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Hindu Astronomy - acharya - 08-25-2006

<img src='http://newsimg.bbc.co.uk/media/images/42012000/jpg/_42012422_solar_system_planets3_416.jpg' border='0' alt='user posted image' />

http://news.bbc.co.uk/2/hi/science/nature/5282440.stm

Pluto loses status as a planet
Artist's impression of Pluto, BBC
Pluto's status has been contested for many years
Astronomers have voted to strip Pluto of its status as a planet.

About 2,500 scientists meeting in Prague have adopted historic new guidelines that see the small, distant world demoted to a secondary category.

The researchers said Pluto failed to dominate its orbit around the Sun in the same way as the other planets.

The International Astronomical Union's (IAU) decision means textbooks will now have to describe a Solar System with just eight major planetary bodies.

Pluto, which was discovered in 1930 by the American Clyde Tombaugh, will be referred to as a "dwarf planet".

There is a recognition that the demotion is likely to upset the public, who have become accustomed to a particular view of the Solar System.

Named after underworld god
Average of 5.9bn km to Sun
Orbits Sun every 248 years
Diameter of 2,360km
Has at least three moons
Rotates every 6.8 days
Gravity about 6% of Earth's
Surface temperature -233C
Nasa probe visits in 2015



Hindu Astronomy - acharya - 08-25-2006

2.2. ANCIENT HINDU ASTRONOMY

2.2.1. Astronomical tables

One of the earliest estimates of the date of the Vedas was at once among the most scientific. In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BC.3 His proposal was dismissed as absurd by some, but it was not refuted by any scientist.

Playfair’s judicious use of astronomy was countered by John Bentley with a Scriptural argument which we now must consider invalid. In 1825, Bentley objected: “By his [= Playfair’s] attempt to uphold the antiquity of Hindu books against absolute facts, he thereby supports all those horrid abuses and impositions found in them, under the pretended sanction of antiquity. Nay, his aim goes still deeper, for by the same means he endeavours to overturn the Mosaic account, and sap the very foundation of our religion: for if we are to believe in the antiquity of Hindu books, as he would wish us, then the Mosaic account is all a fable, or a fiction.”4

Bentley did not object to astronomy per se, in so far as it could be helpful in showing up the falsehood of Brahminical scriptures. However, it did precisely the reverse. Falsehood in this context could have meant that the Brahmins falsely claimed high antiquity for their texts by presenting as ancient astronomical observations recorded in Scripture what were in fact back-calculations from a much later age. But Playfair showed that this was impossible.

Back-calculation of planetary positions is a highly complex affair requiring knowledge of a number of physical laws, universal constants and actual measurements of densities, diameters and distances. Though Brahminical astronomy was remarkably sophisticated for its time, it could only back-calculate planetary position of the presumed Vedic age with an inaccuracy margin of at least several degrees of arc. With our modern knowledge, it is easy to determine what the actual positions were, and what the results of back-calculations with the Brahminical formulae would have been, e.g.:

“Aldebaran was therefore 40’ before the point of the vernal equinox, according to the Indian astronomy, in the year 3102 before Christ. (…) [Modern astronomy] gives the longitude of that star 13’ from the vernal equinox, at the time of the Calyougham, agreeing, within 53’, with the determination of the Indian astronomy. This agreement is the more remarkable, that the Brahmins, by their own rules for computing the motion of the fixed stars, could not have assigned this place to Aldebaran for the beginning of Calyougham, had they calculated it from a modern observation. For as they make the motion of the fixed stars too great by more than 3” annually, if they had calculated backward from 1491, they would have placed the fixed stars less advanced by 40 or 50, at their ancient epoch, than they have actually done.”5

So, it turns out that the data given by the Brahmins corresponded not with the results deduced from their formulae, but with the actual positions, and this, according to Playfair, for nine different astronomical parameters. This is a bit much to explain away as coincidence or sheer luck.

2.2.2. Ancient observation, modern confirmation

That Hindu astronomical lore about ancient times cannot be based on later back-calculation, was also argued by Playfair’s contemporary, the French astronomer jean-Sylvain Bailly: “The motions of the stars calculated by the Hindus before some 4500 years vary not even a single minute from the [modem] tables of Cassini and Meyer. The Indian tables give the same annual variation of the moon as that discovered by Tycho Brahe - a variation unknown to the school of Alexandria and also the Arabs.”6

Prof. N.S. Rajaram, a mathematician who has worked for NASA, comments: “fabricating astronomical data going back thousands of years calls for knowledge of Newton’s Law of Gravitation and the ability to solve differential equations.”7 Failing this advanced knowledge, the data in the Brahminical tables must be based on actual observation. Ergo, the Sanskrit-speaking Vedic seers were present in person to record astronomical observations and preserve them for a full 6,000 years: “The observations on which the astronomy of India is founded, were nude more than three thousand years before the Christian era. (…) Two other elements of this astronomy, the equation of the sun’s centre and the obliquity of the ecliptic (…) seem to point to a period still more remote, and to fix the origin of this astronomy 1000 or 1200 years earlier, that is, 4300 years before the Christian era”.8

All this at least on the assumption that Playfair’s, Bailly’s and Rajaram’s claims about the Hindu astronomical tables are correct. Disputants may start by proving them factually wrong, but should not enter the dispute arena without a refutation of the astronomers’ assertions. It is something of a scandal that Playfair’s and Bailly’s findings have been lying around for two hundred years while linguists and indologists were publishing speculations on Vedic chronology in stark disregard for the contribution of astronomy.

2.2.3. The start of Kali-Yuga

Hindu tradition makes mention of the conjunction of the “seven planets” (Saturn, Jupiter, Mars, Venus, Mercury, sun and moon) and Ketu (southern lunar node, the northern node/ Rahu being by definition in the opposite location) near the fixed star Revati (Zeta Piscium) on 18 February 3102 BC. This date, at which Krishna is supposed to have breathed his last, is conventionally the start of the so-called Kali-Yuga, the “age of strife”, the low point in a declining sequence of four ages. However, modem scholars have claimed that the Kali-Yuga system of time-reckoning was a much younger invention, not attested before the 6th century AD.

Against this modernist opinion, Bailly and Playfair had already shown that the position of the moon (the fastest-moving “planet”, hence the hardest to back-calculate with precision) at the beginning of Kali-Yuga, 18 February 3102, as given by Hindu tradition, was accurate to 37’.9 Either the Brahmins had made an incredibly lucky guess, or they had recorded an actual observation on Kali Yuga day itself.

Richard L. Thompson claims that in Indian literature and inscriptions, there are a number of datelines expressed in Kali-Yuga which are older than the Christian era (and a fortiori older than the 6th century AD).10 More importantly, Thompson argues that the Jyotisha-shAstras (treatises on astronomy and, increasingly, astrology, starting in the 14th century BC with the VedANga Jyotisha as per its own astronomical data, but mostly from the first millennium AD) are correct in mentioning this remarkable conjunction on that exact day, for there was indeed a conjunction of sun, moon, Mercury, Venus, Mars, Jupiter, Saturn, Ketu and Revati.

True, the conjunction was not spectacularly exact, having an orb of 370 between the two most extreme planetary positions. But that precisely supports the hypothesis of an actual observation as opposed to a back-calculation. Indeed, if the Hindu astronomers were able to calculate this position after a lapse of many centuries (when the Jyotisha-ShAstra was written), it is unclear what reason they would have had for picking out that particular conjunction. Surely, such conjunctions are spectacular to those who witness one, and hence worth recording if observed. But they are not that exceptional when considered over millennia: even closer conjunctions of all visible planets do occur (most recently on 5 February 1962).11 If the Hindu astronomers had simply been going over their astronomical tables looking for an exceptional conjunction, they could have found more spectacular ones than the one on 18 February 3102 BC. And why would they have calculated tables for such a remote period, sixteen centuries before the Aryan invasion, nineteen before the composition of the Rg-Vedic hymns, a time of which they had no recollection?
http://www.voiceofdharma.com/books/ait/ch22.htm




Hindu Astronomy - acharya - 08-25-2006

Surya-Siddhanta: A Text Book of Hindu Astronomy (Paperback)
by Ebeneezer Burgess


This is an translation of a thousand plus year old Hindu textbook on astronomical calculations (originally written in Sanskrit). The English translation is included (verse by verse) along with extensive notes and explanations by the translator. The text gives prescriptions on Hindu calendar calculations (including the rather complicated Hindu lunar calendar), calculating the celestial coordinates of the Sun, Moon and visible planets, along with the ascending and descending node of the Moon, and calculations of the circumstances of solar and lunar eclipses. A prescription is given for creating a sine function table (a Hindu invention) to be used with the astronomical calculations.

This old textbook is not for the mathematically faint of heart. Even the translators extensive notes are difficult in places to wade through. If you have some ability in algebra, trigonometry and geometry and you are persistent you can, however, follow the calculations with the help of the translators notes. Many of the calculations are in base 60 arithmetic (much like our modern hour and minutes of time notations). In places the text and notes are a little difficult to follow. However, there are worked-out-examples of the calculations to help your understanding. I worked through all the calculations for the predictions of a solar eclipse, and, in all but a few places, exactly reproduced the examples given by the translator of the text. The results were quite accurate predictions of the times for solar eclipses. The predictions were most accurate for tenth century eclipses as that is the approximate date of the data provided in the text.

This is a fascinating book if you are interested in ancient astronomical calculations. The Hindu prescriptions appear to be a somewhat modified versions of the calculations prescribed by the second century Greek astronomer Ptolemy in his book the Almagest.


