinin yenilenmesi gerekmi\u015fti. Gelgelelim, Lise 1 k\u00f6t\u00fc ba\u015flad\u0131 idi. Emin Oktay Tarihi ile ba\u015f\u0131m zaten oldum olas\u0131 dertte idi. (#) Bu dertlere bir de Matematik ama daha do\u011frusu [m\u00fcfredattaki Cebir, Trigonometri, Kartezyen Geometri (Sentetik Geometri) ile pek sorunum yoktu ama (Uzay Geometrisi gibi bir alt dal\u0131 da olan) ] \u0130spatl\u0131 Geometri (Analitik Geometri) dersi eklenmi\u015fti. Dursun Ek\u015fi (Sayg\u0131, sevgi ve bor\u00e7lulukla anar\u0131m.) \u00f6\u011fretmen s\u0131n\u0131fa girerken s\u0131n\u0131f defterini imzalayaca\u011f\u0131 kalemi ceketinin i\u00e7 cebinden \u00e7\u0131kart\u0131rken, sa\u011fa sola bakmaz d\u00fcmd\u00fcz ad\u0131mlarla k\u00fcrs\u00fcye ilerlerken \u201cTiyor\u011fem bir!\u201d derdi. Bir_iki dakika sonra da devam\u0131n\u0131 yazd\u0131r\u0131rd\u0131. \u0130\u015fte o ba\u015ftaki haftalarda bu fakir aval aval bak\u0131nmaktan ba\u015fka hemen hemen hi\u00e7bir \u015fey yapamad\u0131 \u0130spatl\u0131 Geometri saatleri boyunca. Dursun \u00f6\u011fretmen sadece, \u00f6n s\u0131ralarda oturan iki senelik Emine arkada\u015f\u0131 kald\u0131r\u0131rd\u0131 bazen tahtaya, ispatlar\u0131 yaps\u0131n diye. \u0130\u015fte bu nedenle, ar\u0131m\u0131 yenip sormu\u015ftum Emine arkada\u015fa nas\u0131l oluyordu da \u0130spatl\u0131 Geometri ile aras\u0131 bu denli iyi olabiliyordu. \u201c\u2014Hii\u00e7!\u201d dedi idi, hemen sonras\u0131nda da ekledi idi \u201cEzbeeer!\u201d<\/p>\n El insaf! Matematik ezberlenir mi hi\u00e7? Zaten \u00e7ok denedim ama ezberleyemedi idim kitaptan bir tek teorem ispat\u0131n\u0131 bile. \u0130lk matematik s\u0131nav notum da 10 \u00fcst\u00fcnden 6 geldi, hayli zay\u0131f bir not bekliyordum h\u00e2lbuki. \u0130htimal, kentten ve \u00f6\u011frencisi oldu\u011fum okuldan Fen Lisesi\u2019ni kazanmay\u0131 ba\u015farm\u0131\u015f ikinci delikanl\u0131 (ilk kazanan, ortaokulumuzun bir y\u0131l \u00f6nceki mezunlar\u0131ndan O\u011fuz Durumeri\u00e7 (##) Fen Lisesi\u2019ne gitmi\u015f idi.) olmakl\u0131\u011f\u0131md\u0131r bunun sebebi. Dahas\u0131, meskenimizin bah\u00e7esindeki odunlukta kendi kurdu\u011fum bir laboratuvar\u0131m vard\u0131, Sat\u00fcrn IV, V roketlerinin g\u00f6ky\u00fcz\u00fcnde dola\u015ft\u0131\u011f\u0131 g\u00fcnlerde idol\u00fcm Wernher von Braun (###) \u00a0idi ve bah\u00e7ede kendi \u00e7ap\u0131mda roket yap\u0131p f\u0131rlat\u0131rd\u0131m. Daha da garibi, tavuk yumurtas\u0131 ile ozmoz deneyleri ve okulda s\u0131n\u0131f s\u0131n\u0131f dola\u015farak ozmoz g\u00f6sterileri yapard\u0131m. Ama en garibi, kar\u015f\u0131 