The exaltations of Greco-Roman astrology and their relation to Babylonian Normal Star positions

In Greco-Roman astrology there are specific positions in the zodiac known as exaltations (hypsomata), where the planets, the moon, and the sun attain their greatest power or significance.¹ Along with triplicities, houses, decans, and terms, the exaltations represent another set of zodiacal positions that could be mobilized for interpreting planetary configurations in horoscopy and other astrological practices. In some astrological treatises, such as the Tetrabiblos of Claudius Ptolemy (second century CE), the exaltations are defined as whole zodiacal signs, which is also how they were often used in astrological practice. It has been known since Weidner² that the zodiacal signs of the exaltations correspond to the Mesopotamian “places” and “houses of secrecy” (ašar/qaqqar niṣirti, bı̄t niṣirti),³ which were defined in terms of constellations (Table 1).⁴ Babylonian horoscopes, unknown to Weidner, also mention planetary places and houses of secrecy, but in a sense inconsistent with the exaltations.⁵ Their meaning has recently been clarified by Pilloni.⁶

Since the cuneiform evidence for places and houses of secrecy predates the Greco-Roman exaltations, there is no doubt that the latter were derived from the former. The present paper addresses a hitherto unexplained aspect of the Greco-Roman exaltations, namely that many sources assign them to specific degrees within the zodiacal signs.⁷ It is shown that these longitudes derive from Babylonian Normal Star positions, with the exception of the exaltation of the sun. The rest of the paper is structured as follows. First the evidence for the longitudes of the exaltations is summarized. After that the evidence for the longitudes of Babylonian Normal Stars located in the zodiacal signs of the exaltations is presented. Subsequently the two sets of longitudes are compared. The paper concludes with a summary and conclusions.

In at least fourteen ancient and Late Antique sources the exaltations are specified to degrees within the zodiacal signs (Table 2).⁸ The exaltations are often paired with depressions (tapeinomata), which are located at diametrically opposite positions in the zodiac. Nearly all sources mention the same set of seven values, but some report different values. An effort was made to include in the analysis only values preserved in manuscripts and exclude all emendations. The transmission history of the longitudes and the question of which variants are genuine or result from textual corruption cannot be addressed here. However, at first sight 21 Libra for Saturn could be a genuine variant of 20 Libra, since it is attested in multiple sources. The other variants more likely result from textual corruption.

Most of the sources are Greek, except for three in Latin (Pliny the Elder, Firmicus Maternus, Martianus Capella), one in Demotic (P. Carlsberg 81+), and one in Sanskrit (Yavanajātaka). One of the earliest sources is Pliny the Elder’s Natural History (first century CE), which includes a confusing account of the exaltations.⁹ For the sun and Venus some manuscripts of the Natural History mention alternative longitudes, but it is not clear which ones go back to Pliny.¹⁰ P. Mich. 149, a Greek papyrus from Egypt dated to the late first or early second century CE, preserves four longitudes.¹¹ In this text exaltations and depressions are uniquely referred to as thrones and prisons, respectively:¹² “thrones upon which zodiac signs they [i.e. the planets] are exalted and have [general] power, and prisons upon which they are depressed . . . and become adverse(?).” Other Greek and Latin sources that were consulted are the Anthology of Vettius Valens (second century CE),¹³ Against the Astrologers by Sextus Empiricus (ca. 200 CE),¹⁴ who mentions a longitude only for the sun, the Introduction by Paul of Alexandria (fourth century CE),¹⁵ the Apotelesmatika by Hephaistio of Thebes (fourth and fifth century CE),¹⁶ the Mathesis by Firmicus Maternus (fourth century CE),¹⁷ the Marriage of Philology and Mercury by Martianus Capella (fifth century CE),¹⁸ and Rhetorius (sixth–seventh century CE).¹⁹ Hephaistio of Thebes ascribes the longitudes to Dorotheus of Sidon, who probably lived in Alexandria in the first century CE. Firmicus Maternus states that “the Babylonians called the signs in which the planets are exalted their houses,” which echoes the element “house” in the term “house of secrecy.”²⁰ Longitudes are also attested in a fragment published by Cumont, which Heilen tentatively ascribes to Imbrasius of Ephesus (first century CE).²¹ The Introduction to the Tetrabiblos of Ptolemy, a work sometimes ascribed to Porphyry of Tyre (third century CE), reports longitudes in a section ascribed to Antiochus of Athens (first to second century CE).²² P.Carlsberg 81+ (second century CE?) proves that the longitudes of the exaltations also circulated among Egyptian astrologers writing in Demotic.²³ Finally, longitudes are preserved in the Yavanajātaka by Sphujidhvaja, a Sanskrit treatise from the sixth century CE.²⁴

