In ultimul timp temele principale ale stirilor a fost legata de reactia ostila mpotriva cetatenilor romani din Italia si mai nou si din alte tari europene.
Aceasta reactie fara precedent indreptata impotriva tuturor romanilor stabiliti in aceste state a pornit mai ales de la comportamentul anormal si infracţional al unei etnii minoritare de cetateni romani, si anume tiganii sau etnia romilor. Această etnie nu este specifică Romaniei, ea intalnindu-se in majoritatea tarilor europene in diverse proportii, dar noua sa denumire de romi (roma/romani/romanies in engleza) este asimilata mai ales cu numele tarii noastre: Romania, raspandindu-se astfel o confuzie care s-ar putea dovedi fatală pentru viitorul european al poporului roman.
Cand cetateanul italian, de pilda, citeste un articol in care se intrepatrund termenii "romeno" si "rom", este normal sa se afunde intr-o confuzie care, incetul cu incetul, duce la o suprapunere mentala a celor două denumiri.
Odata aceasta suprapunere instalandu-se, ea funcţioneaza si in sens invers; astfel auzim cum pe stadioane suporterii unor echipe adverse scandeaza: "tiganii, tiganii", referindu-se la romani. Rezultatul pe termen mediu si lung pentru populaţia Romaniei in raport cu popoarele europene poate fi devastator, instalandu-ne in coada Europei. De aceea, inainte de a vedea ce este de facut, merita studiat cum s-a ajuns in aceasta situatie.
Tiganii sunt un popor migrator. Migrarea tiganilor din India in Europa s-a facut intre secolele al IX-lea şi al XIV-lea, in mai multe valuri. Odata cu intrarea lor in Imperiul Bizantin, la mijlocul secolului al XI-lea, au capatat si numele etnic pe care il poarta astazi , Tigani. Aflandu-se pe teritoriul Greciei si-au atribuit denumirea unei secte religioase grecesti cu numele Athinganis sau Atsinganos care insemna "de neatins". Prima atestare a tiganilor in Imperiul Bizantin este conţinuta intr-un text hagiografic georgian, care datează din jurul anului 1088; aici se face referire la aşa-numitii Adsincani, renumiti pentru vrajile si faptele rele pe care le fac. Istoria europeana a tiganilor incepe la inceputul secolului al XIV-lea, cand acestia au patruns in Turcia, venind din Asia Mica. Prin anii 1415 - 1419 ii intalnim in toata Europa Centrala, din Ungaria pana in Germania. Pe la 1422, o banda numeroasa de tigani coboara in Italia, pana la Roma (precum se vede, istoria lor pe acele meleaguri a inceput mult inainte de valul de tigani veniti din Romania). In deceniul urmator au ajuns pana in Franta, Spania, Anglia si Scandinavia. Aici ei preiau denumirea de "egipteni" (Gypsies), foarte curand li s-a fixat numele pe care il poarta si astazi.
Foarte interesant este ca tiganii si-au atribuit intotdeauna numele altor etnii sau popoare care le-au ingaduit sa-şi ascunda etnia:
"Satra" vine de la casta Kshatria (razboinica) careia nu i-au apartinut niciodata.
"Tigan/Zigeneur/Zingaro etc" vine de la "Athinganoi", secta religioasa grecesca recunoscuta pentru activitatea de prezicere, tiganii n-au au apartinut niciodata acestei secte.
"Gypsy" vine de la "Egyptian" cum si-au spus acum vreo 600 de ani pentru a primi bani, locuinte si mancare pe gratis, pretinzand ajutor ca fiind crestini egipteni aflati in pelerinaj.
"Yansser" cum sunt cunoscuti la New York, vine de la ienicer turc, cum s-au prezentat tiganii emigrati in America pe la 1900. In Germania numele cele mai folosite sunt Zigeuner si Sinti. In limba franceza s-a impus numele Gitanes. In limbile engleza si spaniola, Gipsy, respectiv Gitano. In Danemarca, Suedia si Finlanda s-au prezentat sub numele de Tattan (tatari).
Precum se vede, tiganii s-au raspandit in toată Europa, venind din India prin Asia Mica si nu constituie sub nici o forma o problemă legata de poporul roman, mai mult decat de cel maghiar, francez sau spaniol, de exemplu. Cea mai timpurie informatie scrisa despre prezenţa tiganilor pe teritoriul Romaniei datează din 1385. De la primele atestari ale prezenţei lor in Tara Romaneasca si Moldova, tiganii au fost robi si vor ramane timp de mai multe secole, pana la legile de abolire a robiei de la mijlocul secolului al XIX-lea. In mod paradoxal, perioada cea mai buna a tiganilor a fost in perioada regimului comunist. In anii '70 PCR-ul in primii ani ai comunismului a manifestat in ce-i priveşte pe tigani, un fenomen de neconceput inainte: in aparatul de partid, in militie, armata si organele de securitate au fost angajati un numar relativ mare de tigani care au lansat o politica de formare a unui nationalism tiganesc de colonizare a satelor satesti si svabesti cu tigani adusi nu numai din toata Romania, dar adusi si din exteriorul Romaniei (Cum va explicati ca in satele din sasime sau svabime in care nu vezi tipenie de alta etnie decat de tigani ce vorbesc limbi precum bulgara, rusa, slovaca etc?). Imediat dupa '90 Nicolae Gheorghe apare ca membru GDS, publica la Revista 22, este trimis la tot felul de simpozioane internationale, devine membru Soros, lanseaza tot felul de programe pentru tigani, precum si infiintarea de catedre universitare tiganesti. Aceasta ascensiune a unor tigani s-a petrecut mai ales in conditiile politicii sociale a regimului comunist, care urmarea incurajarea categoriilor sarace si distrugerea vechii structuri sociale, refractara noilor randuieli. Asa se explica de ce, nu in putine comune, in funcţia de primar a fost pus un tigan. Datorită originii sociale "sanatoase" tiganii au fost promovaţi mai departe, facand cariera politica, ajungand in aparatul superior de partid. Ascensiunea lor s-a datorat nu originii lor etnice, pe care de altfel cei mai mulţi o declinau, ci pentru ca proveneau din categoriile sarace. Acesti tigani adevarati, oameni ajunsi in anumite functii, vor avea un rol important in promovarea etnica si in regimul ce a urmat regimului comunist. Si sub aspect locativ tiganii au facut un important progres in anii socialismului. Cocioabele care reprezentau habitatul natural al tiganilor pana in anii '50 au fost schimbate cu apartamente in blocurile nou construite, iar din anii '70, '80, cu locuinte in case nationalizate. Asa s-a ajuns in situatia de astazi, cand centrul multor orase mai este ocupat de tigani.
Sunt cateva elemente importante care nu pot fi ignorate:
1) Generalul (seful) securitatii din jud. Sibiu in '71 era un tigan care fusese deportat cu familia in Transnistria de unde a fugit
2) Nicolae Gheorghe devine secretarul personal al lui Cioaba in '71-'72
3) Cioaba e var primar cu Ion Iliescu (se poate verifica)
4) Cioaba participa la primul congres tiganesc de la Londra din '71 unde apare prima oara etnonimul de Rom
5) Anii '70 inseamna plecarea masiva a sasilor
6) Securitatea organizeaza un program de colonizare cu tigani a sasimii si svabimii
7) Scopul nu a fost integrarea tiganilor. Integrare inseamna o populatie minoritara tiganeasca intr-o populatie majoritara de alta etnie. O majoritate tiganeasca cu o minoritate ignorabila de alta etnie nu duce la integrarea tiganilor, ci la asimilarea celorlalti.( Dau cazul unor moldoveni din Galati asimilati in tigania din Garcini, de langa Brasov ).
Dupa 1989 s-au produs unele transformari majore in comportamentul populatiei de tigani. Pe fondul liberalizarii economice, o parte din ei au inceput diverse afaceri, dintre care multe profitand de haosul legislativ de la inceputul anilor '90, dar si de dispretul general fata de legi, au ajuns sa aducă unei parti a tiganilor sume importante pe care s-au cladit clanuri puternice, care folosindu-se de patura saraca a tiganilor, domina lumea interlopa, cu ramificatii importante in sfera politicului. De asemenea, profitand de deschiderea granitelor, o mare parte dintre ţigani au emigrat, stabilindu-se mai ales in Spania, Italia şi Franţa, unde constituie comunităţi importante. Dupa 1996 se axeaza exclusiv pe dezvoltarea organizatiilor politice tiganesti din Ardeal, a promovarii tiganilor ardeleni in tot felul de organizatii politice, de a infiltra absolut totul. Este clar ca e vorba de nasterea unui nationalism tiganesc, bazat pe etnonimul roma, bazat pe ideea teritoriala, Romania.
Este interesant ca, mai ales in afara granitelor, ei nu se autoidentifica drept tigani, ci romani.
Schimband saracia din tara cu ghetourile din strainatate, aceasta populatie de tigani dezradacinati, si pierzand si urma de identificare culturala, comite un numar important de infractiuni, care atrag asupra ei antipatia populaţiilor native ale acestor tari. Această antipatie, datorită confuziei create de denumirea de roman cu cea de rom, ca o denumire moderna a tiganilor, se transfera asupra poporului roman in ansamblu. Ca si cum denumirea de "rom" simpla nu ar fi fost de ajuns etnonimul a ajuns pana la forma "romani/romanies" in limba engleza care este limba in jurul careia se invarte intrega lume. Recentele evenimente din Italia o dovedesc din plin. Dar cum s-a ajuns la denumirea de rom si la impunerea ei ca obligatorie in actele oficiale din Romania?
