Ezinsukwini eziyishumi nanhlanu ezedlule, omunye wabafundi balokhu kubuyekezwa okuthobekile wasishiya kumazwana ezinye izinkulumo esizizwile izikhathi eziningi. Ekuqaleni komcabango, njengakwezinye izikhathi, siphendula endaweni efanayo lapho kwenziwa khona. Nokho, ezindla kancane kancane, wacabanga ukuthi kungase kuthakazelise ukunikeza isihloko sonke kule mishwana, njengoba kunabantu abaningi, ngokwezinkulumo zabo, abacabanga okufanayo, futhi abakholelwa ngobuqotho ukuthi banephutha. Uyazi, ama-comments anjengokuthi 'selokhu ngayeka isikole angizange ngisebenzise izibalo' noma 'izibalo azisizi ngalutho kimi'. Imigqa elandelayo ayihloselwe ukukholisa noma ubani. Kodwa-ke, ngicabanga ukuthi kuwukuhlola okudingekayo njengombhangqwana esikubonisa kancane mayelana nokunemba 'kwezinganekwane zasemadolobheni' (ngingathi, njengoba i-anglicism isemfashinini, 'inkohliso') yohlobo oluveziwe. Ngiyaqonda ukuthi zichazwa ngesizotha, futhi ngaphandle kwenhloso embi, yingakho ngicabanga ukuthi kuwumsebenzi wethu (wochwepheshe bezibalo, ososayensi, othisha noma ochwepheshe) ukuzama ukuzicacisa, noma okungenani sinikeze izizathu zokungavumelani kwethu. Njengoba, ngaphezu kwalokho, ngizozama ukunikeza izibonelo ezibambekayo, ngicabanga ukuthi kuhambisana kahle nokudalula, okuyincazelo yokugcina yalokhu kucabanga esikuletha lapha masonto onke. Ngizobiza bonke abafunde baphothula umsebenzi wasenyuvesi kulowo mkhakha wezibalo; njengamanje uneziqu ze-bachelor ku-mathematics, i-bachelor degree in mathematics ngaphambilini. Kuyincazelo ebanzi kakhulu, ngiyazi, ngoba kuzoba khona abathatha ongoti bezibalo kuphela labo abenza ucwaningo lwezibalo, hhayi labo abazinikela kuphela ekufundiseni, ekufinyeleleni, njll. Impela abakuqala yibo abanegunya elengeziwe lokusebenzisa leyo nombolo, ngoba bazama ukuqhubekisela phambili udaba ngomsebenzi wabo. Kodwa njengoba ngizokhuluma ngokuqeqeshwa engikutholile, kungalo mqondo lapho ngizama khona ukwelula isikhathi esibonisiwe. Isiphi isazi sefilosofi osaziyo esingazange ngandlela-thile sihlakulele ukucabanga okunengqondo noma izibalo? Ukuqala ndawana thize, uphawula ngokuthi angicabangi ukuthi kungatholakala ochwepheshe bezibalo abaningi abangayisho ifilosofi kanye nomlando wefilosofi njengento ebalulekile ohlelweni lwezifundo lwanoma yisiphi isakhamuzi esinemfundo ephakeme, yanoma yiluphi uhlobo. Futhi ngizoyiphikisa ngombuzo: Isiphi isazi sefilosofi osaziyo esingazange sihlakulele ingqondo noma izibalo ngandlela-thile? Ingabe kuyadingeka ukwenza uhlu lwezazi zefilosofi ezingezona ezezibalo? U-Háganla uzothola inombolo ephansi kakhulu kunesethi yazo zonke izazi zefilosofi. Futhi isizathu sisobala: izibalo azicabangi nje kuphela izici zobuchwepheshe ezisekelwe ekubaleni (lokho kuyingxenye kuphela, isethi encane esingakusho ngokwemibandela yesihloko sethu, kanye nesethi yamanani ayisisekelo angaphansi kwesikhala esiphelele), kodwa futhi siphishekela Incazelo kanye nokuboniswa kwanoma yiluphi udaba, usebenzisa izilimi nokucabanga okufanele kakhulu kuhlobo lwenkinga. Izibalo azifuni nje kuphela isixazululo esiphathekayo, njengoba sifundiswa empilweni yethu yesikole, kodwa ngaphezu kwakho konke ukucabanga, ukuhlaziya, ukuthuthukiswa kwamasu; Ngemva kokuba lawo masu atholakele, ingxenye ecacile yesinqumo izothengiswa, okungeke kusaba ingxenye yemishini yesixazululo sokugcina. Njengoba ngisho, lokhu kuyingxenye yokugcina kuphela, ingxenye yezobuchwepheshe, ebaluleke kakhulu eqinisweni, ngoba into ebalulekile ukuthola, ukuthola