Friday, November 27, 2015

Hindu cosmology & Astronomy -Part 3

`Veda' means knowledge. And Yoga-
Patanjali Yoga Sutra 1:2
Yogas chitta vritti nirodhah
Yoga is the mastery of fluctuations of the mind.

For quite some time scholars believed that this knowledge amounted to no
more than speculations regarding the self; this is what we are still told in some schoolbook
accounts. New insights in archaeology, astronomy, history of science and Vedic scholarship
have shown that such a view is wrong. We now know that Vedic knowledge embraced physics,
mathematics, astronomy, logic, cognition and other disciplines. We find that Vedic science
is the earliest science that has come down to us.
Briefly, the Vedic texts present a tripartite and recursive world view. The universe is
viewed as three regions of earth, space, and sky with the corresponding entities of Agni,
Indra, and Vishve Devah (all gods).
Vedic Rishi and old education institutes alse read modern science but name was different.
These were Vedic science-
logic (nyaya) and physics (vaisheshika), cosmology (sankhya) and psychology
(yoga), and language (mimamsa) and reality (vedanta).
The Five Levels

In the Taittiriya Upanishad, the individual is represented in 5 levels that enclose the individual's self. These levels, shown in an ascending order, are:
The physical body (annamaya kosha)

Energy sheath (pranamaya kosha)

Mental sheath (manomaya kosha)

Intellect sheath (vijnanamaya kosha)

Emotion sheath (anandamaya kosha )

The emotion sheath, is innermost .
This is a recognition of the fact that eventually meaning is communicated by associations

The energy that underlies physical and mental processes is called prana.

Further description of above-
According to yogic theory & philosophy, a human being is comprised of 5 layers. These layers are called koshas, or sheath. Each layer is more subtle than the other.
The first is annamaya kosha, or literally mean ‘food sheath’ – it is the physical body: the bones, muscles, tissues, organs, bloods, etc. The grossest of the layers. It is made of the elements: earth, water, fire, air, and space. It is on this layer the gateway to the external world, the five receiving senses and the five action sense are located, so it is through this layer that one is experiencing life.
The second is pranamaya kosha, or the energy body, the prana layer. More subtle than the physical body, this layer not visible to the naked eye, but one can feel it. The chakras, or energy centers, are within this layer. Without prana, there is no life.
The third is manomaya kosha, the mind body. This is the mind that interacts with the inputs from the senses, carry out day to day operation of keeping oneself alive and well – eg if there’s a danger, move away – if there’s a reward, come closer. Manomaya kosha is full of emotions – a reaction to the input from the senses. It is key for survival.
The fourth is vijnanamaya kosha, sometimes called the higher mind. Also referred to as the ‘wisdom body’ – this is where awareness, insight, discernment, and consciousness located. Without awareness, one will be only reacting to whatever comes one’s way. With awareness, one can stop to only reacting and choose to response with intention.
The fifth is called anandamaya kosha, the bliss body. Sometimes also called the causal body. This is the innermost layer covering the essence – the soul, or spirit, or self, or atman. The unchanging eternal reality.
Using a computer as analogy, annamaya kosha is like the hardware. The receiving sense organs are keyboards, mouse, touchscreen, microphone. The action sense organs are the monitor, speaker, printer. Pranamaya kosha is like the electricity powering the computer – without plugging it into the electricity the computer can’t turn on. It’s the current that goes through the hardwares. Manomaya kosha is like the operating system – basic operation of the computer is controlled from here. Vijnanamaya kosha is like the more advanced software, with which the computer can interact in a more useful way, be productive, be of service. I can’t think yet of the parallel for anandamaya kosha in a computer… can you think of one? Although not yet complete, I think this computer analogy helps me understand more about the koshas.

The Structure of the Mind
The Sankhya system takes the mind as consisting of ¯ve components: manas, ahankara,
chitta(MEMORY BANK) buddhi, and atman. Again these categories parallel those of Figure ABOVE.
This mental complex surrounds the innermost aspect of consciousness which is called
atman, the self, brahman, or jiva.

In his famous paper on the origin of mathematics, Seidenberg (1978) concluded: Old-
Babylonia [1700 BC] got the theorem of Pythagoras from India.
Barend van Nooten (1993) has shown that binary numbers were known at the time of
Pingala's Chhandahshastra. Pingala, who lived around the early Frst century B.C.E., used
binary numbers to calssify Vedic Mantras.

The Puranas speak of countless universes, time  owing at different rates for different observers and so on.
Advanced Ancient Indian Science-
The Mahabharata speaks of an embryo being divided into one hundred parts each becoming, after maturation in a separate pot, a healthy baby; this is how the Kaurava brothers are born. There is also mention of an embryo, conceived in one womb, being transferred to the womb of another woman from where it is born; the transferred embryo is Balarama and this is how he is a brother to Krishna although he was born to Rohini and not to Devaki.

There is an ancient mention of space travellers wearing airtight suits in the epic Mahabharata which may be classi¯ed as an early form of science ¯ction. According to the well-known Sanskritist J.A.B. van Buitenen, in the accounts in Book 3 called The Razing of Saubha" and The War of the Yakshas":
the aerial city is nothing but an armed camp with fame-throwers and thundering cannon, no doubt a spaceship. The name of the demons is also revealing: they were Niv¹atakavacas, clad in airtight armor," which can hardly be anything but space suits. (van Buitenen, 1975, page 202)
Universes de¯ned recursively are described in the famous episode of Indra and the ants
in Brahmavaivarta Purana. Here Vishnu, in the guise of a boy, explains to Indra that
the ants he sees walking on the ground have all been Indras in their own solar systems in
different times! These Fights of imagination are to be traced to more than a straightforward
generalization of the motions of the planets into a cyclic universe.


Aryabhata is the author of the first of the later siddhantas called Aryabhatiyam which
sketches his mathematical, planetary, and cosmic theories. This book is divided into four
chapters: (i) the astronomical constants and the sine table, (ii) mathematics required for
computations, (iii) division of time and rules for computing the longitudes of planets using
eccentrics and epicycles, (iv) the armillary sphere, rules relating to problems of trigonometry
and the computation of eclipses.
The parameters of Aryabhatiyam have, as their origin, the commencement of Kaliyuga
on Friday, 18th February, 3102 B.C.E. He wrote another book where the epoch is a bit
Aryabhata took the earth to spin on its axis; this idea appears to have been his innovation.
He also considered the heavenly motions to go through a cycle of 4.32 billion years; here he
went with an older tradition, but he introduced a new scheme of subdivisions within this
great cycle. According to the historian Hugh Thurston, \Not only did Aryabhata believe
that the earth rotates, but there are glimmerings in his system (and other similar systems)
of a possible underlying theory in which the earth (and the planets) orbits the sun, rather
than the sun orbiting the earth. The evidence is that the basic planetary periods are relative
to the sun."

That Aryabhata was aware of the relativity of motion is clear from this passage in his
book,Just as a man in a boat sees the trees on the bank move in the opposite direction, so
an observer on the equator sees the stationary stars as moving precisely toward the west."

