1. 1. 1 ABOUT THIS ARTICLE: - As a faculty of International Academy for Creative Teaching (under Jain Group of Institutions, Bengaluru) conducting workshops for Teachers of a few schools in Coimbatore during 2003 2009, I faced difficulty in sharing the contributions of Indian mathematicians, specially of Aryabhata-I (5th c. AD) with those teachers (who are not familiar with Devnagari Script). Tamizh is one of the longest surviving classical languages in the world and it has been described as the only language of contemporary India which is recognizably continuous with a classical past. The variety and quality of classical Tamil literature has led to its being described as "one of the great classical traditions and literatures of the world". [Ref. Wikipedia]. But, Tamizh has fewer scripts than in Devnagari. Scripts of any language are cryptic symbols for the sounds needed in writing them to communicate with the public. Tamizh Grantham Scripts are akin to Malayalam scripts, and it is difficult to adapt it to Devnagari. That is the reason for attempting to this venture. Modified Tamizh scripts equivalent to Devnagari Scripts (shown within brackets): - Vowels: (swara) (), (), (), (), (), (), [ ()], (), (), (), (), (), (), , Aytham () Vyanjana, Consonants: (Vargakshara) = (), 1 ( ), 2 ( ), 3 (), ( ) = (), 1 ( ), [ 2 , ()], 3 (), () = ( ), 1 ( ), 2 ( ), 3 (!), () = (), 1 (), 2 (%), 3 (), () = ( ), 1 (), 2 ( ), 3 ( ), ( ) Vyanjana, Consonants: (Avargakshara) (), (), ( ), ( ), ( ), ( ), ( ), ! (4 ) " (). [#, $ and % ()] are special scripts for Tamizh only. [& and '] are samyuktakshara (compound alphebts) in Devnagari.
2. 2. 2 Relevance of Ancient Knowledge to the present century: De-coding Aryabhatiya Cryptic Numerals, and its application to Modified Tamizh Script and Kannada Script to find (1) the number of revolutions of Geo-centric planets in a Mahayuga (43,20,000 Years), comparison of their sidereal periods with their present day values, and (2) Reason for naming weekdays from Aryabhatiya of Aryabhata-I. Compiled by: Venkatesha Murthy, Hon.Head, Vedic Maths, National Institute of Vedic Sciences, # 58, Raghavendra Colony, Chamarajapet, Bangalore-560018., Mobile; 09449425248. email: tippurgopu@gmail.com [Note: - This article is prepared using Baraha Unicode software.] Introduction: - Base ten place-value system having ten digits from 1 to 9 and 0 for number reckoning is the universally acclaimed invention by the visionaries of ancient India. Indian zero is unique from the zeroes of Babylonian, Mayan and Chinese civilizations having place-value systems. (i) Indian zero is a separator of positive and negative numerals. (ii) Indian zero is a place-holder, for example; numeral for two thousand and six is 2006 in which significant digits 2 and 6 of place-values thousands and units are spelt without mentioning the names of digits of place-values hundreds and tens. The digit 1 to 9 is figurate, and 0 is null figurate as it occupies the place-values that are not spelt while naming numbers. Therefore zero is also referred as null. Cryptic numerals using words and alphabets were popular in Sanskrit texts to denote numbers in rhythmic slokas for easy memorization. Aryabhata-I (5th c. AD) has invented a unique cryptic numerical method to denote the astronomical numbers like number of revolutions of Geo-centric planets in a Mahayuga (43,20,000 years). It is really surprising that these Aryabhatiya Cryptic numerals on conversion into their sidereal periods (time taken to go round ones in their orbits) almost agree with their present-day values.
3. 3. 3 1. Rule for Aryabhatiya Devanagari Varnamala Cryptic Numerals : - 789 ::78 %@ B :: CD: 2 2 2 2 | 1 2 2 2 2 || | || Purport: - Aryabhata-I, in his cryptic method, used (I) Consonant, FG (a) 78 ( ), ) and (b) 78, ( , )] to denote numbers, and (II) Vowels, B ( , ) to specify the number of zeros to follow the numbers denoted by consonants, FG. The meaning of the rule could be explicitly explained thus with Tables: - 1. I (a). 78 ( , ) from (! = %) to (" = & ) denote numbers from 1 to 25 sequentially. I (a). (i) 78 ( , ) from (! = %) to (# = ') denote numbers from 1 to 10 sequentially. Table I (a) (i)
4. 4. 4 I (a) (ii). 78 ( , ) from ($ = ()) to (" = &)) denote numbers from 11 to 25 sequentially. Table I (a) (ii) 1. I. (b) 78 ( , ) from ( = )) to 4 (% = *) denote numbers from 3 to 10 sequentially. Table I (b) 1. II. II (a). (i) Number of zeros to follow the numerals of 78 from to ( , from ! to ", % + & ) with svara is nil, and with svara to are denoted with one group of eight sets of even number of zeros. II (a). (ii) Number of zeros to follow the numerals of 78 from to 4 ( from to %, ) + * ) is denoted with another group of nine sets of odd number of zeros.
