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THE USE OF ZERO, PLACE VALUE SYSTEM, LARGE NUMBERS AND SMALL NUMBERS IN ANCIENT INDIAAncient Indians were the first who invented zero and decimal place value system during Rigvedic period. The scientific naming system of numerals in Vedic Sanskrit indicates that decimal place value system was well established. The compounded words for numerals like Ekadasa (Eka+dasa) = one and ten, Ekavimshati (Eka+vimshati) = one and twenty, Ekatrimshat (Eka + trimshat) = one and thirty etc. indicate that Eka will be always the first word and Dasa will be always second word which implies the position of a number is most important since the symbol of unit & the symbol of ten cannot interchange their positions without affecting the value of the numbers. Thus units must be counted first later tens and so on. The use of large numbers up to 10^12 considering the powers of 10 in Yajurveda was also not possible without having the knowledge of place value system and zero.Ramayana gives the counting of large numbers from 10 to the power of 7 to 10 to the power of 62.Koti = 100000 x 100 = 10^7Shanku = Koti x 1000 x 100 = 10^12Mahashanku = Shanku x 1000 x 100 = 10^17Vrinda = Mahashanku x 1000 x 100 = 10^22Mahavrinda = Vrinda x 1000 x 100 = 10^27Padma = Mahavrinda x 1000 x 100 = 10^32Mahapadma = Padma x 1000 x100 = 10^37Kharva = Mahapadma x 1000 x 100 = 10^42Mahakharva = Kharva x 1000 x 100 = 10^47Samudra = Mahakharva x 1000 x 100 = 10^52Mogha = Samudra x 1000 x 100 = 10^57Mahaugha = Mogha x 1000 x100 = 10^62Mahabharata also used large numbers up to 10^52.Lalitavistara is a biography of Buddha and belong to Mahayana school of Buddhism written around 100 AD. Lalitavistara gives the evidence of use of infinitely large and small numbers.According to the story of Lalitavistara, A svayamvara (competition for marriage) was organized for Princess Gopa in which Prince Siddhrtha participated. Apart from other competitions like horse riding, archery etc., Siddhartha had to undergo the test of mathematics.Arjuna a great mathematician asked Siddhartha "Do you know the procedure of Kotishatottara (counting after hundred crores)". Explaining the procedure of Kotishatottara,Siddhartha counted large numbers starting from Koti (10^7), calculating in multiples of 100 up to Tallakshana (10^53) referring as first numeration.Koti x 100 = Ayuta (10^9)Ayuta x 100 = Niyuta (10^11)Niyuta x 100 = Kankara (10^13)Kankara x 100 = Vivara (10^15)Vivara x 100 = Akshobhya (10^17)Akshobhya x 100 = Vivaha (10^19)Vivaha x 100 = Utsanga (10^21)Utsanga x 100 = Bahula (10^23)Bahula x 100 = Nagabala (10^25)Nagabala x 100 = Titila (10^27)Titila x 100 = Vyavasthanaprajnapti (10^29)Vyavasthanaprajnapti x 100 = Hetuhila (10^31)Hetuhila x 100 = Karahu (10^33)Karahu x 100 = Hetvindriya (10^35)Hetvindriya x 100 = Samaptalambha (10^37)Samaptalambha x 100 = Gaganagati (10^39)Gaganagati x 100 = Niravaravadya (10^41)Niravaravadya x 100 = Mudrabala (10^43)Mudrabala x 100 = Sarvabala (10^45)Sarvabala x 100 = Visangyagati (10^47)Visangyagati x 100 = Sarvasangya (10^49)Sarvasangya x 100 = Vibhutangama (10^51)Vibhutangama x 100 = Tallakshana (10^53)Building on this first numeration, next eight numerations also have 23 multiplicative steps of 100 and the last number expressed by Siddhartha was 10^421(Uttaraparamanurajahpravesha).Again replying to Arjuna, Siddhartha talked about "Paranamu"(subtle atoms) with bottom up approach and particles composed of atoms.Paramanu (subtle atom) x 7 = Renu (fine particle)Renu x 7 = Truti (small particle)Truti x 7 = VatayanarajahVatayanarajah x 7 = shasharajahshasharajah x 7 = EdhakarajahEdhakarajah x 7 = GorajahGorajah X 7 = LiksharajahLiksharajah x 7 = sarshapasarshapa x 7 = Yava (breadth of barley)Yava x 7 = AnguliAnguli x 12 = VitastiVitasti x 2 = Hasta (cubit)Hasta x 4 = DhanuDhanu x 1000 = KroshaKrosha x 4 = YojanaAssuming an Anguli = finger is 4 centimetres long, the "Paramanu"(subtle atom) is therefore, 4 centimetres divided by 7 ten times, which is 0.04 meter x 7 to the minus 10 or 0.00000000001416 meter (70 trillionths of a meter), which comes amazingly close to the actual size of carbon atom.After discussing infinitely large and small numbers, Siddhartha accepted the challenge to calculate the mass of one Yojana. Siddhartha calculated the mass of one Yojana as 10003000000000000060320512000 atoms. According to Buddhist cosmology, there are three thousand crore worlds in the universe each measuring 34000 yojanas. The question arises how many atoms are there in the universe. Siddhartha replied that there are Asamkhyata (innumerable) atoms in the universe. When 7 paramanus combine each other then only paramanus occupy space but there are innumerable paramanus in the world do not combine each other, thus, do not occupy space. Therefore, in view of Siddhartha, paramanus in the universe are innumerable. In the modern theory of quantum-mechanics, quarks enter into existence and disappear all the time in the vacuum. Therefore the quantum information is not fixed or innumerable.What a glorious heritage!!!! Lalitavistara was translated into Chinese during 2nd century. Therefore, Lalitavistara cannot be dated later than 1st century. Possibly, it might have written few hundreds years before 2nd century.Unfortunately, Modern textbooks teach us that Aryabhata invented zero in 5th century and Indians had no knowledge of zero and place value system before 5th century. Interestingly, one grant of Katachchuri king Taralswami is dated in the year 346 and the year is recorded in decimal place value notation. Historians declared this grant as forgery because Indians had no knowledge of plave value system before 5th century. Shame on these historians.Evidently, Indians had the knowledge of zero and place value system since Vedic period. Racist western and Eurocentric scholars do not accept this fact. Therefore, we teach our children that Indians had no knowledge of Zero and place value system before 5th century.WE LOOK FOR A CERTIFICATE FROM WEST. (Mera Muajjim hi mera katil hai ab anjame insaaf kya hoga!!!!)SHAME ON US !!!! WE ARE "NALAYAK" DESCENDANTS OF A GLORIOUS HERITAGE.

