{"id":34798,"date":"2019-06-23T03:33:28","date_gmt":"2019-06-23T00:33:28","guid":{"rendered":"https:\/\/bilimvegelecek.com.tr\/?p=34798"},"modified":"2019-06-26T14:54:44","modified_gmt":"2019-06-26T11:54:44","slug":"bilimin-onculeri-euclides-oklid","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2019\/06\/23\/bilimin-onculeri-euclides-oklid","title":{"rendered":"Bilimin \u00d6nc\u00fcleri: Euclides (\u00d6klid)"},"content":{"rendered":"

R\u00f6nesans sonras\u0131 Avrupa\u2019da, Kopernik\u2019le ba\u015flayan, Kepler, Galileo ve Newton\u2019la 17. y\u00fczy\u0131lda doru\u011funa ula\u015fan bilim\u00adsel devrim, k\u00f6kleri Helenistik D\u00f6nem\u2019e uzanan bir olayd\u0131r. O d\u00f6nemin se\u00e7kin bilginlerinden Aristarkus, G\u00fcne\u015f-merkezli ast\u00adronomi d\u00fc\u015f\u00fcncesinde Kopernik\u2019i \u00f6ncelemi\u015fti; Ar\u015fimet yakla\u015f\u0131k i\u00adki biny\u0131l sonra gelen Galileo\u2019ya esin kayna\u011f\u0131 olmu\u015ftu; \u00d6klid \u00e7a\u011flar boyu yaln\u0131z matematik d\u00fcnyas\u0131n\u0131n de\u011fil, matematikle yak\u0131ndan ilgilenen hemen herkesin g\u00f6z\u00fcnde \u00f6zenilen, yetkin bir \u00f6rnekti. \u00d6klid, M\u00d6 300 s\u0131ralar\u0131nda yazd\u0131\u011f\u0131 13 ciltlik yap\u0131t\u0131yla \u00fcnl\u00fcd\u00fcr. Bu yap\u0131t, geometriyi (dolay\u0131s\u0131yla matemati\u011fi) ispat ba\u011flam\u0131nda aksiyomatik bir dizge olarak i\u015fleyen, ilk kapsaml\u0131 \u00e7al\u0131\u015fmad\u0131r. 19. y\u00fczy\u0131l sonlar\u0131na gelinceye kadar alan\u0131nda tek ders kitab\u0131 olarak akademik \u00e7evrelerde okunan, okutulan Elementler\u2019in, kimi yeter\u00adsizliklerine kar\u015f\u0131n, de\u011ferini bug\u00fcn de s\u00fcrd\u00fcrd\u00fc\u011f\u00fc s\u00f6ylenebilir.<\/p>\n

Egeli matematik\u00e7i \u00d6klid\u2019in ki\u015fisel ya\u015fam\u0131, aile \u00e7evresi, ma\u00adtematik d\u0131\u015f\u0131 u\u011fra\u015f veya meraklar\u0131na ili\u015fkin hemen hi\u00e7bir \u015fey bilinmemektedir. Bilinen tek \u015fey; \u0130skenderiye Kraliyet Enstit\u00fc\u00ads\u00fc\u2019nde d\u00f6nemin en sayg\u0131n \u00f6\u011fretmeni; alan\u0131nda y\u00fczy\u0131llar boyu e\u015fsiz kalan bir ders kitab\u0131n\u0131n yazar\u0131 olmas\u0131d\u0131r. E\u011fitimini Atina\u2019da Platon\u2019un (M\u00d6 428\/427 – 348\/347) \u00fcnl\u00fc akademisinde tamam\u00adlad\u0131\u011f\u0131 san\u0131lmaktad\u0131r. O akademi ki giri\u015f kap\u0131s\u0131nda, \u201cGeometriyi bilmeyen hi\u00e7 kimse bu kap\u0131dan i\u00e7eri al\u0131nmaz!\u201d levhas\u0131 as\u0131l\u0131yd\u0131.<\/p>\n

