Ancient Zodiacs, Star Names, and Constellations: Essays and Critiques

The Myth of Babylonian Knowledge of Precession by Gary D. Thompson

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The Myth of Babylonian Knowledge of Precession

A constant question is: Did pre-Hipparchan records or narratives identify precession before it was expressed in scientific terms by the Greek astronomer Hipparchus of Rhodes (2nd-century BCE)? Certainly no Babylonian text discovered so far shows a knowledge of "precession," e.g., of a movement of the Vernal point. Nothing in Babylonian heliacal astronomy or calendar systems suggests knowledge of precession. It is not directly indicated that the Babylonians recognised that star rise azimuths (i.e., movement along the horizon) and heliacal times/dates of rising and setting changed through time. If they did, which one would suppose they did, they did not leave any precise records of calculations involving such observations. It is often overlooked that Babylonian astronomy was not primarily observational. For most of its history Babylonian astronomy was primarily schematic. The absence of exactness in Babylonian astronomy existed until the last half of the 1st-millennium BCE.

A central claim of the Panbabylonists (a group of German Cuneiform Philologists and Assyriologists at the beginning of the 20th-century) was that the Babylonians had discovered precession. The various forms of proof included arguments involving: believed early Babylonian ability for accurate observations and involved calculations, calendrical systems, believed early zodiacal scheme, solstice-equinox-Sirius texts, the Astronomical Diaries, zero points in System A and System B, and legends and symbols. Many persons continue to postulate the truth of an unproved claim: The ancient Babylonians (and others) were great observers of the night sky and therefore must have noticed the precession of the equinoxes. The hypothesis that the Babylonians knew precession can be confidently dismissed. The hypothesis has been adequately refuted by the studies of the astronomer and Assyriologist Franz Kugler, the mathematician Otto Neugebauer, and the Assyriologist Abraham Sachs. Even in the late period (the Persian, Macedonian, and Seleucid periods) when mathematical astronomy really flourished in Babylon, the precession of the equinoxes still remained unnoticed by the Babylonians.

For key examples of the claims of Babylonian knowledge of precession see: Das alter der Babylonischen Astronomie by Alfred Jeremias (1909). Alter und Bedeutung der babylonischen Astronomie und Astrallehre by Ernst Weidner (1914). "Kidenas, Hipparch und die Entdeckung der Präzession." by Paul Schnabel (Zeitschrift für Assyriologie und Verwandte Gebiete, Volume 37, 1927, Pages 1-60). Die Kultrichtung in Mesopotamien by Günter Martiny (1932). Both Alfred Jeremias and Ernst Weidner were Panbabylonists. These works are based on insufficient data; they contain only inferences. There is nothing convincing about their various discussions - all are flawed. There are no Babylonian texts containing statements about the subject. Schnabel mistook scribal errors in a solar ephemerides (VAT 7821) for corrections because he only had parts of broken clay tablets available to him. When additional fragments were identified his theory could no longer be maintained. (Basically, a new join to VAT 7821 disproved Schnabel's conclusions. It also showed scribal errors regarding the numbers 7 and 4, which are very similar signs and frequently misread by scribal copyists. The 2nd-half of VAT 7821 was found in the University of Chicago collection (A 3417).) The work of Otto Neugebauer shows there is no evidence of empirical corrections within ephemerides. See: "The Alleged Babylonian Discovery of the Precession of the Equinoxes." (Journal of the American Oriental Society, Volume 70, Number 1, 1950, Pages 1-8). It comprises an excellent discussion and demonstration of Schnabel's errors. See also the discussion in: Otto Neugebauer, Astronomical Cuneiform Texts Part 1, 1955, Page 27.

Franz Kugler was a pioneer of the study of mathematical-astronomical cuneiform texts and also calendrical texts. His refutation of the Panbabylonist arguments for Babylonian knowledge of precession is contained in his Sternkunde und Sterndienst in Babel (1907-1924). The ideas that a 12-constellation equally divided Babylonian zodiac originated circa 6000 BCE (promoted by the Panbabylonists Fritz Hommel and Alfred Jeremias) did not begin to be entirely discarded until the monumental multi-volume Sternkunde und Sterndienst in Babel by Franz Kugler began publication in 1907. Franz Kugler, in his numerous clashes with the Panbabylonists Fritz Hommel, Alfred Jeremias, and Ernst Weidner, convincingly demonstrated that the Babylonians had a late and sidereal zodiac and a late mathematical astronomy. This meant that precession could not have been marked at an early date through either the constellations or signs of the zodiac. Also, from his study of cuneiform texts Kugler pointed out that the concept of precessional movement of the tropical points through ecliptic constellations was not contained in early Babylonian astronomical texts. There is nothing in the Babylonian texts to prove a Twins-, Bull-, and Ram-period of precession. The ecliptic only became important in the 1st-millennium BCE. There was certainly no pre-1st-millennium zodiac for observing and measuring precessional "zodiacal ages." A zodiac for being able to do such only came into existence in the last half of the 1st-millennium BCE. (The concept of precessional "world ages" can be traced back to Origine des tous les cultes: ou, Religion universelle by Charles Dupuis (1794). The concept of 'zodiacal ages/astrological ages' was developed by 19th-century theosophy and early 20th-century astrology.)

In addition to the above Otto Negebauer pointed out ("Babylonian Planetary Theory.", Proceedings of the American Philosophical Society, Volume 98, 1954, Page 64): "There is no trace of any definition of the vernal point as the intersection of ecliptic and equator (which appears nowhere in Babylonian astronomy)." Note: In the Glossary to his Astronomical Cuneiform Texts (1955), Neugebauer explains that the (late) term for the vernal equinox is basically "ina hun lal-mes."

The Ram was an important cult figure in both ancient Egyptian and Babylonian civilizations - but not a constellation. The Ram is a Greek constellation. When the Greeks borrowed the zodiacal system from Babylonian uranography the Babylonian constellation of the "Hired Man" was replaced by the Ram. (For a philological explanation of how this may have occurred see "Zodiacal Signs among the Seal Impressions from Hellenistic Uruk." by Ronald Wallenfels in: The Tablet and the Scroll edited by Mark Cohen et. al., 1993, Pages 282-283.)

Unfortunately the myth of a prehistoric 12-constellation zodiac (of equal divisions) is not yet dead. The importance of the ecliptic and the development of the 12-constellation zodiac does not appear anywhere until its origin in Babylonia circa 700 BCE.. The development of the equally divided 12-constellation zodiac does not appear until after the start of the Persian Period in Babylonia (circa 500 BCE). The cuneiform tablet evidence clearly establishes that it was the astronomy of the Mul.Apin scheme (circa 1000 BCE) that established the preconditions for the importance of the ecliptic and the establishment of the Babylonian zodiacal scheme which was later adopted by the Greeks. The Babylonian scheme of 12 zodiacal constellations was derived from a system of 18 constellations (established during the Assyrian Period beginning circa 1100 BCE) along the ecliptic to mark the path of the Moon. (Prior to circa 1000 BCE the ecliptic was not specifically marked in Babylonian astronomy. The three path system of the "three stars each" was established and in effect was an equatorial system. However, the Babylonians clearly had no concept of a celestial equator.) Circa 700 BCE (toward the Neo-Babylonian Period) the scheme of 18 constellations used to mark the path of the moon were then reduced to a scheme of 12 (unequal) constellations along the ecliptic to suit a schematic year of 12 months of 30 days each. This scheme was finally achieved with the division of the zodiac into 12 equal divisions (during the Neo-Babylonian period). (The constellations not wholly occupying the ecliptic were removed.) The scheme of 12 constellations (and 12 zodiacal divisions of equal length) was the last scheme of constellations (and divisions) to be finalised (and is not older than the 5th-century BCE). However, the individual constellations included in the zodiacal scheme have far earlier origins and some can be dated back 1500 years to the Old Babylonian Period. The evidence is conclusive that a system of 12 equal zodiacal divisions did not exist until circa 450 BCE. This date is the earliest from which there was a possible basis for the determination of precessional "zodiacal ages." However, precession remained undiscovered until the work of the Greek astronomer Hipparchus circa 120 BCE. Hipparchus is perhaps best known for his discovery of precessional movement and an explanation of the precession of the equinoxes. By calculating the longitude of Spica against previously recorded observations of astronomers such as Timocharis and Aristullus, Hipparchus was able to prove that Spica’s longitude had increased by nearly two degrees. It is generally stated he argued that this motion was a slight progression of the stars eastward with regard to the ecliptic and not the retrogression of the equinoctial points. However, exactly how Hipparchus understood precession and why it occurs is unclear. It appears Hipparchus calculated a rate for precession rather than identifying what was happening and why.

Hipparchus had the benefit of the concept of the ecliptic and 12 zodiacal constellations, a solid concept of the equinoxes and solstices, plus a geometrical model of the earth in space, to work with. Importantly, he also had the positions (i.e., declinations) of some 25 stars near the ecliptic (established the previous century by the Greek astronomers Timocharis and Aristyllos). There is no evidence to establish that anybody earlier than the Greeks circa 500 BCE had the same collection of concepts. If the Babylonians (or some other cultural group) were aware of precession prior to 1000 BCE then they did not have the combined benefit of the concept of the ecliptic, an equally-divided 12-constellation zodiac, a geometrical perspective of the heavenly bodies, and the abstract moving points of the equinoxes and solstices. Thus if an early group became aware of precession they can not be expected to have explained it in the same way Hipparchus did. The Greek philosopher and polymath Aristotle (384-322 BCE) had never heard of precession. Using John Dreyer's History of the Planetary Systems from Thales to Kepler (1906) we find that in the Greek-Roman world precession was only mentioned by Hipparchus of Rhodes (circa 190-circa 120 BCE, Greek astronomer and mathematician), Claudius Ptolemy (Greek-Roman citizen and astronomer and mathematician, circa 100-circa 165 CE), Proclus Lycaeus (412-485 CE, a Greek Neoplatonic philosopher) who emphatically denied its existence, Theon of Alexandria (circa 335-405 CE, Greek mathematician and astronomer), and Origen Adamantius (184/185-253/254 CE, early Christian Alexandrian scholar and theologian). Interestingly, ancient astrologers were happy to use Ptolemy's astronomical tables (Handy Tables) but remained unconvinced by his observational demonstrations for the theory of precession. It is one thing to claim - as some writers do - precession was known by circa 200 CE and another to provide reasonable proof of the claim. On similar lack of evidence it can be claimed that precession was denied by the early fathers of the Church. Precession was not mentioned by Geminus of Rhodes (Greek astronomer and mathematician, flourished 1st-century BCE), Cleomedes (flourished 1st-century CE, Greek (Stoic) philosopher and astronomer), Theon of Smyrna (circa 70-circa 135 CE, Greek philosopher and mathematician), Marcus Manilius (flourished 1st-century CE, Roman poet, astrologer, and author of a poem in five books called Astronomica), Pliny the Elder ((Gaius Plinius Secundus), 23-79 CE, Roman author, naturalist, and natural philosopher), Censorinus (flourished 3rd-century CE, Roman grammarian and miscellaneous writer), Achilles Tatius (flourished 3rd-century CE, Greek writer (referred to by Firmicus Maternus)), Chalcidius ((Calcidius) flourished 4th-century, Greek philosopher (possibly a Christian), Ambrosius Macrobius (flourished early 5th-century CE, Roman scholar), and Martianius Capella (circa 365-circa 440 CE, Roman school teacher at Carthage).

In his 3-volume encyclopedic scientific work Kitab al-qanun al-Masudi, the Arab-Islamic polymath Al-Biruni (973-1048 CE) mentions those in his time who opposed the concept of precession and maintained the view that the fixed stars did not move at all.

The dissemination of knowledge in the ancient world (including the Hellenistic period) was neither fast nor efficient. Many astronomers well into the early medieval period either did not know of - or did not accept - precession. Some simply believed in trepidation (= backtracking). The theory of trepidation is oscillation in the precession of the equinoxes. The origin of the idea of trepidation comes from the Small Commentary to the Handy Tables written by Theon of Alexandria in the 4th-century CE. The theory was popular in European and Arab-Islamic astronomy from the 9th to the 16th centuries. The most widely used theory of trepidation during the Middle Ages was that of the 9th-century Arab-Islamic astronomer, Thabit ibn Qurra. Thabit ibn Qurra is generally credited with first postulating the theory of the progressive and regressive (oscillating) motion of the stars, also known as access and recess. Uncertainty regarding precession is evidenced in the European Medieval period. John of Sicily who flourished in Paris at the end of the 13th-century CE as a member of the Paris scientific community, in his commentary (dated circa 1291) of Gerard of Cremona's translation of the canons of al-Zarqali's planetary tables, rejected the trepidation theory and supported the theory of precession of the equinoxes. Isaac Newton (1642-1727) understood the nature of precession and had accurately calculated its annual rate. He is credited with the first full theoretical explanation of the precession of the equinoxes. It is obvious that discovering precession is not as easy as having a grandfather who has a tree and passes down stories about his lifetime observation of the night sky.

When the zodiacal system was first being devised (over the period circa 700 BCE to 500 BCE) it is evident that precession had not been discovered. The Babylonian astronomers who first originated the zodiac did not attempt to measure the zodiac from an invisible tropical point they were unable to observe (and could only approximate). It was easiest for them to observe the fixed stars and the zodiac was tied to the fixed stars. The Babylonian astronomers simply defined the starting points of the zodiacal signs by their positions relative to the fixed stars. The Babylonians simply placed the tropical points in the middle of the relevant signs (i.e., 15 degrees Aries per Mul.Apin) or related them to fixed stars (i.e., put the vernal point at 10 degrees Aries per System A, or 8 degrees Aries per System B). (It appears it was the Greek astronomer Hipparchus who was the first to identify the "first point of Aries" with the vernal point.) It would appear that the Babylonians had no suitable understanding of the tropical points, at least for most of their history. Up til the 7th-century BCE most administrative and astronomical texts show an almost exclusive use of a schematic calendar comprised of twelve 30-day months. Its use is evidenced in administrative texts from Uruk III at the end of the 4th-millennium BCE and from Jemdet Nasr throughout the 3rd-millennium BCE. In astronomical texts its use is evidenced in BM 17175 (from the Old Babylonian Period); the series Mul.Apin (from the Assyrian Period); Tablet 14 of the omen series Enuma Anu Enlil (circa the Cassite Period); the series I.NAM.GIS.HUR.AN.KI.A (from the Middle Babylonian Period); and also in the various "Three Stars Each" star calendar texts (which date from the Middle Babylonian Period. In all these astronomical texts the solstices and the equinoxes are equidistantly spaced at the midpoints (i,e, day 15) of certain months - usually months 3 (summer solstice), 6 (autumn equinox), 9 (winter solstice), and 12 (spring equinox). (In the series Mul.Apin (and also in BE 13918 and the "Ivory Prism," both from the Neo-Assyrian Period) there is a change in calendar practices and the dates of the solstices and equinoxes are shifted by one month.) The basic method of the Babylonians for determining the tropical points was simply to observe the summer solstice and then the position of the other solstice and the equinoxes were found by adding approximately 3, 6, or 9 months. (For a discussion of the methods used to determine the solstices and equinoxes see: Astral Sciences in Mesopotamia by Hermann Hunger and David Pingree (1999; Pages 75-77).)

