saitis
dasawyisisken
:

 

brius direqtori

 

rimanis namdvili biografia jer kidev dasaweria

 

 

 

 

 

originali:

Bruce Director

«Riemann's Definitive Biography is Yet to Be Written»,

21st Century, Science&Technology;

Summer 2000, pp.74-77.

 

 

 

 

avtori—brius direqtori  aris[2000w.] lindon la-ruSis TanamoRvawe, konstituciuri dacvis fondis (The Constitutional Defence Fund) direqtori[2000w.].

brius direqtoris sxva statiebi:

 

 

 

 

 

 

 

 

 

 

 

 

 

esaa recenzia wignisa:

Bernhard Riemann 1826-1866¾

Turning Points in the Conception of Mathematics

{revoluciuri cvlilebebi maTematikis gaazrebaSi}.

wignis avtori: Detlef Laugwitz

(ingl. mTargmn. Abe Shenitzer);

Boston: Birkhäuser,1999; 357 pp.

(internetSi)

 

 

 

 

Targmna niko guniam

 

 

 

 

Sinaarsi

 

 

 

 

o   [winaTqma]

o   rimani—revolucioneri

o   yuradRebis miRma darCenili istoriuli garemoebani

o   maTematika, rogorc poezia

o   nikolas kuzanelma daafuZna  Tanamedrove mecniereba

o   niutonis uxeSi Secdoma

o   gausidan rimanamde

 

 

 

 

 

[winaTqma]

Sinaarsisken

 

 

 

 

bernhard rimani iyo is revoluciuri moazrovne, romlis aRmoCenebma maTematikaSi, fizikaSi, fiziologiaSi da filosofiaSi, gardaqmna kacobriobis codna. msgavs moazrovneTa arasaxarbielo xvedri aseTia: maTi aRmoCenebi farTed xdeba cnobili da poulobs gamoyenebas, magram am aRmoCenaTa mTavari revoluciuri originalobebi maTgan amoglejilia da daufasebeli. amdenad, im Teslis msgavsad, romelic Caagdes civ da mSral niadagSi, rimanis originaluri aRmoCenebi darCa gauRvivebeli. es gagrZeldeba manamde, vidre ar gamoCndeba sxva revolciuri moRvawe, romelic gaaTbobs am niadags, mohfens axal Suqs, izrunebs masze. amas SeiZleba mohyves Teslis aRmoceneba da msxmoiare mcenared gardaqceva.

mokled, revoluciuri moazrovne cnobili rom gaxdes, saWiroa sxva aseTive moRvawe. detlef laugvitci, rimanis geniis Tayvanismcemeli, sulac ar gaxlavT revolcioneri, uTuod. mis mier dawerili biografia savsea saintereso momentebiT. igi mimoixilavs rimanis Sromebs da cotaoden iyureba rimanis naazrevTa siRrmeSi. sinamdvileSi mifuCeCebulia rimanis yvelaze arsebiTi wvlili, ganxilulia ra isini rimanis epistemelogiur[1] mterTa poziciidan.

laugvitcs jiutad surs rimani ganixilos niutonisa da eileris tradiciis mecnierad, romelic opoziciuradaa ganwyobili kuzanelis, kepleris da laibnicis mimarT. aseTi Secdoma damaxasiaTebelia me‑20 saukunis akademiuri wreebisaTvis, metwilad imaTTvis, vinc yuradRebas ar aqcevs istorias da romlebic rimans icnoben mxolod meoradi wyaroebiT. xolo imaTT, vinc rimans icnobs gamouqveynebeli Tu gamoqveynebeli wyaroebiT—aseTia laugvitci—msgavsi Secdomebi ar epatieba. laugvitci an dabrmavebulia Tanamedrove maTematikuri formalizmisadi Tavisi erTgulebiT an mizanmimarTulad Tvalmaqcobs.

 

 

 

 

nax.1. bernhard rimani—Bernhard Riemann, 1826-66, didi germaneli maTematikosi, romelmac udidesi zegavlena moaxdina maTematikis da saerTod mecnierebis ganviTarebaze.