kom\u015fumuzun o\u011flu Ekrem ile cilli (cam bilye) ortakl\u0131\u011f\u0131m\u0131zdan kazan\u0131p b\u00f6l\u00fc\u015ft\u00fc\u011f\u00fcm\u00fcz para ile, kette hen\u00fcz in\u015fas\u0131 s\u00fcrmekte olan K\u00fclt\u00fcr Park\u2019taki havuz ba\u015flang\u0131c\u0131ndan mahalleli \u00e7ocuklara kurba\u011fa toplat\u0131rd\u0131m, \u00fccreti mukabili. Niye mi kurba\u011fa toplat\u0131rd\u0131m? Hii\u00e7! Alessandro Giuseppe Antonio Anastasio Volta\u2019n\u0131n kurba\u011fa deneylerini tekrarlayabilmek i\u00e7in. (####) \u00c7ocukluk akl\u0131 i\u015fte; bir ucu sabit bir ucu da ince telden kald\u0131ra\u00e7lara ba\u011fl\u0131 kurba\u011fa bacaklar\u0131na elektrik verince hareket eden robotlar yapm\u0131\u015f idim. O kurba\u011fa par\u00e7alar\u0131n\u0131, evdeki buzdolab\u0131n\u0131n (O zamanlardaki ad \u015fimdiki gibi \u2018so\u011futucu\u2019 de\u011fildi.) ek buz par\u00e7alar\u0131yla da \u00f6rt\u00fclm\u00fc\u015f bir b\u00f6l\u00fcmde saklard\u0131m. Belki de b\u00f6ylelikle ama fark\u0131nda olmaks\u0131z\u0131n memleketin ilk organ bankas\u0131n\u0131 i\u015fte o delikanl\u0131 kurmu\u015ftu! Ne yani, \u015fimdi de daha d\u00fc\u015f\u00fck beklemesine kar\u015f\u0131n matematikten 6 alm\u0131\u015f, \u00e7ok mu?<\/p>\n \u0130\u015fte o s\u0131nav sonras\u0131 g\u00fcnlerin bir gecesinde, masa ba\u015f\u0131nda kafa patlatmaktayd\u0131m geometri belas\u0131 y\u00fcz\u00fcnden. Biss\u00fcr\u00fc \u015fekil \u015femal, bisss\u00fcr\u00fc de teorem, teorem, teorem! \u00dcstelik, hi\u00e7 unutmam, misafir odam\u0131z t\u0131kl\u0131m doluydu. \u00dc\u00e7l\u00fc be\u015fli konu\u015fmalar\u0131n, olur olmaz kahkahalar\u0131n ve teoremlerin aras\u0131nda cebelle\u015firken, hay\u0131r beyaz \u0131\u015f\u0131k g\u00f6r\u00fcnmedi ama kafam\u0131n i\u00e7i p\u0131r\u0131l p\u0131r\u0131l ayd\u0131nlan\u0131verdi bir anda. Hani karikat\u00fcrlerdeki gibi, kafam\u0131n \u00fcst\u00fcnde bir ampul par\u0131lday\u0131verdi sanki. Sonraki birka\u00e7 saniyeyi an\u0131msayam\u0131yorum; masadan nas\u0131l kalkt\u0131m da sandalyemi devirdim? Ne oldu, ni\u00e7in kap\u0131da davul \u00e7almaya ba\u015flad\u0131m? Misafir odas\u0131ndan \u00fcst\u00fcme u\u011frayan kalabal\u0131\u011fa ne dedim, durumu nas\u0131l izah ettim? Ettim mi, edebildim mi?<\/p>\n Ne gam! Umursamad\u0131m bile! \u0130spatl\u0131 Geometri\u2019yi \u00e7\u00f6zm\u00fc\u015ft\u00fcm. Ad\u0131 \u00fcst\u00fcnde ispatlayacaks\u0131n! Nas\u0131l m\u0131? Hipotezleri, aksiyomlar\u0131 do\u011fru olarak kabul edeceksin. Sonra, bunlardan i\u015fine yarayanlar\u0131, i\u015fine yarayacak s\u0131rada arka arkaya dayay\u0131p, t\u0131pk\u0131 basamaklama gibi, t\u0131pk\u0131 iki \u015fi\u015f bir yumak \u00f6rg\u00fc ipiyle \u00f6rer gibi ilerleyeceksin.