Kugler also pointed out that the lack of accurate calculation and observation in early records of eclipses and of the planets demonstrates the absence of a precise system of measuring location and time in the sky. Precise date and position details are not given for any early observations. The total eclipse observed in 763 BCE was only recorded by the simple statement: "In the month Sivan an eclipse of the Sun took place." (Note: Working against the high antiquity of scientific astronomy in Babylonia is the fact that in the Old Babylonian omen literature the Babylonians used to predict eclipses by the risings, settings, and colours of the planets, and by liver- and oil-divination, and astronomical omens such as halos, and fog. See: Antike Beobachtungen farbiger Sterne by Franz Boll (1916, Page 24); "Babylonian Celestial Divination." by Erica Reiner. In: Ancient Astronomy and Celestial Divination edited by Noel Swerdlow. (1999, Pages 21-37; Page 23); Observations and Predictions of Eclipse Times by Early Astronomers by John Steele (2000); and "Eclipse Prediction in Mesopotamia." by John Steele (Archive for History of Exact Sciences, Volume 54, Number 5, February, 2000, Pages 421-454; See Page 426).) Not until the Assyrian period were attempts made to predict eclipses using sound astronomical knowledge. Circa the early 7th-century BCE lunar eclipses could be predicted only shortly before  their occurrence. There is no evidence that the Babylonians possessed a physical theory of eclipses. Knowledge of precession requires: (1) a series of reasonably accurate observations/records spread over a considerable period of time, and (2) a reasonably accurate knowledge of the length of the year. The latter will will eventually lead to the differentiation between the tropical and the sidereal year. Texts show that sophisticated mathematics existed in the Old Babylonian Period. Texts also show that Babylonian astronomy of comparable sophistication did not exist until the Seleucid Period. Only from about the 5th-century BCE onwards, the Babylonians employed the 19-year cycle for reconciling the lunar year with the solar. Aided by this, they were able to make an accurate calculation of new moons, new years and leap-years, and to fix them accordingly.

John Major Jenkins writes: "The Babylonians also seem to have been aware of precession. As early as 1906, historian of science J.L.E. Dreyer noted that three Babylonian tablets, each from a different era, give three different positions for the equinox, proving that the Babylonian astronomers were aware of precessional movement.6" (The reference seems to be John Dreyer's, History of the Planetary Systems from Thales to Kepler (1906).) However, I cannot find it there. What I can find in Dreyer's book (Page 48) is "It is also more than likely that the Babylonians, who at the latest at the end of the eighth century B.C. observed eclipses, must have noticed that the sun at equinox or solstice did not from one century to another stand at the same star2." (Referencing Kugler's Babylonische Mondrechnung (1900), page 108.) There is no evidence other than the Babylonians believed the earth to be a secure basic frame of reference. It is not indicated that the Babylonians experienced any frame-of-reference crisis. (Or frame-of-time as Hamlet's Mill termed it. The movement of the planets as seen from earth are subject to precession. The Babylonians could not separate the effects of precession from: (1) observational error, and (2) calendar accuracy problems. A nearly perfect calendar was not developed until the reign of king Nabonassar (first king of the 9th dynasty of Babylon, ruled circa 747–734 BCE) when Babylonian astronomers recognised that 235 lunar months are almost identical to 19 solar years. (The difference is only 2 hours.) They concluded that 7 out of 19 years ought to be leap years with 1 extra (intercalary) month. The intercalary months were at first announced by the king (on the advice of his astronomer) but, after the capture of Babylon by the Persian king Cyrus in 539 BCE, priestly officials took over the function. They investigated the introduction of a standard procedure for the intercalation of months. The standard procedure for regulating the calendar was introduced in 503 BCE (but perhaps earlier) by Darius I the Great.

It was not until quite late (circa 500 BCE) that the Babylonians were able to predict some of the astronomical events that are required for a successful luni-solar calendar.

Until the (Late) Assyrian Period Mesopotamian astronomy is simply qualitative. The oldest astronomical document of a really scientific character date to the 6th-century BCE in the reign of Kambyses. Astronomical observations during the early period of Mesopotamian astronomy show little exactness. The Venus observations made during the reign of Ammizaduqa were made in order to provide empirical material for omina. It is only from the (Late) Assyrian Period that the mathematical treatment of astronomy begins. Also, it is only from this period that systematic observational reports begin to appear.

Importantly, the development of latitude and longitude as astronomical coordinates did not occur before circa 200 BCE. (It was only during the Seleucid Period (beginning circa 200 BCE) that techniques were developed for determining the positions of celestial bodies in terms of degrees of latitude and longitude.) The inaccurate nature of the calendar for approximately 2000 years is inconsistent with an ability for careful and systematic observations. Before the 7th-century BCE almost all astronomical texts used the schematic calendar of twelve 30-day months. (It is worth noting that in the late 1st-millennium CE, in the calculation of Babylonian planet tables normal months of 30 days were assumed.) The absence of an accurate calendar also makes it difficult to easily discover precessional change. (See: Sternkunde und Sterndienst in Babels, Buch 2, Teil 1,1909/10, Pages 20-31; and Buch 2, Teil 2, Heft 2, 1924.) A reliable chronology was not possible before the reign of King Nabonasser, 747-734 BCE. The lack of an accurate calendrical system and the lack of exactitude in early Babylonian astronomy makes it implausible to believe that a continuous series of precise observations, and accompanying accumulation of continually maintained records, was possible. Changes in the position of the sun relative to the tropical points is a fraction of a degree per year and difficult to observe simply because when the sun is visible the fixed stars are not. The return of the Sun to the equinox point could not be timed with accuracy by the Babylonians. This means it would be difficult to make the distinction between the sidereal year and the tropical year. The Babylonian astronomical and calendrical texts do not distinguish a sidereal year and a tropical year.

In his 1914 paper "Die Entdeckung der Präzession, eine Geistestat babylonischer Astronomen." (Babyloniaca, Tome 7, Pages 1-19) Ernst Weidner attempted to prove that the Babylonians knew of precession at least by circa 1500 BCE. His argument was that the dates of the solstices and equinoxes in a tablet (CBS 11901) which he dated to circa 1500 BCE were approximately correct as were the dates of the solstices and equinoxes in tablets dating from circa the 6th-century BCE. However, Kugler (Sternkunde und Sterndienst in Babels, Erganzungen 2 für Buch 1 und Buch 2, Pages 233-242) demonstrated that the cuneiform tablet (CBS 11901 (= LBAT 1478)) that Weidner dated to circa 1500 BCE was actually to be correctly dated to 424/3 BCE.

Standardisation of the calendar was necessary for the discovery of precession. The lunar calendar scheme was unsuitable for anything but approximate time timekeeping. The early introduction of the use of the ideal or schematic year of 360 days still posed problems for accurate time measurement. (The observation-based Babylonian month had 29 or 30 days. If the crescent moon was already visible at the beginning of day 30 in a month, this day 30 was rejected, which meant that the month only had 29 days.) Early Babylonian calendars were rather awful regarding accuracy and were simply adjusted (intercalated) on an arbitrary basis. They remained chaotic through to the late 1st-millennium BCE. For most of their history the Babylonians had no method of keeping the lunar year and the solar year together. This precludes the keeping of accurate astronomical records. The Assyrian calendar of the 2nd-millennium BCE did not use intercalation at all and drifted all through the solar year. (The early Babylonians were more interested in having a calendar comprised of uniform numbers than dealing with the non-uniform numbers resulting from exactness.) In Babylonia the year began at about the time of the spring equinox.

It was not until the 3rd- or 2nd-century BCE, when the development of exact astronomical methods had supplanted largely empirical/observational study of the firmament, that the Babylonians were able to calculate the appearance of the true new moon. By this time, too, the progress of astronomical knowledge allowed them to adopt the more accurate calendarizing of the lunation into months of 29 and 30 days, 5 of the former, and 7 of the latter, length.

In the Astrolabes of the late 2nd-millennium BCE the first day of the first month of the year, the first of Nisan (= March/April), was marked by the approximate conjunction of the first visible crescent Moon with the star group Mul.Iku (= The Field). The observation of the heliacal rising of Mul.Iku on the eastern horizon (just before sunrise) and then the first appearance of the crescent new Moon at dusk on the western horizon marked the beginning of the new year. In the Mul.Apin series of the 1st-millennium BCE Mul.Mul (= Pleiades) was the star group that functioned to mark the new year (the first of Nisan). In the spring when the Pleiades rose heliacally on the eastern horizon (just before sunrise) in conjunction with the first visible crescent Moon on the western horizon (at dusk) it marked the first day of the month Nisan (and the beginning of the new year). However, the sequence of years of 12 and 13 months was very irregular, sometimes the year began earlier and sometimes it began later. (The identification of the Babylonian calendar months were aided by the use of the scheme of the "three stars each" which enabled the Babylonians to know when the lunar months were shifting out of correlation with the seasons. The "three stars each" consisted of a month-by-month listing of constellations, stars, and planets which rose heliacally (on the eastern horizon) in each of the twelve 30-day months of the schematic year. For each month a star was assigned to each of the "three ways" (i.e., the paths of Anu, Enlil, and Ea) and rose at 10 day intervals. At first they were recorded as a circular pictorial representation and then later as a listing only.) No cyclically regulated intercalation (to control the calendar) existed in Babylonian prior to the Persian Period (circa 450 BCE). When finally introduced the unit of intercalation was simply the lunation (and was used as needed to keep the calendar year in line with the seasons). When the grain was ready for harvest was the key issue in determining intercalation. The time of a star's heliacal rising changes at the rate of about a month approximately every two thousand years. The way the Babylonian calendar operated there is no reason to suppose that the calendar error would become really conspicuous until after approximately 2000 years. This brings us down to the Late Hellenistic Period. Also, there is no identified tradition of long-term seasonal displacement of familiar stars used as markers.

In his book Psychanodia (Volume 1, 1983) the Romanian scholar Ioan Culianu (1950-1991) discusses a late Babylonian text that mentions the Pleiades not rising on time and therefore being 'evil.' In his book Babylonian Star-Lore (2007) Gavin White attributes a working knowledge of precession and its long-term effects on celestial coordinates to Babylonian astrologers of the late 3rd-millennium BCE. His speculation is accompanied by the mix of words, including: "I believe," "strongly supports," "supports the idea," "no doubt," "implies," "implied," "was necessary," and "necessitated." No evidence or no compelling evidence is offered.

Evidence that may show that an ancient culture knew of the displacement of a certain star or stars cannot be cited as evidence that they knew about the phenomenon of precession. Precise knowledge of the effect of precession on the position of various stars over long periods of time is a different matter to the observation that certain stars may no longer rise and set where they once did. The latter observation is likely to be made in any society which might have observed particular stars from fixed monuments over a long period of time, but does not necessarily suggest any awareness of precession. The 2 concepts should not be confused in discussion.

In 1923 the cuneiform scholar Paul Schnabel (Orientalist, 1887-1947) credited the Babylonian astronomer Kidinnu (flourished 4th-century BCE) with the discovery of the precession of the equinoxes prior to Hipparchus. However, this claim by Schnabel was decisively refuted by Otto Neugebauer in 1950. There is no evidence that even the later Babylonians had a sufficiently accurate system of measuring the heavens to enable them to identify the precession of the equinoxes. Also, the Babylonian calendar - and its system of adding extra months (some irregularly ordered by the reigning king) did not accurately make up for the accumulated differences between the solar year and the lunar year - remained quite confused (and inexact) until circa 300 BCE, when the Babylonians began to use a more reliable system.

Otto Neugebauer spent a life-time engaged in the study of mathematical-astronomical cuneiform texts. His decisive demolition of Paul Schnabel's argument for Babylonian knowledge of precession ("Kidenas, Hipparch und die Entdeckung der Präzession." (Zeitschrift für Assyriologie und Verwandte Gebiete, Neue Folge, Band 3 (Band 37), 1927, Pages 1-60)) is contained in his paper "The Alleged Babylonian Discovery of the Precession of the Equinoxes." (Journal of the American Oriental Society, Volume 70, Number 1, 1950, Pages 1-8). In this paper and his earlier book Berossos und die babylonisch-hellenistische Lieratur (1923, Pages 233-237) Schnabel.had claimed that the Babylonian astronomer Kidinnu had discovered precession at (mistakenly, due to an earlier translation error made by Franz Kugler) Sippar. The date offered in 1923 was 313 BCE but this was changed in his 1927 paper (in which he offered further arguments to counter the criticisms made by Franz Kugler in Sternkunde und Sterndienst in Babel (Buch 2, Teil 2, Heft 2, 1924) Pages 582-621 and Pages 627-630) to 378 BCE. Paul Schnabel basically proposed that the 4th-century BCE astrologer/mathematician Kidinnu discovered precession when distinguishing between sidereal and tropical years. Schnabel is wrong for a number of reasons. Kidinnu never calculated a value for precession. The evidence does not support the claim that he was even aware of precession. Schnabel's argument for the Babylonian discovery of precession was based on a commonly made scribal numerical error (the interchange of cuneiform 4 and 7). The other half of the text used by Schnabel was later located in Chicago and it contained other scribal errors that more than outbalanced the one that Schnabel had taken seriously. Also included in Schnabel's main argument for the Babylonian discovery of precession was that System B developed from System A. This was undermined by (1)  evidence for the near contemporary development of both systems, and (2) their different provinces in Babylon (for System A) and Uruk (for System B). Also, System A and System B were used contemporaneously. Tablets for both systems have been found in both Babylon and Uruk. Tablets based on System B have been found mostly in Uruk, but the somewhat earlier System A tablets came predominantly from Babylon.

In his monumental A History of Ancient Mathematical Astronomy (3 Parts, 1975) Neugebauer wrote (Part 1, Page 369): "We have no evidence from Babylonian sources about a recognition of precession and we have no reason to assume that the difference of zero points in System A and B had anything to do with it, knowingly or unknowingly. ... That the vernal point maintained in each of the two systems a fixed sidereal longitude indicates that precession was unknown."