Pranshu saxena

Date of Mahabharata war:Some Extreme Daters claim thatAryabhatta claims that Mahabharata was 3100 BC....Now, Aryabhatta states 3 yugapadas and 6 Manus and 27 yugas elapsed at the point ofMahabharata.The stanza of the sloka starts with Shastyabdanam Shadbhiryada vyateetastra yascha yuga padah.....Shastyabdanam Shadbhi means 60 x 6 = 360. While printing the manuscript, the word Shadbhi was altered to Shasti, which implies 60 x 60 = 3600 years after Kali Era......and that was used to denote that Mahabharat was 3100 BC. Clearly Aryabhatta is describing something else which occured 360 years ago.Actually, another interpretation is that he is describing the Yugic cycle as a day or week and then what part has elapsed.Anyway, the change of Shadbhi to shasti is arbitrary. It makes the calculation 3600 instead of 360.Aryabhattas birth time was fixed as 476 A.D so 360 years back was 116 AD which was also a Date for a great upheaval in Mathura from Numismatic and other evidence. the overthrow of Kanishka most likely and establishment of Vaishanava kushana kings.(The story of Vrishni overthrow of Kamsa may have been repeated by overthrow of similar sounding Kanishka by Soorsainis, Yaudheyas, Malavas and Arjunayanas. Last three claiming descent from three Kaunteyas.)Since in every genuine manuscript (from a point of view, well the critical edition), we find the word Shadbhi and not the altered Shasti.Aryabhatta is describing an event 360 years earlier to him....Actually the extreme daters use circular logic.They state that as Kaliuga started 3102 BC then Aryabhataa was ancient mathematician in 2742 BC!!...On one end they state that Mahabharata was 3100 BC on evidence of Aryabhata and when that evidence is overturned, they make this claim.......They are tied to this 3102 BC date without any evidence and thus, try to make all the evidence conform to it and when that is overturned, they overturn the history....The Puranas and Kharavela inscriptions all give 1050 (or 1015 years Sanskrit is read left to right or right to left) as gap between Mahapadma Nanda and Parikshita....This textual evidence backed by 9th cen BC Vrishni Sangh coins depicting Vasudeva ties us to lower dates. I am not saying that is hard and fast. The evidence for 1400 BC date is more and is in logical sequence....The Extreme daters make 3102 BC as Kaliyuga and then place Mauryas in 2000 BC.....The connection of Mauryas and especially Asoka to the Greek states in Central Asia is attested with Epigraph evidence. Disconnecting them subverts the entire world history on its head.....Even if extreme daters are right, they do not create a conclusive argument around the rest of history like Bhartiya Vidya Bhawan and others like Chatursena and Sanskritayana using the 1450 BC date....The extreme daters even try to move Buddha by 1200 years. Which is again possible....The Sramana sects that were later co-opted by followers of Buddha (and Mahavira) may be extant centuries before under different names..There is no maybe!Mahabharata describes them in Vana parva in Yudhishthara's retinue.Like Jains have 24 Teerthankars, some Buddha sects especially sarvasti-vada has multiple Buddhas also and that is the basis of Jatakas....But tying one of Bodhisatvas born 1200 years prior to Buddha to Asoka (epigraphic evidence again would make Alexander older than Moses for extreme daters!)....Extreme daters fail the test of world history. Unless Mahabharat occured on another planet which is possible!! Never close any avenue or option till conclusively closed....Another popular involuntary co-conspirator of Extreme daters is Varaha Mihira.Again i do need to emphasize two things. Mihira was from west and probably even of persian/ central asian origin(having said that Indian culture flourished there in those regions even till 800 AD and eve

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