1. ûû §&rûm ûû Tulasee’s RaamCharitMaanas: A Mathematician’s perspective Prof. Hansraj P Joshi Department of Mathematics and Statistics York University, Toronto, Canada. www.yorku.ca/hjoshi

2. Whatever science is found in Vedic period is supposed to have originated and grown to help social educational and religious activities. This was true to certain extent in all civilizations, but more so with Hindoo’s. I have given more than one talk on this topic. Here I present more evidences to support above assertion. We base our discussion on Tulasee’s work.

3. We look into Maanas for examples and purpose of Simple counting Word numerals (i.e. Bhoot-Sankhya) Katapayaadi convention Numeral 9, Tulasee’s favorite number Counting and classification of Chhand Some Examples for Swaantah-sukhaaay

4. About his Maanas Tulsee writes >·init moir sb gun riht, ibSv ibidt gun Ek so ibc·ir suinhih sumit, ijNh ke ibml ibbek 1.9 We begin with something for r·m cirt je sunt a`·h&, rs ibse¸· j·n· itNh n·h& 7.52.1 and for all of us.

5. r·m skl n·mNh te aiñk·, hoü n·q a` óg gn biñk· 3.41.8 And on top of that this Naam is mgl >·vn amgl h·r&, üm· siht jeih jpt pur·r&1.9.2 He chooses the “Naam” bNdü n·m r·m r`uvr ko, hetu kOs·nu >·nu ihmkr ko 1.18.1 Why this name? Because Naarad asked and He promiced

6. >·le >·vn ab b·yn d&Nh·,p·vhuge fl a·pn k&Nh· 1.136.5 ­­­­ ZU#I len· ZU#I den·,ZU#I >·ojn ZU# cben·, 7.38.7 d&ó inW·dn·q >·l $olU, kheü bj·ü juZ·Ë ßolU,2.191.3 This ( aeih mh r`upit n·m ) means r·m or ist·r·m or their representative letters r, m, s. t, are ‘there’ in each of 9388 Chaupaa-ee. So far I have found 3 Exception of missing r, m, s. t

7. J··w pw ijy n hoit kui$l·IR,t·w kt l&Nh sNg k$k·IR. 2.188.4 Etn· kht z&k >·Ib b·E,kheü sguinaNh <·et suh·E, 2/191.4 J··w pw INhih d&Nh bnb·sU,k&Nh b·id ibiñ >·og ibl·sU 2.119.5 ñNy so desu swlu bn g·Ë,jh jh j·ih ñNy soI #·Ë. 2.121.6 tny jj·itih j·wbnu dyË,iptu aGy· a` ajsu n >·yË,2.173.8 lón spn yh n&k n hoIR,ki#n kuc·h sun·Iih koIR. 2.225.7 ibnu pUze”kzu khü gos·IR,sevku smy n ß&# iß#·IR.2.226.8 j·t pvnsut devNh deó·,j·nw khu bl buiñ ibseW·. 5,1.1 kh lNkes kvn te k&s·,keih ke bl `·leih bn ó&s·. 5.20.1 k·hU k& j·w sunih b@·IR, Sv·s leih jnu jU@& a·IR, 7.39.2 More exception, missing only r, m,

8. Dandee Swaamee Pragyaanaanand Saraswatee in his Maanas-Goodhaarth- chandrika and Pandit Jwaala Prasaad Mishra in his voluminous work on Maanas, both give some interesting counts. Some of these numbers are also found in Maanas Peeyoosh, published by Geeta press, Gorakhpur. In Maanas, word ‘Raam’ appers 1233 times (1+2+3+3=9), Raamu: 199, and Raamoo: 6+. It is interesting to note that names Siy, Seey, Seeya, Lakhan and Lakhanu, are not used after Ayodhya_kaand. Pem (for Prem) is used only in Ayodhya-kaand in doha numbers 207 to 325 mainly for description of Prem between Bharat and Raam. More on Eih mh r`upit n·m üd·r·.

