Hindu Cosmological Time Cycles

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Exegesis of Hindu Cosmological Time Cycles

by 
Dwight William Johnson    (11/03)



©1985, 1991, 1996 Dwight William Johnson
All rights reserved



There are more things in Heaven and earth, Horatio,
Than are dreamt of in your philosophy.
                              (Shakespeare, Hamlet)



Table of Contents 1. INTRODUCTION 2. WESTERN SCHOLARS AND THE ORIGIN OF INDIAN ASTRONOMY 3. OVERVIEW OF HINDU COSMOLOGICAL TIME CYCLES 4. INDIAN SEXAGESIMAL DIVISION OF THE DAY 5. INFRASTRUCTURE OF THE CATURYUGA PERIOD 6. INFRASTRUCTURE OF THE KALPA PERIOD 7. BRAHMA'S LIFE 8. THREE MEAN MOTIONS OF THE SUN 9. EXACT FORMULAE OF THE ASTRONOMICAL QUANTITIES 10. ASTRONOMICAL BASIS OF THE SEXAGESIMAL NUMBER SYSTEM 11. DEMONSTRATION OF THE SEXAGESIMAL NUMBER SYSTEM 12. DEMONSTRATION OF THE SIDEREAL YEAR 13. DEMONSTRATION OF THE CONSTANT OF PRECESSION 14. DERIVATION OF THE TROPICAL YEAR 15. RECTIFICATION OF THE KALIYUGA EPOCH 16. TROPICAL INITIAL POINT OF HINDU COSMOLOGICAL TIME CYCLES 17. FIXED INITIAL POINT OF THE SIDEREAL SPHERE 18. FULL MOON POINTS 19. PISCEAN AGE EPOCH 20. COINCIDENCE WITH THE SURYASIDDHANTA FIXED INITIAL POINT 21. PRECESSIONAL YEAR EPOCH 22. SIRIUS AND THE PLACE OF THE SPRING EQUINOX 23. COMPARISON WITH MODERN SCIENCE 24. COMPARISON WITH THE CURRENT PRACTICE OF INDIAN ASTRONOMY 25. THE 360 + 5 DAY YEAR CALENDARS OF ANTIQUITY 26. EVIDENCE OF THE VEDAS 27. WHO CREATED THE TIME CYCLES? 28. CONCLUSION BIBLIOGRAPHY AND SUGGESTED FURTHER READING
1. INTRODUCTION Long regarded as non-astronomical by historians of science, Hindu cosmological time cycles are shown here to be the most accurate solar calendar known, the progenitor of the sexagesimal number system and the 360 + 5 day calendars of antiquity, and one of the greatest achievements of humanity. Hindu cosmological time cycles, as well as common units of measuring time and angles, are generated from the concept that the Sun has three distinct mean motions. The exact solar year and constant of precession used in the construction of the cycles may be inferred from their infrastructure. With the astronomical quantities known, the kaliyuga epoch establishes the summer solstice as the beginning of the tropical year and 147108 B.C. as the last conjunction of the summer solstice with the initial point of the sidereal sphere, verifies the fixed initial point of the sidereal sphere given in the SuryaSiddhanta, and points to Sirius as true reference star. Not only does the astronomical basis of the cycles conclusively prove the non-Greek origin and ancient age of Indian astronomical science, but the extremely high level of astronomical knowledge used and method of construction of the cycles cannot be placed in any known historical frame of reference. The implications of these findings for mankind are, therefore, very far-reaching. 2. WESTERN SCHOLARS AND THE ORIGIN OF INDIAN ASTRONOMY For more than a century European and American scholars have held to the conclusion that Indian astronomy must somehow have been borrowed from the Greeks following the invasion of Alexander the Great, even though the Indians have no tradition of this, and Indian astronomy has a form quite unlike Greek astronomy. This conclusion is supported by the following facts: 1) there was extensive trade between India and the West during the Hellenistic period; 2) Indian astronomical science is united with a form of astrology very similar to that cultivated by the Greeks during the Hellenistic period; 3) there are no historical records or accurate chronology to substantiate the Indian's own traditions of the origin of their astronomical science. These scholars concede that Hindu cosmological time cycles, the form around which Indian astronomy is built, are indigenous to Indian culture, but they believe them to be crude number speculations. This view is clearly expressed by the editors of the Burgess translation of the SuryaSiddhanta when they aver of Hindu cosmological time cycles: 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. This conclusion, however, is in error. Below we demonstrate the astronomical basis of Hindu cosmological time cycles. There are many references to Hindu cosmological time cycles in works of Indian literature which are known to be older than Alexander the Great's invasion of India. Also, the astronomical quantities used in the construction of Hindu cosmological time cycles are vastly more accurate than those achieved by the Greeks. We prove by this, therefore, that Indian astronomy was not borrowed from the Greeks. But the significance of the astronomical basis of Hindu cosmological time cycles extends far beyond this. 3. OVERVIEW OF HINDU COSMOLOGICAL TIME CYCLES 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. The key to understanding Hindu cosmological time cycles is the idea of three mean motions for the Sun. But to demonstrate the astonishing accuracy of 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: There are 14 Manus in a day of Brahman [a kalpa], and 72 yugas constitute the period of a Manu. Since the beginning of this kalpa up to the Thursday of the Bharata battle 6 Manus, 27 yugas, and 3 yugapadas have elapsed. The following complete description comes from the Burgess translation of the SuryaSiddhanta: 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 of the demons. 