Hindu Astronomy - acharya - 08-25-2006

<img src='http://www.sanskrit.org/www/Astronomy/rahu.jpg' border='0' alt='user posted image' />

http://www.sanskrit.org/www/Astronomy/Hindutimeeras.html

Hindu Time Eras

India has many time eras. In general there are two kinds of eras: those named after prominent religious leaders and those named after kings. In addition, there are two annual time periods that mark the beginning of an era: the month of Caitra (March-April) and the month of Karttika (October-November). In the north the custom is to begin each year with Caitra (March-April) and each month with the full moon. But in the south and in Gujarat the years begin with Karttika (October-November) and the months with the new moon. The two most important eras are the Sakabda and the Samvat.

The Sakabda or Salivahana era (AD 78), now used throughout India, is the most important of all. It has been used not only in many Indian inscriptions but also in ancient Sanskrit inscriptions in Indochina and Indonesia. The reformed calendar promulgated by the Indian government from 1957 is reckoned by this era. It is variously alleged to have been founded by the Hindu king Salivahana. To reduce Saka dates to dates AD, 78 must be added for a date within the period ending with the day equivalent to December 31 and 79 for a later date.

The Samvat or Vikrama era (58 BC) is said in the Jain book Kalakacaryakatha to have been founded after a victory of King Vikramaditya over the Sakas. But some scholars credit the Scytho-Parthian ruler Azes with the foundation of this era. It is sometimes called the Malava era because Vikramaditya ruled over the Malava country, but it was not confined to this region, being widespread throughout India. The years reckoned in this era are generally indicated with the word vikramasamvat, or simple samvat. To reduce Vikrama dates to dates AD, 57 must be subtracted from the former for dates before January 1 and 56 for dates after.

The Bengali era is also known as the Laksmana era (AD 1119) said to have been founded by the king Laksmanasena of Bengal and still used throughout Bengal and preserved until modern times. To convert Bengali era to AD, 593 years must be added. The Caitanya era starts from the appearance of Caitanya Mahaprabhu in 1486. To convert the Caitanya era to dates AD add 1486 years to the Caitanya date. The Caitanya dating system is only in use by Caitanya Vaisnavas.


'Makara Sankranti


Most dates on the Hindu calendar are based on the movements of the Moon and not the Sun. For this reason the Hindu calendar is a lunar calendar. One exception to this is Makara Sankranti which is calculated according to solar movements and so always takes place on January 14th.

Makara refers to the Makara rashi which is the sign of the zodiac corresponding to Capricorn. Sankranti means “to cross into.” Makara Sankranti is therefore the day that the sun moves into the sign of the zodiac known as Capricorn.

This event is marked by different celebrations all over India with various customs such as flying kites in Gujarat, bringing of different sesame offerings to temples, and so on.
'
Hindu Months and Time Eras

The Hindu Months
In Hindu astrology, as in Western astrology, the zodiac is divided into twelve signs (rasis). Each of the twelve signs is in thirty degree segment of the full zodiac. In addition to the twelve signs, the Hindu zodiac is further divided into twenty-seven naksatras or lunar mansions. Each naksatra is a thirteen degree and twenty minute segment of the zodiac. Specifically, a naksatra is the number of degrees the moon travels across the sky in a twenty-four hour period. The degrees of the twenty-seven naksatras when totaled together equal the three hundred and sixty degrees of the entire zodiac. The names of the Indian months originated from the names of the naksatras where purnima (the full moon) always takes place. Of the twenty-seven naksatras only twelve of them have full moons.

The names of the Hindu months with their corresponding Western periods are as follows:
Naksatra

Hindu Month

Western Month
Visakha Vaisakha April-May
Jyestha Jyaistha May-June

Purva-asadha Asadha June-July
Sravana Sravana July-August
Purva-bhadrapada Bhadra August-September
Asvini Asvina September-October
Krttika Kartika October-November
Ardha Agrahayana November-December
Pusya Pausa December-January
Magha Magha January-February
Uttara-phalguni Phalguna

February-March
Citra Caitra March-April

Hindu Time Eras

India has many time eras. In general there are two kinds of eras: those named after prominent religious leaders and those named after kings. In addition, there are two annual time periods that mark the beginning of an era: the month of Caitra (March-April) and the month of Karttika (October-November). In the north the custom is to begin each year with Caitra (March-April) and each month with the full moon. But in the south and in Gujarat the years begin with Karttika (October-November) and the months with the new moon. The two most important eras are the Sakabda and the Samvat.

The Sakabda or Salivahana era (AD 78), now used throughout India, is the most important of all. It has been used not only in many Indian inscriptions but also in ancient Sanskrit inscriptions in Indochina and Indonesia. The reformed calendar promulgated by the Indian government from 1957 is reckoned by this era. It is variously alleged to have been founded by the Hindu king Salivahana. To reduce Saka dates to dates AD, 78 must be added for a date within the period ending with the day equivalent to December 31 and 79 for a later date.

The Samvat or Vikrama era (58 BC) is said in the Jain book Kalakacaryakatha to have been founded after a victory of King Vikramaditya over the Sakas. But some scholars credit the Scytho-Parthian ruler Azes with the foundation of this era. It is sometimes called the Malava era because Vikramaditya ruled over the Malava country, but it was not confined to this region, being widespread throughout India. The years reckoned in this era are generally indicated with the word vikramasamvat, or simple samvat. To reduce Vikrama dates to dates AD, 57 must be subtracted from the former for dates before January 1 and 56 for dates after.

The Bengali era is also known as the Laksmana era (AD 1119) said to have been founded by the king Laksmanasena of Bengal and still used throughout Bengal and preserved until modern times. To convert Bengali era to AD, 593 years must be added. The Caitanya era starts from the appearance of Caitanya Mahaprabhu in 1486. To convert the Caitanya era to dates AD add 1486 years to the Caitanya date. The Caitanya dating system is only in use by Caitanya Vaisnavas.






Hindu Astronomy - Guest - 08-25-2006

<b>Pluto demotion vindicates Aryabhatta </b>
Press Trust Of India
Posted Friday , August 25, 2006 at 20:17
Updated Friday , August 25, 2006 at 22:18

<i>ARYABHATTA'S ASTROLOGY: Aryabhatta and Varahamihira had ruled out Pluto as a planet in the sixth century.</i>

Mumbai: Indian astrologers on Friday said the announcement about dropping Pluto as a planet had endorsed the mathematical and astrological treatises written by Aryabhatta and Varahamihira centuries ago.

<b>"Indian astrology did not include Pluto as a planet and the latest announcement by leading global astronomers after a marathon week-long meeting at Prague on Thursday only endorsed the Indian mathematical astrology of Aryabhatta and Varahamihira in the sixth century," </b>eminent mathematical astrologer Mangal Prasad told PTI.

"Western astrology uses Pluto as a planet while Pluto was always out of Indian astrology and we do not use it in our calculations. This is the practice from the days of Aryabhatta and Varahamihira," Prasad said.

"Indian astrology is mathematically concerned with the nine planets, two of which are Rahu and Ketu that are nothing but derivatives from the diameter of the Earth, which is a circle having a value Pi (22/7) imbedded in the equator of earth," he said.

<b>"This was discovered and mathematically shown by Aryabhatta and Varahamihira in the sixth century during the golden period of the Guptas," </b>said Prasad, the author of books based on the work of the two great sixth century scientists.
<b>Indian astrology is concerned more with astronomy and the derivations are from the equator of the Earth, diameter of the moon, the solar year and how the planets are viewed in the northern lattitudinal region during January and February, soon after the sun has crossed the Tropic of Capricon and moved towards the northern part of the hemisphere,</b> he said.

http://www.ibnlive.com/news/aryabhatta-sai...t/19719-11.html


"A warrior relaxes and abandons himself; he fears nothing.Only then will the powers that guide human destiny open the road for a
warrior and aid him. Only then...."

Hindu Astronomy - Hauma Hamiddha - 09-06-2006

In Greco-Roman star lore the constellation Auriga is the charioteer. Traditionally, in India too the constellation is refered to as the sArathi, which means the same thing. The mainstream Western scholarship has believed that this is a recent acquisition of the constellation name from the Greco-Roman world.

If Auriga is the charioteer, where is his car? India star-lore records an unsual name for the Hyades cluster in constellation of Taurus: rohINi shakaTa: The cart of roHiNi (alpha Tauri) [sUrya siddhAnta, 8.13]. Not surprisingly, the constellation is also called the shakaTa of prajApati or brahmA [ pa~ncha siddhAnta 238-241]. Traditionally, Hindu astronomy records the star Capella (alpha-Aurigae) as brahma-hR^idaya (the heart of brahmA). This suggests that the Hyades, which indeed look like a simple cart was the cart of rohiNi or prajApati, thus linking the cart to the charioteer. Hence, while lateral Greco-Roman influence cannot be ruled out entirely, it is likely that the basic concepts concerning this constellation go back to the misty Indo-European past when Greeks and Indians shared a common ancestor.