Varahamihira (died 587) lived in Ujjain and he wrote three important books: Panchasiddhan-
tika, Brihat Samhita, and Brihat Jataka. The ¯rst is a summary of  five early astronomical
systems including the Surya Siddhanta. (Incidently, the modern Surya Siddhanta is different
in many details from this ancient one.) Another system described by him, the Paitamaha
Siddhanta, appears to have many similarities with the ancient Vedanga Jyotisha of Lagadha.
Brihat Samhita is a compilataion of an assortment of topics that provides interesting
details of the beliefs of those times. Brihat Jataka is a book on astrology which appears to
be considerably influenced by Greek astrology.

Brahmagupta of Bhilamala in Rajasthan, who was born in 598, wrote his masterpiece,
Brahmasphuta Siddhanta, in 628. His school, which was a rival to that of Aryabhata, has
been very influential in western and northern India. Brahmagupta's work was translated into
Arabic in 771 or 773 at Baghdad and it became famous in the Arabic world as Sindhind.
One of Brahmagupta's chief contributions is the solution of a certain second order inde-
terminate equation which is of great significance in number theory.
Another of his books, the Khandakhadyaka, remained a popular handbook for astronomical computations for centuries.
Bhaskara (born 1114), who was from the Karnataka region, was an outstanding mathemati-
cian and astronomer. Amongst his mathematical contributions is the concept of di®erentials.
He was the author of Siddhanta Shiromani, a book in four parts: (i) Lilavati on arithmetic,
(ii) Bijaganita on algebra, (iii) Ganitadhyaya, (iv) Goladhyaya on astronomy. He epicyclic-
eccentric theories of planetary motions are more developed than in the earlier siddhantas.
Subsequent to Bhaskara we see a °ourishing tradition of mathematics and astronomy
in Kerala which saw itself as a successor to the school of Aryabhata.

Madhava (c. 1340-1425) developed a procedure to determine the positions of the moon every
36 minutes. He also provided methods to estimate the motions of the planets. He gave power
series expansions for trigonometric functions, and for pi correct to eleven decimal places.
Nilakantha Somayaji
Nilakantha (c. 1444-1545) was a very prolific scholar who wrote several works on astronomy.
It appears that Nilakantha found the correct formulation for the equation of the center of
the planets and his model must be considered a true heliocentric model of the solar system.
He also improved upon the power series techniques of Madhava.

The methods developed by the Kerala mathematicians were far ahead of the European

mathematics of the day.
7 Concepts of space, time, and matter
Yoga-Vasishtha (YV) is an ancient Indian text, over 29,000 verses long, traditionally attributed to Valmiki, author of the epic Ramayana- Of which some random translations are given here from
book done by Venkatesananda (1984).

² Time cannot be analyzed... Time uses two balls known as the sun and the moon for

its pastime. [16]
² The world is like a potter's wheel: the wheel looks as if it stands still, though it revolves

at a terrific speed. [18]
² Just as space does not have a fixed span, time does not have a fixed span either. Just

as the world and its creation are mere appearances, a moment and an epoch are also

imaginary. [55]
² Infinite consciousness held in itself the notion of a unit of time equal to one-millionth

of the twinkling of an eye: and from this evolved the time-scale right up to an epoch

consisting of several revolutions of the four ages, which is the life-span of one cosmic

creation. Infinite consciousness itself is uninvolved in these, for it is devoid of rising

and setting (which are essential to all time-scales), and it devoid of a beginning, middle

and end. [72]
² There are three types of space|the psychological space, the physical space and the

in¯nite space of consciousness. [52]
The in¯nite space of individed consciousness is that which exists in all, inside and

outside... The ¯nite space of divided consciousness is that which created divisions of

time, which pervades all beings... The physical space is that in which the elements

exist. The latter two are not independent of the ¯rst. [96]
² Other universes. On the slopes of a far-distant mountain range there is a solid rock

within which I dwell. The world within this rock is just like yours: it has its own

inhabitants, ...the sun and the moon and all the rest of it. I have been in it for

countless aeons. [402]
² The entire universe is contained in a subatomic partice, and the three worlds exist

within one strand of hair. [404]
² In every atom there are worlds within worlds. [55]

² (There are) countless universes, diverse in composition and space-time structure... In

every one of them there are continents and mountains, villages and cities inhabited by

people who have their time-space and life-span. [401-2]
² Direct experience alone is the basis for all proofs... That substratum is the experiencing

intelligence which itself becomes the experiencer, the act of experiencing, and the

experience. [36]
² Everyone has two bodies, the one physical and the other mental. The physical body

is insentient and seeks its own destruction; the mind is ¯nite but orderly. [124]
² I have carefully investigated, I have observed everything from the tips of my toes to the

top of my head, and I have not found anything of which I could say, `This I am.' Who

is `I'? I am the all-pervading consciousness which is itself not an object of knowledge or

knowing and is free from self-hood. I am that which is indivisible, which has no name,

which does not undergo change, which is beyond all concepts of unity and diversity,

which is beyond measure. [214]
² I remember that once upon a time there was nothing on this earth, neither trees and

plants, nor even mountains. For a period of eleven thousand years the earth was

covered by lava. In those days there was neither day nor night below the polar region:

for in the rest of the earth neither the sun nor the moon shone. Only one half of the

polar region was illumined.

Then demons ruled the earth. They were deluded, powerful and prosperous, and the

earth was their playground.

Apart from the polar region the rest of the earth was covered with water. And then

for a very long time the whole earth was covered with forests, except the polar region.

Then there arose great mountains, but without any human inhabitants. For a period

of ten thousand years the earth was covered with the corpses of the demons. [280]
² The same in¯nite self conceives within itself the duality of oneself and the other. [39]

² Thought is mind, there is no distinction between the two. [41]

² The body can neither enjoy nor su®er. It is the mind alone that experiences. [109-110]

² The mind has no body, no support and no form; yet by this mind is everything con-

sumed in this world. This is indeed a great mystery. He who says that he is destroyed

by the mind which has no substantiality at all, says in e®ect that his head was smashed

by the lotus petal... The hero who is able to destroy a real enemy standing in front of

him is himself destroyed by this mind which is [non-material].
² The intelligence which is other than self-knowledge is what constitutes the mind. [175]

² The absolute alone exists now and for ever. When one thinks of it as a void, it is

because of the feeling one has that it is not void; when one thinks of it as not-void, it

is because there is a feeling that it is void. [46]
² All fundamental elements continued to act on one another|as experiencer and experience|

and the entire creation came into being like ripples on the surface of the ocean. And,

they are interwoven and mixed up so e®ectively that they cannot be extricated from

one another till the cosmic dissolution. [48]

² The entire universe is forever the same as the consciousness that dwells in every atom.

² The ¯ve elements are the seed fo which the world is the tree; and the eternal conscious-

ness if the seed of the elements. [48]
² Cosmic consciousness alone exists now and ever; in it are no worlds, no created beings.

That consciousness re°ected in itself appears to be creation. [49]
² This consciousness is not knowable: when it wishes to become the knowable, it is known

as the universe. Mind, intellect, egotism, the ¯ve great elements, and the world|all

these innumerable names and forms are all consciousness alone. [50]
² The world exists because consciousness is, and the world is the body of consciousness.

