{"id":571,"date":"2025-03-29T15:47:25","date_gmt":"2025-03-29T12:47:25","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/caglart\/?p=571"},"modified":"2025-05-20T18:45:16","modified_gmt":"2025-05-20T15:45:16","slug":"insanligin-zeka-duzeyi-ve-bilim","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/caglart\/2025\/03\/29\/insanligin-zeka-duzeyi-ve-bilim\/","title":{"rendered":"\u0130nsanl\u0131\u011f\u0131n zek\u00e2 d\u00fczeyi ve Bilim"},"content":{"rendered":"

\u0130\u00e7erik: Bir arpa boyu ilerle_YEB\u0130L_dik mi?<\/p>\n

Fizik 19<\/p>\n

\u00d6N NOT: \u015eimdiye dek hi\u00e7bir yaz\u0131m\u0131z\u0131 silmedik; ufak tefek maddi hata d\u00fczeltmeleri d\u0131\u015f\u0131nda hi\u00e7bir yaz\u0131m\u0131z\u0131 da de\u011fi\u015ftirmedik. Ama \u015fimdi okumakta oldu\u011funuz bu yaz\u0131n\u0131n her a\u015famas\u0131 en \u00fcstteki ba\u015fl\u0131k alt\u0131nda yer alacak ve tabii ki, g\u00fcnden g\u00fcne ve hatta dakikadan dakikaya bile de\u011fi\u015fiklik g\u00f6sterip tamamlanmas\u0131 uzun s\u00fcrebilecektir. O arada, alttaki notlarda yer alan b\u00f6l\u00fcmler de yer de\u011fi\u015ftirebilir yaz\u0131 olgunla\u015ft\u0131k\u00e7a\u2026<\/p>\n

1. NOT
\u0130lk yaz\u0131m\u0131zdan beri s\u00f6yleyegelmekteyiz ki, Bilim\u2019in ne oldu\u011funu, Fizik\u2019in ne oldu\u011funu bilmiyor insanl\u0131\u011f\u0131n \u00e7o\u011funlu\u011fu. Oysa hi\u00e7bir ki\u015finin, hi\u00e7bir canl\u0131n\u0131n bir nano saniyesi bile Bilimsiz Fiziksiz ge\u00e7iyor de\u011fil. Hani 16. y\u00fczy\u0131l \u015fairlerimizden Hay\u00e2l\u00ee\u2019nin \u015fu gazelindeki (*) gibi;
\u201cCih\u00e2n-\u00e2r\u00e2 cih\u00e2n i\u00e7indedir *\u00e2r\u00e2y\u0131 bilmezler
Ol *m\u00e2h\u00eeler ki dery\u00e2 i\u00e7redir dery\u00e2y\u0131 bilmezler!\u201d
Bu bilmezlik, insanla bilimin (birbirinden) ayr\u0131lmaz unsurlar, birbirini tamamlayan par\u00e7alar olu\u015fundand\u0131r diye san\u0131yorum; Hay\u00e2l\u00ee\u2019nin bal\u0131klar\u0131n\u0131n denizde(n) yarat\u0131lm\u0131\u015f olu\u015fu gibi.<\/p>\n

(*) https:\/\/1000kitap.com\/ol-mahiler-ki-derya-icredir-deryayi-bilmezler–2275107?sayfa=2<\/p>\n

Sorarsan ehl-i d\u00fcnyaya nedir d\u00fcnyay\u0131 bilmezler
Sanup ukb\u00e2y\u0131 d\u00fcnya nitekim *ukb\u00e2y\u0131 bilmezler
G\u00f6r\u00fcrler \u00e2lemi r\u00fcy\u00e2 gibi r\u00fcy\u00e2y\u0131 bilmezler
Olurlar t\u00e2lib-i Mevl\u00e2 g\u00f6r\u00fcp Mevl\u00e2y\u0131 bilmezler
Cih\u00e2n-\u00e2r\u00e2 cih\u00e2n i\u00e7indedir *\u00e2r\u00e2y\u0131 bilmezler
Ol *m\u00e2h\u00eeler ki dery\u00e2 i\u00e7redir dery\u00e2y\u0131 bilmezler<\/p>\n

2. NOT
\u2018Pisagor, Zeno, G. Galilei\u2019nin babas\u0131 ve Kuvantum T\u00fcnellemesi (\u2018Quantum Tunelling\u2019)\u2019 (*) ba\u015fl\u0131kl\u0131 yaz\u0131m\u0131zda Hotanto kabilesinden s\u00f6z etmi\u015f idik. Bu kabilenin Aritmetik\u2019inde sadece \u00fc\u00e7 rakam ve dolay\u0131s\u0131 ile sadece 3 say\u0131 var imi\u015f, \u20181, 2, 3, \u2026 Sonsuz\u2019 adl\u0131 kitab\u0131nda George Gamow\u2019un belirtti\u011fine g\u00f6re. Daha b\u00fcy\u00fck \u00e7okluklar i\u00e7in de \u2018\u00e7ok\u2019 anlam\u0131nda bir s\u00f6zc\u00fck kullan\u0131r imi\u015fler.
San\u0131r\u0131m, daha \u00e7ok rakam ve dolay\u0131s\u0131 ile say\u0131 kullanmaya ihtiya\u00e7lar\u0131n\u0131n olmay\u0131\u015f\u0131ndand\u0131r.<\/p>\n

(*) https:\/\/blog.metu.edu.tr\/caglart\/2024\/12\/22\/pisagor-zeno-g-galileinin-babasi-ve-kuvantum-tunellemesi-quantum-tunelling\/<\/p>\n\n\n

3. NOT<\/p>\n\n\n\n

Bizim Say\u0131 Sistemimiz Hotanto\u2019lar\u0131nkine k\u0131yasla daha zengin ama \u015f\u00f6ylesi sa\u00e7mal\u0131klar\u0131 da bar\u0131nd\u0131rmakta:<\/p>\n\n\n\n

1\/3 = 0,333\u2026 ve 3x(1\/3) = 3×0,333\u2026 yani 1 = 0,999\u2026<\/p>\n\n\n\n

Dolay\u0131s\u0131 ile, 2 = 1,999\u2026 , 3 = 2,999\u2026 ve 0 = ? yani her say\u0131 pek \u00e7ok ba\u015fka say\u0131ya e\u015fit.<\/p>\n\n\n\n


Dahas\u0131, benzeri pek \u00e7ok ba\u015fka sa\u00e7mal\u0131klar da mevcut!<\/p>\n\n\n\n

Acaba, Say\u0131 Sistemi\u2019mizdeki bu sa\u00e7mal\u0131klar nereden kaynaklan\u0131yor?<\/p>\n\n\n\n

4. NOT<\/p>\n\n\n\n

Say\u0131lardaki, 3.NOT\u2019ta belirtilen zay\u0131fl\u0131\u011f\u0131n yan\u0131 s\u0131ra Trigonometri de pek \u00e7ok zay\u0131fl\u0131k i\u00e7ermekte. \u00d6rne\u011fin, N ve M tam say\u0131lar olmak ko\u015fuluyla ve derece cinsinden (180N) \u2013 30 ile 90M d\u0131\u015f\u0131nda hi\u00e7bir a\u00e7\u0131n\u0131n sin\u00fcs de\u011ferini bilmiyoruz. Ancak yakla\u015f\u0131k de\u011ferler saptayabiliyoruz. Bu de\u011ferlerin ondal\u0131k virg\u00fclden sonraki basamak say\u0131s\u0131 artt\u0131k\u00e7a hata pay\u0131 b\u00fcy\u00fcyor.<\/p>\n\n\n\n

Sin\u00fcs30 = \u00bd de Sin\u00fcs(31) = ?<\/p>\n\n\n\n

Keza, \u03c0 say\u0131s\u0131n\u0131n da tam de\u011ferini bilmiyoruz. Her hesaplama ad\u0131m\u0131nda ondal\u0131k virg\u00fclden sonraki basamak say\u0131s\u0131 artt\u0131k\u00e7a hata pay\u0131 da b\u00fcy\u00fcyor. Karek\u00f6k i\u00e7inde 2, k\u00fcp k\u00f6k i\u00e7inde 3 gibi say\u0131lar da b\u00f6yle.<\/p>\n\n\n\n

5. NOT<\/p>\n\n\n\n

Geometri\u2019de durum daha da vahim. Her \u015fekil, her a\u00e7\u0131 nokta ve \u00e7izgilerle tan\u0131mlan\u0131yor ama \u2018Nokta nedir?\u2019 sorusunun yan\u0131t\u0131 \u2018\u0130ki \u00e7izginin kesi\u015fti\u011fi yer.\u2019 de \u2018Peki, \u00e7izgi nedir?\u2019 sorusunun yan\u0131t\u0131 \u2018Uzunlu\u011fu olan ama geni\u015fli\u011fi ve derinli\u011fi olmayan \u015fey.\u2019 ise, sormamak m\u00fcmk\u00fcn m\u00fc \u2018\u015eey nedir?\u2019 diye?!<\/p>\n\n\n\n

\u2018Evrende nokta veya \u00e7izgi var m\u0131?\u2019 sorusunun da yan\u0131t\u0131n\u0131 bil_E_miyoruz. \u00c7\u00fcnk\u00fc nokta saptayacak (\u2018detect\u2019) herhangi bir organ\u0131m\u0131z veya ayg\u0131t\u0131m\u0131z yok. Zaten olmayan bir noktay\u0131 nas\u0131l saptayabilirsiniz ki?<\/p>\n\n\n\n

Ayn\u0131 ba\u011flamda, evrende \u00e7ember de yok, parabol, hiperbol gibi geometrik \u015fekiller de yok. Bunlar sadece hay\u00e2l \u00fcr\u00fcnleri. Yani, nesnel kar\u015f\u0131l\u0131klar\u0131 yok.<\/p>\n\n\n\n

S\u00f6z\u00fcn \u00f6z\u00fc, kulland\u0131\u011f\u0131m\u0131z matematik hem eksikli hem de nesnel kar\u015f\u0131l\u0131ktan yoksun.<\/p>\n\n\n\n

Matemati\u011fi Fizik\u2019in ve hatta evrenin dili sananlar fena halde yan\u0131l\u0131yorlar. D\u00fcnya Ay\u2019\u0131 ve G\u00fcne\u015f\u2019i; G\u00fcne\u015f, D\u00fcnya ve Ay\u2019\u0131; Ay, D\u00fcnya ve G\u00fcne\u015f\u2019i \u00e7ekerken matematik mi kullan\u0131yor? \u201c\u2014Evet!\u201d diyenler, bu g\u00f6ksel nesnelerin matemati\u011fi nereden bildi\u011fini s\u00f6ylesin l\u00fctfen!<\/p>\n\n\n\n

