Hindu Reflections: March 2018

KNOWLEDGE & MYSTICISM OF NUMBERS IN HINDU SCRIPTURES

(Consolidated by N.R. Srinivasan from the E-mails sent to HR Forum)

MARCH, 2018

OUR SAGES USED LARGE NUMBERS

It may be surprising to know that Indian sages used large numbers up to power of 10 raised to the power of 62 and that too millions of years ago. Sage Valmiki, Author of Ramayana , Aadi Kaavya, was the first to use it. Following verse from Ramayana said to be written in Tretâyuga, presents a number system of 10 raised to the power of 62:

satam satasahsrânam, kotim âhurmanisinah satam kotisahasrânam sankurityabhidhiyate ||

Above verse can be precisely translated as satam satasahsram = One Koti i.e. Hundred hundred thousand = 100, 00,000 = 1 crore = 107 (1 followed by 7 zeros satam Kotisahsram = One Sanku i.e. Hundred thousand crore = 100, 000, 0000,000 = sanku = 1 followed by 12 zeros.

1 Koti = 1followed by 7 zeros = 1 crore
1 sanku = 1 followed by 12 zeros = 1 lakh crore
1 Mahasanku = 1 followed by 17 zeros
1 Vrndam = 1 followed by 22 zeros
1 Mahavrndam = 1 followed by 27 zeros
1 Padmam = 1 followed by 32 zeros
1 Mahapadmam = 1 followed by 37 zeros
1 Kharvam = 1 followed by 42 zeros

1 Mahakharvam = 1 followed by 47 zeros
1 Samudram = 1 followed 52 zeros
1 Ougham = 1 followed by 57 zeros
1 Mahaugham = 1 followed by 62 zeros

This number is actually the count of the monkey soldiers who built the historic Ram Sethu (Also known as Adam Bridge). While inhabitants of other continents were using stones and fingers to count, Vedic sages counted in trillions & trillions to measure the cosmic concepts of this universe with present day knowledge of mathematics.

Number system in Vedas

Many Vedic texts point to the decimal number system. Yajurveda describes the number system with place value up to 18 places, the highest called as parardha used in Sankalpasa (religious resolution).

For Example, after preparing bricks for a Vedic ritual, Sage Medhâtithi prays to the Lord of fire, Agni thus:

Imâ me Agna istakâ dhenava
Santvekâ ãa desa ãa satam ãa
Sahasram  ćāyutam ãa niyutam ãa
Prayutam  ćārbudam ãa nyarbudam ãa
Samudrasãa madhyam  ćāntasãa
Parârdhasãaita me agna ishtakâ
Dhenavasantvamutrâmushmimlloke .

Oh Agni! Let these bricks be milk giving cows to me
Please give me one and ten and hundred and thousand
Ten thousand and lakh and ten lakh and
One crore and ten crore and hundred crore,
A thousand crore and one lakh crore in this world and other worlds too.

This can be deduced to:

eka - 1 - one
dasa - 10 - ten
satam - 100 - hundred

sahasram - 1000 - thousand
ayutam - 10000 - ten thousand
niyutam - 100000 - one lakh

prayutam -1000000 - ten lakh - million
arbudam -10000000 - one crore- ten million
nyarbudam -100000000 - ten crore hundred million
samudram -1000000000 - hundred - billion
madhyam -1000000000 - thousand crore- ten billion
antam -100000000000 - ten thousand crore- hundred billion
parardham -1000000000000- one lakh crore -- trillion

Please note that the Vedic altar itself is a geometric construction.

Even the concept of Fibonacci number can be found in Vedic verse translated as The sun flower smiles at you with 34, 55 florets. (34, 55 are the numbers in the sequence of Fibonacci number.)

The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144 and so forth.

Indian scholars expressed all large numbers using the decimal number system. The highest power of 10 named today is 1030 (Deca). But ancient Indian mathematicians had exact names for powers up to 1053.