Also relevant are the solstice-equinox-Sirius texts. (These texts formed part of the Astronomical Diaries. Hermann Hunger and David Pingree write (Astral Sciences in Mesopotamia (1999) Page 151): "The only aspects of solar motion mentioned in the diaries are the dates of the occurrences of solstices and equinoxes and of the heliacal rising and setting and the acronychal rising of Sirius.") The phases of Sirius and other fixed stars were put into a definite relation to the solstice-equinox scheme. (The term "phases" of a star relates to horizon aspects of apparent movement. The four important "phases" of a star were heliacal rising (its first visible rising above the eastern horizon just before sunrise) and heliacal setting (its last visible setting below the western horizon just after sunset); and acronychal rising (when it first rises above the eastern horizon just as the sun sets below the western horizon) and acronychal setting (when it first sets below the western horizon just as the sun rises above the eastern horizon). Both the heliacal and acronychal risings and settings are directly observable phenomena.) These texts contain information setting out the positions of Sirius and other stars relative to the solstice and equinox points. The discussion by Neugebauer (A History of Ancient Mathematical Astronomy, Part 1, Page 543) of these solstice-equinox-Sirius texts, which date from circa the 6th-century BCE through to the Seleucid Period, shows that the position of Sirius relative to the solstices and equinoxes does not change over time with precession as would be expected had the Babylonians known of such. The earliest Sirius dates circa 600 BCE are the same as those of the later period. (The scheme found in BM 36731 lists equinoxes, solstices, and heliacal risings and settings of Sirius from, it would appear, 615-587 BCE. The solstice-equinox-Sirius dates are resumed again by the Astronomical Diaries in 330 BCE.) Neugebauer (A History of Ancient Mathematical Astronomy, Part 1, Page 543, Note 13) concludes: "This is, incidentally, further evidence for the fact that the Babylonian astronomers were not aware of the existence of precession."

See also the early study by Abraham Sachs on the dates of the phases of Sirius related to the solstice and equinox schemes: "Sirius Dates in Babylonian Astronomical Texts of the Seleucid Period." by Abraham Sachs (Journal of Cuneiform Studies, Volume 6, 1952, Pages 105-114). Simply, the dates of all solstices and equinoxes found in Seleucid texts are the result of computation according to a fixed scheme. Observation was not involved. A succinct summary explanation is given by Hermann Hunger in his booklet, Astrology and Other Predictions in Mesopotamia (1997, Page 29): "The dates of the equinoxes and solstices and the appearance of the star Sirius are all given according to a schematical computation; so these are not observations." For the Babylonians the arrangement of the solstices and equinoxes are part of the schematic year - they are simply established within the time frames of the ideal 360-day year. The Babylonians show no awareness of actual periodicities and only modest observational foundations are indicated as forming the basis for their calculated schemes. See also the discussion in Astral Sciences in Mesopotamia (1999), Pages 200-202.

Within the methods and results of Babylonian astronomy very great emphasis was placed on schematization. The main concern of Babylonian astronomy was convenience of numerical manipulation and the intent to solve complicated periodic relationships by the use of successive approximations based on arithmetical progressions. As such the dates of solstices and equinoxes were the result of computation according to a fixed scheme. There is no evidence at all that during the entire Assyrian Period the spring equinox had any significance for the beginning of the year. The equinoxes and solstices had no effect on the Mesopotamian calendar.

The idea that the Babylonian knew precession is also refuted by the study of two tablets from Uruk for the computation of summer solstices. (See: "Schematische Berechnungen der Sonnenwenden." by Hermann Hunger (Baghdader Mitteilungen, Volume 22, 1991, Pages 513-519).)

Abraham Sachs spent the latter part of his career in a detailed study of the Astronomical Diaries. (His work has been continued by the Assyriologist Hermann Hunger.) His detailed studies of these and related texts has established that this uninterrupted 800 year long observational program did not lead to Babylonian knowledge of precession. (See further: Annals of Science, Volume 58, Number 3, July 1, 2001, Pages 323-326.) The data in the Astronomical Diaries and the Almanacs is frequently contradictory. In Babylonian texts the dates of various celestial phenomena may be either observed or computed. The use of calculations based on a combination of theory and observations was frequent. Much of the data recorded in both Astronomical Diaries and Almanacs are not observation-based but computation-based. The comparison of the data in the Astronomical Diaries and Almanacs demonstrates the absence of one unifying and exact observation and computation scheme. Interestingly, all of the data recorded in Normal Star Almanacs are predictions. Again, it is obvious that discovering precession is not as easy as having a grandfather who has a tree and passes down stories about his lifetime observation of the night sky.

In his 1993 book, The Eye of Heaven : Ptolemy, Copernicus, Kepler the American historian of science Owen Gingerich offered a succinct explanation for the appearance of preciseness in Babylonian computation schemes (Page 21): "But how could the Babylonians find the length of the seasons so well, since it would have been no easier for them than for Ptolemy to find the time of the solstice by direct observation? The answer seems to lie in the idea that the Babylonian astronomy was thoroughly dependent upon lunar observations, and particularly on a long series of lunar eclipses. Over the past century the astronomical cuneiform tablets have gradually been deciphered, and one of the most surprising things that has emerged is the relatively high accuracy with which parameters can be extracted from very approximate observations. Provided there are enough records over a considerable period of time, even crude measurements furnish quite reliable figures for planetary periods and for their non-uniform motion along the ecliptic. In particular, the Babylonians discovered that the lunar eclipses repeated in certain patterns, and that the possible eclipses positions were more crowded together in the direction of Sagittarius than in Gemini. This meant that the Sun was moving more slowly when it was in Gemini, and more rapidly in Sagittarius. From this observation it was possible to work backward and establish when the seasons began without actually making daytime measurements of the solstices."

The Babylonians had no method of keeping the lunar and the solar year together. In his paper "The Young Avestan and Babylonian Calendars and the Antecedents of Precession." (Journal for the History of Astronomy, Volume 10, 1979, Pages 1-22) Willy Hartner suggests that the tropical and sidereal year were distinguished in Babylonian astronomy by 503 BCE and that it implies knowledge of precession. However, there is no evidence that the Babylonians differentiated between the tropical and sidereal year at all. Though the Babylonians, quite late, came to realize that there was a difference between the tropical and the sidereal mean longitude of the sun there is no evidence that they could rationalise the discrepancy and understand it as the Greek astronomer Hipparchus later did. In his review of Bartel van der Waerden's 1988 book, Die Astronomie der Griechen Alexander Jones writes (Isis, Volume 81, 1990, Page 332): "... van der Waerden revives the old bogey of a Babylonian discovery of precession, because of the discrepancy between the "sidereal" year underlying the system A and B lunar theories and the "tropical" year derivable from the Uruk solstice scheme. But this tropical year is merely a consequence of the nineteen-year calendric cycle, which is both older and of a lower order of accuracy than the lunar theories; the tropical year implicit in system A is identical with the sidereal year, while in system B there is only a small discrepancy that results from the arithmetrical constraints of the zigzag functions."

In the later period (Persian (Achaemenid) Period (539-331 BCE)) the effect of precession was still not recognised by the Babylonians as their zodiac - introduced circa 450 BCE - was always sidereally fixed.

It is difficult to understand what is meant when it is claimed by the "new" Panbabylonists such as Giorgio de Santillana and Hertha von Dechend that early cultures must have recognised or understood precession. In seeking to establish who was the first to be aware of precession the zodiac, the tropical points, and the mechanism of precession are not wholly relevant. The questions to ask are: (1) Who in antiquity appears to have been aware of precession?; (2) Can a date for the awareness be assigned?; (3) How did they come to notice it?; (4) What did they notice?; and (5) Was an explanation attempted? However, some sort of vague realisation without quantification or ability to describe it in terms of a precise astronomical coordinate system is not exactly a firmly established discovery. (See: Appendix 3: Defining Discovery) The expected easiest observations of precession (by some early culture at a continuously settled site) would perhaps be (1) the 'shifting' horizon and changes in the heliacal risings of stars (marker stars or otherwise), (2) the pole-star and the replacement of one (marker star) by another over time, and (3) calendrical systems and the adjustments to such. None of the efforts using these arguments have been found to convincingly demonstrate the awareness of precession prior to Hipparchus. However, to perhaps vaguely realize something about the effects of precessional shift is one thing, and it is another thing entirely to suppose that they could have discovered the precession of the equinoxes as did the later Greek astronomer Hipparchus. (For 'discovery' to be made there would be no need to match Hipparchus and his coordinate system explanation; simply concluding the rate of stellar movement/shift is a systematic continuous displacement , would be sufficient. Additionally identifying that it was able to be calculated would be perhaps an unnecessary requirement to consolidate 'discovery.') In his article "The Celestial David and Goliath." published in 1995 (Journal of the Royal Astronomical Society of Canada, Volume 89, Number 4, Pages 141-154) F[?]. Millar argued that the ancient fear that "the sky is falling" was a description that identified knowledge of precession. (Peasant belief in ancient Greece, and Rome shared with the Celts, and Bastarnians (a Germanic tribe) the fear that the sky might fall.) The article by Millar assumes that an early culture, using the horizon as a measuring instrument, could identify both the slow tilting effect of the sky and also the slow displacement of the pole star and interpret the effects of both as a slow lowering of the sky. (For a further example of pole star myths and collapsing skies see the myth of Boahje-naste discussed in Finno-Ugric and Siberian Mythology by Uno Holmsberg (1927).) The "sky is falling" myth may be connected with the horizontal position of the Milky Way dropping below the western horizon. However, in interpreting ancient myths we can easily succumb to reading into them whatever we would like to believe. Moreover, the interpretation of myths most usually remains unverifiable. The theme of the "sky falling down" appears in traditional South American myths. The explanation is linked to volcanic activity.

For a short critique by Otto Neugebauer of the inaccuracies of Giorgio de Santillana as an historian of early science see "The Survival of Babylonian Methods in the Exact Sciences of Antiquity and Middle Ages." in Proceedings of the American Philosophical Society, Volume 107, Number 6, December 20, 1963, Page 531. See also the short critique of Giorgio de Santillana by Asger Aaboe in the book review "Historians of Science." in The Yale Review, Volume 52, Winter, 1962, Pages 326-328.

The authors of Hamlet's Mill hold that the clearest statement of precession exists in the Erra-Epic (also known as the Erra and Ishum Epic). (See: Hamlet's Mill by Giorgio de Santillana and Hertha von Dechend (1969) Pages 325.) The authors write: "... it is necessary to leave Era's somber prophecy unfulfilled, relating as it does to a coming world age: "Open the way, I will take the road, The days are ended, the fixed time is past." But with it comes the clearest statement ever uttered by men or gods concerning the Precession. Says Marduk: When I stood up from my seat and let the flood break in, then the judgement of Earth and Heaven went out of joint ... The gods, which trembled, the stars of heaven - their position changed, and I did not bring them back." The authors fail to to engage in any developed discussion, scholarly or otherwise, of this section of the text. The source of the "Marduk quote" in Hamlet's Mill is the late version of the Erra-Epic, generally believed by scholars to have been written circa the eighth-century BCE, and is likely derived from (the German-language) book Das Era-Epos by Felix Gössmann (1956). (The author of the Erra-Epic, Kabti-ilani-Marduk of the Dabibi-family, claimed that the work was revealed to him in a dream. The Erra-Epic is written as a dialogue between gods.) Which author of Hamlet's Mill made the English-language translation is not known. Unfortunately Gössmann's edition of the Erra-Epic has problems. In his review of the book (Archive für Orientforschung, Achtzehnter Band, 1957-1958, Pages 395-401) the Assyriologist Wilfred Lambert concluded it was not generally reliable. In the Erra-Epic there is a scenario involving disorder affecting the earth and heavens when Marduk temporarily leaves his throne. The context is an apocalyptic type scenario similar to the Biblical book, Apocalypse of John (i.e., Book of Revelation). (See the discussion in Cosmos, Chaos and the World to Come by Norman Cohn (1993). Erra is an Akkadian warrior god. The result of Erra's assault is that the world is plunged into darkness and as a result Marduk is displaced from his throne and forced to descend to the underworld. Erra temporarily seizes control of Babylon from Marduk during the latter's temporary absence. As the phenomena of precession is completely unconnected with any occurrence of celestial darkness this type of imagery can hardly be descriptive of precession. The actual overall point being made by the story is the equilibrium of the physical and moral world (both equally divine appointments) depend on the presence of the god Marduk.

The theme of the chosen imagery of the Erra-Epic is believed to refer to a disastrous military event that occurred to the city of Babylon in the "dark age" at the beginning of the 1st-millennium BCE. The central theme of the poem is concerned with the assault by Erra on the kingdom of Marduk. Babylon was the residence of the god Marduk and the centre of the universe. The disaster was interpreted in religious terms as the temporary replacement of Marduk by Erra. It is likely the poem is descriptive of a raid by the semi-nomadic Sutian people on the city of Babylon. It is most likely the Sutû raids of the 11th-century BCE were the background of the Epic. The Sutû tribes created havoc in Babylonia shortly after 1100 BCE. The Sutû (Aramaean tribes who lived along the Euphrates River) periodically raided Mesopotamian cities. The attacks on the Mesopotamian cities are stated in the Epic to be the work of the Sutû. The Assyriologist Wilfred Lambert held that the reign of Adad-apal-iddina fits the account of the Epic quite well. It has also been proposed that the epic was composed following the recovery of the statue of Marduk from Susa by Nebuchadnezzar 1 after its removal by the Elamite king Kutir-Nahhunte. (The cult statue was an important feature of Mesopotamian religion. The removal of cult-statues (or the key cult statue) of sacked city's patron god/goddess by a victorious army as booty was viewed as a grievous event by the inhabitants of the sacked city. It implied they had been abandoned by their patron god/goddess.) This event is dated to the 12th-century BCE. Circa 1160 BCE King Kutir-Nahhunte invaded Mesopotamia and took the city of Babylon. Included amongst the items he brought back from Babylon was the Code of Hammurapi. Circa 1120 BCE King Nebuchadnezzar 1 conquered Elam.