15. Twelve thousand of these divine years are denominated a caturyuga; of ten thousand times four hundred and thirty-two solar years 16. 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: 17. 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. 18. 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. 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 krtayuga. 20. 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. 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 first kalpa. 22. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvant, twenty-seven caturyugas are past; 23. 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 Earth, 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. 4. INDIAN SEXAGESIMAL DIVISION OF THE DAY Table I shows the Indian sexagesimal division of the day. The structural correspondence with the longer time intervals established by the three mean motions of the Sun proves that the Indian sexagesimal division of the day is an intrinsic part of the original system. 10 long syllables (gurvakshara) = 1 respiration (prana) 6 respirations = 1 vinadi 60 vinadis = 1 nadi 60 nadis = 1 day TABLE I 5. INFRASTRUCTURE OF THE CATURYUGA PERIOD Table II shows the infrastructure of the caturyuga period. The caturyuga period is 4320000 sidereal years made up of four major subperiods (yugapadas): the krtayuga of 1728000 years, the tretayuga of 1296000 years, the dvaparayuga of 864000 years, and the kaliyuga of 432000 years. A Divine Year is 360 sidereal years. PERIOD DIVINE YEARS SOLAR YEARS Dawn 400 144000 Krtayuga 4000 1440000 Twilight 400 144000 ---- ------- Total 4800 1728000 Dawn 300 108000 Tretayuga 3000 1080000 Twilight 300 108000 ---- ------- Total 3600 1296000 Dawn 200 72000 Dvaparayuga 2000 720000 Twilight 200 72000 ---- ------- Total 2400 864000 Dawn 100 36000 Kaliyuga 1000 360000 Twilight 100 36000 ---- ------- Total 1200 432000 ----- ------- Caturyuga Total 12000 4320000 TABLE II 6. INFRASTRUCTURE OF THE KALPA PERIOD Table III shows the infrastructure of the kalpa period. The kalpa period is 4320000000 sidereal years made up of 1000 caturyugas of 4320000 years or 10000 kaliyugas of 432000 years. An additional unit, the manu, an interval of 71 caturyugas with an added twilight of 1728000 years, is made to fit into the kalpa 14 times along with an introductory dawn of 1728000 years. INTERVAL CATURYUGAS KALIYUGAS SIDEREAL YEARS introductory dawn 0.4 4 1728000 71 caturyugas 71.0 710 306720000 a twilight 0.4 4 1728000 ------------------ --- --------- 1 manu 71.4 714 308448000 14 manus 999.6 7(1428)=9996 4318272000 ------------- ------ ------------ ---------- 1 kalpa 1000.0 10000 4320000000 TABLE III 7. BRAHMA'S LIFE The kalpas are said to alternate between "days of Brahma" and "nights of Brahma". During the night of Brahma all sentient creatures meet their Maker. But after one hundred 360 day years of days and nights of Brahma, even the matter in the solar system, which has served as the "body" of Brahma, is resolved into chaos. Finally, after an interval of time equal to his life, Brahma and the solar system are again reborn. day of Brahma 4320000000 sidereal years night of Brahma 4320000000 sidereal years ---------- 8640000000 sidereal years days in a year 360 ----------- one year of Brahma 3.11041012 sidereal years one hundred years 100 ----------- Brahma's Life 3.11041014 sidereal years. Brahma's Death 3.11041014 sidereal years. And thus, the Hindu cosmological time cycles are completed. 8. THREE MEAN MOTIONS OF THE SUN The three mean motions of the Sun used in the construction of Hindu cosmological time cycles are 1 sidereal year = 360 (I) 6 (II) 0.2563795... (III) -------------- 366.2563795... diurnal revolutions of the Earth. As the number of diurnal revolutions of the Earth in a year is one greater than the number of mean solar days, we also have 1 sidereal year = 365.2563795... mean solar days. The three mean motions are like the hour, minute, and second hands of a clock. Their cycles are completed and counted separately. Using the three mean motions, the ancients developed a system of time reckoning that put the day, year, and longer time intervals into exact correspondence with each other. 