The rohiNI shakaTa bheda is a peculiar conjunction mentioned repeatedly in Hindu astronomy. It is technically defined in the sUrya-siddhAnta (8.13) thus:
vR^iShe saptadashe bhAge yasya yAmyo .aṃshakadvayAt |
vikShepo .abhyadhiko bhindyAd rohiNyAH shakaTaM tu saH ||
In the constellation of vR^iSha (Taurus), at 17th degree, a planet of which the latitude is a little more than 2 degrees, south, will split the cart of rohiNI.
In his bR^ihat saMhitA, varAhamihira mentions that the planets that are considered for this conjunction are arkanandana (the son of the sun, the inauspicious shanaishchara- Saturn), rudhira (the red Mars) or shikhI (a tufted one or a comet). varahamihira himself cites the Atharvavedic astronomer vR^iddha garga (author of the atharvanic nakShatra hymns, although I was unable to locate a direct reference to the event in the surviving sUkta-s and nivid-s of garga from the atharvan saMhitA as well as nakShatra kalpa) as the authority who described this type of conjunction. The shakaTabheda is believed by the Hindus to be a harbringer of immense destruction or the flooding of the world by the ocean. The medieval Maharatta astronomer gaNesha daivaj~na correctly noted that the shakaTabheda by the Moon was relatively common but that by Saturn or Mars was not possible in the current yuga and might possibly occur/ed in some very distant yuga.

The shakaTabheda by Mars or Saturn is a rather remarkable conjunction, which would, based on the sUrya siddhAnta definition, essentially place these planets in between the triangle formed by alpha, epsilon and gamma Tauri. Most western scholars have believed that this is a typical fanciful Hindu exaggeration that was never observed actually in the sky. However, Hindu astronomers never claimed to have observed it themselves, and gaNesha daivaj~na even clearly states that it is not possible in the current yuga and may be something of a distant yuga. The pioneer of Hindu astro-chronology, SB Dixit in the late 1800 began an investigation astronomical references of the Hindus with the objective of dating them. With the then available ephimerides of the Maharatta astronomers he calculated a shakaTabheda by Saturn in 5371 BC, but with modern planetary data this was shown to be unreal.

More recently Indian astronomer Vahia and his coworkers have used modern ephimerides and the commercial program Skymap to show that shakTabheda by Saturn is indeed unlikely to have really happened since 10,000 BCE. However, they provide evidence that shakaTabheda by Mars did happen 4 times between 10,000 BCE and now. The dates they arrive at are: 5284 BCE (7287 BP), 9339 BCE (11,342 BP), 9371 BCE (11,374 BP) and 9860 BCE. Based on this they conclude that shakaTabheda was based on genuine observations. They argue that given that it was known to Hindu astronomers that shakaTabheda-s by the two planets were not at all observed in their yuga and their correlation with global catastrophes was of little general astrological value it must be real tradition. Vahia et al go ahead to make an even bolder claim that these dates for shakaTabheda by Mars generally overlap with periods to flooding caused by rises in sea level as can be judged from recently available sea-level records. These sea-level changes occured over relatively prolonged periods. So it is not clear if there were sharp correlations and this is the weakest aspect of their proposal. But it is not impossible that some ancient traditions formed around particular conjunctions. If this claim were true then the shakaTabheda by Mars will be one of the oldest recorded events surviving in Hindu tradition. It is already known that Hindu tradition preserves memory of fairly ancient conjunctions like the one observed at the start of the traditional kali yuga. The planetary conjunction of 3102 BCE in the region of the constellation of Pisces can be verified with modern ephimerides and there is not much doubt that this was observed rathern than back-calculated because it was in fact not a particularly dramatic conjunction in any case.

Thus, the contention of von Dechend and de Santillana regarding preservation of astronomical knowledge in the language of myth over great stretches of time seems to be supported by Hindu astronomical observations.

Hindu Astronomy - Guest - 09-13-2006

<b>The ruling races of prehistoric times in India: southwestern Asia, and southern Europe</b>

Read Essay VII

Hindu Astronomy - acharya - 10-21-2006



Why 108 ?

Dr Koenraad ELST, Ph.D.



In the Hindu-Buddhist civilizational sphere, the number 108 is among the most sacred and appears as the true or fictitious cardinal number of all manner of philosophical sets and religious series. What makes this number so special? We will try to position ourselves as best as possible into the minds of profundity-oriented symbolists in order to extract their kind of meaning from this unusual number.


Insufficient reasons



Since matters of religious symbolism typically attract self-styled esotericists who have a dislike for serious logical ratiocination, the usual explanations of the sacred status of the number 108 don’t amount to much. Just as those people “explain” the status of the number 12 by merely enumerating “the 12 months, the 12 apostles” etc., they will merely enumerate a number of instances where the number 108 is in evidence.

Thus, I have seen it claimed by Western esotericists that 108 = 6² + 6² + 6², the sum of the squares of the three equal numerals making up the Biblical-Apocalyptic “number of the Beast”, 666. The calculation isn’t incorrect, but it remains unclear why squares should be counted, or why 666 should be of any importance. This number has some strange numerical properties in its own right, but they are not the reason for its popularity among the mystery-minded. The real reason is that through a numerical-alphabetical manipulation best known by its kabbalistic name gematria, the number refers to a Roman emperor disliked by the first Christians who called him “the Beast”. Emperor or “Caesar” seems to be the meaning of the component 60, this being the numerical value of the Greek letter Ksi, shorthand for its Greek rendering Kaisar. This probably doesn’t refer to Nero, as has been assumed for long, but to “Divus Claudius”, the 6th emperor, who came after Julius Caesar, Octavian August, Tiberius, Germanicus (who received the imperium maius but was murdered; his caesarian status is shown by the fact that the succession devolved to his sonSmile, Caligula. Even Claudius’ mother considered Claudius ugly like a beast, and his initials DC were read in Latin as the number 500 + 100 = 600. So, probably 666 means “the 6th Caesar/60, named D.C./600”.

Admittedly, there are other explanations, but whatever the details, the reference to “the number of the Beast” is merely an expression of the abysmal hatred of Rome by some early Christians, a mere footnote in history. At any rate, the abusive religio-political slogan “666” is totally irrelevant to any serious philosophy. It is equally irrelevant to Hindu-Buddhist culture, and relating it to the status of 108 is anachronistic since it appeared on the scene centuries after the number 108 gained its aura of sacredness.

Even where the explainers try to prove their point with proper Hindu-Buddhist examples, they fail to get to the bottom of the matter. Thus, the Upanishads (philosophical texts completing the Vedic corpus) are classically counted as 108, eventhough their actual number, depending on which ones you include, can range from 13 to more than 200. Rosaries east of the Indus have 108 beads, the Nepalese parliament has 108 seats. The poses of Bhârata Natyam dancing, the number of gopî-s (cowgirls) enamoured of Krishna, the number of sacred sites in the tradition of Vishnu worship, the number of Buddhist arhat-s (realized saints), and many other sacred sets are all conventionally counted as 108. Likewise with derived numbers, e.g. the Rg-Vedic verses are conventionally counted as very approximately 10800, the Purâna-s as 18, the Bhagavad-Gîtâ has 18 chapters, and many Hindu monks carry titles like “Swâmi 1008 Padmânanda”.

All very fine, but that list doesn’t explain anything. The number 108 has been chosen in these instances, and often forced upon rather unwilling sets as their cardinal number, because it was already a sacred number to begin with. We need something more objective as a basis for the special status of this number.

Among attempts to find a more solid basis, we still have to be wary of cheap and easy proposals. Thus, I have seen it claimed that “108 x 20 = 2160, the number of years spent by the equinox in each Zodiac sector”, on the assumption that the total precessional cycle takes 2160 x 12 years, i.e. 25,920 years or neatly 1° per 72 years (and the extra assumption that the Vedic seers knew and cared about the precessional cycle). But in reality, the cycle takes ca. 25,791 years, which doesn’t yield any round number when divided by 108.

It is already better to note that 108 lurks in a corner of the Hindu (or actually Indo-European) number 432 with any number of zeroes added. Thus, 432,000, the number of years sometimes attributed to a Yuga, a world age, which happens to be equal to the number of guardians of the Germanic Walhalla or heaven (viz. 800 for every one of its 540 gates), can be analysed as 108 x 4000. Or as 18 x 24000, for that matter. This is true, but is it important? Many numbers are related to other numbers. Is it relevant to anything?

So, we will try to do better than that and give correct data which underlie the special status of our sacred number in a more compelling manner. We will distinguish between a pair of contingent astronomical facts singling out the number 108 and four mathematical properties of the number 108, two of these conditional and two unconditional.


Solar and lunar distances


<span style='color:blue'>
It could have been otherwise, but it so happens that the distance between the earth and the sun equals about 108 (actually 107-odd) times the sun’s diameter. Likewise, it so happens that the distance between the earth and the moon equals about 108 (actually 109-odd) times the moon’s diameter. That sun and moon look equally big in the earthly sky is the immediate result of their having the same ratio between distance and diameter. Moreover, it so happens that the sun’s diameter approximately equals 108 times the earth’s diameter.</span>

These are contingent data, which means that they could have been different. And they are subject to change, meaning that if you look deep enough into the past or the future, you find values considerably different from the present ones of ca. 108. While the distance between the sun and its planets is fairly stable, the distance between the earth and the moon is subject to steady and ultimately very sizable changes. In the times of the dinosaurs, the moon was so close to the earth that a lunar revolution (i.e. a month) took only a few earthly days, with the days themselves also being shorter than today. In the future, the lunar revolution will take thirty days, forty days, etc. Its distance from the earth will then equal 110 lunar diameters, 120 etc.

