Final copy of decoding aryabhatiya numerals into modified tamizh script & kannada script

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: உய ெர (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), ( )
= (च्), 1 ( ), [ 2 , (ज्)], 3 (झ्), (ञ्)
= ( ), 1 ( ), 2 ( ), 3 (!), (ण्)
= (त्), 1 (थ्), 2 (%), 3 (ध्), (न्)
= (प ्), 1 (फ्), 2 (ब ्), 3 (भ ्), (म ्)
Vyanjana, Consonants: உய ெம எ (Avargakshara)
(य़्), (र्), (ल ्), (व ्),  (श् ), (ष ् ), (स् ), ! (4 )
" (ळ्).
[#, $ and % (न्)] are special scripts for Tamizh only.
[& and '] are samyuktakshara (compound alphebts) in Devnagari.

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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.

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1. Rule for Aryabhatiya Devanagari Varnamala Cryptic Numerals : -
वगा78रा9ण वग:ऽवग:ऽवगा78राणी कात् मौ यः ।
ख%@वनवके Bवरा नव वग:ऽवग: नवाCDयवग: वा ॥
வ கா2 ராண வ ேக2ऽவ ேக2ऽவ கா2 ராண கா ெமௗ யஃ |
க1 வ 2நவேக வரா நவ வ ேக2ऽவ ேக2 நவா ய வ ேக2 வா ||
ವ ಾ ಾ ವ ೇ ಽವ ೇ ಽವ ಾ ಾ ಾ ಯಃ |
ಖ ನವ ೇ ಸ ಾ ನವ ವ ೇ ಽವ ೇ ನ ಾಂತ ವ ೇ ಾ ||
Purport: - Aryabhata-I, in his cryptic method, used (I) Consonant, FयGजन (a) मूलवगा78र
(ைமஎ ), ಮೂಲ ವ ಾ ರ) and (b) मूलअवगा78र, (உய ைமஎ , ಮೂಲ ಅವ ಾ ರ)]
to denote numbers, and (II) Vowels, Bवरा (உய எ , ಸ ಾ ರ) to specify the
number of zeros to follow the numbers denoted by consonants, FयGजन.
The meaning of the rule could be explicitly explained thus with Tables: -
1. I (a). मूलवगा78र (ைமஎ , ಮೂಲವ ಾ ರ) from क् (! = %) to म् (" = & )
denote numbers from 1 to 25 sequentially.
I (a). (i) मूल वगा78र (ெம எ , ಮೂಲವ ಾ ರ) from क् (! = %) to ञ् (# = ')
Table I (a) (i)

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I (a) (ii). मूल वगा78र (ெம எ , ಮೂಲವ ಾ ರ ) from ($ = ()) to म ् (" = &))
Table I (a) (ii)
1. I. (b) मूल अवगा78र (உய ைமஎ , ಅವ ಾ ರ) from य् ( = )) 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 मूलवगा78र from क् to म ् (ெம
எ , from ! to ", ವ ಾ ರ % +ಂದ & ವ ೆ ೆ) with svara अ is nil, and with svara इ to
ओ are denoted with one group of eight sets of even number of zeros.
II (a). (ii) Number of zeros to follow the numerals of मूलअवगा78र from य् to 4
(உய ெம எ from to %, ಅವ ಾ ರ ) +ಂದ * ವ ೆ ೆ) is denoted with
another group of nine sets of odd number of zeros.

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Table II (a)
The above rule could be modified thus;
II(b). (i) Place values in powers of 10 of the numerals of मूलवगा78र from क् to म ्
(ெம எ , from ! to ", ವ ಾ ರ % +ಂದ & ವ ೆ ೆ) 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 मूलअवगा78र from य् to 4
(உய ெம எ from to %, ಅವ ಾ ರ ) +ಂದ * ವ ೆ ೆ) is denoted with
another group of nine sets of odd powers of ten (starting from the index 1).
Table II (b)