 

 

 

 

rimani—revolucioneri

Sinaarsisken

 

 

 

 

am recenziis avtori xelsayrel viTarebaSi aRmoCnda imis gamo, rom is TanamSromlobs Tanamedroveibis iseT moazrovnesTan, romelmac moaxdina gadatrialeba rimanis revoluciuri azrovnebis gagebaSi. ganaxorciela ra Tavisi SemoqmediTi garRveva  fizikur ekonomikaSi, lindon la-ruSma, mogvianebiT gaacnobiera paralelebi sakuTar aRmoCenebsa da im aRmoCenebs Soris, romlebic gaakeTa rimanma geometriaSi. Cveni am mimoxilvis miznebisaTvis ukeTesi iqneba, Tu mokled mimovixilavT l. la-ruSis fundamentur aRmoCenas[2][1].

eZebda ra ekonomikis zrdis namdvil wyaroebs, la‑ruSma SeniSna, rom ekonomikis potencialis zusti maCveneblebi izrdeba mosaxleobis simWidrovis matebis Sesabamisad. man gaacnobiera, rom erTaderTi wyaro am matebisa, romelsac ekonomikur progress uwodeben, aris adamianTa individualuri gonebebis SesaZlebloba—ganaxorcielos universaluri principTa aRmoCena. la‑ruSis mixedviT, adamianTa SemoqmediTi aRmoCenebis buneba gavs gamiznul cvlilebebs evkliduri geometriis aqsiomebis, gansazRvrebebis da postulatTa sistemaSi. aseTi cvlilebebi ver gakeTdeba deduqciuri procesiT sistemis SigniT, misi aqsiomebis, gansazRvrebebisa da postulatebis meSveobiT. msgavsi {sistemis  gare, SemoqmediTi} aRmoCenebi tipiuria araevkliduri geometriis Seqmnis procesisaTvis, rogorc es gviCvena rimanma.

amasTanave, la-ruSma ganaxorciela sxva unikaluri aRmoCenac: adamianTa SemoqmediTi aRmoCenis igive principebi gamosadegia, efeqturi fizikuri kanonebis aRmoCenis saqmeSi da klasikuri xelovnebisadmi. rimanis mravlad-bmuli mravalsaxeobis cneba la-ruSma gamoiyena am kognitivur procesebsa da fizikuri ekonomikis sakiTxebs Soris TanafardobaTa gamosaxatavad[3][2].

la-ruSis midgoma erTaderTi kompetenturi meTodia rimanis naSromTa Sesaswavlad. ase rom, rimani unda ganvixiloT la-ruSis poziciidan—adamianTa uwyveti SemoqmediTobis Sesaxeb, da ara ise, rogorc amas laugvitci akeTebs—rimanis Sromebis reviziiT, Tanamedrove formaluri maTematikis leqcionaruli suliskveTebis mixedviT. laugvitci aSkarad mouTmenelia amaSi da rimaniseul koncepciebs ganixilavs Tanamedrove maTematikuri formalizmis mixedviT. igi acnobierebs amas da Tavis naSromis SesavalSi wers: "aRsaniSnavia, rom maTematikosTa Sexedulebebi me‑19 saukunis adreul periodSi ase gansxvavdeboda Tanamedrove Tvalsazrisebisagan¼"

 

 

 

 

Wikipedia

nax.2.

gotfrid laibnici.

1646-1716

Wikipedia

nax.3.

karl fridrix gausi.

1777-1855

 

 

 

 

yuradRebis miRma darCenili istoriuli garemoebani

Sinaarsisken

 

 

 

 

imisaTvis rom TviT rimanis meTodebi gamoviyenoT missave Sesaswavlad, upirveles yovlisa saWiroa gvesmodes istoriul-epistemelogiuri maxasiaTeblebi im ideaTa erTobliobebisa, romelTa garemocvaSi cxovrobda da moRvaweobda rimani. is iyo abraham gotheld kestneris (Kästner) studentTa momdevno Taobis warmomadgeneli. me-18 saukuneSi, kestneri iyo gulmxurvale damcveli keplerisa, laibnicisa da baxisa. kestnerma, romelic aRzrdili iyo laibnicis ideebze, Seasrula gadamwyveti roli mecnierebaSi. getingenis universitetSi misi studentebi iyvnen gausi, boliai (Bolyai), olbersi (Olbers) da bartelsi(Bartels).

