Episodic Survey of the History of the Constellations


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E: Late Mesopotamian Constellations

11: Babylonian world and universe

BM 92687 (82-7-14, 509) "Mappa Mundi." Babylonian "map of the world" in the British Museum, London. (This photograph was likely taken prior to some small fragments being rejoined by Irving Finkel, a curator at the British Museum (currently (2016) Assistant Keeper of Ancient Mesopotamian script.) The so-called Babylonian "map of the world" is a rare visual depiction of the world. It is the single example of an ancient Mesopotamian world map. The earth is depicted in the drawing and the heavens are treated principally in the accompanying text. (The text on the reverse is divided into 9 sections comprising 27 lines of text.) The world in this map is conceived of as a disk (i.e., as circular and flat). Irving Finkel (2014) states: "It is one of the most remarkable cuneiform tablets ever discovered ...." Francesca Rochberg (2012) states: "Its provenance is uncertain but its British Museum catalog number [BM 92687], and the onomastics of the scribe who copied the tablet point to the city of Borsippa. (One source states it was most likely recovered from Sippar.) The hole in the centre is probably the place where one leg of the compass was fixed. (Curved lines are rare on cuneiform tablets but in this case it is obvious a compass was used.) Above the central hole, an oblong shape is marked "Babylon"and has 2 lines running through it from north to south, perhaps depicting the 2 banks of the river Euphrates. This river takes its rise from the north-west mountains and runs into the oblong marsh or swamp in the south. Around the city of Babylon are located the known lands within the area surrounded by a circular outer ocean/great river. Some cities and lands are indicated by circles. To the right of Babylon, Assyria is situated, and north of it Armenia. There are (were) 7 triangles ("islands") pointing outward from the edges of the the surrounding ocean/great river. The top section is a cuneiform inscription describing the various regions, plus great kings and heroes (king Sargon and the hero Utnapishtim who survived the flood and who attained immortality) and mythical beasts/monsters. This literary section is incomplete due to damage. However, it obviously sets out an imagined cosmical landscape.

Identification of the main parts of the Babylonian "map of the world." The map was not intended to be a precise or literal cosmological or geographical depiction. Representations of the Egyptians and Persians - both peoples well-known to the Babylonians - are omitted any representation. Source: Several sources reproduce this illustration and its captions i.e., MyHistoryLabTM.

Identification of the geography of the Babylonian "map of the world." Source: Mesopotamian Cosmic Geography by Wayne Horowitz (1998, Pages 21 & 22).

(1) The Babylonian "map of the world"

BM 92687 (82-7-14, 509) "Mappa Mundi" is a Babylonian "map of the world" in the British Museum, London. The term "Mappa Mundi" is derived from it best matching the category of medieval period maps termed "mappamundi." Medieval "mappamundi" typically show a spherical world picture encircled by the "ocean sea." The tablet contains a diagrammatic image of the world as conceived late 8th- or 7th-century BCE, and a written description. (Wayne Horowitz has pointed out that the description written to accompany the map has an integral, but complicated relation to it.) The "Mappa Mundi" is the earliest extant map having such a wide scope. Earlier known maps are limited to local areas (immediate environment), town maps, etc. The earliest cuneiform map discovered is a regional map dating to the late 3rd-millennium BCE. (The earliest examples of historical maps originate in the ancient Near East. A coherent tradition of Mesopotamian cartography is not evident.) The map is unique from other Mesopotamian maps because it is not merely local but international in its scope, and contains features that appear to indicate a cosmological intention. Rochberg (2012, Pages 33-34) writes: "The historical and literary references in the description accompanying the map resonate with the historical and cosmical atmosphere of its iconographic representation of the world." Typically for Mesopotamian maps, it is drawn as if looking down from above. Also, it is not drawn to scale. It is not of course a surveyed and measured image. Unfortunately, the tablet is badly damaged. The clay tablet is 12.2 cm tall. The map occupies two-thirds of the obverse. (The actual map is only 8 cm by 8 cm in size.) The remainder of the obverse and the entire reverse contain related textual information. The actual map is considered enigmatic in its implications regarding content and scale. However, it confirms that the ancient Mesopotamians believed that the earth's surface consisted of 3 main components: a central continent, a cosmic sea, and land(s) across the sea. (The Babylonians at least believed that a cosmic ocean encircled the continental portion of the earth's surface.) Texts provide little information about the distant lands across the seas at the far reaches of the earth's surface. The map was composed in Babylonia and is the only Babylonian map drawn on an international scale. It includes the local geographic environment and also attempts to depict quite distant regions i.e., as triangular "regions" beyond the sea and the limits of empirical knowledge. Its provenance and date of composition is uncertain. The tablet is placed within the 82-7-14 collection at the British Museum. This particular collection primarily comes from Sippar. However, because it has been given the out-of-sequence number 509 within the 82-7-14 collection this suggests it is not from Sippar. The colophon information suggests the tablets actually comes from Borsippa. It is usually stated it is a Neo-Babylonian (Persian Period, circa 500 BCE) copy of an original dating to the Sargonid Period, circa late 8th- or 7th-century BCE. In his 1998 discussion Wayne Horowitz states on philological grounds the World Map tablet can be dated to between the 9th- and the 7th-century BCE. (The map at least is no older than the 9th-century BCE.) From the colophon information again it is known that there was at least one earlier map. Whether BM 92687 represents older concepts is difficult to say.

Wayne Horowitz writes (Mesopotamian Cosmic Geography, (1998, Page 40): "The emphasis on distant places in the texts accompanying the map suggests that the purpose of BM 92687 was to locate and describe distant regions. The map illustrated where these distant areas were located in relation to familiar locales, such as Babylon, Assyria, and the Euphrates. The obverse related these distant places to familiar literary figures and exotic animals, and the reverse conditions in far-away regions. The ancient author's interest in distant places reflects a general interest in distant areas during the first half of the first millennium, when the Assyrian and Babylonian empires reached their greatest extents." Also (Mesopotamian Cosmic Geography, (1998, Page 42): "... it is possible that geometric conventions, as well as cosmographic traditions, influenced the development of The Babylonian Map of the World."

The German assyriologist Felix Peiser, during a stay in London to access tablets in the British Museum, came across the tablet. Johann Strassmaier made a drawing of the tablet for Felix Peiser to publish in his article Eine babylonische Landkarte (ZA, Band 4, 1889, Pages 361-370). (At least one source mistakenly states the article as a book title published 1899.) The clay tablet is a drawing and textual description of the Babylonian cosmos. It is now concluded that it is oriented to the north-west. However, no directions are actually indicated on the map. (It is uncertain whether the accompanying cuneiform text was composed together with the map. Rochberg (2012), relying on Horowitz (1988) writes: "It has an integral, but complicated, relation to the image.") It is the only known map of the world dating from the Neo-Babylonian Period. All other maps have a purely local focus.

Wayne Horowitz states: "In 1906, R. C. Thompson re-copied the tablet as CT 22, 48. This second copy served as the basis for later studies by E. F. Weidner in BoSt 6 (1922), 85–93 and E. Unger in Unger, Babylon, 254–8 (1931)." Wayne Horowitz also points out: "Unfortunately, neither the early copy by Peiser, nor CT 22, 48, is completely reliable. The two copies disagree on a number of points, and a new collation of the tablet revealed a number of errors. For instance, Peiser drew two nagû at the bottom of the map which are omitted in CT 22, 48, and both copyists read the label in the lowest oval inside the circle (no. 8) sideways!" (According to Irving Finkel in The Ark Before Noah (2014), a lost nagû has recently been located by a volunteer worker at the British Museum. Portions of 5 nagû are preserved on the World Map, and are located across the circular ocean, and 8 nagû are described on the reverse side of the tablet.

The map depicts a "bird's-eye" view of the world (the world as seen from above) and shows a flat, round world with the city of Babylon in the centre. (Circa 500 BCE Babylon was still a flourishing city and regarded as the centre (i.e., the "hub") of the world. In the 3rd millennium BCE Nippur was considered to be the city at the centre of the world.) It is likely that the Sumerians made the city of Nippur the centre of the universe (a Sumerian Rome) from about 2300 BCE (just prior to the Ur III Period). Political supremacy was regarded as conditional on the possession of Nippur. With the rise to political supremacy of the Babylonian kings, from the early 2nd-millennium onwards, it was possible for Babylon to claim the central position and replace Nippur as the centre of the universe. Note: During the reign of Assunasirpal II (883-859 BCE) and Sargon II (722-705 BCE) the ideology of Babylon as the new Nippur, the centre of the world and the linchpin of heaven and the underworld was formed.

The map depicts the world as two concentric circles, with triangular areas/projections (most likely 7 or 8 when complete) radiating outwards from the outer of the 2 circles. The area of the map within the inner circle represents the central continental area of the Earth's surface where Babylon and Assyria are located (= the oikumene (the known part of the inhabited world)). The continent is surrounded by the circle of salty ocean (designated as the "Bitter River"). The area/band between the two circles represents the (earthly) circumambulating cosmic (?) ocean (or great river). (The circular body of water is called the id marratu ("the Salt (Bitter) River").) The area beyond the outer circle (i.e., outside the ocean) consists of the triangular areas, which are the uncharted distant transoceanic regions, or distant region across or associated with the sea in Babylonian texts. Only 5 of these triangles survived of the original 7 or 8. However, further damaged has occurred to these. (The several (originally 7?/8?) outer triangular 'distant unspecified regions' or 'islands' are called nagû. The term nagû has the sense of "island.") The mythical 7 (or 8) regions/islands are depicted as equal triangles, only 2 of which are now completely preserved. The text on the reverse describes 8 nagû and there is room for this number.

The continent on the map contains various geometric shapes representing places and topographic features. The place names include the countries of Assyria (indicated north-east of Babylon), Urartu (Armenia) (indicated north of Assyria), the land of Habban (South Yemen) (indicated south-west of Babylon) and the city of Babylon. (Wayne Horowitz identifies that the kingdom of Urartu is placed among the most important places of the ancient world.) The topographic features include a mountain, a swamp, and a channel. (The mountains are located at the top, in the north.) Babylon is represented by a large rectangle encompassing almost half the width of the central continent. Assyria is represented as a small oval. (Various nameless places are also indicated by ovals.) The Euphrates River, which originates in the mountains at the top of the map, runs through Babylon and flows into the marshes at the bottom of the map. The map schematically portrays the entire kingdom of Babylonia. The text contains the names of countries and cities but, on the reverse side, the text is largely concerned with a description of the 7 (or 8) unnamed outer regions ("islands") which are depicted in the form of equal triangles rising beyond the encircling earthly (cosmic?) ocean. Some parts of the map cannot be identified. As example: According to Wayne Horowitz thinks the crescent-shaped area extending from the east bank of the Euphrates River may represent either an arm of the ocean separating southern Babylonia from Elam, or might be an arm of the Euphrates River, a canal, or even a road.

Rochberg (2012) relying on Horowitz (1998) writes: "Circles represent cities ... and parallel lines rivers. The largest demarcated area, shown as a rectangle on the upper central portion, is Babylon, the point of view from which the map was presumably made. Also on the map are the states of Urartu and Assyria .... The cities of Der and Susa and the territory of Bit Yakin are included. The regions, cities, and other geographic features such as the swamp and the water channel are all arranged inside a circle bounded by the waters of the ocean, designated as the "Bitter River" around the entire circling band."

There is text accompanying some parts of the map. The text (on both sides of the tablet) shows that the map attempts to depict the entire world. The emphasis on distant places in the text accompanying the map indicates that the likely purpose of the map was to locate and describe distant regions. The text of the reverse of the tablet describe the "7 islands" (8 islands?) in detail. (From the paucity of the information given it is evident that the Babylonians knew little about these "islands." Mostly, the description given is mostly about their various degrees of brightness.) From the text on the reverse of the tablet, and the inscriptions on the map itself, it can be determined that the first "island" lay in the south-east. the second "island" lay in the south-west, and so on, so that the sequence of the "islands" is somewhat analogous with the hands of a modern clock. The descriptions of the first and second outer regions are not preserved. (The Babylonians, like many ancient peoples, believed that distant lands were home to legendary beasts, strangely formed peoples, and mysterious natural phenomena.)

Other textual sources describe the earthly ocean as being enclosed by a double range of mountains, those to the east and those to the west (the "sunrise" and "sunset" range, respectively.

The orientation of the map proved to be unclear to early investigators. More recent analysis seems to have clarified the issue. The map has a definite orientation - it is inclined. The orientation is such that the top of the map corresponds to the northwest. Thus the Babylonian system of orientation did not follow the perpendicular plane - north, west, south, and east - of our Western cardinal points. The Babylonian system of orientation was based upon the prevalent winds. The northwest wind was sent from the goddess Ishtar and was a favourable wind. 

For a detailed early discussion of the Babylonian world map see "From Cosmos Picture to the World Map." by Eckhard Unger (Imago Mundi, Volume 2, 1937, Pages 1-7). A detailed recent discussion of the Babylonian world map is by Irving Finkel in The Ark Before Noah (2014). Irving Finkel dates the cosmological system set out on the Babylonian world map to the Old Babylonian period in the 2nd-millennium BCE.

"The most important element is the drawing, which takes up the lower two-thirds of the obverse. (Wayne Horowitz states the drawing occupies the lower half of the obverse.) It is a brilliantly accomplished piece of work. The known world is depicted from far above as a disc surrounded by a ring of water called marratu in Akkadian. Two concentric circles were drawn in with some cuneiform precursor of a pair of compasses whose point was actually inserted south of Babylon, perhaps the city of Nippur, the 'Bond of Heaven and Earth'. Within the circle the heartland of Mesopotamia is depicted in schematic form. The broad Euphrates River runs from top to bottom, originating in the northern mountainous areas and losing itself in canals and marshes in the south. The great river is straddled by Babylon .... [A] ... great ring of water ... surrounds everything, while even further beyond is a ring of vast mountains that marks the rim of the world. These mountains are projected as flat, projecting triangles; each is called a nagû. Originally they numbered eight." (Irving Finkel, The Ark Before Noah (2014; Pages 262-263).)

It has been pointed out that the Babylonian world map deals with a mythologised landscape, not any actual scientific physical geography. As example: The text refers to the "ruined gods" who are likely the 11 composite beings of Tiamat defeated by Marduk in the Enuma Elish.

For a complete description and account of the "Mappa Mundi," see: Wayne Horowitz, Mesopotamian Cosmic Geography, (1998), Pages 20–42.

The pre-Socratic Greek philosopher Anaximander (circa 610-circa 546) who lived in the Ionian city of Miletus was a pioneering cartographer who also drew a map of the world. (The Babylonian map of the earth is approximately contemporary with Anaximander's world map. Anaximander's map being made at a slightly later date). Unfortunately a specimen of his map has not come down to us. The method of mapmaking introduced by Anaximander replaced the Babylonian and Egyptian traditions of making maps of the earth. (It excluded mythical elements. The Babylonian and Egyptian maps may be characterized as a mixture of mythological and symbolical or schematic features.) Although his representation of a flat earth still remained within the limits of the archaic world picture, it may be concluded that Anaximander created a new paradigm in geographical mapmaking. An early Egyptian world map that has survived is drawn on a 4th-century BCE (30th dynasty) Egyptian coffin. On this picture, the goddess of the heaven, Nut, arches over the world that is carried by two arms making the ka sign. There is also a depiction of an encircling Ocean. Inside the Ocean is a ring with the names of the neighbouring countries, then a ring with the hieroglyphs of the Egyptian districts, and in the innermost circle the underworld is represented. Neither the Babylonian world map nor the Egyptian world map have a geographical meaning. They both have only a religious or mythological meaning. (The triangular "mountains" outside the Bitter River on the Babylonian map, and the goddess Nut arching over the world on the Egyptian map are considered essential features of these maps.) Moreover, the Babylonian and Egyptian world maps maps do not show contours of lands and seas (apart from the depiction of the encircling Ocean). There are only a few schematic lines on the Babylonian world map, and a list of geographical names on the Egyptian world map.

