Bane - ko albarka
Dalibai gabaɗaya ba sa son ƙidaya da logarithms. A ka'ida, an san su don sauƙaƙe ninka lambobi ta hanyar rage su zuwa ? yafi sauki? Bugu da kari, amma a zahiri kun dauki shi a banza. Wanene zai damu? a yau, a zamanin da ake amfani da na'urorin ƙididdiga na ko'ina ko da a cikin wayoyin hannu? damu cewa ninkawa ya fi rikitarwa a zahiri fiye da ƙari: bayan duka, duka sun sauko don danna ƴan maɓalli?
Gaskiya. Amma sai kwanan nan? aƙalla akan ma'auni na lokaci na waɗanda aka sanya hannu? ya sha bamban. Bari mu dauki misali kuma muyi kokarin ninka ba tare da amfani da kalkuleta ba? wasu manyan lambobi biyu; bari mu ce mu yi aikin 23 × 456. Ba aiki mai kyau ba ne, ko ba haka ba? A halin yanzu, lokacin amfani da logarithms, komai ya fi sauƙi. Muna shiga rubutaccen magana:
log (23 456 789 × 1 234 567) = log 23 456 789 + log 1 234 567 = 7,3703 + 6,0915 = 13,4618
(muna iyakance kanmu zuwa wurare huɗu na ƙima, saboda yawanci wannan shine ainihin madaidaicin tsararrun logarithmic), haka logarithm yake? wanda kuma muka karanta daga teburi - kusan 28. Ƙarshen batu. Mai gajiyawa amma mai sauƙi; sai dai idan, ba shakka, kuna da kwanciyar hankali logarithms.
A koyaushe ina mamakin wanda ya fara wannan tunanin? kuma na yi baƙin ciki sosai sa’ad da ƙwararren malamin lissafi na makaranta Zofia Fedorovich ya ce ba zai yiwu a kafa shi gaba ɗaya ba. Wataƙila wani Bature mai suna John Napier, wanda aka fi sani da Napier. Ko watakila dan uwansa Henry Briggs? Ko watakila abokin Napier, Swiss Jost Burgi?
Ban sani ba game da Masu Karatun wannan rubutu, amma ina son shi idan wani ƙirƙira ko ganowa yana da marubuci ɗaya. Abin takaici, yawanci ba haka lamarin yake ba: yawanci mutane da yawa suna da ra'ayi iri ɗaya a lokaci guda. Wasu suna jayayya cewa mafita ga matsala yawanci yana bayyana daidai lokacin da bukatun zamantakewa, galibin tattalin arziki, bukatun; kafin wannan, a matsayin mai mulkin, babu wanda yayi tunani game da shi?
To wannan lokacin kuma? kuma shi ne karni na sha shida, ya kasance. Ci gaban wayewar da aka tilasta don inganta hanyoyin sarrafa kwamfuta; juyin juya halin masana'antu a zahiri yana kwankwasa kofofin Turai.
Daidai a tsakiyar karni na 1550? na XNUMX? An haife shi a Scotland, a cikin gidan gidan Merchiston Castle kusa da Edinburgh, Ubangiji John Napier da aka ambata. A bayyane yake, an dauki wannan mutumin a matsayin mai ban tsoro tun yana karami: maimakon rayuwa ta yau da kullun da kuma nishadantarwa na aristocrat, abubuwan ƙirƙira sun burge shi? da kuma (wanda ya riga ya zama nakasassu a lokacin) lissafi. Har da? me, akasin haka, ya kasance al'ada? alchemy? Ya yi ƙoƙari ya nemo hanyar da zai zubar da ma'adinan kwal; ya }ir}iro nau'in injuna, wanda a yau muna la'akari da irin nau'in tanki ko jirgin ruwa; yayi ƙoƙari ya gina tsarin madubi wanda yake so ya ƙone jiragen ruwa na Babban Armada na Katolika na Mutanen Espanya wanda ya yi barazana ga Furotesta Ingila? Ya kuma kasance mai kishin bunkasa noma ta hanyar amfani da takin zamani; a takaice, dan Scotland na da kai ba cikin fareti ba.