It is a cosmic stroke of luck that the solar and lunar distances happen to match the number 108, a remarkable number for non-contingent reasons we will discuss below, right at the time when life on earth was reaching a level of intelligence sufficient to start astronomical observations and wonder at this coincidence. Just as it is a cosmic stroke of luck that in this same age, the moon is at such a distance from the earth that its annual number of revolutions is approximately 12, another number with unique non-contingent properties.

Can we be sure that this remarkable astronomical state of affairs has played a role in the selection of 108 as a sacred number? Did the ancient Indians know about the moon’s diameter or its distance from the earth? According to Richard L. Thompson (Mysteries of the Sacred Universe, Govardhan Hill Publ. 2000, p.16, p.76), the medieval Sûrya-Siddhânta gives an unrealistically small estimate for the distance earth-sun, but the estimate for the distance earth-moon and the lunar diameter differs less than 10% from the modern value. The ratio between distance and diameter of the moon is implicitly given there as 107.5, admittedly a very good approximation.

However, I have never heard of any text, whether from the Vedic or the medieval period, that explicitly derives the importance of the number 108 from these or any other astronomical data. But this is merely an argument from silence, with limited proof value. For on the other hand, the estimation of the relative distance of sun or moon isn’t that difficult to calculate even without any instruments: “Take a pole, mark its height, and then remove it to a place 108 times its height. The pole will look exactly of the same angular size as the moon or the sun.” (Subhash Kak: “Shri 108 and Other Mysteries”, Sulekha.com, 27 Nov. 2001) Also, in some respects the Vedic-age astronomers were more advanced than their medieval successors, who had jettisoned part of their own tradition in favour of Hellenistic import.

So, it remains speculative but quite possible that the solar and lunar data were estimated with a good degree of accuracy at the time when 108 was selected as a sacred number. But it is also possible that the selection was made purely on the basis of the non-astronomical considerations discussed in the following sections.

Big 1, little 8



One of the arithmetical properties of 108 is dependent on the choice of counting system. In the near-universally used decimal counting system, the quantity 108 is expressed as “108”, meaning “1 hundred, 0 tens, 8 units”. In other counting systems, it would look different, e.g. in a duodecimal (12-based) system, it would be written as “90”, and in the binary system, it is written as “1101100”. Assuming the conventional decimal system, what is remarkable about “1-0-8”?

Like 18, it brings together the numerals 1 and 8, with the former in the leading and the latter in the lowly position. The main difference (valid even more in subsequent numbers like 1008) is merely that an abyss of worshipful distance is created between the regal 1 and the servile 8. So, let us briefly focus on this symbolism of 1 and 8. It is chiefly remarkable as a reference to yet other important symbols.



8 1 6

3 5 7

4 9 2



In the magic square of 9, there is 1 little square in the middle and 8 on the periphery. Also, the 1 central number is 5, the sum of the 8 peripheral numbers is 40, yielding a ratio of 1:8. The magic square itself, with equal sums of the three numerals on every line, is an important symbol of cosmic order, balance and integration. Painted on walls or wrought into little metal plates it is used as a luck-charm.

Moreover, consider the sums in the magic square, adding the central number and a number in the middle of the sides, yielding the number in an adjoining corner (counting only the units): 5 + 1 = 6; 5 + 7 = 2 (12 modulo 10, as it were); 5 + 9 = 4 (14 modulo 10); 5 + 3 = 8. If you draw lines following the numerals in these sums, you get the Swastika, yet another lucky symbol in Hindu-Buddhist culture.

The “nine planets” of Hindu astronomy are also often depicted in a square arrangement for ritual purposes such as the Navagraha Agnihotra (nine-planet fire ceremony), with the sun in the middle and the 8 others around it: moon, Mercury, Venus, Mars, Jupiter, Saturn, Râhu (northward intersection of lunar orbit and ecliptic, “Dragon’s head”) and Ketu (southward intersection, “Dragon’s tail”). So, 18 or 108 may add some detail to the symbolism of 9 as representing the planets. This is, however, of lesser importance than the magic square because the number of planets is contingent and changeable whereas mathematical properties are intrinsic and forever.



The Golden Section and 108°



A conditional geometrical property of 108 is dependent on the conventional division of the circle into 360°. This division is arithmetically very practical, it also alludes to the division of the year in ca. 365 days, it is now universally accepted, yet it is contingent and essentially only the result of a human convention. At least one alternative division is known, viz. the division into 400° introduced during the French Revolution on the assumption that the division into religion-tainted numbers like 7 and 360 was less “rational” than the division into 10 or 100 or their multiples. Hence also the Revolutionary replacement of the 7-day week by a 10-day week and the definitional choice of the meter as one hundred-thousandth of one “decimal degree” measured on the earth’s equator of 40,000 km.

But for now, we may settle for the division in 360°. In that case, the angle of 108° has a unique property: the ratio between the straight line uniting two points at 108° from each other on a circle’s circumference (in effect one of the sides of a 10-pointed star) and the radius of that circle equals the Golden Section. Likewise, the inside of every angle of a pentagon measures 108°, and the pentagon is a veritable embodiment of the Golden Section, e.g. the ratio between a side of the 5-pointed star and a side of the pentagon is the Golden Section. So, there is an intimate link between the number 108 and the Golden Section. But why should this be important?

The Golden Section means a proportion between two magnitudes, the major and the minor, such that the minor is to the major as the major is to the whole, i.e. to the sum of minor and major. The general equation yielding the Golden Section is A/B = (A + B)/A, or alternatively but equivalently, X = 1 + 1/X. In numbers, X = (1 + square root 5)/2; or decimally, X = 1, 618… This infinite series of decimals can be replaced with a more predictable infinite series of numbers, viz. X equals the limit of the series G/F in which F is any member and G is the very next member of the Fibonacci series, i.e. the series in which every member equals the sum of the two preceding members: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,… This means that every next fraction G/F, i.e. 1/1, 2/1, 3/2, 5/3, 8/5 etc. forms a better approximation of the Golden Section, whose value can be approximated to any desired degree of precision if fractions of sufficiently highly-placed members of the Fibonacci series are considered.

In art and architecture, it is found that the Golden Proportion is naturally pleasing to our inborn tastes. In living nature, there are plenty of sequences where every member stands to the preceding member in a Golden Proportion or its derivatives (square root etc.), e.g. the distances between or the sizes of the successive twigs growing on a branch, the layers of petals on a flower, the rings of a conch, the generations of a multiplying rabbit population, etc. What this symbolizes is the law of invariance: in every stage of a development, the same pattern repeats itself. The son is to the father as the father was to the grandfather. Wheels within wheels: every whole consisting of parts is itself likewise part of a larger whole. And the principle of order: the underling obeys the orders of his master to the same extent that the master obeys the requirements of the whole. Or with a pre-feminist maxim: “he for God alone, she for God in him”, i.e. the wife serves the husband because (and to the extent that) the husband serves the cosmic order defining his duties. As Confucius said, the authority of the ruler, his capability of making the people willingly obey him, is that he himself obeys the Laws of Heaven.

So, the Golden Section is a meaningful symbol in the cosmological, aesthetical and ethical realms. And somewhere in a corner of Golden Section lore, in the pentagon and decagon, we see the number 108 participating. This is meritorious though perhaps a bit too indirect to count as sensational.



Sacred 9 times sacred 12



An intrinsic and ever-unchangeable property of 108 is that it equals 9 times 12, the product of two smaller sacred numbers. It is the number of divisions in the Zodiac in the so-called Navamsha horoscope, a horoscope which Hindu astrologers always calculate along with the basic horoscope, and in which all original positions expressed in angular distance from the beginning point of the Zodiac are multiplied by 9. This implies, for example, that a planet at 8° Aries is projected to 72°, meaning 12° Gemini. In effect, the whole sector between 6°40’ and 10° Aries is projected onto Gemini (i.e. between 60° and 90°) and given a Gemini colouring, just as the sector between 10° and 13°20 Aries is navamsha-projected onto Cancer, etc. This way, every one of the 12 signs is subdivided into 9 sectors, or 108 in total. But of course, this doesn’t explain the status of 108, as the idea of subdividing the Zodiac this way apparently results from the awe in which 108 or 9 x 12 was already held.

As we have seen, 9 is the Hindu number of planets, and 12 is the Zodiac, so 108 is the total number of planet-in-Zodiacal-sign combinations. This makes it into the total set of all possible planetary influences taken separately, or in a more generalized symbolism, the matrix containing all possibilities. However, to purists, 9 as the number of planets isn’t good enough. For one thing, the Hindu definition of a planet is pre-heliocentric, counting sun and moon and their two eclipse points as planets all while failing to count the earth as a planet (though it so happens that planets by the modern astronomical definition are again counted as 9, from Mercury to Pluto including the earth). Also, planets may be added through empirical discovery, as some have indeed been in astronomy and in Western astrology; and in some rare but not-impossible catastrophe, a planet may disappear. They are only creatures, born from dust and returning to dust. If we’re looking for intrinsic properties of numbers, we should not settle for contingent data such as the present number of Hindu “planets”.

