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ûû §&rûm ûû. Fascinating conventions in Vedic scriptures: Concept of Variables (Talk at MNIT, Jaipur Dec. 15-16, 2007) Prof. Hansraj P Joshi Department of Mathematics and Statistics York University, Toronto, Canada. Introduction:-.

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slide1

ûû §&rûm ûû

Fascinating conventions in Vedic scriptures: Concept of Variables

(Talk at MNIT, Jaipur Dec. 15-16, 2007)

Prof. Hansraj P Joshi

Department of Mathematics and Statistics

York University, Toronto, Canada.

introduction
Introduction:-
  • In Vedic period, knowledge was passed on orally, and has survived as ’Shruti’.
  • Our Rishi had to think of various ways of memorizing and teaching their pupils
  • I think one of the most innovative idea they came up with was to weave (imbed) Scientific concepts in daily prayers and daily ritualistic (religious) activities.
slide3
Result is that various concepts that have survived are to be found in the religion we practice.
  • A well known example is the Slok
pu r md pu rimdm pu t pu rmudcyte pu rsy pu rm d y pu rmev vixwyte

Ø pUïR md¶ pUïRimdm pUï·t pUïRmudCyte pUïRSy pUïRm·d·y pUïRmev·vixWyte

Purn madah, Purnam-idam Purnaat Purn-mudachchyate,

Purnsy Purn MaadaayPurn-meva-vashishyate.

in which the concept of zero and the concept of infinity both are recited in our daily prayer
in which the concept of Zero and the concept of Infinity, both are recited in our daily prayer.
  • We have lost most of what did not become part of our daily religious practice. I think we have lost a lot more than we know.
  • In this discussions we shall see some examples and interpretations of what we have in our existing scriptures and can feel proud of our heritage.
  • I do not wish to go into murky field of whether we were the first or some other civilization had an idea before us.
slide6
Personally I am convinced that that our Vedic culture is more than 8000 years old and therefore my ancestors were the first scientists on this planet, but I am not qualified to prove it.

I believe Paanini did not ‘create’ Sanskrit grammar, but he analyzed then known Shrutis (scriptures) and wrote the ‘rules’ as he understood them. Sanskrit literature existed many thousand years before Paanini’s time. (700 BC).

I enjoy discovering what is hidden in our scriptures just for ‘Swaantah Sukhaay’

background
Background:
  • Much has been written trying to prove to the world that Geometry and Astronomy (and hence I say some Mathematics) originated in Vedic period.
  • I am happy that some honest intellectuals are convinced but there are many more skeptics.
  • History credits Thales as creator of geometry and his student Pythagoras (ca. 580-500 B.C.) as ‘organizer’ of geometry. Pythagoras did live in India for some time, went back to Greece, and then formally wrote ‘proofs’. Thales was in Egypt for some time and traveled extensively; possibly to India as well.
  • Democritus (ca. 460-370 B.C), a founder of Atomic theory of matter and follower of Pythagoras also came to India. Therefore, I believe Greeks were aware of and learned geometry from religious practices in India
slide8
The modern idea of Rank ( or hierarchy or well orderedness) was and still is part of our religious practice.
  • For example the statements (a) Gurudevobhav, Maatrudevobhavah, Pitrudevobhav and Atithee Devobhav. (b) Prithavi, Jal, Tej, Vaayu and Aakaash. This specific order conveys proper scientific and logically connected sequential meaning
  • Reading history of Mathematics we understand that Greek philosopher Thales (ca. 625-547 B.C), had idea of whole numbers, the smallest being numeral 2. They had no concept of one or zero or fractions.
slide9

Whereas in Yajurvedeey Ashtaadhyaa-ee Rudree, chapter 8, we find not only concept of integers, but in Slok 24 we have Odd Integers 1 through 33

slide13
So in Yajurved, we have the rudiments of concepts of addition, subtraction, multiplication and square (cube) roots.
  • .
slide14
In Ṛgaved itself (X. 62.7) which refers to the writing of number eight as “Sahasraani MeDadaato Ashtakaranyoh”, sh[Üûin me ddûto a¸$krNyo¶ Rishi is asking his pupil to ‘sort’ cows on whose ear there is a mark for numeral 8. So we had our symbols and numerals that time
conventions
Conventions

The conventions of using the letters of the alphabet and or word, to denote numbers can be traced back to Paanini (700 BC)

More than one such systems were employed over a long period of time.