Mathematical interpretation of Infinity as well as zero can be illustrated by the following popular Veda mantra. Concept of infinity was used repeatedly in Vedic era, latest being Vishnu Sahasranama where Vishnu is praised as Soonyah and Anantah, meaning “zero” and “infinity” or “having no end”. Some of the other words used in Vedic texts are purnam, asamkhyata and aditi. For Ex:Word Asamkhyata is used in Yajurveda and Brihadaranyaka Upanishad to represent the number of mysteries of Indra as Ananta. Following verse from Yajurveda describes the mathematical concept of infinity and 0. However, this verse (Shloka) is more metaphysical than mathematical that I have explained frequently:

Pûrnamadah pûrnamidam pûrnât pûrnamudacyate pûrnâsya pûrnam-aadaya pûrnamevâvasishyate

From infinity is born infinity; when infinity is taken out of infinity, left over is only infinity.

From zero is born zero; when zero is taken out of zero, what is left over is also zero.

Atharvaveda has lot of references to numbers as shown below. The figures within brackets indicate number raised to the power of 10.

Kshobhya (18), Nivahata or vivaha (19), Utsanga (21), Bahula (23), Nagabaalaha,(25), Tilamba (27), Nahtua(28), Titlambha( 31), Karahuhu (33), Ninahuta (35), Hetyendriya (37), Sampatalambha (39), Niravadym (41), Akkohbini (42), Niravadya (43), Sarabalam (45), Vishamagnagati (47), Sarvagna (49), Vibhutagaama (51) Tallakshana (53), Adbuda (56), Nierabbua (63), Ahaha (70), Abada (77), Atata(84), Saganghika (91), Uppala (98), Kumuda( 105), Pundarika (112), Paduma( 119), Kathana (126), Mahakathana (133), Asamkhyeya (140) and Dhvajgranishamani (421)

Many Veda mantras and even some slokas by our ancient sages convey their spiritual messages in number-capsules well protected as well as propagated generation after generation! The successful accomplishment of the decoding of the coded language of Veda will certainly open up the vast fields of knowledge for the benefit of the Public particularly its message secretly preserved in digital codes and mathematics. Different knowledge systems found in the Vedic texts are to be co-related with similar modern systems of knowledge in a useful way. Here we deal with numbers and mathematics. Lot of Vedic research work is going on in India, USA, UK and Germany by governmental and private institutions and I do hope special attention will be given to de-codify the mystery contained in divine numbers concealed in slokas and mantras. Here I have tried to consolidate all that I have conveyed in the past through my E-mails to HR Forum Participants and discourse posted on Hindu Reflections.

Men of older generation used to say that all knowledge is there in the Vedas. Anyone who hears such words will have the first reaction that it is an exaggeration. We should remember here that any sloka in the ancient Hindu manuscripts has more than one meaning.

George Gherveghese Joseph, University of Manchester, United Kingdom says:
“The earliest material evidence of Indian mathematics is found among the ruins of the Harappa civilization, dated at the start of the third millennium B.C. An elaborate system of weights and measures related to binary and decimal series' has been brought to light. A notable feature of the Harappa culture was its use of kiln-fired bricks.

The Sulbasutras and the Sathapatha Brahmana contain valuable information about the geometry of ancient India, including instructions for constructing sacrificial altars (vedi) and locating sacred fires (agni). The altars used during Agnicayana, a 12-day ceremony, are especially interesting in terms of geometry. The procedures described for their construction involve methods for approximating the values for the square roots of 2 and 5.

[The most basic fire altar covers an area by the square of seven lengths of the sacrifice. Four equal parts of the area define the body, one each the two wings and the tail. In many forms of the ritual, however, “the bird altar” is much more elaborate. “Sa vai saptapurusho bhavati| saptapurusho hyayam purusho yanchatvaara aatmaa trayah paksahapucchaani…”—He is composed of seven Purushas(=Agni)is composed of sevcen Purushas, viz. the body is four, the wings and the tail are three… (Satapata Brahmana M-6)]

One of the most celebrated altar was shaped like a bird poised for flight. Its shape and construction were minutely prescribed, while its height could be varied for special occasions. Mathematical problems of its construction involved finding a square equal in area to two or more given squares, and converting other geometrical shapes into a square of equal area, or vice versa. Solutions were achieved through the principle of dissection and reassembly and ingenious algorithms, including the so-
called Pythagorean Theorem”.