From the seventh century BCE until the first century CE, Babylonian scholars reported celestial and other phenomena in astronomical diaries and related texts.²⁵ The positions of the moon and the planets were expressed with respect to reference stars which they pass by while moving through the zodiac. They were referred to as “counting stars” (MUL.ŠID.MEŠ = kakkabū minâti) by the Babylonians and are known as Normal Stars in modern scholarship.²⁶ They include a core of 28 stars, labeled c1–c28 by Jones,²⁷ which were most often used, and about 13 stars, labeled a1–a13 by Jones, which are attested much more rarely in the diaries and related texts. Most Normal Stars are securely identified based on a comparison between reported passages of the moon and the planets with modern synthetic data for these events. At some point in time after the introduction of the uniform zodiac (late fifth century BCE), Babylonian scholars assigned longitudes to the Normal Stars.²⁸ In what follows, they are compared with the longitudes of the Greco-Roman exaltations.

As a first step, the Babylonian longitudes of all Normal Stars located in the zodiacal signs of the exaltations (Ari, Tau, Cnc, Vir, Lib, Cap, Psc) are determined. Three different sources or methods are available for this. First, two Late Babylonian tablets preserve portions of a catalogue with such longitudes.²⁹ BM 36609+ is a compendium with at least 13 sections divided over three or four columns on each side. The Normal Star catalogue is contained in Section 8 (rev. iv 1′–22′), here referred to as Text A. A second tablet, BM 46083, contains a small portion of a similar catalogue. It is partly preserved in col. ii′ 1′–13′ of the legible side, here referred to as Text B. The exact date of these tablets is unknown, but they obviously postdate the introduction of the uniform zodiac and certain features suggest a pre-Seleucid date,³⁰ say 400–300 BCE. However, a somewhat later date in the Seleucid period cannot be excluded. Altogether Texts A and B preserve the longitudes of ten Normal Stars located in the zodiacal signs of the exaltations (Table 3).

Further longitudes of Normal Stars were reconstructed by Huber through a comparison of data in Almanacs and Normal Star Almanacs, which are predictive texts related to the astronomical diaries.³¹ As discovered by Huber, the dates when the planets enter certain zodiacal signs according to the Almanacs coincides with the dates on which they pass by certain Normal Stars according to the Normal Star Almanacs. It follows that these Normal Stars mark the boundary of a zodiacal sign. For some other zodiacal signs the reported date of entry of the planet can differ from the date when it passes by a Normal Star by a number of days, depending on the planet. By dividing the time difference in days by a plausible value of the planet’s daily displacement along the zodiac, Huber obtained estimates of the Babylonian longitudes of some Normal Stars located near the boundary between two zodiacal signs. Values of the planet’s daily motion were reconstructed by Huber from data preserved in astronomical diaries and related texts. Altogether eight Babylonian longitudes derived by Huber with either method were added to Table 3. For five of them (c18, c20, c21, c22, c28) a longitude is also preserved in Text A or B. All five, agree to within ca. 1º with the longitudes obtained by Huber. This suggests that the longitudes listed in Texts A and B are, by and large, the ones that were used for reporting sign entries in astronomical diaries and related texts.