6. NOT<\/p>\n\n\n\n

Olaylar\u0131 anlamak, anlatmak ve bunlardan yararlanmak (*) amac\u0131yla elde edilen bilgi b\u00fct\u00fcnl\u00fc\u011f\u00fc anlam\u0131ndaki Fizik hayli eksiklik ve yanl\u0131\u015fl\u0131k i\u00e7ermektedir. \u00d6rne\u011fin, zaman\u0131n ne oldu\u011funu bilmiyor ama biliyormu\u015f gibi yaparak ulu orta (f\u00fctursuzca) kullan\u0131yoruz. Acaba zaman s\u00fcrekli midir yoksa kesikli mi? Zaman\u0131n anlardan olu\u015ftu\u011fu d\u00fc\u015f\u00fcncesinin \u00e7eli\u015fkilerinden Zeno Paradokslar\u0131\u2019ndan s\u00f6z ederken de\u011finmi\u015ftik. Yak\u0131n \u00e7evremizdeki uzay\u0131n (**) 10-30<\/sup> metrelere dek s\u00fcreklilik g\u00f6sterdi\u011fini ve y\u00f6nse\u00e7mez (\u2018isotropic\u2019) oldu\u011funu deneylere dayal\u0131 olarak biliyoruz. F=ma yaz\u0131yoruz ama F yani kuvvet yani uzaktan etkile\u015fim nedir, nas\u0131l olu\u015fur hi\u00e7 bilmiyoruz. S\u0131cakl\u0131k (T) Is\u0131ldinami\u011fin temel niceliklerindendir ama tam tan\u0131ml\u0131 de\u011fildir. Herhangi bir cismin s\u0131cakl\u0131\u011f\u0131n\u0131 \u00f6l\u00e7emiyoruz, bu nedenle de s\u0131cakl\u0131\u011f\u0131 tan\u0131mlayam\u0131yoruz. Buna ra\u011fmen T\u2019yi de biliyormu\u015f gibi yaparak ulu orta (f\u00fctursuzca) kullan\u0131yoruz. Herhangi bir olgusal (g\u00f6rg\u00fcl, \u2018empirical\u2019) tezin do\u011frulanmas\u0131 i\u00e7in ka\u00e7 s\u0131nama\/deney yap\u0131lmas\u0131 gerekti\u011fi sorusuna kesin bir yan\u0131t veremiyoruz.<\/p>\n\n\n\n

Yukar\u0131daki listeyi uzatmak yerine, yinelemekte yarar var; yine de Fizik\u2019in ve dolay\u0131s\u0131 ile Bilim\u2019in hen\u00fcz kurulu\u015f a\u015famas\u0131n\u0131 tamamlamam\u0131\u015f olmas\u0131ndan yola \u00e7\u0131karak, Fizik\u2019in tam tekmil kurulmas\u0131n\u0131n insanl\u0131\u011fa, daha do\u011frusu o bilime sahip olanlara sa\u011flayaca\u011f\u0131 olanaklara dikkat \u00e7ekmek isteriz.<\/p>\n\n\n\n

B\u00f6ylesi bir tam (eksiksiz) ve (m\u00fcmk\u00fcn m\u00fcd\u00fcr ki) yanl\u0131\u015fs\u0131z Fizik\u2019in mutlaka rassal (\u2018random\u2019) olay ve olgular ile bunlara ili\u015fkin rassal nicelikleri de kapsamas\u0131 gerekti\u011fini ileri s\u00fcrmekte hi\u00e7bir sak\u0131nca g\u00f6rm\u00fcyorum.<\/p>\n\n\n\n

Ho\u015f, herhangi bir zaman serisinin d\u00f6ng\u00fcsel (\u2018periodic\u2019) olup olmad\u0131\u011f\u0131n\u0131; \u00f6rne\u011fin verilmi\u015f bir dizi koordinat \u00e7iftinin bir d\u00fczlemde \u00e7ember \u00fcst\u00fcnde olup olmad\u0131\u011f\u0131n\u0131 saptayamay\u0131z. Asla saptayamay\u0131z!  \u0130lgi periyod ve \u00e7ember yar\u0131\u00e7ap\u0131 hangi b\u00fcy\u00fck ya da k\u00fc\u00e7\u00fck de\u011ferlere sahip olursa olsun saptayamay\u0131z.<\/p>\n\n\n\n

Ayn\u0131 ba\u011flamda, herhangi bir rassal zaman serisi ile d\u00fczenli (regular) zaman serisini de ayr\u0131\u015ft\u0131ramay\u0131z. Dolay\u0131s\u0131 ile, herhangi bir zaman serisi i\u00e7indeki hangi niceliklerin d\u00fczenli bir alt zaman serisine hangi niceliklerin da rassal bir alt zaman serisine ait oldu\u011funu saptayamay\u0131z.<\/p>\n\n\n\n

Ama;<\/p>\n\n\n\n

    \n
  1. do\u011fa bu ayr\u0131\u015ft\u0131rmay\u0131 yap\u0131yor. (***)<\/li>\n\n\n\n
  2. var olan Fizik, rassal olgular\u0131 d\u0131\u015flay\u0131p d\u00fczenli olanlarla ilgilenmekte. \u0130\u015fte bu yakla\u015f\u0131m bir kenara b\u0131rak\u0131lmal\u0131 art\u0131k. Yani, var olan Fizik \u00e7er\u00e7evesi i\u00e7inde rassal diye nitelenen ve d\u00fczenli diye nitelenen olgular birbirinden ayr\u0131\u015ft\u0131r\u0131lmadan de\u011ferlendirilmelidir. (***)<\/li>\n<\/ol>\n\n\n\n

    (*) Rahat ve uzun ya\u015famakla merak gidermekte.<\/p>\n\n\n\n

    (**) Yery\u00fcz\u00fc\u2019ne yak\u0131n yerlerde.<\/p>\n\n\n\n

    (***) Bu konuya yak\u0131n gelecekte de\u011finece\u011fiz.<\/p>\n\n\n\n

    7. NOT<\/p>\n\n\n\n

    Rassall\u0131k ve d\u00fczenlilik i\u00e7in bkz., https:\/\/www.jstor.org\/stable\/3617615<\/p>\n\n\n\n

    8. NOT<\/p>\n\n\n\n

    Evrenin her yerini biliyor de\u011filiz ama bildi\u011fimiz herhangi bir yerine (d\u00fcz ya da e\u011fri) bir \u00e7izgi \u00e7izemeyece\u011fimizi biliyoruz. Bir \u00e7izgi \u00e7izebilseydik, iki \u00e7izgi de \u00e7izebilirdik. Hatta, kesi\u015fen iki \u00e7izgi de \u00e7izip bunlar\u0131n kesi\u015fim yerinde (yerlerinde) bir (\u00e7ok) nokta yaratabilirdik.<\/p>\n\n\n\n

    9. NOT<\/p>\n\n\n\n

    Bildi\u011fimiz herhangi bir yerde bir nokta yaratabildi\u011fimizi varsaysak, bu noktadan ge\u00e7en d\u00fcz bir \u00e7izgi \u00e7izebildi\u011fimizi de varsaysak bile; bu \u00e7izgiye, o noktada dik olan ba\u015fka bir \u00e7izgiyi \u00e7izemeyiz. \u00c7\u00fcnk\u00fc, bu iki d\u00fcz \u00e7izginin tam\u0131 tam\u0131na 90 derecelik bir a\u00e7\u0131 yapmas\u0131 gerekir, 90,000000000000001 olmayaca\u011f\u0131 gibi 89,999\u2026 da olmaz.<\/p>\n\n\n\n

    Demek ki, bu evrende Kartezyen Koordinat Sistemi olu\u015fturamay\u0131z. Yar\u0131\u00e7ap\u0131 R olan ve X2<\/sup> + Y2<\/sup> = R2<\/sup> denklemini sa\u011flayan bir \u00e7ember de \u00e7izilemez. Ayn\u0131 ba\u011flamda, herhangi bir parabol, hiperbol vb. de \u00e7izilemez.<\/p>\n\n\n\n

    Kartezyen Koordinat Sistemi\u2019nin eksenlerini bile olu\u015fturamad\u0131\u011f\u0131m\u0131z bu evren(nin bildi\u011fimiz yerlerin)de, hi\u00e7bir geometrik \u015fekil olu\u015fturam\u0131yor olu\u015fumuz biz insanlar\u0131n yetenek eksikli\u011finden de\u011fil evren(in bildi\u011fimiz yerlerin)in o \u015fekilleri kabul etmeyi\u015finden, o \u015fekillerin olu\u015fturulmas\u0131na olanak tan\u0131may\u0131\u015f\u0131ndan de\u011fil midir?<\/p>\n\n\n\n

    B\u00fct\u00fcn bunlar da evren(in bildi\u011fimiz yerleri)nin geometri kullan_MI_yor olu\u015fundan de\u011fil midir?<\/p>\n\n\n\n

    E\u011fer b\u00f6yle ise, Geometri\u2019yi evren(in bildi\u011fimiz yerleri) i\u00e7in kullanmaya \u00e7al\u0131\u015fmak \u2018abesle i\u015ftigal\u2019 de\u011filse nedir?<\/p>\n\n\n\n

    Demek ki, biz insanlar\u0131n yetenek eksikli\u011fi, evren(in bildi\u011fimiz yerlerin)de var olamayan unsurlar\u0131, evren(in bildi\u011fimiz yerlerin)i anlamakta ve anlatmakta kullanmaya bo\u015funa \u00e7abal\u0131yor olu\u015fumuzda. Ayr\u0131ca, bu eksikli ara\u00e7 ve y\u00f6ntemler yerine evren(in bildi\u011fimiz yerleri) ile uyumlu ba\u015fka, yeni ara\u00e7 ve y\u00f6ntemler bulmam\u0131z gerekti\u011fi apa\u00e7\u0131k ortada.<\/p>\n\n\n\n

    10. NOT<\/p>\n\n\n\n

    POP QUiZ -21- Fizik hakk\u0131nda 5 soru<\/p>\n\n\n\n

    1) K. Popper\u2019\u0131n \u201cG\u00fcne\u015f\u2019in her sabah do\u011fmu\u015f olmas\u0131 yar\u0131n sabah da do\u011facak oldu\u011funa dair kan\u0131t olu\u015fturmaz.\u201d s\u00f6z\u00fcn\u00fc \u015f\u00f6ylece yorumlayabiliriz. N s\u0131f\u0131rdan b\u00fcy\u00fck bir do\u011fal say\u0131 olmak \u00fczere, herhangi bir tezin (kuram\u0131n, yasan\u0131n) deneyle N kez do\u011frulanm\u0131\u015f olmas\u0131, N+1_inci kez de do\u011frulanaca\u011f\u0131na dair kan\u0131t olu\u015fturmaz.<\/p>\n\n\n\n

    Yukar\u0131daki gerek\u00e7elere dayal\u0131 olarak, \u201cHerhangi bir tezin (kuram\u0131n, yasan\u0131n) deneyle N kez do\u011frulanm\u0131\u015f olmas\u0131, N+1_inci kez de do\u011frulanaca\u011f\u0131na dair kan\u0131t olu\u015fturmas\u0131n\u0131n yolunu bulamad\u0131k\u00e7a Fizik ilerlemez.\u201d c\u00fcmlesi do\u011fru mudur?<\/p>\n\n\n\n

    2) Ya da, herhangi bir tezin (kuram\u0131n, yasan\u0131n) deneyle ka\u00e7 kez do\u011frulanmas\u0131 o tezin (kuram\u0131n, yasan\u0131n) do\u011frulu\u011funa kan\u0131t olu\u015fturur?<\/p>\n\n\n\n