Agresiunea lexicala rom/roma/roman - romani/romani - romanies/romanians - romanes/romaneste, a fost aplicata asupra tarii si natiunii noastre imediat dupa 1990, in cadrul unui program complex dezvoltat de Fundatia Soros in Romania. Beneficiind de numerosi membri ai etniei tiganesti in guvernarile Romaniei - sunt notorii Ion Iliescu, Adrian Nastase sau Andrei Plesu - dupa "Memorandumul" lui Petre Roman, care oficializa denumirile paralele, nimic nu le-a mai stat in cale schimbatorilor de limba si istorie. O prima disputa a fost cea legata de cuvantul "romi", romanii fiind prostiti apoi ca aceasta va fi inlocuita cu "rromi", o alta formula care doar a sporit debandada lexicala. De amintit, ca fapt divers, ca in anii 1995, limba cu care Soros vroia sa inlocuiasca tiganeasca primise numele de "romalli", forma care nici nu se putea declina si care a fost inlocuita ulterior cu "romani" si varianta "rromani". Apoi, pentru a se apropia de scopurile reale, a fost modificata cu "roma/romani/romanies". Confuzia este generala, inclusiv la nivelele academice ale intelectualitatii din tarile afectate de valul de imigratie si/sau infractionalitate tiganeasca. Cine ce sa mai inteleaga?!. Strigator la cer este ca denumirea nu are nici o baza istorica, tiganii nu au fost purtat niciodata de-a lungul istoriei acest etnonim si provine din cuvantul "DOM", care pe limba originara a tiganilor inseamna "om".
Prin denaturare (voita) "dom" s-a transformat in "rom" cu "r" accentuat, apoi din "rom" s-a trasformat in "roma" apoi in "romani" si in "romanies" . S-a ajuns astfel incat tiganii sa aibe numele identic cu al romanilor in limba engleza . Romani cu romani si romanies cu romanians ( doar ca in engleza nu exista diacritice dupa cum vedeti iar la o un simpla cautare pe google a cuvantului romani se vor afisa linkuri cu tigani) Practic denumirile sunt identice.
In toata perioada post-decembrista s-a manifestat o presiune constanta din partea unor organizatii sau din partea unor politicieni, personalitati de frunte cu ascendenta roma, in folosirea in documentele oficiale a etnonimului "rom". Ca un raspuns la aceste presiuni, prin Memorandumul H03/169 si 5/390/NV din 31 ianuarie 1995 adresat primului ministru de atunci, Nicolae Vacaroiu, ministrul de externe Teodor Melescanu recomanda folosirea in continuare in documente a cuvantului "tigan" in concordanta cu cuvintele folosite in celelalte limbi europene: zigeuner, gitanes, zingaro etc., pentru evitarea unor confuzii nefericite cu numele poporului roman. Presiunile continua si in 2001, Petre Roman, ministrul de externe, semneaza un nou Memorandum cu numărul D2/1094/29.02.2000 catre prim-ministrul Mugur Isarescu, in care, in virtutea dreptului de autoidentificare al populatiilor, recomanda folosirea obligatorie in toate documentele oficiale romane a denumirii de rom pentru a identifica etnia tiganilor. Mugur Isarescu isi insuseste Memorandumul si emite o hotarare de guvern in acest sens. Trebuie precizat ca documentele UE referitoare la denumirea de "rom" erau indicative, si nu obligatorii.
Pe de alta parte, nimeni nu contesta dreptul la autoidentificare, care este un principiu european general. Dar in cadrul procesului de autoidentificare nu trebuie sa existe suprapuneri peste denumirea istorica a unor popoare europene existente. Sa nu uitam exemplul Greciei care a refuzat sa recunoasca Republica Macedonia pentru ca se crea confuzie cu denumirea unei provincii istorice grecesti (Reteaua Soros Open network fiind si aici vectorul principal in creearea acestei denumiri). Azi s-a ajuns la denumirea de FYR ( Former Yougoslavian Republic) Macedonia. Dar ce putem astepta de la o clasa politica ce este mai preocupata de interesele personale marunte in detrimentul intereselor nationale, compusa din indivizi fara perspectiva istorica, ce se promovează unii pe altii pe criterii de cumetrie, si nu de competenta. Rezultatele se vad. In condiţiile In care Romania ocupă prin Leonard Orban postul de comisar european pentru multilingvism, Republica Moldova impune limba moldoveneasca (o invenţie bolsevica) drept limba oficiala recunoscută in UE. S-a spus la momentul nominalizarii că portofoliul pentru multilingvism este prea mic ca importanta pentru comisarul roman. Realitatea a dovedit contrariul.
In timp ce Bulgaria lupta pentru a impune denumirea de evro pentru euro, oficialii romani nu au schitat nici un gest in problema limbii moldovenesti.Privitor la problema tiganilor in ansamblu si a nefericitei denumiri de rom, fara indoială ca avem nevoie de minti luminate, si nu de teribilismul unui ministru de externe ca si Cioroianu, care in suita gafelor monumentale, declara ca ar fi bine daca am cumpara o parte din Sahara pentru a-i muta pe concetatenii nostrii tigani. Nu de fanfaronada ieftina si paguboasa avem nevoie. Romii romani (suna interesant, nu-i asa?) sunt si ei cetateni cu drepturi egale. Romania trebuie sa conlucreze cu UE in programe de afirmare a identitatii culturale a populaţiei de tigani in paralel cu integrarea lor sociala si cresterea nivelului educativ.
In ceea ce priveste denumirea de rom, chiar daca ne aflam in ceasul al 12-lea, este necesar un plan de masuri diplomatice, intinse poate pe mai multi ani, pentru a sensibiliza organismele europene si a se indrepta aceasta mare eroare de a denumi o populaţie transfrontaliera cum sunt tiganii cu un nume atat de apropiat si generator de confuzii, de numele istoric al poporului roman.Luand in considerare progresia demografica pană in 2025, cand pe fondul declinului de natalitate la romani şi maghiari si al scaderii mortalitatii la tigani, acestia ar putea reprezenta un procent semnificativ din populaţia Romaniei, depasindu-i pe maghiari, la care adaugam confuzia din ce in ce mai pregnanta a numelui de rom cu cea de roman, pozitia Romaniei in familia europeană apare intr-o pozitie tot mai ingrijoratoare.
In absenta unui plan concret ce trebuie urmarit cu consecventa, cred ca sunt toate sansele ca in constiinţa civica europeana sa se consolideze credinta ca Romania chiar este tara romilor (daca nu s-a intamplat deja) si se prefigureaza tot mai mult ideea domnului Teodor Melescanu care spunea ca se doreste creerea unui stat ţiganesc in Romania, ca Romania va fi in curand tara tiganilor .
Orice nationalism se bazeaza pe:
1) limba comuna (in sensul acesta s-au pornit alte campanii mincinoase demarate de reteaua Soros Open Network care incearca sa inventeze o limba tiganeasca impletita cu romana si care au denumit-o Romani Vlax, exact Vlax ! nu era de ajuns ca ne-au furat etnonimul de roman acum vor sa ne compromita si etnonimul de valah/vlah . Aceasta teorie strigatoare la cer este avansata de un anume Ian F. Hancock care isi publica lucrarile prin intermediul organizatiei Soros. Cercetatorul mentionat mai sus si care se recomanda drept "Romani" cu descendenta britanica si maghiara, este profesor de Studii Romani la Universitatea din Texas. El incearca sa si probabil reuseste sa convinga multi naivi, inclusiv pe site-ul Universitatii americane, ca "olahii" sau "vlahii" sunt de fapt tigani, de unde ar veni si denumirea limbii Vlax Romani, prezentata ca "un dialect al limbii romane" vorbit de populatia "Vlax/Vlach". Este revoltator si intolerabil, asistam practic la rescrierea istoriei.
2) etnia comuna = natiunea
3) etnonimul
4) teritoriul
5) statul
6) drapelul
7) istoria comuna
Tiganii au purces pe calea definirii propriului lor nationalism. Au nevoie de un teritoriu. Poporul ales drept victima sunt romanii. Sa lasam minciuna si ipocrizia deoparte, daca considera numele tigan peiorativ atunci sa-si ia numele lor original care este DOM si nu ROM.
joi, 1 iulie 2010
anunturi
Hrana pt animale la preturi bune! ( contracost transport la domiciliu in Bucuresti si Ilfov )
Vand: hrana - diete, umeda, semiumeda si uscata- pt caini ( Biomill, Contagro, Brokaton, Trovet), pisici (Biomill, Contagro, Trovet), rozatoare (, papagali si cai. De asemenea, viatamine pt caini si pisici, cai, pasari (Pet-Phos, Aplazil, Biotin, Rehydra-Kel, Multivit, Efazan, Vitafor, Vitastress, Adevit, Selevikel), sampoane medicinale, antiparazitare interne si externe pt caini si pisici, precum ProMeris - anitparazitar extern; Parazan, Albendazole – antiparazitar intern. Lese si zgarzi pentru caini, casute si custi pt hamsteri, , oase de sepie pt papagali, gustari si recompense pt caini, adapatoare pt papagali. Contact: german.hound@yahoo.com ; tel.: 0762.084.609
Vand: hrana - diete, umeda, semiumeda si uscata- pt caini ( Biomill, Contagro, Brokaton, Trovet), pisici (Biomill, Contagro, Trovet), rozatoare (, papagali si cai. De asemenea, viatamine pt caini si pisici, cai, pasari (Pet-Phos, Aplazil, Biotin, Rehydra-Kel, Multivit, Efazan, Vitafor, Vitastress, Adevit, Selevikel), sampoane medicinale, antiparazitare interne si externe pt caini si pisici, precum ProMeris - anitparazitar extern; Parazan, Albendazole – antiparazitar intern. Lese si zgarzi pentru caini, casute si custi pt hamsteri, , oase de sepie pt papagali, gustari si recompense pt caini, adapatoare pt papagali. Contact: german.hound@yahoo.com ; tel.: 0762.084.609
luni, 22 martie 2010
Tratamentul Cancerului
Tratament naturist cu 37 de preparate
Clinica Nova Vita funcţionează de şapte ani, iar tratamentele oferite sunt cu extracte minerale şi din plante aduse din jungla amazoniană. Specialiştii de aici susţin că au însănătoşit sute de pacienţi care aveau cancer în diferite faze.