 

 

 

 

Wikipedia

 

 

 

 

nax.4. abraham gothelf kestneri, 1719-1800.

mTargmnelisagan: a.g.kestneri iyo germaneli swavluli, laipcigis universitetis profesori (maTematika, filosofia, iurisprudencia), 1756 wlidan getingenis universitetis profesori (bunebismetyveleba, geometria).

kestneris publikaciaTa Sorisaa: "maTematikis safuZvlebi" (Anfangsgründe der Mathematik –Göttingen 1758–1769, 4 Bände; 6. Aufl. 1800) da "maTematikis istoria" (Geschichte der Mathematik—Göttingen 1796–1800, 4 Bände). rogorc aRniSnaven, es nawarmoebebi savsea "gonebamaxviluri dakvirvebebiT". (n.g.)

 

 

 

 

sruliad araa SemTxveviTi is, rom es adamianebi iyvnen damaarseblebi imisa, rac Semdeg cnobili gaxda, rogorc "anti-evkliduri" geometria. maTi Sedegebi, ganxiluli amomwuravad, safuZvlad daedo rimanis cnobil disertacias, romelic man dawera  samsaxurSi misaRebad {universitetSi}—misi saxelwodebaa: "mosazrebebi, romelsac eyrdnoba geometriis safuZvlebi". kestneri Tavad iyo is, vinc pirvelma mravali naSromi miuZRvna aRniSnul Temas, eyrdnoboda ra kuzanelis, keplerisa da laibnicis Sromebs. magram kestneris Sromebi ufro vrceli iyo. maT fokuss warmoadgenda klasikuri metaforebis gafarToeba mecnierebaSi. is Rrmad iyo CarTuli proeqtSi, romelic miznad isaxavda germanuli enis gardaqmnas mecnierebis enad. mas yavda produqtiuli Tanamzraxveli, didi germaneli dramaturgis, gotfrid lesingis saxiT, romelic, mose mendelsonTan erTad, TavgamodebiT icavda platons da laibnics, eileris, volteris da niutonis mimdevari britanuli skolis Semotevebisagan. gausi kestners uwodebda "poets maTematikosTa Soris da maTematikoss—poetTa Soris". kestner-lesing-mendelsonis TanamSromlobam Seqmna germaniis klasikuri periodi, romelic aRiniSna didi miRwevebiT xelovnebaSi da mecnierebaSi, romlis magaliTia rimanis Semoqmedeba.

 

 

 

 

Wikipedia

nax.5. mose mendelsoni,

1729-1786.

Wikipedia

nax.6. gothold lesingi,

1729-1781.

 

 

 

maTematika, rogorc poezia

Sinaarsisken

 

 

 

 

swored am Suqze unda iqnas ganxiluli rimanis Sromebi. gausis msgavsad, ymawvilobaSi rimanic iyo dainteresebuli poeziiT, rac Cans mis maTematikur SromebSi. sinamdvileSi, rimanis miRwevebi maTematikaSi, filologiis ganStoebaa. rimanisaTvis maTematika iyo metaforaTa generatori, romelic adamianis gonebas exmareba im paradoqsebis gagebaSi, romelic TavisTavad Cndeba fizikuri samyaros kvlevisas. maTematikuri formalizmi, riTac dResac xSirad mosaven mis naazrevs, misTvis anaTemas warmoadgenda. amas xvdeba laugvitcic, romelic SeniSnavs, rom rimanis Sromebi Tavisufalia gamoTvlebisagan da formulebisagan, romelsac moiTxovs dRevandeli akademiuri stili.

metaforuli damokidebuleba maTematikisadmi gadmocemulia mis cnobil disertaciaSi, agreTve "filosofiur SeniSvnebSi", romelic gamovida misi gardacvalebis Semdeg[4][3]. pirvel nawilSi, romelic dasaTaurebulia "mcdeloba maTematikisa da fizikis ZiriTad cnebaTa TeoriaSi, rogorc bunebis axsnis safuZveli"[5], rimani wers:

"sabunebismetyvelo mecniereba aris mcdeloba SevimecnoT buneba zusti cnebebis meSveobiT.