It is not surprising that India could have invented the zodiac and circle of 360 degrees. After all, the decimal system and the use of zero came from India. In this regard, as early as the Yajur Veda, we find names for numbers starting with one, ten, one hundred and one thousand ending with one followed by twelve zeros (Shukla Yajur Veda XVII.2).

The Rig Veda has a cryptic verse quoted below that suggests its cosmic numerology. According to it the Cosmic Bull has four horns, three feet, two heads and seven hands (Rig Veda IV.58.3). This sounds like a symbolic way of presenting the great Kalpa number of 4,320,000,000 years.

“Chatvaari Sringo trayo asya paadaa dveseersha sapta hastaaso asya |Triddhaa baddho vrishbho roraveeti maho devo martyaa aavivesa ||

The syllable Om conceived as the Bull possesses five horns, three feet and two heads and seven hands (of oval shape). This Bull connected in a threefold manner, eloquently declares the Supreme. The Self-luminous Deity has entered the mortals everywhere. There are different explanations of this mantra about which I have talked about before. But one that is relevant in the context is the first line simply symbolically represents Brahman as a Kalpa Purusha. We all know Brahman is often referred as Time or Kaala and Samvatsara (Samvatasrova apaam pushpam; Kaalaaya namah). Without explaining its deeper meanings, if we simply write the numbers continuously mentioned in the mantra, it represents 4320000000 Human Years that is Kalpa. 4 comes from four horns, 3 comes from three feet, 2 comes from two heads and 7 zeros that follow comes from seven hands in oval (0) shape! This Brahman appears again and again for each Kalpa with his band of controllers to revive and rule the universe which is indicated by the roar of the bull.

In Hanuman Chalisa it is said:

"Yug sahasra yojan par Bhanu! Leelyo taahi madhur phal janu!!

1 Yug = 12000 divine years
1 Sahasra = 1000
1 Yojan = 8 Miles

Yug x Sahasra x Yojan = par Bhanu

12000 x 1000 x 8 miles = (Towards Sun) 96,000,000 miles

1 mile = 1.6kms

96,000,000 miles x 1.6kms = 1,536,000,000 km/96,000,000 miles to Sun

NASA says that, this is the exact distance between Earth and Sun (Bhanu). That proves Hanuman did jump to Planet Sun, thinking it as a sweet fruit (Madhur phal). It is really interesting how accurate and meaningful our ancient scriptures are. Unfortunately, it is hardly recognized or interpreted accurately or realized by any country in today’s world.

How one Yuga cycle=12000 Divine Years?

The duration of the universe was fixed by the Supreme as 12000 years each of which was 360 human years so that the whole period is 4320000 human years. This duration was divided into four ages which are 4000, 3000, 2000 and 1000 respectively for Krita, Treta, Dvapara and Kali. After each yuga there is a period of darkness. This was 800, 600, 400 and 200 respectively. All together 10000+2000 makes 12000 divine Years;

1 kalpa=4320000x1000=4320000000. Brahman is compared to a mystic bull with 4horns, 3 feet 2 heads band 7 tongues that 4 3 2 and 7 zeros represented in 4-3-2-0000000 as explained above]

The Value of Pi up to 32 Decimals from the Vedas

A Sloka in the 10th book of Rig Veda appears to be written for praising Lord Indra. The technical translation of that Sloka gives the value of Pi up to 28 digits accurately. It is not until the invention of the computers that the western mathematicians could get this value up to 16 digits accurately. Here is a test for those who think that a computer can do any calculation. Use the fastest computer available to you and write a program to calculate the value of Pi up to 28 digits accurately. You will know how difficult it is.

Vedic Numerical Code in the Vedas

In Sanskrit, the following Vedic Numerical code was used in many slokas:

कादि नव --Kaadi nava
टादि नव—Taadi nava
पादि पञ्चक--Paadi panchaka
यद्यश्टक--Yadyasatka
क्ष शुन्यम्—Ksha soobyam

Meaning:

Kaadi Nava Starting from ka, the sequence of 9 letters represent 1, 2,..9
Similarly Taadi Nava, starting from ta
Paadi panchaka (1-5), starting from pa
Yadyashtaka (1-8) starting from ya
and ksha represents 0