Erra is the god of war and pestilence (and ultimately fire). For an authoritative discussion that the Erra poem (a narrative poem) is not myth; it is mythologised history, see the paper "The Epic of Gilgamesh: Thoughts on Genre and Meaning." by the assyriologist Andrew George. For a discussion of some content of the epic of Erra and Išum (its theme of alternating destruction through flood and fire) as a possible mythological antecedent to the later astronomical theory of the 'Great Year' see: "A Possible Babylonian Precursor to the Theory of ecyprōsis." by Marinus van der Sluijs (Culture and Cosmos, Volume 9, Number 2, Autumn/Winter, 2005, Pages 1-19).(For the possibility of an additional astronomical interpretation of the story, see Mesopotamian Planetary Astronomy-Astrology by David Brown (2000, Pages 256-257).) The figure for the Babylonian 'Great Year' was not estimated with reference to precession. The concept is entirely different. The 'Great Year,' and the much later 'Precessional Year' (which had nothing to do with the Babylonians) are different in concept but get mixed by post Hipparchan writers.

If precession was known in early Babylonia we could reasonably expect it to be recognised in some form of the mathematical astronomy that developed and/or later calendar systems. (The Babylonians did identify and record some long-term astronomical cycles such as the synodic periods of the moon and planets.) It would seem that the Babylonians were limited by their lack of interest in theoretical astronomy and they had no geometric scheme to assist them. (See, however, Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and its Kin, by Jens Høyrup (2002), for the proposal that Old Babylonian algebra was not numerical but geometrical in nature.) They simply applied arithmetic to data that the later Greeks would apply geometry to. The 'golden age' of Babylonian observational astronomy is assigned to the period after Alexander the Great. The concept of precession could be realistically discovered and described only when geometric concepts had been developed. This was only achieved by the Greeks. The earliest Greek geometry can be traced to Thales of Ionia (635-543 BCE) and Pythagoras of Ionia (582-496 BCE). (The rudiments of practical geometry are, however, found in the earlier mathematical traditions of Babylonia and Egypt.) It can be confidently stated that the phenomenon of precession was not identified by the Babylonians (and so it is out of the question that it was understood as a systematic continuous variation (i.e., that all stars have slow continuous motions parallel to the ecliptic) and that the rate of precession was measured).

There is no evidence that - even if ancient knowledge of precession is accepted as known - the slow and almost imperceptible process of precession was interesting to ancient societies to the extent that they gave it immense and fundamental importance. The lack of sufficient evidence is one issue. The second issue involves the simple fact that common evidence offered is not irrefragable. On the contrary, the evidence given to support claims for ancient and pre-Hipparchan knowledge of precession is able to be contested/disputed and refuted without difficulty. Several final points: (1) If precession was really recognised in the Neolithic period at least (that is, understood to be a slow movement proceeding at the rate of 30 degrees in every 2155 years), then why, if the zodiacal constellations were also developed/established early were they not also adjusted early (or soon after) from being of unequal extent? (2) If the zodiacal constellations were developed late - long after precession was recognised and understood to be a slow movement proceeding at the rate of 30 degrees in every 2155 years - then why were they not established as being of equal extent.

Appendix 1: Precession

As a simple explanation: The phenomenon of precession is caused by a slow wobble of the Earth's axis that takes approximately 26,000 years to complete a cycle. (The wobble is caused by the Sun and the Moon. Because the Earth’s axis is tilted to its orbital plane the gravitational pull of the Sun and the Moon on the Earth's equatorial bulge tend to pull it back towards the plane of the ecliptic. Because the Earth is spinning, its axis precesses. Planetary precession means the gravitational pull of the planets that perturbs the Earth's orbit and slowly changes the plane of the ecliptic. General precession means the combination of luni-solar and planetary precessions.) The north celestial pole moves in a precessional circle around the pole of the ecliptic resulting in the equinoxes precessing westward around the ecliptic. Because of general precession, the framework of right ascension and declination (ecliptical longitude) is constantly changing. On the other hand, the latitudes of all stars remain unchanged. The effect of general precession on the ecliptical longitude position of stars (right ascension and declination) varies both with the star and with time and the effect is not that easily calculated (but somewhat dependent on method). The calculation of general precession is simple in ecliptic coordinates – a yearly 50 seconds of arc (approximately) increase in longitude and no change in latitude. It gets more difficult to calculate when expressed in terms of right ascension and declination. (There was an apparent lack of precessional movement by Sirius as viewed at the latitude of ancient Egypt. Sirius was long used by the ancient Egyptians as the foundation for 2 of their calendar systems. The calendar year based on the heliacal rising of Sirius did not vary as the position of Sirius showed no apparent variation. Sirius is affected by precession and does move. The reason there was little apparent variation is Sirius happens to move in such a way that the distance between it and the equinoxes appears to remain approximately constant.) As a basis for calculating the effects of general precession it is necessary to state the equator and equinox of the coordinate system to which any position is referred. (See: Miscellaneous Papers of the University Observatory, Oxford, Issue 385 (1928).)

Appendix 2: Babylonian Astronomy

"Astronomy in Mesopotamia is divided historically into a primarily schematic astronomy in the late second and early first millennia B.C., and a scientific, mathematical astronomy in the Seleucid period. The common idea that astronomy in Mesopotamia evolved from an observational to a purely computational science is not supported by extant textual sources. It remains characteristic for Babylonian astronomy that, from the earliest examples, astronomical texts deal with numerical schemata." ("Stellar Distances in Early Babylonian Astronomy: A New Perspective on the Hilprecht Text (HS 229)." by Francesca Rochberg-Halton (Journal of Near Eastern Studies, Volume 42, Number 3, July 1983, Pages 209-217).) From the earliest extant astronomical material from the 2nd-millennium BCE the Babylonians were engaged with schematic computational schemes for predicting phenomena, without recourse to observation.

The assyriologist and astronomer Franz Kugler (Sternkunde und Sterndienst in Babel (1907)) pointed out that the lack of accurate calculation and observation in early records of eclipses and of the planets demonstrates the absence of a precise system of measuring location and time in the sky. Precise date and position details are not given for any early observations. The total eclipse observed in 763 BCE was only recorded by the simple statement: "In the month Sivan an eclipse of the Sun took place." Texts show that sophisticated mathematics existed in the Old Babylonian Period. Texts also show that Babylonian astronomy of comparable sophistication did not exist until the Seleucid Period.

Even during the late Babylonian period when they kept detailed records and developed skillful calculations, there is no trace of an awareness of precession.

The fact is the Mesopotamians combined 10 with 6 to obtain a base figure of 60 - and they counted in multiples of 60.

Appendix 3: The Number 72 in Mesopotamia

In Mesopotamia the use of the number 7 has been derived from magical/mystical thought. The use of the number 7 has a magical significance that is not derived from any literal astronomical realism. Within the context of Mesopotamian number magic it has been noted that all derivatives or multiples of 7 carry with them the idea of wholeness. The number 7 (commonly associated with cosmic perfection) is a most important magical number and is closely associated with other number '7s' principally: 70, 71, 72, and 73. The number 72 can be divided by: 2, 3, 6, 8, 9, 12, 18, 24, and 36. The number 72 has a relationship to the number 70. There are many example where the number 72 is interchangeable with the number 70. Astronomically, the number 72 does figure in the cycle of Venus.

According to proponents of Hamlet's Mill the number 72 is the precessional number that is the foundation for various derivatives and multiples that occur in myths. Hamlet's Mill has an unidentified Neolithic culture establishing a 360 degree circle moving 1 degree every 71.6 years, but in encoding the number in mythology they round it to 72!

Appendix 4: Changes in Symbolism/World Ages Argument

Zodiacal world ages are not indicated by myths and symbols. See the detailed discussion in: "Critique of Alexander Gurshtein's Theory of Constellation Development." by Gary D. Thompson.

The "changes in symbolism" argument used by the authors of Hamlet's Mill to claim that the shift from an "Age of Twins" to an "Age of Taurus" to an "Age of Aries" to an "Age of Fish(es) is identifiable suffers from the dual burden of wishful thinking and absence of evidence. "At time Zero (say, 5000 B.C. - there are reasons for this approximate date), the sun was in Gemini; it moved ever so slowly from Gemini into Taurus, then Aries, then Pisces, which it still occupies and will for some centuries more. The advent of Christ the Fish marks our age. ... The preceding age, that of Aries, had been heralded by Moses coming down from Mount Sinai as "two-horned," that is, crowned with Ram's horns, while his flock disobediently insisted upon dancing around the "Golden Calf" that was, rather, a "Golden Bull," Taurus (Hamlet's Mill, Pages 59-60; see also Page 44)." (Interestingly, Hertha von Dechend, though raising the possibility of such an interpretation in her M.I.T. seminar notes, stated she did not favour this particular explanation.) Additionally, the voyage of the Argonauts for the Golden Fleece (of a ram) introduces the "Age of Aries" (Hamlet's Mill, Page 318).

Interpretations for the date of the fancied change from an 'Age of Taurus' to an 'Age of Aries' range from circa 2150 BCE to circa 1875 BCE. Several major problems are obvious with the Moses example. Firstly, the period of Moses presented in the Hebrew bible is dated between circa 1500 BCE and 1200 BCE. This is some 650/950 years or 375/675 years after the alleged beginning of the 'Age of Aries.' Secondly, the Ram is demonstrably a Greek constellation dating no earlier than circa 500 BCE. There was no Mesopotamian Ram constellation. It is uncertain whether there was an Egyptian Ram constellation/asterism. According to the astronomer Juan Belmonte the southern constellation (decan) sit or srt (seret) on the ceiling of Senmut's tomb could be a sheep (woolly usually horned ruminant mammal related to the goat), ram (male sheep), or goat (hollow-horned bearded ruminant mammal related to the sheep) = Capricornus or perhaps the stars in the area of Grus and Piscis Austrinus. (See: Belmonte, Juan. and Shaltout, Mosalam. (2009, Reprinted 2010). (Editors). In Search of Cosmic Order: Selected Essays on Egyptian Archaeoastronomy.) This constellation/decan was not connected with the stars of Aries.

Other writers like to add in further examples such as the slaying of the Cretan Minotaur symbolising the end of the "Age of Taurus." The cult of the Apis bulls in Ancient Egypt is held to represent the "Age of Taurus" and the Amun cult in Egypt is held to represent the "Age of Aries."

The "changes in symbolism" argument, which goes back to the 19th-century, easily collapses with only a few criticisms. (The "changes in symbolism" argument lacks strength and originates, I think, with the outdated 19th-century constellation ideas of the Assyriologist Archibald Sayce and popular science writer Agnes Clerke.) The date of Moses is usually given as circa 1500 BCE. There was no zodiac circa 1500 BCE, so it is impossible to have zodiacal world ages at this early date. Certainly there was no scheme for equally dividing the ecliptic, or other established convenient frame of coordinates, at this early date. As such equally timed changes in "world ages" is out of the question. In the case of Moses having horns we have a simple translation error. The Hebrew root KRN can be keren meaning "horn" or karan meaning "radiant." When the Hebrew bible was translated into Latin the Hebrew KRN was mistranslated as "horned" (and so instead of Moses' face being radiant it was horned). It has not been demonstrated that the search by Greek heroes for the "Golden Fleece" has anything to do with a constellation or astronomy. The Golden Fleece of the Argonautica may be connected with the holy fleece of Hittite ritual. It was a Hittite custom to hang a container made from the skin of a sheep from a sacred evergreen tree in the centre of a grove. The fleece were decorated with gold and the sheep skin container filled with offerings to their gods/goddesses. However, it is common to interpret the Argonautica as an adventure story recalling how early Greek mariners searched for new territories to expand Greek trade.

The Cretan Minotaur was half bull and half man. Taurus is simply a truncated bull. Why exactly the Cretan Minotaur should represent the "zodiacal" bull (Taurus) is never explained. Why Theseus killing it should represent the end of the "Age of Taurus" is also never explained. Nothing at all is known of Minoan constellations so no proof of any intended association with a Minoan bull constellation is possible. The Apis bull was believed to be the incarnation of the Egyptian god Ptah. It has not been demonstrated that the Apis bull has anything to do with astronomy. The identification of native Egyptian constellations is mostly uncertain. The Apis bull has never been linked with a native Egyptian bull constellation (at any time - let alone during a supposed "Age of Taurus"). Chronologically the cult was more popular during the supposed "Age of Aries" than it was during the supposed "Age of Taurus." The Egyptian god Amun was originally frequently depicted as the Nile goose and later more frequently depicted as a ram, or as a ram-headed man. However, from the cult's beginning's Amun could be depicted as either a Nile goose or as a ram, or as a ram-headed man. Chronologically the cult originated in the supposed "Age of Taurus."

David Ulansey (The Origins of the Mithraic Mysteries (1989)) has never provided any evidence that 'zodiacal ages/astrological ages' was a concept understood anywhere at all in the ancient Greco-Roman world. (Ulansey claims that Mithraism had a cosmology associated with the precession of the equinoxes and the signs of the zodiac.)

The argument that the early Catholic Church used Vesica Pisces as the symbol of Jesus Christ with the intent to promote Jesus Christ as the Lord of the Age of the Fish is without evidence. In all early Christian writings, including those that deal with cosmology and history (including Gnostic texts) there is no mention of any such thing.

It is also worth mentioning that in his Republic, Plato's emphasis on the organisation of the city-state is unconnected with the idea of 'zodiacal ages.' It has to do with modelling social organisation on the cosmos.

The concept of precession-based zodiacal "world ages" is largely a 19th-century Theosophical concept invented by the occultist Helena Blavatsky. Nick Campion identifies that the concept draws "partly on Hesiod's sequence of ages outlined in the Works and Days, the Hindu Yugas, some 19th-century studies of comparative religion and Madame Blavatsky's own theory of racial and spiritual evolution (Hastro-L, 13 April, 2000)." (However, the concept of precessional "world ages" can also be traced back to Origine des tous les cultes: ou, Religion universelle by Charles Dupuis (1794).) Additionally, the constellations are all of uneven size and we have no knowledge of the boundaries of any early constellations. We have no knowledge of even the boundaries of the Greek constellation scheme of Aratus of Soli circa 275 BCE.

Appendix 5: The Invention of Zodiacal/Precessional World Ages

See: Campion, Nicholas. (2004). 'The Sun is God.' (Culture and Cosmos, Volume 8, Numbers 1 and 2, Spring/Summer and Autumn/Winter, Pages 45–56). Note: Excellent investigation of the modern origin of astronomical 'world ages'.