"aucileblad iTvleba, rom is zogadi warmodgenebi da ideebi, romlebic avsebs da aZlierebs Cvens SegrZnebebs, ra warmatebiTac aqamde gvexmareboda bunebis SecnobaSi, iseve gagviwevs samsaxurs momavlis ganWvretaSic. anu, im  xarisxiT, ramdenadac warmodgenaTa es sistema araa sruli, momavlis ganWvretac saalbaToa; xolo im ideaTa Sesabamisad rasac ¢SesaZlebeli¢ niSnavs, momavali determinirebulia (aris ¢aucilebeli¢, an piriqiT, ganuxorci-elebeli). amave dros, yoveli calkeuli movlenis ¢SesaZleblobis¢ (anu ¢albaTobis¢) xarisxi, romelic am koncepciis Tanaxmad gamoiyureba rogorc SesaZlebel, SeiZleba aRiweros maTematikurad, Tu amisTvis arsebuli cnebebi sakmarisia.

"am Tvalsazrisis Tanaxmad, Tu adgili aqvs imas, rac aris aucilebeli an SesaZlebeli mocemuli koncepciaTa mixedviT, maSin es adasturebs am koncepciebs da im rwmenas, romelic safuZvlad daedo am koncepciaTa damadasturebeli cdebs. magram, Tu raime iseTi moxda, rac moulodneli iyo Cvens mier miRebuli daSvebebiT, anu rac gamoricxuli iyo an ara-SesaZlebeli maTi mixedviT, maSin Cndeba maTi Sevsebis saWiroeba; anda, Tu es aucilebelia, saWiro iqneba aqsiomebis ise gadamuSaveba, rom rac iyo aRqmuli rogorc SeuZlebeli, Sewyvets iyos aseTi. ideaTa da cnebaTa sistemis aseTi Sevseba Tu gaZliereba-gardaqmna, warmoqmnis cdaTa moulodneli Sedegis "axsnas". am procesis meSveobiT, bunebis movlenebis Cveni gageba, TandaTan xdeba ufro da ufro sruli da koreqtuli; amdenad, Cven miT ufro Rrmad SevdivarT movlenaTa xiluli fardis miRma.

"kauzaluri sabunebismetyvelo mecnierebis istoria, drois ra siSoridanac Cven SegviZlia misi ganxilva, gviCvenebs rom igi faqtiurad bunebisadmi Setevis gzaa. is cnebiTi baza, romelic  amJamad aris sabunebismetyvelo mecnierebaTa safuZveli, TandaTanobiT warmoiqmna  Zveli konceptualuri sistemis TandaTanobiTi transformaciiT. mosazrebebi, romelTac mivyevarT axali modis axsnebisaken, yovelTvis SeiZleba piruku dayvanili iqnas winaaRmdegobebze, romlebic aseTad gamoiyreba Zveli modis axsnaTa mixedviT.

"axal  koncefciaTa Camoyalibeba, ramdenadac es procesi eqvemdebareba dakvirvebas, am gziT xdeba.

"herbartma gza gaukvala im cnebebis damkvidrebas, romlebic saSualebas gvaZlevs SevicnoT samyaro. es iseTi cnebebia, romelTa wyaroebs Cven ver vipoviT verc istoriaSi da verc Cvens naSromebSi, radganac isini Cven gadmogvecema Cveni enis meSveobiT, sagangebo SeTanxmebebis gareSe da Tavisi originalebisagan SeiZleba imdenad gansxvavdebodes, ramdenadac isini azris martiv xatTa ubralo kombinaciebia; amasTanave, es cnebebi ar unda gansxvavdebodes adamianuri azris zogierTi specifikuri konstituentebisagan, romlebic win uswrebs yovelive cdas (rogorebicaa kantis kategoriebi).