Appendix: There is a limited knowledge of Mesopotamian understanding of geography. The so-called Sargon Geography traditions (modern name) are known from 2 texts. The main text is the Neo-Assyrian VAT 8006 (KAV 92) found in 1910 at Assur, and also the Neo-Babylonian duplicate BM 64382 (82-9-18, 4361), which duplicates (overlaps) lines 23-47 of the main Neo-Assyrian text (the last 25 lines) and has 14 additional lines (lines 23-61). The exact date and provenance of the Neo-Babylonian tablet are unknown. The Sargon Geography is composed basically of lists of place-names (and in one section the names of peoples, such as the Amorites) interspersed with information relating to the reign of Sargon of Akkad. Though both texts date to the 1st-millennium BCE, Wayne Horowitz states that some traditions may date to locations that were important circa the Old Babylonian period. Wayne Horowitz (Mesopotamian Cosmic Geography, (1998, Page 93) states: "Sargon's empire in The Sargon Geography, excluding the lands across the seas, corresponds to the continent on the World Map."

(2) The levels of the Babylonian universe

The longest single extant account of the building of the Babylonian universe is found in the 7 tablet epic Enuma Elish. The Babylonian Enuma Elish sets out a political cosmology i.e., (1) a theogony culminating in the victory of Marduk, and (2) connecting civil order to kingship. Human kingship is a reflection of divine kingship and the earthly king is the earthly keeper of order and justice. In this epic poem the god Marduk constructs heaven and earth (but not the underworld) from the body of Tiamat, and organises some other features of the universe such as fashioning the cosmic bonds between heaven, earth, and the Apsu, and the building of Babylon. From the Enuma Elis account it appears that the Apsu already exists when Marduk separates heaven and earth. A number of other Sumerian and Akkadian texts preserve lengthy and brief accounts of creation. In the earliest of these texts the creators/rulers of the universe are the gods Anu, Enlil, and Enki/Ea. In later texts the creator god is Marduk.

The assyriologist Wilfred Lambert (1926-2011) and Wayne Horowitz have pointed out there is no direct evidence that the ancient Mesopotamians thought the visible heavens comprised a (solid) dome. They had no clear word for sphere or dome. The ancient Babylonians viewed the cosmos as a series of flat, superimposed layers of the same size separated by space, held together by ropes (cosmic bonds).

Basically, they had 6 superimposed levels of the universe, 3 heavens and 3 earths (but some texts indicate slightly greater detail. The vertical levels of the (generalised) Mesopotamian (Sumero-Akkadian) universe are indicated as:

Region Above the Heaven of Anu (See: The Etana Epic, Section B 30-43) (Open space implied by The Etana Epic)

Upper Heaven (High Heaven) of Anu (Highest Region of the Universe)

Middle Heaven (Intermediate High Heaven) of (300) Igigi (One source assigns 300 Igigi to the Upper Heaven)

Lower Heaven of the (Visible) Sky (Stars, Planets, Sun, and Moon) (Thought to be circular in shape)

The "Atmosphere" (Either not specifically listed (not considered a separate level of the universe) or identified as Part of Visible Sky (Lower Heaven); or Separate Geographical Level)

Upper Earth (Humankind, The Level of the Earth's Surface (Dry Land and Sea))

Middle Earth, Apsu of Ea (Enki/Ea) (Cosmic Subterranean Water)

Lower Earth, Underworld of Nergal (King) and Ereškigal (Queen) (Realm of the Dead) (Lowest Region of the Universe) (300/600 Anunnaki are locked in the Lower Earth/Underworld)

The existing accounts of Mesopotamian cosmology are rather limited. Unfortunately they are also conflicting. (The 2 key tablets are KAR 307 and AO 8196.) For a detailed discussion of Mesopotamian cosmology, including the Babylonian world map, see Mesopotamian Cosmic Geography by Wayne Horowitz (1998). Babylonian cosmology distinguished 3 heavens. The lower two only were considered to be visible to humankind: the heaven of Enlil, where the main god Marduk/Bel had his particular dwelling, and the heaven of Ea, or lower sky on which the movements of the stars and planets could be observed. The mystical religious text KAR 307 states that the sky (the lowest of the 3 heavens) is made of jasper (modern jasper is generally opaque but in ancient descriptions jasper is often described as translucent), the middle heaven above the sky is made of saggilmud-stone (a variety of the blue lapis-lazuli), and the upper heavens (the heaven of Anu) are made of luludānītu-stone. Jasper from Persia was sky blue. Generally, the Mesopotamian accounts of the structure of the universe remained constant throughout the approximate 2500 years from the earliest evidence to the end of cuneiform writing. Some change in Mesopotamian conceptions of the universe did occur as Mesopotamian astronomy improved. No text deals with the bounds of the physical universe or what might exist beyond the described structure/limits of the universe. It was believed that the floor of the Middle Heaven could be seen through the floor of the Lower Heaven. It was also believed that nothing existing above the blue saggilmud-stone floor could be seen (i.e., the residences of the gods/goddesses and the Upper Heaven).

The Sumerian cosmological account, The Duties and Powers of the Gods sets out the distinction between the (300) Igigi (the great gods) of the heavens and the Anunnaki of the underworld.

(3) The physical structure of the heavenly regions

Cuneiform texts of the 1st millennium BCE record a tradition of 3 superimposed heavenly realms. The High Heaven belonged to the god Anu and was also the abode of 300 Igigi or great gods. The Middle Heaven belonged to the Igigi, and Marduk also had his throne there. The stars and constellations were drawn (etched) directly upon the surface of the Lower Heaven. It is indicated that all astronomical activity takes place in the lower heavens. (Invocations to 7 heavens and 7 earths occurring in Sumerian incantations have magical than cosmological significance and are not related to the 3 heavens and 3 earths found in other texts.) The texts recording a cosmological picture of 3 heavens also contain poetic speculation about the heavens being made of different stones of varying colours. (It is to be assumed that what is meant is the floors of each level of the heavens were composed of a different type and colour of stone, and that there was open space between each stone floor, just as there is open space between the level of the Upper Earth and the Lower Heaven. Also to be assumed is each stone floor was visible from below and served as a roof for the region below. See: Mesopotamian Cosmic Geography by Wayne Horowitz (1998, Page 9).) The High Heaven of Anu was reddish, speckled with white and black; the Middle Heaven was blue like lapis lazuli; the Lower Heaven was translucent jasper, either blue or grey. This concept is not an attempt at empirical description but has a likely connection with mythological and/or other associations between stones and gods. The statement that the stars were drawn, or inscribed as 'writing,' upon the stone surface of the heavens is also poetic. This metaphor stressed the meaning of the stars as signs 'written' by the gods for people to observe and use to make forecasts about the future. In literary/mythological texts the term 'firmament' (and sometimes the term 'base of heaven') is used to denote the celestial realm of the planetary deities.

The term 'sky,' not 'firmament,' was used in the terminology of astronomical texts to refer to the place where celestial phenomena were observable. Both celestial divination and astronomical texts required a terminology to specify the positions and times for the occurrence of celestial phenomena. A variety of systems denoted celestial positions (without the use of the conception of the celestial sphere and its coordinates). A major frame of reference was the horizon. The 3 systems of importance were: (1) The 3 'paths.' The terminology of the 'paths' of Anu, Enlil, and Ea was used in early astronomical texts. The path of the god Anu had its gate in the center of the 'cattle pen,' or eastern horizon; the path of the god Ea lay to the south, and the path of the god Enlil lay to the north. The stars may have been associated with the gods Anu, Ea, and Enlil even earlier than the establishment of the path system, but were assigned to these paths according to where on the horizon their risings were observed (= according to their circles of declination, the distance north or south of the celestial equator). (2) Another system implied to denote celestial positions is implied in the device called a 'string.' The Babylonian GU text on BM 78161 arranges stars in 'strings' that lie along declination circles and therefore measure right-ascensions or time intervals. A 'string' established a relation between stars of similar right ascensions that crossed the meridian at the same time. (3) The other 'path' of importance was 'the path of the moon,' marked by 17/18 constellations, and used at least by circa 750 BCE. The 17/18 constellations in 'the path of the moon' were unequal in size and could not be used as a standard of reference for the calculation of 'distance' along 'the path of the moon.'

(Mul.Apin tablet 1 describes the Path of Sin (= the way of the Moon) which crossed the boundaries between the Paths of Anu, Enlil, and Ea. This referred to 17/18 constellations/stars marking the path of the Moon ("gods standing on the path of the moon."). It was a fixed path in the sky. (When the ecliptic started to become a primary reference line the 17/18 (depending on how you interpret the list) constellations/stars marking the path of the Moon were basically formed out of the "three stars each" (i.e., monthly calendar star) system of menologies and other constellations/stars were added.))

Later, these 17/18 constellations were reduced to 12 to form the basis for the zodiac, to mark the passage of the sun with respect to the fixed stars through the months of the year. Because the planets were observed to hold close to the path of the sun (the ecliptic), a larger group of ecliptical stars was identified for the purpose of observing the movement of the planets. "Although the twelve constellations of the zodiac gave their names to the zodiacal signs, once the signs were defined by longitude rather than constellation, they became a mathematical reference system of twelve 30-degree parts, counted from a defined starting point. In this way, no geometrical dimension was attributed to the heavens in mathematical astronomical texts, whose predictive schemes were strictly arithmetical and linear, and consequently shed no light on the question of the spatial structure of the heavens. (Rochberg, Francesca. (2005). "Mesopotamian Cosmology." In: Snell, David. (Editor). A Companion to the Ancient Near East. (Pages 316-329).)"

The stars of the zenith were also separated by right-ascension differences. Zenith stars were a group of stars whose culminations are used for keeping time, known as ziqpu-stars after the Akkadian term for culmination, ziqpu. Ziqpu-stars were stars "so chosen that one crosses the meridian before dawn, in the middle of each month, as another constellation is rising heliacally." (See: Mul.Apin by Hermann Hunger and David Pingree (1989) Page 142.) The ziqpu-stars were useful if, for whatever reason, the eastern horizon was obscured and the heliacal rising of important stars was unable to be directly observed. (According to the assyriologist Wayne Horowitz the use of ziqpu stars for measurement can be described in terms of the measurement of the positions of 3 stars: 'star a' at the apex of the sky (ziqpu point), 'star b' at halfway point between east horizon or west horizon and apex of the sky, and 'star c' at the east horizon or west horizon.) The most common version of the ziqpu-star list contained 25 stars. Another major frame of reference was a fixed celestial frame of 33 bright stars, so-called 'normal stars,' unevenly distributed along the ecliptic within a few degrees of the paths of the sun, moon, and planets. (10 degrees north latitude and 7.5 degrees south latitude (of the ecliptic).)  The reasons for the uneven distribution are not understood. 'Normal stars' were used as reference points in the sky to indicate the relative position of the moon and planets and a (normal) star, where the (normal) star becomes the reference point. In the astronomical texts the position of the moon or of a planet is given by stating that it is 'in front of' a Normal Star (which means to the west of the star), or that it is 'above' 'below,' or 'behind' (which means to the east of the star) the star, often in terms of the Babylonian units cubit and digits (finger(s)). In the late Babylonian period celestial phenomena were recorded in terms of the 31/33 Normal Stars (the Akkadian term is Mul.Sid) that were marked along the ecliptic path. The Babylonian astronomical terms used with the Normal Stars have not yet been absolutely clarified. (There would appear to be 32 normal stars usually identified in the Astronomical diaries and Normal Star Almanacs. However, there appears to be a total of 34 stars known to be used as Normal Stars. A list of 32 usual Normal Stars is given in Astronomical Diaries, Volume 1, by Abraham Sachs and Herman Hunger (1988). It is pointed out in this volume that stars other than those identified in the list are occasionally used as Normal Stars.)

The 17/18 stars in 'the path of the Moon' were recognised at least by the 2nd-quarter of the 1st-millennium BCE. Hence circa 750 BCE the use of 17/18 'counting stars' along the path of the moon to measure the progress of the moon through the month. In the Mul.Apin series (Tablet 1, Section 4, Lines 38-39) the list of the stars in 'the path of the Moon' is defined as: "All these are the gods who stand in the path of the Moon through whose regions the Moon in the course of a Month passes, and whom he touches." The system of Normal Stars was in use at least as early a circa 600 BCE. The system of 36 stars marking the 'three ways/paths' gave way to a system involving 31/33 (perhaps 34) 'normal stars' (= reference stars) being placed along the ecliptic, to serve as markers (primarily) for the paths of the planets. Actual (particular) 17/18 stars in 'the path of the Moon' were not denoted in the Mul.Apin series - those 'stars' used were basically asterisms.  The 31/33 stars used in the scheme of Normal Stars were not necessarily the same as those used previously in the Mul.Apin scheme for 'the path of the Moon.'

(4) The cosmic waters (Apsu)

Mesopotamian texts preserve a number of different views of the Apsu.

In Sumerian and Akkadian mythology there was a cosmic realm called Apsu (the Abyssal (subterranean waters) comprising watery depths beneath the earth. The Apsu was located directly beneath the earth's surface. The Apsu contained the freshwater ocean and provided the source of water for all the springs, wells, streams, rivers, and lakes of the world. The Persian Gulf, which lay to the south of Sumer, was believed to be  a source of an outflow of the Apsu. The Apsu was the creation, abode, and kingdom of the god Enki. The temple of Enki in the very early Sumerian city of Eridu was called the E-Abzu 'House of the Abyss.' Enki's son, Marduk, was known as 'first-born son of the Apsu.' Because Enki was associated with wisdom, magic, and incantations, the Apsu was thought of as the fount of wisdom and source of the secret knowledge of incantations. The later temple of Marduk in erected in Babylon was explained as the replica of Apsu. As the counterpart to Enki's cosmic abode, Marduk's temple was also the home of all the gods. Enki's shrine in Eridu too was known as the 'holy mound.' The association of the Apsu with the 'holy mound' showed the cosmic importance of Ea's domain as a place for the divine assembly and where destiny was decreed. The assyriologist Wayne Horowitz writes (Mesopotamian Cosmic Geography (1998, Page 342)) that the Apsu and the underworld were, in some texts, confused with each other.

There is not enough information to decide whether the interior of the Apsu was completely filled with water. There are reasons for supposing the Apsu was a cosmic subterranean lake that maintained a constant level of water. No figure is mentioned for the depth of the Apsu beneath the earth's surface (or the actual depth of the Apsu itself). One text indicates the Apsu had borders and it was possible to travel from the underworld to the the higher regions by passing outside the borders of the Apsu. 

In KAR 307, the Apsu is the middle earth, is located between the earth's surface and the underworld, and belongs to Ea. In Ee V 119-122, Marduk indicates that the city of Babylon on the earth's surface is to be located above the Apsu. In some texts the Apsu is a cosmic region on a par with the heavens.

The gate of the Apsu is mention in Ee V 73-76.

(5) The realm of the dead

The furthest realm in the direction downward was 'the netherworld.' The underworld was the lowest region of the Mesopotamian universe. There were various ideas of the land of the dead in literary texts. In the only known text where cosmic regions were placed relative to one another within an overall scheme the location of the netherworld was specified as being below the Apsu. As such it was the lowest of all regions. In literary texts the netherworld was depicted as a land that was dark and distant, inhabited by ghosts, demons, or gods who ruled over the dead or who brought death.

Eric Burrows in The Labyrinth (Eric Burrows (Jesuit assyriologist/epigraphist), "Some Cosmological Patterns in Babylonian Religion." In: The Labyrinth edited by Samuel Hooke (1935, Pages 45-70).) considers evidence for the relation of the Babylonian temples to (1) heaven, (2) earth, and (3) the underworld, proposed that the Babylonians held the idea that the temple was a vertical column stretching up to heaven (expressed by the height of the temple) and down to the underworld (expressed by placement of drains or pipes for libations to the underworld). These ratu/arutu were found at Ur. According to the CAD A/2 324, clay pipes (arutu) were placed in the earth as conduits for libations to the dead.