There is no division, no di®erence, no distinction. Hence the universe can be said

to be both real and unreal: real because of the reality of consciousness which is its

own reality, and unreal because the universe does not exist as universe, independent of
consciousness. [50]

² Consciousness is pure, eternal and in¯nite: it does not arise nor cease to be. It is ever

there in the moving and unmoving creatures, in the sky, on the mountain and in ¯re

and air. [67]
² Millions of universes appear in the in¯nite consciousness like specks of dust in a beam
of light. In one small atom all the three worlds appear to be, with all their components

like space, time, action, substance, day and night. [120]
² The universe exists in in¯nte consciousness. In¯nite consciousness is unmanifest,

though omnipresent, even as space, though existing everywhere, is manifest. [141]
² The manifestation of the omnipotence of in¯nite consciousness enters into an alliance

with time, space and causation. Thence arise in¯nite names and forms. [145]
² The Lord who is in¯nite consciousness is the silent but alert witness of this cosmic

dance. He is not di®erent from the dancer (the cosmic natural order) and the dance

(the happenings). [296]

Might then one accept the claim of Srinivasa Ramanujan that his theorems were revealed to him in his dreams by the goddess Namagiri? This claim, so persistently made by Ramanujan, has generally been dismissed by his biographers (see, for example, Kanigel, 1991). Were Ramanujan's astonishing discoveries instrumented by the autonomously creative potential of consciousness, represented by him by the image of Namagiri? If that be the case then the marvellous imagination shown in Yoga-Vasishtha and other Indian texts becomes easier to comprehend.

Is nature and animals, human all are molecule- Yes partly with consciousness.
ET (1)ET (2)ET (3)ET (4)ET (6)

ET (5)
ET (7)
ET (8)


13.7 BYASeconds after Bang13.2 BYA4.4 BYA4.1 BYA3.9 BYA45 MYA150,000 Year Ago

Sarma, K.V. 1985. A survey of source materials. Indian Journal of History of Science

Staal, F. 1988. Universals. Chicago: University of Chicago Press.

Venkatesananda, S. (tr.), 1984. The Concise Yoga V¹asis. t.ha. Albany: State University of

New York Press.
Barrow, J. 1992. Pi in the Sky. Oxford: Oxford University Press.

Brown, J.W. 1994. Morphogenesis and mental process. Development and Psychopathology.

van Buitenen, J.A.B. 1975. The Mah¹abh¹arata, vol. 2. Chicago: University of Chicago


Chapple, C. 1984. Introduction and bibliography in Venkatesananda (1984).
Dasgupta, S. 1975 (1932). A History of Indian Philosophy. Delhi: Motilal Banarsidass.

Feuerstein, G., S. Kak and D. Frawley, 1995. In Search of the Cradle of Civilization.
Wheaton: Quest Books.

Filliozat, J. 1970. The expansion of Indian medicine abroad. In Lokesh Chandra (ed.)
India's Contributions to World Thought and Culture. Madras: Vivekananda Memorial

Committee. 67-70.

Francfort, H.-P. 1992. Evidence for Harappan irrigation system in Haryana and Rajasthan.
Eastern Anthropologist. 45.87-103.

Frawley, D. 1994. Planets in the Vedic literature. Indian Journal of History of Science.

Kak, S. 1986. The Nature of Physical Reality. New York: Peter Lang.

1987. The Paninian approach to natural language processing. Intl. Journal of

Approximate Reasoning. 1.117-130.

1990. Kalidasa and the Agnimitra problem. Journal of the Oriental Institute 40.51-

1994a. The Astronomical Code of the R.

gveda. New Delhi: Aditya.

1994b. The evolution of writing in India. Indian Journal of History of Science.

1994c. India at Century's End. New Delhi: VOI.

1995a. The astronomy of the age of geometric altars. Quarterly Journal of the Royal

Astronomical Society. 36.385-396.

1995b. From Vedic science to Ved¹anta. The Adyar Library Bulletin. 59.1-36.

1996a. Knowledge of planets in the third millennium B.C. Quarterly Journal of the

Royal Astronomical Society. 37.709-715.

1996b. Re°ections in clouded mirrors: selfhood in animals and machines. In Pri-
bram, K.H. and J. King (eds.) Learning as Self-Organization. Mahwah, NJ: Lawrence

Kanigel, R. 1991. The Man Who Knew In¯nity: A Life of the Mathematical Genius,

Ramanujan. New York: C. Scribner's.

Kulaichev, A.P. 1984. µSriyantra and its mathematical properties. Indian Journal of History

of Science 19.279-292.
McClain, E.G. 1978. The Myth of Invariance. Boulder: Shambhala.

Sarma, K.V. 1985. A survey of source materials. Indian Journal of History of Science

Seidenberg, A. 1978. The origin of mathematics. Archive for History of Exact Sciences.

Sengupta, P.C. 1947. Ancient Indian Chronology. Calcutta: University of Calcutta Press.

Staal, F. 1988. Universals. Chicago: University of Chicago Press.

van Nooten, B. 1993. Binary numbers in Indian antiquity. Journal of Indian Philosophy.

Venkatesananda, S. (tr.), 1984. The Concise Yoga V¹asis. t.ha. Albany: State University of

New York Press.

Thursday, November 26, 2015

Hindu Cosmology -Part 2

Hindu Cosmology upholds the idea that creation is timeless, having no beginning in time. Each creation is preceded by dissolution and each dissolution is followed by creation. The whole cosmos exists in two states - the unmanifested or undifferentiated state and the manifested or differentiated state. This has been going on eternally. There are many universes - all follow the same rhythm, creation and dissolution (the systole and diastole of the cosmic heart). According to the Bhagavad Gita this srishti (creation) and pralaya (dissolution) recur at a period of 1,000 mahayuga or 4.32 billion years or 4,320 million years:
For a thousand ages lasts One day of Brahma, And for a thousand ages one such night;
This knowing, men will know (what is meant by) day and night.
At the day's dawning all things manifest; Spring forth from the Unmanifest;
And then at nightfall they dissolve again, In (that same mystery) surnamed "Unmanifest."