To the unique properties of 12, revealing it to be a logical symbol of cosmic order, we have devoted a separate paper, Why Twelve?, where we have focused on its unconditional properties, both arithmetical and geometrical. We may add that, conditional upon the choice of the decimal system, 12 is structured as 1 tenfold plus 2 units: 1 big, 2 small. Which to a freely-associating symbolist mind can mean: 1 precedes 2 (as indeed it does, in fact it is the most elementary observation to be made in the number series, e.g. long preceding the realization that there must be a zero), unity is superior to division, oneness precedes and underlies polarity, the odd/yang dominates the even/yin. Note however that for all their inequality, the numbers 1 and 2 and all that they symbolize are at any rate united and synthesized in the number 12 and in whatever the latter symbolizes. Meanwhile, this conditional arithmetical property of 12 must remain inferior to the unconditional properties of 12, especially those of 12 conceived geometrically as the regular dodecagon, e.g. the fact that its construction uniquely flows automatically from the construction of the circle, keeping the same compass width; and the fact that it bridges the gap between straight/radius and round/circumference by dividing both rationally in a single move (the radius into 2, the quarter-circumference into 3).

Like 12, the number 9 has its unusual properties. Once more, we cannot be satisfied with simply enumerating instances where 9 has been used in a sacred context: the 9 worlds of Germanic cosmology, the 9 Muses, etc. We want objective properties, and when looking for these, we must again distinguish between conditional and unconditional properties. Thus, it is often remarked that 9 is the highest among the decimal numerals, and hence symbolizes anything that is highest, including God, who, in comparison with anything you may propose, is always Greater. However, this property is conditional upon our choice of numeral system, i.c. decimal rather than binary or any other: in the binary system, the number 1 would have this property, and in the duodecimal one, the number eleven would. Likewise, 9’s property of equalling the sum of the numerals in its own multiples (e.g. in 9 x 8 = 72, we find that 7 + 2 = 9) is again dependent on our choice of the decimal system.

For unconditional properties, we might look at some characteristics of the enneagon (9 x 40°). This is the first polygon with a non-prime base (as distinct from the heptagon, 7 being a prime number) that eludes construction with ruler and compass. This contrasts sharply with the division of the circle into 4 or 6 or 12, which is so simple and natural, or with its division into 5 or 10, which is more complicated but very rewarding (yielding the Golden Section) and at any rate possible. So, 9, though analysable as 3 x 3, is elusive. Does anyone care to read some symbolism into this property? If 7 represents the mystical eluding the rational, what should be represented by 9, which is more structured yet equally eludes rational construction? Let’s see: how about God, who always eludes our concepts? Allahu Akbar, God is greater!

But we need not look that far. Whatever else 9 may be, its most immediate arithmetical property is certainly that it equals 3², or 3 x 3. Unlike the neat balance of even numbers like 2 or 4, suggesting stability and a waiting matrix of potentialities, the number 3 expresses motion, as even the most vulgar book on number symbolism will tell you. The number 9, therefore, is a movement affecting the movement, i.e. acceleration. It is dynamic par excellence, Shakti as the dynamic expression of static Shiva. The primal form of acceleration is the change from rest to motion, i.e. setting things in motion, starting the whole process from zero. This, of course, is the doing of the Creator who is Greater. Or as the Scholastics used to say: God is not Potency, God is pure Act.

So, whereas 12 represents synthesis of opposites within an ordered cosmos (3 x 4, time-space, motion-structure) and harmonization of self and non-self, 9 represents unfettered dynamism, pure self-expression riding roughshod over the non-self, the joy of being entirely oneself. It transcends and leaves behind all compromise in favour of purity and absorption. Its structure as 3 x 3 actually explains its elusiveness: whereas divisions of any angle into 2 and its multiples are always feasible and simple, the division into 3 is impossible, though very good approximative techniques have been developed. Even folding a letter into three requires a manual jump, an approximation rather than a slow but sure technique guaranteeing an exact division into equal parts. The enneagon is the first regular polygon which requires for its construction the trisection of a known angle (120°, itself easily constructed though not by trisecting the “angle” of 360°), an impossible operation with ruler and compass. Likewise, according to poets, the Absolute cannot be caught in a conceptual net but can only be approximated, hinted at, spoken of in parables and metaphors.

Let’s put ourselves into the mood of god-seekers in order to understand this. As 9 x 12, the number 108 infuses the cosmic order represented by 12 with the god-drunkenness, the enthusiasm free of all doubts, the pure dedication represented by 9. That makes it an excellent number for the prayer-wheel or rosary, which is used in a disciplined and systematic manner in order to lift up the spirit towards god-absorption.



Square times cube



Among other intrinsic and ever-unchangeable properties, it may be hard to choose which one is sufficiently relevant. Thus, 108 equals the sum of the first 9 multiples of 3, viz. 0, 3, 6, 9, 12, 15, 18, 21 and 24. This reconfirms its intimate relation with the richly symbolic number 9, but then, so what?

Slightly more remarkable is that 108 equals the product of the second power of 2 and the third power of 3, i.e. the first non-trivial even and odd numbers multiplied by themselves as many times as themselves. In figures: 108 = 2² x 3³, or 108 = 2 x 2 x 3 x 3 x 3. This way, it unites on their own terms the polar opposites of even and odd, the numerical counterparts of female and male, yin and yang, etc. If nothing else, at least it’s cute, is it not? That may well be the most we can expect of number symbolism.



(copyright: author, October 2003)



(in case we have missed some important symbolically-charged properties of the number 108, we welcome feedback at: koenraadelst@hotmail.com)


http://koenraadelst.voiceofdharma.com/arti...isc/why108.html


Hindu Astronomy - acharya - 10-21-2006

The Significance of the number 108

The Indian Subcontinent rosary or set of mantra counting has 108 beads. 108 has been a sacred number in the Indian Subcontinent for a very long time. This number is explained in many different ways.

The ancient Indians were excellent mathematicians and 108 may be the product of a precise mathematical operation (e.g. 1 power 1 x 2 power 2 x 3 power 3 = 108) which was thought to have special numerological significance.

Powers of 1, 2, and 3 in math: 1 to 1st power=1; 2 to 2nd power=4 (2x2); 3 to 3rd power=27 (3x3x3). 1x4x27=108

Sanskrit alphabet: There are 54 letters in the Sanskrit alphabet. Each has masculine and feminine, shiva and shakti. 54 times 2 is 108.

Sri Yantra: On the Sri Yantra there are marmas where three lines intersect, and there are 54 such intersections. Each intersections has masculine and feminine, shiva and shakti qualities. 54 x 2 equals 108. Thus, there are 108 points that define the Sri Yantra as well as the human body.

9 times 12: Both of these numbers have been said to have spiritual significance in many traditions. 9 times 12 is 108. Also, 1 plus 8 equals 9. That 9 times 12 equals 108.

Heart Chakra: The chakras are the intersections of energy lines, and there are said to be a total of 108 energy lines converging to form the heart chakra. One of them, sushumna leads to the crown chakra, and is said to be the path to Self-realization.

Marmas: Marmas or marmastanas are like energy intersections called chakras, except have fewer energy lines converging to form them. There are said to be 108 marmas in the subtle body.

Time: Some say there are 108 feelings, with 36 related to the past, 36 related to the present, and 36 related to the future.

Astrology: There are 12 constellations, and 9 arc segments called namshas or chandrakalas. 9 times 12 equals 108. Chandra is moon, and kalas are the divisions within a whole.

Planets and Houses: In astrology, there are 12 houses and 9 planets. 12 times 9 equals 108.

Gopis of Krishna: In the Krishna tradition, there were said to be 108 gopis or maid servants of Krishna.

1, 0, and 8: 1 stands for God or higher Truth, 0 stands for emptiness or completeness in spiritual practice, and 8 stands for infinity or eternity.

Sun and Earth: The diameter of the sun is 108 times the diameter of the Earth.

Numerical scale: The 1 of 108, and the 8 of 108, when added together equals 9, which is the number of the numerical scale, i.e. 1, 2, 3 ... 10, etc., where 0 is not a number.

Smaller divisions: The number 108 is divided, such as in half, third, quarter, or twelfth, so that some malas have 54, 36, 27, or 9 beads.

Islam: The number 108 is used in Islam to refer to God.

Jain: In the Jain religion, 108 are the combined virtues of five categories of holy ones, including 12, 8, 36, 25, and 27 virtues respectively.

Sikh: The Sikh tradition has a mala of 108 knots tied in a string of wool, rather than beads.

Chinese: The Chinese Buddhists and Taoists use a 108 bead mala, which is called su-chu, and has three dividing beads, so the mala is divided into three parts of 36 each.

Stages of the soul: Said that Atman, the human soul or center goes through 108 stages on the journey.

Meru: This is a larger bead, not part of the 108. It is not tied in the sequence of the other beads. It is the quiding bead, the one that marks the beginning and end of the mala.

Dance: There are 108 forms of dance in the Indian traditions.

Pythagorean: The nine is the limit of all numbers, all others existing and coming from the same. ie: 0 to 9 is all one needs to make up an infinite amount of numbers.

We have listed below 108 Upanishads as per the list contained in the Muktikopanishad . We have arranged them in four categories according to the particular Veda to which each of them belong.

Rigveda(10): Aitareya , Atmabodha, Kaushitaki, Mudgala, Nirvana, Nadabindu, Akshamaya, Tripura, Bahvruka, Saubhagyalakshmi.

Yajurveda(50): Katha, Taittiriya , Isavasya , Brihadaranyaka, Akshi, Ekakshara, Garbha, Prnagnihotra, Svetasvatara, Sariraka, Sukarahasya, Skanda, Sarvasara, Adhyatma, Niralamba, Paingala, Mantrika, Muktika, Subala, Avadhuta, Katharudra, Brahma, Jabala, Turiyatita, Paramahamsa, Bhikshuka, Yajnavalkya, Satyayani, Amrtanada, Amrtabindu, Kshurika, Tejobindu, Dhyanabindu, Brahmavidya, YogakundalinI, Yogatattva, Yogasikha, Varaha, Advayataraka, Trisikhibrahmana, mandalabrahmana, Hamsa, Kalisantaraaa, Narayana, Tarasara, Kalagnirudra, Dakshinamurti, Pancabrahma, Rudrahrdaya, SarasvatIrahasya.