There is almost no evidence for the size and shape of the underworld. No text provides any dimensions. It was indicated to be very large and a single text indicates it to be circular in shape, like the heavens and the earth's surface. The distance/depth of the underworld beneath the earth's surface varies with texts. One text gives the exact distance of 100 leagues. Given that a league is approximately 5.5 kilometres the distance under the earth to the netherworld is 550 kilometres. The underworld is generally in darkness (referred to in literary texts as the "House of Darkness") but the sun-god passes through the underworld at night on his way from the western horizon to the eastern horizon.

Wayne Horowitz states (1998, Page 350): "Almost all known features of the underworld are architectural rather than topographical." There are few details describing the underworld river, its source and outlet, and size. One text describes it as a great river.

Note: The Enuma Elish does not mention the Lower Earth/Underworld. There is little clear information regarding creation of the underworld. In one text it was apparently a part of earth.

(6) The gates the stars, moon, and sun use when rising and setting

There are numerous sources (i.e., Enuma Elish, Prayers to the Gods of the Night) mentioning gates which the stars, moon, and sun pass through when entering and departing the sky. Both Sumerian and Akkadian texts mention the stars, moon, and sun come out of gates on the eastern horizon and enter back through gates on the western horizon. These gates exist for both the (nonvisible) high heavens and the visible heavens. Various gods/goddesses open (unbolt) the gates (or open a particular door) of heaven. Texts do not explain how the sun, moon, stars, and planets reach the gates of heaven. Akkadian literature contains 3 explanations for ways the gates of heaven can be reached: (1) to fly like Etana (an ancient Sumerian king of the city of Kish) and the eagle, (2) to take a roadway, and (3) to climb a stairway.

For the mountains of sunrise and sunset (the Sun-god depicted as rising and setting through a gate by mountains) see: (1) "The Sun at Night and the Doors of Heaven in Babylonian Texts." by Wolfgang Heimpel, Journal of Cuneiform Studies, Volume 38, Number 2, Autumn, 1986, Pages 127-151. [Wayne Horowitz gives: W. Heimpel, JNES, Volume 38, Pages 143-146.] (2) JoAnn (Jo Ann) Scurlock, Journal of the American Oriental Society, Volume 108, 206, Number 1?/2?, 1988, Pages 18-23. [I have yet to fully identify this reference.] (3) "At the Edge of the World: Cosmological Conceptions of the Eastern Horizon in Mesopotamia." by Christopher Woods (Journal of Ancient Near Eastern Religions, Volume 9, Issue 2, 2009, Pages 183-239). Every morning the sun god Shamash enters the sky through the eastern gateway of the Mashu mountains. At the end of the day Shamash exits the sky through a gateway located on the western peak of the Mashu mountains. Guardians of the gateway in this mountain are depicted as hybrid creatures like scorpion-men or bull-men. The god Nergal is mentioned in relation to the 'Gate of Sunset' in a damaged text. Also, the god Nergal, the king of the underworld, is associated with a mountain of sunrise in one text.

The gate of heaven is guarded by heavenly (cosmic) beings. There are also gates to the underworld. Texts commonly mention a road to the underworld but give no exact details of the route. Some texts state this road leads to the underworld gates and others state it ends at the underworld river which must then be crossed. Steps leading down into the underworld is also indicated.  In The Death of Gilgamesh it is indicated that it may have been possible to enter the underworld by crossing distant mountains. The gates of heaven and the gates of the underworld were identical in structure to city gates on the earth's surface.

(7) Names of key parts of the sky

There are Sumerian terms and Akkadian equivalents that name parts of the sky, including: (1) Horizon (Heaven's base/The base of heaven; also Heaven's edge). Referring to the lower portion of the sky, including the actual horizon where heaven and earth meet, and a band above the horizon (= the lower part of the eastern sky above the horizon that is tinged red by the approaching sun). (2) Zenith (Heaven's top/The heights of heaven; also Heaven's tip/The tip of heaven). (3) Middle of the sky (The middle of the heaven). Regarding "middle of the sky" Wayne Horowitz states: (1998, Page 239): "Although it may be assumed that the "Middle of Heaven" included the center of the sky around the apex of the celestial dome, it is not possible to determine how far the "Middle of Heaven" extended downward." Wayne Horowitz also comments (1998, Page 233): "These terms [horizon, zenith, and middle of the sky] are not used in a consistent manner. They often seem to be synonymous with one another or to refer to overlapping areas." The border between Horizon and Zenith is not defined in any known Sumerian or Akkadian text.

Appendix 1: Babylonian Pole Star(s)?

Introduction

The pole star (polestar)/north star refers to the star that happens to be nearest to the north celestial pole (pole of the celestial equator) around which all the stars seen from the northern hemisphere appear to rotate. In other words: Usually, pole stars are simply those stars nearest to the vacant (northern) apex.

Pole of the equator

In brief: north celestial pole (star) = pole of the (celestial) equator. Some definitions: (1) The celestial north pole is the imaginary point in the sky directly above the earth's geographic north pole around which the stars appear to rotate over the course of the night. (2) A pole star is a visible star that is approximately aligned with the earth's axis of rotation, that is, a star whose apparent position is close to one of the celestial poles, and which is positioned approximately directly overhead when viewed from the earth's geographic north pole or geographic south pole. The current north pole star (north star) is the bright star Polaris. There is no bright star presently coinciding with the Earth's south celestial pole. Sigma Octantis (in the dim constellation Octans) is presently the closest naked-eye to the south celestial pole. It is over 1º away from the pole, with a barely visible magnitude of 5.5 (requiring a clear night to see it). (3) The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words it is an imaginary projection of the terrestrial equator out into space. Because of the axial tilt of the earth the celestial equator is inclined 23.4º with respect to the ecliptic plane.

For the last 10,000 years the only star to come within 1º of the equatorial North Pole (circa 3000 BCE, and remaining there for 200 years) was Thuban (Bayer designation Alpha Draconis (α Draconis)), a 4th magnitude  (presently + 3.65 but may have been brighter in the historic past) yellow star in the constellation Draco. (It is calculated that Thuban (α Draconis) was the northern pole star from 3942 BCE when it moved farther north than Theta Boötis, until 1793 BCE.)

Pole of the ecliptic

The ecliptic pole is the point on the celestial sphere where the celestial sphere meets the imaginary line perpendicular to the ecliptic, the path the Earth travels on its orbit around the Sun. The obliquity of the ecliptic is the inclination of the plane of the ecliptic to the plane of the celestial equator. The 'ecliptic north pole' (as it is called by modern astronomer) is entirely separate from, and 23.4 degrees distant from, the 'celestial north pole' (as it is called by modern astronomers) which is tilted away from the vertical by 23.4 degrees. (The so-called obliquity of the ecliptic.) Unlike the pole of the celestial equator, the pole of the ecliptic is permanently located (it does not move). The north pole of the ecliptic (north ecliptic pole) is in the constellation Draco. Draco is circumpolar (i.e., never setting), and can be seen all year from northern latitudes. The south pole of the ecliptic (south ecliptic pole) is in the constellation Dorado. Dorado is circumpolar (i.e., never setting), and can be seen all year from southern latitudes. There are no bright stars near the north pole of the ecliptic. The pole of the ecliptic (northern ecliptic pole) is located in the coils of the constellation of Draco (the Dragon), approximately between the stars Zeta Draco (magnitude 3.17) and Al Tais (Altais) (magnitude 3.07). (The northern pole of the ecliptic is also described as between the stars Grumium (magnitude 3.75) and Chi Draconis (magnitude 3.55).) Its location is almost impossible to detect within one or many lifetimes.

The ecliptic plane passes through the 12 zodiacal constellations.

Precession

Due to precession the celestial pole is in continual motion, revolving round the pole of the ecliptic. The celestial north pole makes a complete revolution round the pole of the ecliptic approximately every 25,700 years. Owing to this motion of the celestial pole the celestial equator moves also, continually sliding along the ecliptic, and carrying the equinoxes with it.

In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. The precession of the equinoxes is caused by the gravitational forces of the sun and the moon, and, to a lesser extent, of the planets, on the equatorial bulge of the earth. The term "precession" typically refers only to the largest part of the wobbling motion; other changes in the alignment of Earth's axis - nutation and polar motion - are much smaller in magnitude.

Precession causes the Earth to wobble on its axis with a period of approximately 25,700 years. The Earth rotates once a day around its rotational axis; this axis itself rotates slowly (similar to a wobbling top), completing a rotation in approximately 25,700 years. (Looking down on the ecliptic plane from the north, the earth's axis is pivoting clockwise.) The traditional/historical term, precession of the equinoxes, refers to the motion of the equinoxes along the ecliptic (the plane of Earth’s orbit) caused by the cyclic precession of Earth’s axis of rotation. Earth's precession was traditionally/historically called the precession of the equinoxes, because the equinoxes moved westward along the ecliptic relative to the fixed stars, opposite to the yearly motion of the Sun along the ecliptic.

Discussion

Discussion on whether or not the Babylonians, and perhaps even the Sumerians were aware of both the Pole of the Equator and the Pole of the Ecliptic (or one or the other) is, at times, confused. The discussion of an alleged Babylonian pole star (by convention = north pole of equator) by Robert Brown Junior in his Primitive Constellations, Volume II, 1900, Pages 176-191 is muddled, unreliable, and outdated. According to Brown Junior (Primitive Constellations, Volume II) "The Pole Star is Dugga-Kaga-gilgatil." In an early article (The Babylonian and Oriental Record, Volume 1, 1887) Brown maintained Vega was the pole-star, called in Akkadian Tir-anna, ("Life-of-heaven"), and in Assyrian Dayan-samê ("Judge-of-heaven"), as having the highest seat or throne. Persons who maintain the Babylonians, and perhaps even the Sumerians were aware of both the Pole of the Equator and the Pole of the Ecliptic basically use out-dated references to try and prove it. (The attempted argument by Gavin White in his book Babylonian Star-Lore (2007) ) that the celestial pole was stressed in Babylonian star-lore is erroneous and is likely influenced by reliance on outdated references (but the author gives very few references for the content of his book; but years later did publish them separately on the internet).) However, there is no credible proof the Sumerians and/or Babylonians had established a Pole of the Equator and a Pole of the Ecliptic.

Update note: Gill Zukovskis (6/10/2012) has kindly brought to my attention that a bibliography for Babylonian Star-Lore has appeared at Solaria Publications website: "Reference Notes to Babylonian Star-lore, 2nd Edition, posted on April 11, 2012" by Gavin White. Amongst the references is "Page 135 §1: Identified as Pole star. Reiner 1995, pages 20-1." See below for Reiner's dated (and sole) source. 

It is puzzling that people want keep using Peter Jensen and Alfred Jeremias. Likely it is because few other persons make these kind of statements. However, Peter Jensen is outdated and Alfred Jeremias is biased and dated. Neither can be regarded as authoritative. In his very early book (1890) on Babylonian astronomy, Die Kosmologie der Babylonier the pioneering Assyriologist Peter Jensen includes a diagram associating Anu with the North Pole of the Ecliptic and Bil-Enlil with the North Pole of the Equator (which is opposite to the assignments given later (1913) by Alfred Jeremias), but in his brief discussion on Page 19 Jensen also offers that the assignments could be reversed. In his Die Kosmologie der Babylonier (Pages 190-191), Jensen also indicates a knowledge of the two poles when he writes (English translation courtesy Leroy Ellenberger (Hastro-L)): "Since it is absolutely unthinkable that the sun and the moon, as also the 'god stars' Anu and Bil (that is, the two north poles!), could be related to the Earth in any shape, form or fashion, we shall break neither our or anyone else's noggins over VR 46, 15-16ab. This text presents no problem unless one is dead set to create difficulties where there [really] are none." 

The cuneiform text VR 46 is a star list dated to the Late Babylonian Period - for simplicity it can be dated circa 500 BCE. The text equates stars/constellations with gods/goddesses and it associates Anu with the 'wolf star.' However, the late 'theological' cuneiform text KAR 142 associates Enlil with the 'wolf star.' Hunger/Pingree Astral Sciences in Mesopotamia (1999) have Wolf as alpha Trianguli. (The Plough constellation is α. + β Trianguli and γ Andromedae.) However, it was also associated with Sirius. It is difficult to understand how the text relates to the Pole of the Equator and the Pole of the Ecliptic being established/identified in Babylonian astronomy.

In the entry for "Enlil am Himmel" in the scholarly fascicle Reallexikon der Assyriologie Volume II, Page 389, the claim that the Babylonians identified the Pole of the Equator and the Pole of the Ecliptic is repeated: "Wo der »Standort« des Enlil am Himmel zu lokalisieren ist, läßt sich nicht mit Sicherheit entscheiden. Es kann sich um den Höhepunkt des scheinbaren Sonnenlaufes zur Zeit der Sommersonnenwende (unter der Breite von Babylon etwa 7,5° südlich vom Zenit) oder um den Pol der Ekliptik (s. Jensen Kosmologie, S. 19ff. und KB VI, I, S.347; Weidner Handb. babyl. Astron., S. 33) handeln." Reallexikon der Assyriologie Volume II is a dated publication (and the author of the entry is using dated references). Volume 2 was published circa the mid 1930s. There is no mechanism for updating RLA entries. (Weidner is actually simply repeating the claims he made in his book Handbuch der babylonischen Astronomie. For example, in Handbuch der babylonischen Astronomie Weidner holds that (Pages 32-34) Nibiru is the Pole of the Ecliptic (= Enlil is the Pole of the Ecliptic), and (Page 97) kakkab MU-SIR-KEŠ-DA = kakkab Niru, is the Pole of the Equator (= Anu is the Pole of the Equator).) Handbuch der babylonischen Astronomie by Ernst Weidner (1914) was written from the Panbabylonism standpoint and is a veritable wonderland of Panbabylonism. (It was completed several years prior to its publication in 1914, and was in press from 1913.) In Handbuch der babylonischen Astronomie Weidner declared a sophisticated Babylonian astronomy existed at least circa 2,000 BCE, misunderstood and incorrectly used 'The Hilprecht Text' (HS 245) – which he could not date (but is Middle Babylonian Period circa latter part of the 2nd-millennium BCE) - as evidence of an early sophisticated mathematical astronomy (before the Kassite Period), and asserted texts from the library of King Ashurbanipal go back to at least 4,500 BCE. (For Weidner 'The Hilprecht Text,' which he believed likely dated to the 3rd-millennium BCE, provided evidence for an equator-based system of coordinates for measuring the the locations of fixed stars.)

Recently Gavin White in his popular (and misleading) book Babylonian Star-Lore supported the identifications made by Alfred Jeremias in 1913 and identified Bil-Enlil with the Pole of the Ecliptic (Plough-star) and Anu with the Pole of the Equator. However, Gavin White, though quite knowledgeable, is not an expert on Babylonian astronomy and astral lore. Simply, since 1920 there has been a vast increase in our knowledge of how to interpret cuneiform languages. Cuneiform translations prior to 1920 may be unreliable and involve questionable interpretations. What the pioneering Assyriologists sometimes thought they were reading is simply mistaken. Even the Assyriologist (and staunch Panbabylonist) Ernst Weidner warned that interpretations and translations earlier than 1920 needed to be used with caution. 

Auguste Bouché-Leclercq in L'Astrologie grecque (1899, Page 122) writes: "On sait que le pole par excellence était pour les Chaldéens le pole de l'écliptique, lequel est dans la constellation du Dragon." Here Bouché-Leclercq briefly mentions a late source, Diodorus Siculus (1st century CE), for the Chaldeans identifying Anu with pole of the ecliptic in the constellation of the Dragon. Bouche-Leclercq is relying on what Diodorus Siculus (1st century AD) had to say on Mesopotamian astrology/astronomy in their own day. The reputation of Diodorus Siculus for accuracy and reliability is rather dubious. He basically copied his information from other sources, without up-dating it. He was a writer, not a researcher. Some of the information he gives on Mesopotamia is confused. 