    3) Yahut da, en \u00fcstteki, 1) nolu \u015f\u0131ktaki gerek\u00e7eyi, \u201cEvrende ve dolay\u0131s\u0131 ile Fizik\u2019te hi\u00e7bir (kan\u0131tlanm\u0131\u015f) yasa yoktur.\u201d bi\u00e7iminde yorumlayabilir miyiz?<\/p>\n\n\n\n

    4) Evrendeki rassal olaylar ve onlara ba\u011fl\u0131 nicelikler umursanmad\u0131k\u00e7a, herhangi bir Fizik tezine (kuram\u0131na, yasas\u0131na) g\u00fcven duyabilir miyiz?<\/p>\n\n\n\n

    5) Fizik, gelece\u011fe y\u00f6nelik do\u011fru (ge\u00e7erli) tahmin (\u00f6ng\u00f6r\u00fc, \u2018foresee\u2019, \u2018prediction\u2019) yapmam\u0131za olanak sa\u011flad\u0131\u011f\u0131 i\u00e7in k\u0131ymetli oldu\u011funa g\u00f6re; hem rassal olaylar\u0131 ve onlara ba\u011fl\u0131 nicelikleri kullanan hem de gelece\u011fe y\u00f6nelik do\u011fru (ge\u00e7erli) tahmin (\u00f6ng\u00f6r\u00fc, \u2018foresee\u2019, \u2018prediction\u2019) yapmam\u0131za olanak sa\u011flad\u0131\u011f\u0131 i\u00e7in Finans Fizi\u011fi de k\u0131ymetli midir?<\/p>\n\n\n\n

    11. NOT<\/p>\n\n\n\n

    Derler ki, \u201c\u2014Yaz\u0131 tura at\u0131\u015flar\u0131nda yaz\u0131 (Y) veya tura (T) gelme olas\u0131l\u0131\u011f\u0131 \u00bd\u2019dir.\u201d Kar\u015f\u0131 taraf da \u015f\u00f6yle yan\u0131tlar; \u201c\u2014Eh, mant\u0131kl\u0131! \u0130ki se\u00e7enek (Y veya T) oldu\u011funa ve bu se\u00e7eneklerin her birinin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 e\u015fit oldu\u011funa g\u00f6re Y ve T\u2019nin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 \u00bd\u2019dir.\u201d Bu sat\u0131rlar\u0131n yazan\u0131 da der ki, \u201c\u2014Deney yapal\u0131m \u015fu halde! Paray\u0131 ard\u0131 ard\u0131na iki kez havaya f\u0131rlatal\u0131m. Bakal\u0131m herhangi bir at\u0131\u015fta Y ve di\u011ferinde T geliyor mu?\u201d<\/p>\n\n\n\n

    Hemen itiraz ederler: \u201c\u2014Gelmeyebilir. Ancak \u00e7ok say\u0131da at\u0131\u015f yaparsan\u0131z ger\u00e7ekle\u015fme oranlar\u0131 \u00bd ve \u00bd olur!\u201d<\/p>\n\n\n\n

    Hay\u0131r, olmaz! Diyelim ki, s\u0131f\u0131rdan farkl\u0131 ve Do\u011fal bir \u00e7ift Say\u0131 olarak M (=2, 4, 6, \u2026 ) kez at\u0131\u015f yap\u0131ld\u0131ktan sonra ger\u00e7ekle\u015fme oranlar\u0131 tam da \u00bd ve \u00bd oldu. Hemen bir sonraki at\u0131\u015fta bu e\u015fitli\u011fin bozulaca\u011f\u0131 a\u00e7\u0131k!<\/p>\n\n\n\n

    Tahminen \u015f\u00f6ylen k\u0131nayacaklar bu fakiri; \u201c\u2014Siz \u2018ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131\u2019 ile \u2018ger\u00e7ekle\u015fme oran\u0131\u2019n\u0131 kar\u0131\u015ft\u0131r\u0131yor olabilir misiniz?\u201d<\/p>\n\n\n\n

    Yoo, hi\u00e7 de de\u011fil! \u201c\u2014At\u0131\u015f say\u0131s\u0131 artt\u0131k\u00e7a ger\u00e7ekle\u015fme oranlar\u0131 ayn\u0131 de\u011fere yani \u00bd de\u011ferine yak\u0131nsar. Ama, e\u015fitlik, bu durumda tan\u0131ml\u0131 de\u011fildir.\u201d<\/p>\n\n\n\n

    Haks\u0131z m\u0131y\u0131m?<\/p>\n\n\n\n

    Ek okuma i\u00e7in bkz., https:\/\/www.youtube.com\/watch?v=9SafeYziRCA<\/a>   Ayr\u0131ca bkz., https:\/\/www.youtube.com\/watch?v=gIwbGNK02Po&list=PLcNWqzWzYG2ufnZbJYffUkgYkhh3kS44L<\/a><\/p>\n\n\n\n


    12. NOT<\/p>\n\n\n\n

    Eski dostlar an\u0131msayacakt\u0131r; 2005 y\u0131l\u0131 dolay\u0131nda \u015funu s\u0131k\u00e7a sorard\u0131m: \u2018D\u00fczenli olaylar bozunarak m\u0131 rassal olaylar ortaya \u00e7\u0131k\u0131yor zaman i\u00e7inde yoksa rassal olaylar m\u0131, hani bir \u015fekilde kristalize olur gibi, d\u00fczenlile\u015fiyor?\u2019 Bu konunun entropi ile \u015f\u00f6yle de bir ili\u015fkisi olabilirdi; hani derler ya \u201c\u2014Evrende d\u00fczensizlik art\u0131yor dolay\u0131s\u0131 ile evrenin entropisi b\u00fcy\u00fcyor.\u201d<\/p>\n\n\n\n

    Bu ba\u011flamda, rassal olaylar\u0131n d\u00fczenlilik olu\u015fturabildi\u011finin bir \u00f6rne\u011fine ge\u00e7mi\u015fte de\u011finmi\u015ftik; Yery\u00fcz\u00fc\u2019ndeki herhangi bir yerle\u015fkenin n\u00fcfusu (\u2018population\u2019) P olsun. \u0394P sabit ve n\u00fcfuslara k\u0131yasla k\u00fc\u00e7\u00fck bir Ger\u00e7ek Say\u0131 olmak ko\u015fuluyla (P \u00b1 \u0394P) kadarl\u0131k n\u00fcfusa sahip yerle\u015fke say\u0131s\u0131 N ise, NP \u221d 1 ba\u011f\u0131nt\u0131s\u0131 g\u00f6rg\u00fcl olarak (g\u00f6zlem sonucu, \u2018empirical\u2019) saptanmaktad\u0131r. (*)<\/p>\n\n\n\n

    Yerle\u015fke n\u00fcfuslar\u0131n\u0131n rassal da\u011f\u0131l\u0131m izledi\u011fi varsay\u0131m\u0131 alt\u0131nda yakla\u015f\u0131k ayn\u0131 n\u00fcfusa sahip yerle\u015fkelerin da\u011f\u0131l\u0131m\u0131 (NP \u221d 1) d\u00fczenlilik g\u00f6stermektedir.<\/p>\n\n\n\n

    Rassall\u0131k ile d\u00fczenlili\u011fi sorgulayan pek \u00e7ok kitap ve makale mevcuttur. Bu arada, bu fakirin eski bir makalesi de de\u011ferinin anla\u015f\u0131laca\u011f\u0131 g\u00fcnleri beklemektedir ki, oradaki kaynak listesinden de yararlan\u0131labilir. Bkz., arXiv:0710.2023<\/a>  veya https:\/\/arxiv.org\/abs\/0710.2023<\/a> veya https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129183108012261?srsltid=AfmBOorVP_A7R01Ec6OF6Lvfx2ssHnvlpelo8Iqsi3bMhoM55uC6WVSp<\/a><\/p>\n\n\n\n

    (*) Yerle\u015fke n\u00fcfuslar\u0131n\u0131n b\u00fcy\u00fckten k\u00fc\u00e7\u00fc\u011fe do\u011fru s\u0131ralanmas\u0131 (\u2018Rank Order\u2019) ile de ayn\u0131 sonuca ula\u015f\u0131labilir.<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    13. NOT<\/p>\n\n\n\n

    Ge\u00e7mi\u015fte de\u011finmi\u015f idik; Matematik\u2019ten \u2018=\u2019 i\u015faretini kald\u0131r\u0131n, geriye anlams\u0131z simgeler y\u0131\u011f\u0131n\u0131 kal\u0131r. Evren(nin bildi\u011fimiz yerlerin)de ise, e\u015fitlik yoktur. Hi\u00e7bir nesne ba\u015fka hi\u00e7bir nesneye e\u015fit de\u011fildir. (*) (**) (***) Atomlar veya temel par\u00e7ac\u0131k diye adland\u0131rd\u0131\u011f\u0131m\u0131z, \u00f6rne\u011fin elektronlar\u0131n ve hatta fotonlar\u0131n, pek \u00e7ok \u00f6zelli\u011fi pek \u00e7ok ba\u015fkalar\u0131yla ortak olsa bile, bu \u00f6zellikler onlar\u0131 e\u015fitlemeye yetmez. \u00d6rne\u011fin, k\u00fctleleri tam\u0131 tam\u0131na e\u015fit olan iki elektron bulamayaca\u011f\u0131m\u0131z gibi enerjileri tam\u0131 tam\u0131na e\u015fit iki foton da bulamay\u0131z. \u00c7\u00fcnk\u00fc, en az\u0131ndan, bu ama\u00e7la yap\u0131lm\u0131\u015f herhangi bir \u00f6l\u00e7\u00fcm bir ba\u015fka \u00f6l\u00e7\u00fcmle ayn\u0131 sonucu vermeyecektir. Bu saptama ziyadesiyle \u00f6nemlidir ama her ne hikmetse lay\u0131k oldu\u011fu de\u011fere sahip de\u011fildir hen\u00fcz.<\/p>\n\n\n\n

    (*) Her t\u00fcrl\u00fc genellemenin belirsizlik i\u00e7erdi\u011fi konusunu okuyucuya an\u0131msatmak isterim.<\/p>\n\n\n\n

    (**) Herhangi iki nesnenin herhangi iki \u00f6zelli\u011fi herhangi bir zaman aral\u0131\u011f\u0131nda t\u0131pat\u0131p ayn\u0131 olsa bile, sonraki zamanlarda bozunma yani temel par\u00e7ac\u0131k tepkimelerinden \u00f6t\u00fcr\u00fc bu ayn\u0131l\u0131k ortadan kalkacakt\u0131r. Ortadan kalkmam\u0131\u015f oldu\u011fu zamanlardan s\u00f6z ediyor olsak bile, iki nesneden s\u00f6z ediyor oldu\u011fumuz a\u00e7\u0131kt\u0131r. Bunlar birbirine e\u015fit olsa, iki nesneden s\u00f6z ediyor ol_A_mazd\u0131k.<\/p>\n\n\n\n

    Ayr\u0131ca, herhangi bir nesnenin \u00f6rne\u011fin bir elektron veya bir insan\u0131n kendisine e\u015fit olmas\u0131 bile ancak k\u0131s\u0131tl\u0131, s\u0131n\u0131rl\u0131 bir s\u00fcre i\u00e7in (\u2018temporal\u2019) ge\u00e7erli (tan\u0131ml\u0131) olacakt\u0131r.<\/p>\n\n\n\n