Astrological (= zodiacal) ages is an modern astrological concept with its origins in speculations about astronomical mythology, and the antiquity of astronomical knowledge. The determination of the starting dates of the astrological ages are without consensus and are dependent on the numerous methods of calculation used. The introduction of the imaginary system of 12 zodiacal signs was a late Babylonian mathematical device that redefined constellations along the ecliptic. Its introduction is not indicated as being connected with astral omenology. The precession of the equinoxes determines so-called precessional (zodiacal) ages. Some modern popular belief systems (such as astrological mythology, and Theosophical beliefs and New Age beliefs derived from Theosophy) imagine that the so-called zodiacal (astrological) ages distinctively influence historical events. (In popular culture, the "Age of Aquarius" simply refers to the advent of the New Age movement in the 1960s and 1970s.) Non-speculative evidence for an ancient theory of successive precessional ages (let alone their supposed influence) is wanting. Speculative evidence for an ancient theory of precessional ages - such as David Ulansey's ideas on Mithraism - abound. Ulansey claims that Mithraism had a cosmology associated with the precession of the equinoxes and the signs of the zodiac. Arguing for the idea of astrological world ages originating in the ancient world is one thing; providing evidence that the idea was also linked to the precession of the equinoxes is quite another. The concept of precession-based zodiacal "world ages" is largely a 19th-century Theosophical concept largely invented by the occultist Helena Blavatsky. In her publications Blavatsky discussed a variety of belief systems involved with astronomical cycles. In a footnote to an 1888 article Blavatsky asserted there was a cycle founded on the precession of the equinoxes and the signs of the zodiac. Earlier, in her book Isis Unveiled (2 Volumes, 1877) Blavatsky mentioned the statements by Charles Dupuis, Constantin Volney, and Godfrey Higgins regarding cycles. Nick Campion identifies that the concept draws "partly on Hesiod's sequence of ages outlined in the Works and Days, the Hindu Yugas, some 19th century studies of comparative religion and Madame Blavatsky's own theory of racial and spiritual evolution (Hastro-L, 13 April, 2000)." But Godfrey Higgins was a major influence on Blavatsky. (See also the essay: "Blavatsky and the Great Year: Astrology in the Bible." by Robert Tulip (2011, 11 pages).) However, the concept of precessional "world ages" can also be traced back to Origine des tous les cultes: ou, Religion universelle by Charles Dupuis (1794). Also influential was Anacalypsis (2 Volumes, 1833-1836) by Godfrey Higgins who asserted the Chaldeans had a cyclical system of world ages of 2160 years each. Higgins claimed that a cycle of precessional astrological (world) ages of 2160 years each was discovered by the Chaldeans and was subject to encoding in language by use of significant names and phrases, and letters having having numerical equivalents. In all of this speculation ancient constellation boundaries remains an issue. The constellations are all of uneven size and we have no knowledge of the boundaries of any early constellations. We have no knowledge of even the boundaries of the Greek constellation scheme of Aratus of Soli circa 275 BCE.

The Pole-star and its possible connection with changing "World Ages" has also been raised.

More modern proponents of ancient knowledge of precession and/or a system of zodiacal world ages are the French occultist René Adolphe Schwaller de Lubicz (1887–1961) , and the Swiss mystic, psychiatrist, and psychotherapist Carl Jung (1875-1961). In his Sacred Science: The King of Pharaonic Theocracy (1961), René Adolphe Schwaller de Lubicz claimed knowledge of precession in ancient Egypt. In his Aion (1951, also in Collected Works of C. G. Jung, Volume 9, Part 2) Carl Jung popularised the concept of astrological ages. The original 2 Swiss editions had different subtitles: "Researches into the History of Symbols" and then "Contributions to the Symbolism of the Self."

Some ancient societies were organised according to models of the cosmos and also there were prophetic theories of history. But this does not mean that ancient (e.g. Hellenistic) astrologers believed in the Ages of Pisces or Aquarius or that they believed in other aspects of modern astrology. The Greek literary sources for historical (cosmic) periodisation and astrological theories of periodic (cosmic) destruction are Hesiod's Works and Days and Plato's Timaeus and Republic, none of which have anything to do with precession or astrological ages as currently understood. In Plato's Great Year the world comes to an end and is reborn when all the planets form a mean conjunction at the place of their creation. This was understood by later Platonists to be Aries. In the version that came from the Babylonian priest Berossus, and was publicised by Pliny, there were two points - Cancer and Capricorn.

The Origin of the Age of Aquarius

Helena Blavatsky was one of the several founders of Theosophy/Theosophical Society (at New York City in 1875). It appears there is no direct reference to an "Age of Aquarius" to be found in Blavatsky’s writings. Isis Unveiled by Helena Blavatsky (2 Volumes) was first published in 1877. It is the "Bible-book" of Theosophy. It does not mention an "Age of Aquarius." There is no mention of precession leading to any specific, forthcoming astronomical/astrological age or epoch. The Secret Doctrine by Helena Balavatsky (3 volumes) was first published in 1888. It does not mention an "Age of Aquarius." Blavasky has a lot of material regarding time cycles of enormous length (influenced by Vedic cosmological thinking) including precession of equinoxes but there is no hint of precession being associated with these various cycles. Blavatsky died in 1891. The modern precessional idea of an "Age of Aquarius" appears to originate with the Theosophist William Judge who wrote about the term "Age of Aquarius" in 1893 in his book, The Ocean of Theosophy. Judge was a close associate of Blavatsky. It seems indicated that the idea of an "Age of Aquarius" had not originated until after Blavatsky's death. (Note: The "Age of Aquarius" is earlier than Blavatsky. For example: Aside from the ideas of Charles Dupuis (late 18th-century) and Godfrey Higgins (early 19th-century), this appears to be is the earliest reference we have referring to the zodiac, precession and different "ages." Max Heindel (born Carl Louis von Grasshoff in Aarhus, Denmark), who later established the astrology focused Rosicrucian Order (Point Loma, California), promoted from its very inception the notion of an "Age of Aquarius." Heindal was for a time the vice-president of Judge's American branch of the Theosophical Society. The Austrian esotericist Rudolf Steiner is indicated as being the first person to develop the concept of an "Age of Aquarius" in the form recognised today.

By way of noting: It was Gerald Massey who introduced the term Age of Aquarius into the English language (in 1887 in his pamphlet on the mythical Jesus).

Judge wrote: "The great Sidereal year is the period taken by the equinoctial points to make in their precession a complete revolution of the heavens. It is composed of 25,868 solar years almost. It is said that the last sidereal year ended about 9,868 years ago, at which time there must have been on this earth a violent convulsion or series of such, as well as distributions of nations. The completion of this grand period brings the earth into newer spaces of the cosmos, not in respect to its own orbit, but by reason of the actual progress of the sun in an orbit of its own that cannot be measured by any observer of the present day, but which is guessed at by some and located in one of the constellations. ... [M]an is also affected by astronomical cycles because he is an integral part of the whole, and these cycles mark the periods when mankind as a whole will undergo a change. In the sacred books of all nations these are often mentioned, and are in the Bible of the Christians, as, for instance, in the story of Jonah in the belly of the whale. This is an absurdity when read as history, but not so as an astronomical cycle. "Jonah" is in the constellations, and when that astronomical point which represents man reaches a point in the Zodiac which is directly opposite the belly of Cetus or the whale on the other side of the circle, by what is known as the process of opposition, then Jonah is said to be in the center of the fish and is "thrown out" at the expiration of the period when that man-point has passed so far along in the Zodiac as to be out of opposition to the whale. Similarly as the same point moves thus through the Zodiac it is brought by opposition into the different constellations that are exactly opposite from century to century while it moves along. During these progresses changes take place among men and on earth exactly signified by the constellations when those are read according to the right rules of symbology. It is not claimed that the conjunction causes the effect, but that ages ago the Masters of Wisdom worked out all the problems in respect to man and found in the heavens the means for knowing the exact dates when events are sure to recur, and then by imprinting in the minds of older nations the symbology of the Zodiac were able to preserve the record and the prophecy. Thus in the same way that a watchmaker can tell the hour by the arrival of the hands or the works of the watch at certain fixed points, the Sages can tell the hour for events by the Zodiacal clock."

Appendix 6: The Myth of Knowledge of Precession in Ancient Egypt

The principal source for the claim that the ancient Egyptians were aware of precession is the book, The Death of Gods in Egypt by Jane Sellers (1992; 2nd revised edition 2003, 3rd revised edition 2007). Jane B. Sellers, who is not a professional Egyptologist, was born in Chicago(?) in 1926. She uses Egyptian mythology to test the ideas in Hamlet's Mill. Sellers set out to find evidence of precessional mythology in Egypt because she thought the topic was neglected in Hamlet's Mill. Two criticisms are: (1) She looked at the evidence selectively. (2) She 'force fits' evidence to the theory. (3) She used a lot of material that was 20 plus years out of date when doing her work. Jane Sellers "gained her BA late in life, at Goddard College, Vermont, and went on to study Egyptology at the University of Chicago's Oriental Institute." For reasons unrelated to the course the author did not complete her Ph.D. in Egyptology (under Dr. Klaus Baer) at the Oriental Institute, University of Chicago. Juan Villar, in his book The Seventh Wonder (2005), incorrectly/falsely identifies Jane Sellers as an Egyptologist at the University of Chicago, and thus associates her book with the University of Chicago. A revised and updated 2nd edition of her book was first privately published (unbound, i.e., loose sheet form) by the author in 1999 and then published as a bound volume by a minor publisher in 2003 (and this later 2nd edition is the preferred volume to use). She was "Author of the Month" for November 2003 at The popular pseudo-historian Graham Hancock deems Sellers to be an "archaeo-astronomer." Sellers believes the death of Osiris in Egyptian mythology was a precessional death. Elements of the Osiris myth are found in the Pyramid Texts dating to circa 2450 BCE, but Sellers uses the Osiris myth from The Egyptian Myth of the Dead [The Egyptian Book of the Dead] dated circa 1550 BCE. According to Sellers the Osiris myth was encoded with a group of key (precessional) numbers: 360, 72, 30, and 12 (and 5). Sellers claims that these numbers are equated with the precession of the equinoxes. According to Sellers the most important number in the "code" is 72. That the true figure for the rate of precession (measured in degrees) is 71.6 years is glossed over as being too difficult to insert into the narrative structure i.e., you can't have 71.6 persons.

The explanation (not explicit in The Egyptian Myth of the Dead) of the so-called precessional numbers according to Sellers:

12 = the number of zodiacal constellations.

30 = the number of degrees of one "age" in the precessional cycle (= 2160 years) / the number of degrees allocated along the ecliptic to each zodiacal constellation.

72 = the number of years for the sun to complete a precessional shift of 1 degree along the ecliptic.

360 = the number of degrees completing the precessional cycle (= 25,920 years) / the number of degrees comprising the entire ecliptic of 12 zodiacal constellations.

5 = used as a multiplier number.

We then get the usual assumption of multiplying the following combination of numbers: 72 x 30 = 2160; 12 x 2160 = 25,920; 5 x 72 = 360; 72 x 360 = 25,920.

However, in the Osiris myth, the god Set (the brother of Osiris) conspired with Aso (an Ethiopian queen) and 72 other accomplices to enclose Osiris in a coffin. This totals 74, not 72. The number 72 is separated out in order to assign it precessional significance. Also, a non precessional use of 72 is: Thoth, in an Egyptian creation myth, wins a 72nd of each day of the year from the Moon in a game of draughts, as a favour to Nut, the Sky Goddess. He uses these portions to make the five intercalary days on which the remaining Gods and Goddesses are born. In Egypt the use of the number 72 had application to the number of people, and the number of days. The number 72 was popular in Greece and Egypt during the Hellenistic period. (For a detailed discussion of the number 72 during the Hellenistic period see especially: The Meaning of the Letter of Aristeas by Ekaterina Matusova (2015).)

The dominant precessional number is held to be 72. According to proponents of Hamlet's Mill the number 72 is the precessional number that is the foundation for various derivatives and multiples that occur in myths. Hamlet's Mill has an unidentified Neolithic culture establishing a 360 degree circle moving 1 degree every 71.6 years, but in encoding the number in mythology they round it to 72. (The rate of precession is not constant. (Precessional movement is irregular rather than constant.) A representative recent figure is 25720 years = 2143 years per 'zodiacal age' = 71.4 years per 1 degree. With 72 years for precession to move 1 degree = 2160 per 'zodiacal age' = 25920 years for the entire cycle to repeat. According to John Major Jenkins ( the traditional estimate of precession was 25920 years. In the writings of Joseph Campbell (which can be generally classed as 'alternative' literature) the mythical 540 gates of Valhalla are interpreted as one quarter of 2160 (= one twelfth of the precession period (of 25920 years). The question is: If we accept ancient knowledge of precession then is this a real or rounded/ideal figure? Interestingly, David Ulansey in his precessional interpretation of the religion of Mithras (The Origins of the Mithraic Mysteries (1989)) uses the annual precessional rate of 50.3 seconds of arc per year = 1 degree every 71.6 years = so-called 'precessional great year' of 25,700 years.) As Jason Colavito has pointed out in his 27/11/2012 website article "Civilization and Precession (Part 1"): "[T]he numbers ... identified in myth have a much simpler explanation: they are all multiples of 2 and 3, the smallest numbers capable of generating complex multiples. ... Early peoples who did not use a decimal system, tended to use multiples of 2 and 3 because these were the easiest numbers for generating large multiples."

The question that needs answering is: Why should any of these numbers be teamed together and transformed in the way chosen by proponents of pre-Hipparchan knowledge of precession? Why are these particular calculations (mathematical gymnastics) – usually involving addition, multiplication, division, and subtraction engaged in. Simply, why are the numbers and processes chosen and used (i.e., how and why), and why are they to be taken as evidence of pre-Hipparchan knowledge of precession? What other more tangible, historical evidence exists for establishing pre-Hipparchan knowledge of precession? Proponents do not seem to know, or care to explain any of these questions. I cannot find any example where this request is actually met. The process of mathematical gymnastics engaged in readily invites the criticisms that it is a subjective exercise and also that it involves filtering and shaping. I remain underwhelmed by the whole exercise. It is perhaps likely that some people at least are working backwards from the answer they want to achieve as a way of choosing numbers and processes to achieve the outcome.

Appendix 7: The Myth of Knowledge of Precession in the Eddas

It is not unusual to hear the claim repeated that knowledge of precession appears in the Eddas (a collection of old Norse poems and tales dating circa 10th-century CE). The claim simply rests on verse 23 of the poem Grimnismál in the Eddas. At Ragnarok ("end of the world") out of each of the 540 doors of Valholl ("hall of the dead" or "hall of the slain") will come 800 warriors. (It is also pointed out that in verse 24 of the poem there are 540 rooms (or "floor-rooms") in Thor's palace of Bilskirnir.)