<\/p>\n O gece nas\u0131l uyudu\u011fumu, uyuyup uyuyamad\u0131\u011f\u0131m\u0131 da hat\u0131rlam\u0131yorum \u015fimdi. Ama ertesi g\u00fcn, Dursun \u00f6\u011fretmen s\u0131n\u0131fa girer girmez parmak kald\u0131rd\u0131\u011f\u0131m, birka\u00e7 dakika \u00f6nce olmu\u015f gibi g\u00f6z\u00fcm \u00f6n\u00fcnde. \u201c\u2014Ne var \u00c7a\u011flar!\u201d<\/p>\n \u201c\u2014S\u00f6zl\u00fcye kalkmak istiyorum \u00f6\u011fretmenim.\u201d<\/p>\n Tahta ba\u015f\u0131na eri\u015fip tebe\u015firi elime alm\u0131\u015ft\u0131m ki, \u201c\u2014Yaz bakal\u0131m; bir \u00fc\u00e7genin\u2026\u201d Bu c\u00fcmleyi ben tamamlam\u0131\u015ft\u0131m bir taraftan da yazarken; \u201c\u2026 i\u00e7 a\u00e7\u0131lar\u0131n\u0131n toplam\u0131 y\u00fcz seksen derecedir.\u201d Ama yazmay\u0131 tamamlayamad\u0131m; \u201c\u2014Otur! On!\u201d O ilk d\u00f6nem de karneme matematik on geldi, sonrakilerde de.<\/p>\n Ama as\u0131l \u00e7\u00f6z\u00fcm; ertesi sene, Teo Gr\u00fcnberg\u2019in \u201cModern Mant\u0131k\u201d kitab\u0131ndan izledi\u011fimiz Mant\u0131k-Felsefe dersinde geldi. \u201cp ise q\u201d (if p then q) veya (p\u2192q) basit g\u00f6steriminde oldu\u011fu gibi \u2018p\u2019 do\u011fru ise \u2018q\u2019 da do\u011frudur. Aksiyomlar\u0131n ve \u00f6nceki ispatlanm\u0131\u015f teoremlerim \u2018p\u2019 olmak \u00fczere yeni \u2018q\u2019lar bulacaks\u0131n. Ama bunlar da sonra eskiyip, eski \u2018p\u2019ler olup yeni \u2018q\u2019lar bulmakta kullan\u0131lacak!<\/p>\n Emine\u2019ye dedim ki, bir teneff\u00fcs s\u0131ras\u0131nda, \u201c\u2014Geometri neymi\u015f bak s\u00f6yleyeyim: p ise q! Hepsi bu!\u201d Emine de kat\u0131la kat\u0131la g\u00fclm\u00fc\u015ft\u00fc bana.<\/p>\n K\u0131ssadan hisse: Bir tak\u0131m say\u0131lar yani simgeler icat edeceksin. Aralar\u0131nda da bir tak\u0131m kural oldu\u011funu varsayacaks\u0131n. O simgelerin aras\u0131ndaki, bu kurallara uygun ili\u015fkilerine Cebir diyeceksin. Say\u0131 yerine \u015fekiller icat edip, aralar\u0131nda bir tak\u0131m kural bulundu\u011funu var sayacaks\u0131n. \u00d6rne\u011fin, \u2018Y\u00f6nde\u015f dar a\u00e7\u0131lar e\u015fittir.\u2019 gibi asla kan\u0131tlanamaz veya daha basitinden \u2018Kesi\u015fmeyen do\u011frular paraleldir.\u2019 gibi daha basit g\u00f6r\u00fcnen ama bir evvelki gibi asla kan\u0131tlanamaz olan (\u0130ki do\u011fruyu nereye dek izleyeceksin de kesi\u015fip kesi\u015fmediklerini saptayacaks\u0131n?) varsay\u0131mlar aksiyom, postulat veya premis (\u2018premisses\u2019) olacak. B\u00fct\u00fcn bunlar\u0131 \u00fcst \u00fcste koyarak da matemati\u011fi in\u015fa edeceksin.