MATHS,
MESSAGE AND DEPTH OF KNOWLEDGE CONTAINED IN NUMBERS IN VEDAS AND HINDU SCRIPTURES
(Consolidated by N.R. Srinivasan from the
E-mails sent to HR Forum, MAY 2019)
INTRODUCTION
Mysticism and Knowledge of Numbers as well Mathematics contained in Hindu Scriptures is amazing. I have come across few mantras and slokas that I would like to share with you. This needs a systematic study and deep research of all our scriptures.
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.
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.
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 Rig Veda has a cryptic verse that contains the secret of 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.
In Hanuman Chalisa "Yug sahasra yojan par Bhanu! Leelyo taahi madhur phal janu” reveals the distance to Sun from Earth is 96,000,000 miles. NASA says that, this is the exact distance between Earth and Sun (Bhanu).
Indian researcher R. N. Narasimhan has found a relationship between the geometric design of Sri Chakra and Pyramid, and from the maze of data of enmeshed triangles identifies 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)iangles, 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
Rudra Namkam-Chamakami from Yajurveda encompasses mathematical concepts of number theory and progression combined.
A Sloka in the 10th book of Rig Veda translation gives the value of Pi up to 28 digits accurately.
Vishnu Sahasranama surprises us that Lord Vishnu is both Sunyah or Zero as well as Anantah or Infinity revealingthe Truth contained in Veda mantra Isavasyamidam sarvam, the whole world is pervaded by Brahman in his role as Vishnu (vyaapyate iti Vishnuh) --From 0 to infinity it is all Vishnu alone
” Mathematical secrets of the universe are mentioned in the Vedas like a time cycle of 4,320,000,000 years and names for numbers from one to ten to ten followed by twelve zeroes (1,000,000,000,000,000). The zodiacal number 360 and its divisions and derivatives are common in Vedic texts. Vedic mantras are said to be inherent in the rays of the Sun. Noted Vedic scholar Subhash Kak has found a planetary code in the numbering of the books of the Rig Veda.
edic astrology contains an extensive knowledge not only of the planets, signs and houses but of the 27 Nakshatras or lunar constellations going back to the Vedas. The Vedas relate the Nakshatras to various deities and rishis and states that after death the soul can travel to the star it is most connected to in life. The mythology of the Nakshatras is quite profound and helps us understand the ancient star lore of many cultures.
Vedic astrology divides the lunar month of twenty nine and a half solar days into thirty equal lunar days or tithis. This amounts to 371 tithis in a solar year of 365 days. The number of deities in the Rig Veda are 3339, or 371 X the mystic number 9, reflecting the importance of the influence of the Moon. The Vedas were oriented to astronomical influences of a profound order and at perhaps a much earlier date than that of Babylonia” says Padmabhushan Vamadeva Sasatri, David Frawley.
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 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
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 .
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.
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
dasa - 10 - ten
satam - 100 - hundred
sahasram - 1000 - thousand
ayutam - 10000 - ten thousand
niyutam - 100000 - one lakh
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.
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 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
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
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
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
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
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.
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.
Among
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.]
[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 3rd
column whose square root is in the 4th 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
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
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.
The
mathematical achievements of ancient India have largely remained hidden, but
thanks to the internet age are coming to the surface in recent times. Many
books have been written about the advanced mathematics, including trigonometry
and calculus discovered in India which reached Europe in the Middle Ages
through the Arabs. Here, I want to go into an even more basic mathematical idea
which turns out to be one of the biggest leaps of imagination also. This is
the ancient Indian numeric system.
Other Civilizations
The most basic indicator of the
mathematical abilities and imagination of any civilization is the numeric
system used by them and the largest number which they have arrived at. The
following are some of the numbers used by ancient civilizations.
The largest number having any representation in ancient China was 10,000. That's it.
The largest number having any representation in ancient China was 10,000. That's it.
Chinese wrote Ten Thousandszymbolized
Similarly, the largest named number
for the ancient Greeks was a Myriad, which was 10,000. To be fair, Archimedes
did write a paper calculating the number of sand grains in the universe and
therefore did imagine numbers as large as 1063, but that knowledge
remained unused and quickly forgotten.
Even the Romans, Persians and Egyptians never went beyond One Million.
Even the Romans, Persians and Egyptians never went beyond One Million.
Persian one million - میلیون
\Egyptians wrote one million this Of course, Arabs received all knowledge from
India, so they should not even be counted. Compared to the above numbers from
other civilizations, ancient India went far ahead.
Some of the largest numbers
are referred to and defined in the Valmiki Ramayan. Valmiki defines
these numbers while describing the size of Sri Ram's army in the Yuddha
Kanda, (६-२८-३३)
शतम् शतसहस्राणाम् कोटिमाहुर्मनीषिणः || शतम् कोटिसहस्राणाम् शङ्कुरित्यभिधीयते |
"Wise men call a Shata
Shata Sahastra as a Koti. A Shata Sahastra Koti is reckoned as a
Shanku."
Shata is a hundred and Sahastra is a
thousand. So a Koti is 10,000,000 (10 Million) and Hundred
Thousand Koti is a Trillion. These days, what we
call as "one lakh crore" for lack of proper terminology,
actually had a name in ancient times - a "Shanku"!
So One Shanku (1012)
is basically One Trillion.