9. EXACT FORMULAE OF THE ASTRONOMICAL QUANTITIES The defining relations of the sidereal year and constant of precession used in Hindu cosmological time cycles may be manipulated algebraically to yield statements of natural law in which the numbers seven and 366 are prominent components. These formulae demonstrate the extreme economy of numbers used in the construction of the cycles. 1 sidereal year = 366.2563795... 366 = --------- 7 1 - ----- 10000 70 71 = 6(60+1)(------ + ------ + . . . 100000 100001 7n + ------ + . . . ) diurnal revolutions 10000n of the the Earth 366 = --------- - 1 mean solar days. 7 1 - ----- 10000 366 1 1 tropical year = --------- ---------- diurnal revolutions 7 7 of the Earth. 1 - ----- 1 + ------ 10000 180000 precession in 1 sidereal year = 0.014 7 366 = -------- --------- 500(360) 7 1 - ----- 10000 1 366 = -- --------- diurnal revolutions 18 10000 of the Earth. ----- - 1 7 3rd mean motion of the Sun = 0.2563795... 366 = --------- diurnal revolutions of the 10000 Earth in one sidereal year ----- - 1 7 = 18 times the precession in 1 sidereal year = 0.252 per year. 10. ASTRONOMICAL BASIS OF THE SEXAGESIMAL NUMBER SYSTEM The first two mean Solar motions, a year consisting of 360 + 6 Earth revolutions, generate the sexagesimal number system in its entirety. These two mean motions of the Sun form the basis for the 366 day year of the Jyotisha Vedanga and are discernible in the SuryaSiddhanta from the fact that the radius of the orbit of the asterisms is given as 60 times that of the Sun. Since in this astronomical system the speed of rotation of a body varies as the inverse of the radius of its orbit, this implies that the asterisms should rotate six degrees while the Sun is rotating 360 degrees. 11. DEMONSTRATION OF THE SEXAGESIMAL NUMBER SYSTEM A count of six for every 360 is equivalent to one for every 60. This is the basic counting principle behind the six Indian seasons. Counting six days per year (see Table IV), the second mean motion of the Sun completes a cycle of 360, the number of degrees in a circle, after 60 years (the Babylonian sossos). YEAR 1ST MEAN MOTION 2ND MEAN MOTION TOTAL 1 360 6 366 2 720 12 732 3 1080 18 1098 4 1440 24 1464 5 1800 30 1830 . . . . . . . . . . . . 10 3600 60 3660 . . . . . . . . . . . . 60 (sossos) 21600 360 21960 . . . . . . . . . . . . 600 (neros) 216000 3600 219600 . . . . . . . . . . . . 3600 (saros) 1296000 21600 1317600 TABLE IV In the same interval the first mean motion (see Table IV) completes a count of 21600=36060, the number of minutes in a circle. A count of the nadis, 1/60ths of a day, in this interval for the first mean motion is 1296000, the number of seconds in a circle. A count of the nadis in this interval for the second mean motion is 21600, the number of minutes in a circle. A count of the first mean motion of the Sun for 600 years (the Babylonian neros) is 216000 (see Table IV), the number of long syllables (gurvaksharas) in a day. A count of the second mean motion of the Sun for 600 years is 3600 (see Table IV), the number of vinadis in a day. After 3600 years (the Babylonian saros), the first mean motion of the Sun has completed a count of 1296000 (see Table IV), the number of seconds in a circle, while the second mean motion of the Sun has completed 21600 (see Table IV), the number of minutes in a circle. 12. DEMONSTRATION OF THE SIDEREAL YEAR The kaliyuga of 432000 years is the unit of reference for determining the length of the sidereal year in Hindu cosmological time cycles. There are seven rotations of the 3rd mean solar motion, counted separately through the sidereal year, in 10000 sidereal years. For a single year the count is 0.2563795... diurnal revolutions of the Earth. For two years it is 2(0.2563795...). For a complete rotation there are 366.2563795... 10000 -------------- = ----- = 1428 4/7 sidereal years. 0.2563795... 7 The integral part of this interval, 1428 years, summed 432000(7) times is equal to 14 manus (see Table III). Thus 432000(7)(1428) years = 4318272000 years. The fractional part of this interval, 4/7 years, summed 432000(7) times is equal to the introductory dawn (see Table III). Thus 432000(7)(4/7) years = 1728000 years. 13. DEMONSTRATION OF THE CONSTANT OF PRECESSION The caturyuga of 4320000 years is the unit of reference for determining the constant of precession used in the construction of Hindu cosmological time cycles. The constant of precession is 50".4 = 0.014 = 7/500 degrees of precession per sidereal year. This is equivalent to one degree of precession in 71 3/7 = 71.42857... sidereal years. The relevant infrastructure of the kalpa period (see Table III) is 1 manu = 71.4 caturyugas 1/14 of introductory dawn = 0.02857... caturyugas --------------------------------------- 1/14 kalpa = 71.42857... caturyugas. In the interval of 1/14 kalpa there are (71 3/7)(4320000)(0.014) = 4320000 degrees of precession = 12000 precessional years. Other relations of interest are 1 precessional year = 25714 2/7 sidereal years 7 precessional years = 180000 sidereal years = 126 = 718 cycles of the 3rd mean motion of the Sun 724=168 precessional years = 1 caturyuga 168000 precessional years = 1 kalpa. 14. DERIVATION OF THE TROPICAL YEAR In a caturyuga there are 4320000 sidereal years = 4320000 + 168 tropical years where 168 is the number of precessional years. Therefore, 4320000(366.2563795... - 1) 1 tropical year = --------------------------- 4320168 = 365.2421756... mean solar days. 15. RECTIFICATION OF THE KALIYUGA EPOCH By some authorities the kaliyuga epoch is said to have begun at Lanka (Ujjain) sunrise on Friday 18 February 3102 B.C. of the Julian calendar, while by others the previous midnight. Indian tradition posits an eclipse of the Sun at the start of the kaliyuga epoch. The Low-Precision Formulae For Planetary Positions by T.C. Van Flandern and K.F. Pulkkinen give the time for this eclipse (conjunction in longitude) as 2:36 p.m. at Greenwich on Julian day 588465. This corresponds to 7:39 p.m. mean local time at Ujjain (75 47' E). The given kaliyuga epoch is therefore a civil epoch, the first day of a lunar month. The modern SuryaSiddhanta in the commentary states that at the kaliyuga epoch the mean longitude of the Sun coincides with the fixed initial point of the sidereal sphere and is 54 from the mean vernal equinox. This is sufficient information to calculate the true astronomical kaliyuga epoch. From the kaliyuga epoch to the next succeeding mean vernal equinox there are 54 ---- 365.2421756 = 54.78632634 mean solar days. 360 We use Simon Newcomb's expression for the Sun's mean longitude in the Explanatory Supplement to calculate the Julian date of the 1900 mean vernal equinox. Thus 360 = 279.696678 + 0.9856473354 d d = 81.47267193 mean solar days JD = 2415020.0 + 81.47267193 = 2415101.473. Therefore, the mean vernal equinox nearest the kaliyuga epoch will be on mean Greenwich Julian date 2415101.473 - (3101 + 1900)365.2421756 = 588525.3525. The astronomical kaliyuga epoch is, therefore, on mean Greenwich Julian date 588525.3525 - 54.78632634 = 588470.5662 or from Lanka (Ujjain) on Julian Date 75 47' 588470.5662 - ------ = 588470.3556. 360 The required rectification constant to convert from the midnight civil kaliyuga epoch to the astronomical kaliyuga epoch is 588470.3556 - 588465.5 = 4.8556455 mean solar days. 16. TROPICAL INITIAL POINT OF HINDU COSMOLOGICAL TIME CYCLES From the beginning of the kalpa up to the present kaliyuga epoch there are 4567 intervals of a kaliyuga calculated as follows: 1 introductory dawn = 4 kaliyugas 6 manus 714 = 4284 " 27 caturyugas 10 = 270 " 1 krtayuga = 4 " 1 tretayuga = 3 " 1 dvaparayuga = 2 " -------------- 4567 kaliyugas A week of seven precessional years is 180000 sidereal years. From the beginning of the kalpa up to the present kaliyuga there are 4567(432000) ------------ = 10960.8 weeks of precessional years. 180000 From the beginning of the present week of precessional years to 1 January 2000 mean Greenwich noon, Julian date 2451545.0, there are 0.8(180000)(365.2563795) + (2451545.0 - 588470.5662) ---------------------------------------------------- = 149106.5291 365.2421756 tropical years. Counting backward 0.5291 tropical years from 1 January brings the calendar date to 21 June, the day of the summer solstice. As we shall see, if we call the tropical year initial point of Hindu cosmological time cycles a mean summer solstice, the derived fixed initial point of the sidereal sphere used in the construction of Hindu cosmological time cycles is identical with that given by the SuryaSiddhanta. Henceforth, therefore, we shall consider the initial point of the sidereal sphere for Hindu cosmological time cycles to be the sidereal position of the mean Sun at the mean summer solstice of the year 0.8(180000) = 144000 sidereal years or 365.2563795 144000 ----------- = 144005.6 tropical years 365.2421756 before the kaliyuga epoch. In a fictitious true tropical calendar the date of this event would have been 21 June 147108 B.C. 17. FIXED INITIAL POINT OF THE SIDEREAL SPHERE From the kaliyuga epoch to mean noon at Greenwich 1 January 2000, Julian date 2451545.0, there are 0.014(2451545.0 - 588470.5662) ------------------------------- = 71.41023002 degrees of precession. 365.2563795 There are 16.8 precessional years in a kaliyuga. From the beginning of the kalpa to the kaliyuga epoch there are 4567(16.8) = 76725.6 precessional years. At the kaliyuga epoch the tropical year initial point is 0.6(360) = 216 of precession from the fixed initial point. Therefore, on 1 January 2000 the fixed initial point of the sidereal sphere used in the construction of Hindu cosmological time cycles, considered to be, as above, the sidereal position of the mean Sun at the mean summer solstice of the year 144000 sidereal years before the kaliyuga epoch will be 0.6(360) + 71.41023002 = 287.41023002 along the ecliptic from the mean summer solstice initial point, or, since ninety degrees separate the mean vernal equinox from the mean summer solstice, at 287.41023002 - 90 = 197 24' 36".8281 ecliptic longitude. 