5. 5. 5 Table II (a) The above rule could be modified thus; II(b). (i) Place values in powers of 10 of the numerals of 78 from to ( , from ! to ", % + & ) is denoted with one group of nine sets of even powers of ten (starting from the index 0). (ii) Place values in powers of 10 of the numerals of 78 from to 4 ( from to %, ) + * ) is denoted with another group of nine sets of odd powers of ten (starting from the index 1). Table II (b)
6. 6. 6 ; means = ( ) = (1x1)=1; [ = 1] It gives reason for number of zero to B is 1, and the numerical value of any 778 to start from = 1. Even numbers of zeros for B from to are from 2 to 14 zeros. means = [( + ) x ] = [(5+25) 1] = [30] = (310) = = ( ) = (3 10) = 30 ; [ = 10]. It gives reason for number of zeros to follow 78 is one, and then odd number of zeros for B from to . The numerical values of 78 to start from = 3 ( = 3, ) = 3). 1. III The two important Rules illustrated by above reasons; Rule 1: When a FG ( , ) is connected with a B ( , ), it forms a 98, ( , 0 ) and their numerical values are to be multiplied. [Note: 9 = multiply] Example: @ = ( x ) = (' ) = (2 ) = (6 1000) = (6 103 ) = 6000. Rule 2: When a FG ( , ) is connected with another FG ( , ), it forms a Q8 ( , 4 ), and their numerical values are to be added. [Note: Q = add] Example: Q = [( x ) + ( x ) + (x )] ! = [( x ) + (! x ) + ( x )] = [(9 x 105 ) + (1 x 1) + (16 x 1)] = 900000 + 1 + 16 = 900017 Another Example: - Number of revolutions made by (Geo-centric) Planets in a Yuga (= 43,20,000 years) mentioned in Aryabhatiya through the Devanagari script are only Cryptic.
7. 7. 7 The same Cryptic words may be Adapted to other language scripts, (for example; in Kannada, Tamizh etc.,), and describe the values of Geo-centric Planers stated in Aryabhatiya of AryabhataI (499 AD). 2. Cryptic Devnagari Alphabetical Numerals denoting the Number of revolutions of Geo-centric planets in Aryabhatiya of Aryabhata-I (5th c. AD). @ R, T UV , V @[, 9]^, %T, T, _ [(2) p.18] Number of revolutions made by (Geo-centric) Planets in a Yuga (= 43,20,000 years) stated above are in the Devanagari script. They are only Cryptic words having no meaning in reality. They could be written in any language script. Now, the above statement in Devanagari script is written in Modified Tamizh & Kannada Scripts. Modified Tamizh Script: - 02 32: !10!3 , 2 5271 8 : ;3 !2 !3, 52< !1=703, 5 3 2@!1 , A23 52 1 , B 352 2517 || Kannada Script: - 57: :, < >?A + EAGH, IJ , L, ? = 5,77,53,336, Saturn; vl RXubu; ;3 !2 !3, EAGH = 1, 46,564, Jupitor; a, Zcrp, !1=703, IJ = 3,64,224, Mars; Me (qXaV), pSsfl , 3 2E3@!1 , L = 22, 96,824, Mercury; ok, xavjl, 52 1 , < = 1,79,37,020, Venus; pa, ew ZN , 25171 , R = 70,22,388. These numerical values could be verified by the application of Tables I, and II based on Aryabhatiya Devanagari Varnamala Cryptic Numerals, and these could be adapted to Modified Tamizh and Kannada Scripts;