In detail it is as follows:

ka (क) – 1, kha (ख) – 2, ga (ग) – 3, gha (घ) – 4,gna (ङ) – 5, cha (च) – 6, cha (छ) – 7, ja (ज) – 8, jha (झ) – 9

ta (ट) – 1, tha (ठ) – 2, da (ड) – 3, dha (ढ) – 4,~na (ण) – 5, Ta (त) – 6, Tha (थ) – 7, Da (द) – 8, Dha (ध) – 9

pa (प) – 1, pha (फ) – 2, ba (ब) – 3, bha (भ) – 4, ma (म) – 5

ya (य) – 1, ra (र) – 2, la (ल) – 3, va (व) – 4, Sa (श) – 5, sha (ष) – 6, sa (स) – 7, ha (ह) – 8

kshah (क्ष) – 0.

Value of Pi hidden in a sloka

Based on the above guidelines there are many slokas in mathematics. For example here is a sloka that contains the Pi value:

गोपीभाग्य मधुव्रातः श्रुंगशोदधि संधिगः |खलजीवितखाताव गलहाला रसंधरः ||

gopeebhaagya maDhuvraathaH shruMgashodhaDhi saMDhigaH
khala-jeevitha-khaathaava galahaalaa rasaMDharaH

ga-3, pa-1, bha-4, ya -1, ma-5, Dhu-9, ra-2, tha-6, shru-5, ga-3, sho-5, dha-8, Dhi -9, sa-7, Dha- 9, ga-3, kha-2, la-3, jee-8, vi-4, tha-6, kha-2, tha-6, va-4, ga-3, la-3, ha-8, la-3, ra-2, sa-7, Dha-9, ra-2

3.1415926535897932384626433832792… (The value of Pi up to 32 decimals)

The above sloka has actually 3 meanings: 1. In glorification of Lord Shiva 2. In glorification of Lord Krishna, and 3. The value of Pi up to 32 decimals.

There were many inventions in the field of science and technology in ancient India, we just have to sift through the sands of time to find them.

--Source: vedic-dharma.blogspot.in

The Cosmic Power of Srichakra and the Great Pyramid

Srichakra is always adored for its remarkable powers, in bringing prosperity and breaking misfortune; its very possession is deemed sufficient. Perks application of Cosmic Sakti overflowing the Pyramidal enclosure reveals even a small Pyramid, kept in a room purifies air-pollution, kills disease-causing germs and keeps the inmates sound and healthy both in body and mind. Existence of Pyramidal connection with Srichkra in manifesting Cosmic Power has been long recognized by spiritual thinkers. Indian researcher R. N. Narasimhan has found such a relationship in their geometric design thus making an advancement from the maze of data of enmeshed triangles to identify three basic triangles from which the Srichakra diagram can be drawn. Srichkra is mainly composed of a set of five (Sakti) triangles, altitude falling upon a single vertical line, bases neatly coming up horizontally parallel and enmeshed with another set of four (Siva) triangles, similarly arranged about the same vertical axis of symmetry, serving as the diameter of the circle enclosing all the nine triangles. The three tringles of Pyramid identical with three triangles of Srichakra are as follows:

THE GREAT PYRAMID SRI CHAKRA

1.

SHOULD WE FOLLOW HINDU INDIAN PATTERN
1. Vertical Cross-Sectional Triangle The fourth & biggest Siva triangle

2. Facial Triangle The fifth of the Sakti Triangle

3. Basal Triangle The second of the Sakti Triangle

Such a coincidence between 3-dimensional Pyramid and 2-dimensional Srichakra is more than a chance coincidence and needs a serious attention for better understanding of Srichakra from what we gather by personal experience from the Great Pyramid.

A
mong many scientific riddles that confronts the modern thinking with, in offering an objective approach in accessing Aakaasaa directly (reaching heaven) the Great Pyramid of Cheops of fourth dynasty of Pharaohs of Egypt, raised some 4000 years ago, functions as a ‘generator’ of Cosmic Power in some inexplicable manner. Fortunately for us, a 18-foot Pyramid stands in the sprawling campus of Perks International Foundation at Coimbatore exhibiting bio-friendly properties of health and healing disease to enable any further study as to the power of Akasa under the cover of pyramidal shape. For a detailed Mathematical approach on Srichkra, The Pyramid and Pi please refer to the studies of R. S. Narasimhan in Srividyaa-Kosa by Prof. S.K. Ramachandra Rao of Kalpatharu Research Academy, Bangalore.