"es afuZnebs Tavis wyaroebs Cvens unarSi gavigoT is, rac gveZleva grZnobad aRqmaSi, mniSvnelovania CvenTvis, vinaidan am gzaze mxolod isaa is erTaderTi, romlis mniSvneloba SeiZleba damakmayofilebeli iyos mecnierebisaTvis¼"

rimanma icis, rom paradoqsebi, romelTac warmoSobs aseT axal koncepcias CvenSi, aRmoCenil iqna arawrfivobis kvlevaSi, usasrulod mcireSi. es rimans aSkarad ayenebs kuzanelis sokrateseul gzaze, romelic diametralur opoziciaSia, aristoteledan momdinare usasrulod mcireSi gawrfivebis meTodTan—niutonisa, eilerisa da koSisa.

es gansxvaveba yvelasaTvis cxadia, vinc icis mecnierebis realuri istoria. aq mogvyavs am istoriis mokle gadmocema, raTa mkiTxvelma mis konteqstSi SeZlos laugvitcis wignis Sefaseba.

 

 

 

 

nikolas kuzanelma daafuZna  Tanamedrove mecniereba

Sinaarsisken

 

 

 

 

1440 wlisaTvis, roca gamovida nikolas kuzanelis naSromi On Learned Ignorance (mecnieruli umecrebis Sesaxeb), mis avtors ukve Secvlili qonda ptolemeos-aristoteles fiqsirebuli samyaro. es man ganaxorciela berZnul-egvipturi codnis reanimaciiT—heliocentruli samyaros Sesaxeb. amave dros mas gamoTqmuli qonda mosazreba, rom planetaruli moZraoba xasiaTdeba regularuli da ara-mudmivi mrudebiT.

kuzanelis moZRvrebis kvalze, iohan keplerma dainaxa am wirTa zusti bunebis Seswavlis aucilebloba. Tavis axal astronomiaSi (New Astronomy, 1609), keplerma aCvena, rom sami, radikalirad gansxvavebuli sistemebi—ptolemeosis, brahesi da kopernikis—miuxedavad imisa, rom isini maTematikurad eqvivalenturia, mainc gansxvavdeba planetaTa xiluli moZraobebisagan. planeta marsisaTvis am gansxvavebaTa detalurad Seswavlis safuZvelze, keplerma ipova maTi Secdoma—samive uSvebda, rom planetebis moZraobebi xasiaTdeba mudmivi simrudis wirebiT, aramudmivi {simrudis} wirebis sapirispirod. keplerma win gauswro rimanis ufro zogad midgomas maTematikuri fizikisadmi da aCvena, rom Secdoma mdgomareobda ara TavisTavad ptolemeosis, brahes da kopernikis maTematikaSi, aramed maT fizikur principebSi, romelTa mixedviT iqmneboda saTanado maTematikuri modelebi.

kepleri aCvenebs, rom aseTi meTodebi—romlebic gavs aw ukve diskreditirebul meTodebs sistemuri analizisa da informaciis Teoriisa—Tavs moxveulia fizikur samyaros; daSvebebi, romlebTac efuZneba isini, Cadebulia maTematikur modelSi—am SemTxvevaSi esaa mudmivi simrude. keplerma ukuagdo aristoteles midgoma, riTac moaxdina axali revolucia maTematikur fizikaSi da SemoiRo Tavisi hipoTezebi, planetaTa fizikuri moZraobis Sesaxeb. es fizikuri principebi ixilavs mzis sistemas, rogorc mTliansa da harmoniulad mowyobils. planetaTa orbitebis Siga da gare maxasiaTeblebi ganisazRvreba im principebiT, romlebic devs am harmoniul wesrigSi. kepleri cxadyofs, rom am principebs SeiZleba Cawvdes adamianis goneba.

kepleris aRmoCenebi paradigmulia {magaliTis Zalisaa} im moTxovnebisaTvis, romelsac rimani ayenebs daSveba- aqsiomaTa gadamuSavebis Taobaze, imisaTvis, rom SevqmnaT axali cnebiTi sistema, romelic aucilebelia Cveni codnis gasaZliereblad.

amjerad ukve kepleris fizikurma hipoTezebma warmoSves saWiroeba  axali maTematikuri modelebisa, vinaidan maSindeli maTematikuri aparatiT SeuZlebeli iyo gaezomaT aramudmivi simrudeebi usasrulod mcireSi. amis Semdeg keplerma gardaqmna Tavisi fizikuri principebi ise, rom isini misadagebuli yofiliyo maTematikuri sisusteebisadmi da iTxovda axali maTematikis Seqmnas. New Astronomy-is bolo gverdebze kepleri mouwodebda momaval mecnierebs SeeqmnaT axali koncepciebi, auculebeli aramudmivi simrudeebis gasazomavad usasrulod mcireSi, romelic ganxorcielebuli iqna laibnicis usasrulod mcireTa aRricxvis SeqmniT.