Duk da haka, babu ɗaya daga cikin waɗannan ra'ayoyin da zai yiwu ya ba shi damar canzawa zuwa tarihin kimiyya da fasaha, idan ba don logariths ba. An buga cannon sa na logarithmic a cikin 1614? kuma nan da nan ya sami talla a duk Turai.
Lokaci guda ? kuma da kansa, ko da yake wasu suna magana a gaban ubangijinmu? Abokinsa na kusa, Swiss Jost Burgi, shi ma ya zo da ra'ayin wannan lissafin, amma aikin Napier ya zama sananne. Masana sun ce Napier ya gyara aikinsa da kyau kuma ya yi rubutu da kyau, cikakke. Da farko dai, rubutunsa ne aka sani ga Henry Briggs, wanda bisa ka'idar Napier, ya kirkiro tebur na farko na logarithms tare da ƙididdige ƙididdiga na hannu; kuma wadannan tebura ne suka zama mabuɗin shaharar asusun.
Kamar yadda kuka ce? Makullin yin lissafin logarithms shine tsararru. John Napier da kansa ba shi da sha'awar wannan gaskiyar: ɗaukar ƙarar ƙarar da kuma neman lambobi masu dacewa a ciki ba shine mafita mai dacewa ba. Ba abin mamaki ba ne cewa mai kaifin baki (wanda, ta hanyar, bai zama babban matsayi a cikin matsayi na aristocratic ba, na biyu daga kasa a cikin nau'in darajojin Ingilishi) ya fara tunanin gina na'urar da ta fi dacewa fiye da tsararru. Kuma? ya yi nasara, kuma ya bayyana tsarinsa a cikin littafin "Rabdology", wanda aka buga a 1617 (wannan, ta hanyar, ita ce shekarar mutuwar masanin kimiyya). Don haka an ƙirƙiri ƙwanƙwasa, ko ƙasusuwan Napier, babban mashahurin kayan aikin kwamfuta? karama! ? kimanin karni biyu; ita kanta rhabdology tana da wallafe-wallafe da yawa a cikin Turai. Na ga kwafin waɗannan kasusuwa da yawa ana amfani da su a ƴan shekarun da suka gabata a gidan tarihi na fasaha da ke Landan; an yi su a cikin nau'i-nau'i da yawa, wasu daga cikinsu suna ado sosai da tsada, zan ce - dadi.
Yaya ta yi aiki?
Kyawawan sauki. Napier kawai ya rubuta sanannen tebur ɗin ninkawa akan saitin sanduna na musamman. A kowane mataki? katako ko, misali, na kashi, ko a cikin mafi tsada nau'in hauren giwa mai tsada, wanda aka yi wa ado da zinariya? Samfurin mai ninkawa lokacin da aka ninka shi da 1, 2, 3, ..., 9 yana samuwa musamman da basira. Sandunan sun kasance murabba'i kuma an yi amfani da dukkan bangarorin hudu don adana sarari. Don haka, saitin sanduna goma sha biyu ya ba mai amfani da samfuran samfura 48. Idan kuna son yin ninkawa, dole ne ku zaɓi daga cikin saitin tsiri waɗanda suka yi daidai da lambobi masu yawa, sanya su kusa da juna a kan tasha, sannan karanta wasu samfuran ɓangarori don haɗa su tare.
Yin amfani da ƙasusuwan Napier ya kasance mai dacewa; a lokacin ya ma dace sosai. Bugu da ƙari, sun 'yantar da mai amfani daga haddace teburin ninkawa. An yi su a cikin nau'i-nau'i masu yawa; Af, an haifi ra'ayin maye gurbin sandunan quadrangular? yafi dacewa kuma yana ɗaukar ƙarin rollers bayanai.
Ra'ayin Napier? daidai a cikin sigar tare da rollers - haɓakawa da haɓakawa ta Wilhelm Schicckard a cikin ƙirar injin ƙididdige injin sa, wanda aka sani da "Agogon lissafin".
