"Introduction to Siribhūvalaya" - Talk at Jain Academy of Scholars

"Siribhūvalaya" is one of its kind mind-boggling creations in the whole world. This grand poetry has been crafted by Ācārya Kumudēndu in Numeral Script in 9th century. It is a treasure house of knowledge and encompasses verses in many languages.

1. Siribhūvalaya : An Introduction Virtual Talk at Jain Academy of Scholars 27 th February 2024 by Er . Anil Kumar Jain FIETE, FIE(I), SMCSI, LM-ISCA email: [email protected] Siri Bhūvalaya Śōdha evam Praśik ș aṇa Kēndra Kundakunda Jñānapīṭha Shri Digambar Jain Udasin Ashram Trust 584, M. G. Road, Indore - 452001

2. Siribhūvalaya : Key Historic Transitions ProCreation Period : 9 th Century (about 1200 years ago) Setting : Ancient Karnataka, Near Bengaluru Focal Characters : Acārya Kumudendu - Outstanding inimitable Genius who scripted this inimitable epic. Mahāmata Mallikabbe - Ardent Benefactor who distributed copies of Siribhūvalaya – one of these survived to be rediscovered in twentieth century. Long Intermission: Wonderful Masterpiece laid into oblivion for next 1000 years due to complexity in deciphering it. Resurrection : In early 20 th Century By Pa ņ dit Yellapp ā Śā str ī (The arduous Redeemer who strived resurrection efforts till his death )   2

3. One Cakra from Original Manuscript in Aṅka-Lipi 3

4. Transliteration by Pa ņ dit Yellapp ā Śā str ī (Preserved at National Archives of India, N. Delhi) 4

5. First Chakra of Siribhūvalaya 5 IMPORTANT : Aṅka-Lipi (Numeral Script) allowed efficient implementation of Transposition and Substitution Ciphers (Cryptographic Mechanisms) by Acārya Kumudendu .

6. Partitioning of 27x27 Matrix of Cakra into Nine 9x9 Sub-Matrices Sub-Matrix 3 Sub-Matrix 2 Sub-Matrix 1 Sub-Matrix 4 Sub-Matrix 9 Sub-Matrix 5 Sub-Matrix 6 Sub-Matrix 8 Sub-Matrix 7 6

7. Substitution Cipher Key (KCT) for different scripts कुमुदेन्दु कोड सारणी में देवनागरी, कन्नड़ एवं ब्राह्मी लिपि के ध्वन्याक्षर 7

8. Conversion of a Word into Numbers (Encoding) शब्द वर्ण विच्छेद अङ्क-लिपि भूवलय भ् ऊ व् अ ल् अ य् अ 51-8-56-1-55-1-53-1 ज्ञानपीठ ज् ञ् आ न् अ प् ई ठ् अ 35-37-2-47-1-48-5-39-1 क्षितिश्री क् ष् इ त् इ श् र् ई 28-58-4-43-4-57-54-5 8 This is an example of Alphabetic Writing System which represent the phonological structure of the language. Vowels and Consonants have equal status and are presented in a sequence. This type of writing system is in contrast with Abugida ( Alphasyllabary ), in which a single symbol denotes the combination of one consonant and one vowel. Example - Most of the European Scripts - which are descendents of Latin and Greek writing systems.

9. Conversion of Numbers into Word (Decoding) अङ्क-लिपि वर्ण प्रस्थापन शब्द 59. 4. 54. 4. 51. 8। 56. 1. 55. 1. 53. 1 स् इ र् इ भ् ऊ व् अ ल् अ य् अ सिरि भूवलय 1. 58. 38. 1. 52. 1. 60. 2. 48. 54. 2. 43. 4. 60. 2. 54. 53. 1 अ ष् ट् अ म् अ ह् आ प् र् आ त् इ ह् आ र् य् अ अष्ट महाप्रतिहार्य 9 An Abugida ( Alphasyllabary ) is a writing system in which Consonant-Vowel sequences are written as units; each unit is based on a Consonant, and Vowel notation is secondary, like a diacritical mark. Example - Scripts used in Indian Subcontinent. Another Important Characteristics of Aṅka-Lipi Aṅka-Lipi (Numeral Script) allows transliteration in any of the Script of choice, without any need to know any other script .