<\/p>\n \u00d6zet: Matematik t\u00fcm\u00fcyle mant\u0131k (#####) \u00fcr\u00fcn\u00fcd\u00fcr!<\/p>\n Yak\u0131n ileriki yaz\u0131lar i\u00e7in bir soru: Matematik ger\u00e7ek evrenle nas\u0131l (\/ni\u00e7in) \u00f6rt\u00fc\u015f\u00fcr?<\/p>\n Hadi ileriye b\u0131rakmadan burac\u0131kta yan\u0131tlay\u0131verelim; (ilk yaz\u0131m\u0131zda konu edindi\u011fimiz ve sonraki yaz\u0131larm\u0131z\u0131n temeli olan, Einstein\u2019\u0131n \u2018comprehension\u2019 ikileminde sundu\u011fu gibi) bizim kavray\u0131\u015f\u0131m\u0131zdan ayr\u0131k bir evren yok ki! Evren hakk\u0131nda, ger\u00e7eklik hakk\u0131nda bildi\u011fimiz her \u015fey, bizim evren sand\u0131\u011f\u0131m\u0131zdan, bizim ger\u00e7eklik sand\u0131\u011f\u0131m\u0131zdan ibaret. De\u011fil mi?<\/p>\n Evrenin, ger\u00e7ekli\u011fin bizim anlad\u0131\u011f\u0131m\u0131zdan farkl\u0131 oldu\u011funu nas\u0131l tespit edece\u011fiz, saptayaca\u011f\u0131z, (hadi \u00e7ekinmeden yazal\u0131m) anlayaca\u011f\u0131z?<\/p>\n (*) https:\/\/tr.wikipedia.org\/wiki\/Sonsuz#\/media\/Dosya:Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif<\/a><\/p>\n (**) https:\/\/plato.stanford.edu\/entries\/paradox-zeno\/<\/a><\/p>\n (***) Avukat\u0131ma soray\u0131m; \u2018O yaz\u0131\u015fmalar\u0131 a\u00e7\u0131klayabilir miyim?\u2019 diye. Yan\u0131t olumlu olursa, s\u00f6z o yaz\u0131\u015fmalar\u0131 a\u00e7\u0131klar\u0131m. Hatta, \u00e7\u0131k\u0131nlar\u0131m\u0131 bir kurcalayay\u0131m bakay\u0131m; belki N. Huggett makalesinin ilk versiyonu bilgisayarlar\u0131mdan veya ta\u015f\u0131nabilir belleklerden birinin bir yerlerinde mevcuttur.<\/p>\n (****) https:\/\/www.google.com\/search?q=Salmon%2C+space%2C+time%2C+and+motion+pdf&sca_esv=5201d3bfa78652ae&sxsrf=ADLYWILnq46n4fFK_WCOalFmjVYAo3BAsA%3A1733518900602&ei=NGZTZ4qvJOSMxc8Pt_by2Qw&ved=0ahUKEwiKmaCShZSKAxVkRvEDHTe7PMsQ4dUDCA8&uact=5&oq=Salmon%2C+space%2C+time%2C+and+motion+pdf&gs_lp=Egxnd3Mtd2l6LXNlcnAiI1NhbG1vbiwgc3BhY2UsIHRpbWUsIGFuZCBtb3Rpb24gcGRmMgUQIRigAUiJpgFQwQtYupEBcAF4AZABAJgBgQGgAeMDqgEDMC40uAEDyAEA-AEBmAIDoAL_AcICChAAGLADGNYEGEfCAgcQIxiwAhgnwgIIEAAYExgNGB7CAgoQABgTGAgYDRgemAMAiAYBkAYIkgcDMS4yoAfRCg&sclient=gws-wiz-serp<\/a><\/p>\n (#) https:\/\/www.google.com\/search?q=emin+oktay+ger%C3%A7ek+ad%C4%B1<\/a><\/p>\n Ayr\u0131ca; https:\/\/www.google.com\/search?q=emin+oktay+tarih+kitab%C4%B1&sca_esv=5201d3bfa78652ae&sxsrf=ADLYWIKdS-cxIH0nf-7yGTn6qX0e1FR5ww%3A1733520789097&ei=lW1TZ4TBBauAxc8Pj-OtaQ&oq=emin+oktay+&gs_lp=Egxnd3Mtd2l6LXNlcnAiC2VtaW4gb2t0YXkgKgIIAjIKECMYgAQYJxiKBTIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABEjROlC-CViaIXABeAGQAQCYAa8BoAGbCaoBAzEuObgBAcgBAPgBAZgCCqACwwnCAggQABiABBiiBJgDAIgGAZIHAzEuOaAH2i0&sclient=gws-wiz-serp<\/a><\/p>\n<\/a>