Wilhelm Schickard (an haife shi a ranar 22 ga Afrilu, 1592 a Herrenberg, ya mutu ranar 23 ga Oktoba, 1635 a Tübingen) - Masanin lissafin Jamus, masanin harsunan Gabas kuma mai tsarawa, farfesa a Jami'ar Tübingen kuma lallai malamin Lutheran ne; ba kamar Napier ba, shi ba ɗan boko ba ne, amma ɗan kafinta ne. A cikin 1623? Shekarar da aka haifi babban masanin Falsafa dan kasar Faransa kuma daga baya wanda ya kirkiro na’urar arithmometer Blaise Pascal ya umurci shahararren masanin falaki Jan Kepler ya gina daya daga cikin kwamfutoci na farko a duniya da ke aiwatar da kari, ragi, ninkawa da rarraba integers. , "Agogon" da aka ambata. Wannan injin katako ya kone a shekara ta 1624 a lokacin Yaƙin Shekaru Talatin, kusan watanni shida bayan ƙarewar; Baron Bruno von Freytag ne ya sake gina shi a cikin 1960? Leringhof bisa kwatanci da zane-zane da ke ƙunshe a cikin wasiƙun da aka gano na Schickard zuwa Kepler. Injin ya ɗan yi kama da ƙira da ƙa'idar zamewa. Hakanan yana da kayan aiki don taimaka muku ƙidaya. A gaskiya ma, abin al'ajabi ne na fasaha don lokacinsa.
Tare da ku? Watch? Akwai wani sirri a Shikard. Tambayar ta taso: menene ya sa mai zanen, bayan da ya lalata na'urar, bai yi ƙoƙari ya sake yin shi ba kuma ya daina aiki gaba daya a fannin fasahar kwamfuta? Me ya sa sa’ad da yake ɗan shekara 11, ya tafi har mutuwarsa ya gaya wa kowa game da ‘agogonsa? Bai ce ba?
Akwai shawara mai ƙarfi cewa lalata injin ɗin ba na haɗari ba ne. Ɗaya daga cikin hasashe a cikin wannan harka shi ne cewa Ikilisiya ta ɗauki nauyin gina irin waɗannan inji (ka tuna daga baya, kawai shekaru 0, hukuncin da Inquisition ya zartar a kan Galileo!) Kuma don halakar da "agogo"? Shikard an ba shi sigina mai ƙarfi don kada ya yi ƙoƙarin "maye gurbin Allah" a wannan yanki. Wani ƙoƙari na share asirin? a ra'ayi na undersigned, mafi m? ya ƙunshi gaskiyar cewa wanda ya kera na'urar bisa ga tsare-tsaren Schickard, an hukunta wani Johann Pfister, mai agogo, ta hanyar lalata aikin da abokansa suka yi a cikin shagon, wanda ba ya son yin wani abu bisa ga wasu mutane. tsare-tsaren, wanda aka yi la'akari da cin zarafin ka'idar guild.
Ko menene? da sauri aka manta da motar. Shekaru dari bayan mutuwar babban Kepler, Empress Catherine II ta sami wasu takardunsa; Bayan shekaru sun ƙare a shahararriyar cibiyar nazarin taurarin Soviet a Pulkovo. An shigar da shi cikin wannan tarin daga Jamus, Dokta Franz Hammer ya gano wasiƙun Schickard a nan cikin 1958; kusan lokaci guda, an gano zane-zanen Schickard da aka yi nufin Pfizer a cikin wani tarin takardu a Stuttgart. Dangane da waɗannan bayanan, an sake gina kwafin “agogo” da yawa. ; daya daga cikinsu IBM ne ya ba da izini.
Af, Faransanci ba su ji daɗi da wannan duka labarin ba: ɗan ƙasarsu Blaise Pascal shekaru da yawa an ɗauke shi a matsayin mai tsara tsarin ƙidayar farko na nasara.
Kuma wannan shi ne abin da marubucin waɗannan kalmomi ya ɗauka mafi ban sha'awa da ban dariya a tarihin kimiyya da fasaha: cewa a nan ma, babu wani abu kamar yadda kuke tunani?