10. 10 अ ष् ट् अ म् अ ह् आ प् र् आ त् इ ह् आ र् य् अ व् अ य् भ् अ व् अ द् इ न् द् अ अ ष् ट् अ ग् उ ण् अ न् ग् अ ळ ओो ळ ओो म् द् अ म् स् र् ष् ट् इ ग् ए म् अ न् ग् अ ळ अ प् अ र् य् आ य् अ द् इ न् इ त् अ अ ष् ट् अ म् अ ज् इ न् अ ग् ए र् अ ग् उ व् ए न् उ ||1|| 𑀅 𑀱 𑀝 𑀅 𑀫 𑀅 𑀳 𑀆 𑀧 𑀭 𑀆 𑀢 𑀇 𑀳 𑀆 𑀭 𑀬 𑀅 𑀯 𑀅 𑀬 𑀪 𑀅 𑀯 𑀅 𑀤 𑀇 𑀦 𑀤 𑀅 𑀅 𑀱 𑀝 𑀅 𑀕 𑀉 𑀡 𑀅 𑀦 𑀕 𑀅 𑀍 𑀒 𑀍 𑀒 𑀫 𑀤 𑀅 𑀫 𑀲 𑀭 𑀱 𑀝 𑀇 𑀕 𑀏 𑀫 𑀅 𑀦 𑀕 𑀅 𑀍 𑀅 𑀧 𑀅 𑀭 𑀬 𑀆 𑀬 𑀅 𑀤 𑀇 𑀦 𑀇 𑀢 𑀅 𑀅 𑀱 𑀝 𑀅 𑀫 𑀅 𑀚 𑀇 𑀦 𑀅 𑀕 𑀏 𑀭 𑀅 𑀕 𑀉 𑀯 𑀏 𑀦 𑀉 ||𑁧|| ಅ ಷ್ ಟ್ ಅ ಮ್ ಅ ಹ್ ಆ ಪ್ ರ್ ಆ ತ್ ಇ ಹ್ ಆ ರ್ ಯ್ ಅ ವ್ ಅ ಯ್ ಭ್ ಅ ವ್ ಅ ದ್ ಇ ನ್ ದ್ ಅ ಅ ಷ್ ಟ್ ಅ ಗ್ ಉ ಣ್ ಅ ನ್ ಗ್ ಅ ಳ್ ಓ ಳ್ ಓ ಮ್ ದ್ ಅ ಮ್ ಸ್ ರ್ ಷ್ ಟ್ ಇ ಗ್ ಎ ಮ್ ಅ ನ್ ಗ್ ಅ ಳ್ ಅ ಪ್ ಅ ರ್ ಯ್ ಆ ಯ್ ಅ ದ್ ಇ ನ್ ಇ ತ್ ಅ ಅ ಷ್ ಟ್ ಅ ಮ್ ಅ ಜ್ ಇ ನ್ ಅ ಗ್ ಎ ರ್ ಅ ಗ್ ಉ ವ್ ಎ ನ್ ಉ || ೧ ||   a ṣ ṭ a m a h ā p r ā t i h ā r y a v a y bh a v a d i n d a a ṣ ṭ a g u ṇ a n g a ḷ ō ḷ ō m d a m s r ṣ ṭ i g ē m a n g a ḷ a p a r y ā y a d i n i t a a ṣ ṭ a m a j i n a g ē r a g u v ē n u ||1|| Easy Transliteration of Aṅka-Lipi into various scripts

11. Conjoining Mūla Varṇā s into words, phrases results in Pada s and Ślōkas 11

12. स्तम्भ-काव्य युक्ति से प्रकट अन्तर-साहित्य सक्रमवर्त्ती - प्राकृत अट्टविहकम्म वियला णिट्टिय कज्जा पणट्टसंसारा । दिट्ट सयलत्थ सारा सिद्धिआ सिद्धिम् मम दिसन्तु ।।1।। अक्रमवर्त्ती - संस्कृत ओकारम् बिन्दु संयुक्तं नित्यम् ध्यायन्ति योगिनः। कामदं मोक्षदम् चैव ओंकाराय नमो नमः ।। 1 ।। 12

13. Khaṇḍa / Volumes of Siribhūvalaya Entire content of Siribhūvalaya is segmented into nine divisions called Khaṇḍa and each of Khaṇḍa s is further divided into Adhyāya s . Each Adhyāya is constituted with a number of related Cakra s. These Khaṇḍa s (Volumes) have been named by Acārya Kumudendu as: 13

14. Basic Elements of Siribhūvalaya - 1 Cakra : One Cakra is an encrypted arrangement of integer numbers (in range 1 to 64) in a matrix of 27 rows and 27 columns. Transcript of the first Cakra from the first Adhyāya of Siribhūvalaya is shown in a previous slide. This Cakra will be referred as an example for explanation of cryptographic mechanisms in Siribhūvalaya . Upa -Cakra :   Upa-Cakra is a matrix of size 9x9 and is derived by partitioning of a Cakra Matrix into 9 Nine sub-matrices in an ordered manner as shown in previous slide. These partitioned sub-matrices of a Cakra are decoded in various permutations in different Adhy āyas as part of encryption scheme termed as Navamānk -Bandha . Bandha : Bandha is manner in which contents from a Cakra is revealed. Bandha basically describes the method to traverse the Cakra (27x27 matrix) and substitute respective numbers into Mūla Varṇas to uncover the Ślokas or verses hidden therein the Cakra . Acārya Kumudendu has enumerated many Bandha s, which are deployed in encryption of Siribhūvalaya . Śreṇī Bandha with its two variants viz. Cakra-Bandha and Navmānk-Bandha is applied in the first Khaṇḍa i.e. ṁagala Prābhr̥ta .   14

