Vedāṁga Jyotiṣa – Part 1

I will organize this presentation in leiu of the work of Professor T.S. Kuppanna Sastry and Dr. K.V Sarma. It combines the two versions of Vedāṁga Jyotiṣa found in Ṛg and Yajur Veda.

Introduction

I purify myself by bowing my head to the Creator, whom I envision as being the power within the five-year cycles [“yuga”], and the body on which days, months, seasons, and half-years are limbs.

I also bow my head to the Goddess of Intellect, Sarasvati – so that I may write on the science of time, as explained by Sage Lagadha.  This science is meritorious and dear to the learned, because by it one can understand the perfect times to make auspicious endeavors.

The Vedas exist so that we can successfully obtain the results of our efforts and sacrifices, but doing so is very dependent on timing. Therefore one who understands the science of time, Jyotiṣa, also understands the science of successful efforts.  So they say that this science of Jyotiṣa is the foremost appendix to Vedic knowledge – much like the feathers of a peacock, or the treasures of a dragon.

Anyone who understands the Vedas and also understands the movements of the Sun and Moon will become prosperous in this world and afterwards will go to where the Sun and Moon move about in the heavens.

Measuring Time

The time it takes to pronounce a long vowel is an akṣara. Five of them is a kāṣṭhā. Four groups of thirty-one kāṣṭhā are a kalā. 10.05 kalā is a nāḍikā. Two nāḍikā are a muhūrta. Thirty muhūrta are a day, which is equivalent to 603 kalā.

A year is 366 days. It has two ayana, six ṛtu, and twelve months.

A yuga is five years.

Also: a nāḍikā is three sixteenths of an āḍhaka, during which time a clepsydra will drain 50 pala of water. Four āḍhaka are a droṇa. And a Ṛtu equals 4.5 constellations.

Comment:

Assuming for now that a day is “24 hours” the approximate modern values of these time units are as follows.

Droṇa:                 512 minutes (>8.5 hours)

Āḍhaka:             128 minutes

Muhurta:           48 minutes

Nadika:               24 minutes

Kalā:                     2.4(-) minutes

Kāṣṭhā group: 4.5(-) second

Kāṣṭhā:                1(+) second

Akṣara:                ¼ of a second

Now, for the longer periods of time, approximately:

Yuga:                    5 years

Year:                     366 days

Ayana:                 183 days

Ṛtu:                       61 days

Month:                30(+) days

The text gives three ways to check the measurements in the real world. We can do it starting from the Akṣara, assigning it the amount of time it takes to pronounce two short-vowel syllables or one long-vowel syllable in normal speech. Or we can start from the āḍhaka, assigning it the amount of time it takes to drain a clepsydra (basically a pot with a pinhole in it) holding a fixed amount of water. Or we start from the ṛtu, assigning it the amount of time it takes the Sun to move 60 degrees of arc in reference to a zodiac star.

Since we have mentioned the zodiac stars, lets now pull together the definitive verses concerning the zodiac constellations.

Zodiac Constellations

The zodiac constellations with their deities are:

1. Kṛttikā                           Agni (God of fire)
2. Rohiṇī                            Prajāpati (the Creator, Brahmā)
3. Mṛgaśīrṣā                     Soma (God of the immortal elixir)
4. Ārdrā                             Rudra (God of destruction)
5. Punarvasu                   Aditi (Goddess of space)
6. Puṣya                             Bṛhaspati (God of prayer)
7. Āśleṣā                            Naga (Dragons)
8. Maghā                           Pitṛ (Ancestral spirits)
9. Pūrva Phālgunī           Bhaga (God of love)
10. Uttara Phālgunī         Aryamā (God of vows)
11. Hasta                             Savitā (God of awakening)
12. Citrā                               Tvaṣṭā (God of design)
13. Svāti                               Vāyu (God of breath/air)
14. Viśākhā                         Indrāgñi (God of sacrificial fire)
15. Anurādhā                     Mitra (God of devotion/ friendship)
16. Jyeṣṭhā                         Indra (Chief of the gods)
17. Mūla                              Nirṛti (Goddess of destruction)
18. Pūrva Aṣāḍhā             Apa (Goddess of water)
19. Uttara Aṣāḍhā            Viśvadeva (All divinities)
20. Śravaṇa                         Viṣṇu (God of existence)
21. Dhaniṣṭhā                    Vasu (Gods of elements)
22. Śatabhiṣaj                    Varuṇa (God of night/ the underworld)
23. Pūrva Bhādrapadā    Ajaikapāt (Fire dragon)
24. Uttara Bhādrapadā Ahirbudhnya (Water dragon)
25. Revatī                            Pūṣan (God of protection)
26. Aśvinī                             Aśvini (Twin children of the Sun)
27. Bharaṇī                         Yama (God of death)

Those who understand the science of sacrifice recall that the names of these gods should be used in place of our own name, according to the constellation under which we are born, whenever we make serious sacrifices and efforts.