SamaVeda(16): Kena, Chandogya, Mahat, Maitrayani, Vajrasuci, Savitri, Aruneya, Kundika, Maitreyi, Samnyasa, Jabaladarsana, Yogacudaman, Avyakta, Vasudevai, Jabali, Rudrakshajabala.

Atharvaveda(32): Prasna , Mandukya, Mundaka, Atma, Surya, Narada-Parivrajakas, Parabrahma, Paramahamsa-Parivrajakas, Pasupatha-Brahma, Mahavakya, Sandilya, Krishna, Garuda, Gopalatapani, Tripadavibhuti-mahnarayana, Dattatreya, Kaivalya, NrsimhatapanI, Ramatapani, Ramarahasya, HayagrIva, Atharvasikha, Atharvasira, Ganapati, Brhajjabala, Bhasmajabala, Sarabha, Annapurna, TripuratapanI, Devi, Bhavana, SIta.

The Significance of the number 108

We must agree that all measuring systems are merely reference frames. They give us a starting point. It doesn’t really matter if you call them farenheits or cycles. All science is based on fundamental assumptions of the mechanics of this universe. Yet, these assumptions, if correct, connect like building blocks.

Much in the same way, the number ‘108’ is just a reference frame. It is symbolic of a bigger picture: that of humility. When devotees recite 108 Hanuman Chalisas, in their minds they believe, they are proving their love for God, and that there is in fact a need to prove their love. When devotees assign a 108 names to Shri Ganesh, they are once again gauging their devotion through numbers. This, of course, may be considered unreasonable, since it suggests that 108 chants are more effective than 109 chants. How do they know this? Have they proved it? Is 108 the magic number of the universe? No, it is not! It is a reference frame. What is important is that a system is imposed to guide us through the fundamental struggles encountered in any evolutional process. Otherwise, chaos and anarchy follow and nothing gets done.

Having said that, I will show you justifications from a few subcultures in India. Obviously, I consider the Vedic rationale to be the most consistent with the fundamental laws of this universe. The others have borrowed and built, but it still smells of Vedic beginnings.

In present times, we can find many rationales for the proliferation of ‘108’ throughout our scriptures. In fact, this number seems to garner its unfair share of attention from myriad cults and faith systems around the world. I will give you a few justifications that have been brought to my attention.

JYOTISH SHASTRA {VEDIC SYSTEM}
This universe was created by the five elements: space, air, fire, water and earth. From these elements came the three attributes: Raj {birth}, Sat {protection} and Tam {destruction or death.}

The mathematical or geographical evidence proves that one circle has 360 degrees in space. Why is this circle or wheel of life considered to be of 360 degrees only? If we take a circle and start dividing it using the four elements and three attributes, all the logic can be observed.

The circle itself, is considered the first element of space, since we must consume space in drawing a circle. In this space {or circle}, the four remaining elements and three attributes create the idea of time. The circle is divisible by the product of four elements multiplied by three attributes. This involves the belief that the three attributes exist in the circle. By moving three times, each element completes its revolution.

So now we have the number 12 {3 x 4}. This division gave birth to our 12 months, and also to the 12 horas {1/2 of the day or Ahoratri}. We now have 360 degrees as well as 12 divisions. We can now further divide the wheel of time: there are 27 fixed stars (nakshatras) along with three attributes that divide the time in smaller portions. So this 27 + 3 = 30 is interpreted as 30 degrees or days of one part of the wheel (circle) or month. All of this is only half of a day. The night is yet unaccounted for. Therefore, we multiply these 30 degrees by 2. This gives us our reference of 60 seconds in a minute.

Thus the 360º x 30º = 10,800. Zero {0} is considered ‘Purna’ or complete. So we take out the last zeros and are left with 108. The idea of our total universe is represented by this number of 108. Offering 108, devotees believe that they are showing ultimate or complete respect to the Supreme.

There are many other justifications but all can be traced back to this system. A few are explained below:

SHOSHU BUDDHIST
Followers use 108 beads in their malas. They implement the following formula:
6 x 3 x 2 x3 = 108
6 senses [sight, sound, smell, taste, touch, thought]
3 aspects of time [past, present, future]
2 condition of heart [pure or impure]
3 possibilties of sentiment [like, dislike, indifference]

BUDDHA’S FOOTPRINT
All Buddhists accept the Buddha Footprint with its 108 Auspicious Illustrations. These areas are considered to have been marked on the Buddha’s left foot when his body was discovered.

BUDDHISM
108 beads on the Hindu maalaa {rosary}
108 Arhats or Holy Ones

HINDUISM
108 Gopis {consorts} of Lord Krishna
108 Holy places for Vaishnavas
108 beads on the Japa maalaa {rosary}
108 Upanishads
108 Divyadeshes - Divine or Sacred Tirtha throughout India and Nepal
108 sacred water taps in Muktinath - Nepal

TANTRA SHASTRA
108 Pitha {Sacred Places}
The story goes that Lord Shiva was in deep and incessant meditation. His asceticism was creating great heat in the universe. All existence was in peril and Lord Brahma was deeply concerned. Lord Brahma asked the Mother of the Universe, Maa Shakti, to use Her strength and wile to seduce Lord Shiva. Maa Shakti agreed and was born as Sati, daughter of Shri Daksha. Lord Shiva was so entranced by Sati’s asceticism and extraordinary beauty that he took human form and they were married. Years later, at a feast, Sati’s father insulted Lord Shiva. Sati was so humiliated that she began a deep meditation which led to her immolation. Lord Shiva was completely heart broken. He reached into the sacrificial fire and pulled out as much of His beloved’s body as he could grab. As He ascended to heaven, bits of Sati’s body fell to earth. 108 bits to be precise! In time, these places were acknowledged and worshipped.

SANATANA DHARMA
In a book by Khurana, the explanation closely mirrors the original Vedic justifications:
A circle has 360 degrees, which when multiplied by 60 gives us 21,600 minutes in a circle. 60 comes from the 60 'ghatis' which Sanatana Dharmiks believe in. One ghati is equal to 24 minutes and 60 ghatis come to 24 hours.

One ghati is divided into 60 parts or 'palas'.
So the 60 ghatis multiplied by 60 palasa comes to 3,600.
This is further multiplied by 60 (becase a pala contains 60 vipalas) which gives us 21,600.
Half of this is for the day, and the other half for the night. So, 21,600
divided by 2 gives us 10,800. For practical purposes, we use 108. Using the
number 108 helps us coordinate the rhythm of time and space & we remain in harmony with the spiritual powers of nature.





Hindu Astronomy - acharya - 10-21-2006

On the origin of number 108 from OM

The number 108 is quite significant in Hinduism. Even the rosary used during Hindu prayers has 108 beads. There are several legends about the significance of this number and they are mentioned in “The Significance of the number 108” -- http://www.salagram.net/108meaning.html

In addition to the reasons mentioned in the above article about auspiciousness of number 108, there is another possibility (not considered earlier) as indicated below.

The number 108, for example, may be some kind of numeral representation (in some ancient language, Brahmi, Sanskrit or Tibetan, etc.) of the holy word Om, expanded and written as ‘aum’ or ‘om:’ in that (or other) language.

In other words, the letters / sounds ‘a’, ‘u’ and ‘m’ (or ‘o’, ‘m’ and ‘:’), written in some ancient language, appear identical or somewhat similar, respectively, to the numbers 1, 0 and 8 expressed in the same or another language.

This could have given rise to number 108 becoming the numeral form of the holy word OM (expressed as AUM or OMSmile. Thus the number 108 would be used widely in many legends, religious rituals and articles (e.g. the number of beads in a rosary).

- Seva



Hindu Astronomy - Guest - 11-11-2006

I don't really know much about Hindu astronomy. I'd like to learn more about it. For example, What does Hindu astronomy look like? How does the constellations and zodiacs appear on the map? Is there any connection between the Hindu astonomy and astrology? How does one influence another? And finally, how does Hindu astronomy and or astrology influence the Hindu/Indian Calendars?

Hindu Astronomy - acharya - 11-11-2006

Welcome to IF
Start with Google and Wikipedia

http://en.wikipedia.org/wiki/Hindu_astronomy
http://voiceofdharma.org/books/ait/ch22.htm


http://libibm.iucaa.ernet.in/wslxRSLT.php?A1=858

http://www.crystalinks.com/indiastronomy.html
http://www.sanskrit.org/www/Astronomy/Hindutimeeras.html

<img src='http://www.sanskrit.org/www/Astronomy/rahu.jpg' border='0' alt='user posted image' />

Surya-Siddhanta: A Text Book of Hindu Astronomy (Paperback)
by Ebeneezer Burgess "

This is an translation of a thousand plus year old Hindu textbook on astronomical calculations (originally written in Sanskrit). The English translation is included (verse by verse) along with extensive notes and explanations by the translator. The text gives prescriptions on Hindu calendar calculations (including the rather complicated Hindu lunar calendar), calculating the celestial coordinates of the Sun, Moon and visible planets, along with the ascending and descending node of the Moon, and calculations of the circumstances of solar and lunar eclipses. A prescription is given for creating a sine function table (a Hindu invention) to be used with the astronomical calculations.