indlela. Lapho 'unesithombe' salokho okubhekwa 'njengesazi sefilosofi sokuqala', uThales waseMiletus, okungenzeka uyazi, futhi odume ngethiyori evumele sonke isintu ukwenza izinto ezifana nokulinganisa amabanga ukusuka ezindaweni ezingafinyeleleki. Ubungeke ungcole nasekhaya Ngisho noma kuwukukhuluma iqiniso, njengoba sivula amehlo njalo ekuseni, sisebenzisa izibalo. Singatshala igeyimu ebizwa ngokuthi 'Ungakwenzi okudingayo ngandlela thile izibalo ukuze ukwazi ukukwenza'. Vele, bazovuka lapho umzimba wabo ubatshela ukuthi benze kanjalo, ngoba iwashi le-alamu ngeke livunyelwe. Khohlwa ngamathebulethi, omakhalekhukhwini, amakhompyutha, omabonakude, ama-microwave, izitofu, izifudumezi, imishini yokuwasha, njll., noma iyiphi idivayisi enomjikelezo omncane ohlanganisiwe, njengoba wazi, ethobela i-algorithm ethile yezibalo. Ngesizathu esifanayo, ngeke ukwazi ukusebenzisa ukushintshwa kokukhanya, ngakho-ke uma ikhaya lakho lingaphakathi endlini, thola ikhandlela elihle elinesibani sekhandlela elifakiwe ukuze ukwazi ukuliphatha ngokunethezeka, ngoba i-flashlight, njengenye enye. Kuzodingeka ube namabhakede amahle amanzi ukuze uthele phansi endlini yangasese ngoba asikwazi ukusula iketango noma ukuvula umpompi ngoba ukwakheka kwamapayipi, ukusebenza kwawo, kudinga izibalo nezilinganiso ezithile ezenziwe ngomunye ukuze asebenze. Vele, yiba namaqabunga esihlahla alungiselelwe ukuzihlanza gcina ingxenye, ngoba noma yiluphi uhlobo lwephepha lunezilinganiso nobukhulu ongeke ukwazi ukusisebenzisa, ingasaphathwa eminyango yezakhi zokwakheka kwakho (lokhu kuthinta amaphilisi akho nemithi futhi akakwazi ukuphuza) . Kungani i-toilet paper roll i-cylindrical futhi ingeyona i-prismatic, i-spherical, njll.? Ah, uxolo, asikwazi ukusebenzisa amagama ezibalo. Izibalo azifuni nje kuphela ukuxazulula okukhonkolo, kodwa ngaphezu kwakho konke ukucabanga, ukuhlaziya, ukuthuthukiswa kwamasu. Ngendlela efanayo, kufanele sibe nqunu ngokuphelele emgwaqweni, ngoba ukuma kwezingubo akuyona nje noma yikuphi. Kuye kwadingeka bayenze ngokosayizi othize, futhi yakhiwe ngamajamo anezilinganiso ezanele. Akufanele futhi izinhlamvu zemali, izikweletu (Uke wazibuza ukuthi kungani sisebenzisa izinombolo 1, 2 kanye no-5 kanye nokuphindaphinda kwazo, njengenani lemali? Kungani kungenjalo 1, 3, 7, ngokwesibonelo, noma amanye amanani?), amakhadi esikweletu nanoma yiluphi olunye uhlobo (uyazi, ngenxa yamabhakhodi, i-PIN nezinye), futhi ngeke banake imvamisa yebhasi nezinye izindlela. ezokuthutha (ama-GPS asekelwe ku-sphere intersection theorem). Uthola ukuthi izinombolo azikho. Futhi uma ubazi, awukwazi ukuhleleka kwabo (Yeka ukuthi kuhle kangakanani 'Incwadi Yesihlabathi' kaJorge Luis Borges, kunjalo! umbhalo wesandla, ngoba amafonti njengamanje aklanywe ngemisebenzi yezibalo nezindlela ezithile zokuhumusha; khumbula imithetho yalo mdlalo, ungasebenzisi lutho olunezibalo kuwo). kufanele bahambe noma yikuphi lapho beya khona, kodwa hhayi ngendlela emfushane kakhulu, ngoba kunqunywa ngasiphi isisekelo ukuthi iyiphi emfishane? Futhi, kusho ukuthini 'okufushane'? Kusobala-ke ukuthi angeke sidle noma yini engatholwanga ngezibalo ezithile, ngakho-ke, ukuzila lokho kunempilo kakhulu, futhi masiye ensimini siyokha isithelo sasendle, ngoba ngesaba ukuthi ngeke ikwazi ukubamba noma yini lapho ingadi inqunyelwe khona, uhlobo lokunisela, ilungiselelo lembewu, njll. Esithombeni, umklami wohlamvu 'a' kufonti ye-Helvetica, enamajika e-Bezier. Ukusebenzisa le ndlela, ngaphezu kwamaphuzu lapho ukumelwa kokugcina