Persons having a preference for uncritically using old material to make their case need to present supportive reasons for maintaining their continued adoption. In his bibliography in Die Rolle der Astronomie in den Kulturen Mesopotamiens (1993) the Assyriologist Christopher Walker comments that Weidner´s Handbuch der babylonischen Astronomie is "now very out of date." In the same volume (?) (or elsewhere) the Assyriologist Francesca Rochberg cautions against reliance on Handbuch der altorientalischen Geisteskultur (2nd edition 1929) by Alfred Jeremias. On Page 134 of the 2nd edition Jeremias insisted that 'Nibiru' in all star texts of later times indicated Canopus. (Also, Francesca Rochberg has remarked in a personal communication (4 December 1995) to Leroy Ellenberger regarding her translation of section 94, "Die Offenbarung der vier Planeten in den Erscheinungen der Sonne und des Mondes," in Jeremias' Handbuch der altorientalischen Geisteskultur (1913) (Ellenberger, Hastro-L, 10 December 2009): "I find this Jeremias passage to be totally incomprehensible. I may not have produced a thoroughly correct translation, but I think it is close enough. The evidence, such as it is, is not presented in such a way as anyone can use it, and the very passages that you were interested in ... are not given in Akkadian and no text refs are provided. The whole notion of the representation ... of the planets ... in various guises of the moon and/or sun is hard to understand. If these are genuine astrological correspondences, we do not understand what their purpose might have been. Jeremias never comes clean with what he thinks it all means either. ..."

A pioneering study of Mesopotamian astronomy was initiated with the 3 articles by Archibald Sayce and Robert Bosanquet published during 1879-1880 in Monthly Notices of the Royal Astronomical Society. By at least 1887 Sayce was identifying a Pole Star (Lectures on the Origin and Growth of Religions). He held that "The Star/Constellation of Anu was the "Yoke of Heaven" = Draco, alpha Draconis. In an early Volume of Transactions of the Society of Biblical Archaeology he stated: "The Akkadian term "Ditar-Anki" ("the Judge of Anki") and the Assyrian term "Dayen-Same" are designations of the Pole Star (North Celestial Pole). The assertion by Sayce of ""Yoke of Heaven" = Draco, alpha Draconis" may possibly be matched to the modern translation "Hitched Yoke" which Hunger/Pingree (1999) tentatively identify with α Draconis. (Note: The Yoke star, mul.SUDUN/nīru, is equated with (approximately Boötes (or Arcturus (and parts of Boötes).)

In his Handbuch der babylonischen Astronomie Weidner explained "man-za-az il Enlil" as the north pole of the ecliptic. (Relying on K 13 774?) Jensen went for similar in his book Die Kosmologie der Babylonier. However, he later withdrew this argument (changed his interpretation) in his book Assyrische-babylonische: Mythen und Epen (1906). This does not seem to be widely known by persons who like to quote his earlier book. (It also helps to demonstrate the lack of any real familiarity with these early authors.) 

The term Nēberu ("Crossing") is also discussed regarding its meaning/s. The term Nēberu ("Crossing") first appears in Astrolabe B as the name of a star in month XII. Astrolabe B was composed in the same political context as as the so-called creation story Enūma eliš and reflects the victory of Nebuchadnezzar I over Elam circa 1100 BCE.

In the early history of Assyriology the term "Nebiru (Neberu)" was sometimes interpreted as meaning the Pole Star, Pole, or Pivot (especially in the Enuma Elish). The Assyriologist Leonard King, using K 13 774, interpreted "man-za-az Neberu" as the Pole Star of the Equator in his book The Seven Tablets of Creation (1902). Anu is identified as the Pole Star of the Ecliptic. In his Babylonien und Assyrien (1920-25, 2 Volumes) the Assyriologist Bruno Meissner identifies 'Nibiru' with the celestial north pole (but likely is simply following Weidner). According to the Dutch assyriologist Francisco Bohl, the station of Nebiru was the point of entry of Jupiter into the path of Anu observed during the night of the vernal equinox, the Babylonian New Year. (According to Astrolabe KAV 218, during this period, the equinox occurred when the sun entered the constellation Mul Aš-Gan (= Iku) which was the "Field" constellation (= Alpha, Beta, Gamma, and Delta Pegasus + Andromedae). The "Field" was enclosed by the rivers of paradise (the constellation of Pisces).)

The concept of nēberu changed over time. Nēberu, written MULNe2-bi-ru (the term is usually transliterated nebiru, neberu, or nibiru.), can mean Jupiter in culmination or in other specific positions, but can also denote the North Star (α Ursa Minor) and Canopus (α Carina), and even the constellation Perseus or a meteor. (It is presently rather usual to explain that the Akkadian name/term Nebiru is the planet Jupiter and the astral name of Marduk.) It is clear that the Mesopotamians used the term 'Nebiru' to mark an astronomical event; a "crossing" at some point in the sky of Jupiter, Mercury, and a star. Nēbiru perhaps defines a turning point (kunsaggû) of the sky. "Station" appears to refer to position in the sky. (One text has "If Mercury crosses the sky and stops it is Nebiru.")

The concept/astronomical meaning of nēberu in the Enuma Elish (2nd millennium BCE) is not clear. It has been stated that the early concept of nēberu as a star in the centre of the sky (i.e., fixed) is not reconcilable with the later (1st-millennium BCE) conception of Marduk as a planet (or planets) (i.e., mobile). In the Enuma Elish the pole star idea is seen, by some scholars, as imminent in nēberu. In the circular astrolabes Marduk's own star is deemed to be in the centre of the inner circle (i.e., the centre of the Stars/Path of Enlil; the centre of the sky). "In [tabular] Astrolabe B, Neberu and the stations of Enlil and Ea are identified with either the last month of the old year (Adar), or the first month of the new year (Nisan). Astrolabe B lists Mardul's star, Neberu, as the Adar-star for the Path of Anu and identifies this star with the New Year (KAV 218 B ii 29-32). The station of Enlil can be identified as mulapin 'The Plough Star', the Enlil star for Nisan in KAV 218 B iii 1-3. Here this star is identified as 'Enlil who determines the destinies'. The station of Ea can be identified with mulku6 'Piscis Austrinus', the Ea star for Adar in Astrolabe B .... Thus, Neberu and the stations of Enlil and Ea apparently regulate the heavens by leading the remaining stars of the Paths of Anu, Enlil, and Ea through their annual courses." (Mesopotamian Cosmic Geography by Wayne Horowitz (1998, Page 116).) In the Enuma Elish priority is given to the organisation of the stars. In the Enuma Elish the god Marduk is stated to have (in order): (1) organised the (stars into) constellations, (2) organised the calendar, (3) fixed the stand of nēberu, and (4) gave the moon and sun orders about their motion. The organisation of the calendar was achieved by 3 constellations of stars being established for each of the 12 months, to fix the days of the year. They are simply placed in their cosmic position as constellations in the 3 Ways/Paths. Marduk does not create the stars - they are the 'great gods.' In her book, Mesopotamian Astrology (1995, page 117), Ulla Koch-Westenholz states the astronomical meaning of nēberu (both in the Enuma Elish and elsewhere) is not clear.

Among modern scholars who, based on the Enuma Elish, identify nēberu with the pole-star are B. Landsberger and J. Wilson ("The Fifth Tablet of Enuma Elish." JNES, Volume 20, 1961, page 173). As well as holding that Marduk fixing the stand of nēberu refers to the pole-star some scholars also hold that the statement in Tablet V:9-11 where Marduk placed the zenith in the belly of Tiamat is also a reference to the pole-star. 

Donald Mackenzie (Myths of Babylonia and Assyria (1915) and The Migration of Symbols (1926)) has the Babylonians calling the pole star Ilu Sar ("the god Sar (Star)" or Anshar ("Star of the Height" or "Star of the most High") but cites no reference(s). According to James Bonwick, Egyptian Belief and Modern Thought (1878), the Chaldean pole-star was Cagagilgate. In his book, Myths and Legends of Babylonia and Assyria (1916), Lewis Spence writes (mistakenly) that "Anu is the Pole Star of the ecliptic, Bel the Pole Star of the equator, while Ea, in the southern heavens, was identified with a star in the constellation  Argo" (Chapter VIII, Page 235).

Felix Gössmann Planetarium Babylonicum oder die sumerisch-babylonischen Stern-Namen (1950) comments that 'nibiru' appears to be used for various stars or regions of sky including: (1) north celestial pole or pole star (= Alcor?), (2) Canopus, near the Pisces-Aries region of the zodiac, and (3) Jupiter. (Though Nibiru could be Jupiter (the texts that place Marduk "in the centre of heaven" support the identification of Jupiter, which is located in the centre of the line of planets) it was once identified with Mercury.) Some modern authors still translate 'Neberu' as 'Pole Star.' Recent examples are the Assyriologist Wayne Horowitz (Mesopotamian Cosmic Geography (1998)) who is followed by the British Assyriologist Stephanie Dalley (translating and interpreting the Enuma Elish) and the British cuneiform philologist and mathematician Eleanor Robson (who is likely simply following Dalley). The particular text is Astrolabe B, 'Rising Stars' list, Month 12 (Adar) for the Path of Anu (Column 2, Lines 29-32). The term 'Neberu' which has the determinative dinger = god (= Marduk) - preceded by the determinative MUL = star - is translated as 'Pole Star' (MUL BI dingir Né-bé-ru dingir AMAR.UD). There is nothing in the text that compels the identification as 'Pole Star.' The translation simply is "This star is Nibiru-Marduk." The full passage translates: "The red star which stands in the south after the gods of the night [the stars] have been finished, dividing the the sky in half, this star is Nibiru-Marduk." (Wayne Horowitz translates: "The red star, which stands at the rising of the south-wind after the gods of the night have finished their duties and divides the heavens, this star is Neberu, Marduk.") (The 'red star' suggests an identification with Mars - but this would be incorrect. Comparing Astrolabe B, Column 2, Lines 29-32 with BM 86378 (Mul.Apin, Tablet 1), Column 1, Lines 36-38 the interpretation Jupiter is seemingly valid. Mul.Apin, Tablet 1 set out: "When the stars of Enlil have disappeared, the great, faint star [Jupiter remaining faintly visible in the morning when the other stars have disappeared], which bisects the heavens and stands, is mul dinger Marduk-Niribu, mul SAG.ME.GAR; he (the god) changes his position and wanders over the heavens." Wayne Horowitz (The Three Stars Each (2014)) has identified that in the Astrolabe texts and Enuma Eliš, Marduk's star (= 'red star') is the planet Mercury. Regarding again the term 'Neberu' which has the determinative dinger = god (= Marduk) - preceded by the determinative MUL = star - and translated by some 'Pole Star' (MUL BI dingir Né-bé-ru dingir AMAR.UD). The 'Pole Star' (of the equator) identification is likely done, however, because in the cuneiform texts Nibiru is not only described as mobile but is also described as a 'fixed' star. It needs to be kept in mind the Babylonians had no concept of a celestial equator.

The northern constellation of the Wagon had small rotations and served as a "pole star" (of the equator) and general indicator for the north. The Neo-Assyrian literary fragment K 7067 contains the lines: "The great gods divided up the st[ations ... / In the station, the pole [... ." There is no definite indication of a pole star in this fragmented text.

In her book Astral Magic in Babylonia (1995) Erica Reiner, discussing HUL.BA.ZI.ZI ('Begone, Evil') a collection of incantations, writes (pages 20-21): "A magic effect is sought by praying to a deity called First-born of Emah: O First-born of Emah, First-born of Emah, you are the eldest son of Enlil. You are descended from Ekur and you stand in the middle of the sky with the Wagon. The stellar nature of this divine being addressed is evident from the middle line, where he is described as standing in the middle of the sky, with the Wagon Star. As for the astronomical identity of the "first-born of Emah," such a star, described as "first-born son of Anu," is listed in an astronomical compendium from about 1000 B.C. [MUL.APIN] as the star that stands in the "rope" of the Wagon, and has been identified with the Pole Star. A prayer to it is prescribed in the hemerology for the month of Ulūlu (month VI)." Reiner is reliant on studies by Carl Bezold and Franz Kugler dating almost 100 years earlier. The star that stands in the rope of the Wagon of Heaven was identified as the Pole Star by the pioneering assyriologists Carl Bezold (Zenit- und Aequartorialgestirne am babylonischen Fixsternhimmel (1913, page 43) and Franz Kugler (Sternkunde und Sterndienst in Babel. Ergänzungen zum ersten und zweiten Buch. I. Teil. (1913, page 57)) as β Ursa Minor (in Ursa Minor).

Both Reiner/Pingree (Babylonian Planetary Omens 2 (1981)) and Hunger/Pingree (Astral Sciences in Mesopotamia (1999)) simply render the Month 12 for the Path of Anu in Astrolabe B (Column 2, Lines 29-32) as Neberu. In the composite so-called "Pinches Astrolabe" (which combines information from 4 astrolabe tablets and 2 star-lists) Month 12 for the Path of Anu has Fox (sometimes translated as Jackal), which is circumpolar and usually identified as a star (associated with the Great Bear constellation). The Fox (Sumerian MUL.KA.A or MUL.KA5.A , Akkadian sēlebu) has been variously identified. Felix Gössmann (1950) has 80-86 [= 80] Ursa Major (?) (= Alkor), and in a circular astrolabe it appears in the Path of Enlil; whilst other have ε (?) Ursa Major, or the magnitude 4.0 star Alkor(Alcor) ?, a star on the tail of the Great Bear (Ursa Major); or the constellation Canis Minor. (The modern Vulpecula, the Fox, is a small constellation with no bright star.) The 'Fox Star' is one of the 7 names of Mars. In the Star-list K 250 the 'Fox Star' is a name for Mars. The celestial movements of the 'Fox Star' represent Erra (= Irra).

It is worth noting that the British Assyriologist Stephen Langdon, in his detailed discussion of the astrolabes (The Babylonian Epic of Creation (1923, Pages 154-156)) does not make - or even suggest - a pole star identification for various descriptors applied to Marduk.

Some translate the term 'Nusku' as the Pole of the Equator. In her article "The Shape of  the Cosmos According to Cuneiform Sources." (Journal of the Royal Asiatic Society, Third Series, Volume 7, 1997, Pages 189-198) Margaret Huxley brings together evidence from a range of sources and argues that in ancient Mesopotamia the sky was thought to be a rotating sphere with a polar axis. Nusku is the Babylonian and Assyrian god of light and fire altar - and a symbol of the heavenly and terrestrial fire. The god Nusku is indistinguishable from the god Girra. I have not seen any details of why Nusku would be translated as the pole of the equator.

I do not know of any cuneiform text that explicitly mentions/establishes/describes a Pole Star (equator or ecliptic) in Babylonian astronomy. (The poorly preserved Neo-Assyrian literary fragment K 7067 has opening lines describing the great gods apparently arranging the stars in the sky. Two of the opening lines (both damaged) are usually translated: "In the station, the pole [..." and "[...] the pole [..." but I am presently not aware of the transcriptions.) A modern case, using principally Astrolabe B has been made by Wayne Horowitz. (Astrolabe B is a combination of menology and star lists compiled from older sources.) The god Marduk's pivotal position was at the centre of Astrolabe B. This places Marduk at the centre of the sky (= Marduk being associated with the pole-star of the equator). It was connected with Marduk's role in controlling/regulating the movement of the stars. The star of Marduk is stated/identified in Astrolabe B as the last month of the year (Adar) or the first month of the new year (Nisan). This is clearly associated with Marduk's role to control/regulate the movement of the stars. (The star of Marduk marked the passage from the old year to the new year.) Hence Wayne Horowitz translating text of Astrolabe B as: "The red star, which stands at the rising of the south-wind after the gods of the night have finished their duties and divides the heavens, this star is the pole star [Neberu], Marduk." Wayne Horowitz (The Three Stars Each (2014)) has identified that in the Astrolabe texts and Enuma Eliš, Marduk's star (= 'red star') is the planet Mercury. Marduk's star Nēberu, the 12th star in the Path of Anu, divides the stars of of the outgoing old year from those of the incoming new year. Referring to the (now completed) Chicago Assyrian Dictionary should help to clarify matters. It would be helpful for proponents of a Babylonian pole star to cite: (1) catalogue number of relevant cuneiform text, (2) relevant transcription, (3) translation, (4) possible date, and (5) reference for such.