The Rig Veda describes the origin of the universe as:
"Then was not non-existence nor existence: there was no realm of air, no sky beyond it. What covered in, and where? and what gave shelter? Was water there, unfathomed depth of water? Death was not then, nor was there aught immortal: no sign was there, the day's and night's divider. That One Thing, breathless, breathed by its own nature: apart from it was nothing whatsoever. Darkness there was at first concealed in darkness this. All was indiscriminated chaos. All that existed then was void and form less: by the great power of Warmth was born that Unit. Thereafter rose Desire in the beginning, Desire, the primal seed and germ of Spirit. Sages who searched with their heart's thought discovered the existent's kinship in the non-existent. Transversely was their severing line extended: what was above it then, and what below it? There were begetters, there were mighty forces, free action here and energy up yonder. Who verily knows and who can here declare it, whence it was born and whence comes this creation? The devas are later than this world's production. Who knows then whence it first came into being? He, the first origin of this creation, whether he formed it all or did not form it, Whose eye controls this world in highest heaven, he verily knows it, or perhaps he knows not" - (Rig Veda 10.129.1-7)

Structure of the universe

The Yugas

  • Satya or Krta (1,728,000 years): Satya means "truth"; the age is also known as Krta, "action," i.e., the age in which the people did unquestioningly what their benevolent elders told them.
  • Treta (1,296,000 years): Treta means "three," the third age, counting backwards from the present: also the age in which the feelings and forces of good are as three parts, and those of evil as one; also the age in which people were specially "protected," trayate, by their elders.
  • Dva-para (864,000 years): Dva-para means "two-sided," hence doubt also.
  • Kali (432,000 years) which rotates in succession. Kali means "discord," "struggle".
And all of these add to 4,320,000 years. Now, these four yugas, taken together, constitute one Mahayuga. One thousand Mahayugas are one day of Brahma. Brahma's one day is one Kalpa. So one day of Brahma will be 432 crores or 4,320 million years or 4.32 billion years. A similar expanse of time will make His one night, and that is another Kalpa. Our wildest imagination staggers in conceiving Brahma's life-span. This is the expansive view of time. No other culture had this unique vision of the infinity of time as well as the infinity of space.
vedic mathematics 

Hindu cosmology-Part 1

Western archeologists have a curious notion that although human beings have been around for hundreds of thousands of years, civilization itself is a recent invention of only six thousand years ago. It is believed and taught that the cradle of civilization began in the fertile crescent of the
The problems in tracing origins back through time are many. First is the fact that great periods of time have a tendency to erase traces of cultures. When all traces decay then the culture is effectively obliterated. Whatever is left undestroyed by time becomes subjected to the cultural and personal opinions of archeologists. Such opinions may destroy and obliterate knowledge of the culture much more effectively than time ever could. In the west we have a tradition of trying to understand life by studying corpses or trying to know health by studying disease. Archeology becomes an exercise of the imagination when trying to reconstruct a living culture based on remains of pot shards, bones and bricks.
Prior to the nineteenth century, it was piously believed in western civilization that the earth was created in seven days at around five thousand years ago. The Biblical version of creation was challenged by the dual developments of Darwinism and the discovery of dinosaur fossils. Even though the gradual acceptance of these new ideas forced a revision of geological time scales, a corresponding revision within archeological studies lagged. Part of this may have been due to another emerging ideology of the nineteenth century called progressivism. Progressivism is the idea that human beings are in a progressive march towards a goal of better living and greater knowledge. This seductive ideology had its roots in earlier centuries but had its greatest impact in the second half of the nineteenth century where it influenced the thinking of such great men as Darwin and Marx.
The western tradition of writing history may be traced to the Judeo‐Christian scriptures wherein one group of people with shared beliefs write about the happenings of that group and the people outside that group. The six‐thousand year barrier seems to be a common trait to that tradition. Other cultures, the Hindus for example, regard the earth in terms of billions of years old and civilization in terms of hundreds of thousands of years. The Hindus do not think of time in linear terms with a beginning and an end. Rather, they think in terms of great cycles of thousands and millions of years.
Hindu scriptures were routinely disparaged by early British indologists as exaggerated stories an myths. Biblical stories on the other hand where accepted by the same indologists as being somewhere between salient fact and articles of faith. German indologist Max Müller proposed the theory about Aryan invaders colonizing India from the north. This implies that the Indians are so inferior that it is unlikely, if not impossible, for them to civilize themselves without outside help. Native versions of the Indian origins found within living tradition and culture were totally ignored and thought to be unreliable. The British occupation of India produced scholars who's pious duty was to discredit the Hindu tradition and culture. Dates of events given in Hindu scripture based thousands of years ago were redated by the English to have occurred after the birth of Christ for no other reason than one could never rely on the version of a Hindu; the speculations of an English nobleman being wholly preferable. It remains ironic, however, that even if the dates given by the English be accepted at face value, the Hindu accomplishments in art, architecture, science, mathematics, literature, medicine and philosophy were made at a time when the English and all of Europe were still living a neolithic lifestyle.
Contrary to this point of view, it can be shown that not only did the Hindus develop a mature culture independent from western influences, the western cultures borrowed from the Hindus more often than otherwise.

Hindu astronomy, their method of observation and the resulting calendrics differs considerably from the Greeks. Now the question arises that if the Hindus borrowed from the Greeks why didn't the Hindus also modify their calendar with the Greek calendar? Remember that ancient astronomy and calendrics were inseparable. Another point: It is a usual occurrence that a borrowed concept takes along a borrowed technique. The methods of observation usually accompanies the knowledge of the things observed. Why is it that the Hindus have a totally unique system of measurement and observation indigenous to their astronomical lore? The champions of western culture would have us overlook these details.
It seems highly evident that the co‐existing Indian and Mesopotamian cultures exchanged ideas long before the Greeks learned how to civilize themselves. Any similarity between Greek and Hindu sciences is either co‐incidental or due to Greek plagiarism of Indian and Mesopotamian concepts. Yet the bias regarding Greek primacy in all things ancient persists in western educational institutions today. Cultural bias is as destructive of fact as is the passage of time erasing artifacts. What is often passed off as profound knowledge and discovery is nothing more than the reinforcement of bias.
The main concern that would indicate the existence of civilization long before six thousand years ago is that of time measurement or calendrics, the study of which reveals much of what is missing from the digging and dating of bones. The calendar is a vital point of focus for any organized culture or society. Religious, economic and agricultural activities revolve around the calendar. To construct accurate tables of heavenly cycles, a culture must observe the sky for many centuries or at least borrow tables from another culture that has spent centuries studying the heavens. The amount of accuracy derived from observing the heavens over a long period of time suggests that the roots of civilization and some of its earliest accomplishments are much older than six thousand years. Specifically the Indian and Mesopotamian cultures.

Basis of the Sexagesimal System

The sexagesimal system of measurement is based on the number sixty. There are sixty seconds in a minute, sixty minutes in a hour. When we measure angles, we use the sexagesimal to express units in degrees, minutes and seconds. This method of measurement familiar to both the Indian and Mesopotamian cultures. It may be that one culture borrowed from the other or that both developed the system independently. Or it could be of such antiquity that both cultures shared a common origin. Whatever the case, it seems quite evident that the sexagesimal system may be based in large part upon the observation of the planets, specifically Jupiter and Saturn.
After every sixty years, Jupiter and Saturn will return to the same relative place in the zodiac. Even though they conjoin every twenty years, it is every third conjunction that they will be in the same zodiacal position as they were sixty years before. Jupiter takes twelve years to complete one circuit of the zodiac. It takes thirty years for Saturn to complete a similar circuit.
Consider the following:
  1. Jupiter takes twelve years years to transit the zodiac. The zodiac has twelve signs. Jupiter travels an average thirty degrees or one complete sign in one solar year.
  2. Saturn takes an average thirty years to transit the zodiac. Each zodiacal sign has thirty degrees and Saturn travels one degree per month. Thirty months for Saturn to travel one sign. Three hundred and sixty months for Saturn to transit the entire zodiac. Jupiter divides the zodiac into twelve parts or signs. The number derived from Saturn's motion suggests the division of each sign into thirty parts or degrees.
  3. Jupiter and Saturn take sixty years between conjunctions to reach the same place in the zodiac. This joint motion suggests the third and fourth division of the degree into sixty minutes and each minute into sixty seconds.
The sixty years cycle of Jupiter and Saturn gives rise to another interesting number. In a sixty year period, Jupiter will complete five circuits of the zodiac and Saturn will complete two circuits. The combined individual cycles equal seven which is also the total number of visible planets plus the two luminaries.

