Tuni tsoffin masana kimiyyar Girka suka yi mamakin shin mutum ya kirkiri lissafi ko kuma ya wanzu kuma yana jagorancin ci gaban Duniya da kansa, kuma mutum yana iya fahimtar ilimin lissafi har zuwa wani lokaci. Plato da Aristotle sun yi imani cewa mutane ba za su iya canzawa ko kuma tasiri da ilimin lissafi ba. Tare da ci gaba da cigaban ilimin kimiyya, bayanan cewa ilimin lissafi wani abu ne da aka bamu daga sama, ya ƙarfafa sosai. Thomas Hobbes a cikin karni na 18 kai tsaye ya rubuta cewa ilimin lissafi a matsayin kimiyya an sadaukar da shi ga mutum ga Allah. Wanda ya ci lambar yabo ta Nobel Eugene Wigner tuni a karni na ashirin ya kira harshen lissafi a matsayin "kyauta", amma, ba a sake yin hakan ba a yanzu, kuma a cewar Wigner, mun samu kyautar ne daga kaddara.
An kira Eugene Wigner "mai hankali"
Sabanin da ke tsakanin ci gaban lissafi a matsayin kimiyya da karfafa imani a yanayin duniyarmu, wanda aka kaddara daga sama, a bayyane yake kawai. Idan mafi yawan sauran ilimomi suna koyo game da duniya, asali, masani - masana kimiyyar halitta sun sami sabon nau'in kuma sun bayyana shi, masu ilimin kimiya sun bayyana ko ƙirƙirar abubuwa, da dai sauransu - to ilimin lissafi ya bar ilimin gwaji tuntuni. Haka kuma, zai iya kawo cikas ga ci gabanta. Idan Galileo Galilei, Newton ko Kepler, maimakon yin zato game da motsin taurari da tauraron dan adam, ya leka ta telescope da daddare, ba za su iya gano wani abu ba. Tare da taimakon lissafin lissafi ne kawai suka kirga inda za a nuna hangen nesa, kuma sun sami tabbacin tunaninsu da lissafin su. Kuma da ya sami kyakkyawar ka'ida, kyakkyawar akidar lissafi game da motsin halittun samaniya, ta yaya zai yiwu a gamsu da wanzuwar Allah, wanda ya tsara Duniya cikin nasara da ma'ana?
Don haka, yayin da masana kimiyya ke koyo game da duniya kuma suka bayyana ta da hanyoyin lissafi, abin mamaki shine yadda ake amfani da kayan aikin lissafi da dokokin yanayi. Newton ya gano cewa ƙarfin ma'amala da hankali yana daidai da murabba'in tazarar da ke tsakanin jiki. Ma'anar "murabba'i", wato, digiri na biyu, ya bayyana a cikin lissafi tuntuni, amma ta hanyar mu'ujiza ya zuwa bayanin sabuwar doka. Isasan misali misali ne na mafi mahimmancin amfani da ilimin lissafi ga kwatancen hanyoyin nazarin halittu.
1. Mai yiwuwa, ra'ayin cewa duniyar da ke kewaye da mu ta dogara ne akan ilimin lissafi ya fara zuwa zuciyar Archimedes. Ba ma game da sanannen jumlar da ke nuna cikakken iko da juyin duniya ba. Archimedes, tabbas, ba zai iya tabbatar da cewa duniya ta dogara ne akan ilimin lissafi ba (kuma da ƙyar kowa zai iya). Masanin lissafi ya sami nasarar jin cewa komai na dabi'a ana iya bayyana shi ta hanyoyin lissafi (anan ga shi, fulcrum!), Kuma ko da abubuwan binciken lissafi na gaba sun riga sun kasance cikin yanayi a wani wuri. Ma'anar ita ce kawai don nemo waɗannan abubuwan cikin jiki.