\u00d6klid\u2019in bilimsel ki\u015fili\u011fi, unutulmayan iki s\u00f6z\u00fcnde yans\u0131mak\u00adtad\u0131r: D\u00f6nemin kral\u0131 I. Ptolemy, okumada g\u00fc\u00e7l\u00fck \u00e7ekti\u011fi Ele\u00admentler\u2019in yazar\u0131na, \u201cGeometriyi kestirmeden \u00f6\u011frenmenin yolu yok mu?\u201d diye sordu\u011funda, \u00d6klid \u201c\u00d6z\u00fcr dilerim, ama geomet\u00adriye giden bir kral yolu yoktur\u201d der. Bir g\u00fcn dersini bitirdi\u011finde \u00f6\u011frencilerinden biri yakla\u015f\u0131r, \u201cHocam, verdi\u011finiz ispatlar \u00e7ok g\u00fczel; ama pratikte bunlar neye yarar?\u201d diye sordu\u011funda, \u00d6klid kap\u0131da bekleyen k\u00f6lesini \u00e7a\u011f\u0131r\u0131r, \u201cBu delikanl\u0131ya 5-10 kuru\u015f ver, vaktinin bo\u015fa gitmedi\u011fini g\u00f6rs\u00fcn!\u201d demekle yetinir.<\/p>\n

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Egeli matematik\u00e7i \u00d6klid\u2019in ki\u015fisel ya\u015fam\u0131, aile \u00e7evresi, ma\u00actematik d\u0131\u015f\u0131 u\u011fra\u015f veya meraklar\u0131na ili\u015fkin hemen hi\u00e7bir \u015fey bilinmemektedir. Bilinen tek \u015fey; \u0130skenderiye Kraliyet Enstit\u00fc\u00acs\u00fc\u2019nde d\u00f6nemin en sayg\u0131n \u00f6\u011fretmeni; alan\u0131nda y\u00fczy\u0131llar boyu e\u015fsiz kalan bir ders kitab\u0131n\u0131n yazar\u0131 olmas\u0131d\u0131r.<\/figcaption><\/figure>\n

\u00d6klid hakl\u0131 olarak \u201cgeometrinin babas\u0131\u201d diye bilinir; ama ge\u00adometri onunla ba\u015flam\u0131\u015f de\u011fildir. Tarih\u00e7i Herodotus (M\u00d6 500) geometrinin ba\u015flang\u0131c\u0131n\u0131, Nil Vadisi\u2019nde y\u0131ll\u0131k su ta\u015fmalar\u0131ndan sonra arazi s\u0131n\u0131rlar\u0131n\u0131 belirlemekle g\u00f6revli kadastrocular\u0131n \u00e7a\u00adl\u0131\u015fmalar\u0131nda bulmu\u015ftu. Geometri \u201cyer\u201d ve \u201c\u00f6l\u00e7me\u201d anlam\u0131na gelen \u201cgeo\u201d ve \u201cmetrein\u201d s\u00f6zc\u00fcklerinden olu\u015fan bir terimdir. M\u0131s\u0131r\u2019\u0131n yan\u0131 s\u0131ra Babil, Hint ve \u00c7in gibi eski uygarl\u0131klarda da geli\u015fen geometri o d\u00f6nemlerde b\u00fcy\u00fck \u00f6l\u00e7\u00fcde, el yordam\u0131, \u00f6l\u00e7\u00adme, analoji ve sezgiye dayanan bir y\u0131\u011f\u0131n i\u015flem ve bulgudan iba\u00adret \u00e7al\u0131\u015fmalard\u0131. \u00dcstelik ortaya konan bilgiler \u00e7o\u011funlukla kesin olmaktan uzak, tahmin \u00e7er\u00e7evesinde kalan sonu\u00e7lard\u0131. \u00d6rne\u011fin, Babilliler dairenin \u00e7emberini \u00e7ap\u0131n\u0131n \u00fc\u00e7 kat\u0131 olarak biliyorlard\u0131. Bu \u00f6ylesine yerle\u015fik bir bilgiydi ki; pi\u2019nin de\u011ferinin 3 de\u011fil, 22\/7 oldu\u011funu ileri s\u00fcrenlere, bir t\u00fcr \u015farlatan g\u00f6z\u00fcyle bak\u0131l\u0131yordu. M\u0131s\u0131rl\u0131lar bu konuda daha duyarl\u0131yd\u0131lar: M\u00d6 1800 y\u0131llar\u0131na ait Rhind pap\u00fcr\u00fcslerinde onlar\u0131n pi\u2019yi yakla\u015f\u0131k 3.1604 olarak belir\u00adledikleri g\u00f6r\u00fclmektedir; ama M\u0131s\u0131rl\u0131lar\u2019\u0131n bile her zaman do\u011fru sonu\u00e7lar ortaya koydu\u011fu s\u00f6ylenemez. Nitekim, kesik kare pira\u00admidin oylumunu (hacmini) hesaplamada do\u011fru form\u00fcl\u00fc bulan M\u0131s\u0131rl\u0131lar, dikd\u00f6rtgen i\u00e7in do\u011fru olan bir alan form\u00fcl\u00fcn\u00fcn, t\u00fcm d\u00f6rtgenler i\u00e7in ge\u00e7erli oldu\u011funu san\u0131yorlard\u0131.<\/p>\n