9. One count of number of Chaupaa-ee in Maanas is 9388. Of 523 Chaupaa-ee in Sundar-kaand only 75 do not end with sound “aa or ee”

10. More than 75% Ardhaali of Chaupaa-ee of Maanas end in sound ‘aa’ or ‘ee’, why? One explanation is that Tulasee is chanting / suggesting to chant Seeta-Raam with sounds ‘ee=Seeta’ and ‘aa=Raam’. So we have explained mathematically that Eih mh r`upit n·m üd·r·,. For ‘Swaantah-sukhaay’ we make following statement, i.e I believe:

11. Simple counting: To understand appreciates Maanas, simple counting is emplyed / used be viewed carefully. Here is one of a controversial Chaupaa-ee: ढो l gv·r suÌ psu n·r&, skl t·@n· ke aiñk·r& 5-58-6

12. Question: How many are mensioned in this Chaupaa-ee? Coomonly answer is FIVE. But that is NOT correct. In Kiskindha Kaand, he writes sevk s# nOp kOpn kun·r&, kp$& im+ sUl sm... ? One may fill-in the blank and read it as sevk s# nOp kOpn kun·r&, kp$& im+ sUl sm þ·r&. and can count six (Sevak, sath, nrip, kripan, kunaaree and kapatee mitr) or less/

13. In fact Tulaseedaas-jee wrote sevk s# nOp kOpn kun·r&, kp$& im+ sUl sm c·r&. 4-7-9 where in his count of FOUR is Sevak sath, Kripaan Nrip, Kunaaree and kapatee mitr.

14. Now read again the Chaupaa-ee as

15. Additional source / reason in miss interpretation, is the improper meaning of the words “Taadan” and ‘Adhikaaree’ Both are ment for all three, but relate different for each one of them. For ‘Dhol’ Taadan means to hit it. For ‘Gavaar sudr’ Taadan is to guide him, where as for ‘Pasu-naaree’ it means teach her (what is proper for the family). No, Tulasee did not say ‘hit’ a woman. The Word; Adheekaar’ is synonyms to ‘permission’ to use or have ‘right’. That means use Taadan only when necessary, not for every one and not all the time. And: Gavaar-sudr and Pasu-naaree have right (Adhikaar) to ask for /seek advice and guidance.

16. Katapayaadi Convension: Mathematical view of Pabramh Paramaatma Raam: In folliwn Doha, is brest feeding Raam, but Tulasee writes “Brahm” instead of Raam We explain this ‘mathematically’

17. In our scriptures Katapayaadi convention hs been used to express numbers. Following table explains this

18. “Kausalyaa ke God” is Raam or “So aj=vyaapak Brahm” Let us explaine the mistry with Katapayaadi convenstion table (relevant part). 1234567890 kóg`H·czjZÐ $#@ßïtqdñn pfb>·m yrlvsxWh

19. This table indicates that in our Vedic scriptures letters were used to represents numbers. Is this not an “origin” of algebra? There are five known variation of this convention. We consider that which is by “sound” and not strictly conjoined letters. It is obvious on the basis of the table that Katapayaadi number for three words : r·m, kO¸ï, bÈ each one is number 52. Thus Tulasee has mathematical base to state “ r·m pr bÈ prm·tm· hw “ because r·m = kO¸ï = bÈ = 52

20. I find several occurrences of use of pUïR·½uu 9 as number of chaupaa-ee in a Doha in places where Tulasee has described Raam as Avataar of Parbrahm Parmaatma. Tulasee’s favorite numeral 9 In “Prastaavana Khand, Maanas Goodhaarth Chandrika” Dandee Swaamee Pragyaanaanand Saraswatee (pages 117 – 121) gives an interesting list of use of pUïR·½uu 9 as number of Doha in various episodes, like Raam / Seeta janm teethe, Raam / Shiv vivaah etc. Here is one more; my favourite.

21. Some Examples: Naarad xamaa yaachana – 7.51

22. Garud – Bhusundee Samwaad-7.64

23. Kaike-ee varadaan prakaran2.29 This example is better for my contasion

24. Hanumaan – Raavan Samvaad-5.21. Hanumaanjee explains to Raavan purpose of Raam ‘avataar’

25. Few more examples: Sankaadi Stutee-7.35

26. Hanumaan – Raam Milan

27. Promise to Dev, that He will come down to earth (take Avataar)

28. Baal-charit HARI bhubidhi keenha

29. Well in Sundar-kaand we have Kathaa of two Avataar; Shiv avatar ShreeHanumaan-jee and Bhagawaan ShreeRaam. As such there are more Doha with 9 Chaupaa-ee. Besides these, there are more instances of 9 chaupaa-ee in Sundar-kaand, and elsewhere descriptive of Avataar and otherwise aslo.