    (***) \u015eeytan i\u015fba\u015f\u0131nda ve okuyucunun akl\u0131na \u015fu konuyu d\u00fc\u015f\u00fcrm\u00fc\u015f olabilir: \u2018A=B ve B=C ise, A=C\u2019 \u00f6nermesi ile yukar\u0131daki ifadeler \u00e7eli\u015fir mi?<\/p>\n\n\n\n

    Hay\u0131r, \u00e7eli\u015fmez! Zira, dikkat ediniz, \u2018ise\u2019 ko\u015fulu vard\u0131r orada. Yani, \u201c\u2014A\u2019ya e\u015fit bir B ve B\u2019ye e\u015fit bir C bulabilir iseniz, A ve C e\u015fit olur.\u201d denmektedir.<\/p>\n\n\n\n

    Ayr\u0131ca, ilgili \u00f6nermede A’n\u0131n B’ye nas\u0131l e\u015fit olabilece\u011fi sorusu a\u00e7\u0131ktad\u0131r. <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    14. NOT<\/p>\n\n\n\n

    Varsayal\u0131m ki, elimizde, birbiriyle t\u0131pat\u0131p ayn\u0131 (atom, molek\u00fcl cins ve say\u0131lar\u0131 bile t\u0131pat\u0131p ayn\u0131) olan iki tane metal para var ve birbiriyle t\u0131pat\u0131p ayn\u0131 ko\u015fullarda (\u00f6rne\u011fin r\u00fczg\u00e2rs\u0131z, hava ak\u0131nt\u0131s\u0131z bir ortamda, ayn\u0131 k\u00fctle\u00e7ekim ivmesi alt\u0131nda, hep ayn\u0131 kuvvetle ve hep ayn\u0131 y\u00fcksekli\u011fe, vs.) f\u0131rlat\u0131l\u0131yor. Yani, her f\u0131rlat\u0131l\u0131\u015f bir di\u011feriyle t\u0131pat\u0131p ayn\u0131 diye varsayal\u0131m. Dahas\u0131, hep YAZI (Y) veya TURA(T) gelsin ama hi\u00e7bir seferde hi\u00e7bir para ince kenar\u0131 \u00fcst\u00fcne d\u00fc\u015f\u00fcp \u00f6ylece kalmas\u0131n. Bu ko\u015fullar alt\u0131nda Y ve T gelme olas\u0131l\u0131klar\u0131n\u0131n, at\u0131\u015f say\u0131s\u0131 artt\u0131k\u00e7a \u00bd\u2019ye yak\u0131nsayaca\u011f\u0131n\u0131 deneylerle biliyoruz.<\/p>\n\n\n\n

    Yine de, bu rassal olaylarda \u00f6rne\u011fin, Y ve ard\u0131ndan T; sonras\u0131nda ard\u0131 ard\u0131na iki kez Y ve sonras\u0131nda iki kez T; daha sonra da \u00fc\u00e7 ard\u0131\u015f\u0131k kez Y ve sonra da \u00fc\u00e7 ard\u0131\u015f\u0131k kez T gelmesi gibi \u2018d\u00fczenli\u2019 olaylara rastlanabilir. At\u0131\u015f say\u0131lar\u0131 artt\u0131k\u00e7a bir \u00fcst sat\u0131rda de\u011finilmi\u015f olan t\u00fcrden ve daha uzun s\u00fcrm\u00fc\u015f olan \u2018d\u00fczenli\u2019 olaylara da rastlanabilir. Hatta, b\u00f6ylesi \u2018d\u00fczenli\u2019 olaylar, at\u0131\u015flar\u0131n hemen ba\u015f\u0131nda da g\u00f6zlenebilir.<\/p>\n\n\n\n

    \u015eimdi de diyelim ki, bir Excel 30×30 matrisin h\u00fccrelerini \u2018=RASTGELEARADA(0;1000)\/1000\u2019 komutu ile \u00fcretilmi\u015f 0 ile 1 aras\u0131ndaki say\u0131larla doldurup Y\u00fczey (Kontur) grafi\u011fini elde ettik. B\u00f6ylesi grafikler, rassal say\u0131lara ba\u011fl\u0131 olarak de\u011fi\u015fikliler g\u00f6sterse de yerel d\u00fczenlilikler de i\u00e7erebilir, alttaki \u00f6rnekte incelenebilece\u011fi gibi.
    <\/p>\n\n\n\n

    \"\"<\/figure>
    \n

    <\/p>\n<\/div><\/div>\n\n\n\n

    \u015eimdi de, say\u0131 eksenini yukar\u0131daki gibi be\u015f de\u011fil de on e\u015fit b\u00f6l\u00fcme ay\u0131ral\u0131m. Hemen alttaki gibi bir da\u011f\u0131l\u0131m elde edilecektir.<\/p>\n\n\n\n

    \"\"<\/a><\/figure>\n\n\n\n

    Say\u0131 eksenini yirmi e\u015fit b\u00f6l\u00fcmle g\u00f6sterecek olursak matrisimiz hemen alttaki bi\u00e7ime d\u00f6n\u00fc\u015f\u00fcr.<\/p>\n\n\n\n

    \"\"<\/figure>
    \n

    <\/p>\n<\/div><\/div>\n\n\n\n

    \u015eu \u00e7\u0131karsamaya kat\u0131l\u0131r m\u0131s\u0131n\u0131z acaba? Rassall\u0131k i\u00e7inde d\u00f6nem d\u00f6nem ve yerel olarak d\u00fczenlilikler ortaya \u00e7\u0131kabilir.<\/p>\n\n\n\n

    Yukar\u0131da k\u0131saca de\u011findi\u011fimiz \u2018Random Pixel\u2019 konusunda \u015fu kaynaklar\u0131 \u00f6nerebilirim.<\/p>\n\n\n\n

    https:\/\/www.jstor.org\/action\/doBasicSearch?Query=Random+Pixel&so=rel<\/a><\/p>\n\n\n\n

    https:\/\/arxiv.org\/search\/?query=Random+Pixel&searchtype=all&source=header<\/a><\/p>\n\n\n\n

    https:\/\/arxiv.org\/abs\/physics\/0612136<\/a>    Opinion Crystallography: Polarizations, Symmetries, Bonds, and Bands Authors: Caglar Tuncay<\/a><\/p>\n\n\n\n

    Abstract: May randomness (real numbers, opinions) evolve into order (regularity) with time? We study some polarization and symmetry properties, which emerge in time evolution of opinions (real numbers) within entries of two and three-dimensional lattices, which had initial randomness.<\/p>\n\n\n\n

    15. NOT<\/p>\n\n\n\n

    Bilindi\u011fi gibi, atoma ba\u011fl\u0131 bir elektronun ba\u015fka herhangi bir yerde bulunma olas\u0131l\u0131\u011f\u0131 aradaki uzakl\u0131\u011f\u0131n karesi ile ters orant\u0131l\u0131d\u0131r ve dolay\u0131s\u0131yla asla s\u0131f\u0131r olmaz. ABD ba\u015fkanlar\u0131ndan John Fitzgerald Kennedy\u2019nin iddia edildi\u011fi gibi \u2018iki mermiden sekiz yara a\u00e7\u0131larak\u2019 ya da \u2018sihirli kur\u015fun\u2019 ile \u00f6ld\u00fcr\u00fcl\u00fc\u015f\u00fcn\u00fcn m\u00fcmk\u00fcn oldu\u011fu da elektronun o \u00f6zelli\u011fine dayand\u0131r\u0131lm\u0131\u015ft\u0131. (*)<\/p>\n\n\n\n

    Bu ba\u011flamda, bir \u00fcst nottaki 30×30 matrisin meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayal\u0131m: Bu matrisin her h\u00fccresindeki say\u0131 \u2018=RASTGELEARADA(0;1000)\/1000\u2019 komutu ile \u00fcretilmi\u015f oldu\u011fu i\u00e7in, 1\/1000=10-3<\/sup> olas\u0131l\u0131kla ger\u00e7ekle\u015fme olana\u011f\u0131na sahiptir. Bu t\u00fcreden say\u0131 i\u00e7eren 30×30=900 h\u00fccre var oldu\u011funa g\u00f6re, bir \u00fcst nottaki 30×30 matrisin meydana gelme olas\u0131l\u0131\u011f\u0131 10-3<\/sup>\/ 900 yani yakla\u015f\u0131k olarak 10-6<\/sup> ya da s\u00f6zc\u00fcklerle ifade edecek olursak, yakla\u015f\u0131k milyonda birdir.<\/p>\n\n\n\n

    \u0130lgili matrisin boyutunu, N bir pozitif tam say\u0131 olmak ko\u015fuluyla NxN olarak g\u00f6sterip her h\u00fccre i\u00e7indeki ondal\u0131k say\u0131n\u0131n noktadan sonraki basamak say\u0131s\u0131n\u0131 yine bir pozitif tam say\u0131 olan n ile g\u00f6sterirsek; s\u00f6z konusu matrisin meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 \u015f\u00f6ylece hesaplayabiliriz; 10-n<\/sup> \/(NxN).<\/p>\n\n\n\n

    Bu durumda, \u00f6rne\u011fin noktadan sonra 6 basamakl\u0131 ondal\u0131k say\u0131lardan olu\u015fan 100×100 b\u00fcy\u00fckl\u00fc\u011f\u00fcndeki bir matrisin meydana gelme olas\u0131l\u0131\u011f\u0131 10-10<\/sup> (= 10-6<\/sup> \/(100×100) ) olacakt\u0131r.<\/p>\n\n\n\n

    (*) Bkz. alttaki filmin, filmin saatiyle 2:46:00 ve 2:51:00 dolay\u0131 ve baz\u0131 ba\u015fka enstantaneleri.<\/p>\n\n\n\n

    https:\/\/www.google.com\/search?q=jfk+film+izle&sca_esv=cff81f964af1e5d4&udm=7&biw=1920&bih=955&sxsrf=AHTn8zqU5wiWJWevCefWf9ctWSGHk1iscg%3A1745567950767&ei=zkALaKPOLtyTxc8Pm630KA&ved=0ahUKEwij7Yut2_KMAxXcSfEDHZsWHQUQ4dUDCBE&uact=5&oq=jfk+film+izle&gs_lp=EhZnd3Mtd2l6LW1vZGVsZXNzLXZpZGVvIg1qZmsgZmlsbSBpemxlMgUQABiABDIFEAAYgAQyBhAAGBYYHjIIEAAYgAQYogRIrxtQ0QhY8BZwAXgAkAEAmAFyoAHvBKoBAzEuNbgBA8gBAPgBAZgCBqACrgTCAgYQABgHGB7CAgoQABiABBhDGIoFwgIJEAAYBxjHAxgewgIEEAAYHsICCBAAGBYYChgemAMAiAYBkgcDMS41oAenGrIHAzAuNbgHowQ&sclient=gws-wiz-modeless-video#fpstate=ive&vld=cid:24898509,vid:NfAkeuLPCBg,st:0<\/a><\/p>\n\n\n\n