„Terapia noastră activează sistemul imunitar al pacientului pe o cale nonspecifică, activând celulele NK (n.r. - natural killers, care «omoară» celulele canceroase), creând mai multe enzime în celulele canceroase, ceea ce duce la distrugerea lor. Cele mai bune rezultate le avem în organe cu ţesuturi bine irigate de vase, în cazuri de cancer localizat la sân ori în sistemul digestiv, urinar, genital sau respirator”, a spus dr. Marija Kozomara. Tratamentul se face cu 37 de preparate naturiste (capsule, tablete, soluţii sau granule din plante şi minerale).
Românii diagnosticaţi cu cancer pulmonar, interesaţi să se trateze naturist, îşi pot aduce dosarele medicale la sediul Farmaciilor Vlad din Timişoara, cu care Nova Vita a început un parteneriat (strada Timotei Cipariu nr. 9 tel./fax 0256.49.28.66).
Documentele vor fi traduse în limba sârbă şi vor fi trimise clinicii belgrădene, după care le vor urma şi pacienţii. O altă variantă este să trimită actele la Belgrad, la adresa Ul. Patrijarha Dimitrija 3611000 Beograd, Srbija, tel.: +381 (0)11.356.52.10 begin_of_the_skype_highlighting +381 (0)11.356.52.10 end_of_the_skype_highlighting, e-mail: researchinstitute@novavita.net.yu, novavita@net.yu.
Managerul clinicii Nova Vita, Milomir Kandic, a declarat că nu se va face o selecţie propriu-zisă a cazurilor, ci bolnavii vor fi preluaţi pe măsura depunerii actelor. „Acolo unde este şi cea mai mică şansă de reuşită, vom interveni”, a declarat managerul.
Clinica Nova Vita funcţionează de şapte ani, iar tratamentele oferite sunt cu extracte minerale şi din plante aduse din jungla amazoniană. Specialiştii de aici susţin că au însănătoşit sute de pacienţi care aveau cancer în diferite faze.
„Terapia noastră activează sistemul imunitar al pacientului pe o cale nonspecifică, activând celulele NK (n.r. - natural killers, care «omoară» celulele canceroase), creând mai multe enzime în celulele canceroase, ceea ce duce la distrugerea lor. Cele mai bune rezultate le avem în organe cu ţesuturi bine irigate de vase, în cazuri de cancer localizat la sân ori în sistemul digestiv, urinar, genital sau respirator”, a spus dr. Marija Kozomara. Tratamentul se face cu 37 de preparate naturiste (capsule, tablete, soluţii sau granule din plante şi minerale).
Românii diagnosticaţi cu cancer pulmonar, interesaţi să se trateze naturist, îşi pot aduce dosarele medicale la sediul Farmaciilor Vlad din Timişoara, cu care Nova Vita a început un parteneriat (strada Timotei Cipariu nr. 9 tel./fax 0256.49.28.66).
Documentele vor fi traduse în limba sârbă şi vor fi trimise clinicii belgrădene, după care le vor urma şi pacienţii. O altă variantă este să trimită actele la Belgrad, la adresa Ul. Patrijarha Dimitrija 3611000 Beograd, Srbija, tel.: +381 (0)11.356.52.10 begin_of_the_skype_highlighting +381 (0)11.356.52.10 end_of_the_skype_highlighting, e-mail: researchinstitute@novavita.net.yu, novavita@net.yu.
Managerul clinicii Nova Vita, Milomir Kandic, a declarat că nu se va face o selecţie propriu-zisă a cazurilor, ci bolnavii vor fi preluaţi pe măsura depunerii actelor. „Acolo unde este şi cea mai mică şansă de reuşită, vom interveni”, a declarat managerul.
duminică, 21 martie 2010
Dieta Daneza
Cica slabesti si schimbi si metabolismul. Adica nu mai pui la loc. HMMM
Ziua 1:
Dimineata: Cafea + 1 cub de zahar
Pranz: 2 oua fierte tare + 400 gr de spanac + 1 rosie
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 2:
Dimineata: Cafea + 1 cub de zahar
Pranz: 250 gr sunca + 1 iaurt natural
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 3:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua fierte tare + 1 felie de sunca + salata verde
Seara: 1 telina fiarta + 1 rosie + 1 fruct
Ziua 4:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 200 ml zeama de fructe + 1 iaurt
Seara: 1 ou fiert tare + 1 morcov ras + 250 gr fructe
Ziua 5:
Dimineata: 1 morcov mare ras + lamaie
Pranz: 200 gr peste cod fiert + lamaie
Seara: 200 gr friptura vita + unt + telina rasa
Ziua 6:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua tari + morcov ras
Seara: 1/2 pui + salata verde cu ulei; lamaie
Ziua 7:
Dimineata: ceai gol
Pranz: apa chioara
Seara: 200 g cotlet de miel + mar
Ziua 8:
Dimineata: Cafea + 1 cub de zahar
Pranz: 2 oua fierte tare + 400 gr de spanac + 1 rosie
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 9:
Dimineata: Cafea + 1 cub de zahar
Pranz: 250 gr sunca + 1 iaurt natural
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 10:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua fierte tare + 1 felie de sunca + salata verde
Seara: 1 telina fiarta + 1 rosie + 1 fruct
Ziua 11:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 200 ml zeama de fructe + 1 iaurt
Seara: 1 ou fiert tare + 1 morcov ras + 250 gr fructe
Ziua 12:
Dimineata: 1 morcov mare ras + lamaie
Pranz: 200 gr peste cod fiert + lamaie
Seara: 200 gr friptura vita + unt + telina rasa
Ziua 13:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua tari + morcov ras
Seara: 1/2 pui + salata verde cu ulei; lamaie
Mai multe info:
http://forum.oneden.com/topic/1192-dieta-daneza-de-schimbare-a-metabolismului/
Ziua 1:
Dimineata: Cafea + 1 cub de zahar
Pranz: 2 oua fierte tare + 400 gr de spanac + 1 rosie
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 2:
Dimineata: Cafea + 1 cub de zahar
Pranz: 250 gr sunca + 1 iaurt natural
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 3:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua fierte tare + 1 felie de sunca + salata verde
Seara: 1 telina fiarta + 1 rosie + 1 fruct
Ziua 4:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 200 ml zeama de fructe + 1 iaurt
Seara: 1 ou fiert tare + 1 morcov ras + 250 gr fructe
Ziua 5:
Dimineata: 1 morcov mare ras + lamaie
Pranz: 200 gr peste cod fiert + lamaie
Seara: 200 gr friptura vita + unt + telina rasa
Ziua 6:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua tari + morcov ras
Seara: 1/2 pui + salata verde cu ulei; lamaie
Ziua 7:
Dimineata: ceai gol
Pranz: apa chioara
Seara: 200 g cotlet de miel + mar
Ziua 8:
Dimineata: Cafea + 1 cub de zahar
Pranz: 2 oua fierte tare + 400 gr de spanac + 1 rosie
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 9:
Dimineata: Cafea + 1 cub de zahar
Pranz: 250 gr sunca + 1 iaurt natural
Seara: 200 gr friptura vita + salata verde + ulei, lamaie (friptura)
Ziua 10:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua fierte tare + 1 felie de sunca + salata verde
Seara: 1 telina fiarta + 1 rosie + 1 fruct
Ziua 11:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 200 ml zeama de fructe + 1 iaurt
Seara: 1 ou fiert tare + 1 morcov ras + 250 gr fructe
Ziua 12:
Dimineata: 1 morcov mare ras + lamaie
Pranz: 200 gr peste cod fiert + lamaie
Seara: 200 gr friptura vita + unt + telina rasa
Ziua 13:
Dimineata: Cafea + 1 cub de zahar + 1 felie de paine prajita
Pranz: 2 oua tari + morcov ras
Seara: 1/2 pui + salata verde cu ulei; lamaie
Mai multe info:
http://forum.oneden.com/topic/1192-dieta-daneza-de-schimbare-a-metabolismului/
sâmbătă, 20 martie 2010
Despre Fructe
Fructele sunt recomandate in curele de slabire, dar nu ca desert! Sa nu uiti niciodata aceasta regula. Daca combini fructele cu alte feluri de mancare sau daca le consumi ca desert, nu vor face altceva decat sa retina in corp toate glucidele consumate la masa respectiva, vor intarzia procesul de digestie, vor duce la fementarea celorlalte alimente si, in final, la ingrasare.