\u00a0Wesley C. Salmon\u2019un kitab\u0131ndan baz\u0131 b\u00f6l\u00fcmleri hemen altta incelemek m\u00fcmk\u00fcnd\u00fcr.<\/a><\/p>\n<\/a><\/p>\n<\/a><\/p>\n<\/a><\/p>\n
![https:\/\/tr.wikipedia.org\/wiki\/Sonsuz#\/media\/Dosya:Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif<\/a><\/p>\n(**) https:\/\/plato.stanford.edu\/entries\/paradox-zeno\/<\/a><\/p>\n(***) Avukat\u0131ma soray\u0131m; \u2018O yaz\u0131\u015fmalar\u0131 a\u00e7\u0131klayabilir miyim?\u2019 diye. Yan\u0131t olumlu olursa, s\u00f6z o yaz\u0131\u015fmalar\u0131 a\u00e7\u0131klar\u0131m. Hatta, \u00e7\u0131k\u0131nlar\u0131m\u0131 bir kurcalayay\u0131m bakay\u0131m; belki N. Huggett makalesinin ilk versiyonu bilgisayarlar\u0131mdan veya ta\u015f\u0131nabilir belleklerden birinin bir yerlerinde mevcuttur.<\/p>\n(****) https:\/\/www.google.com\/search?q=Salmon%2C+space%2C+time%2C+and+motion+pdf&sca_esv=5201d3bfa78652ae&sxsrf=ADLYWILnq46n4fFK_WCOalFmjVYAo3BAsA%3A1733518900602&ei=NGZTZ4qvJOSMxc8Pt_by2Qw&ved=0ahUKEwiKmaCShZSKAxVkRvEDHTe7PMsQ4dUDCA8&uact=5&oq=Salmon%2C+space%2C+time%2C+and+motion+pdf&gs_lp=Egxnd3Mtd2l6LXNlcnAiI1NhbG1vbiwgc3BhY2UsIHRpbWUsIGFuZCBtb3Rpb24gcGRmMgUQIRigAUiJpgFQwQtYupEBcAF4AZABAJgBgQGgAeMDqgEDMC40uAEDyAEA-AEBmAIDoAL_AcICChAAGLADGNYEGEfCAgcQIxiwAhgnwgIIEAAYExgNGB7CAgoQABgTGAgYDRgemAMAiAYBkAYIkgcDMS4yoAfRCg&sclient=gws-wiz-serp<\/a><\/p>\n(#) https:\/\/www.google.com\/search?q=emin+oktay+ger%C3%A7ek+ad%C4%B1<\/a><\/p>\nAyr\u0131ca; https:\/\/www.google.com\/search?q=emin+oktay+tarih+kitab%C4%B1&sca_esv=5201d3bfa78652ae&sxsrf=ADLYWIKdS-cxIH0nf-7yGTn6qX0e1FR5ww%3A1733520789097&ei=lW1TZ4TBBauAxc8Pj-OtaQ&oq=emin+oktay+&gs_lp=Egxnd3Mtd2l6LXNlcnAiC2VtaW4gb2t0YXkgKgIIAjIKECMYgAQYJxiKBTIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABEjROlC-CViaIXABeAGQAQCYAa8BoAGbCaoBAzEuObgBAcgBAPgBAZgCCqACwwnCAggQABiABBiiBJgDAIgGAZIHAzEuOaAH2i0&sclient=gws-wiz-serp<\/a><\/p>\n(##) https:\/\/math.uiowa.edu\/people\/oguz-durumeric<\/a><\/p>\nO\u011fuz da, ben de Dilek Sinemas\u0131\u2019n\u0131n Cumartesi 14:20 seans\u0131 m\u00fcdavimlerindendik. Dahas\u0131, \u0130spanyol gitar kursuna giderdik. O y\u0131l Milliyet Gazetesi\u2019nin m\u00fczik eki \u2018Hey\u2019 dergisi, liseleraras\u0131 m\u00fczik yar\u0131\u015fmas\u0131 d\u00fczenlemi\u015f idi. Ama M\u00fczik \u00f6\u011fretmenimiz (T\u00fcrkiye g\u00fczelimiz Aydan \u015eener\u2019in babas\u0131) Nezir beyefendinin \u00e7ok arzulamas\u0131na kar\u015f\u0131n ailelerimiz izin vermedi\u011fi i\u00e7in (Nil Karaibrahimgil\u2019in babas\u0131n\u0131n da fiilen destekledi\u011fi) orkestram\u0131z gayet k\u0131sa \u00f6m\u00fcrl\u00fc oldu.