The Seven Day Week

The primacy given to Saturn and Jupiter becomes apparent by the study of the origination of the seven day week which, contrary to common opinion, was not followed by everyone in the ancient world.
The ancient Egyptians had a ten‐day week. The Vedic Indians had a six‐day week. The ancient Babylonians who started the month on the day after the new moon, had the first, eighth, fifteenth and the twenty second day marked out for religious services. This was a kind of seven‐day week with sabbaths, but the last week might be of eight or nine days duration, according as the month, which was lunar, had a length of 29 or 30 days. The ancient Iranians had a separate name for each day of the month, but some days, at intervals of approximately seven, were marked out as Din‐i-Parvan, for religious practices. The pattern followed appears to have been similar to the Babylonian practice.
The continuous seven‐day week was evolved on astrological grounds by unnamed Chaldean astronomers at an unknown epoch, but at least, long before the first century AD, the Jews adopted it as a cardinal part of their faith during the days of their contact with the Chaldeans.
Chaldean astronomers flourished between the seventh century BC and the third century AD. They gave particular attention to the study of the movement of the Sun, the Moon, and the planets, which they identified with their gods. They believed the destiny of kings and states were controlled by the gods, (the planets), and attached the greatest importance to the observation of their positions and movements. They attached magical value to the number seven which was the number of planets or gods controlling human destiny. The two outermost planets, Jupiter and Saturn, moved slowly and solemnly and therefore determined the measured boundaries of all planets within. After every sixty years Jupiter and Saturn meet in the same general area of the zodiac. During that sixty years, Jupiter completed five circuits of the zodiac and Saturn completed two circuits. The combined number of circuits for these ponderous planets is seven.
Jupiter and Saturn along with the Sun, Moon, Mercury, Venus and Mars, were identified with the chief gods of the Babylonian pantheon.
Table 1: Babylonian gods represented in the heavens by the planets.

Body God Function
1SaturnNinibGod of Pestilence and Misery
2JupiterMardukKing of the Gods
3MarsNergalGod of War
4SunShamashGod of Law and Justice
5VenusIshtarGod of Fertility
6MercuryNabuGod of Writing
7MoonSinGod of Agriculture
Notice that the order of the planets in Table 1 coincides with the apparent average daily motion of the planets from the slowest, Saturn, to the fastest, the Moon.
These seven gods, sitting in solemn conclave, control the destinies of kings and countries, and it was believed that their will and judgment with respect to a particular country or its ruler could be obtained from an interpretation of the position of the seven planets in the heavens, and the nature of the motion of the planets (direct or retrograde). Part of the divinatory practices included knowing what part of the day or night was being ruled or watched over by the gods. Occurrences during a particular watch was believed to forebode particular events consistent with the nature of the watching god.
The day was divided into 24 hours, and each of the seven gods was supposed to keep watch on the world over each hour of the day in rotation. The particular day was named after the god who kept watch at the first hour at Sunrise. Thus on Saturday, the watching god on the first hour was Saturn, and the day was named after him. The succeeding hours of Saturday were watched by the seven gods in rotation as follows:
Figure 1
Above shows the picture for Saturday. On this day Saturn keeps watch at the first hour, so the day is named after him. The second hour is watched over by (2)Jupiter, third by (3)Mars and so on. Saturn is thus seen to preside at the 8th, 15th and 22nd hours of Saturday. Then for the 23rd, 24th and 25th hours come in succession (2)Jupiter, (3)Mars and (4)Sun. The 25th hours is the first hour of the next day, which is accordingly named after the presiding planet of the hour, viz, (4) which is the Sun. We thus get Sunday following Saturday. If we now repeat the process, we get the names of the week days following each other, as follows:
Figure 2
Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday.
The Jews, it may be mentioned, reckon the days by ordinal numbers—the first, second, third…seventh day. Although they derived their calendar almost entirely from the Babylonians, they eschewed the god names as being inconsistent with their monotheistic religion. the ordinal first day is Saturday, which is their sabbath.
The ancient Indians did not use the seven day week. The most ancient usage of day names used in India was that of the Nakshatra. There are twenty seven lunar asterisms or constellations in the old lunar zodiac. This number was derived from the average number of days it took the Moon to complete one circuit of the heavens in relation to any particular star (one sidereal revolution). Since the Hindus didn't use hours to divide their day, the natural consequence of using a seven day week would not follow. Instead they divided a day into 60 equal parts called ghatikas. Each ghatika is equal to 24 minutes. The word "ghatika" means little jar and thus the use of water clocks suggest itself. A ghatika is further divided into 60 vinadikas. So between the two cultures, it was the Hindus who made direct use of the sexagesimal system whereas the Chaldeans used an indirect method of 24 hours.
It wasn't until much later in the third century AD where we find the first usage of the seven day week in India. Indeed much of the rest of the world had not adopted it until after the first century AD. It was unknown to the writers of the New Testament who did not mention anything about the day of the week on which Christ was crucified or the the week day which he is alleged to have ascended to heaven. The fixing of Friday and Sunday for these incidents is a later concoction, dating from the fifth century after Christ. All that the New Testament books say is that he was crucified on the day before the Hebrew festival of Passover which used to be celebrated and is still celebrated on the full‐moon day of the month of Nisan. The continuous seven day week was unknown to the classical Greeks, the Romans, the Hindus and early Christians. It was introduced into the Christian world by an edict of the Roman emperor Constantine, about 323 AD, who changed the Sabbath to the Lord's Day (Sunday), the week day next to the Jewish Sabbath. Its introduction into India is about the same time and from the same sources. The week days are not found in earlier Hindu scriptures like the Vedas of the classics like the great epic Mahabharata. They occur only from 484 AD, but not in inscriptions of 300 AD or earlier. Even now, they form but an unimportant part in the religious observances of the Hindus which are determined by the Moon's phases and lunar asterisms.
In the schema of the Moon's phases we see a repeated pattern to that of Jupiter and Saturn. A lunar month is made up of 30 tithis. Each tithi is determined when the moon moves in advance of twelve degrees ahead of the Sun. Here we see the numbers 30 and 12 that are common with Saturn and Jupiter. A complete synodic period (a complete revolution around the zodiac in relation to the Sun) of the Moon, however, takes only 29 civil days. (A civil day for the Indians is reckoned from sunrise to sunrise). It is quite a regular occurrence for a tithi to be expunged from the consecutive civil day count. This characteristic of the Hindu calendar is not found in the Greek, Chinese or Mesopotamian calendars. Other cultures, without exception, use solely a civil day count of 28, 29 and 30 days for their lunation cycles and had not even considered a pure lunar day count independent from the civil reckoning. The consistency of the Hindu astronomical methods make it unlikely that they borrowed their knowledge from other sources. And the repeated usage of the sexagesimal measurement makes it more like that they were the inventors of the system.
The lunar asterisms (nakshatras) are derived from the average daily motion of the Moon's mean sidereal cycle, which is 13° 20′ of arc. In a circle of 360 degrees this would make twenty seven nakshatras. Each nakshatra has a planetary ruler and they are shown as follows:
Table 2: Nakshatras and their associated planetary rulers.