Fructele se mananca fie ca masa de sine statoare (cel mai indicat, dimineata, la micul dejun), fie cu o ora inainte de masa, fie dupa 3 ore de la masa de pranz sau de la cina. Chiar si daca bei doar un suc de fructe, aceste intervale orare trebuie respectate!
Pentru acest sezon, iti recomand fructele exotice, in curele tale de slabire. Intaresc imunitatea, accelereaza digestia si reduc colesterolul.
LAMAIA – tonic cardiac si un diuretic excelent
Desi se spune ca iti creeaza aciditate gastrica si ca nu e bine sa o mananci pe stomacul gol, acesta este doar un mit. In realitate, lucrurile stau exact invers. Lamaia scade aciditatea gastrica. Specialistii recomanda sa bei, pe stomacul gol, un pahar cu apa calduta, in care ai stors 3,4 felii de lamaie. Si, dupa fiecare masa, este recomandata o limonada, in acelasi scop. Continutul mare de vitamina C, face ca lamaia sa creasca imunitatea, sa previna si sa trateze racelile. Este un tonic cardiac si un diuretic excelent.
ANANASUL – miraculos in curele de slabire
Ananasul este un excelent antiadipos, antiedematos si tonic digestiv. Accelereaza metabolismul si sustine remodelarea corporala, reducerea tesutului adipos si a celulitei. Ajuta la eliminarea surplusului de apa din organism, reduce edemele si previne umflarea picioarelor. Contine o enzima asemanatoare celor digestive umane, care ajuta la o digestie buna si rapida.
GRAPEFRUIT – un tonic excelent
Grapefruit-ul scade nivelul grasimilor din sange (colesterolul si trigliceridele, cele vinovate de depunerile de pe vasele de sange, care duc, in timp, la infarct). Ajuta in curele de slabire, ca orice aliment amar, pentru ca determina digerarea salivara si gastrica. Este un tonic excelent.
MANGO – contine fibre, vitamina C si caroten. Consumul frecvent de mango poate preveni aparitia afectiunilor cancerigene. Il poti minca simplu sau cu iaurt sau muesli.
PORTOCALELE – contin vitamina C, care ajuta la intarirea sistemului imunitar si la prevenirea racelilor. Ele iti sunt recomandate si in probleme circulatorii.
KIWI - este singurul fruct care contine doza de vitamina C necesara zilnic unui adult. Contine, de asemenea, vitamina E si fibre. Ajuta la intarirea sistemul imunitar, in vindecarea problemelor digestive si la mentinerea unui aspect frumos al pielii.
AVOCADO – bogat in vitamina E, te ajuta sa-ti mentii sanatatea pielii si are efecte antioxidante, antiinflamatoare, de protejare a ficatului si de scadere a nivelului glicemiei şi colesterolului. Ajuta la cicatrizarea mai usoara a ranilor. Poate fi consumat ca atare sau poate fi inclus in diverse retete (miezul lui, pus in maioneza, ii confera acesteia un gust special).
PAPAYA – bogat in fibre, reduce nivelul colesterolului din singe. Este indicat si pentru stomac, deoarece contine enzime care grabesc procesul de digestie. Feliile de papaya se pot adauga si in salate de legume.
POMELO are proprietati diuretice, ajutand la tratarea obezitatii. Are doar 42 calorii la 100 g pulpa. Este un stimulator digestiv ideal. Multi sustin efectele sale impotriva stresului. Este bogat in vitamina C. Contine luteina, betacaroten, potasiu, fier, magneziu si calciu, vitaminele B1, B2, B3, B5 si B9.
RODIA – contine antioxidantii (mai puternici ca cei din vinul rosu), care ne protejeaza de diverse forme de cancer. Rodia elimina virusurile din organism si ne fereste de raceli, in sezonul rece. Previne imbatranirea pielii si reduce ridurile deja existente. Contine vitaminele B si C, acid folic si acid pantotenic.
Fructele se mananca fie ca masa de sine statoare (cel mai indicat, dimineata, la micul dejun), fie cu o ora inainte de masa, fie dupa 3 ore de la masa de pranz sau de la cina. Chiar si daca bei doar un suc de fructe, aceste intervale orare trebuie respectate!
Pentru acest sezon, iti recomand fructele exotice, in curele tale de slabire. Intaresc imunitatea, accelereaza digestia si reduc colesterolul.
LAMAIA – tonic cardiac si un diuretic excelent
Desi se spune ca iti creeaza aciditate gastrica si ca nu e bine sa o mananci pe stomacul gol, acesta este doar un mit. In realitate, lucrurile stau exact invers. Lamaia scade aciditatea gastrica. Specialistii recomanda sa bei, pe stomacul gol, un pahar cu apa calduta, in care ai stors 3,4 felii de lamaie. Si, dupa fiecare masa, este recomandata o limonada, in acelasi scop. Continutul mare de vitamina C, face ca lamaia sa creasca imunitatea, sa previna si sa trateze racelile. Este un tonic cardiac si un diuretic excelent.
ANANASUL – miraculos in curele de slabire
Ananasul este un excelent antiadipos, antiedematos si tonic digestiv. Accelereaza metabolismul si sustine remodelarea corporala, reducerea tesutului adipos si a celulitei. Ajuta la eliminarea surplusului de apa din organism, reduce edemele si previne umflarea picioarelor. Contine o enzima asemanatoare celor digestive umane, care ajuta la o digestie buna si rapida.
GRAPEFRUIT – un tonic excelent
Grapefruit-ul scade nivelul grasimilor din sange (colesterolul si trigliceridele, cele vinovate de depunerile de pe vasele de sange, care duc, in timp, la infarct). Ajuta in curele de slabire, ca orice aliment amar, pentru ca determina digerarea salivara si gastrica. Este un tonic excelent.
MANGO – contine fibre, vitamina C si caroten. Consumul frecvent de mango poate preveni aparitia afectiunilor cancerigene. Il poti minca simplu sau cu iaurt sau muesli.
PORTOCALELE – contin vitamina C, care ajuta la intarirea sistemului imunitar si la prevenirea racelilor. Ele iti sunt recomandate si in probleme circulatorii.
KIWI - este singurul fruct care contine doza de vitamina C necesara zilnic unui adult. Contine, de asemenea, vitamina E si fibre. Ajuta la intarirea sistemul imunitar, in vindecarea problemelor digestive si la mentinerea unui aspect frumos al pielii.
AVOCADO – bogat in vitamina E, te ajuta sa-ti mentii sanatatea pielii si are efecte antioxidante, antiinflamatoare, de protejare a ficatului si de scadere a nivelului glicemiei şi colesterolului. Ajuta la cicatrizarea mai usoara a ranilor. Poate fi consumat ca atare sau poate fi inclus in diverse retete (miezul lui, pus in maioneza, ii confera acesteia un gust special).
PAPAYA – bogat in fibre, reduce nivelul colesterolului din singe. Este indicat si pentru stomac, deoarece contine enzime care grabesc procesul de digestie. Feliile de papaya se pot adauga si in salate de legume.
POMELO are proprietati diuretice, ajutand la tratarea obezitatii. Are doar 42 calorii la 100 g pulpa. Este un stimulator digestiv ideal. Multi sustin efectele sale impotriva stresului. Este bogat in vitamina C. Contine luteina, betacaroten, potasiu, fier, magneziu si calciu, vitaminele B1, B2, B3, B5 si B9.
RODIA – contine antioxidantii (mai puternici ca cei din vinul rosu), care ne protejeaza de diverse forme de cancer. Rodia elimina virusurile din organism si ne fereste de raceli, in sezonul rece. Previne imbatranirea pielii si reduce ridurile deja existente. Contine vitaminele B si C, acid folic si acid pantotenic.
miercuri, 17 martie 2010
Demonstratia existentei lui Dumnezeu
GODEL'S THEOREMS AND TRUTH
By Daniel Graves, MSL
Summary
Famed mathematician Kurt Godel proved two extraordinary theorems. Accepted by all mathematicians, they have revolutionized mathematics, showing that mathematical truth is more than logic and computation. Does Godel's work imply that someone or something transcends the universe?
Truth and Provability
Kurt Godel has been called the most important logician since Aristotle.(1) Such praise is evidence of how seriously Godel's ideas are taken by mathematicians. His two famous theorems changed mathematics, logic, and even the way we look at our universe. This article explains what Godel proved and why it matters to Christians. But first we must set the stage.
There are many systems of math and logic. One kind is called a formal system. In a formal system there are only a few carefully defined symbols and rules. Examples of commonly used symbols are a, +, x, y, <, and so forth. Following strict rules, symbols are combined into new patterns (proofs). The symbols are actually little more than place-holders. Some represent operations such as addition. Others represent slots that can be filled with numbers or sentences. The reason that empty symbols are used is so that we can be sure that proofs are created without the mistakes that human emotion and misinterpreted words can cause. After a proof is made in a formal system, statements or numbers can be substituted for the symbols, and we then know that the results on the last line of the proof are one hundred percent logical. Serious math often uses formal systems. A very simple formal system cannot support number theory but such a system is easily proven to be self-consistent. All we have to do is to show that it can't make a silly proof such as A=Non-A, which would be like saying 2=17. To handle number theory a complex formal system is needed. But as systems get more complex, they are harder to prove consistent. One result is that we don't know if our number theories are sound or if there are contradictions hidden in them. Godel worked with such problems. He especially studied undecidable statements. An undecidable statement is one which can neither be proven true nor false in a formal system. Godel proved that any formal system deep enough to support number theory has at least one undecidable statement.(2) Even if we know that the statement is true, the system cannot prove it. This means the system is incomplete. For this reason, Godel's first proof is called "the incompleteness theorem". Godel's second theorem is closely related to the first. It says no one can prove, from inside any complex formal system, that it is self-consistent.(3) Hofstadter says, "Godel showed that provability is a weaker notion than truth, no matter what axiomatic system in involved."(4) In other words, we simply cannot prove some things in mathematics (from a given set of premises) which we nonetheless know are true. Shaking up geometry
Godel's work really goes all the way back to Greek geometry. Euclid showed that in geometry a few statements, called axioms, could be made at the start and a vast system of sophisticated proofs derived from them. Axioms are ideas which are too obvious to be proven. They just seem as if they must be true. An example is the idea that you can add one to any number and get a bigger number. When a system needs as many axioms as number theory does, doubts begin to arise. How do we know that the axioms aren't contradictory?
