
penrose-lucas tark

penrose-lucas tark ack taarkik tark haye joe aanshik roop seey ganitshastri aur tarkashastri curt godel dwara vikasit ack siddhant parr adharit haye. 1931 mein, unhone saabit kiya kii buniyaadi ankganit koo saabit karane mein saksham pratyek prabhaavi roop seey utpann siddhant yaa tou susangat honey mein whiffle rahata haye yaa poorna honey mein whiffle rahata haye. aupchaarik pranali key godel vaakyon kii sachchai koo dekhane kii maanav kshamata key kaaran, yeh tark diyaa jaataa haye kii maanav munn kii ganana ack turing machine parr naheen kii jaa sakati haye joe pino ankganit parr kaam karati haye kyonki baad vaalaa apane godel vaakya kaa satya moolya naheen dekh sakata haye, jabaki maanav munn curr sakata haye. ganitshastri roser penrose ney chetna parr apani pahali pustak, "samrat kaa nayaa munn" (1989) mein tark koo sanshodhit kiya, jahan unhone ise apane chetna key siddhant kaa aadhar pradaan karane key liye istemal kiyaah uddeshyapurna kamee.
prishthabhoomi.
godel ney dikhaaya kii apani sthirata key bayaan sahit aisaa koee bhee siddhant asangat haye. pramaan kaa ack pramukh tatva siddhant key liye ack "godel vaakya" kaa nirmaan karane key liye godel sankhya kaa upayog haye, joe apani apurnata key ack kathan koo kootbaddh kartaa haih "yeh siddhant iss kathan koo saabit naheen curr sakata haye"; yaa "main iss pranali mein siddh naheen curr sakata huun. yaa tou yeh kathan aur isaki nakaratmakta donon apramaanit hain (siddhant adhura haye) yaa donon hii siddh karane yogya hain (siddhant asangat haye). pahali sthiti mein kathan sahaj gyaan seey sach haye (kyonki yeh siddh karane yogya naheen haye); anyatha, kathan sahaj gyaan seey galat haye-halanki siddh karane yogya haye. 
ack anuroop kathan kaa upayog yeh dikhaane key liye kiya gayaa haye kii manushya machines key samaan seemaon key adheen hainh "leukas lagaatar iss sootra parr jore naheen dey sakate hain. lucas, jey kii raksha mein. ee. martin aur key. aich. angleman ney "munn kii aaee kii dou aankhen hain" mein tark diyaa kii lucas pehchaan sakata haye kii vaakya sach haye, kyonki ack drishtikon haye jisase vaha samajh sakata haye kii vaakya usey kaise chaal kartaa haye. iss drishtikon seey lucas iss baat kii sarahana curr sakata haye kii vaha vaakya kaa daavaa naheen curr sakata haye-aur parinamswarup vaha isaki sachchai koo pehchaan sakata haye. phir bhee, yeh aalochana kewal tabhi kaam karati haye jaba humm yeh maan lein kii humm lucus key tark koo ack aupchaarik pranali key saath badal sakate hain jisamen ack godel vaakya haye, lekin penrose-lucus tark anyatha saabit karane kii koshish kartaa haih ankganit key iss star koo samajhane kii hamari kshamata ack aupchaarik pranali naheen haye jise ack nirdhaarak turing machine mein anukaran kiya jaa sakata haye.
penrose ney tark diyaa kii ack aupchaarik pramaan pranali apani sthirata saabit naheen curr sakati haye, lekin maanav ganitvidon dwara spasht parinam diye jaa sakate hain. vaha iss asamaanta koo iss arth mein lete hain kii maanav ganitshastri aupchaarik pramaan pranaliyon key roop mein varnit naheen hain, aur isaliye ack gair-computable algorithm chalaa rahey hain. godel kii pramey key nihitarth key baare mein isi tarah key daavon kaa mool roop seey 1940 key dashak key anta mein turing dwara samarthan kiya gayaa thaa, apane swayam key godel dwara 1951 key "gibbs vyakhyan" mein, ee dwara. nagel aur jey.aar. 1958 mein neuman, aur baad mein 1961 mein oxford key merton college key daarshanik johnn lucas dwara lokpriya banaaya gayaa.
parinam.