Ārdrā, Citrā, Viśākhā, Śravaṇa and Aśvinī have “fierce” qualities. Maghā, Svāti, Jyeṣṭhā, Mūla and Bharaṇī  have “harsh” qualities.

Importance of Cross Multiplication

The following very common elementary equation will often be used in our calculations: a/b = c/x. Which is solved as: x = bc/a.

To be continued… stay tuned…

- Vic DiCara

www.vicdicara.com

Response to a paper seeking to establish a Sidereal Indian Zodiac

I published my article explaining that the original Indian zodiac is tropical (not sidereal as is currently in use).

Today a rebuttal was published.

Here is my reply to that rebuttal.

Tale of Two Zodiacs Reply

Dear Antardwipa Dasa and Shyamasundara Dasa,

Respectful thanks a well written and knowledgeable article. I will reply to a few points.

You expressed uncertainty about my phrase “center of space.” I use that phrase to refer to the point at which the ecliptic intersects the equator, providing a “center” for observational space.

The fact that there are not 12 equal-sized constellations among the stars is only one of several observations depreciating the concept that the 12 signs are intrinsically stellar. But even so, you proceeded on with your article without offering any specific counterpoint to this particular observation.

I agree that the rashi system (12 sections of 30 degrees) can be, and often is, abstracted to a mathematical principle of circular geometry, including the measure of sidereal phenomenon. However, the actual rashi themselves are intrinsically tropical (i.e. defined with reference to solstice and equinox) as per Surya Siddhānta 14.7-10 and the Puranas viz. Bhāgavatam 5.21.2-6.

Thus SS 1.28 states that such a system of seconds, degrees, signs, etc. can be used to measure sidereal space. But SS 14.7-10 makes it explicitly clear that the 12 signs themselves (not as mathematical abstractions, but the signs themselves) are tropical. SS 1.28 does not say that the signs are sidereal, merely it states that 12 divisions of 30 degrees is used to measure sidereal space. Thus I agree that both tropical and sidereal space can be measured in 12 30 degree sections. However, the origin of the 30 degree system is tropical – and thus the 12 30 degree signs are inherently tropical, although they have sidereal mathematical application.

I agree with and appreciate your statement that certain calculations (declination, rising signs, etc) are impossible to make without a tropical zodiac.

You make an interesting statement that planetary longitude is not included among the tropical calculations indicated in Surya Siddhānta. My reply:  (a) As you noted, the Siddhānta uses the word “etcetera” (adhikam) in its list of this to be tropically figured. (b) Planetary positions amongst the sidereal nakṣatra is very important, in fact far more important to the original indigenous Vedic astrology, than planetary positions among the 12 signs.

I agree that calculations of planetary revolutions per Surya Siddhānta are done with reference to Revatī, and that these reference points are observably fixed and stable. As you noted, this data is calculated first (in chapter 2), and then the lagna is calculated tropically (in chapter 3). If one wants planetary positions in reference to the nakṣatra, there is no further work to be done. If one wants the sidereal location of the lagna, the ayana must be subtracted from it. If one wants planetary positions in reference to the rashi (not as mathematical sections, but as actual rāśi themselves, divisions of space relative to the equinox), one must add the ayana to the previous calculations.

You quoted Bhāgavatam 5.22.2, but I feel you have misrepresented. It does define the planets moving differently than the signs and nakshatras. However, it does not state that the signs and nakshatras do not move with respect to one another.  This is an implication which you infer, it is not in the text itself.

It is misleading in the extreme to say that 5.22.2 gives a sidereal “definition” of the zodiac signs. A definition has already been given in 5.21.2-6 (and that definition is tropical). Definitions are explicit. They are not analogies. Furthermore, your inference from the analogy certainly does not qualify as a “definition.”

5.22.5 explains that a solar month is equivalent [not identical] to 2.25 nakshatras. Sripad Vijayadhvaj Tirtha is from the 15^th century and explained this according to the prevalent custom of his time.