    16. NOT<\/p>\n\n\n\n

    Diyelim ki, bir Excel 30×30 matrisini \u2018=RASTGELEARADA(0;1000)\/1000\u2019 komutu ile \u00fcretilmi\u015f say\u0131larla doldurduk. \u0130\u015fbu A(30,30) matrisini 90 elemanl\u0131 ve i\u00e7inde tesad\u00fcf\u00ee (\u2018occasional\u2019) d\u00fczenlilik(ler)  i\u00e7eren iki boyutlu (2D) bir evren olarak varsayabiliriz. Bu evrenin, Efes\u2019li topra\u011f\u0131m\u0131z Heraklit\u2019e atfedilen \u2018Panta Rhei\u2019 (*) ilkesine \u00f6rnek te\u015fkil edecek bi\u00e7imde zamanla B(30,30) 2D evrenine evrilece\u011fini de varsayal\u0131m.<\/p>\n\n\n\n

    Dikkatli okuyucu fark etmi\u015f olmal\u0131 ki, A(30,30) ve B(30,30) matrisindeki say\u0131lar Benze\u015fik Da\u011f\u0131l\u0131m (\u2018Homogenous Distribution\u2019) g\u00f6sterir. Ama, her say\u0131y\u0131 o say\u0131n\u0131n de\u011ferinden ba\u011f\u0131ms\u0131z olarak herhangi bir varl\u0131k olarak, yani herhangi bir varl\u0131\u011f\u0131 temsil etti\u011fini (\u2018representation\u2019) varsayabiliriz.<\/p>\n\n\n\n

    Bir 2D rassal evrenimiz olan A(30,30) matrisimizin B(30,30)\u2019a d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc elemanlar\u0131 zamana ba\u011fl\u0131 bir O(30,30) matrisi kullanarak \u015f\u00f6ylece g\u00f6sterebiliriz;<\/p>\n\n\n\n

    B(30,30) = O(30,30)*A(30,30)<\/p>\n\n\n\n

    Yukar\u0131daki e\u015fitlikte matris \u00e7arp\u0131m\u0131 yer almay\u0131p y\u0131ld\u0131z i\u015fareti A(30,30) matrisi \u00fcst\u00fcnde operasyon (d\u00f6n\u00fc\u015ft\u00fcr\u00fcc\u00fc) yap\u0131ld\u0131\u011f\u0131n\u0131 belirtmektedir.<\/p>\n\n\n\n

    A(30,30)\u2019un B(30,30)\u2019a d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn do\u011frusal (\u2018linear\u2019) oldu\u011funu varsayal\u0131m. Bu demektir ki, A\u2192B d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn \u00e7ok yava\u015f ilerledi\u011fini varsayd\u0131k. (**)<\/p>\n\n\n\n

    Bu s\u00f6zleri bir ba\u015fka dil olan Matematik\u00e7e ifade edecek olursak, 0 ile 1 aras\u0131ndaki (0 ile 1 d\u00e2hil) de\u011ferler alabilen t de\u011fi\u015fkeni kullanarak \u015f\u00f6yle yazabiliriz;<\/p>\n\n\n\n

    B(I,J) = t(B(I,J)-A(I,J)) + A(I,J) .<\/p>\n\n\n\n

    B\u00f6ylece, t=0 i\u00e7in A(30,30) matrisinden t=1 i\u00e7in (B30,30) matrisi elde edilebilir.<\/p>\n\n\n\n

    Alttaki grafiklerde, t=0, t=1\/3, t=2\/3 ve t=1 i\u00e7in A\u2192B d\u00f6n\u00fc\u015f\u00fcm\u00fc \u00f6rneklenmi\u015ftir.<\/p>\n\n\n\n

    \"\"<\/a><\/figure>\n\n\n\n

    \u0130lgili d\u00f6n\u00fc\u015f\u00fcm\u00fcn her a\u015famas\u0131nda ortaya \u00e7\u0131kan d\u00fczenlilikler incelenebilir. Bunlar\u0131n ancak k\u0131s\u0131tl\u0131, s\u0131n\u0131rl\u0131 bir b\u00f6lgede ve k\u0131s\u0131tl\u0131, s\u0131n\u0131rl\u0131 bir s\u00fcre i\u00e7in (\u2018temporal\u2019) var olabildikleri dikkat \u00e7ekicidir. Ayr\u0131ca, A\u2192B d\u00f6n\u00fc\u015f\u00fcm\u00fc i\u00e7in daha \u00e7etrefilli \u00f6rne\u011fin Normal Da\u011f\u0131l\u0131m g\u00f6steren d\u00f6n\u00fc\u015ft\u00fcr\u00fcc\u00fcler de kullan\u0131labilir.<\/p>\n\n\n\n

    Yukar\u0131daki a\u00e7\u0131klamadaki A ve B matrisleri g\u00f6\u00e7 eden bir insan toplulu\u011funun dilindeki de\u011fi\u015fmeleri modellemekte gayet yararl\u0131 olacakt\u0131r. \u00d6rne\u011fin, A(30,30) matrisi 900 s\u00f6zc\u00fckl\u00fc bir dil olarak varsay\u0131labilir. Her h\u00fccredeki say\u0131, de\u011ferinden ba\u011f\u0131ms\u0131z olarak bir s\u00f6zc\u00fck veya gramer kural\u0131n\u0131 temsil eder. Topluluk g\u00f6\u00e7 edip yeni insan topluluklar\u0131yla etkile\u015ferek dili, s\u00f6zc\u00fck ve o s\u00f6zc\u00fcklerin kullan\u0131m kurallar\u0131yla birlikte de\u011fi\u015febilir zamanla. Bu da gayet g\u00fczel, iyi bir dergide bas\u0131labilir makale demektir. B\u00f6yle bir makaleyi ben yapmayaca\u011f\u0131m. Yapmaya istekli(ler) \u00e7\u0131kaca\u011f\u0131 umuduyla, o \u00e7aba i\u00e7in kolayl\u0131k ve ba\u015far\u0131lar dilerim.<\/p>\n\n\n\n

    A\u00e7\u0131kt\u0131r ki, dil evrimi gibi biyolojik evrimler de yukar\u0131daki yakla\u015f\u0131m alt\u0131nda modellenebilir ve do\u011frusal evrim modeli yerine Normal Da\u011f\u0131l\u0131m (Gauss Da\u011f\u0131l\u0131m\u0131) g\u00f6steren de\u011fi\u015fimler ve hatta \u00e7e\u015fitli kom\u015fuluk etkile\u015fimleri i\u00e7eren Kan\u0131 Dinami\u011fi (\u2018Opinion Dynamics\u2019) y\u00f6ntemleri kullan\u0131labilir.<\/p>\n\n\n\n

    (*) Bkz., son paragraf; https:\/\/tr.wikipedia.org\/wiki\/Kilikyal%C4%B1_Simplikios<\/a><\/p>\n\n\n\n

    (**) Bkz, https:\/\/en.wikipedia.org\/wiki\/Power_series<\/a> Ayr\u0131ca; https:\/\/en.wikipedia.org\/wiki\/Taylor_series<\/a> ve https:\/\/en.wikipedia.org\/wiki\/Colin_Maclaurin<\/a><\/p>\n\n\n\n

    17. NOT<\/p>\n\n\n\n

    Bir Excel 30×30 matrisini \u2018=RASTGELEARADA(0;1000)\/1000\u2019 komutu ile \u00fcretilmi\u015f say\u0131larla doldural\u0131m. Bu matris, bildi\u011fimiz ve bilmedi\u011fimiz b\u00f6l\u00fcmleriyle, evrenimizi temsil etsin. Ayr\u0131nt\u0131l\u0131 olarak modelimiz \u015fudur: 1) Evren, \u015fu an bildi\u011fimizden \u00e7ok daha b\u00fcy\u00fck ve \u00e7ok daha ya\u015fl\u0131d\u0131r. 2) Biz ancak 46 milyar \u0131\u015f\u0131k y\u0131l\u0131 yar\u0131\u00e7apl\u0131 bir b\u00f6l\u00fcm\u00fcn\u00fc g\u00f6zlemleyebiliyoruz. Bu b\u00f6l\u00fcm\u00fcn de yakla\u015f\u0131k 14 milyar ya\u015f\u0131nda oldu\u011funu tahmin ediyoruz. 3) Evrenin de\u011fi\u015fik yerlerindeki d\u00fczenlilikler ve d\u00fczensizlikler zamanla de\u011fi\u015fip birbirine d\u00f6n\u00fc\u015febilir veya yepyeni bi\u00e7imlere evrilebilir. Bu d\u00f6n\u00fc\u015f\u00fcmlerin temel dinami\u011fini (\u2018underlying dynamics\u2019, \u2018fundamental mechanism\u2019) bilmiyoruz. 4) Dolay\u0131s\u0131 ile, bildi\u011fimiz evren b\u00f6l\u00fcm\u00fcndekilere benzemeyen d\u00fczenliliklere sahip b\u00f6l\u00fcmlerle ku\u015fat\u0131lm\u0131\u015f olabiliriz. Bu b\u00f6l\u00fcmlere de Karanl\u0131k Madde (\u2018Dark Matter\u2019) diyoruz. (*) 5) Evrenin birbirinden \u00e7ok uzak baz\u0131 b\u00f6l\u00fcmlerinde, yani Karanl\u0131k Madde ile dolu b\u00f6l\u00fcmlerin \u00f6tesinde, bizimkilere benzer d\u00fczenlilikler var olabilir.<\/p>\n\n\n\n

    \u0130lgili benzetimi (\u2018simulation\u2019) \u015fu \u015fekilde kurabiliriz. Ba\u015flarken s\u00f6z\u00fcn\u00fc etti\u011fimiz matriste, i\u00e7erdi\u011fi say\u0131 0,495 ile 0,505 olan h\u00fccrelerden birinde ya\u015fad\u0131\u011f\u0131m\u0131z\u0131 var sayal\u0131m. Di\u011fer b\u00f6l\u00fcmleri, Karanl\u0131k Madde olarak niteleyelim. Sonu\u00e7, benzetimden benzetime yani farkl\u0131 evren zamanlar\u0131n\u0131 temsilen de\u011fi\u015fiklik g\u00f6sterecektir. Alttaki grafikte, bunlardan sadece rasgele se\u00e7ilmi\u015f bir tanesi \u00f6rneklenmi\u015ftir.<\/p>\n\n\n\n

    \"\"<\/a><\/figure>\n\n\n\n

    (*) Alttaki kaynaklar yararl\u0131 olabilir.<\/p>\n\n\n\n

    \nhttps:\/\/www.jstor.org\/action\/doBasicSearch?Query=dark+matter&so=rel\n<\/div><\/figure>\n\n\n\n
    \nhttps:\/\/arxiv.org\/search\/?query=dark+matter&searchtype=all&abstracts=show&order=-announced_date_first&size=50\n<\/div><\/figure>\n\n\n\n
    \nhttps:\/\/tr.wikipedia.org\/wiki\/Karanl%C4%B1k_madde\n<\/div><\/figure>\n\n\n\n
    \nhttps:\/\/tr.wikipedia.org\/wiki\/Karanl%C4%B1k_madde#\/media\/Dosya:UniverseComposition.svg\n<\/div><\/figure>\n\n\n\n