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कात् मौ यः ;
कात् means क = (क्× अ) = (1x1)=1; [अ = 1] It gives reason for number of zero to
Bवरा अ is 1, and the numerical value of any पूण7वगा78र to start from क = 1. Even numbers
of zeros for Bवरा from इ to औ are from 2 to 14 zeros.
मौ यः means म = [( + म ्) x अ] = [(5+25) × 1] = [30] = (3×10) = य = (य्× अ) =
(3 × 10) = 30 ; [अ = 10].
It gives reason for number of zeros to follow मूलअवगा78र य् is one, and then odd number
of zeros for Bवरा from इ to औ. The numerical values of मूलअवगा78र to start from य्= 3
( = 3, ) = 3).
1. III The two important Rules illustrated by above reasons;
Rule 1: When a FयGजन (ைம எ , ವ ಂಜನ) is connected with a Bवर (உய
எ , ಸ ರ), it forms a गु9णता8र, (உய ைமஎ , ಗು 0ಾ ರ) and their
numerical values are to be multiplied. [Note: गु9णत = multiply]
Example: @व = (व ्x इ) = (' × இ) = (2 × ಇ) = (6 × 1000) = (6 × 103
) = 6000.
Rule 2: When a FयGजन (ைம எ , ವ ಂಜನ) is connected with another FयGजन
(ைம எ , ವ ಂಜನ), it forms a संयुQता8र (உய ைம எ ,
ಸಂಯು ಾ4 ರ), and their numerical values are to be added. [Note: संयुQत = add]
Example: सूQत = [(स ् x ऊ) + (क् x अ) + (त्x अ)]
ஸூ!த = [( x ஊ) + (! x அ) + ( x அ)]
= [(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.

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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 Aryabhata–I (499 AD).
2. Cryptic Devnagari Alphabetical Numerals denoting the Number of revolutions of
Geo-centric planets in Aryabhatiya of Aryabhata-I (5th
c. AD).
युगर@वभगणाः Rयुघृ, शTश चयUगVयङुशुछृ ऌ,
शVन ढु @व[व, गु 9]^युभ, कु ज भ%Tलझुनुखृ,
बुध सुगुTशथृन, भृगु जष_बखुछृ ॥ [(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: -
0க2ரவ ப3க2ணா: !10!3 , ஶஶி சயகி2ய 52ஶு71 8
ஶன: ;3 !2வ !3வ, 52< !1=70ப3, 5ஜ ப3 2லிஜு@!1 ,
A2த3 ஸு52ஶி 1 ன, B 352 ஜஷப 2517 ||
Kannada Script: -
ಯುಗರ5ಭಗ7ಾ: ಖು ಘ:, ಶ< ಚಯ>?ಙುAಶುಛೃಲೃ
ಶ+ ಡುEಿAGಘH, ಗುರು IJಚು ಭ, ಕುಜ ಭ Lಝುನುಖೃ,
ಬುಧ ಸುಗು<ಥೃನ, ಭೃಗು ಜಷRಖುಛೃ
Sun; UÌuÉ, ZrÉÑbÉ×, !10!3 ; = ಖು ಘ: 43,20,000,
Moon; xÉÉåqÉ, cÉrÉÌaÉÌrÉXÒûvÉÑNØûI, , சயகி2ய Dஶு71 8 ; ಚಯ>?ಙುಶುಛೃಲೃ = 5,77,53,336,
Saturn; vÉÌlÉ RÒûÎXçuÉbuÉ; ;3 !2வ !3வ, ಢುEಿAGಘH = 1, 46,564,
Jupitor; aÉÑÂ, ÎZÉëcrÉÑpÉ, !1=70ப3, IJಚು ಭ = 3,64,224,
Mars; MÑüeÉ (qÉXèaÉVû), pÉÎSèsÉfÉÑlÉÑख ्ऋ, ப3 2லிE3@!1 , ಭ Lಝುನುಖೃ = 22, 96,824,
Mercury; oÉÑkÉ, xÉÑaÉÑÍvÉjÉ×lÉ, ஸு52ஶி 1 ன, ಸುಗು<ಥೃನ = 1,79,37,020,
Venus; pÉ×aÉÑ, eÉwÉÍब ्ZÉÑNØû , ஜஷப 25171 , ಜಷRಖುಛೃ = 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;