This old textbook is not for the mathematically faint of heart. Even the translators extensive notes are difficult in places to wade through. If you have some ability in algebra, trigonometry and geometry and you are persistent you can, however, follow the calculations with the help of the translators notes. Many of the calculations are in base 60 arithmetic (much like our modern hour and minutes of time notations). In places the text and notes are a little difficult to follow. However, there are worked-out-examples of the calculations to help your understanding. I worked through all the calculations for the predictions of a solar eclipse, and, in all but a few places, exactly reproduced the examples given by the translator of the text. The results were quite accurate predictions of the times for solar eclipses. The predictions were most accurate for tenth century eclipses as that is the approximate date of the data provided in the text.

This is a fascinating book if you are interested in ancient astronomical calculations. The Hindu prescriptions appear to be a somewhat modified versions of the calculations prescribed by the second century Greek astronomer Ptolemy in his book the Almagest.




Hindu Astronomy - Hauma Hamiddha - 12-03-2006

The vedA~NGa jyotiSha has been a strikingly difficult text to fathom despite its small size. It is the the late vedic text that appears to be a guide for quick and handy calenderical calculations. It has attracted much attention of Western scholars, despite not understanding much of it. Yet they use it as a starting point to suggest how the Hindus were definitely astronomical idiots. This trend set by the early Western scholars regarding Hindu astronomy is repeated to this date as a part of their program to present the picture of "India as the cul de sac" (vide Michael Witzel, a German Indologist). The view of the early white Indologists on Hindu astronomy is epitomized by the American Indologist Whitney (the translator of the atharva veda)'s comments on the VJ: "And when we come to add that the Jyotisha (VJ) has no definable place in Sanskrit literature, or relation to the Vedic ceremonial.. we shall see that this famous datum, which has seemed to promise so much, has caused so much labour and discussion, and is even yet clung to by some scholars as the sheet-anchor of ancient Hindu chronology, is nothing but a delusive phantom."
While this and succeeding views of the white Indologists and their Japanese imitators have acquired wide currency, Hindu scholars have labored on interpretting the text correctly to a great measure. However, to give where credit is due an early white scholar Thibaut was fairly effective in interpretting a number of verses. The first Hindu scholar to make a major in road was S.B. Dikshit, who labored on this text not far from the place where I spent a good part of my life. Dikshit's work unfortunately did not acquire wide readership because it was written in the Maharatti language. He was followed by the Northerner Chote Lala and Sudhakara Dvivedi the paNDita from Kashi who successfully interpretted a little more of the text, though they were locked in conflict between themselves. The great B.G. Tilak then further clarified some points. The final assault on the text along with a modern English translation was provided by the smArta savant shrI kuppanna shAstrI, who more or less interpretted most of the text. If we can today understand some of the elegant devices of the VJ, it is only because of kuppanna shAstrI's enormous scholarship, setting the true standards for the kind of scholarship needed to tackle complex texts.

The vedic calenderic knowledge which provides the background for the VJ needs some description. There is clear evidence that the vedic kavI-s were fully aware of the precession of the equinox, and they had observations from the remote past of at 4000 BCE or beyond. From the early times the Arya knew of the year being approximately 365 days-- the sAmidhenI hymns contain 360 syllables in the form of 15 gAyatrI-s + the oM bhurbhuvasvaroM forming the year by supplying the remaining days and its fraction. Two great vedic shrauta masters, the pa~nchAla prince babara prAvAhaNi and sArvaseni shaucheya declare the logic behind the pa~ncharAtra sacrifice. They say that the year which is the ya~jna is complete only by adding the 5 days. They say that 4 days is too few while 6 days is two many so to complete the year we add 5 last days to the year . This is how the 365 day approximate year is laid out (TS 7.1.10). Right in the R^igveda the shunaHshepa, the son of ajigarta notes that the intercalary month is used to correct for the imperfect match of the lunar and solar years (RV1.25.8).

Thus, the calenderical system presented by the VJ is not something present in isolation or borrowed from some Middle Eastern source (as some white authors foolishly propose) but it was based on what was considered common knowledge in the vedic sacrificial ritual. There are two extant jyotiSha-s the yajur and R^ik versions that differ some what in their contents but are over-all consistent. There is an atharvaNa jyotiSha, but it is unrelated and mainly a manual for reckoning muhurta. Dating by precession gives the date of the VJ as being around 1300 BC because the it states that the winter solistice was in the beginning for shraviShThA and summer in the mid-point of AshleShA. This is important because in the maitrAyaNi brAhmaNa, shAkhAyanya tells king bR^ihadratha that the winter solistice was in the middle of shraviShThA (MBU 6.14). Thus, the lagadha was clearly aware of the change from the epoch time little before his times. Subsequently, the Hindu encyclopedist varAhamihira, who was an acute observer, writing around 550 AD states that the spring equinox fell 10' East of Zeta Piscium in revatI. An important observation made by Kuppanna Shastri concerns the intermediate period. We have a text of the nagna nAstIka-s, termed sUrya-praj~nApti, where the same system of calenderics as the VJ is expounded. But the jaina-s correct the winter solstice to shravaNa, suggesting that they were after the VJ in the period when you would actually expect the jaina-s to be around. Thus, we have a continuous system of precessional corrections even in the period around the VJ, leave alone the vedic antiquity. Hence, it is clear that the VJ was indeed composed in the period we can astronomically infer.

Interestingly, the total variation in day-light time is given as 6 muhUrta-s which corresponds approximately to the latitude of 35° N. This will be north of kubhA (kabul in modern Afghanistan), and might imply that the observations were inherited from the time the Aryas occupied the BMAC archaeological sites.

Some basics of the VJ:
----------------------
The vedic measures of time as per VJ:
5 gurvakShara-s [long syllables]= 10 mAtrA-s
= 1 kAShTha
124 kAShThA-s = 1 kalA
10 1/20 kalA-s = 1 nADikA*
2 nADIkA-s = 1 muhUrta
30 muhUrta-s = 1 ahorAtra (civil day)
366 days = 1 saMvatsara= 12 mAsa-s
= 6 R^itu-s= 2 ayana-s
5 years = 1 yuga*
This progression is an old vedic system we have in the taittirIya AraNyaka: “kalA muhUrtAH kAShThAsh chaahotrAsh cha sarvavashaH | ardhamAsA mAsA R^itavas saMvatsarash cha kalpantAM ||”

* Time is kept using a water-clock. The volume of water of weight 50 pala-s, at room temperature, is one Adhaka (a volume measure).
4*Adhaka = 1 droNA (a volume); 1/16 of Adhaka = 1 kudava;
In a standard vedic water-clock 1 droNa- 3*kudava is that volume of water that drains in one 1 nADikA. Thus, the vedic water clock drained in 24 minutes or 1 nADikA. The water-clock is mentioned in the kAla sUktaM of the bhArgava-s in atharva veda. Thus, both the time units and the water clock find mention in the veda, suggesting that the systems mentioned in the VJ was a standard aspect of the vedic time keeping.

* A yuga is defined as the “pairing (from the root yug- same as English yoke, Germanic *yuminaz=Gemini)” or coming together of two celestial bodies, or their nodes or their apogees in the same place on the ecliptic. Approximately the moon and the sun meet in the same asterismal position in 5 years. Hence this is the basic yuga in vedic parlance. The years of the yuga were named in the veda as: saMvatsara, parivatsara, idAvatsara, anuvatsara and idvatsara.

The yuga concept clarifies why the saMvatsara is described as 366 days, even though, even babara prAvAhaNi and sArvaseni shaucheya already knew in the days of the yajur veda that 366 was too much. In a yuga there are 366*5= 1830 days (yuga value) and this gives the required approximation for the yuga definition that is meeting of sun and moon in a nakShatra. It also gives a base to derive a number of other critical values for the period of the yuga easily:
1) Number of risings of shraviShThA above the horizon (the nakShatra at the winter solstice) = yuga + 5 = 1835
2) Number of moon rises = yuga-62=1768

The Number of nakShatra-s traversed by the sun in 1830 days is 135. The number of ayanas of the moon 1 less than that number= 134.

The value of the yuga also can be used to relate to the following easily, as explained in the yajur jyotiSha 31:
1) Number of sAvana months in on 1 yuga (that is the traditional months of the vedic ritual) = 61= 30 days
2) Number of synodic months in a yuga, i.e. the period between two new moons in a yuga = 62 = 29.51 days, a reasonable approximation (modern value= 29.530).
3) Number of sidereal months in yuga = 67 = 27.31 (modern value=27.32).

Given any 3 elements of the yuga that are not completely dependent on each other we can get every other element. This is an important computational device of the VJ. Thus, for example
Given any 3 elements of the yuga that are not completely dependent on each other we can get every other element. This is an important computational device of the VJ. Thus, for example:
Number of sidereal days (i.e. the time interval between two successive rising of a star) in a yuga = yuga +5 = 1835
Thus, we have ratio of sidereal day : civil day = 0.99727 (modern value= 0.997269)
So one can see that the for a vedic ritualist at 1300 BC the VJ gives decent quick approximations for key calenderical values using the yuga concept, and can hence be hardly called a primitive work.

titihis and nakShatra's for some key days
-----------------------------------------
The yugArambha is given as when sun and moon are in the nakShatra of shraviShTha in the bright fortnight of the month of magha. Then the determination of the pakSha (kR^iShNa/shukla- k/s) and approximate nakShatras (n) and tithis (t) at the beginning of each of the ayana-s of the sun in the yuga is given:
1 n=shraviShThA, t=1s; 2 n=chitrA t=7s; 3 n=ArdrA, t=13s 4 n=pUrva-proShThapadA, t=4k; 5 n=anurAdhA, t=10k; 6 n=ashleShA, t=1s; 7 n=ashvini, t=7s; 8 n=pUrvAShADhA, t=13s; 9 n=uttara phalguni, t=4k; 10 n=rohiNi, t=10k;
These are days on which the solsticial sacrifices are performed.