8. 8. 8 Sun; Uu, Zrb, !10!3 , ; 43,20,000. R = ( x ) + ( x ) + ( x ) !10!3 = (!1 x ) + ( x ) + (!3 x ) = (U x ) + () x ) + (X x ) = (2 x 104 ) + (3 x 105 ) + (4 x 106 ) = (20000) + (300000) + (4000000) = 4320000 Moon; xq, crarXvNI,, 2 D71 8 ; >? ; 5,77,53,336 crarXvNI, = ( x )+ ( x )+ ( x )+ ( x )+ ( x )+ ( x )+ ( x )+ ( x ) 2 5271 8 = (7. ) + ( . ) + (!2. ) + ( . ) + ( . ) + (H. ) + (71. ) + (8. ) >? = (Z . ) + () . ) + ( . ) + () . ) + (] . ) + (^ . ) + (_ . ) + (` . ) = (6 x 100 ) + (3 x 101 ) + (3 x 102 ) + (3 x 103 ) + (5 x 104 ) + (7 x 105 ) + (7x 106 ) + (5 x 107 ) = 57753336 Saturn ; zl, RXubu, 3 2 3, ; 1, 46,564 RXubu = ( . ) + ( . ) + ( . ) + ( . ) + ( . ) ;3 !2 !3 = ($3. ) + ( . ) + ('. ) + (!3. ) + ('. ) EH = (a . ) + (] . ) + (2 . ) + (X . ) + (2 . ) = (14 x 104 ) + (5 x 102 ) + (6 x 103 ) + (4 x 1) + (6 x 10 ) = 140000 + 500 + 6000 + 4 + 60 = 1,46,564. Jupitor ; a ; Zcrp, 2 3 , = 3,64,224 Zcrp = ( . ) + ( . ) + ( . ) + ( . ) + ( . ) !1=70B3 = (!1. C) + ( . C) + (7. ) + ( . ) + (B3. ) IJ = (U . ) + (b . ) + (Z . ) + () .) + (c . ) = (2 x 102 ) + (4 x 103 ) + (6 x 104 ) + (3 x 105 ) + (24 x 1) = 200 + 4000 + 60000 + 300000 + 24 = 3,64,224. Mars ; Me, qs , pSsflZ , 3 2 3 1 , = 22,96,824. = ( . ) + (% . ) + ( . ) + ( . ) + ( . ) + ( . ) 3 2@!1 = (B3. ) + ( 2. ) + (8. ) + (73. ) + ( . ) + (!1. ) L = (c . ) + (d . ) + (` . ) + (e . ) + (f . ) + (U . ) = (24x1) + (18x102 ) + (5x103 ) + (9x104 ) + (20x104 ) + (2x106 ) = 24 + 1800 + 5000 + 90000 + 200000 + 2000000 = 22,96,824.
9. 9. 9 Mercury ; ok , xazjl, 2 1 , = 1,79,37,020. xazjl = ( . ) + ( . ) + ( . ) + ( . ) + ( . ) 52 1 = ( . ) + (!2. ) + (H. ) + ( 1. ) + (K. ) < = (g . ) + ( . ) + (^ . ) + (h . ) + (f . ) = (9x105 ) + (3x104 ) + (7x 103 ) + (17 x106 ) + (20x1) = 900000 + 30000 + 7000 + 17000000 + 20 = 1,79,37,020 Venus ; pa, z , ewoZN, 2 1 1 , = 70,22,388. _ = ( . ) + ( . ) + ( . ) + ( . ) + ( . ) 2517 = (L. ) + (M. ) + (B2. ) + (!1. ) + (71. ) R = (i . ) + (j . ) + (c . ) + (U . ) + (_ . ) = (8 x 1) + (8 x 10) + (23 x 102 ) + (2 x 104 ) + (7 x 106 ) = 8 + 80 + 2300 + 20000 + 7000000 = 70,22,388 2. I. Table showing The number of Revolutions (velocity) of (Geo-centric) Planets in a Yuga (43,20,000 yrs.) arranged in the increasing order in Aryabhatiya Cryptic Numerals and in International Numerals. Table IV [Similar Tables may be prepared in Kannada Scripts wherever the are missing].
10. 10. 3 1. Rule for Aryabhatiya Devanagari Varnamala Cryptic Numerals : - 789 ::78 %@ B :: CD: 2 2 2 2 | 1 2 2 2 2 || | || Purport: - Aryabhata-I, in his cryptic method, used (I) Consonant, FG (a) 78 ( ), ) and (b) 78, ( , )] to denote numbers, and (II) Vowels, B ( , ) to specify the number of zeros to follow the numbers denoted by consonants, FG. The meaning of the rule could be explicitly explained thus with Tables: - 1. I (a). 78 ( , ) from (! = %) to (" = & ) denote numbers from 1 to 25 sequentially. I (a). (i) 78 ( , ) from (! = %) to (# = ') denote numbers from 1 to 10 sequentially. Table I (a) (i)
11. 11. 11 4. Reason for naming weekdays from Aryabhatiya of Aryabhatiya-I. b f% g Th hg7 C j% l [(2) p.214] B : H 2 1!" !3 | !3!7 1 1K 2 2 || kl0 m n oq r sJ