18. FULL MOON POINTS It is common in naked-eye observations to determine the position of the Sun at a point in opposition to the position of the full Moon. By this means, especially during eclipses, very accurate observations of the position of the Sun may be made. The full Moon point for the fixed initial point of Hindu cosmological time cycles on 1 January 2000 is 197 24' 36".8281 - 180 = 17 24' 36".8281 ecliptic longitude. This point turns out to be identical to the fixed initial point used by the SuryaSiddhanta. 19. PISCEAN AGE EPOCH The epoch marking the beginning of the Piscean Age occurred when the full Moon point of the fixed initial point of Hindu cosmological time cycles crossed the mean vernal equinox 17.41023002(3600) ------------------ = 1243.587858 sidereal years ago 50".4 on JD = 2451545.0 - 1243.587858(365.2563795) = 1997316.601 = 2:25:50.9 a.m. May 10, 756 A.D. of the Julian calendar. 20. COINCIDENCE WITH THE SURYASIDDHANTA FIXED INITIAL POINT By Indian tradition the fixed initial point is very close to the star zeta Piscium. The Indian Astronomical Ephemeris For The Year 1981 gives the position of zeta Piscium on 1.432 January 1981 as 19 36' 40."64 ecliptic longitude. According to the modern SuryaSiddhanta commentary, the initial point of the sidereal sphere coincided with the mean vernal equinox after year 3600 of the kaliyuga had expired and the annual precession is 54". Therefore, at the kaliyuga epoch the fixed initial point of the SuryaSiddhanta sidereal sphere was at 360 - 54"(3600) ---------------- = 306 ecliptic longitude. 3600" At the kaliyuga epoch, the fixed initial point of Hindu cosmological time cycles was 216 from the mean summer solstice. The corresponding full Moon point was therefore at 216 + 180 - 90 = 306 ecliptic longitude. The full Moon point of the fixed initial point of Hindu cosmological time cycles and the fixed initial point of the SuryaSiddhanta are, therefore, identical. 21. PRECESSIONAL YEAR EPOCH The ecliptic position of the mean summer solstice was last at the fixed initial point 287.41023002 365.2563795 ------------- ----------- = 20530.10051 tropical years 0.014 365.2421756 before 1.5 January 2000. This event occured 15428 4/7 sidereal years before the kaliyuga epoch. In a fictitious true tropical calendar the date of this event would be 1.5 January 2000 - 20531.10051 = 25 November 18532 B.C. 22. SIRIUS AND THE PLACE OF THE SPRING EQUINOX Indians have traditionally begun the new year with the spring equinox. The Vedas refer to this point as the "mouth" of the year. Also, the six Indian seasons synchronize with the equinoxes. The summer and winter solstices each occur in the middle of a season. No evidence exists that the Indians ever began their tropical year with the summer solstice. It is highly significant that the star Sirius is the full Moon point for the spring equinox corresponding to the initial point of Hindu cosmological time cycles. The spring equinox full Moon point of Hindu cosmological time cycles on 1 January 2000 Greenwich mean noon is at 287 24' 36".8281 - 180 = 107 24' 36".8281 ecliptic longitude. The Indian Astronomical Ephemeris For The Year 1981 gives the position of Sirius on 1.432 January 1981 as 103 49' 10".27 ecliptic longitude and its annual proper motion in longitude as -0".553. Based on this proper motion, Sirius would have been at the full Moon point (103 49' 10".27 - 107 24' 36".8281) ------------------------------------ + 19 = 23394.331 -0".553 tropical years before 1 January 2000. When the mean vernal equinoctial point was last at its initial point on 25 November 18532 B.C., Sirius would have been at (-0".553)(-20530.10051) 103 49' 10".27 + ---------------------- = 106 58' 23".42 3600" ecliptic longitude, and its deviation from exact opposition to the vernal equinoctial point would have been 107 24' 36".83 - 106 58' 23".42 = 0 26' 13".41. We need not concern ourselves with this modest deviation, since nothing is known about the proper motion of Sirius over a long period of time. Other major stars are either too far away or their proper motion carries them in the wrong direction to line up with any of the initial solstice or equinox positions of Hindu cosmological time cycles. It is quite likely from the alignment of Sirius with the spring equinox initial position of Hindu cosmological time cycles, together with the facts that the Hindu tropical new year is the spring equinox and that Sirius is the brightest fixed star in the heavens, that Sirius is the stellar reference for Hindu cosmological time cycles. 23. 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 31 December 1899) are 1 tropical year (1900.0) = 365.2421988 mean solar days precession in longitude in 1 tropical year (1900.0) = 50".2564. The sidereal year and its precession may be derived from these values. 