Odd Numbers Prayed up on in Rudra-Chamakam

The following verse of Rudra Namkam-Chamakami is from Yajurveda. It encompasses mathematical concepts of number theory and progression combined.

Ekaa cha may tisracha may pancha cha may sapta cha may nava cha may ekaadasa cha may trayodasa cha may panchadasa cha may saptadasacha may navadasa cha may ekavi(ga)msatischa may trayovi(ga)msatischa may panchavi(ga)msatischa may saptavi(ga)msatischa may navavi(ga)msatischa may ekatri(ga)msacha may trayastri(ga)msascha may chatasrascha may ashtau cha may dvaadasa cha may shodasa cha may vi(ga)msatischa may chaturvi(ga)msatischa may ashtaavi(ga)msatischa may dvaatri(ga)mscha may shat-tri(ga)mscha may chatvaari(ga)mscha may chatus-chatvaari(ga)mscha may ashtaa-chatvaari(ga)mscha may vaajascha prasavascaa-pijascha kratuscha suvascha moordhaa cha vysniyascha-antyaayanascha-antyascha bhouvanascha bhuvanascha-adhipatischa ||11||

[May I be granted the odd numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, and 33 as well as even numbers 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, and 48 to ensure food and its continuity and the urge to enjoy the origin of all creation—the Sun, the heaven, the head of all, the infinite, the all- pervading like the sky, time and the like present at the end of total consummation exists at the end of it on the earth as universal form, the Antaryamin, the immortal, the inner ruler of everything, the Omnipresent and Omnipotent.]

We can mathematically create a table of orderliness arbitrarily linking 33 with 17 as follows:

Odd Number arrangement corresponding Square root

0+0=0	0
1+ 0=1	1
3+ 1= 4	2
5+ 4= 9	3
7+ 9= 16	4
9+ 16=25	5
11+ 25=36	6
13+ 36=49	7
15+ 49=64	8
17+ 64=81	9
19+81=100	10
21+100=0121	11
23+121=144	12
25+144=169	13
27+169=196	14
29+196=225	15
31+225=256	16
33+256=0289	17

We may add 0 before all these numbers without changing value. It then signifies the pervading Brahman without actual involvement and as silent observer.

If we add to first number in any column the second number in the previous column we get a sum total in 3^rd column whose square root is in the 4^th column. This series could be taken to 33 and 17 for our limited purpose.

The first row of all zero represents Brahman. Applying our knowledge of elementary arithmetic we could possibly find an explanation as to why 0 is Brahman. Poornam represents Nirguna (un-manifested) Brahman which is also represented as zero. Please recall the famous Vedic mantra: “Poornamadah poornamidam poornaat poornamad-uchyate poornasya poornamaadaaya poornameva avashishyate—(Br. Up. 5.1). 0 in mathematics is indispensable and controls the world of mathematics and computers. Nirguna Brahman is indispensable and is inner controller of all beings. This mantra goes well with the mathematical concept of zero for e.g., If we remove 0 from 0 what remains is also 0 etc., There is the other spiritual meaning: That which lies beyond is Plenum, (full and undiminished). That which appears as this here (i.e., as the universal) is also Plenum, equally full and undiminished. Out of Plenum, Plenum arises. Plenum having been taken away out of Plenum, what remains is still the same (undiminished) Plenum.

We stopped the above table at 33 to represent 33 Vedic deities that have relationship with t 17 representing Jeevatama, a body-life-mind complex of seventeen entities (five Praanas (vital forces) + five organs of action +five sense organs + mind + Intellect).