Aritmetik ve cebir alan\u0131nda Babilliler, M\u0131s\u0131rl\u0131lar\u2019dan daha ilerdeydiler. Geometride de \u00f6nemli bulu\u015flar\u0131 vard\u0131. \u00d6rne\u011fin, \u201cPythagoras Teoremi\u201d dedi\u011fimiz, bir dik a\u00e7\u0131l\u0131 \u00fc\u00e7gende dik ke\u00adnarlarla hipoten\u00fcs aras\u0131ndaki ba\u011f\u0131nt\u0131ya ili\u015fkin \u00f6nerme \u201cBir dik \u00fc\u00e7genin dik kenar karelerinin toplam\u0131, hipoten\u00fcs\u00fcn karesine e\u015fittir\u201d bulu\u015flar\u0131ndan biriydi. Ne var ki, do\u011fru da olsa bu bilgiler ampirik nitelikteydi; mant\u0131ksal ispat a\u015famas\u0131na ge\u00e7ilememi\u015fti hen\u00fcz. Egeli Filazof Thales\u2019in (M\u00d6 624-546), geometrik \u00f6ner\u00admelerin ded\u00fcktif y\u00f6ntemle ispat\u0131 gere\u011fini \u0131srarla vurgulad\u0131\u011f\u0131, bu yolda ilk ad\u0131mlar\u0131 att\u0131\u011f\u0131 bilinmektedir. M\u0131s\u0131r gezisinde tan\u0131\u015ft\u0131\u011f\u0131 geometriyi, da\u011f\u0131n\u0131kl\u0131ktan kurtar\u0131p, tutarl\u0131, sa\u011flam bir temele oturtmak istiyordu, ispatlad\u0131\u011f\u0131 \u00f6nermeler aras\u0131nda; ikizkenar \u00fc\u00e7genlerde taban a\u00e7\u0131lar\u0131n\u0131n e\u015fitli\u011fi; kesi\u015fen iki do\u011frunun olu\u015f\u00adturdu\u011fu kar\u015f\u0131t a\u00e7\u0131lar\u0131n birbirine e\u015fitli\u011fi vb. ili\u015fkiler vard\u0131.<\/p>\n

Klasik \u00c7a\u011f\u2019\u0131n \u201cYedi Bilgesi\u201dnden biri olan Thales\u2019in a\u00e7t\u0131\u011f\u0131 bu yolda, Pythagoras ve onu izleyenlerin elinde, matematik b\u00fc\u00ady\u00fck ilerlemeler kaydetti, sonu\u00e7ta Elementler\u2019de i\u015flenildi\u011fi gibi, olduk\u00e7a soyut mant\u0131ksal bir dizgeye ula\u015ft\u0131. Pythagoras, mate\u00admatik\u00e7ili\u011finin yan\u0131 s\u0131ra, say\u0131 mistisizmini i\u00e7eren gizlili\u011fe ba\u011fl\u0131 bir tarikat\u0131n \u00f6nderiydi. Buna g\u00f6re, say\u0131sall\u0131k evrensel uyum ve d\u00fczenin asal niteli\u011fiydi; ruhun y\u00fccelip Tanr\u0131sal kata eri\u015fmesi ancak m\u00fczik ve matematikle olas\u0131yd\u0131.<\/p>\n