The Menology KAV 218 A and Astrolabe KAV 218 C (2 sections of Astrolabe B = KAV 218) list the Iku-star (GÁN (Ikû) = α, β, γ Pegasi and α Andromedae) of (the month) Nisannu as the new year's star. The heliacal rising of the Iku-star would have occurred on the eastern horizon just before dawn on Nisannu 4. However, the akitu festival, which included a celebration of the turning of the New Year, actually began on Nisannu 1. Though the akitu festival began on Nisannu 1 it appears the start of the Babylonian New Year actually began on Nisannu 4, with the heliacal rising of the Iku-star.

The most recent informed discussion of the topic is by the assyriologist Wayne Horowitz at the 2007(?) CAENO Foundation conference. But now see also his The Three Stars Each: The Astrolabes and Related Texts (2014 (but actually published 2015?)). (Published for Archiv fur Orientforschung Beihefte-series; Archiv für Orientforschung Beiheft 33.)

Not seen (and apparently never published): Stadhouders, Henry. and van Gent, Robert. (2005). "How the Babylonians May Have Fixed the Pole and the North by Means of the Margidda Twin's Culminations." (Paper presented at "Time and Astronomy in Past Cultures" Conference held in Toruń, Wednesday March 30 to Friday April 1, 2005.)

Note: Mercury is the star of Marduk when it is the New Year star. Mercury as Nebēru is apparently only found in Neo-Assyrian reports by scholars.

A Near Eastern/European Polar God/Goddess?

In Mesopotamia, for whatever reason, the Wagon constellation (= modern Big Dipper asterism) was apparently regarded as the (pivotal) centre of the sky and served as a 'pole star.' The association the god Marduk = Nebiru = Pole Star (variously identified with different stars) has been made. Also, I think the identification of the god Nusku has been made.

There is a slight indication that at least in medieval European theology the north celestial pole had a status in relation to divinity (as it did in China). It appears that in (some) medieval German theological literature Mary is termed the pole-star. See: The Dark Figure in Medieval German and Germanic Literature, Volume 448 of Göppinger Arbeiten zur Germanistik, Editors: Edward R. Haymes and Stephanie Cain Van d'Elden (1986, Page 58). David Barrie wrote (Sextant, 2014): "The theologian Alexander Neckham (1157-1217) likened Mary to the Pole Star standing at 'the fixed hinge of the turning sky' by which the sailor at night directs his course." In the later Middle Ages Mary was frequently associated with the moon.

Appendix 2: Babylonian Astronomy

Mesopotamian science/astronomy was the product of an academic scribal culture. Scientific astronomy, in the sense of the use of recorded observations, started in Babylonia, an ancient cultural region occupying southeastern Mesopotamia between the Tigris and Euphrates rivers. Because the city of Babylon was the capital of this area for centuries centuries, the term Babylonia has come to refer to the entire culture that developed in the area from the time it was first settled, circa 4000 BCE. Before Babylon’s rise to political prominence (circa 1850 BCE.), the area was divided into two countries: Sumer in the southeast and Akkad in the northwest.

"We have to reconstruct it [Babylonian astronomy] exclusively from texts and a few schematic drawings accompanying them. No instruments relating to astronomy have been found. These texts were written on clay in cuneiform script which was used in the Near East from ca. 3000 BCE to 100 [CE]. It was completely forgotten and only deciphered in the middle of the 19th century Since then, hundreds of thousands of clay tablets have been found in archaeological excavations, mostly in present-day Iraq. Among these are a few thousand [fragmented] tablets related to astronomy. Many have been published, but more still need to be worked on. And of course an unknown number of such texts is still buried under the sands of Iraq." (Hunger, Hermann. (2011). "The relation of Babylonian astronomy to its culture and society." In: Valls-Gabaud, D. and Boksenberg, A. (Editors). The Role of Astronomy in Society and Culture. Proceedings of the IAU Symposium No. 260, 2009. (Page 62).) "The goal of the Babylonian scholars can best be called knowledge of the sky without any quantification whether it is a science or not." (Hunger, Hermann. (2011). "The relation of Babylonian astronomy to its culture and society." In: Valls-Gabaud, D. and Boksenberg, A. (Editors). The Role of Astronomy in Society and Culture. Proceedings of the IAU Symposium No. 260, 2009. (Page 62).)

Rigorous technical science originated with the Semitic Babylonians. The idea is still common that astronomy in Mesopotamia developed from an observational basis to a purely computational basis. However, this is not supported by the extant textual sources. "Observations were of far less importance than we would expect; simple schematic models for the movement of the celestial bodies were for a long time considered sufficient." (Hunger, Hermann. (2011). "The relation of Babylonian astronomy to its culture and society." In: Valls-Gabaud, D. and Boksenberg, A. (Editors). The Role of Astronomy in Society and Culture. Proceedings of the IAU Symposium No. 260, 2009. (Page 62).)

Astronomical schools existed at Babylon, Borsippa, Sippar, Uruk, and likely Nippur. It is customary to equate the term "oppida Hipparenum" with Sippar; but it is also thought by some to be Nippur. More than 4000 astronomical tablets have been recovered from Babylon. Several hundred astronomical tablets have been recovered from Uruk and approximately the same number from Nineveh. A small number of astronomical tablets have been found at Ashur and Nimrud. A handful of astronomical tablets have been recovered from Sippar, and likewise Nippur and Ur. Outside of Mesopotamia proper, a small number of astronomical cuneiform tablets have been found at the Neo-Assyrian city of Sultantepe. A single astronomical text from Nippur dates to the Seleucid period. All mathematical astronomical texts known presently come from Babylon or from Uruk. The astronomical texts from Nineveh come from the library of king Assubanipal - not from an astronomical school situated in Nineveh. The bulk of the Mesopotamian astronomical texts come from only 3 locations: Nineveh (Kouyunjik), Babylon, and Uruk. Mathematical astronomy texts of known provenance come from a number of sites scattered over ancient Mesopotamia. Most of the omen texts - centred on the omen series Enūma Anu Enlil - come from Ashurbanipal's library in Nineveh. The 2-tablet Mul.Apin series - quite astronomical in content - comes from Ashurbanipal's library in Nineveh. Most of the observational texts i.e., nonmathematical texts (Astronomical Diaries, Almanacs, and Goal-Year texts) come from the city of Babylon from what must have been an extensive astronomical archive somewhere in the city. Mathematical astronomy texts also come from the city of Babylon. A group of mathematical astronomy texts also come from Uruk. The Royal Reports (Sargonid period) dealing with astral omens come from various cities within Assyria. The mathematical astronomy texts date from the last 4 centuries BCE.

Based on the nature of the surviving texts, astronomy in Mesopotamia divides historically into 2 approaches/methods. The first approach existed during the late 2nd- and early 1st-millennia BCE; the second approach existed during the Seleucid period.  The earliest examples of astronomical texts show that a characteristic feature of the first approach of Babylonian astronomy was to deal with numerical schemata. Early Babylonian astronomy was highly schematic. This early schematic computational means of predicting phenomena without use of detailed observations prepared the way for the eventual development of lunar and planetary theories. This late approach appeared in the Seleucid period (after 300 BCE). The foundation of Babylonian mathematical astronomy was built upon the recognition of period relations. These took 2 forms - lunar and planetary periodicity. Periodicity was a central preoccupation. It was conceived of and dealt with in a quantitative arithmetical way (i.e., through counting). The goal of Babylonian astronomy was the determination of the date and position of individual phenomena. The determination of the motion of a planets - and the idea of continuous motion along a circular path - was irrelevant. (See the recent article: Rochberg, Francesca. "Periodicities and Period Relations in Babylonian Celestial Sciences." (2014). In: Kozuh, Michael. et al. (Editors). Extraction & Control: Studies in honor of Mathhew W. Stolper. (Pages 211-218).)

There is no formal astronomy in Sumerian texts. Sumerian literary texts, however, contain astronomical references. (Some knowledge of Sumerian astronomy exists in literary texts and references to calendars.) The Sumerian term UDU.IDIM.MES (Akkadian bibbu) = wild sheep = planets. In the religious text Nanna-Suen Hymn 1 (Sumerian period, 3rd-millennium BCE), the mention of cows is an allusion to the stars in the night sky. (Nanna-Suen (Bronze Age Mesopotamian moon god) Hymn I (of 15 hymns to Nanna-Suen known) has a section on stars and cows. There is an allusion to stars and planets as cattle and the sky as a cattle pen. In a later text the sun and the moon are herdsmen who keep the sky ordered. There is no evidence that the Sumerians were familiar with domes. For the Sumerians the sky is like the curved roof of a cattle pen.) In the religious text the Exaltation of Istar (Middle Babylonian period, circa 1150-1000 BCE), the sun and moon are herdsmen keeping the stars (as cattle) in their order.

The earliest known Mesopotamian astronomical and astral omenology texts date from the Old Babylonian period onwards. "A few texts (i.e., lists) also mentioning stars and constellations date to the 3rd millennium BCE. However, Hermann Hunger points out that no principle is evident in the order of these celestial objects. "It is only in the 2nd millennium BCE that texts appear which are dealing with phenomena in the sky. In these texts we see a desire to find out how the skies are organised, and a belief that this organization can be understood and described in relatively simple ways. The use of observation is limited: while obviously one must look at the sky to be able to say something about it, schematic approaches were predominant .... An example for this are the so-called Three-stars-each texts which probably go back to between 1500 and 1000 BCE. They list, for each month of the Babylonian calendar, three constellations which are supposed to become visible in this month: one constellation to the North, one near the equator [there is no word for equator in these texts], and one to the South; it is furthermore stated that the same constellations disappear again after six months. This gives a neat scheme of 36 constellations from whose risings one could tell the time of year. However, it would not work in practice: first of all, the period of visibility is different for stars depending on their declination; it is simply incorrect to assign all of them a visibility of six months. Then, the Babylonian calendar is not easily attuned to the solar year so that helical risings of stars will not stay in the same month every year. And, just to indicate that we are far from a secure interpretation, the lists also include planets, which are subject to entirely different visibility conditions, independent of the time of the year; finally there are even variant forms of the list which have only ten constellations - instead of 12 - which makes an alignment with the months of the year impossible. The Three-stars-each lists may be seen as attempts to organise what is known about stars. At about the same time an astronomical text was compiled, called Mul-Apin (which means Plough star) after its first word. It is only attested on tablets from the 7th century [BCE] onwards, but probably goes back to the 13th century BCE." (Hunger, Hermann. (2011). "The relation of Babylonian astronomy to its culture and society." In: Valls-Gabaud, D. and Boksenberg, A. (Editors). The Role of Astronomy in Society and Culture. Proceedings of the IAU Symposium No. 260, 2009. (Pages 62-33).)

The Venus tablets of Ammisaduqa are the oldest surviving texts on planetary astronomy. However, the formation of Babylonian astronomy was not primarily dependent upon observation but more upon the development of schematic models. Babylonian astronomy - at any stage - was not primarily observational. Babylonian astronomy was concerned with the description of celestial phenomena by numerical schemes. In early Babylonian astronomy observations played a minor role. In the development of late Babylonian astronomy observations still played a minor role. (However, from circa mid 8th-century BCE onwards observations/skywatching became systematic.) The absence of exactness in Babylonian astronomy existed until the last half of the 1st-millennium BCE. The last stage of Mesopotamian astronomy dated from the Persian period to the end of cuneiform writing. This late and final phase of Mesopotamian astronomy involves the production of precise mathematical tables describing lunar, solar, and planetary theory (i.e., motion). This genre of late mathematical astronomy represents a departure from traditional astronomical materials such as the so-called "Astrolabes" and Mul.Apin. The earlier traditional astronomy of the "Astrolabes" and Mul.Apin were concerned with the course of observable events in the sky and the endeavour to correlate astronomical activity with the passage of time (i.e., with the days of the ideal astronomical year consisting of 12 months of 30 days each). A typical observational event was the helical risings of stars (i.e., fixed stars, constellations, and planets).

The city of Babylon's rise to power and prominence began in 1894 BCE when Sumu-Abum, an Amorite chieftain, founded the first royal dynasty there. The city reach its first peak during the reign of Hammurabi (1792-1750 BCE) its sixth king. During Hammurabi's reign it became the centre of the first great Babylonian empire. After his death the Babylonian empire began to become smaller, due in part to the rise of a new rival dynasty called the Sealand (which originated in the marshlands of southern Mesopotamia).

Circa the beginning of the 20th-century, the pioneering work of of Jesuits Joseph Epping and Franz Kugler showed that there existed in the ancient Near East an astronomical tradition that was different to that known from the works of the Hellenistic astronomer and mathematician Claudius Ptolemy and his successors. Cuneiform tablets recovered in the 19th-century from Babylon and Uruk revealed details of an astronomy that was both observational (but not rigidly so) and computational, and based on arithmetical functions rather than kinematic/geometrical models. The primary goal of Babylonian astronomy was the calculation of certain phenomena for the moon and the planets, such as the length of the lunar month, the eclipses of the sun and moon, the first and last visibilities of the planets, rather than the determination of the position of the celestial bodies at an arbitrary time. The methods by which the Babylonian astronomers calculated these phenomena were not based on kinematic/geometrical models such as those used by Claudius Ptolemy. Instead they used arithmetical functions based on the periodicities in the motions of the sun, moon, and planets. (The empirical rules of eclipse prediction in Babylonia did not require a physical explanation.)

Source: Steele, John. (2014). "Late Babylonian ziqpu-star lists." In: Bawanypeck, Daliah. and Imhausen, Annette. (Editors). Traditions of Written Knowledge in Ancient Egypt and Mesopotamia. (Pages 123-151, Page 124).

The progress in astronomy made at different periods of Babylonian history is now quite well understood. During the first 2-3 millennium of Mesopotamian history there is really only limited empirical observations and the development of schematic models. A scheme of continual empirical observations was only begun during the first half of the 1st-millennium BCE. In the mid 8th-century BCE, under king Nabonassar (first king of the 9th dynasty of Babylon, ruled circa 747–734 BCE), there was a revival of interest in astronomy. During the reign of Nabonassar (mid 8th-century BCE) there was a significant increase in the quality and frequency of astronomical observations. A system of sophisticated mathematical astronomy was only developed during the last half of the 1st-millennium BCE.

The 3 fundamental coordinate systems in astronomy are the horizon system, the equator system, and the ecliptic system. The Babylonian method of designating celestial positions went through 3 stages of development. The early method involved the use of the horizon. The natural horizon, especially in a level region, was the first readily available reference device. In Mesopotamia the horizon system was important. Also, the 3 ways of Ea, Anu, and Enlil (= the stars of Ea, Anu, and Enlil) were developed in the early 2nd-millennium BCE. It was loosely equatorially based. (There is no word for 'equator' in the astrolabe texts. The celestial equator was not known for most of the history of Mesopotamian astronomy. In Mesopotamian astronomy there was no coordinate system based on the celestial equator.) Prior to circa 1100 BCE, in the so-called astrolabe texts (based on the 3 ways/paths of Ea, Anu, and Enlil), the positions of celestial bodies were cited with respect to the particular path at the horizon. After circa 1100 BCE the system of 17/18 marking stars/asterisms "in the path of the moon" was used. Later, this system was replaced by the zodiac (which has survived to the present day in the Greek constellation set). The method used in the Seleucid period (312/311 BCE-64/63 BCE) for non-mathematical astronomical texts involved the positions of celestial bodies (longitudes) being located with reference to another system of marking stars; the approximately 30 "standard" stars/asterisms along the ecliptic called (after Epping's terminology) Normalsterne/Normal-stars (but 'counting stars' is a better descriptor). Concurrently, the Seleucid period mathematical astronomical texts expressed longitudes in degrees within the 12 zodiacal signs, estimated from a "vernal point" (established by a bright star).

