Final Copy of Decoding Aryabhatiya numerals into Modified Tamizh Script & Kannada Script
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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 (5 th 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: உயெர (swara) அ (अ), ஆ (आ), இ (इ), ஈ (ई), உ (उ), ஊ (ऊ), [ (ऋ)], எ (ए), ஏ (ए), ஐ (ऐ), ஒ (ओ), ஓ (ओ), (औ), ஃ , Aytham (◌ः) Vyanjana, Consonants: ெம எ (Vargakshara) = (क् ), 1 (ख ्), 2 (ग् ), 3 (घ् ), () = (च ्), 1 (), [2 , (ज् )], 3 (झ् ), (ञ ्) = (), 1 (), 2 (), 3 (!), (ण ्) = (त ्), 1 (थ ्), 2 (%), 3 (ध् ), (न ्) = (प ्), 1 (फ्), 2 (ब् ), 3 (भ् ), (म ्) Vyanjana, Consonants: உயெம எ (Avargakshara) (य़ ्), (र्), (ल ्), (व ्), (श ् ), (ष ् ), (स ् ), ! (4 ) " (ळ्). [#, $ and % (न ्)] are special scripts for Tamizh only. [& and ’] are samyuktakshara (compound alphebts) in Devnagari.
Final Copy of Decoding Aryabhatiya numerals into Modified Tamizh Script & Kannada Script
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 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:
[email protected] [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 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 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 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 ; 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 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;
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. 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 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