Bulu\u015f ve ispatlar\u0131yla matemati\u011fe \u00f6nemli katk\u0131lar yapan Pytha\u00adgoras\u00e7\u0131lar, sonunda inan\u00e7lar\u0131yla ters d\u00fc\u015fen bir bulu\u015fla a\u00e7maza d\u00fc\u015ft\u00fcler. Bu bulu\u015f, karenin kenar\u0131 ile k\u00f6\u015fegenin \u00f6l\u00e7\u00fc\u015ft\u00fcr\u00fcle\u00admeyece\u011fine ili\u015fkindi. \u00c52 gibi, baya\u011f\u0131 kesir \u015feklinde yaz\u0131lamayan say\u0131lar, onlar\u0131n g\u00f6z\u00fcnde gizli tutulmas\u0131 gereken bir skandald\u0131. Rasyonel olmayan say\u0131larla temsile elveren b\u00fcy\u00fckl\u00fckler nas\u0131l olabilirdi? [Pythagoras\u00e7\u0131lar\u2019\u0131n t\u00fcm \u00e7abalar\u0131na kar\u015f\u0131n \u00fcstesinden gelemedikleri bu s\u0131k\u0131nt\u0131y\u0131, daha sonra tan\u0131nm\u0131\u015f bilgin Eudoxus (M\u00d6 408 – 347), olu\u015fturdu\u011fu irrasyonel b\u00fcy\u00fckl\u00fckler i\u00e7in de ge\u00ad\u00e7erli olan, Orant\u0131lar Kuram\u0131\u2019yla giderir.]<\/p>\n

\u00d6klid, Pythagoras gelene\u011fine ba\u011fl\u0131 bir ortamda yeti\u015fmi\u015fti. Platon gibi, onun i\u00e7in de \u00f6nemli olan soyut d\u00fc\u015f\u00fcnceler, d\u00fc\u00ad\u015f\u00fcnceler aras\u0131ndaki mant\u0131ksal ba\u011f\u0131nt\u0131lard\u0131. Duyumlar\u0131m\u0131zla i\u00e7ine d\u00fc\u015ft\u00fc\u011f\u00fcm\u00fcz yanl\u0131\u015fl\u0131klardan, ancak matemati\u011fin sa\u011flad\u0131\u011f\u0131 evrensel ilkeler ve salt ussal y\u00f6ntemlerle kurtulabilirdik. Kaleme ald\u0131\u011f\u0131 Elementler, kendisini \u00f6nceleyen Thales, Pythagoras, Eudo\u00adxus gibi, bilgin-matematik\u00e7ilerin \u00e7al\u0131\u015fmalar\u0131 \u00fcst\u00fcne kurulmu\u015f\u00adtu. Geometri bir \u00f6nermeler koleksiyonu olmaktan \u00e7\u0131km\u0131\u015f, s\u0131k\u0131 mant\u0131ksal \u00e7\u0131kar\u0131m ve ba\u011f\u0131nt\u0131lara dayanan bir dizgeye d\u00f6n\u00fc\u015fm\u00fc\u015f\u00adt\u00fc. Art\u0131k \u00f6nermelerin do\u011fruluk de\u011feri, g\u00f6zlem veya \u00f6l\u00e7me veri\u00adleriyle de\u011fil, ussal \u00f6l\u00e7\u00fctlerle denetlenmekteydi. Bu yakla\u015f\u0131mda pratik kayg\u0131lar ve uygulamalar arka plana itilmi\u015fti.<\/p>\n

Ku\u015fkusuz bu, \u00d6klid geometrisinin pratik problem \u00e7\u00f6z\u00fcm\u00fcne elvermedi\u011fi demek de\u011fildi. Tam tersine, de\u011fi\u015fik m\u00fchendislik alanlar\u0131nda pek \u00e7ok problemin, bu geometrinin y\u00f6ntemiyle \u00e7\u00f6z\u00fcmlendi\u011fi; ama Elementler\u2019in, e\u011freti olarak de\u011findi\u011fi baz\u0131 \u00f6rnekler d\u0131\u015f\u0131nda, uygulamalara yer vermedi\u011fi de bilinmektedir. \u00d6klid\u2019in pratik kayg\u0131lardan uzak olan bu tutumunun matematik d\u00fcnyas\u0131ndaki izleri, bug\u00fcn de rastlad\u0131\u011f\u0131m\u0131z bir gelene\u011fe d\u00f6n\u00fc\u015f\u00adm\u00fc\u015ft\u00fcr.<\/p>\n

Ger\u00e7ekten, \u00f6zellikle se\u00e7kin matematik\u00e7ilerin g\u00f6z\u00fcnde, mate\u00admatik \u015fu ya da bu i\u015fe yarad\u0131\u011f\u0131 i\u00e7in de\u011fil, yal\u0131n ger\u00e7e\u011fe y\u00f6nelik, sanat gibi g\u00fczelli\u011fi ve de\u011feri kendi i\u00e7inde soyut bir d\u00fc\u015f\u00fcn u\u011fra\u015f\u0131 oldu\u011fu i\u00e7in \u00f6nemlidir.<\/p>\n