Ekascha may	01+000=001	square root is 01
Triascha may	03+001=004	square root is 02
Pancha cha may	05+004=009	square root is 03
Sapta cha may	07+009=016	square root is 04
Nava cha may	09+016=025	square root is 05
Ekadasa cha may	11+025=036	square root is 06
Trayodasa cha may	13+036=049	square root is 07
Panchadasa cha may	15+049=064	square root is 08
Saptadasa cha may	17+064=081	square root is 09
Nava dasa cha may	19+081=100	square root is 10
Ekavi(g)amsatischa may	21+100=121	square root is 11
Trayovi(ga)msatischa may	23+121=144	square root is 12
Panchavi(ga)msatischa may	25+144=169	square root is 13
Saptavi(ga)msatischa may	27+169=196	square root is 14
Navavi(ga)msatischa may	29+196=225	square root is 15
Ekatri(ga)msascha may	31+225= 256	square root is 16
Trayatri(ga)msascha may	33+256=289	square root is 17

Lord Vishnu is Sunyah or Zero as well as Anantah or Infinity

In Vishnu Shasraanama Vishnu is prayed up on as “shunyah” in sloka No. 79:

suvarnavarno hemango varangas chandhanangadhi
viraha vishamaha sunyo grithasirachalaschalaha

The Sanskrit word “sunya” means “zero”, “nullity”, “cipher”, “emptiness”.

He is also prayed up on as “anantha” the Infinite, in verse 70:

kamadhevaha kamapalaha kami kanthaha krithagamaha
anirdhesya vapurvishnuhu viro ‘nantho dhananjayaha

Since God is Immeasurable it is appropriate to adsdress Him “Ananthaha” the Infinite. But how can we glorify the Almighty as “shunyah” the Cipher?

If Infinity is immeasurable, so is Zero. Mathematically speaking, one could define zero to be anti-infinity. If “Infinity” is immeasurable plenitude, “Zero” is immeasurable emptiness. If we were to think of an interminable series of values, from zero to infinity, floating somewhere out there in endless space, then, surely, Zero would be at one end of it while Infinity would be found at the other end, wherever, that is, the two ends may be found, if at all. “Zero” and “Infinity” are thus the two sides of the same un-graspable coin. By the same logic, we might say, the Sanskrit “ananthaha” and “shunyah” might seem antonymous but in reality they mean the same thing. Hailing God Almighty as “Lord Infinity” is hence no different from hailing Him “Lord Zero”.

Does this make sense? Why the God, who is Infinite Being, is called “sunya”, a Zero – the very opposite of infinity? The traditional commentators of the Vishnu-Sahasranamam offer us logical explanation in their respective “bhashyas”.

Sri Sankaracharya in his Bhashya was the earliest to explain “sunya” as an apt “nama” for God, the Supreme Brahman, who is “nirguna ” – i.e. the Being who is totally devoid of any qualities or attributes. In other words, according to Sankaras school of metaphysics, God is “guna sunyan”.

According to this explanation, God transcends all attributes. His qualities like omnipotence, omniscience etc. only serve to help us in ascertaining His reality but they do not “per se” define Him. The truth of Gods existence cannot be grasped by us with reference to His qualities or “guna” alone, says Sankara. Brahman is to be apprehended as an Absolute Being who stands far apart from and quite beyond any of His infinitely (“ananthaha”) great qualities – i.e. He is “nirguna brahman”, a Being without qualities, a Being with “zero” qualities. Hence it is fit to call Him “shunyah”

Later Sri Parashara Bhattar in his “bhagavadh guna dharpanam” explains “shunyah” in the typical way of the school of Visishtadvaitha theology. According to this school, God is the Supreme Abode of all auspicious attributes. The Almighty is full of innumerable good qualities like “jnaana”, “bala”, “aiswarya”, “virya”, “shakthi” and “tejas”. In Visishtadvaitha, God is “ananthakalyana guna ganan+” (to use a famous expression of Sri Ramanujacharya) – i.e. Brahman is the Being with Infinite Number of Happy and Wholesome Attributes. The theology next states that God, by corollary, is also totally devoid of inauspicious, un-wholesome or negative qualities.

According to Bhattar, in so far as, Brahman is replete with infinitely good attributes, He is to be known as “ananthaha”. And in so far as He is absolutely bereft of defective qualities, He is to be known as the God of “zero-defects” – in other words, He is “shunyah”.

Apart from theological considerations, one can still regard Zero to be a remarkably apt “nama” for the Almighty. Common knowledge of the world around us reveals how all-powerful the concept of Zero, “sunya”, truly is. When we look at the history of Zero, we realize why “sunya” is almighty indeed!