The viShuva days or the equinoctial days are the other important ritual days. A formula is given for the number of pakSha-s(p) and tithi-s(t) having elapsed from the beginning of the yuga to the nth viShuva (n):
6*(2*n-1)*(p+.5*t); thus for vishuvan 1 we have 6*pakShas+3*tithis or it occurs on tritIya.
The viShuva is declared as occurring in the shukla-pakSha at the end of the tR^itIya, navamI and paurNaMasya.

Rule for the tithi on which a R^itu begins is thus explained: The number of R^itus in a yuga is 30. The first R^itu of the yuga is shishira, in the month of tapas, as stated in the yajurveda (TS 4.4.11.1), begins on shukla prathama. The next R^itu begins two tithis later on shukla tritIya, the next on shukla 5 panchami and so on till the 8th R^itu begins on paurNamAsya. Then the R^itu-s continue by the formula modulo(1+2*(n-1),15)

The logic of the peculiar division 124
---------------------------------------
Given that there are 62 synodic months in a yuga, we have 124 pakSha-s in a yuga. Hence to keep the calculations as whole numbers the vedic day is divided into 124 parts or aMsha-s. From the earlier table we have a day having 603 kalA-s=74722 kAShTha-s, the latter being divisible by 124. [1 kAShTha=1.1563 seconds; 1 kalA= 2.388 minutes; part of the day/amsha= 11.612 minutes].

The part of the day when the pakSha ends is critical to determining the day when the sarcfices or iShTi-s are performed. The VJ gives the following procedure to figure out the part of the day when a pakSha ends:
The duration of each pakSha = yuga/124= 15 days – 30 parts (amshas) of the day.
Thus duration of each tithi =1 day – 2 parts of a day.
To find the part of the day the nth pakSha ends:
1) For the nth pakSha obtain x= modulo (n,4).
2) If x=1 then y=n+93; if x=2 then y=n+62; if x=3 then y=n+31; if x=0 then y=n
3) The number of parts of the day when the pakSha ends= modulo (y,124).
If the pakSha ends before 31 parts then it ends before civil mid-day.
E.g. 37th pakSha- x= modulo (37,4)=1; y=37+93=130; So the pakSha ends at modulo (130,124)=6. Thus it ends around 1 hour and 9.6 minutes of the day.

So one can see that the for a vedic ritualist at 1300 BC the VJ gives decent, rough and ready approximation for key values using the yuga concept, and can hence be hardly called a primitive work.

Hindu Astronomy - acharya - 12-29-2006

http://www.vedicastronomy.net/index.htm

Hindu Astronomy - acharya - 12-31-2006

http://www.littlemag.com/2000/sen.htm

Hindu Astronomy - Guest - 03-23-2007

I presented some ideas on indic ASTRONOMY AND THEIR IMpact on the chronology og indian history first at HEC, LA and then in India,, This is a powerpoint presentation

Indic Studies FoundationIndic mathematical Traditions _ astronomy



Hindu Astronomy - Guest - 03-23-2007

I have included historians of astronomy in the
lst of indologists that i am preparing. this is a major work , culminating in the cataloging of alll MSS which in my view is in a unsatisfactory state today. Which is why i am starting a google group on the Chronology Projoect.. I would like Hauma to participate in that as well as anybody who has an interest in this sort of thing

http://groups.google.com/group/indic-exact-sciences

The aims of the group are (ambitious)

1.cataloging of all astronomy and mathematics primary sources
2.develop a time ine of indic contributions and compare with those of Babylon and China

3.Compile an enyclopedia of ancient indic astronomy and Mathematics

Hindu Astronomy - acharya - 05-28-2007

<img src='http://www.vedicastronomy.net/maha/MFIG58.gif' border='0' alt='user posted image' />


Beginning of Kaliyuga

The SuryaSiddhanta based data declare that the Kaliyuga started on the new moon day (Amavasya/Pratipat) when sun was 5 degrees away from vernal equinox (Ref 2). This date has been estimated as February 18, 3102 BCJ. There is also a suggestion that there was a solar eclipse at Ujjain. The picture below shows the view and sun and moon at that time.

The Lodestar pro view of sky on that day shows that there was no eclipse at Ujjain (75 deg 47 min E and 25 deg 15 min N) at Amavasya, but sun was 54 degrees away from vernal equinox. (3 hours 36 minutes from equinox- @15 deg/hour this works out to exactly 54 degrees).


http://www.vedicastronomy.net/mb_kuruxethra.htm




Hindu Astronomy - acharya - 05-28-2007

Dating the "Mahabharatha" - Two eclipses in thirteen days
http://www.vedicastronomy.net/mb_conclusion.htm


<<

Conclusion

>>


The aim of this work was to analyze the unique statement that Mahabharata war took place when an ominous pair of eclipses occurred in "Thirteen days". Initially, Mahabharata texts, contemporarily accepted as most authentic were reviewed and relevant data about Mahabharata and astronomical planetary observations have been presented.

Firstly, this document looked at modern astronomical software with all known corrections, and validated its performance using the clay tablet eclipse information from the Mesopotamia valley during the period 2100 BCJ down to 900 BCJ, with best- known contemporary research data.

Secondly, a search of all eclipses during the period 3300 BCJ to 700 BCJ visible at Kuruxethra, where Mahabharata war took place was made. Amongst nearly 672 possible eclipse pairs, the time from end of one to beginning of next eclipse was found to vary between 13.8 days to 15.8 days. Eighteen naked eye visible eclipse pairs with less than 336 hours (14days) of time gap were found.

The third issue was, what was the definition of a day, and how was the determination that eclipses occurred in "thirteen days" made, has been addressed. Day was taken to be the time between either successive sunrise or successive sunset. This is particularly important when clocks did not exist. Using this method, it was easy to demonstrate that observers from 3000 to 5000 years ago could identify accurately a "thirteen-day "eclipse pair.

Fourthly, eighteen pairs of possible ‘Thirteen day eclipses" were extensively analyzed. Six pairs amongst these, found to be good candidates for Mahabharata, have been illustrated, showing how any observer could conclude that the eclipse pairs occurred in less than 14 days or in "thirteen days". The locations of Jupiter, Saturn, Mars, Venus, Sun and Moon, during the eclipses were identified with reference to Bharateeya 27 star locations.

Finally, it is found that two dates suggested by Indian authors Aryabhata, Varaha Mihira from Gupta period were credible dates for Mahabharata war. It would appear that 3129 BCJ is a first candidate for Mahabharata war followed by 2559 BCJ. Four other dates viz., 2056 BCJ, 1853 BCJ, 1708 BCJ and 1397 BCJ are other candidates which qualify as " Thirteen day" eclipse pairs.

In conclusion, this article has tried to address the basic issue, whether " Thirteen day" eclipse pairs are astronomically possible. The conclusion is that such eclipses have occurred and observers could easily identify the duration using sunset/sunrise transitions. 3129 BCJ and 2559 BCJ dates appear to be very viable dates for Mahabharata war as are a few others. This study provides modern scientific support one critical astronomical statement made in Mahabharata text that "thirteen day" eclipse pair occurred Kuruxethra.
Some related material about Vedic star astronomical locations

The Bharateeya 27/28 daily Star system is a lunar day count used in Vedic Bharata. Two articles in Ref 11 and 12 provide background in this area for those who do not have this information.
Acknowledgements

The Internet web and search engines have been a great boon in providing rare material online, particularly conversion of Devanagari script to English and vice versa. Reference 5 was of great help in finding such basic Mahabharata material, confirmed in Ref 4. Ref 10 provided a method of converting between scripts.



Hindu Astronomy - acharya - 05-28-2007

http://www.svabhinava.org/AITvsOIT/index.php


Astronomy and the dating of the Vedas

Balakrishna, S. - Names of Stars from the Period of Vedas - includes computer-generated graphic views of the Vedic night sky

Elst, K. - Astronomical Data and the Aryan Question

Frawley, D. - Vedic Origins of the Zodiac

Kak, S. - Light or Coincidence - on the alleged measurement of the speed of light by the Vedic Indians

Kak, S. - Astronomy and Its Role in Vedic Culture

Kak, S. - Babylonian and Indian Astronomy

Kak, S. - Birth and Early Development of Indian Astronomy

Narahari Achar, B. N. - Comments on M. Witzel’s e-article ‘The Pleiades and the Bears viewed from inside the Vedic Texts’ - from EJVS 6,2

Narahari Achar, B. N. - On Exploring the Vedic Sky with Modern Computer Software - from EJVS 5,2

Narahari Achar, B. N. - Searching for Naksatras in the Rgveda - from EJVS 6,2

Plofker, K. - How to interpret Astronomical References in Vedic Texts - from EJVS 6,2

Witzel, M. - Looking for the Heavenly Casket - on the Vedic night sky

Witzel, M. - The Pleiades and the Bears viewed from inside the Vedic Texts - from EJVS 5,2