Varaha Mihira also spoke accurately of the correlation of stars and signs extant at his time. As he pointed out, the size of a navāmśa and the size of a nakṣatra pada are identical, and therefore the size of a rashi equals 9 nakṣatra pada.

I agree that Varaha Mihira was aware of the distinction between the tropical and sidereal chakra. I believe the confusion amongst Indian astrologers gradually arose over the several following centuries.

Your article was well written and researched. Thank you for the excellent effort. In it you have clearly demonstrated that 30 degree units called rashis can also be used to make sidereal measurements. However you failed to counter-argue the fact that rashis by definition are inherently tropical, as presented in my argument (http://vicdicara.com/12-signs-of-the-zodiac-1.php).

If this discussion of the zodiac helps us remember Krishna it is useful. Since you are both, Syamasundar and Antardwipa, dear servant of the servant of Krishna, my hope is that the dust of your feet will always be falling towards my lowered head. Please forgive the academic nature of discussion in which this person speaks up with an equal voice in a spirit of healthy debate.

Hare Krishna.

Your servant,

Vraja Kishor das

Astrological Gurus: A Myth

I hate to be the bearer of bad news, but the idea that there are astrological “gurus” with bona-fide astrological “parampara” is just a dream, a fantasy. There are people out there who think they have a “guru” – and in a sense they do. But this guru is not divinely ordained by a spiritual parampara. Such a thing simply does not exist in the astrological world.

Varahamihira was a great astronomer and astrologer, but please do not insist that I treat him as a self-realized divine being, whose every word I must literally accept as absolute truth for all time in all places. That is an absurd misappropriation of the concept of Guru Parampara. I greatly revere Varahamihira, Mantreshwara and other greats as great astronomers and astrologers.

Secondly even if I were to accept these ancients as empowered divine messengers – where is the unbroken chain of similarly realized souls representing them today? No friends, this does not exist. The whole thing is fantastic and mythological. There are no “gurus” and “paramparas” of any importance in the astrological world except in the practical sense where any teacher and school is a guru and parampara.

So when people say that I must “follow gurus” and accept that the correct zodiac is sidereal, I have to say, no. They are not following gurus, they are following tradition. If they can’t tell the difference that is sad. A guru is a person who deeply realizes and understands a subject. A tradition is just established by popular repetition.

So let us not run for smoke and mirrors: “You have not asked the question correctly , that’s why we refuse to explain why we are not wrong.” Or “You do not have a guru, that’s why you cannot understand why we are never wrong.”

Let us be practical and honest. All the Purana’s, including Bhagavat, define the 12 signs tropically (ie. anchored to tropical events – the solstices and equinoxes). The Surya Siddhanta also does. None of them do so with any vagueness, all are very direct, straightforward and unequivocal. There is not a sidereal definition of zodiac signs to be found. Therefore where is the “guru” who has the bile to say that it is “Vedic” to use a sidereal zodiac.

Origin of the Sidereal Zodiac

The stars of sidereal space are a valid and important astrological entity. India (and almost all cultures) has a valid system of dividing sidereal space with the Moon as the focal point, not the Sun as in tropical space. This system has 27 divisions, not 12, because there are that many sunrises during the time it takes the Moon to complete a full circuit of the heavens.

The idea of 12 sidereal signs comes from wrongly assuming that the correlation between the stars and signs is permanent. In fact, there is no permanent correlation between the two, the signs eternally and very gradually drift backwards through the stars – a phenomena commonly known as “precession of the equinox.”

There is a valid need to correlate the signs and stars because their relationship is important for defining very long periods of time (“ages”) and for knowing how and when to keep solar and lunar calendar systems synchronized.

Babylonians measured the correlation of their autumnal equinox with the heliacal rising of stars they called The Scales. Greeks measured the discrepancy of tropical Aries against a stellar counterpart bearing the same name. Ancient and Classical Indians measured the heliacal position of the equinox in reference to their fixed stars. For example, the Ṛg Veda notes Kṛttikā as the “first” star and the beginning of the celestial circle, because in Ṛg Vedic times, four to five thousand years ago, Kṛttikā heliacally rose with the Vernal Equinox. Later Indian works from nearly two thousand years ago note Aśvinī as the first star, because at that time Aśvinī was the star heliacally rising with the equinox.

Projecting the 12 zodiac divisions into space, based on the then-current position of the vernal equinox was useful for mathematics but opened a door for people to think of the signs as stellar entities. It is an easy mistake to make considering that for centuries there was almost no significant difference between the signs and their homonymic sidereal namesakes.