Until the 19th century no one was too worried about this. Geometry seemed rock solid. It had stood as conceived by Euclid for 2,100 years. If Euclid's work had a weak point, it was his fifth axiom, the axiom about parallel lines. Euclid said that if you were given a straight line, you could draw only one other straight line parallel to it through a set point somewhere outside it.
first line
second line
Around the mid-1800s a number of mathematicians began to experiment with different definitions for parallel line. Lobachevsky, Bolyai, Riemann and others created new geometries by saying that there could be two parallel lines through the outside point or no parallel lines. These geometries weren't mere games. In fact, it turns out that Riemann's geometry is better at describing the curvature of space than Euclid's. Consequently Einstein incorporated Riemann's ideas into relativity theory.
These new geometries became known as non-Euclidean. They worried mathematicians. Euclid had been like Gibraltar. Now one of his axioms had been changed. Since arithmetic is more complex than geometry, how could they be sure its axioms were trustworthy? In a bit of brilliant work, a masterful German mathematician, David Hilbert, converted geometry to algebra, showing that if algebra was consistent, so was geometry. This served as a useful crosscheck but wasn't proof positive of either system. The reason is that modern theories are forced to assume that the number line is infinite. Since no one understands infinity, we are naturally uncertain about the systems based on it. Hilbert was confident he had found a way to overcome this difficulty. He laid out a program to do just that.
Paradox in set theory
Uneasy mathematicians hoped that Hilbert's plan would fulfill its promise because axioms and definitions are based on commonsense intuition but intuition was proving to be an unreliable guide. Not only had Riemann created a system of geometry which stood commonsense notions on its head, but the philosopher-mathematician Bertrand Russell had bumped into a serious paradox for set theory.
A set is one of the easiest ideas to understand in mathematics and logic. It is any collection of items chosen for some characteristic which is alike for all its elements. For instance, there is the set of all numbers {1,2,3,4,5.....} or the set of planets which circle our sun {Mercury, Venus, Earth, Mars...}. Handling sets seemed fairly simple.
Russell's paradox was this: Let there be two kinds of sets, he said--normal sets, which do not contain themselves, and non-normal sets, which are sets that do contain themselves. The set of all apples is not an apple. Therefore it is a normal set. The set of all thinkable things is itself thinkable, so it is a non-normal set.
Let ÔN' stand for the set of all normal sets. Is N a normal set? If it is a normal set, then by the definition of a normal set it cannot a member of itself. That means that N is a non-normal set, one of those few sets that actually are members of themselves. But hold on! N is the set of all normal sets; if we describe it as a non-normal set, it cannot be a member of itself, because its members are, by definition, normal, not non-normal.
Russell did not feel that this paradox was insurmountable. By redefining the meaning of Ôset' to exclude awkward sets, such as "the set of all normal sets," he felt that he could create a single self-consistent, self-contained mathematical system. Using improved symbolic logic, he and Alfred North Whitehead set out to do just that. The result was their masterful three volume Principia Mathematica. However, even before it was complete, Russell's expectations were dashed.
Enter Godel
The man who showed once and for all that Russell's aim was impossible was, of course, Kurt Godel. His revolutionary paper was titled "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." In it he showed that a statement in a system could be made to refer to itself in such a way that it said about itself that it was unproveable. His proof was very complicated involving the mapping of prime numbers onto statements. For example, Godelese for (x)(x=x) is the unique prime number code 28 X 311 X 58 X 78 X 1111 X 135 X 1711 X 199.
A Godelian proof
Here is a simpler proof that no number system can generate all the statements which might be true within it. This proof is based on the writings of A. W. Moore and Roger Penrose.
#1. POINT TO PROVE: IT IS IMPOSSIBLE TO DERIVE ALL MATHEMATICAL TRUTH FROM ANY SET OF SELF-EVIDENT AXIOMS.
#2. IF ALL MATHEMATICAL TRUTHS CAN BE DERIVED FROM A CHOSEN SET OF AXIOMS, THEN, IN PRINCIPLE, AN ALGORITHM "A" CAN BE CREATED TO TEST WHETHER OR NOT ANY GIVEN THEOREM DERIVES FROM THE CHOSEN AXIOMSÑI.E.: WHETHER OR NOT IT IS TRUE OR FALSE.
#3. AT PRESENT WE DO NOT HAVE SUCH AN ALGORITHM. IF A CAN BE SHOWN TO BE IMPOSSIBLE, THEN #1 IS ESTABLISHED.
#4. LIST THE FACTUAL STATEMENTS WHICH CAN BE MADE ABOUT NUMBERS. EXAMPLES OF SUCH STATEMENTS ARE "X IS EVEN," "X IS ODD," "X IS PRIME","X IS LESS THAN 100," ETC.
#5. CREATE A TABLE OF SUCH STATEMENTS, BEGINNING WITH THE SIMPLEST AND MOVING TO THE MORE COMPLEX. WE WILL CALL OUR STATEMENTS 1, 2, 3, 4... NOW WE NOTE THAT OUR TABLE CAN REFER TO ITS OWN STATEMENTS. SUPPOSE STATEMENT 0 MEANS: "X IS EVEN", STATEMENT 1 "X IS ODD" ETC... WE LET THE VERTICAL AXIS REPRESENTS THE STATEMENT NUMBER. THE HORIZONTAL AXIS REPRESENTS ALL NUMBERS FROM 0 TO INFINITY. WE THEN ASK OURSELVES FOR EACH NUMBER IN THE HORIZONTAL AXIS, "IS THE VERTICAL STATEMENT TRUE OF THIS NUMBER?" WE WRITE Y BELOW IT IF IT IS TRUE, AND N IF IT ISN'T:
0 1 2 3 ....
0 (EVEN) N N Y N...
1 (ODD) N N Y Y
2 (PRIME) N N Y Y...
3 (x<100 ) Y Y Y Y.... ... .................. #6. FOR ANY NATURAL NUMBER (HORIZONTAL LINE) WE NOW HAVE A METHOD OF DECIDING IF THE VERTICAL STATEMENT IS TRUE. SINCE EVERY POSSIBLE STATEMENT OF THE SYSTEM CAN APPARENTLY BE LISTED AND SINCE EVERY NATURAL NUMBER CAN ALSO BE LISTED, IT APPEARS WE HAVE A COMPLETE SYSTEM OF NATURAL NUMBERS AND AXIOMS. NOTICE THAT EACH STATEMENT ON THE VERTICAL AXIS PRODUCES ITS OWN UNIQUE HORIZONTAL LINE OF Ys AND Ns. #7. CREATE A NEW WELL-DEFINED SEQUENCE OF Ys AND Ns BY FOLLOWING A DIAGONAL ON THE CHART WE HAVE JUST CREATED. DO THIS BY TURNING EACH DIAGONAL ELEMENT INTO ITS OPPOSITE. THE N AT 0/0 ON THE TABLE BECOMES A Y. THE Y AT 1/1 BECOMES AN N. THE Y AT 2/2 BECOMES AN N. THE Y AT 3/3 BECOMES AN N AND SO FORTH. WE GET YNNN... DOES ANY STATEMENT WHICH HAS ALREADY BEEN GIVEN PRODUCE THIS NEW SEQUENCE? #8. STATEMENT 0 DOESN'T BECAUSE IT HAS AN N WHERE THE NEW STATEMENT HAS Y. 1, 2, AND 3 DON'T BECAUSE THEY HAVE Ys WHERE THE NEW STATEMENT HAS Ns. THIS WOULD HOLD TRUE TO INFINITY IF WE COULD MAKE OUR TABLE THAT LONG, #9. WE KNOW WE LEGITIMATELY CREATED THIS NEW Y & N PATTERN, IE: IT IS TRUE. YET NONE OF THE EXISTING AXIOM STATEMENTS PRODUCE THIS DIAGONAL STATEMENT. A NEW AXIOM IS NEEDED TO EXPRESS THE DIAGONAL. 10. IF WE WRITE A NEW STATEMENT (CALL IT R) THAT INCLUDES A PROCEDURE FOR MAKING THIS DIAGONAL , AT SPACE R/R A NEW DIAGONAL LETTER WILL APPEAR AND WE WILL HAVE TO ADD STATEMENT S TO REPRESENT THIS NEW SEQUENCE. BUT AT S/S A NEW DIAGONAL NUMBER WILL APPEAR, REQUIRING A STATEMENT T AND SO ON, INFINITELY. 11. THEREFORE ALGORITHM A IS IMPOSSIBLE, WHICH IS THE PROOF REQUIRED BY #2. IT IS IMPOSSIBLE TO AUTOMATICALLY DERIVE ALL POSSIBLE MATHEMATICAL TRUTH. Immediate Implications
What do Godel's theorems mean for those who believe there is a God? First, Godel shattered naive expectations that human thinking could be reduced to algorithms. An algorithm is a step-by-step mathematical procedure for solving a problem. Usually it is repetitive. Computers use algorithms. What it means is that our thought cannot be a strictly mechanical process. Roger Penrose makes much of this, arguing in Shadows of the Mind that computers will never be able to emulate the full depth of human thought. But whereas Penrose seeks solutions in quantum theory, Christians see man as a spiritual being with understanding that springs not just from the physical organ of the mind but also from soul and spirit.