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Sun; UÌuÉ, ZrÉÑbÉ×, !10!3 ×, ಖು ಘೄ ; 43,20,000.
Rयुघृ = (ख् x उ) + (य् x उ) + (घ् x ऋ)
!10!3 = (!1 x உ) + ( x உ) + (!3 x )
ಖು ಘೄ = (U x ಉ) + () x ಉ) + (X x ಋ)
= (2 x 104
) + (3 x 105
) + (4 x 106
)
= (20000) + (300000) + (4000000) = 4320000
Moon; xÉÉåqÉ, cÉrÉÌaÉÌrÉXÒûvÉÑNØûI,, சயகி2ய Dஶு71 8 ; ಚಯ>?ಙುಶುಛೃಲೄ ; 5,77,53,336
cÉrÉÌaÉÌrÉXÒûvÉÑNØûI,
= (च् x अ)+ (य् x अ)+ (ग् x इ)+ (य् x इ)+ ( x उ)+ (श् x उ)+ ( x ऋ)+ (ल ् x ऋ)
சயகி2ய 52ஶு71 8
= (7. அ) + ( . அ) + (!2. இ) + ( . இ) + ( . உ்) + (H. உ்) + (71. ) + (8. )
ಚಯ>?ಙುಶುಛೃಲೄ
= (Z . ಅ) + () . ಅ) + ( . ಇ) + () . ಇ) + (] . ಉ) + (^ . ಉ) + (_ . ಋ) + (` . ಋ)
= (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 ; zÉÌlÉ, RÒûÎXçuÉbuÉ, 3 2வ 3வ, ಢು ಿಘ ; 1, 46,564
RÒûÎXçuÉbuÉ = ( . उ) + ( . इ) + (व् . इ) + (घ् . अ) + (व ् . अ)
;3 !2வ !3வ = ($3. உ) + ( . இ) + ('. இ) + (!3. அ) + ('. அ)
ಢುEಿಘH = (a . ಉ) + (] . ಇ) + (2 . ಇ) + (X . ಅ) + (2 . ಅ)
= (14 x 104
) + (5 x 102
) + (6 x 103
) + (4 x 1) + (6 x 10 )
= 140000 + 500 + 6000 + 4 + 60
= 1,46,564.
Jupitor ; aÉÑÂ ; ÎZÉëcrÉÑpÉ, 2 ப3 , ಚು ಭ = 3,64,224
ÎZÉëcrÉÑpÉ = (ख् . इ) + (र् . इ) + (च् . उ) + (य् . उ) + (भ ् . अ)
!1=70B3 = (!1. C) + ( . C) + (7. உ) + ( . உ) + (B3. அ)
IJಚು ಭ = (U . ಇ) + (b . ಇ) + (Z . ಉ) + () .ಉ) + (c . ಅ)
= (2 x 102
) + (4 x 103
) + (6 x 104
) + (3 x 105
) + (24 x 1)
= 200 + 4000 + 60000 + 300000 + 24 = 3,64,224.
Mars ; MÑüeÉ, qÉ…¡ûsÉ , pÉÎSèsÉfÉÑlÉÑZÉ× , ப3 2லி 3 1 , ಭ ಝುನುಖೃ = 22,96,824.
भि लझुनुखृ = (भ् . अ) + (% . इ) + (ल ् . इ) + (झ् . उ) + (न् . उ) + (ख ् . ऋ)
ப3 2லிஜு@!1 = (B3. அ) + ( 2. இ) + (8. இ) + (73. உ) + ( . உ) + (!1. )
ಭ Lಝುನುಖೃ = (c . ಅ) + (d . ಇ) + (` . ಇ) + (e . ಉ) + (f . ಉ) + (U . ಋ)
= (24x1) + (18x102
) + (5x103
) + (9x104
) + (20x104
) + (2x106
)
= 24 + 1800 + 5000 + 90000 + 200000 + 2000000 = 22,96,824.

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Mercury ; oÉÑkÉ , xÉÑaÉÑÍzÉjÉ×lÉ, ஸு 2ஶி 1 ன, ಸುಗು ಥೃನ = 1,79,37,020.
xÉÑaÉÑÍzÉjÉ×lÉ = (स् . उ) + (ग् . उ) + (श् . इ) + (थ् . ऋ) + (न् . अ)
ஸு52ஶி 1 ன = ( . உ) + (!2. உ) + (H. இ) + ( 1. ) + (K. அ)
ಸುಗು<ಥೃನ = (g . ಉ) + ( . ಉ) + (^ . ಇ) + (h . ಋ) + (f . ಅ)
= (9x105
) + (3x104
) + (7x 103
) + (17 x106
) + (20x1)
= 900000 + 30000 + 7000 + 17000000 + 20
= 1,79,37,020
Venus ; pÉëÑaÉÑ, zÉÑ¢üÈ , eÉwÉÌoÉZÉÑNØû, ஜஷப 2 1 1 , ಜಷ ಖುಛೃ = 70,22,388.
जष_बखुछृ = (ज् . अ) + (ष ् . अ) + (भ् . इ) + (ख् . उ) + ( . ऋ)
ஜஷப 2517 = (L. அ) + (M. அ) + (B2. இ) + (!1. அ) + (71. )
ಜಷRಖುಛೃ = (i . ಅ) + (j . ಅ) + (c . ಇ) + (U . ಉ) + (_ . ಋ)
= (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].