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\u00d6klid neden, geometrinin \u00f6l\u00e7me sonu\u00e7lar\u0131yla do\u011frulanm\u0131\u015f \u00f6nermeleriyle yetinmemi\u015f, bunlar\u0131 ispatlayarak, mant\u0131ksal bir dizgede toplama yoluna gitmi\u015ftir?<\/figcaption><\/figure>\n

Matemati\u011fin t\u00fcm\u00fcyle ussal bir etkinlik oldu\u011fu do\u011fru de\u011fildir. Bulu\u015f ba\u011flam\u0131nda t\u00fcm di\u011fer bilimler gibi matematik de, s\u0131nama-yan\u0131lma, tahmin, sezgi, i\u00e7e-do\u011fu\u015f t\u00fcr\u00fcnden \u00f6\u011feler i\u00e7ermektedir. Yeni bir ba\u011f\u0131nt\u0131y\u0131 sezinleme, de\u011fi\u015fik bir kavram veya y\u00f6ntemi ortaya koyma, temelde mant\u0131ksal olmaktan \u00e7ok psikolojik bir olayd\u0131r. Matemati\u011fin ussall\u0131\u011f\u0131, do\u011frulama ba\u011flam\u0131nda belir\u00adgindir. Teoremlerin ispat\u0131, b\u00fcy\u00fck \u00f6l\u00e7\u00fcde kurallar\u0131 belli, ussal bir i\u015flemdir; ama sorulabilir: \u00d6klid neden, geometrinin \u00f6l\u00e7me sonu\u00e7lar\u0131yla do\u011frulanm\u0131\u015f \u00f6nermeleriyle yetinmemi\u015f, bunlar\u0131 ispatlayarak, mant\u0131ksal bir dizgede toplama yoluna gitmi\u015ftir?<\/p>\n

\u00d6klid\u2019i bu giri\u015fiminde, onu g\u00fcd\u00fcmleyen motiflerin ne oldu\u00ad\u011funu s\u00f6ylemeye olanak yoktur; ancak, Helenistik \u00c7a\u011f\u2019\u0131n d\u00fc\u015f\u00fcn ortam\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, ba\u015fl\u0131ca d\u00f6rt noktan\u0131n \u00f6ng\u00f6r\u00fcld\u00fc\u00ad\u011f\u00fc s\u00f6ylenebilir:<\/p>\n

1) \u0130\u015flenen konuda \u00e7o\u011fu kez belirsiz kalan anlam ve ili\u015fkilere a\u00e7\u0131kl\u0131k getirmek;<\/p>\n

2) \u0130spatta ba\u015fvurulan \u00f6nc\u00fclleri (varsay\u0131m, aksiyom veya pos\u00adtulatlar\u0131) ve \u00e7\u0131kar\u0131m kurallar\u0131n\u0131 belirtik k\u0131lmak;<\/p>\n

3) Ula\u015f\u0131lan sonu\u00e7lar\u0131n do\u011frulu\u011funa mant\u0131ksal ge\u00e7erlik kazan\u00add\u0131rmak (Ba\u015fka bir deyi\u015fle, teoremlerin \u00f6nc\u00fcllere g\u00f6receli zorun\u00adlulu\u011funu, yani \u00f6nc\u00fclleri do\u011fru kabul etti\u011fimizde teoremi yanl\u0131\u015f sayamayaca\u011f\u0131m\u0131z\u0131 g\u00f6stermek);<\/p>\n