360 1 sidereal year (1900.0) = ---------------(365.2421988) + 1 360 - 50".2564 = 366.2563627 diurnal revolutions of the Earth. precession in longitude 365.2563627 in 1 sidereal year = -----------(50".2564) 365.2421988 = 50".2583. Table V compares the astronomical quantities used in the construction of Hindu cosmological time cycles with those of Simon Newcomb for the epoch 1900.0. QUANTITY HINDU NEWCOMB DIFFERENCE constant of precession 50".4/yr. 50".2583/yr. 0".1417/yr. sidereal year 365.2563795 365.2563627 1.4 sec/yr. tropical year 365.2421756 365.2421988 -2.0 sec/yr. TABLE V There is very close agreement between the length of the year as measured by Hindu cosmological time cycles and that determined by modern science. If the great antiquity of the cycles can be further demonstrated by other evidence, astronomers might do well to look more closely at the supposition that the rotation of the Earth is being sensibly retarded by "tidal friction". 24. COMPARISON WITH THE CURRENT PRACTICE OF INDIAN ASTRONOMY Although traditional Indian astronomical works include a statement of Hindu cosmological time cycles, for actual astronomical computation they employ a mean motion for the Sun and a constant of precession vastly inferior to that used in Hindu cosmological time cycles (see Table VI). QUANTITY HINDU SURYASIDDHANTA DIFFERENCE const. of precession 50".4/yr. 54."0/yr. 3".6/yr. sidereal year 365.2563795 365.258756 -205.4 sec/yr. TABLE VI According to Indian tradition, the modern (after 100 A.D.) Indian astronomical works were compiled from ancient sources no longer available. Aryabhata states of astronomy that "By the grace of God the precious sunken jewel of true knowledge has been rescued by me. . . ." It appears possible, therefore, that by the time the extant Indian astronomical works were compiled, only little understood fragments existed of the astronomical tradition which produced Hindu cosmological time cycles. For Hindus, jyotish (astrology) is the chief of six limbs of the Vedas, the Hindu scriptures. The SuryaSiddhanta closes with the statement that jyotish is "of mysteries in the world the most wonderful, and equal to Brahman". This statement is made because Hinduism is founded on the correspondence between the macrocosm and the microcosm, and jyotish (astrology) is the primary demonstration and formal conceptualization of this correspondence. H.P. Blavatsky claims that the complete seven-fold analysis of the time cycles "belongs to the most secret calculations" of the spiritual mystery schools, but that, nevertheless, it is knowledge "known to every" initiated Brahman. It would be strange, indeed, for a people possessed of the world's most accurate solar chronograph to slavishly reproduce it in exact detail over thousands of years while at the same time having completely forgotten its astronomical basis or how to use it. Scholars must, therefore, entertain as extremely likely the report of, for example, H.P. Blavatsky, that the complete understanding of Hindu cosmological time cycles is being carried forward secretly in the oral tradition of initiated Brahmans. If this be true, what other "precious sunken jewel(s) of true knowledge" might be part of this same oral tradition? 25. THE 360 + 5 DAY YEAR CALENDARS OF ANTIQUITY The oldest records of man's past show such diverse peoples as the Chinese and Egyptians using 360 + 5 mean solar day calendars, and not for brief intervals, but over thousands of years. These were agrarian peoples dependent upon the seasons of the tropical year for survival. They could easily determine the solstices and equinoxes using horizon markers, gnomons, and the like. The 360 + 5 day year deviates so grossly from the tropical year, that it is unlikely to have ever been used to measure the seasons. A much more practical use of the 360 + 5 day year is for chronological and astronomical purposes, the same as the Julian year of 365.25 mean solar days and the Julian century of 36525 mean solar days are used today. We have shown that the year of 360 + 6 Earth revolutions has a precise astronomical basis, which may be inferred from the structure of Hindu cosmological time cycles. However, for the purposes of practical chronology, mean solar days are more practical units for reckoning civil time than diurnal revolutions of the Earth. Since 366 --------- - 1 7 1 - ----- 366 diurnal revolutions 10000 of the Earth = 366 ------------- 366 --------- 7 1 - ----- 10000 7 = 365 ----- mean solar days, 10000 by using leap days corresponding to the 126 cycles of the 3rd mean motion of the Sun in a week of precessional years, the year of 360 + 5 mean solar days may be used interchangeably with the year of 360 + 6 Earth revolutions. We intercalate a leap day every 1440 years with an additional leap day intercalated