The early Vedic hymns on mathematics, time relations and religio-philosophy

Shrutis (especially the Vedas) are a valuable source of information about the life and conditions in society long ago, in addition to being the basic religious texts in Hinduism. Veda means literally knowledge in Sanskrit. Vedas thus represent knowledge which was acquired and compiled by seers and common people many millenniums ago.

(1) The timeline for the Veda

The Vedic hymns were compiled in the present tense if the information in them was of concurrent nature and events mentioned by them were taking place at the same time. On the other hand, events from the past, including the legends, parables and speculative narrations (such as Purusa Sukta in the Rig Veda: Book 10 – Hymn 90) were presented as hymns using the past tense.

Consider the following hymn dedicated to River Sarasvati in the Rig Veda. It is in the present tense and shows the river actually flowing. In reality, the river Sarasvati died and disappeared long ago which, according to the archaeological studies (Ref. 1), happened 7,000 years ago (5,000 BC). This indicates that on the basis of this and similar other Rig Vedic hymns (showing the river Sarasvati actually flowing), the Rig Veda (or at least parts of Rig Veda having such hymns) must at least be 7000 years old or since before 5000 BC.

“Sarasvatī, the mighty flood,—she with her light illuminates,
She brightens every pious thought.” Rig Veda (Book 1: Hymn 3.12)

(2) The information about the decimal system (using base 10) in the Vedas

As indicated in Ref. (2), the following three consecutive hymns in the ancient Rig Veda mention the numbers ten (10), twenty (20), thirty (30), forty (40), fifty (50), sixty (60), seventy (70), eighty (80), ninety (90) and hundred (100) increasing in a sequential order, which seems to be a clear indication that people several millenniums ago (during the time of Rig Veda) were using the decimal system (based on the number 10) in counting and numbering.

“Indra, come hitherward with two Bay Coursers, come thou with four, with six when invocated.
Come thou with eight, with ten, to drink the Soma. Here is the juice, brave Warrior: do not scorn it.” Rig Veda (Book 2: Hymn 18.1)

“O Indra, come thou hither having harnessed thy car with twenty, thirty, forty horses.
Come thou with fifty well trained coursers, Indra, sixty or seventy, to drink the Soma.” Rig Veda (Book 2: Hymn 18.5)

“Come to us hitherward, O Indra, carried by eighty, ninety, or a hundred horses.
This Soma juice among the Śunahotras hath been poured out, in love, to glad thee” Rig Veda (Book 2: Hymn 18.6)

Note also in the above numbers ten (10), twenty (20), thirty (30), ……, ninety (90) and hundred (100), the left digit increasing in sequential order from 1 to 10, which again confirms the use of decimal (10 based) system long ago according to these Rig Vedic hymns.

Similarly, based on the several ancient texts, e.g. the Mahabharata (Book 15: Ch. 15 - V. 8 and Ch. 31 - V. 3) and the Rig Veda (Book 1: Hymn 126.6, Book 3: Hymn 33.13), the concept of zero or shunya (shoonya, shunam or shoonam; meaning void, non-existence, emptiness or nothingness) was already known to people several thousand years ago. Perhaps, based on the philosophical thinking (as indicated in the following hymn) that existent and non-existent can co-exist, they might have started long time ago to use shunya or 0 (the insignificant or empty digit) in conjunction with other significant digits (1, 2, etc.) to create the compound numbers (10, 20, etc.).

"Thereafter rose Desire in the beginning, Desire, the primal seed and germ of Spirit.
Sages who searched with their heart's thought discovered the existent's kinship in the non-existent." Rig Veda (Book 10: Hymn 129.4).

Needless to say, many Rig Vedic hymns (including the one below) mention things in thousands (e.g. 20000, 40000, 90000..) which indicates that people long ago (during Vedic times) were quite at ease in large scale counting and numbering and that would be more likely if zero (0) was already incorporated then in the number system (as 10, 20,.., 100, ..., 1000, and so on).