<\/p>\n(###) https:\/\/www.google.com\/search?q=Wernher+von+Braun<\/a><\/p>\n(####) O g\u00fcnleri ve an\u0131lan olaylar\u0131 anlatt\u0131\u011f\u0131m bir \u2018Gen\u00e7lik Filmi Senaryosu\u2019 ile TRT 25. KURULU\u015e YILI yar\u0131\u015fmalar\u0131nda \u00f6d\u00fcl kazanm\u0131\u015ft\u0131m. \u00d6nceki ba\u015fbakanlar\u0131m\u0131zdan Mesut Y\u0131lmaz\u2019\u0131n Bas\u0131n M\u00fc\u015faviri Sevgi Ulasay han\u0131mefendi \u015fahidimdir.<\/p>\n(#####) Ak\u0131l y\u00fcr\u00fctmek, uslamlamak, muhakeme etmek, \u2018comprehension\u2019 anlam\u0131nda. \u2018Comprehension\u2019 s\u00f6zc\u00fc\u011f\u00fcn\u00fcn hesapla anlam\u0131ndaki \u2018compute\u2019 s\u00f6zc\u00fc\u011f\u00fc ile ortak k\u00f6ke sahip oldu\u011fu g\u00f6zden ka\u00e7\u0131r\u0131lmamal\u0131d\u0131r. \u2018Computation\u2019 s\u00f6zc\u00fc\u011f\u00fcn\u00fcn \u00f6l\u00e7\u00fcm, \u00f6l\u00e7\u00fcmleyi\u015f anlam\u0131na da geldi\u011fini g\u00f6rmek i\u00e7in \u015fu ba\u011flant\u0131ya bak\u0131labilir: https:\/\/tureng.com\/en\/turkish-english\/computation<\/p>\nBenzer ortakl\u0131klar Arap\u00e7a ve g\u00fczel T\u00fcrk\u00e7e\u2019mizde de var elbet. Ama bu husus, ba\u015fka i\u00e7erikli yaz\u0131lar\u0131n konusu olmaya daha \u00e7ok yak\u0131\u015fsa gerektir.<\/p>\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"Fizik \u201311 \/ d\u2013 \u0130\u00e7erik: Ne yapt\u0131\u011f\u0131m\u0131z\u0131n fark\u0131nda olmak ya da ol_A_mamak! \u201cKendimden bahsetmeyi pek sevmem.\u201d diyerek bahsetmi\u015f olay\u0131m kendimden. Hatta bir_iki an\u0131m\u0131 da anlatay\u0131m altta. Hepsi de Matematik ve Geometri yani say\u0131 ve \u015fekil ile ba\u011flant\u0131l\u0131.\u2018Say\u0131 Ekseni\u2019 deyimini ilk kez derste i\u015fiten hemen her \u00f6\u011frenci gibi, bu sat\u0131rlar\u0131n yazan\u0131 fakir de edepsiz ve hatta […]<\/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-389","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/389","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=389"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/389\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"https:\/\/tr.wikipedia.org\/wiki\/Sonsuz#\/media\/Dosya:Infinity_paradoxon_-_one-to-one_correspondence_between_infinite_set_and_proper_subset.gif\"){kind=link}