Valmiki goes further to define even larger numbers:
Valmiki goes further to define even larger numbers:
शतम्
शङ्कुसहस्राणाम् महाशङ्कुरिति स्मृतः
|| महाशङ्क्य्सहस्राणाम् शतम्
वृन्दमिहोच्यते |
शतम् नृन्दसहस्राणाम् महावृन्दमिति स्मृतम् || महावृन्दसहस्राणाम् शतम् पद्ममिहोच्यते |
शतम् पद्मसहस्राणाम् महापद्ममिति स्मृतम् || महापद्मसहस्राणाम् शतम् खर्वमिहोच्यते |
शतम् खर्वसहस्राणाम् महाखर्वमिति स्मृतम् || महाखर्वसहस्राणाम् समुद्रमभिधीयते |
शतम् समुद्रसाहस्रमोघ इत्यभिधीयते || शतमोघसहस्राणाम् महौघ इति विश्रुतः |
Using Shatam Sahastram (same as Laksha) as Hundred Thousand for easy understanding:
Hundred Thousand Shanku = Maha Shanku = 1017
शतम् नृन्दसहस्राणाम् महावृन्दमिति स्मृतम् || महावृन्दसहस्राणाम् शतम् पद्ममिहोच्यते |
शतम् पद्मसहस्राणाम् महापद्ममिति स्मृतम् || महापद्मसहस्राणाम् शतम् खर्वमिहोच्यते |
शतम् खर्वसहस्राणाम् महाखर्वमिति स्मृतम् || महाखर्वसहस्राणाम् समुद्रमभिधीयते |
शतम् समुद्रसाहस्रमोघ इत्यभिधीयते || शतमोघसहस्राणाम् महौघ इति विश्रुतः |
Using Shatam Sahastram (same as Laksha) as Hundred Thousand for easy understanding:
Hundred Thousand Shanku = Maha Shanku = 1017
Hundred Thousand Maha Shanku =
Vrinda = 1022
Hundred Thousand Vrinda = Maha Vrinda = 1027
Hundred Thousand Mahavrinda = Padma = 1032
Hundred Thousand Padma = Mahapadma = 1037
Hundred Thousand MahaPadma = Kharva = 1042
Hundred Thousand Kharva = Maha Kharva = 1047
Hundred Thousand MahaKharva = Samudra = 1052
Hundred Thousand Samudra = Augha = 1057
Hundred Thousand Aughas = Maha Augha = 1062
Hundred Thousand Vrinda = Maha Vrinda = 1027
Hundred Thousand Mahavrinda = Padma = 1032
Hundred Thousand Padma = Mahapadma = 1037
Hundred Thousand MahaPadma = Kharva = 1042
Hundred Thousand Kharva = Maha Kharva = 1047
Hundred Thousand MahaKharva = Samudra = 1052
Hundred Thousand Samudra = Augha = 1057
Hundred Thousand Aughas = Maha Augha = 1062
How big is Maha Augha?
Does anyone know what 1062 is
called in the modern metric system? Probably not, because no one uses numbers
as large as these, except scientists working at the astronomical scale
(counting stars and galaxies) or atomic scale while measuring the number of
atoms in the universe.
Yes, that's how big this number is.
So, considering that there are 1023 stars
and estimated 1080 atoms in the known
universe, that's the scale we are talking about. This is far far
ahead of any civilization in all of earth's history, that came up with a
numeric system.
Even Further
Later
on, the Buddhist monks went even further. The Lalitavistara Sutra (a
Mahayana Buddhist work) recounts a contest which included writing, arithmetic,
wrestling and archery. In it the Buddha was pitted against the great
mathematician Arjuna and showed off his numerical skills by citing the names of
the powers of ten, up to 1 'tallakshana', which equals 1053,
but then going on to explain that this is just one of a series of counting
systems that can be expanded geometrically. The last number at which he arrived
at after going through nine successive counting systems was 10421,
that is, a 1 followed by 421 zeros! But he did not stop there, he actually
named all the numbers up to that, with 10421 being called as
"dhvajagranishamani (ध्वजाग्रनिशमनी)". That is astounding!
Very
small numbers
I can bet many people have no idea
that ancient Indians were interested in very small numbers also, especially
when defining the concept of Time.
How small?
Well, त्रुति (Truti)
was equal to "0.031 µs (micro second)" = 3.1 x 10-8
रेणु (Renu) = 60 Truti = 0.86
µs = 8.6 x 10-7
लव (Lava)
= 60 Renu = 0.11 ms = 1.1 x 10-4
लीक्षक (Leekshak) = 60 Lava = 6.696
ms = 6.696 x 10-3
And so on. I am sure it must come as a surprise to many people that in ancient India we had names for numbers that went to negative powers of ten also!
And so on. I am sure it must come as a surprise to many people that in ancient India we had names for numbers that went to negative powers of ten also!
Infinity
After naming bewilderingly large
numbers, it would have been surprising if ancient Indians did not come up
with a shloka or two to define Infinity.
Om poornam-adah poornam-idah poorna-aat poornam-udachyate,
Poorna-asya poornam-aadaaya poornam-evaa vashishyate
That is whole, This is whole, From
the whole comes the whole. Even if the whole is taken away from whole, still
the wholeness remains.
Yes. That is the exact definition of
Infinity that many of us use in our daily prayers!
Where are we now?
So,
forget about using any of these numbers in our daily lives, the mind boggles
just at the thought of the mathematical imagination of our forefathers.
Remember, Ramayan and Lalita-Vistara were religious scriptures, so it is an ode
to the mathematical genius of ancient Indians, that they found it very normal
to define huge mathematical numbers even in our religious texts.
Maybe, in those days being good in
mathematics was just commonplace.
Compared to this, how does it sound
now, when we hear people using simple terms like "lakh crore" and
"crore core" being used in modern India when our own ancestors were
way smarter than us in using larger numbers?
BIBLIOGRAPHY
1. Frawley,
Vedic Astrology, Internet
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
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