30. Word_Numerals i.e. Bhoot-Sankhya So far only a fewer examples are found but they are relevant to this presentation. On page 120 in the book: The Paleography of India, Pandit Gaurishankar Ojha gave a short list for word numerals. A more comprehensive list is in the book “The concept of Shoony” by A R Bag and S R Sarma

31. A page from Pof. Oza

32. Note that word for numeral 40 is NARAK

33. One interesting example of use of Bhoot-sankhya in Maanas is in the Chaupaa-ee: Rromr·ij a¢·ds >··r·, aiSq swl sirt· ns j·r· (6.14.7)

34. Bhaar is used for number 12,30,1660 (MP, Lanka-Kaand 14.7), just like Raam for number 3 and Narak for 40. Thus 18 Bhaara =18times 12301660 Wishw-roop has these many Romaavali above His bellybutton. This Chaupaa-ee “Rom-raaji Astaadas Bhaara, … “ is on description of Vishwaroop (Manodari to Raavan), where Raam is “Pad paataal sees Aj-dhaama, … “ therefore 12,30,1660 count of romaaavali is no exageration.

35. We have two queries on Hanumaan Chaaleesa First why did Tulaseedaas-jee composed this prayer in 40 Chaupaa-ee and not 38 or 48? And second, according to Tulasee, how many times one should recite Hanumaan Chaaleesa. Earlier we have seen list of Bhoot-sankhya in the book “The Paleography of India, Pandit Gaurishankar Ojha”. Word for numeral 40 is ‘ nrk ‘.

36. For quick fame and easy acceptance, poets over the past five centuries named their prayers as xyz Chaaleesa; like Sai-chaaleesa, Shiv chaaleesa and many more. Pushp-dant composed Mahimn-stotr in 34 verses. Later on some enthusiastic Shiv-bhakt added some slok and we have currently popular version of 42 verses (= 40 +2 Doha in the beginning of Hanumaan Chaaleesa). I think Tulaseedaas-jee opted for 40 Chaupaa-ee in composing Hanuman-jee prayer, to guide us on a path that does not lead us to the hell (Narak) or teach us the ‘right’ behavior hence the word “Chaaleesa” in the title itself.

37. An answer to the question “ How many times one should recite Hanumaan Chaaleesa?” jo st b·r p·# kr koIR, zU$ih biNd mh· suó hoI R What does this Chaupaa-ee mean? üm· khü mw anu>·v apn·, st hir >·jn jgt sb spn· 3.38.6 brW c·ir ds b·su bn muin [bt beWu ah·ru [g·m b·su nih üict suin guhih >·yü duóuu >··ru 2.88 Note here : Chaari Das = 10+4=14 st pNc c·wp·IR mnohr j·in jo nr ür ñrw d·run aib¥· pNc jint ibk·r [s&r`ubr hrw Here “Sat Panch” = 7 + 5 =12 Chaupaa-ee in Baal- Kaand doha 199 (Kaam koti chhabi ….) jog lgn [[gh b·r itiq skl >·E anukl cr a® acr hWRjut r·m jnm suómUl 1.190 Here the “Baar” is used for day of the week (Tuesday; Raam was born).

38. Above we have examples in Tulasee’s work using words Sat and Baar. Tulasee first composed Hanumaan Chaaleesa then Ayodhyaa-kaand then other Sopaan of Maanas.

39. At end of Maanas in a Chhand he wrote

40. When we agree with these usage, of the words st meaning SEVEN and b·r, meanind a day of the week, we must conclude that the statement jo st b·r p·# kr koIR “Jo Sat-baar” means those who recite Hanumaan Chaaleesa seven days of the week (i.e. every day) and we are not told to recite 100 times as is commonly interpreted.

41. Just keep looking for Mathematical concepts and Scientific ideas hidden/preserved in our scriptures and religious practices with faith, and you shall experience divine pleasure as long as you live. Jay Siya Raam A gift from Canada to all retiring Acedemitians of Bhaarat: