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Hindu cosmological time cycles represent numerically the life of our solar system and are a comprehensive system of time measurement based upon the sexagesimal number system with units as small as 1/216000 of a day and as large as 3.11041014 years.

To demonstrate the astronomical quantities which lie behind the cycles, we require only the principal unit of the cycles, namely, the kalpa period, and its three principal subunits: the manu, caturyuga, and kaliyuga intervals.

In Hindu cosmogeny, all things proceed toward perfection in cycles of repeated incarnations. During the vast interval of one kalpa, the god of our solar system manifests all sentient creatures out of himself. Hindus call this a "day of Brahma". After this, the god of our solar system returns all sentient creatures to himself for the interval of one kalpa. Hindus call this a "night of Brahma".

Traditional Indian textbooks on astronomy contain descriptions of Hindu cosmological time cycles as part of their general discussion of the divisions of time. Some scholars say there are two versions of the cycles, but the so-called Aryabhata (circa 500 A.D.) version is really slightly corrupted due to the fact that Aryabhata summed up the entirety of the time cycles in a single verse of his text, thereby leaving out essential details. In the Clark translation of the Aryabhatiya verse 3 we find:

The following complete description of the cycles comes from the Burgess translation of the SuryaSiddhanta:
  1. That which begins with respirations (prana) is called real.... Six respirations make a vinadi, sixty of these a nadi;
  2. 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;
  3. 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.
  4. 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 of the demons.
  5. Twelve thousand of these divine years are denominated a caturyuga; of ten thousand times four hundred and thirty-two solar years
  6. Is composed that caturyuga, with its dawn and twilight. The difference of the krtayuga and the other yugas, as measured by the difference in the number of the feet of Virtue in each, is as follows:
  7. The tenth part of a caturyuga, multiplied successively by four, three, two, and one, gives the length of the krta and the other yugas: the sixth part of each belongs to its dawn and twilight.
  8. One and seventy caturyugas make a manu; at its end is a twilight which has the number of years of a krtayuga, and which is a deluge.
  9. 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 krtayuga.
  10. The kalpa, thus composed of a thousand caturyugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length.
  11. 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 first kalpa.
  12. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvant, twenty-seven caturyugas are past;
  13. Of the present, the twenty-eighth, caturyuga, this krtayuga is past....
Commentaries make plain that in verse 12 "sidereal day" refers to a true revolution of the Earth1, that in verse 13 "a day of the gods" refers to the sidereal year, although "a night of the gods" is half of a sidereal year, and that in verse 21 "his extreme age is a hundred" refers to one hundred years of 360 days, each one of these days being two kalpas long. The text is presented in verse 23 as being composed after a krtayuga, but Indian tradition gives the present age as two yugapadas later. The present yugapada, a kaliyuga, is said to have begun on Friday 18 February, 3102 B.C. of the Julian calendar.

The following three tables, taken from the English commentary to the Burgess translation of the SuryaSiddhanta, clearly present the infrastructure of Hindu cosmological time cycles.

1. In modern astronomy, a sidereal day is the interval of time between two successive passages of the Vernal point across the midheaven. During this interval, the Vernal point is affected by precession. A true revolution of the earth is a 360 rotation not affected by precession.
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