Until about 1500 years ago nobody in the world outside India could count numbers beyond 9 without enormous difficulty. The entire Greco-Roman Western world knew nothing about the Hindu-Arabic system of numerals that prevails in the entire world today. The Romans depended upon alphabets to denote numbers – such as I, X and C or with V, L and D. In their system the number 32 had to be written, for example, as XXXII but writing a number like 3200 or 32000 for the Greeks and Romans presented a huge, often insurmountable problem! For several centuries the Greco-Roman civilization struggled with this cumbersome system of numbering. It was the principal reason why for almost a thousand years Western mathematics hardly advanced beyond being a method of elementary counting and mensuration using crude devices like the abacus. The Greeks and Romans had no knowledge of how to deal with large numbers, ratios, series, complex algebraic functions and calculations – all child’s play for any high-school student today. Western thought simply stagnated for ages since it could just not grapple with the mathematical problem of large numbers and calculations.

Somewhere between 1000 and 1200 AD, the Western world came in contact with the Arab world and that was when the Hindu-Arabic system of numerals opened the eyes of the Europeans to a whole new world of mathematical thought.

The Arabs had for long borrowed and been using the Hindu system of numerals that had been in use in ancient India for more than a thousand years earlier. The Hindu system did not use alphabets but a simple but versatile scheme of numeric symbols starting from “Zero” – the famous “sunya” – and ending with 9. These symbolic numerals made it so easy to represent and calculate numerate values anywhere from zero to infinity in quick time. They enabled complex functions and calculations. They made it possible to represent the most formidable series of values by a mere formula which in turn facilitated further complex mathematical functions! The Western world realized – for the first time ever – the power of the Hindu numeral system: a power that became the inspiration for all the mathematical advancements to later come out of Europe: algebra, ratios, surds, functions such as squares, cube and root, series and progressions, logarithmic tables, quadratic equations… and so on and so forth.

It was the power of Zero, “Sunya”, indeed, that made the European Renaissance possible – the Renaissance that eventually gave birth to all the wonderful discoveries of modern mathematics such as Fibonacci’s series, Pascal’s Probability theory and even Newton’s Calculus! “The concept of Zero unleashed something more profound than just an enhanced method of counting and calculating”. Zero revolutionized the old modes of human thought. It meant firstly people could use only ten digits, from 0 to 9, to perform every conceivable calculation and to write any conceivable number. Secondly, it opened up a whole new world of possibilities for abstract human thinking that had been simply unthinkable before!

How did the ancient Hindus discover such a powerful concept as “sunya” while the rest of the world remained ignorant of “Zero” for ages?

We have all heard about the great Indian mathematician Bhaskaracharya. He wrote several pioneering treatises (in Sanskrit) on Vedic mathematics. In one of the treatises, it is said, he wrote a small dedication: “To the Supreme Brahman, who is Infinity, I offer my salutation”. Bhaskaracharya used the Sanskrit word “khahara” to denote God as “Infinity” in the dedication. It is derived from “kham” which means “Zero” and “hara” meaning “divided”. The word “khahara” was meant to indicate that God who is Infinity is related to Zero.

Bhaskaracharya was the first mathematician to reveal to the world the intimate relationship between “sunya” and “ananthaha”, between Zero and Infinity. Any quantity divided by “sunya” is equal to Infinity, he said. Take a value like 16 and divide it (“haraha”) with progressively decreasing divisors. What happens? The quotient progressively enlarges. For e.g. 16 sdicvidwed by 8 is 2; 16 divided by 4 = 4; and 16 divided by 2 = 8; and eventually when 16 is divided by 0 it equals “Infinity!” Every quantity, every value in the world, when divided by “sunya”, results in the same quotient or result viz. Infinity, “ananthaha”

Such is the mighty power of Zero that it can raise and relate all values on earth to the exalted state of Infinity,that very same state in which God Almighty, the Vishnu of the sacred “Sahasranama”, is said to eternally reside and rule!