niutonis uxeSi Secdoma

Sinaarsisken

nitoni cnobili iyo arasaxabielo reputaciiT, Tavisi okulisturi rwmenis gamo. is aranairad ar Rebulobda kepleris meTodebs, samagirod cdilobda planetaTa moZraobis maTematikur aRweras. ptolemeosis ukve maSin diskreditirebuli meTodebis xelaxla gacocxlebiT, niutoni moiTxovda ar ekeTebinaT araviTari hipoTezebi fizikuri samyaros mimarT; am moTxovnas SemdegSi mwared dascinebs rimani.

TiTqosda, rogorc kepleris parodia, niutonic moiTxovda fizikuri samyaro damorCileboda formalur maTematikur konstruqciebs, Tan daJinebiT irwmuneboda, rom yoveli fizikuri movlena mimdinareobs evkliduri geometriis absoluturi dro-sivrcis fonze. amjerad ki, niutonis amgvarma moTxovnebma ganapirobes misi uZlureba mieRo raime codna fizikuri samyaros Sesaxeb. amitom is TavSesafars poulobs kepleris principebis maTematikur manipulaciebSi, raTa daafuZnos Tavisi moZRvreba planetaruli moZraobis Sesaxeb. laibnicma Zalian kargad icoda niutonis es Secdoma, rac asaxulia laibnic-klarkis SesaniSnav mimoweraSi. am Secdomis gaazreba rimans gadaeca sxvaTa meSveobiT, romelTa Sorisaa kestneri da gausi. rimanma, mis mier niutonis Sromebis erTgvari pozitiuri citirebis miuxedavad, es yvelaferi icoda. es aSkaraa im meTodebidan, romelsac is iyenebs yovel Tavis SromaSi, agreTve im xazgasmuli damokidebulebidan benTlis (Bentley) cnobili naSromisadmi, sadac avtori amtkicebda, rom niutonis Sor-qmedebis principi filosofiuri absurdia.

asea Tu ise, britanul/venecianuri oligarqiis mxardaWeriT, niuton-eileris wrfivi maTematikuri modelirebis meTodma gaimarjva da gavrceleba pova me-18 saukuneSi.

 

 

 

 

gausidan rimanamde

Sinaarsisken

 

 

 

 

1801 wels, karl fridrix gausma Rirsebebi aRudgina kepleris da laibnicis meTods, roca man gansazRvra asteroid cereras orbita, mxolod da mxolod ramodenime dakvirvebis meSveobiT. es miRweva, romelic SeuZlebeli miaCnda eilers, ganxorcielebuli iyo 24 wlis gausis mier, maSin roca yvela avtoritetuli evropeli astronomis mcdeloba—daedginaT j. piacis mier aRmoCenili cereras orbita, uSedego aRmoCnda. maTi uSedegoba gamowveuli iyo maTive meTodis naklovanebiT—maTi damokidebulebiT niuton-eileris usasrulod mcireSi gawrfivebis meTodze.

gausma, romelic iyenebda kepleris princips, romlis Tanaxmad mzis sistema harmoniuladaa mowesrigebuli, SeimuSava nebismier usasrulod mcire SualedSi arawrfivi harmoniuli wesrigis gamoTvlis meTodi.

mogvianebiT gausi imave meTodebs miuyenebs geodeziis sferos da gansazRvravs dedamiwis geometriul zedapirs. am SemTxvevaSic isev saqme gvaqvs gausis aRmoCenasTan, romlis Tanaxmad, virtualuri usasrulod mcire gansxvaveba astronomiulad gazomil meridiansa da dedamiwis zedapirze gazomil mis sigrZes Soris, Sedegia gamoyenebuli principebisa da ara gazomvebis cdomilebisa. kepleris msgavsad, gausma ganaxorciela inteleqtualuri Zalisxmeva, rom eTqva—es usasrulod mcire gansxvaveba (rkalis 16 sekundi), moiTxovs daSvebebisa da aqsiomebis gadamuSavebas. gausma aCvena, rom SeuZlebelia dedamiwis formis dadgena winaswar aCemebuli maTematikuri formiT da Semdeg fizikuri gazomvebis morgebiT am formisadmi. gausi isev esesxeba keplersa da laibnics, qmnis maTematikur formulebs im fizikuri principebidan gamomdinare, romlebzec misi gazomvebi iyo dafuZnebuli. aman gausi miiyvana geometriis sruliad axal koncepciamde

gausis aRniSnuli Sromebi astronomiaSi da geodeziaSi iyo Rrma braldeba imaSi, rom evklides geometriis daSvebebi da aqsiomebi ver axasiaTebs sivrcis namdvil bunebas. miuxedavad amisa, man ar gamoaqveyna Tavisi sruli nafiqrali am saqmis irgvliv. gausi araerTgzis amtkicebda Tavis korespodenciebsa da SeniSvnebSi, rom is darwmunebulia imaSi, rom evkliduri geometria arasworia, da mkacrad akritikebda niutons, eilersa da kants, romlebmac evklides absoluturi sivrce daudes safuZvlad fizikur samyaros. amasTanave, gauss esmoda, rom aqsiomebi, romlebic safuZvlad udevs bunebas, unda ganisazRvros fizikuri gazomvebiT da mxolod aseTebs unda daefuZnos araevkliduri geometria.

gausis am Sromam didi gavlena moaxdina rimanze, rasac is araerTxel aRniSnavs. garda kerZo diskusiebisa, romlebic albaT eqneobodaT am or adamians, rimani isedac guldasmiT swavlobs gausis Sromebs, simrudis geodeziisa da ricxvTa Teoriis Sesaxeb. rimanma xmamaRla ganacxada is, rasac gausi ambobda kerZo saubrebSi—sivrcis araevkliduri bunebis Sesaxeb, Semdeg is Tavad Seudga am koncepciis damuSavebas fizikuri samyaros mimarT. aman rimani miiyvana im axali metaforebis SemuSavebamde, romlebic saWiroa moqmedebaTa gamosaxatavad, araevklidur areSi. es Cans misi Sromebidan, kompleqsuri cvladis funqciaTa Sesaxeb, hipergeometriul funqciaTa Sesaxeb, abelis funqciaTa Sesaxeb da misi sxva maTematikuri Sromebidan. igive antievklidur midgomebs vxedavT mis SromebSi, fizikaSi da biologiur sakiTxebze, rogoricaa magaliTad misi saxelganqmuli Sroma Sokur talRebze, adamianis Tvalis fiziologiidan.

saubedurod, es yvelaferi mxedvelobidan gamorCa avtors, detlef laugvitcs, romelic imeorebs gavrcelebul Secdomas, roca rimanis genias yofen Teoriul, praqtikul da filosofiur nawilebad. es gaugebars xdis rimanis aRmoCenebs.

ase rom, rimanis kompetenturi biografia kvlav dasaweri darCa.

 

 

 

 

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[1] epistemelogia [berZn. Episteme (codna) + logos (moZRvreba)] —Semecnebis Teoria, gnoseologia. (n.g.)

[2][1] meti informaciisaTvis mkiTxvels SeuZlia mimarTos TviT la-ruSis Sromebs, magaliTad Semdeg statias: "Riemann Refutes Euler"{rimani ar eTanxmeba eilers}, 21st Centuri, Winter 1995-96, pp.36-47. la-ruSis es nawyveti, sinamdvileSi winasityvaobaa rimanis "filosofiuri fragmentebis"  jerjerobiT pirveli inglisuri Targmanisa, romelic qveyndeba iqve: Philosophical Fragments, pp.50-62. (b.d.)

[3][2] ix. "The Becoming Death of Systems Analysis", Executive Intelligence Rewiew, March 31, 2000, 10-73. (b.d.)

[4][3] ix. sqol.#2. (b.d.)

[5] originalSi: "Attempt at a Theory of the Fundamental Concepts of  Mathematics and Physics as the Foundation for the Explanation of Nature". (n.g.)