This leaves ten Normal Stars for which neither Texts A and B nor the sign entry data analyzed by Huber provide a longitude. Approximate Babylonian longitudes of these stars were reconstructed from modern values. Recall that the former are defined in a sidereal frame, that is, they are fixed with respect to the stars, whereas the latter employ a tropical frame, that is, they are measured from the vernal equinox, which moves with respect to the fixed stars due to precession. Ideally this results in a uniform offset in accordance with the following expression derived by Huber,³²

where λ_Bab is the Babylonian sidereal longitude and λ_trop is the modern tropical longitude. Babylonian longitudes obtained with equation (1) will be referred to as synthetic values. The term 3;5º represents the mean offset between Babylonian sidereal and modern tropical longitudes in the year 0 (1 BCE) and the term −1.3828 T represents the effect of precession, where T is the epoch of the tropical longitude expressed in Julian centuries from the year 0 (1 BCE). It must be stressed that equation (1) describes the mean offset between the two reference frames. As will become apparent, the offset for individual Normal Stars can deviate from equation (1) by a degree or more. Some of these offsets can be explained by assuming that the Normal Star passage was defined by means of an oblique alignment with a second star, resulting in a passage point that is shifted in longitude with respect to the Normal Star.³³

Modern tropical longitudes of all Normal Stars in Table 3 were computed for the year −100 using positional and proper motion data from the Hipparcos catalogue,³⁴ transformed into synthetic Babylonian longitudes with the help of equation (1), and rounded to multiples of 0;10º. The use of a different epoch for the tropical longitudes, for example, −300, would result in slightly different synthetic longitudes due to the additional proper motion of the star between −100 and −300, but this effect is negligible in all cases. The Babylonian longitudes from Texts A and B and those derived from sign entry data by Huber can differ from the synthetic values by about 1º in either direction, occasionally by a bit more. It follows that the Babylonian zodiac is stretched or squeezed in some zodiacal signs. They all contain 30 uš (degrees), but their actual size implied the synthetic longitudes of the Normal Stars can deviate from 30º by about 1º. For instance, the Babylonian scholars placed the Southern Rein of the Chariot (c7) at 30 Tau and the Rear Twin star (c12) at 30 Gem, but the actual longitudinal distance between them is 28;50º.³⁵ With this in mind, the most plausible Babylonian longitudes of the remaining Normal Stars are estimated from the synthetic values by rounding the latter to whole degrees and adding an uncertainty of 1º in either direction. For example, the Front Star of the Head of the Hired Man (c2) is estimated to have been placed at 8, 9, or 10 Ari, which is rendered as 8–10 Ari in Table 3.

Having established the Babylonian longitudes of all Normal Stars located in the zodiacal signs of the exaltations (Table 3), they are compared with the longitudes of the exaltations (Table 2). The best matches are presented in Table 4. For the most common longitudes of the exaltations of the moon, Mercury, Venus, Saturn, and Venus (those labeled “main” in Table 4) there is one corresponding Normal Star with a longitude deviating by at most 1º. About the same level of agreement is obtained for the variants that deviate from the main value by 1º. Deviations of 1º between an exaltation and a Normal Star may indicate that this exaltation originates from a slightly different Normal Star longitude than preserved in Texts A and B. The alternative longitude of the Rear Foot of the Lion (c18) mentioned in Text A implies that such variants may also have existed for other Normal Stars. Alternatively these deviations could result from truncation or rounding of the Babylonian longitudes. The case of Jupiter (15 Cnc) is exceptional, because there are three matching Normal Stars (a4, a5, c13). The most plausible one is c13, because this star is in the core group, while the other two are very rarely attested. The main value for the sun (19 Ari) cannot be matched with any Normal Star, since the nearest one (c3) is at least 5º away. Most variants deviating by more than 1º from the main values (29 Ari, 5 Cnc, 21 Cnc, 16 Psc, 17 Psc) do not match any Normal Star, the only exception being 10 Ari (sun), which may match Normal Star c2 (β Ari). But this rare variant from the Yavanajātaka is ignored here, because it is absent from the Greco-Roman sources.

With six matches and one anomaly the comparison yields an excellent level of agreement. This can be quantified with a rough statistical argument. If we randomly distribute seven exaltations over the zodiac such that the first one is distributed over all twelve signs, the second one over the remaining eleven signs, and analogously until the seventh, which is distributed over the remaining six signs, then the chance of at least six matches is p⁶ ≈ 0.16%, where p ≈ 123/360 is the estimated chance of a match for one exaltation.⁵⁴ It is therefore very unlikely that the six matches result from a coincidence.