--M.K. Sudarshan; IndiaDivine.org

Divine Mystery Numbers in Hindu Scriptures

Skanda Purana says that when Brahman made this whole creation and its living beings, he also created a circle dividing the entire sky. This Chakra is called Rasi-chakra which has twelve Rasis or zodiac signs of 27 constellations. The whole universe pulsates by the influence of these planets, stars and constellations which is also the cause of any creation, birth, sustenance and death. Adepts of the Kalachakra were well aware of perturbations in planetary cycles, in the year and in the month. Consistent with this view is the concept that people are, like the real solar system, subject to fluctuations, perturbations and inequalities. The periods are based on the numbers 27, 54, 108, 360 and 21600. That which is real is the respiration, say Sanskrit texts. A respiration consists of two halves, an inhalation and an exhalation. The meshing of time and astronomy and breath is the Kalachakra. Kalpa= Mahakala = Brahma = Time. Each Nakshatra has four padas (steps) says modern astrology27x4=108. That is how we attach importance to 108.

Ancient sages divided 360 degrees of the ecliptic by 12 to arrive at 30 degrees of the Zodiac. It takes 72 solar years (which is roughly the average human life) for the solstice to shift one degree proportionate to the fixed stars and it will take 72x30=2160 solar years for the shift to proceed through one zodiac. Total cycle will be 2160x 12=25920 years. This is called a Great Year. Surya Siddhanta gives precession (slow rotation of the rotation axis of spinning body) as 54 seconds of arc of a circle, a year. Modern calculations set this at 50 seconds. To shift one degree it would take 71.6 solar years. This adds up to a complete cycle of 25776 years. Of course constant changes are going on in the Cosmos too. It all shows how far advanced were our sages! How could they do it with their naked eyes and mental thinking remains a mystery!

The Cosmic concept of Kaalachakra in influencing time measurement should not be forgotten. Two straight lines of same length intersecting vertically at their mid points produce four right angles which add up to 360 degrees. Their ends when joined in the form of an arc produce the circle circumscribing their end points. The circle has therefore 360 degrees. When this is divided internally into twelve equal segments each segment has an angular movement of 30 degrees. These twelve segments are the 12 Zodiac signs in astrology. Further, each degree can be divided into 60 minutes and each minute to 60 seconds. One minute of the arc in Sanskrit is also known as "Asu". Modern clocks are designed on this model to give a circular moment of the hands through 360 degrees in 12 hours. In Savana Maanam Hindu Calendar one year has 360 days. One month has 30 days and one Paksha 15 days. 360/12 gives 30 (there are 30 Muhurthas in a day). 30 (Muhurthas) x12 (Zodiac signs) =360 (days in year)

Upanishads say human energy body is built up of 72000 Naadis or energy flows (These are not physical nerves as is often translated). There are 3600 Vinadis in a day. When we multiply 3600 with a number 20 we arrive at 72000 which are the energy flows (astral paths) mentioned in Prasna Upanishad.

In one day, a human being breaths 21600 times when normal, according to Yogasaastra of Patanjali. If we multiply 21600 breaths 20 times we get a figure of 432000 which is the number for the total number of years in Kaliyuga. If we multiply 3600 number of Vinadis in a day 20 times we get 72000 which are the number of energy paths in the human being mentioned in Upanishads. The numbers 20, 60, 3600, 21600, 72000 and 432000 have all a common factor 20, the divine mystery number. Probably, 20 represent 5 panchbhootas+5 Jnaanedriyas+5 Karmendriyas+5 Pancha Praanas ruled by Aatman.

BIBLIOGRAPHY

1. Frawley, Vedic Astrology, Internet

2. http://nrsrini.blogspot.com/2011/09/early-and-medieval-hindus-contribution.html

3. http://nrsrini.blogspot.com/2017/09/rasichakra-of-zodiacis-that-vedic.html

4. vedic.dharma.blogspot.in, The Value of Pi up to 32 Decimals from the Vedas

5. Sudarshan M.K., IndiaDivine.org, Lord Vishnu is Sunyah or Zero

6. Ramachandra Rao, S.K., Srividyaa-Kosa, Kalpatharu Research Academy, Shankar Math, Bengaluru, India

Friday, March 30, 2018

KNOWLEDGE & MYSTICISM OF NUMBERS IN HINDU SCRIPTURES