kudlula khona (ama-node), kunamaphuzu okulawula anembile abonisa ukuthambekela kwejika ngalinye. Isayensi vs. Humanities Ngezizathu ezisobala, ngeke sazi yonke into ngayo yonke into ngendlela ephelele. Ulwazi lwabantu lubanzi kangangokuthi sidinga uchwepheshe. Kodwa-ke, ukuba nesiko, ukwazi okuyisisekelo kukho konke, kuhle kakhulu futhi kuyacebisa. Angazi ngasiphi isikhathi emlandweni othile wanquma ukwenza ukuhlukaniswa phakathi kwesayensi nobuntu, noma ubani ozoba 'ingqondo' ehlakaniphile, kodwa-ke wenza obunye bobuwula obukhulu kakhulu obake baba khona futhi obuzoqhubeka bukhona. Umuntu uyiqoqo lezingxenye eziningi, futhi akahlukaniseki. Idinga futhi isebenzisa zonke izinhlobo zolwazi. Akuyona 'yezinhlamvu', noma 'yesayensi'. Kubili. Izaba ezidumile zokuthi 'Ngingumbhali' yihubo lokulula, ukungabi nangqondo, ukungakwazi. Uma ngizithola ngisembuthanweni lapho bekhuluma khona ngokuthi 'Impilo iyiphupho', ngingagcina kanjani ngithi “angicabangi, ngoba ngiyisayensi”? Noma uma ephendula, "Leya movie ye-Quevedo yinhle." Ayivumelekile njengengxabano. Kuhlakaniphe kakhulu futhi kuwukuhlakanipha ukuthula, noma ukwamukela ukungazi, kunokukhuluma umbhedo. Thina ongoti bezibalo, ososayensi, asisoze salindela ukuthi wonke umuntu axazulule izilinganiso ezihlukene, noma alungise ukusabela kokunciphisa i-oxidation (phakathi kwezinye izinto, ngoba uma kungenjalo, sizoba ngokweqile). Kodwa yebo, njengoba incwadi yolimi i-Lázaro Carreter esiyifundile yasho, “ukwazi ukushintsha irejista”, ngenhloso yokukwazi ukuzwa nokuxoxa kahle noprofesa wesayensi yezokuhlalisana kwabantu kanye nesisebenzi sokuhlanza. Futhi-ke ngaphandle kokuhamba ngezinyawo noma ukucabanga umzuzwana ukuthi eminye imisebenzi iyi-pluses noma mibi kakhulu kuneminye. Bonke bafaneleka ngokulinganayo ngoba bonke bayadingeka ngokuphelele. Mina ngokwami, ngiyilungu leqembu lezincwadi, ngihambisana namamuvi amasha, ngihlala nginolwazi oluningi noma oluncane ngezindaba zansuku zonke (enye into engithakaselayo), futhi ngiyisazi sezibalo. Futhi izingxoxo engifunda nazo kwesinye isikhathi ziqondene ngqo nezibalo kanti ezinye eziningi zimayelana nezifundo 'zobuntu'. Izazi zezibalo, nanoma ubani ozinikele 'kusayensi' akekho odelela 'isintu'. Ngokuphambene nalokho. Kunjalo, 'ukuba ngumuntu', okukhonjiswe ngumfundi ogqugquzele le migqa, akugcini nje kunoma yisiphi isiyalo noma kunoma ubani. Kunalokho, kuwubunikazi balo lonke ulwazi ebesilokhu sivela, okuhle noma okubi, kukho konke ukuhlala kwethu kule planethi, okuthi, ngendlela, ngendlela ehola ngayo, iphele ngaphambi kokuba iLanga libe inkanyezi enkulu ebomvu. Lawa mazwana okugcina angikhumbuza ngemibono emibili emisha emangalisayo yeminyaka yamashumi ayisithupha edlule, angazi noma kuseyizinganekwane zesayensi, okukhona nezinguqulo zamafilimu ayisikhombisa: 'Iplanethi Yezinkawu', kaPierre Boulle, kanye nethi 'Yenza Igumbi, Yenza Igumbi!' ka-Harry Harrison, womabili anokuqukethwe kwezibalo okuthile. Ngoba, njengoba ngisho, yonke into ihlobene futhi isayensi nobuntu akuwona amaqiniso ahlukene. Izibonelo zigcwele kuzo zonke izinhlobo zemisebenzi, nakulokho esikubheka njengezincwadi zasendulo nababhali, abamanje nabadlule. Ingabe siyoke sikwazi ukuyeka ukulalela noma ubani ethi 'Ngingumuntu wesayensi' futhi/noma okuphambene nalokho? Bangethemba kuze kube nini, ngokungangabazeki, bafundi abathandekayo. U-Alfonso Jesús Población Sáez unguprofesa eNyuvesi yaseValladolid futhi uyilungu leKhomishini Yokusabalalisa ye-Royal Spanish Mathematics Society (RSME).