In marking the celestial sphere the concepts used represent the projection of features of the terrestrial environment and scheme of cartography i.e., the 3 celestial roads/paths, and the horizon as the "cattle pen" with the celestial bodies designated the "cattle" and "sheep." In Sumerian and Akkadian mythological poetry heaven and earth were counterparts. Heaven (divine AN) was paired with "earth" (divine KI). "Earth" (ersetu) included everything that lay under heaven. (The most common names for 'heaven' in all periods - both as a whole and for individual levels - is Sumerian singular noun AN (also a god name) and Akkadian plural noun šamû. Numerous examples of AN = šamû appear in bilingual texts and lexical lists.) In texts AN frequently occurs as a name for all of heaven with KI ('earth'), forming the cosmic pair AN.KI. AN and KI were the 2 principal and inseparable parts of physical space. This idea led to terrestrial cartography/metrology terms being used to describe celestial cartography.

According to the assyriologist Wayne Horowitz the Mesopotamian sky was geometric in nature - it was created using rectangles.

By the early 1st-millennium BCE ways to measure time at night was the rising, culmination, and setting of stars/constellations.

The methods of Babylonian astronomy were different from anything else known and were considered to be unique. However, traces of it began to be found in Greek and Indian astronomy, and then in Demotic texts from Egypt. (Demotic script is Egyptian hieroglyphic writing of cursive form that was used in handwritten texts from the early 7th-century BCE until the 5th-century CE.). With the discovery by Alexander Jones of nearly 200 Greek astronomical texts (dating from the 1st-century CE) amongst the papyri in Demotic script recovered in the 19th and 20th centuries at Oxyrhynchus (a city in Upper Egypt, located about 160 km south-southwest of Cairo) it is now known that astronomy reflecting cuneiform sources was contemporary with Claudius Ptolemy. The astronomical papyri contain 2 types of astronomy being practiced at Oxyrhynchus: Greek kimematic/geometrical and Babylonian arithmetical. The astronomy being practiced at Oxyrhynchus was computational; no evidence of astronomical observations exist. The majority of the astronomical papyri were connected with practical astrology. In his book, Alexander Jones has grouped the astronomical papyri into 5 categories (Astronomical Papyri from Oxyrhynchus (2 Volumes, 1999): (1) theoretical and instructional texts, (2) primary tables, (3) ephemerides and almanacs, (4) miscellaneous tables, and (5) horoscopes.

During the 2nd and 1st millennium BCE knowledge of Babylonian astronomy and omenology reached Egypt, Palestine/Israel, Anatolia, India, Greece, and eventually even China. Interchange of Babylonian astronomy with the west was particularly prevalent during the Hellenistic period.

Babylonian astral records comprise 3 main groups of materials: (1) a large omen literature going back to the early 2nd-millennium BCE; (2) the Letters and Reports by scribes to the Assyrian kings (dating mostly from the mid 7th-century BCE); and (3) the Astronomical Cuneiform Texts, Goal Year Texts, Almanacs, etc. (dating from the late 4th-century BCE), that incorporated sophisticated arithmetical models. (Goal-year texts contain collections of past astronomical records, likely abstracted from the Astronomical Diaries, used in the prediction of astronomical events. for a particular "goal-year." Surviving goal-year texts are dated within the period 236-24 BCE.) The early omen literature and so-called astrolabe texts are from Babylonia. The Assyrian period astrological reports are from Nineveh. Cosmology and the observation and interpretation of astral phenomena formed a major field of 1st-millennium BCE Mesopotamian scholarship. During the 8th and 7th centuries BCE, reports of astronomical observations and their interpretation per omenology were regularly sent to the Assyrian kings in Nineveh. The largest variety and largest number of astronomical texts are from Babylon. Astronomical texts (both observational and mathematical) have also been recovered from Uruk but date circa 500 BCE to 150 BCE. There is no firm evidence for similar long-term systematic observational programs in other Mesopotamian cities other than Babylon and its circa 800 year Astronomical Diary program. At Babylon, systematic observations of celestial events began during the mid 8th-century BCE and continued to the 1st-century CE. By the 4th-century BCE sophisticated/complex mathematical schemes had been developed for calculating lunar and planetary phenomena.

The earliest records of Babylonian astronomical observations are the so-called Venus tablets which were written to catalogue Venus omens for the king Ammisaduqa (reigned 17th-century BCE). These particular Venus observations were made in order to provide empirical material for omina. The later Astronomical Diaries and related texts include some 200 records of eclipse observations and predictions. It was only circa the middle of the 7th-century BCE that the practice of keeping permanent records of regular (systematic) astronomical observations began in Babylon. The record-keeping is preserved in the so-called Astronomical Diaries. (The Astronomical Diaries are one of the largest collections of observed data for any period in world history before the modern era. They also the most important source on various aspects of Late Babylonian history.) Note: There are reasons for regarding the so-called Astronomical Diaries and Chronicles as being closely connected. The Mesopotamian (i.e., Assyrian and Babylonian) Chronicles are histographical texts (official records of the royal court) dealing mostly with the 2nd half of the 2nd-millennium BCE and the entire 1st-millennium (to the first century BCE).

There is a paucity of astronomical texts between the Hittite solar omen ("omen of the sun god")/solar eclipse (unknown whether referring to total or annular of several solar eclipses at that period) text (KUB 14.4) of 1335 BCE during the reign of the Hittite king Mursilis II (circa 14th-century BCE) and the reign of Bel-ibni, a Babylonian nobleman who served as king of Babylon for several years as the nominee of the Assyrian king Sennacherib (circa late 8th-century BCE). All that exists in between is the limmu (eponym) list of Bur Sagale (Bur Saggile) (in the reign of king Assur-din III), who witnessed an Assyrian total solar eclipse in 763 BCE. What does exist as records of general Mesopotamian astronomy of the late 2nd-millennium BCE and early 1st-millennium BCE are: (1) the astrological omen series Enuma Anu Enlil, (2) the compendium Mul.Apin, (3) various star lists, and (4) Late Assyrian astrological reports.

Mesopotamian astronomy until the Assyrian period is largely qualitative. Observations during this period of the history of Mesopotamian astronomy show little exactness. It is only from the Assyrian period that systematic observational reports begin to appear and the mathematical treatment of astronomy begins. See also: George, Andrew and Al-Rawi, Farouk. (1991[-1992]). "Enuma Anu Enlil XIV and other early astronomical tables." (Archiv für Orientforschung, Band 38-39, Pages 52-73). The cuneiform material shows the Babylonians used simple mathematical relations for the length of daylight as a function of day of the year. Originating during the Old Babylonian period, it was retained in use. Also, the Babylonians retained their belief that their computations applied only within the narrow area from Uruk to Babylon.

Note: Regarding Tablet 63 of the Enūma Anu Enlil series. The issue is whether it contains real observations or not. An astronomical text with omens, or an omen text related to actual observations or not? The tablet contains a sequence of omens relating to the first visibility/appearance and the last visibility/first disappearance of Venus. Uniquely, unlike the other omens in this omen series, they are associated with specific dates covering the 21 years of the reign of king Ammisaduqa. (Ammisaduqa was the 10th and next to last king of the Old Babylonian dynasty (= First Dynasty of Babylon) The last king of the Hammurabi dynasty was Samsuditana, the successor of Ammisaduqa.) The tablet supposedly records an actual series of observations of Venus. Because the omens are associated with actual dates it has usually been accepted that the omens relate to actual observations of the phenomena of Venus. However, it is well understood that omen statements are not reports of actual observations, but refer only to potentially observable events. This fact is clear from the large number of omens that relate to events that are in fact impossible.

It was understood the planets ("wild sheep") do not appear in the same place with respect to the eastern or western horizons at their first and last visibilities. This prompted a rough estimate of the intervals of their visibility and invisibility to be made.

The stars visible in the Babylonian night sky were originally divided into into 3 paths (ways) = the night sky was divided into 3 parts = northern, central, and southern regions. The stars of the path of Enlil in the northern region of the sky are, in modern terms, estimated to be within + 17 degrees of declination north. The stars of the path of Ea in the southern region of the sky are, in modern terms estimated to be within - 17 degrees of declination south. The stars of the path of Anu, located between the north and south paths, in the central region (but not strictly an equatorial band), are in modern terms, estimated to be within + 17 degrees of declination north and - 17 degrees of declination south. This system originated in the Old Babylonian period and continued until the Neo-Babylonian period.

Mesopotamian astral science was applied science. The study of the sky by the Babylonians was undertaken by the intention to acquire advance knowledge of future events for the king and/or state. The work continued uninterrupted by political turmoil. The scholars and scribes involved in studying astronomy and astrology were based at the palace or in temples. Early Babylonian astronomy was very much concerned about astronomical phenomena at the horizon. The horizon was a key reference point. It provides the basis for accurate measurements of how things are changing in the sky. It is more difficult to accurately measure items above the horizon i.e., overhead. Also, by the 1st-millennium BCE there was much within Babylonian astronomy that was theoretical rather than empirical. Aspects of Babylonian astronomy also conformed to/were shaped by beliefs involving omenology.

Basic stages in the development of astronomy are: (1) the astronomy of the Astrolabe genre; (2) the more accurate astronomy of Mul.Apin (a compendium of star lists and schematic methods of calculating astronomical phenomena); and (3) the principles of the emerging mathematical astronomy of the Late Babylonian period. "Major deities such as Marduk, Anu, Enlil, and Ea were believed to have arranged the stars in heaven in early times, and gods are often identified with stars and constellations in astronomical works such as the "Astrolabes" and Mul-Apin." (Mesopotamian Cosmic Geography by Wayne Horowitz (1998, Page 8).)

For most of its history Babylonian astronomy was observational and descriptive, and based on an ideal scheme of the universe per the astrolabe astronomy organised by the god Marduk. It never really became theoretical and mathematical until the Neo-Babylonian period circa 500 BCE. (Marduk used the body of Tiamat to create the celestial sky, and he also the stars and the progression of time.)

Note: With the Hittite raid in 1595 BCE and the collapse of the Old Babylonian political system much in the way scribal culture also disappeared, and with it disappeared much in the way of mathematics.

Over the 700-800 years covered by surviving cuneiform tablets (since the 8th-century BCE) dealing with astronomy there is an identifiable development in both accuracy and regularity of observation. The few surviving cuneiform tablets dealing with astronomy during the 8th-century BCE indicate an advanced level of both skill and observation. There are insufficient surviving/recovered astronomical tablets to trace the earlier history of astronomy in Babylonia and understand how many centuries it took to develop these capabilities.

The assyriologist David Brown (2000) has made a compelling case that prior to the mid 8th-century BCE there was no interest in predicting celestial events. (Over 100 years ago Franz Kugler, the pioneer of much of our knowledge of Babylonian astronomy, made a similar case.) The period schemes, intercalations, rules, etc. found in such late 2nd millennium texts as Enūma Anu Enlil, and Mul.Apin are aspects of celestial divination, not primitive astronomy or inaccurate astronomy. Even the so-called 'astrolabes' are primarily astrological documents. Only after the mid 8th-century BCE was there a goal to predict celestial phenomena accurately (i.e., to perhaps a day). The Babylonian astronomical techniques that reached their highest point in the Seleucid period circa 200 BCE originated a half a millennium earlier, circa 700 BCE, when prediction became an all-important skill to the astronomers who practised astrological divination in the service of the Assyrian kings. According to David Brown (2000) through divinatory thinking an ideal state (scheme) of the universe was devised. In general, astral omens were not based on empirical observations. Rather they were developed through the application of a strict code. Observations were contrasted with this ideal representation of the universe and mismatches were interpreted as bad omens.

Also, other considerations added to the development of ideal schemes. A 12-month, 360-day year for administrative purposes appears in documents from Uruk from the end of the 4th-millennium BCE (circa 3200-3000 BCE), and is well consolidated by the Ur III period a millennium later. The earliest influential schematic calendar (12 months of 30 days each) dates from the Ur III period (Third Dynasty of Ur i.e., based in the city of Ur) in the last part of the 3rd-millennium BCE (circa 2112 BCE to circa 2004 BCE).

Source: Before Nature: Cuneiform Knowledge and the History of Science by Francesca Rochberg (2017, Page 121).

According to David Brown, the importance of celestial divination texts in the Neo-Assyrian period, and the special place of omen specialists in the royal court brought about the circumstances that eventually led to mathematical astronomy. Prediction of events in the sky began to be a key purpose of the activity of scholars at the Assyrian court in the 7th-century BCE who were involved with the interpretation of celestial omens for the king. Centuries later the prediction of some celestial events was achieved by both mathematical and other procedures.

The high astronomical achievements of the Babylonians are found in the Hellenistic period in the ephemerides, the tables for calculations of new moons and eclipses, and in the planet tables. (By the Seleucid Era, the Babylonians had developed tables for predicting eclipses.) The Babylonians are the first civilization known to possess a functional theory of the planets. They produced individual planetary tables, in particular of Venus.

After circa 750 BCE Babylonian astronomy was developed primarily as mathematical theory (for being able to know/determine (predict) where the positions of the moon and planets would be in the night sky). In the 7th-century BCE, for the first time, Babylonian scholars try to foresee when and where certain phenomena in the sky will happen. (Babylonian mathematical astronomy can be divided into 2 main areas: lunar theory and planetary theory.) The main focus of their effort was solving predictive problems relating to the motions of the moon and planets. In the late 1st-millennium BCE the Babylonians developed sophisticated theories for the motions of the planets. (Babylonian planetary theory was based more on conjunctions with the sun and moon than on conjunctions with the stars.)

Swerdlow has proposed that adverse weather led the Babylonian scribes to develop a mathematical theory of the moon and planets. When the skies were clear then observation of astronomical data for inclusion in the Diaries. When the skies were cloudy/rainy then computation of astronomical phenomena for inclusion in the Diaries.

All cuneiform tablets with mathematical astronomy have been found in the ancient cities of Babylon and Uruk. Both were major Babylonian cities and centres of learning. The mathematical astronomical texts were written between circa 380 BCE and 48 BCE. The mathematical astronomical texts from Babylon cover this entire period. The majority of extant tablets were written after circa 220 BCE. The mathematical astronomical texts from Uruk are fewer and none are later that circa 170 BCE. Mathematical astronomy was used for predicting a wide range of phenomena connected with the Moon, the Sun, and the planets. The earliest known form of mathematical astronomy in antiquity was developed in Babylonia in the 5th-century BCE. Rapid development of mathematical astronomy is indicated with the algorithms reaching their final stage of development by circa 350 BCE - 310 BCE. Hence the formative period of Babylonian mathematical astronomy is circa 400 BCE - 330 BCE. The beginning of Babylonian mathematical astronomy is dated to circa 400 BCE with the invention of the zodiac of 12 equal divisions as a coordinate system. The zodiacal coordinate system became an essential part of mathematical astronomy for computing (predicting) the positions of the Moon, the Sun, and the planets. The lunar tables are the most sophisticated and may contain up to 21 columns, each column tabulating a different astronomical quantity. Babylonian mathematical astronomical texts are dominated by synodic tables. However, the application of such is unidentified. In the Seleucid era the beginning of the lunar month was no longer established by observation of the first lunar crescent, but by predicting it. However, apparently this was not done using the algorithms of mathematical astronomy.