"So, as a prize dear to the strong, the sixty thousand have I gained,
Bulls that resemble vigorous steeds." Rig Veda (Book 8: hymn 46.29)

(3) Vedic hymns related to the day and year (including number of degrees in a circle)

Consider the following hymn talking about twelve spokes in the wheel of Surya's (Sun’s) chariot. The reference about twelve in this case is probably to 12 hour average daily cycle (from sunrise to sunset). Similarly, the seven hundred and twenty (sons) in a pair of wheels in the following hymn might represent the total number of degrees in both wheels (360 degrees in each wheel).

“Formed with twelve spokes, by length of time, unweakened, rolls round the heaven this wheel of during Order.
Herein established, joined in pairs together, seven hundred Sons and twenty stand, O Agni.” Rig Veda (Book 1: Hymn 164.11)

Furthermore, another Rig Vedic hymn (listed below) talks about 360 spokes, each spoke probably representing a degree on the cycle or wheel / circle. There are also twelve fellies according to this hymn, which probably are spread on the wheel one after the other and could represent 12 months in a year (analogous to 12 cycles of Moon around Earth in a year, each cycle lasting a month or 30 days). The three naves below might refer to the three regions, heavens, midair and terrestrial.

“Twelve are the fellies, and the wheel is single; three are naves. What man hath understood it?
Therein are set together spokes three hundred and sixty, which in nowise can be loosened.” Rig Veda (Book 1: Hymn 164.48)

It could be that when the above hymns were composed in the Rig Veda, the Earth completed a circle around the Sun in 360 “days”, unlike 365.25 days at the present time. Thus the number of degrees (360) in a circle was perhaps based originally on the number of “days“ (360) in a year (Earth’s cycle around the Sun long ago), indicating that one degree angle on the circle represented the Earth’s daily movement around the Sun long ago (during perhaps Vedic times).

Incidentally, the discrepancies in the original year (perhaps 360 days during the time of the Rig Veda) and the present year (365.25 days), as well as the differences in the durations involving days and hours during Vedic times and now, could be the result of several factors, including the changes over time in mass distribution and moments of inertia for Earth and Moon and the angle between the Earth’s equatorial plane and the Ecliptic.

As discussed in Ref. (3) in relation to a satellite orbiting the Earth, the Earth-Moon orbiting the Sun in this case is a dynamical system in a gravitational field. The dynamical characteristics of such a system (including the rotational velocities of Earth and Moon and the corresponding yearly, monthly, daily and hourly durations) are subject to mass and inertia properties of rotating members (Earth and Moon for example) which could easily vary over time resulting in differences in year and day etc. now from long ago. Even the extreme temperature and climatic conditions on Earth (including the ice age), along with any changes in the distribution of continental mass on Earth, has the potential to alter Earth’s moment of inertia and rotational speed resulting in changes in the duration of day and hour etc.

Similarly, as shown in the example of Satellite Solar Power Station orbiting the Earth in Ref. 4 (p. 82-84, Fig. 3-13), the rotational speeds for multi-body space systems (including possibly the Earth-Moon orbiting the Sun) can be influenced by the ever changing inclination (angle) between the equatorial plane and the Ecliptic, and that might also lead to differences in day etc. between the Vedic times and now.

In addition, there is the possibility of Earth’s orbit around the Sun getting transformed (enlarged or reduced) over time due to changes in the mass etc. of heavenly bodies (including the Sun) leading to differences in the yearly periods long ago (360 days during the Veda time perhaps) and now (365.25 days).

(4) The earliest philosophical content in the Veda

It is usually thought that deep philosophical knowledge related to God (Brahman), soul and body (matter) surfaced in Upanisads as Vedanta (representing or near the end of Veda). However, that does not seem to be the case according to the following hymns which are from the first Mandala (Book 1) in the Rig Veda, use the famous parable of two birds sitting on a fruit tree (one as soul and the other as body) and set the basis (reality in terms of God, soul and body) for Upanisads.