Nakshatra Ruler
11Purva PhalguniVenus
12Uttara PhalguniSun
20Purva AshadhaVenus
21Uttara AshadhaSun
25Purva BhadraJupiter
26Uttaea BhadraSaturn
In the above table you may have noticed the two strange words "Rahu" and "Ketu". These are the nodes of the moon and their usage in astronomy is important for predicting the eclipses of the Sun and the Moon. Although they possess no mass or density, they are treated as planets in the sense that they have an effect on human affairs.


Whatever constellation (nakshatra) the Moon was in at sunrise, the entire day was named after it. The nine rulers of the nakshatras are repeated three times in sequence. So in this sense you can say that the Hindus followed a nine‐day week. The same effect as a weekday is thereby achieved in terms of socio‐religious significance. Whereas the Chaldeans used an unbroken consecutive day count of hour and day rulers. The Hindus used a more concrete system of the observable Moon in a group of stars. But there is a common thread that is stitched between both the seven‐day week and the twenty seven nakshatras. It is this: As we look back to Figure 2 we see a seven pointed star indicating the weekday lords. Saturn is placed at the top because he is the slowest planet and the week was deemed to start with Saturday. Lets rotate that star and place the Sun at the top.
Figure 3
Now in Figure 4, lets make room for two more planets:
Figure 4
This figure appears in a book by Chiero the famous palmist in which he refers to this as the "Seal of Solomon." Other writers assert that ther are many different Seals of Solomon and that this is only one. Whatever the case may be, if we were to add two more planets to this seal the obvious place would be in the areas vacated by the points of Jupiter and Mercury. Their placement in the seal is shown in Figure 5.
Figure 5
Hindu astrology treats the nodes as planets even though they possess no mass and density. They are sensitive points where the path of the Moon crosses the path of the Sun. Being invisible, it is quite fitting that they should not have a point of the star aiming at them in the diagram shown above.
But note the general position of the planets and see how they are unchanged from the Chaldean star order. Now, the next diagram, Figure 6, will show the connection with the Hindu nakshatra order.
Figure 6
Compare this diagram with Table 2, Nakshatras and Rulers. Here the order is clockwise starting with Ketu, going to Venus, the Sun, down to the Moon, back up to Mars, over to Rahu, Jupiter, Saturn and finally bypassing over to Mercury. The detour down to the Moon doesn't seem so strange when you consider that the nakshatra reckoning is entirely dependent upon the Moon's position in the constellations. In fact, this diagram may taken as a single pointed star with the significant planet being at the single point.
It seems that the similarities between Hindu astronomy and Chaldean magical seals are too great to be a mere coincidence. It is quite likely that the two share a similar origin or that one was derived from the other. But since ancient Hindu tradition and current usage make more consistent usage of a direct base sixty system of counting, and the other cultures use a derivative of that, it seems more likely that the sexagesimal is of Hindu origin.
It may be argued that the sexagesimal was not founded upon the joint cycles of Jupiter and Saturn but upon some other measurement such as the average number of three hundred and sixty days in a year. This, of course, is assuming that ancient man was incapable of counting the correct number of days in a year and that he was infinitely unclever. For the sake of argument, lets accept that position. There still remains the problem of dividing the year into parts that would yield a base sixty system of counting. The Babylonians divided their year into three seasons. The Hindus, however, divided their year into six seasons. Of the two cultures which do you think would arrive at a base sixty system?
But judging from the rest of Hindu astronomical techniques it is clear that they knew precisely how long the solar year was. All the other planetary cycles were also studied with great scrutiny. From this it may be tempting to think that the sexagesimal was arrived at in order to provide the great average mean of measurement for celestial phenomena just as today the binary mode of counting is most convenient for computer science. Three hundred and sixty, which is a multiple of the sexagesimal, is the midpoint number between the 365 day solar year and the 354 day lunar year. One synodic period of mars is 780 days which is equally divided by 60 thirteen times. Between two consecutive conjunctions of Saturn and Jupiter in a twenty year period, Mercury will go retrograde a little over sixty times. The Hindus also based their knowledge of breath control, Pranayama, upon the sexagesimal system. In one twenty four hour period, or between two consecutive sunrises, a person takes an average of 21600 breaths, each breath being four seconds long. This number, 21600 divided by 60 equals 360.
To all but the harshest critic the above may be evidence enough to form an opinion on the origin of the sexagesimal system. But the critic may remain unconvinced for various reasons. The above is only circumstantial. One can apply any number of coincidental facts to any ancient culture and come up with some pretty amazing things. After all, no ancient text were quoted giving support to Hindu origins. To quell these doubts we present final evidence that not only shows the superiority of Hindu astronomy but also proves damaging to the theory that the Greeks were the greatest in all matters of the ancient world.

Hindu Cosmological Time Cycles

The structure of Hindu astronomy is built upon the foundation of their unique concept of cosmological time cycles. No other culture on Earth has or is known to have such a unique system of cosmology. The only other culture to come close to the vast scale of time conceived by the Hindus are the Mayan. Western scholars have completely misunderstood the value of the Hindu cosmological time cycles and believed them to be nothing more than crude number speculations. In their translation of the Surya Siddhanta, the editors Burgess and Whitney routinely disparage the Hindu authors:
The system of periods is not of astronomical origin…Its artificial and arbitrary character is apparent. It is the system of the Puranas and Manu, a part of the received Hindu cosmogony, to which astronomy was compelled to adapt itself… The arbitrary and artificial method in which the fundamental elements of the solar system are here represented is not peculiar to the Surya‐Siddhanta; It is also adopted by all other text books, and is to be regarded as a characteristic feature of the general astronomical system of the Hindus.
Not only is this opinion in error but the astronomical quantities derived from these cosmological time cycles are vastly more accurate than anything achieved by the Greeks. And they were in use at a time when the Britons were still living a neolithic lifestyle.