4) Geometriyi, ampirik genellemeler d\u00fczeyini a\u015fan soyut-sim\u00adgesel bir dizge d\u00fczeyine \u00e7\u0131karmak (Bir \u00f6rnekle a\u00e7\u0131klayal\u0131m: M\u0131\u00ads\u0131rl\u0131lar ile Babilliler kenarlar\u0131 3, 4, 5 birim uzunlu\u011funda olan bir \u00fc\u00e7genin, dik \u00fc\u00e7gen oldu\u011funu deneysel olarak biliyorlard\u0131; ama bu ili\u015fkinin 3, 4, 5 uzunluklar\u0131na \u00f6zg\u00fc olmad\u0131\u011f\u0131n\u0131, ba\u015fka uzunluklar i\u00e7in de ge\u00e7erli olabilece\u011fini g\u00f6steren veriler ortaya \u00e7\u0131k\u0131ncaya dek kestirmeleri g\u00fc\u00e7t\u00fc; buna ihtiya\u00e7lar\u0131 da yoktu. \u00d6yle kuramsal bir a\u00e7\u0131lma i\u00e7in pratik kayg\u0131lar \u00f6tesinde, salt entelekt\u00fcel motifli bir aray\u0131\u015f i\u00e7inde olmak gerekir. Nitekim, Egeli bilginler somut \u00f6r\u00adnekler \u00fczerinde \u00f6l\u00e7meye dayanan belirlemeler yerine, bilinen ve bilinmeyen t\u00fcm \u00f6rnekler i\u00e7in ge\u00e7erli soyut genellemeler aray\u0131\u015f\u0131n\u00addayd\u0131lar. Onlar, kenar uzunluklar\u0131 a, b, c diye belirlenen \u00fc\u00e7geni ele almakta, \u00fc\u00e7genin ancak a2 + b2 = c2 e\u015fitli\u011fi ger\u00e7ekle\u015fti\u011finde dik \u00fc\u00e7gen olabilece\u011fi genellemesine gitmektedir).<\/p>\n

\u00d6klid olu\u015fturdu\u011fu dizgede birtak\u0131m tan\u0131mlar\u0131n yan\u0131 s\u0131ra, be\u015fi \u201caksiyom\u201d dedi\u011fi genel ilkeden, be\u015fi de \u201cpostulat\u201d dedi\u011fi geometri\u00adye \u00f6zg\u00fc ilkeden olu\u015fan, 10 \u00f6nc\u00fcle yer vermi\u015ftir. (\u00d6nc\u00fcller, teorem\u00adlerin tersine ispatlanmaks\u0131z\u0131n do\u011fru say\u0131lan \u00f6nermelerdir.) Dizge t\u00fcm yetkin g\u00f6r\u00fcn\u00fcm\u00fcne kar\u015f\u0131n, asl\u0131nda \u00e7e\u015fitli y\u00f6nlerden birtak\u0131m yetersizlikler i\u00e7ermekteydi. Bir kez verilen tan\u0131mlar\u0131n bir b\u00f6l\u00fcm\u00fc (\u00f6zellikle, \u201cnokta\u201d, \u201cdo\u011fru\u201d, vb. ilkel terimlere ili\u015fkin tan\u0131mlar) gereksizdi. Sonra daha \u00f6nemlisi, belirlenen \u00f6nc\u00fcller d\u0131\u015f\u0131nda baz\u0131 varsay\u0131mlar\u0131n, belki de fark\u0131nda olmaks\u0131z\u0131n kullan\u0131lm\u0131\u015f olmas\u0131, dizgenin tutarl\u0131l\u0131\u011f\u0131 a\u00e7\u0131s\u0131ndan \u00f6nemli bir kusurdu. Ne var ki, ma\u00adtematiksel y\u00f6ntemin olu\u015fma i\u00e7inde oldu\u011fu ba\u015flang\u0131\u00e7 d\u00f6neminde, bir bak\u0131ma ka\u00e7\u0131n\u0131lmaz olan bu t\u00fcr yetersizlikler, giderilemeyecek \u015feyler de\u011fildi. Nitekim, 18. y\u00fczy\u0131lda ba\u015flayan ele\u015ftirel \u00e7al\u0131\u015fmalar\u0131n dizgeye daha a\u00e7\u0131k ve tutarl\u0131 bir b\u00fct\u00fcnl\u00fck sa\u011flad\u0131\u011f\u0131 s\u00f6ylenebilir. \u00dcstelik dizgenin irdelenmesi, beklenmedik bir geli\u015fmeye de yol a\u00e7m\u0131\u015ft\u0131r: \u00d6nc\u00fcllerde baz\u0131 de\u011fi\u015fikliklerle yeni geometrilerin ortaya konmas\u0131. \u201c\u00d6klid-d\u0131\u015f\u0131\u201d diye bilinen bu geometriler, sa\u011fduyumuza ayk\u0131r\u0131 da d\u00fc\u015fseler, kendi i\u00e7inde tutarl\u0131 birer dizgedir. \u00d6klid geo\u00admetrisi, art\u0131k var olan tek geometri de\u011fildir. \u00d6yle de olsa, \u00d6klid\u2019in d\u00fc\u015f\u00fcnce tarihinde tuttu\u011fu yerin de\u011fi\u015fti\u011fi s\u00f6ylenemez.<\/p>\n