“Two Birds with fair wings, knit with bonds of friendship, in the same sheltering tree have found a refuge.
One of the twain eats the sweet Fig-tree's fruitage; the other eating not regardeth only.” Rig Veda (Book 1: Hymn 164.20)

“Where those fine Birds hymn ceaselessly their portion of life eternal, and the sacred synods,
There is the Universe's mighty Keeper, who, wise, hath entered into me the simple.” Rig Veda (Book 1: Hymn 164.21)

“The, tree whereon the fine Birds eat the sweetness, where they all rest and procreate their offspring, — Upon its top they say the fig is luscious: none gaineth it who knoweth not the Father (God).” Rig Veda (Book 1: Hymn 164.22)

“Back, forward goes he, grasped by strength inherent, the Immortal born the brother of the mortal
Ceaseless they move in opposite directions: men mark the one, and fail to mark the other.” Rig Veda (Book 1: Hymn 164.38)

(5) Monotheistic polymorphism in the Veda and the significance of Visnu as a major Vedic deity

The following hymns show that one Brahman (God) is worshipped in the Vedas using many names for the deity. Similarly, even though some people mistakenly believe that Visnu was not a prominent deity during the beginning period of the Vedas, the following hymns in the first Mandala (Book 1) in the Rig Veda do not support such a thinking. Vishnu is indicated in these early Rig Vedic hymns as the major protector, ruler of three worlds and closely allied with Indra and Savitar.

“They call him Indra, Mitra, Varuṇa, Agni, and he is heavenly nobly-winged Garutmān.
To what is One, sages give many a title they call it Agni, Yama, Mātariśvan.” Rig Veda (Book 1: Hymn 164.46)

“The Gods be gracious unto us even from the place whence Viṣṇu strode
Through the seven regions of the earth!” Rig Veda (Book 1: Hymn 22.16)

“Through all this world strode Viṣṇu; thrice his foot he planted, and the whole
Was gathered in his footstep's dust.” Rig Veda (Book 1: Hymn 22.17)

“Viṣṇu, the Guardian, he whom none deceiveth, made three steps; thenceforth
Establishing his high decrees.” Rig Veda (Book 1: Hymn 22.18)

“Look ye on Viṣṇu's works, whereby the Friend of Indra, close-allied,
Hath let his holy ways be seen.” Rig Veda (Book 1: Hymn 22.19)

“The princes evermore behold that loftiest place where Viṣṇu is,
Laid as it were an eye in heaven (with Savitar).” Rig Veda (Book 1: Hymn 22.20)

“Visnu, whose three places that are filled with sweetness, imperishable, joy as it may list them,
Who verily alone upholds the threefold, the earth, the heaven, and all living creatures.” Rig Veda (Book 1: Hymn 156.4)

References:

(1) Subhash C. Sharma, “How old are the Vedas and who can read them?”, Aug. 23, 2006, http://seva.sulekha.com/blog/post/2006/08/how-old-are-the-vedas-and-who-can-read-them.htm

(2) Subhash C. Sharma (Seva Lamberdar), “The Rig Vedic example of counting / numbering in 10-based or decimal system (with numbers e.g. 10, 20, 30, …, 100),” May 8, 2013, https://such.forumotion.com/t12955-the-rig-vedic-example-of-counting-numbering-in-10-based-or-decimal-system-with-numbers-eg-10-20-30-100

(3) Subhash C. Sharma and Willem Stuiver, "Boom Forces in Librating Dumbbell-Type Satellites," AIAA Journal, Vol. 12, No. 4 (1974), pp. 425-440, http://arc.aiaa.org/doi/abs/10.2514/3.49266

(4) Subhash C. Sharma, Dynamics of Single and Multibody Earth Orbiting Systems, Ph.D. Thesis (Mech. Engg.), U.B.C., 1978, https://circle.ubc.ca/bitstream/handle/2429/21279/UBC_1978_A1%20S53.pdf?sequence=1


by: Dr. Subhash C. Sharma
(May 31, 2013 … http://creative.sulekha.com/the-early-vedic-hymns-on-mathematics-time-relations-and-religio-philosophy_603687_blog)

(4) Subhash C. Sharma, Dynamics of Single and Multibody Earth Orbiting Systems, Ph.D. Thesis (Mech. Engg.), U.B.C., 1978, https://circle.ubc.ca/bitstream/handle/2429/21279/UBC_1978_A1%20S53.pdf?sequence=1

in the References needs to use a different URL, as given below,

(4) Subhash C. Sharma, Dynamics of Single and Multibody Earth Orbiting Systems, Ph.D. Thesis (Mech. Engg.), U.B.C., 1978, https://circle.ubc.ca/bitstream/handle/2429/21279/UBC_1978_A1%20S53.pdf

Incidentally, in Section (3) the angle between the Earth’s equatorial plane and the Ecliptic is same as the
tilt of Earth‘s axis of rotation (23.4 deg).