Stanza 23 of Grimnismál (one of the Danish mythological poems of the Poetic Edda) has the descriptive lines:

"Five hundred doors and forty,

Think I there at Valholl;

Eight hundred einhergar go out one door,

When they go to fight with the wolf."

Valholl was the largest building in Asgard, the celestial realm of the Norse gods/goddesses. The number of doors is multiplied by the number of warriors emerging from each door to achieve an end number of 432,000 warriors. (This calculation and the resulting number of 432,000 is not in the Eddas.) The claim is then made that the number 432,000 refers to a precessional "great year." It has also been asserted that this number shows that there is an astronomical lore in the Edda that is part of an ancient astronomical tradition. A link is made with the Vedas.

It is correct that according some sources Valholl has 540 doors each wide enough for 800 warriors. It is correct that the 540 rooms (or "floor-rooms") in Bilskirnir can match the version of 540 doors of Valholl. However, I do not recall any "associated number" such as 800 (or 960) warriors (or whatever) connected with Bilskirnir. Also, according to other sources Valholl has 640 doors each wide enough for 960 warriors. Hence out of the medieval tale we can multiply the former figures and get the resulting number 432,000 or we can multiply the latter figures and get the number 614,400. The figure of 432,000 may be linked with the Babylonian doctrine of "cosmic recurrence" (i.e., a "great year" linked to "powerful" conjunctions, not a precessional "great year"). I have never seen the figure 614,400 touted as belonging to either. (A prime candidate for uncritically promulgating this sort of arithmetic is the Jungian mythologist Joseph Campbell in his (for example) book The Masks of God: Occidental Mythology (1964, Page 459).)

The supporters of knowledge of precession in the Eddas seem to have no knowledge of the old Germanic system of calculation. In the old Germanic system of reckoning the "long hundred" had the value of 120. In Old Norse usage hundrath (hundraô) usually meant120 (of anything), not 100. This form of early measure (long hundred/great hundred) was common during the Viking Age and was continued (in a number of countries influenced by Norse culture) as common usage up till circa 1700 CE. The number 100, now known commonly as “one hundred” was, prior to circa 1700 CE (in countries influenced by Norse culture), known as “the small hundred.” There was also (though less common) a long thousand, meaning 1200. Note: The "long hundred" (120) is mainly attested in Old English and Old Norse. In Old English 2 types of 100 existed: a "hund teontig" (= a short (100) hundred) and a "hund twelftig" (= a long (120) hundred).

In all likelihood the "five hundred ... and forty" and the "eight hundred" have the Germanic "long hundred" value (not the decimal value 100). Hence 640 doors and 960 warriors. Even orthodox writers may or may not indicate knowledge of the old Germanic system of calculation. Norse Mythology by John Lindow (2001) simply gives 540 doors and 800 warriors. World Mythology by Donna Rosenberg (2nd edition, 1994) simply gives 640 doors and 960 warriors. Myth and Religion of the North by Edward Turville-Petre (1964) gives both 540 (or 640) doors and 800 (or 960) warriors. An important discussion of the issues by Magnus Olsen appeared in (the Danish language) Acta Philologica Scandinavica, Volume VI, 1931-1932. (The particular paper was later included in his collected papers Norrone studier (1938).) See also the (English-language) discussions: "Remnants of Medieval Symbolic Number Usage in Northern Europe." by Jens Ulff-Møller (1993). In: Medieval Numerology: A Book of Essays edited by Robert Surles (Pages 143-156); and "Numeracy and the Germanic Upper Decades" by Carol Justus (Journal of Indo-European Studies, Volume 24, 1996). Still useful on Valhalla is the (German-language) book, Walhall by Gustav Neckel (1913). Neckel proposed that the multiple doors of Valhalla were influenced by knowledge of Roman amphitheaters, especially the Coliseum, reaching the Norse in Scandinavia.

References to Valholl can thus have the numbers 540 and 800 or 640 and 960. References to Bilskirnir simply have the number 540 but not 640 nor 800 or 960. Some people are keen to multiply 540 by 800 but not 640 by 960.

For the number 540 Vincent Hopper suggested (Medieval Number Symbolism (1938, reprinted 1978)) that the Medieval Norse (1) had an idealised 360 day year calendar (adjusted by intercalation), (2) calculated time by half years; and (3) 540 denotes a calendar cycle of 3 half years (winter-summer-winter). It seems we may be playing with nothing deeper than mundane calendar-based numbers.

A further (standard) study of Valholl is Walhall by Gustav Neckel (1913). His opinion was the "five hundred ... and forty" doors intends to express nothing more than a large number and was perhaps influence by Norse knowledge of the numerous doorways (and vomitoria) of the Roman Colosseum (Coliseum). There were 80 entrances at ground level. However, the Colosseum incorporated a number of vomitoria - passageways designed so that the venue could quickly disperse people into their seats (in 15 minutes), and evacuate them abruptly (in 5 minutes).

Appendix 8: The Myth of Knowledge of Precession in Ancient India

E[?]. Burgess (Translation of the Suryasiddhanta: A Textbook of the Hindu Astronomy with Notes and an Appendix (1977, Pages 115–120)), claims that knowledge of precession was known to astronomers in India since the Vedic period (circa 2000 BCE/1500 BCE - 1000 BCE). David Pingree ("Precession and Trepidation in Indian Astronomy Before A.D. 1200." (Journal for the History of Astronomy, Volume 3, 1972, Pages 27-35)) states the earliest datable reference to precession/trepidation in India is the Pãncasiddhāntikā by the 6th-century CE Indian philosopher, astronomer, astrologer, and mathematician Varāhamihira (505-587 CE). It was not until the 12th-century CE that precession was estimated to within an accuracy of 1 percent in India.

Appendix 9: Dhruva Does Not Provide Evidence of Knowledge of Precession in India

In the Bhagavata Purana (the god) Dhruva is identified as the Pole Star. It is somewhat usual to identify Dhruva (the Pole Star) with α (alpha) Draconis (Thuban, a pale yellow star) but it could have been perhaps the dim star Ketu (Kappa Draconis, or even α (alpha) Ursa Minor (Polaris). It is perhaps more likely that in the Bhagavata Purana the identification of Dhruva as the Pole Star meant α (alpha) Ursa Minor (Polaris). Dennis Hudson (at circa 2004), Emeritus Professor of Religion, Smith College (USA) is an expert on the Bhagavata Purana. From his research he has concluded that the Bhagavata Purana is a composite work which originated in different places at different periods. He dates its composition over a time span of 1600 years from circa 700 BCE to circa 900 CE. This dating does not give support for the recognition of Thuban as Pole Star. (It appears the Bhagavata Purana remained an oral tradition until written down circa 800 CE.) Also, Hudson's dating and the statement that no one had previously lived in Dhruva's place in the sky seems to support no knowledge of Thuban as a previous pole star.

Hermann Jacobi ("On the Antiquity of Vedic Culture." (Journal of the Royal Asiatic Society, 1909, Pages 721-726)) noted that the Gryha Sutras mention Dhruva as the Pole Star and also that the Maitrayana Brahamana Upanishad states that even the polestar moves (over a long period of time). Jacobi 's argument that these instances preserve memories from ancient times is not supported by mainstream scholarship. (Hermann Jacobi’s claim at the time it was proposed was opposed by William Whitney, A[?]. Keith, and others.) The chronology of Indian history and literature prior to the Middle Ages is notoriously uncertain and astro-archaeological methods arguing for very early dates are generally rejected by mainstream scholarship.

The 7 Rsis were associated with the centre of the sky i.e., the region of the north celestial pole. However, Dhruva (the Pole Star) came to assume this position when precession slightly shifted the location of Ursa Major.

If precession was common knowledge amongst 'intellectual elites' in the Neolithic period, due to diffusion from an original source in the Near East, then it is puzzling that in Hindi mythology the name Dhruva (immovable) is used to denote an astral god, identified with a star in the constellation of Ursa Minor which was the pole star in the last millennium BCE..

Appendix 10: The Recognition of Precession in China

 The earliest archaeological evidence of a Chinese calendar appears on the oracle bones of the late 2nd-millennium BCE. They demonstrate a 12-month lunisolar year with the occasional arbitrary intercalation of a 13th- and even 14th-month. However, Chinese historical records place the origin of a lunisolar calendar (of 366 days) to circa 3000 BCE. The development of a calendar in China was closely related to the development of astronomy and the needs of agriculture. (China was largely an agricultural society.)

The earliest tentative awareness of precession in China took hold in the Hou Han (= later Han) period. (The later Han period is also now referred to as the Eastern Han Dynasty and spanned from 25 to 220 CE.) During this period it was quite widely recognised that the calendar altered (i.e., became unreliable) every 300 years. That is, every 300 years there was a requirement to use a new calendar. Multiple mentions of the fact that the calendar was only good for 300 years appears in the multiple volumes of the Hou Hanshu (= Book of the Later Han) by the historian Fan Ye (flourished 398-445 CE).

According to the sinologist Nathan Sivin (Granting the Seasons (2009, Page 100)): "... for the Chinese the initial point of the year was the winter solstice. ... The conception [of precession] evolved in several steps. Beginning at the end of the first century B.C., astronomers became aware that in observations over long periods the winter solstice point appeared at different locations among the stars. They were not certain, however, whether this was a gradual shift or the result of earlier observational errors." 

The discovery of precession - or at least the hunch of its existence - is attributed by Wolfram Eberhard and Rolf Mueller to the Palace astronomer Chia K'uei (30-101 CE) of the Han dynasty. The date they give for his suspicion is circa 89 CE. (See: "Contributions to the Astronomy of the Han Period III: Astronomy of the Later Han Period." by Wolfram Eberhard and Rolf Mueller in Harvard Journal of Asiatic Studies, Volume 1, Number 2, July, 1936, Pages 194-241.)

The discovery of the precession of the equinoxes in China can be attributed to the scholar Yü Hsi (flourished circa 307-338 CE) circa 320 CE who discussed it in his book, the An Thien Lun written 336 CE. (The book discussed whether the motions of the heavens were stable.) Yü Hsi (281-356) obtained a value of about 1 degree in 50 tropic years for the precessional movement. (This is off by almost 50 percent.)

The brilliant scholar Zu Chongzi (420-500 CE) created the Daming Calendar (some sources say promoted his father's calendar ) which took precession into account for the first time. The most thorough and comprehensive calendar in the history of China was the Dayan Calendar compiled in the Tang Dynasty (616-907 CE) by the monk Yi Xing.

Written Chinese astronomical texts first appear in the Shang Dynasty (circa 17/1600-11/1050 BCE) with the oracle bone divinations. Considerable early Chinese mythology carries sufficient hints to invite an astronomical interpretation. There is the myth of the quarrelling brothers: the legend of E Bo (Ebo) and Shi Chen (Shichen), preserved in the Zuo Commentary. It has astrological content dating to the 2nd-millennium BCE. However, there is no reason to interpret a precessional coding within the astronomical content. Also, there is the myth of the Weaver Woman/Girl (Zhi Nu) and Oxherd (Niulang). It was well established and popular during the upheavals of the Period of Disunity (circa 220-590 CE), between the collapse of the Han Dynasty and the establishment of the T'ang Dynasty. The earliest model for the weaving woman is found in the Classic of Poetry (circa 600 BCE, but a collection of verses from roughly 1000 BCE to 600 BCE) which briefly relates the myth of the stellar goddess Weaver Woman (Chih Nü). (See: Games Poets Play: Readings in Medieval Chinese Poetry by Anne Birrell (2004, Page 148).)

The Hamlet's Mill 'benchmark' is that pre-literate complex myth(s), containing no obvious astronomical indicators, formed a technical language that enabled world-wide transmission of precessional and other astronomical knowledge (i.e., an equally divided 12-constellation zodiac). Chinese examples of astronomical mythology are somewhat scarce and do not meet the Hamlet's Mill 'benchmark.' The particular example of the fictional historical work Mu Tien-tzu chuan (purportedly a book on King Mu's tours to China's northwest borders) is: (1) from the literate period (the example is an early written text by an obviously sophisticated writer), (2) a sophisticated (post-Neolithic) astronomy was in existence, (3) there are sufficient astronomical indicators clearly in the story - even if the story is opaque, (4) this one example is attributable to one person who has no intention to propagate world-wide, and (5) the story is not specifically focused on precessional events. Guo Pu (276-324 CE), a natural historian, scholar, and also a versatile and prolific writer of the Eastern Jin Dynasty (317-420 CE), is identified as the author of the Mu Tien-tzu chuan. However, a Warring States Period (circa 5th- to 3rd-century BCE) date of composition is thought likely by a number of sinologists. For Deborah Porter (From Deluge to Discourse (1996)) the story contains information that derives from precessional effects. In doing so she connects it with the "Yu-kung" section of the Book of Documents (Shujing, earlier Shu-king) or Classic of History, containing the early Yū myths concerning Yū's control of the floodwaters. For a detailed interpretation of the myths of Yū and his control of the great inundation of floodwaters as the observable workings of precession (a theme contained in the Mu Tien-tzu chuan) see, From Deluge to Discourse (1996) by Deborah Porter. This interpretation has also been made by the sinologists John Major and David Pankenier. King Mu was subject to two different legendary traditions in classical Chinese sources.

Interestingly, the renowned sinologist Edward Schafer (1913-1991) (Agassiz Professor of Oriental Languages at the University of California, Berkeley) wrote (Pacing the Void: T'ang Approaches to the Stars (1977, Page 315): "Santillana and Dechend, 1969, 177, referring chiefly to western star lore, write: "... the constellations were seen as the setting, or the dominating influences or even only the garments at the appointed time by the Powers in various disguises on their way through their heavenly adventures." Assuming that this characterization is a reasonable one, it is not entirely applicable to the Chinese stellar hierarchy, which was far from being an adventurous one."

Source: Morgan, Daniel. (2013). Knowing Heaven: Astronomy, the Calendar, and the Sagecraft of Science in Early Imperial China. Page 284. (Note: Unpublished PhD thesis.)

Appendix 11: Possible Knowledge of Effects of Precession in Oceania

Martha Noyes (personal e-mail, 2 December 2009): "... an example of celestial material in Hawaiian from the Kanalu genealogy. This is a genealogy of the priests and chiefs of the Kane tradition that begins after a flood that destroyed much of the islands' population. It is specifically a genealogy of the "star priests." Every 5-7 generations, the priests decide that "the stars must be rearranged." The stars that had been useful for sailing from Hawaii to other Polynesian groups and back were no longer where they need to be, and likewise the seasonal stars were in the wrong place. The priests had to rearrange the sky, to name new stars. I suspect that this is a result of the effects of precession, which is not to say that Hawaiians knew of precession. While the precessional eras, per Hamlet's Mill et al, assumes a fairly widespread knowledge of 2,160 years per era, Hawaiians were concerned with shorter periods of time. On a speck of land on the wide seas, getting to a distant speck of land in the sea required much more than 30 degrees of accuracy. Even 5 degrees of change could be disastrous. At 72 years per degree of change, 360 years would make 5 degrees of change in the location of navigation stars."