    18. NOT<\/p>\n\n\n\n

    Say\u0131 sistemi, \u00f6zellikle Antik Hindistanl\u0131, Antik Mezopotamyal\u0131 ve Nil \u00e7evresindeki antik kavimlerin katk\u0131s\u0131yla geli\u015ftik\u00e7e, \u2018En b\u00fcy\u00fck say\u0131 nedir?\u2019 sorusu \u00f6nem kazanmaya ba\u015flad\u0131. Daha sonralar\u0131 Antik Grekler ve onlar\u0131n hegemonyas\u0131nda ya\u015fayan bilgeler \u2018en b\u00fcy\u00fck say\u0131\u2019y\u0131 temsilen Grek Alfabesi\u2019nin son harfi olan omega \u2018\u03c9\u2019 harfini kullan\u0131r oldular. Zamanla da, \u03c9\u2019n\u0131n iki ucu merkez \u00e7\u0131k\u0131nt\u0131s\u0131yla birle\u015ftirilerek \u221e olu\u015fturuldu. Antik Grek\u00e7e\u2019de \u221e simgesi \u2018aperion\u2019 yani \u2018s\u0131n\u0131rland\u0131r\u0131lamayan\u2019 anlam\u0131nda kullan\u0131lmaktayd\u0131.<\/p>\n\n\n\n

    Gelgelelim, \u221e\u2019u bir say\u0131 imi\u015f\u00e7esine matematikte ilk kullananlar bizim eski g\u00f6z a\u011fr\u0131lar\u0131m\u0131z Alea\u2019l\u0131 Parmenides ve Zeno\u2019dur (M.\u00d6. 500 dolay\u0131). Sad\u0131k okuyucular\u0131m\u0131z an\u0131msayacakt\u0131r; hani, kaplumba\u011fa ile A\u015fil aras\u0131ndaki mesafe hep yar\u0131lanacakt\u0131 ya, bu nedenle i\u015fte! Neyse, Zeno\u2019dan en az 2500 y\u0131l sonra bug\u00fcn bile \u221e\u2019un anlam\u0131 a\u00e7\u0131k, se\u00e7ik ve kesin de\u011fildir. \u00d6rne\u011fin, \u2018finite\u2019 a\u00e7\u0131k, se\u00e7ik ve kesin olarak bellidir de onun z\u0131dd\u0131 olan \u2018infinite\u2019 hayli mu\u011flakt\u0131r. \u00c7\u00fcnk\u00fc en az\u0131ndan; Tam Say\u0131 m\u0131, \u00c7ift Say\u0131 m\u0131, Tek Say\u0131 m\u0131, Ger\u00e7ek Say\u0131 m\u0131 belli de\u011fildir ama bunlar\u0131n hepsi ve \u00e7ok daha fazlas\u0131 i\u00e7in kullan\u0131lmaktad\u0131r Matematik\u2019te.<\/p>\n\n\n\n

    Kullan\u0131ls\u0131n, ne gam! Matematik \u015fiir gibidir ve \u00f6zg\u00fcrl\u00fck alan\u0131 \u015fiirinkinden daha dar de\u011fildir. Ama, i\u015f gelip de \u221e\u2019in Fizik\u2019te kullan\u0131l\u0131\u015f\u0131na dayan\u0131nca, ortal\u0131k kar\u0131\u015f\u0131yor ka\u00e7\u0131n\u0131lmaz olarak. Bir kuvantum dalgas\u0131n\u0131n frekans\u0131 f, Planck sabiti h ise, enerjisi hf olur da, \u221ehf ne anlama gelir? Sonsuz b\u00fcy\u00fck enerji mi? Evrende yok ki sonsuz b\u00fcy\u00fck enerji. O halde, Maxwell, Boltzmann ve Einstein hangi akla hizmeten kullanm\u0131\u015f olabilirler denklemlerinde n\u2192\u221e i\u00e7in nhf ifadesini? <\/p>\n\n\n\n

    \u2018\u2014\u00c7aresizlikten!\u2019 diye i\u00e7 ge\u00e7irenler! Evet, ben de ayn\u0131 kan\u0131day\u0131m! Boltzmann sabiti k ve s\u0131cakl\u0131k T (\u2190her nas\u0131l \u00f6l\u00e7\u00fcld\u00fc ise) i\u00e7in, \u2211n=0<\/sub>exp(\u2013nhf\/kT) toplam\u0131n\u0131 hangi (b\u00fcy\u00fck, b\u00fcy\u00fck, b\u00fcy\u00fck, \u2026) n de\u011ferinde kesmek uygun olur acaba, \u221e\u2019da de\u011filse? Ne yaz\u0131k ki, hi\u00e7bir kar\u015f\u0131l\u0131k bulamazs\u0131n\u0131z bu soruya ili\u015fkin olarak, ilgili Fizik literat\u00fcr\u00fcnde.<\/p>\n\n\n\n

    \u00c7ok tuhaf! De\u011fil mi? Bunca Matematik\u00e7i ve Fizik\u00e7i, \u00e7aresizlik kar\u015f\u0131s\u0131nda boyun b\u00fck\u00fcp tan\u0131ms\u0131z \u221e\u2019\u0131 kullan\u0131p durmak konusunda tam bir mutabakata (oyda\u015fma, \u2018concensus\u2019) varm\u0131\u015flar.<\/p>\n\n\n\n

    \u0130\u015fte, insan zek\u00e2s\u0131n\u0131n b\u00f6ylesi \u00e7aresiz oldu\u011fu durumlar say\u0131lmaya kalk\u0131\u015f\u0131lsa sahifeler t\u00fckenir! Ama ill\u00e2 da ba\u015fka bir \u00f6rnek vermek gerekirse, Matematik ve Fizik\u2019ten hayli uzak bir alan se\u00e7elim. Biliyorsunuz, hukukta, yarg\u0131da \u201cBu yapt\u0131\u011f\u0131m\u0131n (eylemin) su\u00e7 oldu\u011funu bilmiyordum!\u201d demeye hakk\u0131 yoktur zanl\u0131n\u0131n. Ama, \u00e7o\u011fu zaman da avukat da, savc\u0131 da, yarg\u0131\u00e7 da eskiden tu\u011fla tu\u011fla kal\u0131nl\u0131\u011f\u0131ndaki \u2018kara kapl\u0131 kitaplar\u0131\u2019 ya da g\u00fcn\u00fcm\u00fczde \u2018cigabayt cigabayt\u2019 hacimlerindeki ekranlar\u0131 kola\u00e7an etmeksizin s\u00f6z konusu eylemin su\u00e7 olup olmad\u0131\u011f\u0131n\u0131 tespit edemezler. Zanl\u0131n\u0131n \u2018Bilmiyordum.\u201d demeye hakk\u0131 yoktur ama savc\u0131 da, yarg\u0131\u00e7 da bilmiyor olabilir pek al\u00e2. E, peki, ni\u00e7in b\u00f6yledir acep?<\/p>\n\n\n\n

    \u2018\u2014\u00c7aresizlikten!\u2019 diye i\u00e7 ge\u00e7irenler! Evet, ben de ayn\u0131 kan\u0131day\u0131m!<\/p>\n\n\n\n

    Benzer bir \u00e7aresizlik de Heraklit\u2019e atfedilen \u2018\u2014Her \u015fey de\u011fi\u015fir!\u2019 ifadesine ili\u015fkin olarak kar\u015f\u0131m\u0131za \u00e7\u0131kar.<\/p>\n\n\n\n

    Devam\u0131, bir sonraki 19. NOT\u2019da yer alacak.<\/p>\n\n\n\n

    19. NOT<\/p>\n\n\n\n

    Efendim! Derler ki, exp(-nhf\/kT) ifadesi n\u2192\u221e i\u00e7in nhf=En<\/sub>\u2192\u221e bile, exp(-nhf\/kT)\u21920. Dolay\u0131s\u0131 ile \u2018Nema problema!\u2019 diyerek rahatlarlar.
    \u0130yi ho\u015f da, herhangi bir Do\u011fal Say\u0131 i\u00e7in En<\/sub> de\u011ferinin var olmas\u0131 k\u00fc\u00e7\u00fck de olsa s\u0131f\u0131rdan b\u00fcy\u00fck bir olas\u0131l\u0131\u011fa sahiptir. \u2018Olas\u0131l\u0131k\u2019 deyimi olabilirlik ile e\u015fde\u011ferdir. Yani, ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 ne denli k\u00fc\u00e7\u00fck olursa olsun ama s\u0131f\u0131r de\u011filse, bu olay ger\u00e7ekle\u015febilir. Yani, En<\/sub>\u2192\u221e olas\u0131l\u0131\u011f\u0131n\u0131 varsaymaktalar. Bu bir! \u0130kincisi de, be\u015f on graml\u0131k bir, diyelim ki, Bak\u0131r veya \u00c7inko k\u00fctlesinin i\u00e7inde en \u00e7ok hangi b\u00fcy\u00fckl\u00fckte enerji var olabilir ki, En<\/sub>\u2192\u221e olsun?
    Yani, \u0131s\u0131 s\u0131\u011fas\u0131 hesaplanmaya \u00e7al\u0131\u015f\u0131lan k\u00fctle i\u00e7indeki \u2018microcanonical ensemble\u2019 (*) nas\u0131l olur da a\u015f\u015f\u0131r\u0131 y\u00fcksek enerji de\u011ferlere sahip \u2018state\u2019leri ziyaret edebilir? Yani, nas\u0131l olur da sahip olmad\u0131\u011f\u0131 kadar enerjiye sahipmi\u015f gibi davranabilir herhangi bir malzeme?<\/p>\n\n\n\n

    (*)https:\/\/en.wikipedia.org\/wiki\/Maxwell%E2%80%93Boltzmann_distribution<\/a><\/p>\n\n\n\n

    Ayr\u0131ca; https:\/\/en.wikipedia.org\/wiki\/Einstein_solid<\/a><\/p>\n\n\n\n

    Devam\u0131, bir sonraki 20. NOT\u2019da yer alacak.<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    20. NOT<\/p>\n\n\n\n

    S\u00fcr\u00fc davran\u0131\u015f\u0131 (\u2018herding mechanism, behavior\u2019) Fizik\u2019te de ge\u00e7erli midir?<\/p>\n\n\n\n