Second, had Godel been able to affirm that a complex system is able to prove itself self-consistent, then we could argue that the universe is self-sufficient. His proof points us toward a different understanding, one in which we must either declare the universe to be infinite--as some do(5)--or else look for infinity outside the universe as theists do.
The first possibility, that the universe is infinite, is most unlikely. Everything that we have learned about the universe tells us that it is finite. Astronomers have found details that set absolute limits to its age and dimensions. Physicists have estimated the number of protons in all of creation. And even if there were an infinite amount of natural matter, each particle would still suffer the limitations of matter, for no particle is infinite in itself. The Christian therefore is reasonable when he points to a spiritual creator outside the physical universe as an explanation for what goes on within it. Godel recognized these implications and struggled to produce an ontological proof for the existence of God (a proof based on the definition of "God"). Godel was wasting his time in trying to establish this proof. His own theorems strongly suggest that while the finite can infer something bigger than itself, it cannot prove the infinite. As in this article, reason can only show that it is reasonable to believe in a spiritual God who transcends the limits of the universe.
Godel's theorem means that the universe cannot be a vast self-contained computer. One modern scientist, Fredekin, suggests that it is.(6) The fundamental particles of nature (in his view) are information bits in that huge machine. Were he right that the universe is effectively a computer, then Godel's theorems would require that nature, as a whole be understood only outside nature because no finite system is sufficient for itself. This conclusion flows by analogy from what Godel proved. "...if arithmetic is consistent, its consistency cannot be established by any meta-mathematical reasoning that can be represented within the formalism of arithmetic."(7)
As a third implication of Godel's theorem , faith is shown to be (ultimately) the only possible response to reality. Michael Guillen has spelled out this implication: "the only possible way of avowing an unprovable truth, mathematical or otherwise, is to accept it as an article of faith."(8) In other words, scientists are as subject to belief as non-scientists. And scientific faith can let a man down as hard as any other. Guillen writes: "In 1959 a disillusioned Russell lamented: ÔI wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than anywhere...But after some twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.'"(9)
A or Non-A?
Godel showed that "it is impossible to establish the internal logical consistency of a very large class of deductive systems--elementary arithmetic, for example--unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the sytems themselves."(10) In short, we can have no certitude that our most cherished systems of math are free from internal contradiction.
Take note! He did not prove a contradictory statement, that A = non-A, (the kind of thinking that occurs in many Eastern religions). Instead, he showed that no system can decide between a certain A and non-A, even where A is known to be true. Any finite system with sufficient power to support a full number theory cannot be self-contained.
Judeo-Christianity has long held that truth is above mere reason. Spiritual truth, we are taught, can be apprehended only by the spirit. This, too, is as it should be. The Godelian picture fits what Christians believe about the universe. Had he been able to show that self-proof was possible, we would be in deep trouble. As noted above, the universe could then be self-explanatory.
As it stands, the very real infinities and paradoxes of nature demand something higher, different in kind, more powerful, to explain them just as every logic set needs a higher logic set to prove and explain elements within it.
This lesson from Godel's proof is one reason I believe that no finite system, even one as vast as the universe, can ultimately satisfy the questions it raises.
References
(1)Moore, Gregory H., "Kurt Friedrich Godel," in Dictionary of Scientific Biography. New York: Scribner's Sons, 1973.
(2)Edward, Paul. Encyclopedia of Philosophy. Macmillan and Free Press, 1967.
(3)Ibid.
(4)Hofstadter, Douglas R., Godel, Escher, Bach; an Eternal Golden Braid. New York: Vintage, 1979, p.19.
(5)Zebrowski, George. "Life in Godel's Universe: Maps all the Way." Omni. April 1992, p. 53.
(6)Wright, Robert, Three Scientists and Their Gods. New York: Times Books, 1988, pp. 4, 5-80.
(7)Nagel, Ernest and John Newman, Godel's Proof. New York: New York University Press, 1958, p. 96.
(8)Guillen, Michael, Bridges to Infinity. Los Angeles: Tarcher, 1983, pp. 117,18.
(9)Ibid, pp. 20,21.
(10)Nagel, p. 6.
See also:
Blanch, Robert, "Axiomatization," in Dictionary of the History of Ideas Volume I (New York: Scribner's Sons, 1973) p.170.
Moore, A. W. The Infinite. London and New York: Routledge, 1990.
Newman, James R. The World of Mathematics. New York: Simon and Schuster, 1956. Paulos, John Allen, Beyond Numeracy; Ruminations of a Numbers Man (New York: Knopf, 1991) p. 97.
Penrose, Roger. Shadows of the Mind. 1993.
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CHRIST SUFFERED AS TRUTH
"Now if we are children [of God], then we are heirsÑheirs of God and co-heirs with Christ, if indeed we share in his sufferings in order that we may also share in his glory." Rom. 8:17.
In answer to a question put by Pilate, Jesus said, "You are right in saying I am a king. In fact, for this reason I was born, and for this I came into the world, to testify to the truth. Everyone on the side of truth listens to me."
"What is truth?" Pilate retorted. With this he went out again to the Jews and said, "I find no basis for a charge against him..." Then Pilate took Jesus and had him flogged...
The world met truth with force, but truth won.
Godel's proof implies that we must seek final truth outside our finite world. Jesus uttered one of the most ultimate claims ever made by a sane man. "I am the way, the truth, and the life," he told his disciples just hours before he stood before Pilate.
Will we find truth in a transfinite Christ or will we prefer partial truth from within a system that cannot validate itself?
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MATHEMATICIANS OF THE INFINITE
The mathematics of the infinite cannot be understood apart from Judeo-Christianity. Although infinitely theory intrigued all civilizations, especially the Greeks, nowhere has it been so important as in Christendom, where all theology hinged on its implications. Augustine in various writings and Boethius, in The Consolation of Philosophy, wrestled with the idea especially in relation to time and God's eternal existence. Of Learned Ignorance, by Bishop Nicholas Cusa, argued that at infinity all things become one, just as the arc of an infinitely large circle will flatten into a straight line.
Not surprisingly, the world's first systematic treatment of infinity was produced by a theologian. The Czech, Bernard Balzano, pioneered the theory of real numbers, established some properties of infinite sets, and became a precursor of modern logic. Like most pioneers he made serious errors. His theology verged on heresy.
The great Cantor, a Protestant Jew with a Catholic mother, was spurred by religious impulses to create transfinite theory. His profoundly original work was spurned by most contemporaries and he was relegated to minor teaching posts. One of Cantor's greatest contributions was the technique of diagonalization (which we employ in our page seven proof of Godel). Kronecker savaged Cantor in print and in the classroom. Lacking self-confidence, Cantor came to doubt the worth of his own work. Although the Jesuits seized upon his proofs as validation for certain theological tenets, Cantor's uncertainty eventually led him into madness.
Godel, with a Lutheran background, took religious questions seriously and declared himself a theist. Profoundly influenced by his Lutheran predecessor, Leibnitz, he espoused an ontological proof for the existence of God based on his mathematics. This was not successful.
These instances show the power of Christianity to drive first-rate scientific work. No other religion in history has impelled men and women to do such science. The claims of Christianity are so ultimate that at every turn they must either be accepted and substantiated, or denied and challenged. Again and again friend and foe impress new insight upon old theology.
References:
Bell, E. T. Men of Mathematics.
Gillispie, Charles Coulston. Dictionary of Scientific Biography.
Guillen, Michael. Bridges to Infinity.
QUESTIONS FOR ATHEISTS AND AGNOSTICS
If we dwell in a finite world created by an infinite God, is not a Godelian theorem exactly what we should expect to find?
Why was it that Christian theology and Christian thinkers impelled the major modern developments in infinity theory?
Since mathematical theory ultimately rests on faith, why do you denounce Christianity for resting on faith?
The history of science shows that strictly mechanistic views of the world have consistently failed to hold up. Why not acknowledge that the world is not strictly mechanistic as materialistic explanations must suppose?
In light of Godel's proofs and Christ's transfinite claims, won't you yield yourself to God?
By Daniel Graves, MSL
Summary
Famed mathematician Kurt Godel proved two extraordinary theorems. Accepted by all mathematicians, they have revolutionized mathematics, showing that mathematical truth is more than logic and computation. Does Godel's work imply that someone or something transcends the universe?
Truth and Provability
Kurt Godel has been called the most important logician since Aristotle.(1) Such praise is evidence of how seriously Godel's ideas are taken by mathematicians. His two famous theorems changed mathematics, logic, and even the way we look at our universe. This article explains what Godel proved and why it matters to Christians. But first we must set the stage.