It is likely that the influence of missionaries provided Hawaiians with the concept of "flood." Missionary influence on Polynesian stories is still to be clarified A great controversy followed the discovery by the Australian scholar, Ralph Piddington, in 1939 that the Tuamotuan chants on the god Kio (Kiho) that were recorded by the ethnologists J. F. Stimson and K. P. Emery at Vahitahi were similar to the Biblical Genesis. Other Tuamotuan chants embody what appear to be allusions to the Christian Saviour, the Christian Trinity, and the Christian Hell. (See: Essays in Polynesian Ethnology by Robert Williamson and Ralph Piddington (2011).) Tuamotuan = dialects of the Polynesian language = Tuamotu Archipelago, a chain of islands and atolls in present-day French Polynesia.

Once they had memorized the sky throughout the year and over the years, the kilokilo or kilo hoku would readily note anything that was different about a star field/star path. Hawaiian and Polynesian/Oceanic astronomy involved learning hundreds of star fields/star paths with their names and locations. This knowledge was transmitted from one generation to another, by training and oral tradition.

Appendix 12: Temple alignment

If ancient observers were aware of the effects of precession they did not know what it was or how to calculate it. It is argued that with ancient temple orientation (or standing stones), to whatever direction, there is slight adjustment when a new temple is built on the site of an old one. A solstice alignment could only be used for approximately 1000 years, the amount of time it would take to no longer get a valid observation. (This argument is used for sites at Gezer and Golan Heights in the Levant.) Günter Martiny did a lot of work on Babylonian temple orientation regarding precessional adjustments. His proofs, first set out in his 34-page Die Kultrichtung in Mesopotamia (1932), remain controversial. See the (German-language) book reviews in ZA, NF Band 8 (Band 42), 1934, Pages 198-217.

It was claimed by Günter Martiny that his researches had confirmed that Babylonian and Assyrian sanctuaries/temples dating from that of Enlil-Assur-Zikurrat in 2931 BCE to Nabu's Temple in 606 BCE, whose foundation dates were (believed) recorded, were oriented on the 1st Nisan of the foundation year, to the Pedjeshes (= 'stretching the cord,' a ritual performed in the foundation of a temple, comprising an arc of a circle intersecting Benetnash (Alkaid, Eta Ursae Majoris) and Spica). In his doctoral dissertation (published in 1932 as Die Kultrichtung in Mesopotamien) Martiny described in detail the methods upon which he believed they based the orientation of their temples. In his thesis Martiny tabulated the orientation of Assyrian temples for which the dates of foundation could be established (the oldest being circa 1800 BCE). Martiny maintained that Assyrian temples had been reconstructed (at least the foundations altered) during the period of their use; the orientations being varied according to the angle of the precession of the equinoxes. Günter Martiny believed that temple orientation to celestial phenomena began in Mesopotamia in the 3rd-millennium BCE and that by the 2nd-millennium BCE temples were oriented to specific stars, and the cult statue faced the direction of the rising star. According to Martiny the particular star would have heliacally risen on the Assyrian New Year. Günter Martiny believed he had found evidence that the orientation of a succession of Assyrian temples (of which the oldest date of foundation known is 1800 BCE) varies as a function of the angle of precession. (Martiny charted the changes of orientation of temples at Assur from 3000-500 BCE and believed he had identified a "steady" eastward movement in their orientations. His published chart indicates he examined the perceived "steady" eastward movement with changes in azimuths for β Andromedae.) According to Günter Martiny, Assyrian temples oriented to the southeast and Babylonian temples oriented to the northeast. In attempting to interpret Martiny's archaeological data Neugebauer and Schott initially proposed that Neo-Babylonian (i.e., Assyrian) temples were purposely directed towards the azimuth of the hour angle circle passing through the star alpha Virginis (Spica) and intersecting the horizon when the spring equinox is on the horizon. Both Paul Neugabauer (an astronomer) and Albert Schott (an Assyriologist) supported the temple-orientation theory of Günter Martiny.  (As a result of his review of Dr. Günter Martiny's work on the survey of Assyrian sanctuaries, Professor P. V. Neugebauer, (Observatory at the Rechen-Institut in Berlin-Dahlem), believed he had discovered that all Assyrian Temples, from 2930 BCE to 603 BCE, whose foundation dates were recorded, were oriented at dawn on 1st Nisan to the point of intersection with the horizon of a great circle of the sphere, passing through the stars Eta Ursae Majoris (η Ursae Majoris (Ursa Major)) (Eta Ursae Majoris has the traditional names Alkaid (or Elkeid) and Benetnash (Benetnasch)), and Spica.) Neugebauer later discarded this explanation when he could not find evidence that the star alpha Virginis (Spica) had importance in Mesopotamian astronomy. The competent German amateur astronomer and historian of early astronomy Robert Böker disagreed with the alpha Virginis (Spica) explanation given by Neugebauer and Schott. Böker suggested an alternative hypothesis based on the azimuth of the descent of the star alpha Crucis and showed that it had better agreement with the reputed dates and axis azimuths of the temples. (In his short pamphlet Berechnungen zur vorgriechischen Astronomie (1948) Robert Böker showed that in antiquity there was no competent way to determine the equinoctial point with sufficient accuracy or to fix the azimuth of the intersection.) However, Neugebauer's changed explanation held that a clearly recognisable line is formed by the stars alpha Cassiopeiae, eta Cephei, beta Ursae Minoris, alpha Draconis, eta Ursae Majoris, and eta Virginis, and this line formed the meridian used in the centuries before and after circa 3000 BCE, as the basis for the orientation of Neo-Babylonian (Assyrian) temples. (The astronomical orientation, but not precessional re-alignment, of Mesopotamian temples was considered by some 19th-century excavators and briefly considered in Stonehenge and Other British Stone Monuments Astronomically Considered by Norman Lockyer (1906, Chapter XXIX A Short History of Astronomy).) The thesis of Martiny is based on figures from Warka that were later seriously questioned. (Babylonian and Assyrian 'temple sites' included in his study were Uruk (Southern Iraq), Tell El-'Obēd (Tell el-'Ubaid) ) (Southern Iraq), Tepe Gawra (Northwest Iraq), and Assur (on the upper Tigris River in Iraq). One of the methodological issues with the figures produced by Martiny is that he charted the orientation of the Gimilsin Temple and the Palace Chapel according to True Magnetic North rather than True North and he made adjustments accordingly. Also, he gave no explanatory information regarding the data on the orientation of the other temples included in his orientation chart. Further, the "orientation chart," whilst showing the eastward movement of the Assur temples and β Andromedae, is somewhat vague. (There is no persuasive evidence that Mesopotamian temples, of any period, were systematically aligned to any directions.) Circa 1986 Asger Aaboe advised that Martiny's claims were purely hypothetical and that still today nothing is known about if and how the ancient Mesopotamians used astronomy to orient their temples. (See: Revue d'assyriologie et d'archéologie oriental, Tomes 80-81, 1986, Page 39.) The topic of temple orientation has never gained popularity in Assyriology. Martiny's ideas on temple orientation are briefly noted by the assyriologist William Hallo in his book Origins: The Ancient Near Eastern Background of Some Modern Western Institutions (1996, Page 84).

Appendix 13: Plato (circa 428-348 BCE) and the Great Year and Precession

In the Classical world it was Plato of Athens (writing before Berossos' account) who first made a clear statement of the Great Year which he termed the Perfect Year (also translated as Complete Year). Plato defined the Perfect Year as a period at the end of which the fixed stars and planets return to the point from which they started their revolution. The end of Plato's Perfect Year was not marked by a conflagration. Plato's Perfect Year (also known as the Platonic Year) in Timaeus (39d) is linked to the idea of 'powerful' conjunctions (the return of the planets to the same position) and not to the idea of precession or to the equinoxes and solstices. (The Perfect Year (Great Year), in Plato's Timaeus simply refers to a complete circle of all the 8 spheres (the 8th sphere/circuit is presumably that of the Fixed Stars), to the time needed to return again to the same cosmic configuration.) However, in another part of Timaeus Plato states that also the stars have at very lengthy periods of time an aberration of their position causing a great fire etc. This paragraph of Plato is mentioned by Clement of Alexandria in his Stromata (or Stromateis) (2nd-century CE). Later, in the 5th-century, Macrobius Theodosius in his Commentary on the Dream of Scipio writes that the Great Year is not only a return of the planets but involves an even more longer period as a "proper" motion of the stars. Thus the connection between Perfect Year (Great Year) and the motion of the stars in long periods can be traced back as far as Plato.

Note: Nowhere in the Timaeus does Plato talk of precession. In section 38 Plato has clearly defined 2 sorts of celestial motion: (1) the motion of the planets through the sky from west to east, and (2) the diurnal motion of the entire sky from west to east. The motion of the 8th sphere/circuit is clearly a diurnal motion; not precessional motion. If Plato had known of precession and was referring to it he would undoubtedly had to explain it in terms of a 3rd motion.

Plato never gives a figure for his Perfect (Great) Year. Later commentators later gave assumed the value of 36,000 years but a rationale was not given until the 1890s. See (the speculative discussion): The Nuptial Number of Plato by James Adam (1891). James Adam argued that various passages in the Republic could be read as a code justifying the 36,000 year figure. A critical discussion of Adam's method of extracting a period of 36,000 years from Plato's Republic appears in Aristarchus of Samos by Thomas Heath (1913, Pages 171-173). It is only in later Greek and Latin texts that Plato's cosmic period is termed the Great Year. Precession is not involved.

Appendix 14: Ptolemy and Hipparchus' Knowledge of Precession

Ptolemy (2nd-century CE) is the first astronomer known to have continued Hipparchus' work on precession. The Almagest is the principal ancient source for the discussion of precession. Ptolemy's account (Almagest 3.1, and 7. 1-3) of Hipparchus' discovery of precession describes that Hipparchus' description of what his observations showed and ideas (Hipparchus offered several explanations) were tentative and uncertain. It was Ptolemy, working some 3 centuries after Hipparchus made his discovery, who confirmed the precession involved a motion of the entire sphere of the fixed stars with respect to the equinoxes. Ptolemy defined precession as the uniform increase in the longitudes of the fixed stars.

Appendix 15: The Myth of an Age of Pisces in Early Christianity

There was no Age of Pisces at the time Christianity originated. No textual evidence from Dionysius Exiguus, or any contemporary or predecessor, of a perceived Christianity-Pisces link has ever been produced. The association between Christianity and Pisces is of later medieval origin. See: "The "Star of the Messiah." Reconsidered" by Roy Rosenberg in Biblica, Volume 53, 1972, Pages 105-109. It is essentially a discussion of the Jewish philosopher Isaac Abrabanel's (1437-1508) views of the signs Pisces, Aries, and Virgo and their associations. The best attempt at evidence by Rothwangl (Hastro-L, 2 May 2001) is to refer to his belief that the triple alignment (as Rothwangl likes to call it) in Pisces in & BCE was the Star of Bethlehem, and the Fish as a painting and as the pictograph ICHTHYS as the first sign of the Christians. (Excursus: A monumental study is IXΘYC: Das Fischsymbol in frühchristlicher Zeit by Franz Dölger (a German Catholic theologian and church historian, life dates: 1879-1940) (1922-1928, 2 Volumes. First published in 1-Volume in 1910.). Also relevant: Orpheus the Fisher: Comparative Studies in Orphic and Early Christian Cult Symbolism by Robert Eisler (1921).) Some of the several speculative 'vacuum-cleaner' arguments include: (1) Precession was mentioned by Origen Adamantius (184/185-253/254 CE), early Christian Alexandrian scholar and theologian. If he knew about it then other Christian would also. We can suppose the beginning of the Christian revelation would be associated with a new "World Age," especially when it coincided with the beginning of a new "Platonic month," with the movement of the vernal equinox into Pisces. (2) In the brief polemical Latin treatise on baptism, (De baptismo, i) by the Church Father Tertullian (circa 155-circa 240) he writes, "But we little fish, like our Fish Jesus Christ, are born in water ...." These are not effective evidence of a Pisces World Age. The only other comparison is the Christian Bishop Zeno of Verona (circa 300-371) who in a Paschal baptismal homily gives the 12 signs of the zodiac a Christian interpretation to accommodate the "curiositas" as to what sign they are being reborn under. He begins with Aries and ends with Pisces, saying: "How necessary it is that in one sign follows the two Fishes, that is two peoples from the Jews and the Gentiles by the living waters of baptism are signified as one people of Christ by one sign." (See: Ancient Astrology by Tamsyn Barton (1994, Page 71).) This also is not effective evidence of a Pisces World Age. The earliest extant example of precession being used to undermine astrology was written by the Church father and early Christian theologian Origen of Alexandria (circa 184/5-253/254), who spent the first half of his career in Alexandria. Origen was not an astrologer. It is evidence that precession was understood. It is not evidence that system of zodiacal "World Ages" was established or that there was currently an "Age of Pisces." First example, The Philocalia of Origen, (an anthology (compilation of selected passages) of Origen's texts, probably compiled by Basil of Caesarea and Gregory of Nazianzus, English-language translation by George Lewis (1911; XXIII Fate, Astrology, etc., see specifically Page 191, Paragraph 18): "There is a well-known theorem which proves that the Zodiac, like the planets, moves from west to east at the rate of one part in a hundred years, and that this movement in the lapse of so long a time changes the local relation of the signs; so that, on the one hand, there is the invisible sign, and on the other, as it were, the visible figure of it; and events, they say, are discovered not from the figure, but from the invisible sign ...." I have not seen a more recent translation. Second example, referenced as, De Oratione, [= On Prayer; a treatise on prayer] 27 [likely, Origen's Treatise on Prayer: Translation and Notes with an Account of the Practice and Doctrine of Prayer from New Testament Times to Origen by Eric Jay (1954)]: "As the last month is the end of the year, after which the beginning of another month ensues, so it may be that since several ages complete a year of ages, the present age is the end, after which certain ages to come will ensue, of which the age to come is the beginning ...." However, the translation by William Curtis ( differs in text and meaning. Translation by William Curtis of the complete passage: "Well, in conjecture as to matters so great, I believe that, just as the year's consummation is it's last month after which arises another month's beginning, so probably the present age is a consummation of numerous ages completing as it were a year of ages, and after it certain coming ages will arise whose beginning is the coming age, and in those coming ages God shall show forth the riches of His Grace in kindness, when the greatest sinner, who for having spoken ill against the Holy Spirit is held fast by his sin throughout the present age and the coming one from beginning to end, shall after that, I know not how, receive a dispensation." It is pointed out that the first of these 2 remarks relating to a connection between astrology and the zodiac and its movements and how Origen differentiates between "invisible signs" (= the tropical signs?) and their "figures" (the starry constellations?). Also claimed that the suggestion of "new ages" indicates the precession-like conception involved in his thought, and the progression of the "ages." It is an obviously weak argument. It is not able to be claimed as definite evidence for precessional "World Ages" and there is no mention of an "Age of Pisces." With the second of these 2 remarks the translation by Curtis shows clearly there is no connection with astrology or precessional "World Ages" and there is no mention of an "Age of Pisces." (3) There is useful material in David Fideler's book, Jesus Christ, Sun of God: Ancient Cosmology and Early Christian Symbolism (1993). The blurb for the book reads: "The early Christian Gnosis did not spring up in isolation, but drew upon earlier sources. In this book, many of these sources are revealed for the first time. Special emphasis is placed on the Hellenistic doctrine of the "Solar Logos" and the early Christian symbolism which depicted Christ as the Spiritual Sun, the illumination source of order, harmony, and spiritual insight. Based on 15 years of research, this is a unique book which throws a penetrating light on the secret traditions of early Christianity. It clearly demonstrates that number is at the heart of being. Jesus Christ, Sun of God, illustrates how the Christian symbolism of the Spiritual Sun is derived from numerical symbolism of the "ancient divinities."" Both "Precession" and "Age of Pisces" are listed in the index: "Pisces, Age of, and Christian fish symbolism, 161-62; inaugurated by triple conjunction of Saturn and Jupiter, 166, 168-69 ... Precession of the equinoxes, 149-151; described by Origen, 345 n. 12; and religious symbolism, 160-163." There is interesting material in David Fideler's book, but also fanciful speculation. Fideler uses material and arguments from David Ulansey and Carl Jung. A house of cards is constructed. (4) David Ulansey has shown quite convincingly in his book, The Origin of the Mithraic Mysteries (1989) that knowledge of the precession of the equinoxes knowledge of precession is the central secret of the Roman Mithraic mysteries, and is discoverable in Mithraic iconography. Ulansey's claims lack any credible evidence or argument and is nothing more than fanciful speculation. Importantly, David Ulansey has never provided any evidence that 'zodiacal ages/astrological ages' as developed by 19th-century theosophy and early 20th-century astrology was also a concept understood anywhere at all in the ancient Greco-Roman world. (The concept of precessional "world ages" can be traced back to Origine des tous les cultes: ou, Religion universelle by Charles Dupuis (1794).) See further: Page 11-17. Still worth reading is "Hipparchus and the Precession of the Equinoxes." by Maxwell Close (Proceedings of the Royal Irish Academy, Third Series, Volume 6, 1900-1902, Pages 450-456).