    \nhttps:\/\/www.google.com\/search?sca_esv=23e5dd8d03570428&sxsrf=AHTn8zqUfL8OuWwXFK7pXLNcilIvGE3AKQ:1745998243237&q=ku%C5%9F+s%C3%BCr%C3%BCleri&udm=7&fbs=ABzOT_ANQSxQXwgpo-v8UE65NH2rosaQVKZfWxB2sCgzLp7hZaMFF2YhCkQEeStLT4tndKnyo5pL12bDJDw9mylZknd6nFVFGIm0bfZN90OveRFNP2zY6-CRGC-AqcEkXuGF5-TZPTzOrajic7cwET-ejQXslG2Umg8bZmpFHof-LSjrfN1GkkUWa4F7ZG0h6O5onYdjlgrfdp7g0rkt-O3ZjtHQb1_xjTWOkyISmz-KaMi9zxxD0oJG_bLmyC46xmSgAWrhkZww&sa=X&ved=2ahUKEwj_-8Oonv-MAxVjQ_EDHTCaOPIQtKgLegQIDhAB&biw=1920&bih=955&dpr=1#fpstate=ive&vld=cid:46ed34ca,vid:tsONUUziaYE,st:0\n<\/div><\/figure>\n\n\n\n
    \nhttps:\/\/www.google.com\/search?sca_esv=23e5dd8d03570428&sxsrf=AHTn8zrbuNGlA9WlI4vd4ttFHxIY8EnTYQ:1745999206064&q=kar%C4%B1nca+k%C3%B6pr%C3%BCs%C3%BC&udm=7&fbs=ABzOT_DOzhXos0d24-KHXxKLp9il-mIbXbLhcsEeFvPrrJvYIE-xgSxoWpz9vBaiKMcqHBZJxN-tX44sQSE0jmwJbwIHefgy0jHoaRbpnPcGCE5105jpy5uzvkpzucd61HvPAPuEG964e2sZPLwO4cP2KGVQw4J1yKvnx9c-XionQYWQFQGzo3fszNUUOQXR5J-cIrGH4MwWooRWHlE3A-aj1LTnnSapv743BCQDivWWdxeeqyqgLizsCmKgeM2Oa8L5LdpHL1CS&sa=X&ved=2ahUKEwjcnNLzof-MAxWCBNsEHf4qO4MQtKgLegQIGhAB&biw=1920&bih=955&dpr=1\n<\/div><\/figure>\n\n\n\n
    \nhttps:\/\/en.wikipedia.org\/wiki\/Herd_behavior\n<\/div><\/figure>\n\n\n\n
    \nhttps:\/\/arxiv.org\/search\/?query=herding+mechanism&searchtype=all&source=header\n<\/div><\/figure>\n\n\n\n
    \nhttps:\/\/arxiv.org\/search\/?query=herding+behavior&searchtype=all&source=header\n<\/div><\/figure>\n\n\n\n

    Devam\u0131, bir sonraki 21. NOT\u2019da yer alacak.<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    21. NOT<\/p>\n\n\n\n

    D\u00f6ne dola\u015fa gelip yine Parmenides ile Zeno\u2019yla ve dolay\u0131s\u0131yla Zeno \u2018Paradoks\u2019lar\u0131yla ilgileni\u015fimiz, insan zek\u00e2s\u0131 ile ilgileni\u015fimiz sebebiyledir.<\/p>\n\n\n\n

    Bak\u0131n\u0131z, \u00f6rne\u011fin, Zeno\u2019nun hayali bir uzakl\u0131\u011f\u0131 b\u00f6le b\u00f6le hareketin olmad\u0131\u011f\u0131na ikna edi\u015f giri\u015fiminin kendisi yahut dinleyen \u00fczerinden de\u011fil de uzaktaki bir kaplumba\u011fa ile A\u015fil \u00fczerinden anlat\u0131\u015f\u0131 kurgulay\u0131\u015f\u0131 harika bir zek\u00e2 \u00f6rne\u011fi de\u011fil midir? Bu tam bir b\u00fcy\u00fcd\u00fcr. Ayn\u0131 anlat\u0131y\u0131 s\u00f6zel veya mental bir vir\u00fcs olarak nitelemek de uygundur.<\/p>\n\n\n\n

    Zira, kendi \u00fcst\u00fcnden anlat\u0131yor gibi \u201c\u2014Ben \u00f6n\u00fcmdeki bir kaplumba\u011faya yeti\u015femem. \u00c7\u00fcnk\u00fc, oraya eri\u015fmezden evvel yolun yar\u0131s\u0131na, o yar\u0131ya eri\u015fmezden evvel de bu yolun yar\u0131s\u0131na eri\u015fmem gerekir. Ama, daha \u00f6nce de \u2026\u201d diye ba\u015flam\u0131\u015f olsa, kar\u015f\u0131s\u0131ndaki dudak b\u00fck\u00fcp, burun k\u0131v\u0131r\u0131r ve \u2018Bana ne senin ne yap\u0131p yapamayaca\u011f\u0131ndan.\u2019 diye d\u00fc\u015f\u00fcnmesi normal olurdu.<\/p>\n\n\n\n

    Yahut da dinleyen \u00fcst\u00fcnden anlatmaya ba\u015flam\u0131\u015f olsayd\u0131; \u201c\u2014Bak! Sen \u00f6n\u00fcndeki \u015fu kaplumba\u011faya yeti\u015femezsin. \u00c7\u00fcnk\u00fc, oraya eri\u015fmezden evvel yolun yar\u0131s\u0131na, o yar\u0131ya eri\u015fmezden evvel de bu yolun yar\u0131s\u0131na eri\u015fmen gerekir. Ama, daha \u00f6nce de \u2026\u201d diye ba\u015flam\u0131\u015f olsa kar\u015f\u0131s\u0131ndaki dudak b\u00fck\u00fcp, burun k\u0131v\u0131r\u0131r ve yan\u0131t vermesine gerek olmaks\u0131z\u0131n kaplumba\u011faya do\u011fru y\u00fcr\u00fcr giderdi tahminen.<\/p>\n\n\n\n

    Ama, bir hay\u00e2l kurdurtup, A\u015fil ve bir kaplumba\u011fa hay\u00e2li kurdurtup, bu hay\u00e2l \u00fcst\u00fcnden hay\u00e2li bir mesafeyi ha babam de babam b\u00f6ld\u00fcrtmesi, bu sayede insan zek\u00e2s\u0131n\u0131 at\u0131l b\u0131rakmas\u0131, kilitlemesi, \u015fahanenin fevkinde bir zek\u00e2, bir b\u00fcy\u00fc, bir mental vir\u00fcs \u00f6rne\u011fi de\u011fil midir?<\/p>\n\n\n\n

    \u015eunu da teslim etmek gerekir ki, \u221e konusunda Zeno ve hocas\u0131 pek de su\u00e7lu de\u011fil asl\u0131nda. Hadi onlar \u00f6nerdi, (biz) di\u011ferleri ni\u00e7in kabullendi(k)? Simgesinin olu\u015fu bir, bir de ikinci olarak, kavramas\u0131 hayli m\u00fc\u015fk\u00fcl olan (ucu, sonu a\u00e7\u0131k) sonsuzlu\u011fu \u221e simgesi ile adeta sonland\u0131r\u0131lm\u0131\u015f olu\u015fu sebebiyle! De\u011fil mi? Hani, t\u00fcmcelerenin sonuna nokta konulmas\u0131 gibi. T\u0131pk\u0131, nokta konmadan c\u00fcmlenin sonland\u0131r\u0131lmay\u0131\u015f\u0131 gibi. (*)

    (*) Denemesi bedava! Herhangi bir metni al\u0131n, b\u00fcy\u00fck harfleri k\u00fc\u00e7\u00fckleriyle de\u011fi\u015ftirin ve nokta, soru i\u015fareti ve \u00fcnlemleri silin. Bak\u0131n bakal\u0131m o metinden ne kalm\u0131\u015f geriye, anla\u015f\u0131l\u0131r olarak?<\/p>\n\n\n\n

    Devam\u0131, bir sonraki 22. NOT\u2019da yer alacak.<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    22. NOT<\/p>\n\n\n\n

    \u0130lk yaz\u0131m\u0131z BA\u015eLAYI\u015e\u2019dan (*) bu yana demek istiyoruz ki, \u201c\u2014Evreni anlamakta insanl\u0131k hayli yetersiz, yanl\u0131\u015f anlamakta ise gayet mahir!\u201d<\/p>\n\n\n\n

    \u00d6rne\u011fin 2500 y\u0131l \u00f6nceki Elea\u2019l\u0131 Parmenides ve \u00f6\u011frencisi Zeno\u2019ya atfedilen g\u00f6r\u00fc\u015f (iddia, hipotez, kuram) \u2018Evrende hareket yoktur ama biz insanlar varm\u0131\u015f gibi san\u0131yoruz (alg\u0131l\u0131yoruz).\u2019 demekteydi.<\/p>\n\n\n\n

    \u0130ddia ola\u011fan\u00fcst\u00fc b\u00fcy\u00fckt\u00fc elbet inand\u0131r\u0131c\u0131l\u0131\u011f\u0131 (=kand\u0131r\u0131c\u0131l\u0131\u011f\u0131) da o denli b\u00fcy\u00fck oldu; 2500 y\u0131ld\u0131r unutulmad\u0131. Kimilerine g\u00f6re de \u2018hen\u00fcz \u00e7\u00fcr\u00fct\u00fclemedi\u2019 o \u2018paradokslar\u2019.<\/p>\n\n\n\n

    Ger\u00e7ekten de o tabloyu kavramak, biz 2025\u2019liler (bug\u00fcnl\u00fcler) i\u00e7in hi\u00e7 mi hi\u00e7 kolay de\u011fil. Zira, s\u00fcrekli hareket (devinim) h\u00e2lindeki insanlar\u0131n bu h\u00e2li yok say\u0131p k\u0131m\u0131lt\u0131s\u0131z olduklar\u0131n\u0131 sanmas\u0131 \u00e7ok b\u00fcy\u00fck, \u00e7ok m\u00fcthi\u015f bir olay de\u011fil midir?<\/p>\n\n\n\n

    G\u00f6z ard\u0131 etmemi\u015f olal\u0131m; Parmenides ve Zeno\u2019nun \u00f6yle bir fikri terenn\u00fcm edi\u015flerinden bu yana di\u011fer insanlar\u0131n da onaylay\u0131\u015flar\u0131, ba\u015ftan beri s\u00f6z\u00fc edilen zihinsel zay\u0131fl\u0131\u011f\u0131n bir g\u00f6stergesi, kan\u0131t\u0131 de\u011fil midir? Yani, her unsuruyla devinim h\u00e2lindeki bir evreni t\u00fcm\u00fcyle k\u0131m\u0131lt\u0131s\u0131z san(\/y)mak, apa\u00e7\u0131k bir zihinsel zay\u0131fl\u0131k de\u011fil midir?<\/p>\n\n\n\n

    O kadar ki, Aristo dahi evreni k\u0131m\u0131lt\u0131s\u0131z (statik), de\u011fi\u015fmez sanm\u0131\u015f. (**) Bu konuda ziyadesiyle e\u011flenceli yaz\u0131lar ve g\u00f6rseller mevcut. (***) Ama ciddi okuyu\u015flar i\u00e7in yararl\u0131 adresler de var. (****)<\/p>\n\n\n\n

    \u0130lgili okuyucu, \u2018statik evren\u2019 konusunun teolojik ve doktriner siyasi yans\u0131malar\u0131 i\u00e7in de \u00e7e\u015fitli internet arama motorlar\u0131ndan yararlanabilir.<\/p>\n\n\n\n

    B\u00f6ylelikle, s\u00f6z\u00fc da\u011f\u0131tmadan toparlay\u0131p bu yaz\u0131n\u0131n sonucuna ya da i\u015fbu notun (22. NOT)  ilk sat\u0131r\u0131na odaklayacak olursak; g\u00fcn\u00fcm\u00fczden 2500 y\u0131l evvel yani Parmenides ve Zeno ile ayn\u0131 d\u00f6nemde ama Milet-Efes\u2019de ya\u015fam\u0131\u015f olan Heraklit\u2019in (#) \u2018Her \u015fey akar ve s\u00fcrekli de\u011fi\u015fir.\u2019 \u00f6nermesinin ni\u00e7in \u00f6nemsenmedi\u011fini, Parmenides-Zeno ikilisininkilere k\u0131yasla ni\u00e7in geride kald\u0131\u011f\u0131n\u0131 y\u00fcksek sesle sormak gerekir.<\/p>\n\n\n\n