every 180000 years. Thus, 0.0007(1440) = 1.008 mean solar days, and 0.008(180000/1440) = 1 mean solar day for a total of 126 leap days in 180000 years. The Chinese order both days and years in cycles of sixty. We have shown that cycles of sixty days and sixty years as well as the sexagesimal number system are derived from the interaction between the first and second mean motions of the Sun intrinsic to Hindu cosmological time cycles. The ancient Egyptians are known to have counted the cycle of the third mean motion of the Sun separately, using the heliacal rising of Sirius to mark the beginning of their sidereal year. The duration of this cycle is 1428+ sidereal years. Hindu cosmological time cycles prominently represent this same cycle by the factor 1428 in the infrastructure of the kalpa period, and also, Sirius is aligned to the spring equinox initial point of Hindu cosmological time cycles. These considerations, together with the superior astronomical foundation of Hindu cosmological time cycles, strongly support the conclusion that the 360 + 5 day calendars of the Chinese and Egyptians were derived from the Hindu original. 26. EVIDENCE OF THE VEDAS Heretofore scholars have hardly questioned the assumption that the 360 day year is a crude approximation to the tropical year. However, we have shown that the 360 day year is an integral part of Hindu cosmological time cycles--the most profound analysis of the mean solar motion ever undertaken, a conceptual structure based upon three mean motions for the Sun and two seven-fold subcycles of the precession. The Rg Veda, one of the formative documents of Hindu civilization, is acknowledged by even the most pessimistic scholars to have been composed no later than 1000 B.C. Herein we find 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, Rg 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, Rg Veda 1.164.1-5) A more direct or succinct utterance of the substance of the cycles could scarcely be conceived. Our analysis has shown that "navels three" must stand for the three mean motions of the Sun and "seven- wheeled chariot" for the precession of the equinoxes. Thus, there can be no doubt that in Dirghatama's time Hindu cosmological time cycles were already an established conclusion and not in the formative stages. 27. WHO CREATED THE TIME CYCLES? How could such an accurate constant of precession, as that of Hindu cosmological time cycles, have been obtained without modern instruments and techniques? Certainly, at the very least, we must allow for a very long period of observation. It appears possible to make naked-eye observations on the celestial sphere with an accuracy of 1/6 degree. If the precession were a point moving uniformly on the celestial sphere, it would then be just possible to determine the constant of precession to an accuracy of three places of decimals in not less than 50(72 years/1) = 3600 years. Unfortunately, measuring the constant of precession is not so simple. To start off, times of the equinoxes must be very accurately observed. Ptolemy 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 a degree of arc. To this difficulty we must add the proper motions of the stars. The star Sirius, for example, would have been an extremely unfortunate choice for a point from which to measure motions on the celestial sphere because of its large proper motion of -0".553 ecliptic longitude per year. But it would take 1000 years for Sirius to move 1/6 degree and for this mistake to become sensible to a naked-eye observer. We add on, that in such a protracted interval of observation the motion of the Earth's perihelion would become sensible and have to be accounted for. In short, it is difficult to imagine the resolution of these difficulties to produce a constant of precession accurate to three places of decimals in less than 10000 years of continuous naked-eye observations. Similar arguments might be adduced to show that to measure the sidereal period of the Sun to eight places of decimals could be accomplished by naked-eye observations alone in hardly less time. Our minds, already totally unable to comprehend how an undertaking of such magnitude could be accomplished, must still face the incredible genius of the cycles themselves: a calendar for eternity so accurate that its formulations must be seriously considered as laws of nature, while at the same time a structure so simple, symmetrical, and orderly, that the best astronomers of modern times have completely failed to see the astronomical basis. It is hardly to be wondered that Hindus have regarded the cosmological time cycles as a revelation from the gods. The peoples who used the 360 day year were always the most advanced civilizations. But the astronomy of these peoples, by all the available evidence, was in every case vastly inferior to the astronomical science which made possible the