\u00c7a\u011f\u0131m\u0131z\u0131n se\u00e7kin filozofu Bertrand Russell\u2019\u0131n (1872 – 1970) \u015fu s\u00f6zlerinde \u00d6klid\u2019in \u00f6zl\u00fc bir de\u011ferlendirmesini bulmaktay\u0131z: \u201cElementler\u2019e bug\u00fcne de\u011fin yaz\u0131lm\u0131\u015f en b\u00fcy\u00fck kitap g\u00f6z\u00fcyle ba\u00adk\u0131lsa yeridir. Bu kitap ger\u00e7ekten Grek zek\u00e2s\u0131n\u0131n en yetkin an\u0131t\u00adlar\u0131ndan biridir. Kitab\u0131n Grekler\u2019e \u00f6zg\u00fc kimi yetersizlikleri yok de\u011fildir, ku\u015fkusuz: dayand\u0131\u011f\u0131 y\u00f6ntem salt ded\u00fcktif niteliktedir; \u00fcstelik, \u00f6nc\u00fcllerini olu\u015fturan varsay\u0131mlar\u0131 yoklama olana\u011f\u0131 yok\u00adtur. Bunlar ku\u015fku g\u00f6t\u00fcrmez apa\u00e7\u0131k do\u011frular olarak konmu\u015ftur. Oysa, 19. y\u00fczy\u0131lda ortaya \u00e7\u0131kan \u00d6klid-d\u0131\u015f\u0131 geometriler, bunlar\u0131n hi\u00e7 de\u011filse bir b\u00f6l\u00fcm\u00fcn\u00fcn yanl\u0131\u015f olabilece\u011fini, bunun da ancak g\u00f6zleme ba\u015fvurularak belirlenebilece\u011fini g\u00f6stermi\u015ftir.\u201d<\/p>\n

Gene genel r\u00f6lativite kuram\u0131nda \u00d6klid geometrisini de\u011fil, Riemann (1826 – 1866) geometrisini kullanan Einstein\u2019\u0131n, Elementler\u2019e ili\u015fkin yarg\u0131s\u0131 son derece \u00e7arp\u0131c\u0131d\u0131r: \u201cGen\u00e7li\u011finde bu kitab\u0131n b\u00fcy\u00fcs\u00fcne kap\u0131lmam\u0131\u015f bir kimse, kuramsal bilimde \u00f6nemli bir at\u0131l\u0131m yapabilece\u011fi hayaline bo\u015funa kap\u0131lmas\u0131n!\u201d<\/p>\n

Kaynak: <\/strong>Cemal Y\u0131ld\u0131r\u0131m, Bilimin \u00d6nc\u00fcleri, Bilim ve Gelecek Kitapl\u0131\u011f\u0131, 2014, s.58-63<\/p>\n","protected":false},"excerpt":{"rendered":"

R\u00f6nesans sonras\u0131 Avrupa\u2019da, Kopernik\u2019le ba\u015flayan, Kepler, Galileo ve Newton\u2019la 17. y\u00fczy\u0131lda doru\u011funa ula\u015fan bilim\u00adsel devrim, k\u00f6kleri Helenistik D\u00f6nem\u2019e uzanan bir olayd\u0131r. O d\u00f6nemin se\u00e7kin bilginlerinden Aristarkus, G\u00fcne\u015f-merkezli ast\u00adronomi d\u00fc\u015f\u00fcncesinde Kopernik\u2019i \u00f6ncelemi\u015fti; Ar\u015fimet yakla\u015f\u0131k i\u00adki biny\u0131l sonra gelen Galileo\u2019ya esin kayna\u011f\u0131 olmu\u015ftu; \u00d6klid \u00e7a\u011flar boyu yaln\u0131z matematik d\u00fcnyas\u0131n\u0131n de\u011fil, matematikle yak\u0131ndan ilgilenen hemen herkesin g\u00f6z\u00fcnde \u00f6zenilen, […]<\/p>\n","protected":false},"author":429,"featured_media":34799,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[3845],"tags":[4927,4928,4926,675,208,413],"class_list":["post-34798","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bilimin-onculeri","tag-aritmetik","tag-cebir","tag-euclides","tag-geometri","tag-matematik","tag-ronesans"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t