15. Basic Elements of Siribhūvalaya - 2 Ś re ṇ ī Bandha : Ś re ṇ ī Bandha is primarily applied to decode all the Cakras to extract base Kannada verses from all the Adhyāya s of ṁagala Prābhr̥ta Khaṇḍa in Siribhūvalaya . Ś re ṇ ī Bandha has two variants termed as - ‘ Cakra-Bandha ’ and ‘ Navamānk -Bandha ’ . When Ś re ṇ ī Bandha is applied over whole Cakra i.e. on 27x27 matrix, it is called Cakra-Bandha ; and when Ś re ṇ ī Bandha is applied to sub-matrix of Cakra of 9x9 elements, it is called Navamānk -Bandha . Note: It is noteworthy that Ś re ṇ ī Bandha traversal pattern results in Magic Squares of size 27x27 (sum 9855) or 9x9 (sum 369). A Magic Square is a square matrix of Integers wherein sum of integers in any of the rows is equal to sum of integers in any of the columns or sum of integers in any of the diagonals. 15

16. Basic Elements of Siribhūvalaya - 3 Kram a-Cakra : This is the key for Transposition Cipher and is represented as square matrix of order 27. Each of the elements in this matrix contains a distinct integer number in the range 1 to 729 i.e. no two elements are of identical value. Each element of Krama-Cakra represents position of corresponding element (at same row and column) in Cakra in the transformed number vector with 729 elements. Each Adhyaya has distinct Krama-Cakra for decoding Cakra s of that Adhyāya . First Cakra of each Adhyāya contains a 3x3 matrix on the left-hand corner which is representative of the Krama-Cakra applicable to that particular Adhyāya . Following slides show Krama-Cakra for Cakra-Bandha for (27x27) matrix and Navmānk-Bandha (9x9) matrix as applicable to First Adhyaya of ṁagala Prābhr̥ta .   Kumudendu Code Table (KCT) : This is the key for Substitution Cipher. it is used for substituting Numerals in Cakra s into corresponding Phonetic Alphabet Characters ( Mūla Varṇa ) in specific script. Since KCT is script dependent there exist KCTs each of the scripts e.g. Devanāgarī , Kannada or Brāhmī etc. KCT has 64 elements . KCT is the key for Substitution cipher as deployed in ‘ Siribhūvalaya’. 16

17. Transposition Key : Krama -Cakra for Cakra-Bandha l l 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 17

18. Transposition Key: Kra ma-Cakra for Navamānk-Bandha 18

19. Cakra Bandha Example with 5x5 Matrix 1 2 3 4 5 1 4 53 28 45 4 2 1 45 47 59 54 3 7 16 1 56 55 4 28 43 8 1 52 5 10 51 1 7 7   1 2 3 4 5 1 17 24 1 8 15 2 23 5 7 14 16 3 4 6 13 20 22 4 10 12 19 21 3 5 11 18 25 2 9 Example Anka-Cakra (5x5) Example Kram-Cakra (5x5) 28 7 52 7 45 16 47 45 7 28 10 43 1 59 4 54 4 51 8 56 1 55 1 53 1 Result of Applying Bandha 19

20. Applying Substitution using Kumudendu Code Table Result after applying Substitution Cipher into result from De - Transposition from previous slide : 20

21. Step -5 Example of Multi-Lingual content from First Adhyaya 21

22. Step – 5 : Content in Prakrit & Samskrit from First Chakra Checksum 22

23. Step -5 : Example of Multi-lingual contents from first Anubandh of Shrutavatar 23

24. Step – 5 : Content in Prakrit , Geervan , Telugu, Tamil & Apabhramsh from first anubandha of Shrutavatar 24

25. Why is Acarya Kumudendu Inimitable? Master Mathematician who shone with brilliance in creating not only intricate framework of Cakras and Bandhas, but also expressed mathematical interpretations on variety topics. Eminent Scholar of religious foundations, scriptures, practices and ancient sciences of diverse domains. Highly Competent Linguist with proficiency in multiple languages prevalent in India at his time. Extremely genius poet who chose two-dimensional array of numerals for his creative expressions. Great Composer who intertwined verses in multiple languages into a solitary piece of magnificent work. Exceedingly Talented Graphics artist who could implant poetry into multitude of shapes and figures. Strong Proponent of Puşpāyu r ved a ( पुष्पायुर्वेद ) 25

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27. ತುಂಬ ಧನ್ಯವಾದಗಳು धन्यवाद Thank You 27