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4. Reason for naming weekdays from Aryabhatiya of Aryabhatiya-I.
सbतैते होरेशाः शनैfचरा%या यथाgमं Tशhाः ।
शीhgमचतुथा7 भविCत सूयjदया% lदनपाः ॥ [(2) p.214]
ஸBைதேத ேஹாேரஶா: ஶைனHசரா 2யா யதா1!ரம" ஶீ!3ராஃ |
ஶீ!3ர!ரம7ச தா1 ப1வKதி ஸூ ேயா 2 தி2நபாஃ ||
ಸkೆl0ೇ mೋ ೇnಾಃ ಶoೈಶq ಾrಾ ಯsಾಕJಮಂ <ೕtJಃ |
<ೕಘJಕJuಾಚqತುsಾ ಭವಂv ಸೂwೕ ದxಾd ನkಾಃ ||
Purport: - The seven (Geo-centric) planets beginning with Shani (Saturn), which are
arranged in the increasing order of their number of revolutions in a Mahayuga (in
43,20,000 years), are the lords of the successive hours. The planets occurring fourth in the
order of successive velocity are the lords of the successive days, which are reckoned from
sunrise.
Explanation: - The Table given below clearly explains the meaning of the sloka; Lord of
the 25th
hour of ஶன:!கிழைம is ஞாய . But 25th
hour of ஶன:!கிழைம is the 1st
hour of next day to ஶன:!கிழைம and its lord is ஞாய . Therefore the next day of
ஶன:!கிழைம is named after ஞாய [which is the lord of 4th
hour of ஶன:!கிழைம].
Similarly the other week-days are named.
Table VI

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Shani
Saturn
Guru
Jupitor
Mangala
Mars
Bhanu
Sun
Shukra
Venus
Budha
Mercury
Soma
Moon
Shani
Saturn
Guru
Jupitor
Mangala
Mars
Bhanu
Sun
Shukra
Venus
Budha
Mercury
Soma
Moon
1
8
15
22
1
8
15
22
2
9
16
23
2
9
16
23
3 10 17 24
3 10 17 24
4
11
18
25
4
11
18
25
1=2
3
4
5. I. A Working model to explain the reason for naming the week-days: -
(i) Yellow concentric circles are drawn and explanations are written on a blue hard
board.
(ii) A circular disc with mentioned writings on it is made to rotate through the centre of
the yellow concentric circles drawn on the hard board so that the sectors on it having names
of week-days are aliened with the sectors bearing numbers on the hard board.
When a sector in the rotating disc having Shani ruling the 1st hour of Shanivar is aliened
with the sector having 1on the hard board, the name of its next day is the week-day having
the name of the planet Ravi ruling the 4th hour of Shanivar. Hence the name of the next
day to Shanivar is Ravivar.
Figure 1
Write names of Geo-centric planets in the descending order of of their sidereal periods
clockwise.
1. Each hour of a day
is ruled by the
planets in that
order.
2. Name of a day is
the name of the
planet ruling its 1st
hour
3. 1st hour of
Shanivar is ruled by
Shani.
4. Name of its next
day is the name of
the planet ruling its
4th
hour.
5. 4th, 11th, 18th &
25th hr of Shanivar
is ruled by Bhanu,
Ravi.
6. 25th hour of Shanivar is the 1st hr of next day to Shanivar (viz., Bhanuvar).
7. 1st hour of next day to Shanivar is ruled by Bhanu.
8. Hence, next day to Shanivar is Bhanuvar.
9. Next day to Bhanuvar is somavar, and so on.

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Bhanuvar
1
2
3
4
5 6
7
Somavar
Mangalvar
Budhavar
Guruvar
Shukravar
Shanivar
Bhanuvar
1
2
3
4
5 6
7
Somavar
Mangalvar
Budhavar
Guruvar
Shukravar
Shanivar
7
6
5
4
3
2
1
Sidereal
periods
Names of Geo-
centric planets
Sl
.#
7
6
5
4
3
2
1
Sidereal
periods
Names of Geo-
centric planets
Sl
.#
Shani (Saturn): 29. 48 years
Guru (Jupiter) 11. 86 years
Mangala (Mars) 687.00 days
Bhanu (Earth) 365. 256 days
Shukra (Venus) 224. 7 days
Budha (Mercury) 87. 97 days
27. 32 daysSoma (Moon)
5. II. Instruction to Arrange Geo-centric planets in the descending order of sidereal
periods from the Names of Indian week-days: -
1. Write the names of weekdays in each sector of a circle in the clockwise direction as
shown.
2. Draw a table as shown.
3. Start with 1 against Shanivar, skip one sector and write successive numbers in the
anticlockwise direction and write their names in the table each time.
4. Enter sidereal periods of Geo-centric planets referring any recent data book.
5. The names of Geo-centric planets are arranged in the decreasing order of their
sidereal periods.
Figure 2

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Reference: -
1. “A Concise History of Science in India”; D. M. Bose, S. N. Sen, B. V.
Subbarayappa, Editors] INSA, New Delhi
2. “Aryabhatiya, with the commentary of Bhaskara-I and Someswara” :Edited by K S
Shukla, INSA, New Delhi, (1976),
3. “Aryabhatiya, with the commentary of Suryadeva Yajvan” : Edited by K V Sharma,
INSA, New Delhi.
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Karnataka (2013)

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