2. Baturen masanin lissafin nan dan kasar Ingila Godfrey Hardy ya kasance mai matukar son kasancewa masanin kimiyya mai zaman kansa wanda yake rayuwa a cikin babbar duniyar lissafi wanda ya bayyana a cikin littafin nasa, mai taken "Apology of a Mathematician," ya rubuta cewa bai yi wani abu mai amfani a rayuwa ba. Mai cutarwa, tabbas, ma - kawai ilimin lissafi ne kawai. Koyaya, lokacin da likitan Bajamushe Wilhelm Weinberg ya binciki kayyakin halittar mutanen da ke saduwa a cikin jama'a da yawa ba tare da kaura ba, ya tabbatar da cewa tsarin halittar dabbobi ba ya canzawa, ta amfani da ɗayan ayyukan Hardy. An ba da aikin ga dukiyar lambobi na asali, kuma ana kiran doka da Weinberg-Hardy Law. Marubucin marubucin Weinberg ya kasance kwatancen tafiya ne na rubutun "mafi kyau a yi shiru". Kafin fara aiki akan hujja, wanda ake kira. Matsalar binary ta Goldbach ko ta Euler (kowane lamba ma ana iya wakilta a matsayin jimillar primes biyu) Hardy ya ce: duk wani wawa zai yi tsammani wannan. Hardy ya mutu a 1947; har yanzu ba a sami tabbacin rubutun ba.
Duk da yanayin da yake ciki, Godfrey Hardy kwararren masanin lissafi ne.
3. Shahararren Galileo Galilei a cikin litattafan adabinsa na "Assaying Master" kai tsaye ya rubuta cewa Duniya, kamar littafi, a bude take ga idanun kowa, amma wadanda suka san yaren da aka rubuta shi ne kawai zasu iya karanta shi. Kuma an rubuta shi a yaren lissafi. A wannan lokacin, Galileo ya sami nasarar gano watannin Jupiter kuma ya kirga kewayensu, kuma ya tabbatar da cewa tabo a Rana suna nan kai tsaye a saman tauraron, ta amfani da gine-gine guda daya. Tsanantawar da Galileo ya yi da cocin Katolika ya samo asali ne daidai da yardarsa cewa karanta littafin Duniya aiki ne na sanin zuciyar Allah. Cardinal Bellarmine, wanda yayi la'akari da shari'ar wani masanin kimiyya a cikin Holy Holy Congregation, nan da nan ya fahimci haɗarin irin waɗannan ra'ayoyin. Saboda wannan haɗarin ne yasa Galileo ya fitar da matattara cewa tsakiyar duniya shine Duniya. A cikin yaren zamani, ya kasance da sauƙi a yi bayani a cikin wa'azin cewa Galileo ya ci karo da Nassosi Masu Tsarki fiye da bayyana ka'idojin kusanci da nazarin Duniyar na dogon lokaci.
Galileo a shari'arsa
4. Wani kwararren masanin lissafi a fannin lissafi Mitch Feigenbaum ya gano a shekarar 1975 cewa idan kayi aikin injiniya wajen maimaita lissafin wasu ayyukan lissafi a kan microcalculator, sakamakon lissafin ya karkata zuwa 4.669 ... Feigenbaum da kansa ba zai iya bayanin wannan ba daidai ba, amma ya rubuta labarin game da shi. Bayan watanni shida na nazarin takwarorina, an dawo da labarin a gare shi, yana ba shi shawara da ya mai da hankali ga bazuwar haɗuwa - lissafi bayan duka. Kuma daga baya ya zama cewa irin wannan lissafin yana bayanin halayyar helium mai ruwa lokacin da aka zafafa daga ƙasa, ruwa a cikin wani bututu yana juyawa zuwa yanayin tashin hankali (wannan shine lokacin da ruwa ke gudu daga famfon tare da kumfa na iska) kuma har ma da ruwan da ke digowa saboda rufaffiyar bututun da ke kwance.
Me Mitchell Feigenbaum zai iya gano idan yana da iphone a ƙuruciyarsa?