The mathematical basis of Babylonian planetary theory is set out in the form of either 'procedure texts' or as (tabular) 'ephemerides' i.e., tables enabling at least approximate prediction of future lunar and planetary phenomena. 'Procedure texts' contain collections of rules for the computation of 'ephemerides' i.e., explain the calculations for synodic or heliacal phenomena comprising the 'ephemerides.' Most of the predictive Babylonian planetary models that have survived are usually empirical and arithmetical (based on numerical sequences), and usually do not involve geometry, cosmology, or speculative philosophy. 'Procedure texts' date from the Seleucid era. A 'procedure text' (or 'proto-procedure text' representing a non-ACT approach to calculating solar and lunar motion) that may antedate the Seleucid era  is BM 36712. During the Seleucid period (3rd-century BCE) 'goal-year texts' (related to the nontabular 'diaries' (= based on information excerpted from at least more than 12 diaries) and involving simple predictive methods) were used to predict the movements of the planets for a given year. Specifically, 'goal-year texts' "present for a given year the planetary data (dates of the Greek-letter phenomena [synodic or heliacal] and of the passing by of the Normal Stars by the moon and planets) for a certain number of years previous to the given year for each planet. ... There is also a column of lunar phenomena, that is, the occurrences of lunar eclipses and the "Lunar Six," .... (Astral Sciences in Mesopotamia by Hermann Hunger and David Pingree (1999, Pages 167-168)." (Goal-year texts, in summary, contain Lunar Sixes, planetary phases, conjunctions of planets and (= with) Normal Stars, and eclipses.) During this period use of mathematical models replaced use of records of past observations to enable prediction. Most of the 'ephemerides' give calculated dates and longitudes for the synodic phenomena (including distinguishment of conjunctions, oppositions, and stationary positions). Very few give data for the planet between the synodic phenomena. For an inner planet (Mercury, Venus) the synodic phenomena are (1) its first appearance in the morning, Morning First; (2) its subsequent disappearance, Morning Last; (3) its first appearance in the evening, Evening First; (4) its disappearance in the evening, Evening Last; and (5) its stationary points. For an outer planet (Mars, Jupiter, Saturn) the synodic phenomena are (1) its first appearance in the morning, Morning First; (2) its disappearance in the evening, Evening Last; (3) opposition; (4) the beginning of retrogression, Beginning Retrogression; and (5) the end of retrogression, End Retrogression.

System A and System B are arithmetical schemes for computing the position of the sun, moon, and the planets. The variable velocity of the sun, moon, and planets was taken into account in 2 ways: (1) either by the abrupt alternation of larger and smaller values, or (2) by means of values zigzagging up and down between 2 constant extremes. System A uses 'step functions' and System B uses 'linear zigzag functions.' When graphed, the motion of System A looks like a series of steps up and down, and so it is called a 'step' function. System A is more primitive than System B. The earliest preserved System A clay tablets (BM 36651, 36719, 37032, 37053) calculate an ephemeris for the planet Mercury from 424–401 BCE. Even though System B might appear to be a very rough tool for modelling periodic phenomena it is a very convenient computation. It is constructed in such a way that it exactly satisfies a certain period relation. Though at any given time the function may deviate from the empirical (observational) data, there is no accumulation of errors. There are large differences between lunar systems A and B and the planetary systems A and B.

The zigzag and step are useful labels but potentially misleading as the Babylonians are not known to have used graphs. There is no evidence that the Babylonians constructed kinematic/geometrical models of the motions of celestial bodies. There is no evidence they were concerned about the causes of the motions. Also, there is no evidence that they were curious about the physical composition of the celestial bodies. The goal of ancient Babylonian astronomy was to predict astronomical appearances but not to make any further sense of them. Predicting positions did not require any theoretical ideas about the celestial bodies. The Babylonians made astronomical observations and formulated algebraic rules for predicting future positions of the planets, the Sun, and the Moon. They studied how the celestial motions went but not why. Nor did they try to develop a single comprehensive mathematical scheme that encompassed all their data. Otto Neugebauer concluded that Babylonian astronomical texts of the Seleucid period are scientific because everything has been eliminated from the astronomy except observations and the mathematical consequences of an initial hypothesis about the fundamental character of the movements. (Greek astronomers dealt with planetary motions differently to the Babylonians.)

Within the genre of mathematical astronomy texts, copies of texts are recognizable when numbers that are obviously errors (usually typical copyist errors) do not affect the subsequent calculations recorded.

There are 2 important classes of texts in Babylonian mathematical astronomy: ephemerides and procedure texts. Babylonian astronomy, in its most developed and valuable form, comprised the establishment of numerical relationships with the succession of specific celestial phenomena that preoccupied them. During the late period of Babylonian mathematical astronomy various different predictive methods were in use at the same time (there were 5 major systems), and all were considered equally legitimate.

Babylonian Lunar Six. Source: "Babylonian Lunar Six." by Peter Huber and John Steele (SCIAMVS 8, 2007, Pages 3-36), Pages 3.

Babylonian Greek Letter Phenomena for the Planets.

It has been remarked that Babylonian mathematical astronomy appears rather suddenly, without any apparent connection with earlier astronomical texts. This is not quite correct. Several important improvements in observational techniques established the basis for mathematical astronomy. These were the keeping of Astronomical Diaries beginning under king Nabonassar (Nabû-nāşir) in the 8th-century BCE and the later recording of helical rising phenomena beginning circa 500 BCE (but tracing back to the period of the last Sargonids in the 7th-century BCE). The basis for Babylonian mathematical astronomy was the information recorded in the so-called Astronomical Diaries. The fundamental observational text of the Babylonian astronomers, for astronomical, and meteorological data such as types of clouds, rainbows, etc., was the Astronomical Diary. They also contained predictions based on astronomical observations. Additionally, the Astronomical Diaries contain the same kinds of entries for solstices and equinoxes and the Sirius phenomena as recorded in the Almanacs and the Normal Star (NS) Almanacs. The Astronomical Diaries recording project was conceived of and designed circa the middle of the 8th-century BCE (and likely the beginning was the 1st year of king Nabû-nāşir, 746 BCE. The project was then dependably implemented for at least 700 years. The type of information collected and recorded remained almost stable. From the earliest, the astronomical data recorded is also accompanied by terrestrial data: historical comments, ominous events, river levels, market prices, and such. The Astronomical Diaries began by recording data in a simplistic manner but soon used a more exact terminology. The Astronomical Diaries rapidly became records of those phenomena that were recognised to be predictable, with the aim of providing a database that made these phenomena still more accurately predictable. (In the Astronomical Diaries the phenomena dealing with the moon were the most important of the astronomical events recorded. In addition to recording a variety of observed astronomical and atmospheric phenomena, the Astronomical Diaries also record historical, economic, and ecological observations.) The fact that only astronomical phenomena which are periodic and therefore capable of being described mathematically are included - and almost all of the phenomena regarded as ominous in the series Enūma Anu Enlil were constantly ignored, even though still constantly observed, recorded, and interpreted for the royal court at Nineveh - leads to the conclusion that the astronomical observations entered into the Astronomical Diaries (both observations and approximate estimates when observations were unable to be made) were from the beginning of the project intended to be the basis of a mathematical, predictive system. (See: Astral Sciences in Mesopotamia by Hunger/Pingree (1999) Page 144.) The Babylonians used criteria (not yet known) to estimate the "ideal" dates of the planetary phenomena. The ability to predict astronomical phenomena offered new scope for prognostication.

Note: The Diaries are called Astronomical Diaries because they mostly record astronomical and meteorological phenomena. The Diaries are divided into sections with each section recording the almost day-to-day events of one month. At the end of each section there are statements about market prices, the height of the river, and matters of historical interest.

Circa 700 BCE a system of "counting stars" were established - but for some reason unevenly distributed - around the proximity of the ecliptic (i.e., within the path of the moon and planets). The Normal Stars were used as observational reference points and provided the basis for a positional system. Distance with respect to a particular Normal Star was noted in cubits and fingers. Normal Stars are particularly used in the Astronomical Diaries. There is no standardised/complete list of Normal Stars - about 34 Normal Stars are known.

Late Babylonian astronomers used a reference system based on a local observer. Babylonian astronomers measured the sky with their hands. When the arm is extended out the little finger has an apparent width of 1° and the hand span (the distance between the ends of the thumb and little finger) has an apparent width of 15°. The positions of stars in the night sky were measured according to: (1) their altitude (the angle above the observer's horizon), or elevation, in degrees between the horizon (0°) and the zenith (90°) and (2) their azimuth (the angle measured clockwise from north along the horizon to the point on the horizon that lies beneath the star) in degrees from north (0°), east (90°), south (180°) or west (270°). The meridian is an imaginary large circle that passes through the zenith from north to south, dividing the sky in two: the eastern and the western halves. When an object crosses the meridian it has reached its maximum height in the sky. The Sun, or any star culminates when it crosses the (line of the) meridian. (The Sun crosses the line of the meridian around noon every day.) The meridian covers a total angle of 180° (-90° to 90°) and the horizon a total angle of 360°.

A sophisticated system of Babylonian stellar coordinates did not exist until circa the 3rd-century BCE. From the earliest period of Babylonian astral science - the Old Babylonian period dating to the early 2nd-millennium BCE - to the 8th-century BCE a system of 3 "paths" and constellations was used. From the 8th-century BCE to the Seleucid period the position of the moon and planets was given by describing their distance from nearby bright stars or constellations. However, there was no rigidly defined standardised system in place. The earliest known systematic use of spherical coordinates is found in Babylonian astronomical texts dating to the Seleucid period. It comprised a form of ecliptic coordinates. During the last 3 centuries BCE systematic ephemerids for the moon and planets were computed. (According to Otto Neugebauer the completeness of the Babylonian source material makes it unlikely that lunar and planetary ephemerids were computed earlier than the middle of the 3rd-century BCE.) In the ephemerids ecliptic coordinates are used by giving longitudes expressed in degrees in relation to zodiacal signs, and - in the case of lunar ephemerids only - latitudes in degrees north and south of the ecliptic.

Calendar issues contributed to the development of Mesopotamian astronomy. 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.

Circa the 7th-century BCE, at the time of Assurbanipal, the class of sky observers were beginning to understand that the 'mechanics' of the sky is geometric in nature and working with this realisation mathematically eventually led to the more precise mathematical astronomy of the Seleucid period. The establishment of ziqpu stars in the Path of Enlil, and ponderings on stellar motion in the Path of Enlil, contributed to such. Astronomical cuneiform texts from the 6th to the 4th centuries BCE show intermediate stages before the emergence of the fully developed systems of Babylonian mathematical astronomy.

Likely the Babylonians used a simple instrument - similar to the medieval Jacob's staff, which used a graded movable cross-bar - which simplified calculating angular distance between 2 celestial objects (i.e., stars or planets). A Jacob's staff was in use in 284 BCE by Aristarchus.

The later mathematical basis of Babylonian planetary theory (derived from Astronomical Diaries) is set out in the form of either 'procedure texts' (containing collections of rules for the computation of 'ephemerides') or as (tabular) 'ephemerides' i.e., tables enabling at least approximate prediction of future lunar and planetary phenomena. Babylonian Goal-Year texts contain collections of 'raw' astronomical observations (derived from Astronomical Diaries) to make predictions of future astronomical (lunar and planetary) phenomena (for a given year = the "goal year") using known lunar and planetary periodicities. (John Steele makes the point that Goal-Year texts contain collections of (mainly) observational data that could be used in making predictions for that year (rather than a coming "goal-year").) Babylonian almanacs contain collections of predicted astronomical phenomena for a given year. However, the Almanac data is not excerpted from observational texts (Astronomical Diaries) but is computed. Almost all lunar and planetary ephemerides date from the 3rd to the 1st centuries BCE. The so-called 'Goal-Year' texts are contemporary with the ephemerides.

The observational (empirical) data on which Babylonian theoretical astronomy is based is recorded in the so-called Astronomical Diaries. The Astronomical Diaries were a system for accurately describing astronomical phenomena based on regular daily observations. These were meticulously maintained daily records of certain celestial events, kept for circa 800 years from circa 8th-century BCE to the 1st-century CE. The Astronomical Diaries show that the Babylonians were primarily interested in observing cyclical phenomena. The observations in the Astronomical diaries are written in a very abbreviated form of cuneiform script.

The Astronomical Diaries give the time of heliacal phenomena of the planets to the day of the calendar month and the location by zodiacal sign, sometimes specifying beginning or end of zodiacal sign. Also recorded in the Astronomical Diaries was the planets' passings of the Normal Stars, and each other. The moon and the planets are usually stated to be "above," "below," "in front of" (= to the west), or "behind" (= to the east), a Normal Star, and the distances are given in 'cubits' and/or 'fingers.' The only aspects of solar motion recorded in the extant Astronomical Diaries are the dates on the occurrences of the solstices and equinoxes and of the heliacal rising and setting and the acronychal rising of Sirius. Some of these dates for solstices may be based on actual observations, and not computed (= the statement "I did not watch"). The Astronomical Diaries provide a full listing of both lunar and solar eclipses, observed and predicted. Most Astronomical diaries extant cover the period from 385 BCE to 60 CE.

Early Babylonian astronomy was computational. Only from the Seleucid period were there any attempts by the Babylonians to construct mathematical models. The earliest form of mathematical astronomy exists in cuneiform tablets from Babylon and Uruk. Babylonian astronomy acquired complex numerical methods in the Hellenistic Period. (The Mesopotamians used arithmetic and a kind of proto-algebra. The Greeks used geometry.) By at least 600 BCE, methods of predicting the beginning of the new month (indicated by the new moon crescent) up to 18 years in advance had been developed, long with techniques for predicting the months and times at which eclipses of the sun and moon were likely to happen, and certain planetary phenomena. By the end of the 5th-century BCE, complex mathematical techniques were being applied to theoretical systems for calculating lunar and planetary phenomena. Most of the astronomical mathematical texts are ephemerides for the moon and the planets, and also procedure texts which contain rules for computing the ephemerides. There are approximately 300 mathematical astronomical texts known. There are approximately 1500 observational texts (mostly Astronomical Diaries) known.

During the 2nd-half of the 1st-millennium BCE prediction, calculation, and observation were practiced together by the same scribes. Note: The work of Otto Neugebauer (ACT (1955)) shows there is no evidence of empirical corrections within ephemerides.

"Celestial omens are among the oldest ones attested so far. The first collections of them appear in the first half of the 2nd millennium BCE, and concern mostly lunar eclipses. These texts already have a highly structured form, which suggests that they were developed by scholars skilled in the observation of patterns of astronomical phenomena. It should be emphasized, however, that omens from the sky did not play an important role in early times. Divination from the liver of sheep was far more frequent. Only in the first millennium BC did celestial divination become a dominant source of signs. The interest in it, however, had existed for centuries before that, and the pertinent omens were collected like others too. This finally lead to the organisation of celestial omens into an extensive edition comprising about 70 tablets [Enuma Anu Enlil].” Hunger, Hermann. (2011). "The relation of Babylonian astronomy to its culture and society." In: Valls-Gabaud, D. and Boksenberg, A. (Editors). The Role of Astronomy in Society and Culture. Proceedings of the IAU Symposium No. 260, 2009. (Page 66).) It is not possible to say exactly when the omen series Enuma Anu Enlil was compiled but it is thought it was done in the late 2nd-millennium BCE.

The Babylonian astral sciences were carried out by a group of priestly literati within the institutional framework of the great and enduring temples of Babylon and Uruk. In effect, Babylonian professionals systematically observing the sky for purposes of celestial divination developed possession of a quantitative and predictive astronomy. There is nothing in the texts comprising mathematical astronomy that set out: (1) what the practitioners believed they were doing, and (2) what the practitioners believed the heavens were doing. Babylonian astronomy, though technically sophisticated, was not theoretical. Speculation was confined to the content of myths. Babylonian astronomers were analytical (as example: focused on the predictability of astral phenomena) but never tried to explain observational facts.

Also, primitive forms of celestial divination or astrology did not stimulate the growth of scientific astronomy. From the Old Babylonian period onwards, astronomical observation and divination went hand-in-hand until at least the 8th-century BCE. The American assyriologist Erica Reiner (1924-2005) believed that omen astronomy and mathematical astronomy were separate disciplines of scholarship; especially from the 5th-century BCE onwards. The period between 400/450? and 200 BCE might be considered the last period of innovations in Babylonian astral science It was during this period that the zodiac and the horoscope were invented. The Babylonian zodiac developed from the tradition of a series (17/18) constellations (stars/asterisms) marking the path of the moon.