There was an interesting comment by Mr. Rao on Sulekha about Section (1) in the above, "... your blog at Ref.1 that puts timeline for RV-1 around 5000BCE. What is the real proof for that timeline?"

Listed below is my response to him.

Several years ago when I wrote the blog "How old are the Vedas..." (http://seva.sulekha.com/blog/post/2006/08/how-old-are-the-vedas-and-who-can-read-them.htm), the best estimate about the age of the Veda I could make was according to the article "Recent Research on the Sarasvati River" (http://www.stephen-knapp.com/recent_research_on_the_sarasvati_river.htm).


This article by Stephen Knapp claimed at that time that based on the archaeological studies the River Sarasvati existed until 5000 BC or 7000 years ago.


I considered it the best scientific evidence (supported by archaeological studies) in assessing the age of Vedas, since Vedas (Rig Veda especially) describe the River Sarasvati actually flowing at the time of composition of such hymns.


In other words, Vedas must at least be from 5000 BC or 7000 years ago according to the archaeological citing (about River Sarasvati) in the above article (by Stephen Knapp) several years ago.


Btw it’s possible that in the mean time there might have been new archaeological findings about River Sarasvati leading to changes in the above date about Vedas.


In any case, in my opinion it probably is one of the best methods (using the Vedic hymns on River Sarasvati in conjunction with archaeology of river Sarasvati) to correctly assess the date about Vedas (at least on the lower end of the scale, i. e. Vedas being older than the date of dying / disappearance of river Sarasvati).

Just for the record, correction in the following to hymn's number in Section (2).

“Indra, come hitherward with two Bay Coursers, come thou with four, with six when invocated.
Come thou with eight, with ten, to drink the Soma. Here is the juice, brave Warrior: do not scorn it.” Rig Veda (Book 2: Hymn 18.1)

should read as,

“Indra, come hitherward with two Bay Coursers, come thou with four, with six when invocated.
Come thou with eight, with ten, to drink the Soma. Here is the juice, brave Warrior: do not scorn it.” Rig Veda (Book 2: Hymn 18.4)

The early Vedic hymns on reincarnation

The following hymns in the beginning of the Rig Veda (Mandala or Book 1, Hymn 164) affirm that the early Vedic people new and understood the idea of reincarnation (transmigration of the soul).

Note below the close connection (brotherhood) between the immortal soul and the mortal body, the former housed inside the latter, in living beings (RV: 1.164.30, 1.164.38), and the cycles of life and death (coming and departing) seen in the same light (RV: 1.164.19).

The soul, even though immortal and the source of life for the body, remains hidden in the body and gives the impression of death (when body dies) due to its association with mortal body (RV: 1.164.32).

The above points are fundamental to the concept of reincarnation which has the immortal soul “traveling” continually (RV: 1.164.31) on the basis of offerings (actions / karma) on the part of the mortal (temporary, death-prone) body (RV: 1.164.30).

“Those that come hitherward they call departing, those that depart they call directed hither.
And what so ye have made, Indra and Soma, steeds bear as ’twere yoked to the region's car-pole. Rig Veda (Book 1: Hymn 164.19)

“That which hath breath and speed and life and motion lies firmly stablished in the midst of houses.
Living, by offerings to the Dead he moveth Immortal One, the brother of the mortal. Rig Veda (Book 1: Hymn 164.30)

“I saw the Herdsman, him who never stumbles, approaching by his pathways and departing.
He, clothed with gathered and diffusive splendour, within the worlds continually travels.” Rig Veda (Book 1: Hymn 164.31)

“He who hath made him cloth not comprehend him: from him who saw him surely is he hidden.
He, yet enveloped in his Mother's bosom, source of much life, hath sunk into destruction.” Rig Veda (Book 1: Hymn 164.32)

“Back, forward goes he, grasped by strength inherent, the Immortal born the brother of the mortal
Ceaseless they move in opposite directions: men mark the one, and fail to mark the other.” Rig Veda (Book 1: Hymn 164.38)