Most of these system were never meant for use by common people or for purpose of making calculations; there knowledge was strictly confined to the learned and their use to the expression of ideas and numbers in verses, which helped oral transmission of knowledge and scriptures.

Historian have not found prevalence of any one system from Paanini’s time till the time of Aaryabhat I (499 AD).

slide16
Convention of letters representing numbers became more usable. Katapayaadi system is a variation of one found in Aaryabhattiy

There seems to be some disagreement about the origin of this system.

  • According to Datta and Singh, in History of Hindu Mathematics (1938), “The origin of this system can be traced back to the fifth century A D, … system was known to Aaryabhat I (499)”.
slide17

Pandit Gaurishankar Ojha in his book The Paleography of India (1918) says, a reason for adopting such convention was that using word numeral was not convenient in Astrology.

In this system, consonants of Sanskrit alphabet have been used in the place of the numbers 1 through 9 and zero to express numbers as listed in the Appendix A as described in the Sadratnamaala:

n vc c xuny in snrvy k py dy im e tup nt hl sn y n c icntyo hlsvr
nÑ·vcªc xuNy·in sNrVy· k$py·dy¶im§e tUp·Nt hl sN<y· n c icNTyo hlSvr¶
  • In practice the convention is as follows:
  • The vowels n (Na) and Ñ (Iny) denote zero;
  • Letters in succession beginning with k, $, p, y (i.e. Ka, Ta, Pa Ya ) each denote the digits 1 onwards,
  • In a conjoint consonant, only the last one denotes a number.
  • Consonant not joined to a vowel should be discarded.
  • Vowels themselves each stand for zero.
slide20
Further, the consonants with vowels are used in place of the numerical figures just as in the place value notation i.e. a right to left arrangement is employed in the formation of chronograms.
  • The letter denoting the unit figure is written first, then follows the letter denoting the tens figure and so on. In traditional Sanskrit we would follow the opposite, namely a’k·n·’ v·mto git¶ (Ankaanaam Vaamato Gatihi)
  • The following examples further explain the convention:
now we come to the purpose of the talk and my journey
Now we come to the purpose of the talk and my journey.
  • We have been taught to believe and some of us really do live by it, that Bhagavaan Raam and Krishn both are incarnation of Parabhrahm paramaatma and are the same.
  • All Puraan teach us that and ask us to believe in.
slide23
In the History of Hindu Mathematics by Dutta and Singh, on page 71 of volume 1, they state “The following examples taken from inscriptions, grant plates and manuscripts will illustrate the system (i.e. Katapayaadi scheme)” There the first example quoted is the word: rû`vûy (2441)=2441.
  • The date was either 21st or 22nd Dec. 2003 and place was the BHU guest house.
  • Raam-jee kee prerna se prashn utha: Which Katapayaadi number is rûm
  • ?
slide26
Just for Swaantah Sukhaay, I would quote one example from Maanas, Doha number 198 in Baal-Kaand reads:
  • Byaapak Brahm Niranjan, Nirgun Bigat Binod,

So Aj Prem Bhagati Bas, Kausalya Ke God.