development of Hindu cosmological time cycles. The time cycles must, therefore, have been created by a civilization which flourished before the time of these historical civilizations and bequeathed its science to the Hindus, Chinese, fertile crescent civilizations, Egyptians, and Mayas alike. All of the other civilizations are now dead. Only the Hindu still remains. Primary traces of this ancestral culture are the sexagesimal number system and the 360 + 5 day calendar. By the epochs preserved within the time cycles themselves as well as by extensive references throughout Sanskrit literature, the cosmological time cycles appear to be older even than Hindu civilization. Nevertheless, because Hindus are the only people to have preserved the exact dimensions of the cycles and maintained the tradition of their astronomical basis by including them in their textbooks on astronomy as well as in their vast literature, it is clear that Hindu astronomy is in the direct lineage of the astronomical system of the creators of the cycles and not "borrowed" from the astronomy of another people. No other historical or existing people claims or has any claim on the cosmological time cycles. It is in this sense that we call them the "Hindu cosmological time cycles". 28. CONCLUSION From what we now know of Hindu cosmological time cycles, human civilization must be far older and its secrets more profound than what is generally inferred from the available historical and archaeological evidence. History is a story of man's past built up out of written records and dates. Archaeology lays a foundation where history leaves off. But archaeology makes its greatest contribution in places no longer suitable for human habitation. In places of continued human habitation time quickly lays waste to bricks and mortar, metals are melted down and recast, and any object which is of use is reused or made into something else which is then used. Archaeology will not serve us here. And yet, in these places of continued human habitation, man's deepest past lies hidden. To see this deep past of mankind we must look in a different way. Nowhere today are the traditions older than in the living civilization of India. The methodology of the spiritual aspirant may well be more successful here than that of the scientist, the historian or the archaeologist. To the best of my knowledge, I am the first to make an analysis of the astronomical basis of Hindu cosmological time cycles based on the hypothesis that they might represent something other than number mumbo- jumbo. I strongly suspect there are those in India who might explain them far more completely, but they are holding their tongues. To anyone who would work along similar lines, I would advise that you let go of prejudice and skepticism and enter in with an open mind. As Henry David Thoreau, the nineteenth century American transcendentalist philosopher and an enlightened student of the Vedas, once said, Only that day dawns to which we are awake. The Sun is but a morning star. BIBLIOGRAPHY AND SUGGESTED FURTHER READING The Aryabhatiya of Aryabhata, Walter Eugene Clark, translator, Chicago, 1930. Blavatsky, H.P., The Secret Doctrine, 2 Volumes, 1888. Dikshit, Sankar Balakrishna, Bharatiya Jyotish Sastra, Part I, Prof. R.V. Vaidya translator, Calcutta, 1969. Dikshit, Sankara Balkrishna and Sewell, Robert, The Indian Calendar, London, 1896. Explanatory Supplement to the Ephemeris, London, 1977. Friberg, Joran, "Numbers and Measures in the Earliest Written Records", Scientific American, February 1984, pp. 110-118. Griffith, Ralph T.H., The Hymns of the Rgveda, Delhi, 1973, 1889. Gurjar, L.V., Ancient Indian Mathematics and Vedha, Poona, 1947. The Indian Astronomical Ephemeris for the Year 1981, Delhi, 1980. McClain, Ernest, The Myth of Invariance, Boulder, 1978. Mani, Vettam, Puranic Encyclopaedia, article on Manvantara, first English edition, Delhi, 1975. Pingree, David, Jyotihsastra: Astral and Mathematical Literature, A History of Indian Literature, Volume 6, Jan Gonda, editor, Wiesbaden, 1981. Ptolemy, Claudius, The Almagest, R. Catesby Taliaferro, translator, Great Books of the Western World, Volume 16, Chicago, 1952. Roy, S.B., Prehistoric Lunar Astronomy, New Delhi, 1976. Santillana, Giorgio de and Dechend, Hertha von, Hamlet's Mill, Boston, 1977. Sewell, Robert, Indian Chronography, London, 1912. Somayaji, D.A., A Critical Study of the Ancient Hindu Astronomy, Dharwar, 1971. SuryaSiddhanta, Ebenezer Burgess translator, Journal of the American Oriental Society, Volume 6, New Haven, 1860. Tilak, Bal Gangadhar, The Orion or Researches into the Antiquity of the Vedas, Bombay, 1893. Van Flandern, T.C., and Pulkkinen, K.F., "Low-Precision Formulae for Planetary Positions", The Astrophysical Journal Supplement Series, Volume 41, pp. 391-411, November 1979.

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