There are many systems of math and logic. One kind is called a formal system. In a formal system there are only a few carefully defined symbols and rules. Examples of commonly used symbols are a, +, x, y, <, and so forth. Following strict rules, symbols are combined into new patterns (proofs). The symbols are actually little more than place-holders. Some represent operations such as addition. Others represent slots that can be filled with numbers or sentences. The reason that empty symbols are used is so that we can be sure that proofs are created without the mistakes that human emotion and misinterpreted words can cause. After a proof is made in a formal system, statements or numbers can be substituted for the symbols, and we then know that the results on the last line of the proof are one hundred percent logical. Serious math often uses formal systems. A very simple formal system cannot support number theory but such a system is easily proven to be self-consistent. All we have to do is to show that it can't make a silly proof such as A=Non-A, which would be like saying 2=17. To handle number theory a complex formal system is needed. But as systems get more complex, they are harder to prove consistent. One result is that we don't know if our number theories are sound or if there are contradictions hidden in them. Godel worked with such problems. He especially studied undecidable statements. An undecidable statement is one which can neither be proven true nor false in a formal system. Godel proved that any formal system deep enough to support number theory has at least one undecidable statement.(2) Even if we know that the statement is true, the system cannot prove it. This means the system is incomplete. For this reason, Godel's first proof is called "the incompleteness theorem". Godel's second theorem is closely related to the first. It says no one can prove, from inside any complex formal system, that it is self-consistent.(3) Hofstadter says, "Godel showed that provability is a weaker notion than truth, no matter what axiomatic system in involved."(4) In other words, we simply cannot prove some things in mathematics (from a given set of premises) which we nonetheless know are true. Shaking up geometry
Godel's work really goes all the way back to Greek geometry. Euclid showed that in geometry a few statements, called axioms, could be made at the start and a vast system of sophisticated proofs derived from them. Axioms are ideas which are too obvious to be proven. They just seem as if they must be true. An example is the idea that you can add one to any number and get a bigger number. When a system needs as many axioms as number theory does, doubts begin to arise. How do we know that the axioms aren't contradictory?
Until the 19th century no one was too worried about this. Geometry seemed rock solid. It had stood as conceived by Euclid for 2,100 years. If Euclid's work had a weak point, it was his fifth axiom, the axiom about parallel lines. Euclid said that if you were given a straight line, you could draw only one other straight line parallel to it through a set point somewhere outside it.
first line
second line
Around the mid-1800s a number of mathematicians began to experiment with different definitions for parallel line. Lobachevsky, Bolyai, Riemann and others created new geometries by saying that there could be two parallel lines through the outside point or no parallel lines. These geometries weren't mere games. In fact, it turns out that Riemann's geometry is better at describing the curvature of space than Euclid's. Consequently Einstein incorporated Riemann's ideas into relativity theory.
These new geometries became known as non-Euclidean. They worried mathematicians. Euclid had been like Gibraltar. Now one of his axioms had been changed. Since arithmetic is more complex than geometry, how could they be sure its axioms were trustworthy? In a bit of brilliant work, a masterful German mathematician, David Hilbert, converted geometry to algebra, showing that if algebra was consistent, so was geometry. This served as a useful crosscheck but wasn't proof positive of either system. The reason is that modern theories are forced to assume that the number line is infinite. Since no one understands infinity, we are naturally uncertain about the systems based on it. Hilbert was confident he had found a way to overcome this difficulty. He laid out a program to do just that.
Paradox in set theory
Uneasy mathematicians hoped that Hilbert's plan would fulfill its promise because axioms and definitions are based on commonsense intuition but intuition was proving to be an unreliable guide. Not only had Riemann created a system of geometry which stood commonsense notions on its head, but the philosopher-mathematician Bertrand Russell had bumped into a serious paradox for set theory.
A set is one of the easiest ideas to understand in mathematics and logic. It is any collection of items chosen for some characteristic which is alike for all its elements. For instance, there is the set of all numbers {1,2,3,4,5.....} or the set of planets which circle our sun {Mercury, Venus, Earth, Mars...}. Handling sets seemed fairly simple.
Russell's paradox was this: Let there be two kinds of sets, he said--normal sets, which do not contain themselves, and non-normal sets, which are sets that do contain themselves. The set of all apples is not an apple. Therefore it is a normal set. The set of all thinkable things is itself thinkable, so it is a non-normal set.
Let ÔN' stand for the set of all normal sets. Is N a normal set? If it is a normal set, then by the definition of a normal set it cannot a member of itself. That means that N is a non-normal set, one of those few sets that actually are members of themselves. But hold on! N is the set of all normal sets; if we describe it as a non-normal set, it cannot be a member of itself, because its members are, by definition, normal, not non-normal.
Russell did not feel that this paradox was insurmountable. By redefining the meaning of Ôset' to exclude awkward sets, such as "the set of all normal sets," he felt that he could create a single self-consistent, self-contained mathematical system. Using improved symbolic logic, he and Alfred North Whitehead set out to do just that. The result was their masterful three volume Principia Mathematica. However, even before it was complete, Russell's expectations were dashed.
Enter Godel
The man who showed once and for all that Russell's aim was impossible was, of course, Kurt Godel. His revolutionary paper was titled "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." In it he showed that a statement in a system could be made to refer to itself in such a way that it said about itself that it was unproveable. His proof was very complicated involving the mapping of prime numbers onto statements. For example, Godelese for (x)(x=x) is the unique prime number code 28 X 311 X 58 X 78 X 1111 X 135 X 1711 X 199.
A Godelian proof
Here is a simpler proof that no number system can generate all the statements which might be true within it. This proof is based on the writings of A. W. Moore and Roger Penrose.
#1. POINT TO PROVE: IT IS IMPOSSIBLE TO DERIVE ALL MATHEMATICAL TRUTH FROM ANY SET OF SELF-EVIDENT AXIOMS.
#2. IF ALL MATHEMATICAL TRUTHS CAN BE DERIVED FROM A CHOSEN SET OF AXIOMS, THEN, IN PRINCIPLE, AN ALGORITHM "A" CAN BE CREATED TO TEST WHETHER OR NOT ANY GIVEN THEOREM DERIVES FROM THE CHOSEN AXIOMSÑI.E.: WHETHER OR NOT IT IS TRUE OR FALSE.
#3. AT PRESENT WE DO NOT HAVE SUCH AN ALGORITHM. IF A CAN BE SHOWN TO BE IMPOSSIBLE, THEN #1 IS ESTABLISHED.
#4. LIST THE FACTUAL STATEMENTS WHICH CAN BE MADE ABOUT NUMBERS. EXAMPLES OF SUCH STATEMENTS ARE "X IS EVEN," "X IS ODD," "X IS PRIME","X IS LESS THAN 100," ETC.
#5. CREATE A TABLE OF SUCH STATEMENTS, BEGINNING WITH THE SIMPLEST AND MOVING TO THE MORE COMPLEX. WE WILL CALL OUR STATEMENTS 1, 2, 3, 4... NOW WE NOTE THAT OUR TABLE CAN REFER TO ITS OWN STATEMENTS. SUPPOSE STATEMENT 0 MEANS: "X IS EVEN", STATEMENT 1 "X IS ODD" ETC... WE LET THE VERTICAL AXIS REPRESENTS THE STATEMENT NUMBER. THE HORIZONTAL AXIS REPRESENTS ALL NUMBERS FROM 0 TO INFINITY. WE THEN ASK OURSELVES FOR EACH NUMBER IN THE HORIZONTAL AXIS, "IS THE VERTICAL STATEMENT TRUE OF THIS NUMBER?" WE WRITE Y BELOW IT IF IT IS TRUE, AND N IF IT ISN'T:
0 1 2 3 ....
0 (EVEN) N N Y N...
1 (ODD) N N Y Y
2 (PRIME) N N Y Y...
3 (x<100 ) Y Y Y Y.... ... .................. #6. FOR ANY NATURAL NUMBER (HORIZONTAL LINE) WE NOW HAVE A METHOD OF DECIDING IF THE VERTICAL STATEMENT IS TRUE. SINCE EVERY POSSIBLE STATEMENT OF THE SYSTEM CAN APPARENTLY BE LISTED AND SINCE EVERY NATURAL NUMBER CAN ALSO BE LISTED, IT APPEARS WE HAVE A COMPLETE SYSTEM OF NATURAL NUMBERS AND AXIOMS. NOTICE THAT EACH STATEMENT ON THE VERTICAL AXIS PRODUCES ITS OWN UNIQUE HORIZONTAL LINE OF Ys AND Ns. #7. CREATE A NEW WELL-DEFINED SEQUENCE OF Ys AND Ns BY FOLLOWING A DIAGONAL ON THE CHART WE HAVE JUST CREATED. DO THIS BY TURNING EACH DIAGONAL ELEMENT INTO ITS OPPOSITE. THE N AT 0/0 ON THE TABLE BECOMES A Y. THE Y AT 1/1 BECOMES AN N. THE Y AT 2/2 BECOMES AN N. THE Y AT 3/3 BECOMES AN N AND SO FORTH. WE GET YNNN... DOES ANY STATEMENT WHICH HAS ALREADY BEEN GIVEN PRODUCE THIS NEW SEQUENCE? #8. STATEMENT 0 DOESN'T BECAUSE IT HAS AN N WHERE THE NEW STATEMENT HAS Y. 1, 2, AND 3 DON'T BECAUSE THEY HAVE Ys WHERE THE NEW STATEMENT HAS Ns. THIS WOULD HOLD TRUE TO INFINITY IF WE COULD MAKE OUR TABLE THAT LONG, #9. WE KNOW WE LEGITIMATELY CREATED THIS NEW Y & N PATTERN, IE: IT IS TRUE. YET NONE OF THE EXISTING AXIOM STATEMENTS PRODUCE THIS DIAGONAL STATEMENT. A NEW AXIOM IS NEEDED TO EXPRESS THE DIAGONAL. 10. IF WE WRITE A NEW STATEMENT (CALL IT R) THAT INCLUDES A PROCEDURE FOR MAKING THIS DIAGONAL , AT SPACE R/R A NEW DIAGONAL LETTER WILL APPEAR AND WE WILL HAVE TO ADD STATEMENT S TO REPRESENT THIS NEW SEQUENCE. BUT AT S/S A NEW DIAGONAL NUMBER WILL APPEAR, REQUIRING A STATEMENT T AND SO ON, INFINITELY. 11. THEREFORE ALGORITHM A IS IMPOSSIBLE, WHICH IS THE PROOF REQUIRED BY #2. IT IS IMPOSSIBLE TO AUTOMATICALLY DERIVE ALL POSSIBLE MATHEMATICAL TRUTH. Immediate Implications
What do Godel's theorems mean for those who believe there is a God? First, Godel shattered naive expectations that human thinking could be reduced to algorithms. An algorithm is a step-by-step mathematical procedure for solving a problem. Usually it is repetitive. Computers use algorithms. What it means is that our thought cannot be a strictly mechanical process. Roger Penrose makes much of this, arguing in Shadows of the Mind that computers will never be able to emulate the full depth of human thought. But whereas Penrose seeks solutions in quantum theory, Christians see man as a spiritual being with understanding that springs not just from the physical organ of the mind but also from soul and spirit.
Second, had Godel been able to affirm that a complex system is able to prove itself self-consistent, then we could argue that the universe is self-sufficient. His proof points us toward a different understanding, one in which we must either declare the universe to be infinite--as some do(5)--or else look for infinity outside the universe as theists do.
The first possibility, that the universe is infinite, is most unlikely. Everything that we have learned about the universe tells us that it is finite. Astronomers have found details that set absolute limits to its age and dimensions. Physicists have estimated the number of protons in all of creation. And even if there were an infinite amount of natural matter, each particle would still suffer the limitations of matter, for no particle is infinite in itself. The Christian therefore is reasonable when he points to a spiritual creator outside the physical universe as an explanation for what goes on within it. Godel recognized these implications and struggled to produce an ontological proof for the existence of God (a proof based on the definition of "God"). Godel was wasting his time in trying to establish this proof. His own theorems strongly suggest that while the finite can infer something bigger than itself, it cannot prove the infinite. As in this article, reason can only show that it is reasonable to believe in a spiritual God who transcends the limits of the universe.
Godel's theorem means that the universe cannot be a vast self-contained computer. One modern scientist, Fredekin, suggests that it is.(6) The fundamental particles of nature (in his view) are information bits in that huge machine. Were he right that the universe is effectively a computer, then Godel's theorems would require that nature, as a whole be understood only outside nature because no finite system is sufficient for itself. This conclusion flows by analogy from what Godel proved. "...if arithmetic is consistent, its consistency cannot be established by any meta-mathematical reasoning that can be represented within the formalism of arithmetic."(7)
As a third implication of Godel's theorem , faith is shown to be (ultimately) the only possible response to reality. Michael Guillen has spelled out this implication: "the only possible way of avowing an unprovable truth, mathematical or otherwise, is to accept it as an article of faith."(8) In other words, scientists are as subject to belief as non-scientists. And scientific faith can let a man down as hard as any other. Guillen writes: "In 1959 a disillusioned Russell lamented: ÔI wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than anywhere...But after some twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.'"(9)
A or Non-A?
Godel showed that "it is impossible to establish the internal logical consistency of a very large class of deductive systems--elementary arithmetic, for example--unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the sytems themselves."(10) In short, we can have no certitude that our most cherished systems of math are free from internal contradiction.
Take note! He did not prove a contradictory statement, that A = non-A, (the kind of thinking that occurs in many Eastern religions). Instead, he showed that no system can decide between a certain A and non-A, even where A is known to be true. Any finite system with sufficient power to support a full number theory cannot be self-contained.
Judeo-Christianity has long held that truth is above mere reason. Spiritual truth, we are taught, can be apprehended only by the spirit. This, too, is as it should be. The Godelian picture fits what Christians believe about the universe. Had he been able to show that self-proof was possible, we would be in deep trouble. As noted above, the universe could then be self-explanatory.
As it stands, the very real infinities and paradoxes of nature demand something higher, different in kind, more powerful, to explain them just as every logic set needs a higher logic set to prove and explain elements within it.
This lesson from Godel's proof is one reason I believe that no finite system, even one as vast as the universe, can ultimately satisfy the questions it raises.
References
(1)Moore, Gregory H., "Kurt Friedrich Godel," in Dictionary of Scientific Biography. New York: Scribner's Sons, 1973.
(2)Edward, Paul. Encyclopedia of Philosophy. Macmillan and Free Press, 1967.
(3)Ibid.
(4)Hofstadter, Douglas R., Godel, Escher, Bach; an Eternal Golden Braid. New York: Vintage, 1979, p.19.
(5)Zebrowski, George. "Life in Godel's Universe: Maps all the Way." Omni. April 1992, p. 53.
(6)Wright, Robert, Three Scientists and Their Gods. New York: Times Books, 1988, pp. 4, 5-80.
(7)Nagel, Ernest and John Newman, Godel's Proof. New York: New York University Press, 1958, p. 96.
(8)Guillen, Michael, Bridges to Infinity. Los Angeles: Tarcher, 1983, pp. 117,18.
(9)Ibid, pp. 20,21.
(10)Nagel, p. 6.
See also:
Blanch, Robert, "Axiomatization," in Dictionary of the History of Ideas Volume I (New York: Scribner's Sons, 1973) p.170.
Moore, A. W. The Infinite. London and New York: Routledge, 1990.
Newman, James R. The World of Mathematics. New York: Simon and Schuster, 1956. Paulos, John Allen, Beyond Numeracy; Ruminations of a Numbers Man (New York: Knopf, 1991) p. 97.
Penrose, Roger. Shadows of the Mind. 1993.
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CHRIST SUFFERED AS TRUTH
"Now if we are children [of God], then we are heirsÑheirs of God and co-heirs with Christ, if indeed we share in his sufferings in order that we may also share in his glory." Rom. 8:17.
In answer to a question put by Pilate, Jesus said, "You are right in saying I am a king. In fact, for this reason I was born, and for this I came into the world, to testify to the truth. Everyone on the side of truth listens to me."
"What is truth?" Pilate retorted. With this he went out again to the Jews and said, "I find no basis for a charge against him..." Then Pilate took Jesus and had him flogged...
The world met truth with force, but truth won.
Godel's proof implies that we must seek final truth outside our finite world. Jesus uttered one of the most ultimate claims ever made by a sane man. "I am the way, the truth, and the life," he told his disciples just hours before he stood before Pilate.
Will we find truth in a transfinite Christ or will we prefer partial truth from within a system that cannot validate itself?
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
MATHEMATICIANS OF THE INFINITE
The mathematics of the infinite cannot be understood apart from Judeo-Christianity. Although infinitely theory intrigued all civilizations, especially the Greeks, nowhere has it been so important as in Christendom, where all theology hinged on its implications. Augustine in various writings and Boethius, in The Consolation of Philosophy, wrestled with the idea especially in relation to time and God's eternal existence. Of Learned Ignorance, by Bishop Nicholas Cusa, argued that at infinity all things become one, just as the arc of an infinitely large circle will flatten into a straight line.
Not surprisingly, the world's first systematic treatment of infinity was produced by a theologian. The Czech, Bernard Balzano, pioneered the theory of real numbers, established some properties of infinite sets, and became a precursor of modern logic. Like most pioneers he made serious errors. His theology verged on heresy.
The great Cantor, a Protestant Jew with a Catholic mother, was spurred by religious impulses to create transfinite theory. His profoundly original work was spurned by most contemporaries and he was relegated to minor teaching posts. One of Cantor's greatest contributions was the technique of diagonalization (which we employ in our page seven proof of Godel). Kronecker savaged Cantor in print and in the classroom. Lacking self-confidence, Cantor came to doubt the worth of his own work. Although the Jesuits seized upon his proofs as validation for certain theological tenets, Cantor's uncertainty eventually led him into madness.
Godel, with a Lutheran background, took religious questions seriously and declared himself a theist. Profoundly influenced by his Lutheran predecessor, Leibnitz, he espoused an ontological proof for the existence of God based on his mathematics. This was not successful.
These instances show the power of Christianity to drive first-rate scientific work. No other religion in history has impelled men and women to do such science. The claims of Christianity are so ultimate that at every turn they must either be accepted and substantiated, or denied and challenged. Again and again friend and foe impress new insight upon old theology.
References:
Bell, E. T. Men of Mathematics.
Gillispie, Charles Coulston. Dictionary of Scientific Biography.
Guillen, Michael. Bridges to Infinity.
QUESTIONS FOR ATHEISTS AND AGNOSTICS
If we dwell in a finite world created by an infinite God, is not a Godelian theorem exactly what we should expect to find?
Why was it that Christian theology and Christian thinkers impelled the major modern developments in infinity theory?
Since mathematical theory ultimately rests on faith, why do you denounce Christianity for resting on faith?
The history of science shows that strictly mechanistic views of the world have consistently failed to hold up. Why not acknowledge that the world is not strictly mechanistic as materialistic explanations must suppose?
In light of Godel's proofs and Christ's transfinite claims, won't you yield yourself to God?
duminică, 14 martie 2010
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