  • Then come the 12 Cahaupaa-ee describing Baalak Raam-swaroop. The twelfth being :
  • Roop Sakahi Nahin Kahi Sruti Sesha,

So Jaana-i Sapanehu Jehin Dekha

  • Here word Shruti is for Ved. Thus Raam of Raamaayan is the Brahm of Ved.
several questions come to mind
Several questions come to mind.
  • Muni Vashishth-jee gave the name Raam. He believed that Raam was Brahm (avataar). Was Vashishth-jee aware of Katapayaadi like convention?
  • Name Krishn was given by Aachaary Garg Muni, in Dwaapar Yug, and he was also aware that Krishn was Parabrahm Parmatma. Was he too aware of any such convention?
slide28
Did the person or persons who adopted these conventions, deliberately did so to hide the truth [B·È= rûm = kò¸ï from common people?
  • Certainly this is not one of those ‘lucky’ coincidences of our Hindu heritage, as Prof. Subhash Kak says “The Indian texts are either full of the most astonishingly lucky guesses or we do not understand their knowledge framework”
slide29
Katapayaadi number for the word x’kr in the name x’krûcûyR is 215. We know that x’krûcûyR jay’it is on fifth day of the first half of the second month. He was born in the Veekram Samvat 730 (Vaisaakh, ShuklaPax, Panchamee). I believe he was named according to the horoscope. Is there any connection in deciding rûix, in general and this convention?
conclusion
Conclusion:
  • I would like to say that origin of Algebra is in Katapayaadi convention. Certainly here we have used letters of an alphabet as variables in a restricted sense and that is where Algebra began.
a gift from canada to all retiring mathematician of bhaarat
A gift from Canada to all retiring Mathematician of Bhaarat
  • Just keep looking for numbers and concepts hidden in our religious practices and scriptures with faith, and you shall experience divine pleasure as long as you live.

Jay Seeya Raam

another convention
Another Convention:
  • A system (see appendix B) of notation in which sixteen vowels a – a¶, are assigned numbers 1 to 16 and consonants k – D are assigned numbers 1 to 36, the conjoint letter + being 35 (and some variations of this), is found in certain manuscripts from Southern India.
slide34
A similar convention was used by Aaryabha I. There are some interesting and informative revelations when we use this convention:
  • The word (Brahm) [BûÁis made up of four letters, b, r, h, m, (Ba, Ra, Ha, Ma).
  • They are respectively 23rd , 27th , 33rd 25th letters of the Sanskrit alphabet system.

The sum is 23+27+33+25=108, and hence to attain the a[=r-BûÁ (Axar-Brahm) perform Mantr Jaap with 108 beads maala.

  • The words SeetaaRaam (s&tûrûm) and RaadhaaKrishn (rûñûkò¸ï) when interpreted as made up of letters, s, IR, t, aû, r, aû, m and r, aû, ñ, aû, k, Å, W, ï add up to a very fascinating and revealing number.
following the convention of appendix b
Following the convention of Appendix B
  • (s IR t aû) + (r aû m) =
  • (32 + 4 + 16 + 2) + (27 + 2 + 25)

= 54 + 54=108

  • (r aû ñ aû) + (k Å W ï)=
  • (27 + 2 +19 +2) + (1 + 11 + 39 + 15)

= 50 + 58=108

some thoughts chintan on this number
Some thoughts (Chintan) on this number:
  • Hundred and eight beads of a Maala are indicative of both, Aadishakti and Brahm..
  • Raam and Krishn are not Poorn-Brahm unless accompanied by their Aadyaashakti.
  • Seeta and Raam both add up to 54, therefore, now we have mathematical base in believing that Seeta-jee is His Ardhangini.
  • Raadha is only 50 where as Krishn is 58, why so? One explanation is that Raadha-jee is not His Ardhaangini, they never married, but He is not Poorn-Brahm unless accompanied by Raadha, one would not like to see Him alone. (Raadha ke bina Krishn adhura hai)
a gift from canada to all retiring mathematician of bhaarat37
A gift from Canada to all retiring Mathematician of Bhaarat:
  • Just keep looking for numbers and concepts hidden in our religious practices and scriptures with faith, and you shall experience divine pleasure as long as you live.
  • Jay Seeya Raam