yadi sahee haye, tou penrose-lucus tark mastishk mein gair-computable vyavhaar key bhautik aadhar koo samajhane kii aavashyakta paida kartaa haye. adhikansh bhautik niyam ganana yogya hain, aur iss prakaar algorithm hain. haalaanki, penrose ney nirdhaarit kiya kii tarang falan patan ack gair-computable prakriya key liye ack pramukh ummidwar thaa.
quantum yantriki mein, kanon koo shaastriya yantriki kii vastuon seey alag tareeke seey maanaa jaataa haye. kanon koo tarang karyon dwara varnit kiya jaataa haye joe schroedinger sameekaran key anusaar vikasit hotey hain. gair-sthir tarang falan pranali key eigenstate key raikhik sanyojan hain, ack ghatana joe superposition siddhant dwara varnit haye. jaba ack quantum pranali ack shaastriya pranali key saath baatchit karati haye-i.ee. jaba ack avalokan yogya koo maapa jaataa haye-tou pranali ack shaastriya anukool bindu seey avalokan yogya key yaadrichhik eigenstate mein girati dikhaai detee haye.
yadi patan vaastav mein yaadrichhik haye, tou koee bhee prakriya yaa algorithm isake parinam kaa nirdhaaran naheen curr sakata haye. isane gair-computable prakriya key bhautik aadhar key liye ack ummidwar key saath penrose pradaan kiya jise unhone mastishk mein maujood honey kii parikalpana kii thee. haalaanki, unhein paryaavaran seey prerit patan kii yaadrichhik prakriti pasand naheen thee, kyonki yaadrichhikta ganitiya samajh key liye ack ashajanak aadhar naheen thaa. penrose ney prastaav diyaa kii alag-thalag pranaliyon koo abhee bhee tarang falan patan key ack nae roop seey gujarna parh sakata haye, jise unhone vastunishth kamee (yaa) kahaa.
penrose ney antariksh kaal kii sambhaavit sanrachana key baare mein apane swayam key vichaaron kaa upayog karke samanya saapekshata aur quantum siddhant kaa milan karane kii koshish kii. unhone sujhaav diyaa kii plank paimaane parr ghumaavdaar antariksh samay nirantar naheen haye, balki asatat haye. penrose ney yeh abhinirdhaarit kiya kii pratyek alag quantum superposition kaa apana spacetime vakrata kaa tukada hotaa haye, spacetime mein ack fafola. penrose seey pataa chalata haye kii inn antariksh kaal key fafole parr gurutvaakarshan bull lagaaya jaataa haye, joe sootra _ 1 key plank paimaane seey oopar asthir hoe jaataa haye aur kewal ack sambhaavit avastha mein gir jaataa haye. penrose key anirnaya siddhant dwara dee gaee yaa key liye ack nishchit seemaah
kahanh
iss prakaar, vastu kii dravyamaan-oorjaa jitani adhik hogi, utani hii teji seey yeh gujarati haye yaa isake vipareet. paramanu-star superposition koo 10 million varshon kii aavashyakta hogi yaa seema taka pahunchane key liye, jabaki ack alag 1 kilogram vastu 10−37 mein seema taka yaa seema taka pahunch jaayegi. inn dou taraju key beach kaheen naa kaheen vastuein tantrika prasanskaran key liye praasangik samay-seema parr gir sakati hain.
penrose key siddhant kii ack aavashyak visheshta yeh haye kii jaba vastunishth kamee hoti haye tou avasthaon kaa chayan naa tou yaadrichhik roop seey kiya jaataa haye (jaisa kii tarang falan key patan key baad vikalp hain) aur naa hii algorithm key roop mein. balki, avasthaon kaa chayan antariksh kaal jyaamiti key plank paimaane mein antarnihit "gair-computable" prabhaav dwara kiya jaataa haye. penrose ney daavaa kiya kii aisee jaankaari platonic haye, joe plank paimaane parr shuddh ganitiya satya, saundarya aur naitik moolyon kaa pratinidhitva karati haye. yeh teen duniyaon key baare mein penrose key vichaaron seey sambandhit haih shaaririk, mansik aur platonic ganitiya duniya. unake siddhant mein, platonic duniya maulik antariksh kaal kii jyaamiti seey mell khaati haye joe gair-computational soch kaa samarthan karane kaa daavaa karati haye.
aalochana.
maanav buddhimatta key computational siddhanton key liye godel kii apurnata pramey key nihitarth key baare mein penrose-lucas tark kii ganitvidon, computer vaigyaanikon aur daarshnikon dwara aalochana kii gaee thee, aur inn kshetron mein visheshagyon key beach aam sahamati yeh haye kii tark whiffle hoe jaataa haye, vibhinn lekhak tark key vibhinn pahaluon parr hamla karate hain.
lafort ney bataaya kii ack apramaanit godel vaakya kii sachchai koo jaanane key liye, kissy koo pahale seey hii aupchaarik pranali koo susangat honah chaahiye (halanki yeh vaha bindu naheen thaa jise lucas ney banaane kii koshish kii thee); benaseraf kaa sandarbh dete hue, unhone yeh pradarshit karane kii koshish kii kii manushya yeh saabit naheen curr sakate kii way susangat hain, aur sabhi sambhaavanaon mein maanav mastishk asangat algorithm hain joe kissy prakaar key samanantar tark kaa upayog karate hain, udaaharan key roop mein penrose key apane lekhan key bheetar kathit virodhabhason kii or ishara karate hain. isi tarah, minsky ney tark diyaa kii kyonki manushya jhoothe vichaaron koo sach maan sakate hain, isaliye maanav ganitiya samajh koo susangat honey kii aavashyakta naheen haye aur chetna kaa aasaani seey ack nirdhaarak aadhar hoe sakata haye. unake liye kuchh pratikriyaon mein unake prakaashan "antargyaanvaadi naheen (turing) masheenen" mein spasht roop seey shamil hain. penrose ney minsky key khilaf yeh kahate hue bhee tark diyaa kii maanav ganitvidon dwara kii jaane vaali galatiyan aprasangik hain kyonki way sudhaarne yogya hain, jabaki taarkik satya vyaktiyon key liye "anupalabdh satya" hain, joe ack dhwani pranali key parinam hain aur kewal vahee hain joe mayane rakhate hain. galatiyon kaa seedha matlab yeh naheen haye kii maanav munn apane aap mein asangat haih javic jeev sangyanatmak uthal-puthal key adheen hain, deerghakaalik smriti aur dhyaan mein kamee aatee haye; yeye hamari tark kshamataon koo cumm karate hain aur manushyon koo ack pranali key sabhi sambhaavit charon koo dhyaan mein rakhe binaa achetan roop seey kaary karane key liye majboor karate hain.
penrose kii doosari pustak, "munn kii chhaaya" mein german ney vistrit binduon koo galat bataaya. unhone tark diyaa kii ganitshastri pramanon key madhyam seey yaantrik khoj seey pragati naheen karate hain, balki pareekshan aur truti tark, antardrishti aur prerana seey pragati karate hain, aur yeh kii masheenen iss drishtikon koo manushyon key saath saajha naheen karati hain. unhone bataaya kii rosemarra key ganit koo aupchaarik banaaya jaa sakata haye. unhone penrose key platenism koo bhee aswikar curr diyaa. phir bhee, yeh maanav munn kii kathit kshamata key unake mool tark key liye jimmedaar naheen haye joe kii spasht-apramaanit vaakyon koo saabit karane key liye haye. isake alawa, sudridhikaran seekhane parr adharit kritrim buddhimatta sanchayi puraskar kii dhaarana koo adhikatam karane key liye ack vatavaran mein kaarravaai karke kaam curr sakati haye, joe pareekshan aur truti prakriyaon kii tarah kaam karati haye.
searl ney godel key liye penrose kii appeal kii aalochana kii kyonki yeh bhranti haye kii sabhi computational algorithm ganitiya vivaran mein saksham honey chaahiye. ack prati-udaaharan key roop mein, khojkarta ney vaahan panjikaran key hisse key roop mein vishisht vaahan pehchaan sankhya key liye licenses plate sankhya key assignment kaa hawala diyaa. khoj key anusaar, kissy gyaat vee. aaee. aine. koo usake ell. pee. aine. key saath jodane key liye kissy ganitiya kaary kaa upayog naheen kiya jaa sakata haye, lekin kaary kii prakriya kaafee saral haye-arthaat, "pahale aao, pahale paroso"-aur poori tarah seey ack computer dwara kiya jaa sakata haye. haalaanki, iss feifo vidhi koo aasaani seey ack ganitiya kaary key roop mein vyakt kiya jaa sakata haye.