Outline of Hindu Cosmology

Prior to the creation of the universe, Lord Vishnu lies asleep on the ocean of all causes. He rests upon a serpent bed with thousands of cobra‐like hoods. While asleep, a lotus sprouts from His navel. Upon this lotus is born Brahma the creator of the universe. Lord Brahma lives for a hundred years and then dies, while Lord Vishnu remains. One year of Brahma consists of three hundred and sixty days. At the beginning of each day Brahma creates the living beings that reside in the universe and at the end of each day the living beings are absorbed into Brahma while he sleeps on the lotus. One day of Brahma is known as a kalpa. Within each kalpa there are fourteen manus and within each manu are seventy one chatur‐yugas. Each chatur‐yuga is divided into four parts called yugapadas.
From the first chapter of Surya‐Siddhanta, the most revered authoritative source of Hindu astronomy, we have the following passage:
11 That which begins with respirations (prana) is called real… Six respirations make a vinadi, sixty of these a nadi: 12 And sixty nadis make a sidereal day and night. Of thirty of these sidereal days is composed a month; a civil (savana) month consists of as many sunrises; 13 A lunar month, of as many lunar days (tithi); a solar (saura) month is determined by the entrance of the Sun into a sign of the zodiac; twelve months make a year. This is called a day of the gods. 14 The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise to the demons. 15 Twelve thousand of these divine years are denominated a chatur‐yuga; of ten‐thousand times four hundred and thirty two solar years is composed that chatur‐yuga, with its dawn and twilight. 16 The difference of the krita‐yuga and the other yugas, as measured by the difference in the number of the feet of virtue in each is as follows: 17 The tenth part of a chatur‐yuga, multiplied successively by four, three, two, and one, gives the length of the krita and the other yugas: the sixth part of each belongs to its dawn and twilight. 18 One and seventy chatur‐yugas make a manu; at its end is a twilight which has the number of years of a krita‐yuga, and which is a deluge. 19 In a kalpa are reckoned fourteen manus with their respective twilights; at the commencement of the kalpa is a fifteenth dawn, having the length of a krita‐yuga. 20 The kalpa, thus composed of a thousand chatur‐yugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length. 21 His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the firsts kalpa. 22 And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvat, twenty seven chatur‐yugas are past; 23 Of the present, the twenty eighth chatur‐yuga, this krita‐yuga is past…
Now to make plain what is stated above. Commentaries are very clear on the fact that in verse 12 the "sidereal day" refers to a revolution of the Earth relative to any fixed star and is the true revolution reference point of the Earth. Verse 13 refers to "a day of the gods" means one sidereal year. A night of the gods is half a sidereal year. Verse 21 mentions "his extreme age is a hundred refers to the lifespan of Brahma and consists of one hundred years of 360 days. Each of these days being two kalpas long. Verse 23 shows that the Surya‐Siddhanta was composed right after krita‐yuga and during the treta‐yuga. The present yuga we are in right now is the kali‐yuga which is said to have begun on Friday February 18th 3102 BC of the Julian calendar. This becomes clearer when represented in a tabular form.
Table 3: Infrastructure of the Chatur–Yuga period.

Divine Years Solar Years
Krita–Yuga Period
Treta–Yuga Period
Dvapara–Yuga Period
Kali–Yuga Period

Infrastructure of the Kalpa Period

Two kalpas make a day and night of Brahma. The kalpa is 4,320,000,000 sidereal years made up of 1,000 chatur‐yugas or 10,000 kali‐yugas. An additional dawn and twilight of 1,728,000 years each is made to fit the kalpa.
one Chatur‐Yuga =4,320,000 sidereal years
one Manu = 71 Chatur‐Yugas = 306,720,000 sidereal years
+ 1 Krita‐Yuga = 1,728,000 sidereal years
=308,448,000 sidereal years
one Kalpa = 14 Manus = 4,318,272,000 sidereal years
+ 1 Krita‐Yuga = 1,728,000 sidereal years
=4,320,000,000 sidereal years
The entire lifepsan of Brahma may be measured thus:
Day of Brahma4,320,000 sidereal years
Night of Brahma4,320,000 sidereal years

8,640,000 sidereal years
× 360 days in a year3,110,400,000,000 sidereal years
× 100 years311,040,000,000,000 sidereal years
After Brahma dies it takes a period of time equal to his lifespan until he is reborn and the cycle starts over.

Derivation of Astronomical Values

Now that the Hindu cosmological time cycles are completed we can derive useful astronomical values from them. The first is the measurement of the day which begins with the breath. One respiration is a prana. Six prana equal one vinadi. Sixty vinadis equal one nadi, (also known as a ghatika). Sixty nadis equal one sidereal day. A sidereal day equal the time it takes for the earth to make one complete rotation on its axis in relation to a fixed star. A sidereal day is slightly shorter than a civil day of 24 hours. A sidereal day is equal to 23 hours, 56 minutes and 3.4446 seconds.
one sidereal day 23h 56m 03.4446s
sixty nadis 23h 56m 03.4446s
one nadi (ghatika) 23m 56.06s
vinadi 23.93s
one prana 3.99s
It is clear in the text of Surya‐Siddhanta and the current practice of Indian astrology that sidereal measurements are of primary importance. Tropical measurements are also used but in a secondary way.

Three Mean Motions of the Sun

The three mean motions of the Sun used to construct the Cosmological Time Cycles shown above are as follows:
one sidereal year = 360 sidereal days
+ 6 sidereal days
+ 0.2563795 sidereal days
= 366.2563795 sidereal days
Remember we are not talking about civil solar days here, we are talking about the total number of times the Earth rotates on its axis in relation to a single star during the course of one year. This happens to be one greater than the mean solar days in a year which is…
One sidereal year
365.2563795 mean solar days
These three mean motions of the Sun may be compared to the hour, minute and second hands of a clock. Each cycle is counted and completed separately. Using this system of the three mean motions, the ancients reckoned time that put the day, year and longer periods of time into exact correspondence with each other.

Proof of the Sexagesimal Number System

The first two mean solar motions, that of 360 + 6 Earth revolutions, generate the sexagesimal number system completely. A count of six for every 360 is the same as one for every 60. This is the basis of the six seasons of the year observed by the Hindus. Counting six days per year, the second mean motion of the Sun completes a cycle of 360, the number of degrees in a circle, after 60 years which correlates with the Babylonian sossos period and the cycles of Jupiter and Saturn.
Table 4: The structure of the Babylonian sossos period.
(sossos) 6021,60036021,960
(neros) 600216,0003600219,600
(saros) 36001,296,00021,6001,317,600
In the same interval that the first mean motion completes a count of 21600 it has done so at a rate 60 times greater than the second mean motion 360 × 60 and represents the number of arc minutes in a circle. The number 21600 is also the same average number of breaths (prana) a person will make in a 24 hour period.

Vedic Evidence of the Sidereal Year

The Rig Veda, the earliest of the Hindu scriptures says the following:
Twelve spokes, one wheel, navels three. Who can comprehend this? On it are placed together three hundred and sixty like pegs. They shake not in the least. (Dirghatama Rishi, Rig Veda 1.164.48)
A seven‐named horse does draw this three‐naved wheel… Seven steeds draw the seven‐wheeled chariot… Wise poets have spun a seven‐strand tale around this heavenly calf, the Sun. (Dirghatama Rishi, Rig Veda 1.164.1‐5)
The number seven related to the Sun has much significance when understanding the third mean solar motion (0.2563795). The Kali‐yuga of 432,000 years is the unit of reference for determining the length of the sidereal year in Hindu cosmological time cycles. During the course of 10,000 years there are seven rotations of the third mean solar motion. For a single year the count is 0.2563795 diurnal revolutions of the earth. For two years it is .512759 and so on. One complete rotation (to equal 366.2564…) of the third motion takes 1428.571429 sidereal years. Or you can reduce it to a fraction of 1428⁴⁄₇ sidereal years.