5. Mahaifin duk ilimin lissafi na zamani, ban da ilimin lissafi, shine Rene Descartes tare da tsarin daidaitawa wanda aka sanya masa suna. Descartes ya haɗu da aljebra tare da lissafi, yana kawo su wani sabon matakin cancanta. Ya sanya ilimin lissafi ya zama cikakkiyar ilimin kimiyya. Babban Euclid ya bayyana mahimmin abu kamar wani abu wanda bashi da ƙima kuma ba za'a iya raba shi zuwa ɓangarori ba. A cikin Descartes, batun ya zama aiki. Yanzu, tare da taimakon ayyuka, muna bayyana duk hanyoyin da ba layi ba daga amfani da mai zuwa canje-canje a cikin nauyin kansa - kawai kuna buƙatar nemo madaidaiciyar hanya. Koyaya, yawan bukatun Descartes yayi faɗi sosai. Bugu da kari, ranar da ayyukansa suka fi dacewa a lokacin Galileo, kuma Descartes, a cewar nasa bayanin, ba ya son buga wata kalma daya da ta saba wa koyarwar coci. Kuma ba tare da hakan ba, duk da amincewar Cardinal Richelieu, Katolika da Furotesta sun la'anta shi. Descartes ya ja da baya zuwa fagen falsafar tsantsa sannan ya mutu ba zato ba tsammani a Sweden.
Rene Descartes
6. Wani lokaci ana ganin kamar likitan Landan kuma sanannen tarihi William Stukeley, wanda aka ɗauka a matsayin abokin Isaac Newton, yakamata a bijiro masa da wasu hanyoyin daga wurin ajiyar kayan bincike na Holy Holy Inquisition. Da hannunsa mai haske ne almara ta Apple's Newtonian ta zaga duniya. Kamar dai, ko ta yaya zan zo wurin abokina Ishaku da ƙarfe biyar, muna fita zuwa cikin lambun, a can kuma sai tuffa ta faɗi. Auki Ishaku, kuyi tunani: me yasa apples kawai ke faɗuwa? Wannan shine yadda aka haife dokar ɗawainiya ta duniya a gaban bawanka mai tawali'u. Cikakken zagi na binciken kimiyya. A hakikanin gaskiya, Newton a cikin "Ka'idodin Lissafi na Falsafar Halitta" ya rubuta kai tsaye cewa ta hanyar lissafi ya sami ƙarfin nauyi daga abubuwan da ke sama. Girman girman binciken Newton yanzu yana da wahalar tunanin. Bayan duk wannan, yanzu mun san cewa duk hikimar duniya ta dace da wayar, kuma har yanzu za a sami sarari. Amma bari mu sa kanmu a cikin takalmin mutum na ƙarni na 17, wanda ya iya bayyana motsin kusan sammai marasa ganuwa da ma'amalar abubuwa tare da hanyoyin lissafi masu sauƙi. Bayyana nufin Allah cikin lambobi. Gobarar Inquisition ba ta sake ci ba a wannan lokacin, amma kafin mutumtaka akwai aƙalla wasu shekaru 100. Wataƙila Newton da kansa ya fi son cewa ga talakawa haske ne na allahntaka a cikin siffar apple, kuma bai ƙaryata labarin ba - shi mutum ne mai addini sosai.
Tsarin gargajiya shine Newton da apple. An nuna shekarun masanin daidai - a lokacin ganowa, Newton yana ɗan shekara 23
7. Sau da yawa zaka iya cin karo da wata magana game da Allah ta hanyar fitaccen masanin lissafi Pierre-Simon Laplace. Lokacin da Napoleon ya tambaya me yasa ba a ambaci Allah ko da sau ɗaya a cikin mujalladai biyar na Ma'aikatan Celestial Mechanics, Laplace ya amsa cewa baya buƙatar irin wannan tunanin. Laplace hakika kafiri ne, amma bai kamata a fassara amsarsa ta hanyar rashin yarda da Allah ba. A cikin takaddama tare da wani masanin lissafi, Joseph-Louis Lagrange, Laplace ya jaddada cewa zato yana bayanin komai, amma baya hango komai. Masanin lissafin ya tabbatar da gaskiya: ya bayyana halin da ake ciki yanzu, amma yadda ya bunkasa da kuma inda aka dosa, ba zai iya hango komai ba. Kuma Laplace ya ga aikin kimiyya daidai a cikin wannan.
Pierre-Simon Laplace