Appendix 16: A  Modern Argument for Evidence of Knowledge of Precession Before Hipparchus

There is no discussion of precession and calendrical problems caused by it by Greek astronomers before Hipparchus.

In his 2009 paper, "The Knowledge of the Aequinoctial Precession Before Hipparchus," (Articolo in corso di stampa sugli Atti del IX Convegno Annuale della Società Italiana di Archeoastronomia "Cursus Caelestium Siderum" tentenutosi a Firenze, Dipartimento di Astronomia di Arcetri, dal 14 al16 settembre 2009) Mario Codebò discusses 6 'evidences' as clues. These are: (1) the (so-called) Foroughi Cup (actually a bronze bowl, once part of the Mohssen Foroughi collection in Teheran comprising Iranian artifacts from the 2nd-millennium BCE to the late 18th-century CE, now in the Shlomo Moussaieff collection in London); (2) the 4Q318 brontologion; (3) the Biblical date of the creation of the world; (4) the date of the main Biblical events; and (5) the 2 Babylonian zodiacs; and (6) Mithraic symbols. At the conclusion of his arguments the author states the evidence is offered as clues, but not (decisive) proofs. (See:

The bronze bowl referred to by Mario Codebò as the 'Foroughi cup' is unprovenanced but believed to have every likelihood of being genuine, because the complexity of the interior astral design would have taken a long time to prepare. The first published discussion of this inscribed astral bronze bowl (18 cm in diameter and 3.5 cm high), apparently from Luristan (western Iran) or ancient Syria, engraved with a sophisticated astral scene (sun, moon, various stars, and constellations), was first discussed in print by the British archaeologist R. D. Barnett in 1966. The bowl is believed to be manufactured by an Aramaic craftsman during the first half of the 1st-millennium BCE. It is believed to be of Syrian or Phoenician craftmanship due to its similarity to Phoenician copper/bronze bowls of the 8th-7th centuries BCE. Also the 7 tiny Aramaic labels (text) can be dated paleographically and this adds to the evidence in favour of its authenticity. The 7 engraved inscriptions are typical of Aramaic culture for the 6th-7th centuries BCE. The cup reproduces a starry sky with some recognizable constellations and heavenly bodies. The interior of the bowl is completely filled with an astral scene composed of central motifs surrounded by 8 zones. Depicted are constellations, the sun, and the moon, but it is perhaps not intended as a sky map. (See: "La *Coppa Foroughi : un atlante celeste del 1. millennio a. C." by Maria Giulia, Amadasi Guzzo, and Vittorio Castellani. (Rivista italiana di archeoastronomia : astronomia nell'antichità, astronomia storica, astronomia e cultura, 2006, Number 4, Pages 1-8). See the discussion in: The Journal of the Ancient Near Eastern Society of Columbia University, Volume 5, 1973. Also, Younger, Jr., K[?]. (2012). "Another look at an Aramaic Astral Bowl." (Journal of Near Eastern Studies, Volume 71, Number 2, October, Pages 209-230).)

This remarkable bronze bowl gives us a star map of the heavens (or similar construct), that is unique in our surviving material from antiquity. It is also remarkable in illustrating what appears to be a mostly non-Mesopotamian, most probably Iranian, astronomical scheme. It reproduces a starry sky with some recognizable constellations and heavenly bodies (the sun, the moon, perhaps the visible planets). It is also claimed by some persons that comets are depicted. Placed amongst two large (rayed) stars and two constellations shaped as a pair of hunting boots is the starry figure of a hunter-god armed with spear (in his right hand) standing on an ibex. The figure seems to represent the constellation Orion (as a hero), the Babylonian Papsukkal, standing on SUHUR.MASU (he Sumerian goat-fish) or Caper [Caper-bush?]. To his right is (apparently) the Plough and the Pleiades (as ‘7 dots’). (Note, however, it has been commented that the dots appear to be linked by parallel vertical lines and may have had a different meaning altogether i.e., that of a stylized palmette.) To his left is a bull’s head, made of stars, presumably the constellation Taurus; below it is a kind of starry ankh sign, possibly Corona Borealis or Coma Berenices, while above it is a tailed monkey surrounded by twelve stars. The name and relevance of the monkey is unknown. This intriguing symbolism, associating the monkey with the hunter (though in an astronomical depiction), may possibly be relevant to a terracotta plaque of the Old Babylonian period. The two Bears (Ursa Major and Ursa Minor), are respectively positioned at 2 opposite sides of the center in the cup. Interestingly, there are 4 figures (constellations) placed at the tips of a cross, 2 of them appear to represent Taurus and Leo; the 3rd one seems to be Scorpio and the 4th one can no longer be identified (but speculated as Aquarius) because of an additional engraving placed on it.

Monkeys have a long and quite respectable history in the ancient Near East. Monkeys were pets in Egypt and most likely also in Mesopotamia from early times. The idea of animals acting like humans is found in Mesopotamian art and perhaps came to Sumer, along with the monkey, from India. India was the classic home of the animal fable. A well-known terracotta plaque of the Old Babylonian period shows a quite remarkable scene in which a hunter shoot is shooting an arrow at a monkey in a tree. There is a kneeling man behind the hunter who seems to be restraining him. Also, in the scene a boar is approaching the tree. We may have here a depiction of a now lost animal fable. The 12th/13th-century CE Persian poet Nizami's/Nezami's story of Bahram Gur, the famous hero hunter of the onager (wild asses native to the deserts of Syria, Iran, Pakistan, India, Israel, and Tibet) which once thrived in Iran and Syria, was based on a real historical figure, Bahram V, a Sasanian king (reigned 420–438 CE.

Its use as an argument for pre-Hipparchan precessional knowledge is that the bronze bowl is the first graphic representation of a past sky configuration in which the effects of the precession are shown. It is claimed the astral depiction does not show the sky configuation at the time it was made (1st-millennium BCE) but instead the astronomical situation existing in the 4th-/3rd-millennium BCE when the spring equinox was in Taurus, the summer solstice in Leo, the autumn aequinox in Scorpio and the winter solstice in Aquarius. The fatal flaw with this speculation is that it relies on the assumption of an ancient evenly divided 12-constellation zodiac before its clearly documented invention by the Babylonians in the 1st-millennium BCE.

Appendix 17: Defining Discovery

Some persons resolutely claim (including Hamlet's Mill supporters) that the Chinese discovered precession prior to Hipparchus. The nature of what can constitute 'discovery' needs to be qualified/described. A primary concern of any science is the categorisation, description, and definition of phenomena. Definition is fundamental to the scientific enterprise, and listing criterial features of categories is fundamental to the process of definition.

I think it is perhaps rare in science to find definitions on which more than a few persons will agree - even perhaps for the most fundamental terms. Continual breakdowns in the use of terms are readily apparent in professional publications (however, all ideas are remain 'up for grabs'). Many definitions become cluttered with conditional stipulations and can comprise a lengthy paragraph. I believe definitions should be readily functional. I also doubt if 'traditional' concepts of discovery are careless.

If someone convincingly demonstrates they have found a description of precession in a myth then this demonstration becomes a discovery for the person. Whether the material in the myth shows 'discovery' of the phenomenon of precession is a separate issue.

The method/process/stages of scientific investigation for the purpose of discovery should not be confused with actual discovery. The professional literature still reflects the view that the process of discovery is not adequately understood.

I would offer that the process of discovery of phenomenon such as precession involves perhaps: (1) inception (instance of commencement - an intriguing/baffling observation (description - the positions of several marker stars have apparently moved) and decision to follow-up the significance and think through/analyse and make 'sense' of the observation(s)), (2) emergence (something becoming apparent - it is the not inaccurate technique by an observer(s), rather the positions of some marker stars are not fixed) using process of evaluation/analysis, and (3) concept (an idea/inference constructed from specific instances - (the explanation - the marker stars (the other 'fixed' stars) progressively shift position (discovery)). Discovery is an outcome - an achievement. The preceding steps would fall under process.

Precision of language used in an explanation is important for deciding whether a 'discovery' has been made, and the nature of that discovery.

Randomly noting an effect/effects of precession without understanding is only a discovery in the weakest sense - it is a discovery of change (an 'effect' discovery). I would class it as observation/observations of change. The process of investigation and analysis and explanation-making is absent. Knowledge is perhaps not so much the problem to be investigated/solved but the 'answer,' usually, I think, achieved through extrapolation.

The conclusion that the rate of stellar movement is a systematic continuous displacement able to be calculated (within a coordinate system) demonstrates/consolidates the confidence, reliability, and strength of the discovery (a 'technical' discovery).

Observation of change by itself (effect(s)) related to the phenomenon of precession is not discovery of precession and perhaps to label it as 'discovery of change' is not really suitable. This does not exclude the terms 'collective discovery' and 'pre-discovery.' However, their definitions/use become an important issue. Todd Timberlake (Hastro-L, 08-04-2013) makes the point: "... assigning credit for a "discovery" is nearly impossible to do in a historically accurate way.  Discoveries are not singular events, usually.  They happen gradually and in some cases it is hard to spot the transition from when something was definitely not known to when it was definitely known."

A modern analogy is the accidental discovery of the aberration of light (also referred to as astronomical aberration or stellar aberration) by the English astronomer James Bradley. (One of the reasons for the apparent displacement of the stars due to the earth's motion is what is known as aberration.) The discovery arose out of the attempt by James Bradley (1693-1762) and Samuel Molyneux to detect stellar parallax. (A popular account of the course of his discovery is given in Astronomical Discovery by Herbert Turner (1904).) On the basis of quantitative observations the phenomenon was first noticed in late 1725 by way of unexpected changes in the position of γ Draconis, unrelated to parallax. Prolonged observations of changes in the position of γ Draconis convinced him that it could not be parallax he had measured.) Explanations that the anomalous measurement were an error due perhaps to a fault with the telescopic instrument, the plumb-line, or perhaps the effect of refraction were considered and dismissed. Bradley (a determined and meticulous astronomer) was originally ignorant of what his initial observation(s) meant by way of explanation. (The cause of anomalous motion was at first completely obscure.) He pursued an explanation for 3 years before he found the real explanation. In 1729 he communicated his discovery and explanation to the Royal Society (of London) with the publication of his (celebrated) paper in the Philosophical Transactions of the Royal Society (Volume 35). He later discovered the nutation of the earth's axis (the periodic oscillation of the earth's axis, caused by the changing direction of the gravitational pull of the moon on the equatorial bulge He delayed publication of his discovery of nutation until he had tested its reality by minute observations during an entire revolution (18.6 years) of the moon's nodes. He finally announced his discovery in print in 1748 in the Philosophical Transactions of the Royal Society.

Appendix 18:

Robert Tulip in a posting to Biblical Criticism & History Forum - (March 22, 2014; wrote: "The evidentiary method used by Neugebauer, as also advocated by Gary D. Thompson, fails to engage the real evidence, which should rather be looked for in what Heidegger called the fugitive traces of the divine." (This is a reference to the German philosopher and poet Martin Heidegger (1889-1976).) As is frequently the case with a number of people seeking to dismiss/ignore detailed arguments, Tulip is simply another person offering an opinion without any discussion of evidence. Heidegger's concept of looking for "fugitive traces of the divine" is left unexplained. However, Heidegger is looking at issues from the perspective of philosophy. In the first half of the 20th-century, Heidegger helped to introduce phenomenology into philosophy. Also, close readings of poetry are essential to Heidegger's thought.

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