= 10000

= 1428⁴⁄₇ sidereal years
The integer of this sidereal interval, 1428 years, multiplied by the number of years in a Kali‐yuga and then further multiplied by seven equals the number of years of fourteen Manus. (see table 4).
1428 × 432,000 × 7 = 4,318,272,000 = 14 manus
The fractional part of this sidereal interval, ⁴⁄₇ years, multiplied by seven and further multiplied by the number of years in a Kali‐yuga equals the time of an introductory dawn (see table 4).
⁴⁄₇ × 7 × 432,000 = 1,728,000 years = introductory dawn.
Relating the Vedic verses above to what we have just demonstrated it is clear that the "navels three" refer to the three mean motions of the Sun and "seven‐wheeled chariot" to the rate of precession of the equinoxes. Thus, there can be no doubt that the cosmological time cycles were already an established conclusion at the time of the Vedic era and not in the formative stages.

Precesional Constant Demonstrated

Before demonstrating the unmistakable fact of the precession inherent in the cosmological time cycles, let us show the readers how the Western translators of the Surya‐Siddhanta made fools of themselves when they wrote:
To make such a division accurate, the year ought to be tropical, and not the sidereal; but the author of the Surya‐Siddhanta has not yet begun to take into account the precession…The earliest Hindu astronomers were ignorant of, or ignored, the periodical motion of the equinoxes…
Again this opinion is in error. If Burgess and Whitney were not so blinded by cultural arrogance and conceit they might have been able to improve their knowledge by careful study of the Surya‐Siddhanta. The precession is clearly derived from the cosmological time cycles as shown below. The chatur‐yuga of 4,320,000 years is the unit of reference for determining the rate of precession used in the construction of the Hindu cosmological time cycles.
The constant rate of precession is 50″.4 = 0°.014 = ⁷⁄₅₀₀ degrees of precession per sidereal year.
This is the same as one degree of precession in 71³⁄₇ = 71.42857 sidereal years.
This correlates to the cosmological time cycles as follows:
One manu
71.4 chatur‐yugas
¹⁄₁₄th of an introductory dawn
0.02857… chatur‐yugas
¹⁄₁₄th kalpa
71.42857… chatur‐yugas
In the interval of ¹⁄₁₄th kalpa there are:
(71³⁄₇) × 4,320,000 × 0°.014 = 4,320,000 degrees of precession = 12,000 precessional years
From table one we see that a period of one chatur yuga is 4,320,000 years and is equivalent to 12,000 divine years.
Is it just a happy coincidence that the Cosmological Time Cycles agree with the precession? Burgess and Whitney would probably think so.
Other related values of interest are:
1 precessional year
25,714²⁄₇ sidereal years
7 precessional years
180,000 sidereal years
7 × 18 (126) cycles of the 3rd mean mothion of the Sun
7 × 24 (168) precessional years
1 chatur‐yuga
168,000 precessional years
1 kalpa
(4,320,000 ÷ 168) × 0°.014 = 360°

Derivation of the Tropical Year

In a chatur‐yuga there are: 4,320,000 sidereal years = 4,320,000 + 168 tropical years, where 168 is the number of precessional years. Therefore:
1 tropical year =
4,320,000 × (366.2563795… −1)


= 365.2421756… mean solar days
It has been shown conclusively that the Hindu Cosmological time cycles are based upon the diurnal motion of the Earth in reference to any particular fixed star, hence it is purely of sidereal origin. The later practice of adopting the ahargana or "heap of days" is based upon solar and civil day reckoning which is of obvious practical value for calendrics. The sidereal basis of the cosmological time cycles is without question the oldest known positive proof of the origin for the sexagesimal number system.

Comparison With Modern Science

The standard values for the tropical year and annual precession in longitude determined by Simon Newcomb for the epoch 1900.0, mean noon at Greenwich December 31st 1899 are:
One tropical year
Precession in one year
The sidereal year and its precessional constant may be derived from these values.
1 sidereal year (1900.0) =

360° − 50″.2564
× 365.2421988 + 1

= 366.2563627 diurnal revolutions of the Earth
Precession in longitude in one year = 50″.2564 ×


= 50″.2583
The following shows the astronomical quantities used in the construction of Hindu cosmological time cycles with those of Simon Newcomb for the epoch 1900.0

Constant of Precession50″.4 / year50″.2583 / year0″.1417 / year
Sidereal Year (Solar)365.2563795365.25636271.4 seconds / year
Tropical Year365.2421756365.2421988−2.0 seconds / year
The sidereal year in the above table refers to the number of solar civil days it takes for the earth to orbit the sun in relation to any particular star. The former is a sidereal‐diurnal relation and the later is a sidereal‐solar relation. The very close agreement between the length of the year as measured by Hindu cosmological time cycles and that determined by modern science, together with the demonstrated great antiquity of the cycles, shows that the rotation of the Earth is not being sensibly retarded by "tidal friction" or any other cause. Astronomers today would do well to look for lack of accuracy in their measurement of the Sun's mean motion and to the variations of long periods in the rotation of the Earth to explain the so‐called slowing down of the earth.

Breaking The Barrier

The question may be asked how could such accurate constants of precession, as that of the Hindu cosmological time cycles, have been obtained without modern instruments and techniques? At least one thing must be allowed for and that is a very long period of uninterrupted observation.
Naked eye observations are accurate up to one sixth of a degree. In the case of observing the precession moving uniformly on the celestial sphere, it would then be possible to obtain an accurate rate up to three decimal places in not less than 50″ × (72 years ÷ 1°) or 3,600 years. Measuring the precession is not as simple as that, however. Before attempting to measure the precession, the exact times of the equinoxes must be measured first. Ptolemy, the Greek astronomer, speaks with pride in the Almagest of "very accurately" observing the equinox to within a quarter of a day! That is, to within at best one quarter of one degree of arc. Add to this the difficulty presented by the proper motion of the stars. The star Sirius, for example, has a very large proper motion of −0″.553 ecliptic longitude per year. It would take 1,000 years for Sirius to move one sixth of a degree and for this mistake to be noticed by a naked eye observer. In addition to this, still, the motion of the Earth's perihelion would become noticeable and have to be accounted for. With all these factors, it is difficult to imagine how they can be resolved into a system that would allow continuous observation to produce a constant of precession accurate to three decimal places in less than 10,000 years.
Similar arguments can be put forth to show that to measure the sidereal period of the Sun to eight decimal places could not be accomplished by naked eye observations alone in any less time.
Even if we cannot comprehend a civilization going back 10,000 years prior to the six‐thousand year barrier, we still must face the incredible genius of the cosmological time cycles themselves: a calendar for eternity so accurate that its formulations must be considered as laws of nature, while at the same time a structure so simple, symmetrical, and orderly, that the best scholars and astronomers of modern times have completely failed to see the astronomical basis. In this light we can understand why the Hindus regarded this knowledge as a revelation from the gods.