Further support for the connection between Normal Stars and exaltations is offered in BM 36609+.⁵⁵ Section 10 (rev. v′ 1′–17′) partly preserves a list of Normal Stars, their surrounding regions, and the planets associated with them, including the following three entries:

(5′) Single one in Front of the Furrow: Mercury.

(8′) Southern Part of the Scales: Saturn.

(14′) Front one of the Goat [. . .]: Mars.

Each of these entries confirms a connection between a Normal Star and an exaltation from Table 4. Even though the term house or place of secrecy is not used in Section 10, it seems plausible that these associations were created by selecting from each constellation that functioned as a house or place of secrecy one Normal Star and assigning the same planet to it. The three entries from Section 10 can therefore be viewed as a stage in the development from planetary houses or places of secrecy to longitudes of planetary exaltations. This stage was apparently already completed in Babylonia by the early Seleucid period. In its original state, Section 10 may also have included some or all of the other associations between planets and Normal Stars from Table 4.

As pointed out by Kathryn Stevens,⁵⁶ another possible indication that Babylonian scholars selected specific stars or degree positions within the places/houses of secrecy are the microzodiac tablets from Seleucid Uruk with drawings of constellations, markings for degrees, and representations of the moon, Jupiter, and Mercury at specific locations in the zodiacal signs Taurus, Cancer/Leo, and Virgo.⁵⁷ However, the indicated position within the zodiacal sign roughly agrees with the longitude of the exaltation (Table 4) only for Mercury.

Having identified corresponding Normal Stars for six of the seven exaltations, the question arises as to what motivated the selection of these particular Normal Stars and whether they are somehow distinct from the others located in the same zodiacal signs. In order to answer these questions, the longitudes, latitudes (β), and visual magnitudes (m_v) of the Normal Stars are compared (note that a smaller m_v means a brighter star). The exaltation of the Moon is a special case. The Babylonian longitude of the Bristle, 3 Tau, deviates rather strongly from the synthetic value. The fact that the moon’s exaltation coincides with this anomalous longitude lends extra support to a Babylonian origin. In the Babylonian Calendar Treatise, a composition from Babylon dated to the second century BCE, the moon’s house of secrecy is assigned to both “the Old Man and the Bristle” and the “Bull of Heaven.”⁵⁸ These are the only explicit Mesopotamian textual references to the moon’s house of secrecy. In other contexts, the Bristle can refer to the zodiacal sign Taurus, but the inclusion of the constellation Old Man, which roughly corresponds to Perseus, implies that the constellation, that is, Pleiades, is meant here, in spite of the late date of composition. Note that if one makes the reasonable assumption that the moon should be able to reach or pass by near its house of secrecy then the mention of the Old Man is surprising, unless it included stars closer to the ecliptic than Perseus. Since Perseus extends above 10º of latitude, the moon cannot reach it.⁵⁹ The earliest datable Mesopotamian evidence for the moon’s house or place of secrecy is a depiction of the moon next to the Bristle and the Bull of Heaven on VAT 7851, a microzodiac tablet for the sign Taurus from Seleucid Uruk (ca. 200 BCE). The mentioned sources explain why the moon’s exaltation does not correspond to the stars of the Chariot (c6, c7), but they do raise the question of why it does not correspond to the Jaw of the Bull (c5), the brightest Normal Star in Taurus and the only one located near the middle of the sign, features that appear to have triggered the selection of a Normal Star for some other exaltations. Perhaps the moon’s house or place of secrecy was primarily identified with the Bristle because of the extraordinary significance of this constellation.