Babylonian astrology was concerned with the welfare of the state and the king (and it was not horoscopic). Only in Hellenistic astrology was the horoscope of the individual introduced. Omens had importance in the Neo-Assyrian empire (Neo-Babylonian/Assyrian period). The rulers of the Persian (Achaemenid) and Macedonian/Greek (Seleucid and Parthian) empires who successively conquered Mesopotamia took little interest in traditional Babylonian omenology and its focus on the State. Introduced by the Babylonians was horoscopic (zodiacal) astrology involving forecasting the future for individual patrons. All the Babylonian horoscopes are dated to the birth of an individual. The pinnacle of Babylonian astrological influence was reached during the Hellenistic period. Astrology, based on an ancient Babylonian and Egyptian astral beliefs, took shape in the 3rd-century BCE. Extispicy (divination using entrails of sacrificed animals) was astrology's closest rival. Also, "The computational systems of Babylonian mathematical astronomy, which emerged at about the same time as did horoscopic astrology, cannot be accounted for by reason of their serving astrological purposes." (Rochberg, Francesca. "Babylonian Horoscopy: the Texts and their Relations." In: Swerdlow, Noel. (Editor). Ancient Astronomy and Celestial Divination. (1999, Pages 39-59; Page 55).

"In the second half of the first millennium BCE, new techniques were developed to gain insight into the future. One of them is found in what is loosely called horoscopes. It is not really correct to call these Babylonian texts horoscopes because they lack the consideration of the point of the ecliptic rising at the time of birth, which is called horoskopos in Greek. So the very detail from which the name horoscope is derived is not present in them. There are about 30 such texts known; the earliest two of them are datable to 410 BCE. They may be considered precursors of later Hellenistic horoscopes in the sense that they record computed astronomical phenomena on the date of birth." (Hunger, Hermann. (2011). "The relation of Babylonian astronomy to its culture and society." In: Valls-Gabaud, D. and Boksenberg, A. (Editors). The Role of Astronomy in Society and Culture. Proceedings of the IAU Symposium No. 260, 2009. (Page 72).)

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.

After circa 300 BCE, Babylonian culture was subsumed under Greek culture.

Whoever transcribed the Babylonian astronomical data into a format that the Greek astronomers could use must have understood the difficult and specialised Babylonian terms used in mathematical cuneiform astronomy. They were understood by relatively few scribes. The person must have been a Babylonian astronomer having full access to the Babylonian archives. It is highly unlikely to have been a Greek astronomer. We are informed that Callisthenes, Alexander's scholar-in-residence, who certainly stayed in Babylon, caused a lot of Babylonian data to be sent to Athens. There are approximately 20 so-called Graeco-Babyloniaca clay tablets that have been dated from the 1st-century BCE to the 2nd-century CE. They have Sumerian and/or Akkadian script on one side and the same text transliterated in to Greek on the other. Joachim Oelsner (1973) held that the so-called Graeco-Babyloniaca were the final form for the preservation of Sumerian and Akkadian texts when when knowledge of cuneiform was extinct. The Hellenistic Greeks who established colonies in Mesopotamia were basically in Uruk - not Babylon. They were interested in temple/cult issues and a number of them married local women.

Basic Mesopotamian Terms for Phenomena Observed in the Visible Heavens

Term Meaning in Mesopotamian Astral Sciences
Sumerian logogram: mul; = Assyrian: kakkabu The electronic edition of The Pennsylvania Sumerian Dictionary (PSD) basically states: mul (shine) means "star; to shine, radiate (light) ...." and references Early Dynastic IIIb Period (circa 2540-2350 BCE); Lagash II Period (circa 2141-2122 BCE), and Old Babylonian Period (circa 1900/1800-1600 BCE). The assyriologist John Heise (Akkadian Language (1996) discussing signs used as determinatives has: "MUL (before) stars and constellations ... meaning Sum[erian] mul 'star', Akk[adian] kakkabu(m) 'star'.") The assyriologists Michael Rolf and Annette Zgoll also state ("Assyrian Astroglyphs." ZA, Volume 91, 2001) that MUL is a Sumerian logogram that means "star." (To date I have only seen 2 sources state that MUL can mean 'a star' or 'a star constellation.' However, no date references are given for this latter assertion. The assyriologist Jeanette Fincke states that 'MUL' refers to individual stars as well as constellations. The assyriologist Wayne Horowitz (2014) writes that the determinative mul (Sumerian) = kakkabu (Akkadian) was used to "refer to to a full range of observed astronomical phenomena including the fixed stars, but also constellations, planets, mirages, comets, shooting stars, etc." Horowitz adds that most often what is meant is a constellation.) A cursory read of the literature shows that the replicated MUL.MUL means "the stars." Also, MUL.MEŠ means 'stars.' According to the assyriologist Wayne Horowitz (2014), the term MUL.MEŠ may refer to the plurality of stars in constellations. Whilst some people would hold that MUL-AN means "constellation" the PSD basically states: mulan, written mul-an (star), means "heavenly star" and references the term to the Old Babylonian Period. The Chicago Assyrian Dictionary (CAD) identifies that the (Akkadian) term lumāšu means constellation. (According to CAD, the word lumassu can refer to one of several stars whose heliacal rising or setting falls at or near solstices or equinoxes, can be simply a poetic word for stars in general, or can refer to zodiacal constellations.) In Akkadian the term lumāšu referred to the zodiacal constellations and logographically lumāšu was written as MUL.LU.MAS or LU.MAS.ŠI (lumāšu-stars). Picking up on this John Steele writes "The zodiacal signs as a group were referred to using the term LU-MASŬ (Akkadian: lumāsŭ), literally meaning 'constellation'." (See: "Celestial Measurement in Babylonian Astronomy." by John Steele (Annals of Science, Volume 64, Number 3, 2007, Pages 293-325).) It is indicated that MUL, the Sumerian determinative for 'star,' was also generally used to denote all other astral phenomena. There is no exclusive word for constellation. Also, the later Erica Reiner pointed out that the Sumerian dil.bat (DIL.BAT) = "bright or brilliant" = star, and also = Akkadian nebu/nabu (= bright); and Assyrian kakkabu = star.
Sumerian: udu.idem = Assyrian: bibbu (Note: In ancient Mesopotamian usage the 2 categories 'stars' (mul = kakkabu) and 'planets' (udu.idem = bibbu) partly overlap.) In ancient Mesopotamia there were 2 categories of astronomical bodies/objects: 'stars' (mul = kakkabu) and 'planets' (udu.idem = bibbu). The astral category 'stars' includes all astral bodies/objects whose names are usually prefixed with the mul ('star') determinative. These include individual fixed stars, constellations, and the planets. The 7 astral bodies/objects considered planets in ancient Mesopotamia were: the Moon, the Sun, Mercury, Venus, Mars, Jupiter, and Saturn. Excepting for the 5 planets all 'stars' maintain a fixed east-west movement in the sky. This fixed movement is maintained also in relation to the other stars. Also, the position of individual stars in the sky was maintained almost unchanged annually. Because the solar year is 20 minutes longer than the astronomical year, comprising slightly more than 365¼ days (the interval between the the annual helical rising of fixed stars), the discrepancy over 70 years - between solar and true astronomical calendars - is approximately 1 day. This is barely noticeable - if at all - over a single short lifetime expectancy of some 30-40 years in ancient times. The fixed stars were often compared with domesticated sheep and cattle (and goats). The astral category 'planets' appeared to move somewhat independently in relation to the 'stars.' Because of this the planets were compared with wild sheep and given the name bibbu 'wild sheep' in Akkadian/Assyrian. In Mesopotamian astronomy all 7 bibbu were listed as 'planets.' Though the Sun and Moon move from east to west their positions vary in relation to the positions of fixed stars. The planets Mercury, Venus, Mars, Jupiter, and Saturn do not simply move from east to west but sometimes appear to stand still or even move backwards in a retrograde motion. The Akkadian term used for the retrograde motion of the planets is sahāru 'to turn back/'to go around.'

The perpetuation of methods of Babylonian astronomy in Egypt and India during the 1st to 5th centuries CE of the Greco-Roman period. Source: Before Nature: Cuneiform Knowledge and the History of Science by Francesca Rochberg (2016, Page 84).

Appendix 3: The Discovery of Babylonian Use of Geometry With the Planetary Theory for Jupiter

"Ancient Babylonian astronomers calculated Jupiters position from the area under a time-velocity graph." by Mathieu Ossendrijver (sciencemag.org, 29 January 2016, Volume 351, Issue 6272, Pages 482-484). Abstract: "The idea of computing a body's displacement as an area in time-velocity space is usually traced back to 14th-century Europe. I show that in four ancient Babylonian cuneiform tablets, Jupiter's displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time. This interpretation is prompted by a newly discovered tablet on which the same computation is presented in an equivalent arithmetical formulation. The tablets date from 350 to 50 BCE. The trapezoid procedures offer the first evidence for the use of geometrical methods in Babylonian mathematical astronomy, which was thus far viewed as operating exclusively with arithmetical concepts." Acknowledgments: ".... The tablets are accessible in the Middle Eastern Department of the British Museum under the registration numbers BM 40054 (text A), BM 36801, BM 41043, BM 34757 (text B), BM 34081+34622+34846+42816+45851+46135 (text C), BM 35915 (text D), and BM 82824+99697+99742 (text E). H. Hunger (Vienna) is acknowledged for providing an unpublished photograph of BM 40054."

At the time of publication Mathieu Ossendrijver is Professor of History of Ancient Science at the Humboldt-Universität zu Berlin. His main interests are Babylonian astronomy and mathematics between 750 BC and 100 AD, in particular Babylonian mathematical astronomy, transformations of science and contextual aspects of Babylonian science during this period. Mathieu Ossendrijver is working on a new edition and analysis of all cuneiform tablets with mathematical astronomy (procedure texts and tabular texts). A monograph with new editions of the procedure texts and a semantic, mathematical and astronomical analysis of these texts appeared in 2012. A 2nd volume devoted to the tabular texts of this corpus is under preparation.

Ossendrijver translated several Babylonian cuneiform tablets from 350 BCE to 50 BCE and found that they contain a sophisticated calculation of the position of Jupiter. (Mathieu Ossendrijver spent 13 years deciphering the 4 tablets.) Ossendrijver knew that 4 of the tablets described such calculations, and probably were connected with astronomy. But he unsure until he found and translated a 5th tablet in 2014, after receiving an old photograph of it from a colleague. That tablet contained a set of instructions for calculating Jupiter's movement using geometric principles - exactly the procedures laid out in the other 4 tablets. The new evidence reveals that Babylonian astronomers in the several centuries BCE, apart from complex arithmetical methods, also employed sophisticated geometric methods that used a forerunner of calculus to do it: They calculated the area under a curve - a basic operation in calculus - in a graph of Jupiter's velocity versus time. The method (which anticipates integral calculus) relies on determining the area of a trapezium under a graph. This technique was previously thought to have been invented at least 1400 years later in 14th-century Oxford. In the 1950s Otto Neugebauer, described 2 tablets from the later Babylonian period, that appeared to describe some trapezoid calculations related to astronomical observations. However, it was not clear what the Babylonian astronomers were calculating.

Ossendrijver was alerted to the existence of several other unexamined ACT tablets in the British Museum when shown photographs by a visiting scholar.

One photograph of a tablet did not mention trapezoids, but it recorded the motion of Jupiter, with the numbers matching those on the tablets with the trapezoid calculations. It was a figure that described a graph of velocity against time. This preliminary analysis made Ossendrijver certain that it was a planetary theory for Jupiter. Ossendrijver, in his research at the British Museum in September 2015, turned up 2 more tablets. The discovery was made on his re-examination of known clay tablets. Mathematical calculations on 4 other tablets show that the Babylonians realized that the area under the curve of a graph of velocity against time represented distance travelled.

Space.com (28 January 2016): When Ossendrijver first encountered the Babylonian tablets, he didn't understand why calculations on a trapezoid were included along with tables related to Jupiter's position, he said. Only after he saw a fifth, uncataloged tablet, which showed a different procedure for finding Jupiter's position using the same examples as the trapezoids, did he realize the connection between the figure and the tables, Ossendrijver said. Eventually, he understood a second trapezoid calculation on the tablets, too: dividing it into two trapezoids with equal area, which would correspond to finding when Jupiter had traveled half the distance, he said. The advanced technique has been found only on the four tablets so far, which all use slightly different wording but the same example, he said. There isn't any evidence yet of the process being more widespread, Ossendrijver said. "This would open up new ways of computing motion they could have applied to other planets, other parts of Jupiter's motion," Ossendrijver said. "We don't have [examples of that]. We only have these four tablets, and they all deal with Jupiter — and they all deal with the same segment of 60 days. That's quite strange."

Mathematicians of the Old Babylonian period circa 1800 BCE to 1600 BCE knew how to calculate the area of a trapezoid, and how to divide a trapezoid into two smaller trapezoids of equal area. When Jupiter first appears in the northern night sky, it moves at a certain velocity relative to the background stars. Because Jupiter and Earth both constantly move in their orbits, to observers on Earth, Jupiter appears to slow down, and 120 days after it becomes visible, it comes to a standstill and reverses course. The Babylonians were calculating the distance Jupiter travelled in the sky from its appearance to its position 60 days later. Using the technique of splitting a trapezoid into two smaller ones of equal area, they then figured out how long it took Jupiter to travel half that distance.

It was an abstract concept that was not known elsewhere at this period. Ancient Greek astronomers and mathematicians did not make plots of something against time. Until Ossendrijver's discovery this type of planetary theory calculation was not known until the 14th-century CE by scholars in England and France. It is conjecture whether the mathematicians of the Middle Ages had seen some as yet unknown texts containing Babylonian techniques, or if they developed the same techniques independently.

Ossendrijver has not posited any astronomical or astrological motivation for these calculations.

Nature News (28 January 2016): "Although the Babylonians never used graphs or geometric figures explicitly, it seems that they had already grasped the same method centuries earlier, Ossendrijver says. In this, they were even more sophisticated than the ancient Greeks, who used aspects of geometry in astronomy — they conceived of planets travelling in orbits — but didn't use the kinds of abstract constructions described by the tablets, which connect velocity, time and distance. Hermann Hunger, a specialist on Babylonian astronomy at the University of Vienna, says that the work marks a new discovery. However, he and Ossendrijver both point out that Babylonian mathematicians were well accustomed to geometry, so it is not entirely surprising that astronomers might have grasped the same points. "These findings do not so much show a higher degree of sophistication in geometric thinking, but rather a remarkable ability to apply traditional Babylonian geometric thinking to a new problem", Hunger says. Science historian Jens Høyrup at Roskilde University in Denmark says, however, that this might not be the first hint of geometric ideas in Babylonian astronomy. The thinking behind the forecasting of certain lunar configurations, he says, "also shows kind of geometric combination of phenomena at the setting and rising positions of the Moon"."

physicsworld.com (January 28, 2016): "Not everyone is entirely convinced, however. The physicist and historian James Evans, at the University of Puget Sound in the US, says that it is "far from clear that the Babylonian scribes would have seen it that way," noting that there is an absence of any graphs on the tablets, unlike other mathematical tablets showing the geometrical measurement of land. "So while I don't think it is reasonable to see the Babylonian scribes as anticipating the graphical methods described by [European scholar] Nicole Oresme in the 14th century, it does seem fair to say they had an instinctual grasp of the mean-speed theorem. That’s new and very interesting." The tablets are all damaged in some way, so perhaps the sections containing the graphs had broken off, suggests Ossendrijver. Alternatively, perhaps there are tablets yet to be discovered that feature the graphs. Equally puzzling is why the trapezoid method seems to be limited to only a handful of tablets describing Jupiter, and why the knowledge was subsequently lost before being reinvented in Medieval Europe. Ossendrijver suggests one possibility is that it could have been "invented by a very clever astronomer, but wasn’t then taken up or understood by others""

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