    \u2018Heraklit\u2019in ate\u015f kavram\u0131\u2019 konusunu ayr\u0131 ve \u00f6zel bir potansiyel makalede irdelemeye ay\u0131rarak \u015fu \u00f6nermelerine dikkat \u00e7ekmek isterim:<\/p>\n\n\n\n

    “\u03c0\u03bf\u03c4\u03b1\u03bc\u03bf\u1fd6\u03c3\u03b9 \u03c4\u03bf\u1fd6\u03c3\u03b9\u03bd \u03b1\u1f50\u03c4\u03bf\u1fd6\u03c3\u03b9\u03bd \u1f10\u03bc\u03d0\u03b1\u03af\u03bd\u03bf\u03c5\u03c3\u03b9\u03bd, \u1f15\u03c4\u03b5\u03c1\u03b1 \u03ba\u03b1\u1f76 \u1f15\u03c4\u03b5\u03c1\u03b1 \u1f55\u03b4\u03b1\u03c4\u03b1 \u1f10\u03c0\u03b9\u03c1\u03c1\u03b5\u1fd6.”<\/p>\n\n\n\n

    “Ayn\u0131 \u0131rmaklara girenlerin \u00fczerinden farkl\u0131 sular akar”<\/p>\n\n\n\n

    “\u03a0\u03bf\u03c4\u03b1\u03bc\u03bf\u1fd6\u03c2 \u03c4\u03bf\u1fd6\u03c2 \u03b1\u1f50\u03c4\u03bf\u1fd6\u03c2 \u1f10\u03bc\u03b2\u03b1\u03af\u03bd\u03bf\u03bc\u03ad\u03bd \u03c4\u03b5 \u03ba\u03b1\u1f76 \u03bf\u1f50\u03ba \u1f10\u03bc\u03b2\u03b1\u03af\u03bd\u03bf\u03bc\u03b5\u03bd, \u03b5\u1f36\u03bc\u03ad\u03bd \u03c4\u03b5 \u03ba\u03b1\u1f76 \u03bf\u1f50\u03ba \u03b5\u1f36\u03bc\u03b5\u03bd.”<\/p>\n\n\n\n

    “Ayn\u0131 \u0131rmaklara gireriz ve girmeyiz. Hem var\u0131z hem yokuz.”<\/p>\n\n\n\n

    Heraklit gayet hakl\u0131! De\u011fil mi?<\/p>\n\n\n\n

    Ama \u00f6yle g\u00f6r\u00fcn\u00fcyor ki, sevgili insan akl\u0131 burada da tuza\u011fa d\u00fc\u015fm\u00fc\u015f ve \u015f\u00f6yle d\u00fc\u015f\u00fcn\u00fcyor:<\/p>\n\n\n\n

    \u2018Heraklit hakl\u0131 olsa, yani her \u015fey de\u011fi\u015fiyor olsa, ben de de\u011fi\u015fir(d)im. Oysa ben de\u011fi\u015fmiyorum; hep ayn\u0131y\u0131m. Demek ki, Heraklit hakl\u0131 de\u011fil. \u00dcstelik, her \u015fey de\u011fi\u015fse, de\u011fi\u015fiyor olsa her \u015feyin de\u011fi\u015fti\u011finin de de\u011fi\u015fmesi, de\u011fi\u015fiyor olmas\u0131 gerek. Bu da, fazladan, tam bir \u00e7eli\u015fki!\u2019<\/p>\n\n\n\n

    Biraz altta da de\u011finilece\u011fi gibi, bir \u00fcst paragraftaki g\u00f6r\u00fc\u015fler t\u00fcm\u00fcyle yanl\u0131\u015ft\u0131r; \u2018De\u011fi\u015fmeyen tek \u015fey de\u011fi\u015fimin kendisidir.\u2019 s\u00f6z\u00fc Heraklit\u2019e ait olsa bile. Buradaki ayr\u0131m, evrene ait olan \u2018\u015fey\u2019lerle evrene ait olmayan zihinsel, hayali, do\u011fa yap\u0131s\u0131 olmay\u0131p insan yap\u0131s\u0131 olan \u2018\u015fey\u2019ler aras\u0131ndad\u0131r. \u0130ki kez ikinin d\u00f6rt etti\u011fi de asla de\u011fi\u015fmez. \u00c7\u00fcnk\u00fc, 2 de, \u00e7arp\u0131m tablosu da tamam\u0131 ile insan taraf\u0131ndan yap\u0131lmad\u0131r, zihinseldir, hayalidir, evrene ait de\u011fildir. (##) T\u0131pk\u0131, nokta ve \u00e7emberin evrene ait olmay\u0131\u015flar\u0131 gibi. Evet! Tam\u0131 tam\u0131na \u00f6yle demeye \u00e7al\u0131\u015f\u0131yorum; insan zihnindeki evren ile ger\u00e7ek evren farkl\u0131d\u0131r. Baz\u0131 yerlerde \u00e7ak\u0131\u015fsa da, tam\u0131 tam\u0131na ayn\u0131 de\u011filler.<\/p>\n\n\n\n

    \u00c7ok kez de\u011findik; A\u015fil fiziksel olarak kaplumba\u011faya eri\u015febiliyor ama hayali olarak aradaki mesafeyi kat edebilmesi i\u00e7in \u00f6nce yar\u0131s\u0131n\u0131, bunu kat edebilmesi i\u00e7in de \u00f6nce bunun yar\u0131s\u0131n\u0131, vb. diye d\u00fc\u015f\u00fcnerek devinim olmad\u0131\u011f\u0131na kendini inand\u0131rm\u0131\u015f zihin sahipleri hayli \u00e7ok. (###) Dolay\u0131s\u0131 ile, ger\u00e7ek evrenden farkl\u0131 bir evreni \u015fahsi imgeleminde olu\u015fturup ta\u015f\u0131yanlardan s\u00f6z ediyoruz.<\/p>\n\n\n\n

    Bunun gibi, evrene ait \u2018\u015fey\u2019ler de\u011fi\u015firken evrene ait olamayan \u2018\u015fey\u2019lerin de\u011fi\u015fmeyebilece\u011fi ayr\u0131m\u0131n\u0131 yapmak gerekiyor.<\/p>\n\n\n\n

    Evrene ait her \u2018\u015fey\u2019 de\u011fi\u015fiyor diye, tamam\u0131 ile insan zihninin \u00fcr\u00fcn\u00fc olan \u201c\u2014Her \u2018\u015fey\u2019in de\u011fi\u015fti\u011fi de de\u011fi\u015fmelidir! B\u00f6yle olamayaca\u011f\u0131na g\u00f6re, de\u011fi\u015fmeyen tek \u2018\u015fey\u2019 de\u011fi\u015fimin kendisidr.\u201d s\u00f6z\u00fc (ilgili en hafif deyimlerden biri ile) bo\u015fta kalmaktad\u0131r; bu s\u00f6z Heraklit\u2019e ait olsa bile.<\/p>\n\n\n\n

    Sonu\u00e7: Evrene ait her \u2018\u015fey\u2019 de\u011fi\u015fir.<\/p>\n\n\n\n

    \u0130kinci sonu\u00e7: \u0130nsan zihnindeki evren ile ger\u00e7ek evren farkl\u0131. (####)<\/p>\n\n\n\n

    (*) https:\/\/blog.metu.edu.tr\/caglart\/2024\/09\/11\/baslayis\/<\/a><\/p>\n\n\n\n

    (**) https:\/\/tr.wikipedia.org\/wiki\/Aristoteles_fizi%C4%9Fi<\/a><\/p>\n\n\n\n

    (***) https:\/\/www.google.com\/search?q=Aristoteles+statik+evren&sca_esv=19c6d868d61db842&sxsrf=AHTn8zrpSPqmTPmElVAMtobVA-SSw7iXAg%3A1747551118688&ei=joMpaOLoKduJxc8Pg9OT6Qc&ved=0ahUKEwji55-dt6yNAxXbRPEDHYPpJH0Q4dUDCBA&uact=5&oq=Aristoteles+statik+evren&gs_lp=Egxnd3Mtd2l6LXNlcnAiGEFyaXN0b3RlbGVzIHN0YXRpayBldnJlbjIKEAAYsAMY1gQYRzIKEAAYsAMY1gQYRzIKEAAYsAMY1gQYRzIKEAAYsAMY1gQYRzIKEAAYsAMY1gQYRzIKEAAYsAMY1gQYRzIKEAAYsAMY1gQYRzIKEAAYsAMY1gQYR0jVCVAAWABwAXgBkAEAmAEAoAEAqgEAuAEDyAEAmAIBoAIKmAMAiAYBkAYIkgcBMaAHALIHALgHAA&sclient=gws-wiz-serp<\/a><\/p>\n\n\n\n

    (****) https:\/\/www.jstor.org\/action\/doBasicSearch?Query=static+universe&so=rel<\/a><\/p>\n\n\n\n

    (#) https:\/\/tr.wikipedia.org\/wiki\/Heraklitos<\/a><\/p>\n\n\n\n

    (##) Tekrarlamakta beis yok; \u015fekil olarak 2\u2019yi k\u00e2\u011f\u0131t \u00fcst\u00fcne yazd\u0131\u011f\u0131n\u0131zda evrene ait hale getirebilirsiniz. Ama evrende say\u0131 olarak 2 (ve di\u011ferleri) yer almaz, \u00e7arp\u0131m tablosu da yer almaz. \u00c7\u00fcnk\u00fc evren, bizimki gibi aritmetikle ve matematikle \u00e7al\u0131\u015fmaz. G\u00fcne\u015f, D\u00fcnya\u2019n\u0131n yar\u0131\u00e7ap\u0131n\u0131 (yakla\u015f\u0131k da olsa?) ve k\u00fctlesini (yakla\u015f\u0131k da olsa?) biliyor mudur dersiniz? Dahas\u0131, evrenin bildi\u011fimiz hi\u00e7bir yerinde \u015fekil olarak de\u011fil, varl\u0131k olarak 2 saptanm\u0131\u015f, g\u00f6zlenmi\u015f de\u011fildir. D\u00fcnya\u2019n\u0131n ve ba\u015fka gezegenlerin 2 kutbu olmas\u0131, evrende 2\u2019nin varl\u0131\u011f\u0131na kan\u0131t de\u011fildir.<\/p>\n\n\n\n

    (###) Ho\u015f, hareketin ne ve nas\u0131l oldu\u011funu, o harekete yol a\u00e7an (uzaktan) etkile\u015fimin ne ve nas\u0131l oldu\u011funu da biliyor de\u011filiz. Gel gelelim, bu cahilli\u011fimizi, zay\u0131fl\u0131\u011f\u0131m\u0131z\u0131 kabul edebilenimiz de hayli az.<\/p>\n\n\n\n

    (####) Yani, insan zihni evreni kavrayam\u0131yor, tam olarak \u2018comprehend\u2019 edemiyor. Demek ki, insan zihnindeki evren ile ger\u00e7ek evren ayn\u0131 de\u011fil.<\/p>\n\n\n\n

    Komik! De\u011fil mi?<\/p>\n\n\n\n

    Kal\u0131r m\u0131 baki bu kubbede bir ho\u015f sad\u00e2 olarak, \u015fimdi acep bir \u015fen kahkaha daha salsak?<\/p>\n\n\n\n

    <\/p>\n\n\n\n