With regard to Jupiter’s exaltation it was argued that the Babylonian longitude of the Rear Star of the Crab to the South (c13) was most probably 15 Cnc, in exact agreement with the exaltation, or 14 Cnc. It is the only Normal Star from the core group near the middle of Cancer. Moreover, it is closest to the ecliptic and the brightest Normal Star near the middle of Cancer. In the case of Mercury, the Single one in Front of the Furrow (c19) is also the only Normal Star in Virgo located near the middle of the sign. Moreover, the other Normal Star in Virgo, c18, is not a suitable candidate, because it belongs to the Babylonian constellation Lion (roughly Leo), while Mercury’s house of secrecy was the constellation Furrow (roughly Virgo). In the case of Saturn, the Southern Part of the Scales (c21) is much closer to the ecliptic and also to the middle of Libra than the only other candidate in Libra (c22). With regard to the exaltation of Mars in Capricorn it is remarkable that the Front Star of the Goat-Fish (c27) is neither closest to the ecliptic (c28), nor closest to the middle of the sign (c26), nor the brightest Normal Star in Capricorn. Therefore no tentative explanation can be offered for the selection of this Normal Star. The exaltation of Venus matches the Ribbon of the Swallow (a13), which most likely corresponds to ζ Psc. The only other candidate in Pisces, a23, does not come into question, because it belongs to the constellation the Great One, roughly corresponding to Aquarius, but the house of secrecy of Venus was the constellation Swallow and Neck of Anunītu, roughly corresponding to Pisces.

The exaltation of the sun is the only one that definitely cannot be matched to a Normal Star, because the nearest one (c2) is at least 5º away. This anomaly may reflect the sun’s exceptional status. For instance, the sun cannot be seen together with the Normal Stars. As pointed out by Rochberg-Halton,⁶⁰ the location in Aries suggests an underlying calendaric rationale, because the sun is in Aries at the beginning of the Babylonian year. Moreover, the distance of 14º between the exaltation of the sun and that of the moon corresponds to their elongation about 1 day after the conjunction. This suggests that the longitude of the sun’s exaltation was obtained by subtracting 14º from the Babylonian longitude of the Bristle, which represents a schematic or ideal position of the first crescent. As argued by Hunger and Steele,⁶¹ a similar arrangement of the moon, the sun, and the Bristle underlies the schematic calendar in the astral compendium Mul.Apin, which dates to the eighth century BCE. It is therefore possible that the longitude of the sun’s exaltation has a Babylonian origin, even though it does not correspond to a Normal Star. In the second century CE Claudius Ptolemy used a similar rationale to connect the exaltations of the sun and the moon in the Tetrabiblos:⁶² “And since the moon, coming to conjunction in the exaltation of the sun, in Aries, shows her first phase and begins to increase her light and, as it were, her height, in the first sign of her own triangle, Taurus, this was called her exaltation.” Whereas Ptolemy’s explanations of the other exaltations are viewed as far-fetched,⁶³ this one could have a core of truth.

As a final step, the longitudes are compared with values from other ancient star catalogues (Table 5), namely Books VII–VIII of Ptolemy’s Almagest (ca. 150 CE)⁶⁴ and estimated values for the time of Hipparchus (ca. 125 BCE). The latter were reconstructed by subtracting 2;40º from the former in accordance with the precession rate of 1º per century used by Ptolemy.⁶⁵ The underlying assumption is that Ptolemy may have obtained some of his longitudes by applying a similar correction to coordinates inherited from Hipparchus.⁶⁶ Except for the Pleiades (η Tau), the comparison reveals significant deviations in the range 1;40º–3;40º (Almagest) and 4;20º–6;20º (Hipparchus). The Babylonian longitude of the Bristle is anomalous, as mentioned earlier, and accidentally close to the longitudes of the Pleiades in the Almagest. It can therefore be ruled out that the longitudes of the exaltations originate from these catalogues.

It has been shown that the longitudes of up to six Greco-Roman exaltations derive from Babylonian Normal Star longitudes. A comparison between both sets of longitudes yields excellent agreement. This is confirmed by the associations between Normal Stars and planets listed in Section 10 of the Late Babylonian tablet BM 36609+. It was argued that they constitute an intermediate stage in the transformation from Mesopotamian houses and places of secrecy, defined in terms of constellations, to Greco-Roman exaltations, specified to degrees within the zodiacal signs. A more detailed reconstruction of the stages of this transformation and of the times, places, and contexts in which they took shape remains out of reach. The only certain exception is the sun’s exaltation, which appears to have been defined in relation to the Bristle (Pleiades), which became the Moon’s exaltation, using arguments that can be traced back to the Mesopotamian schematic calendar. It is striking that not a single Greco-Roman or Late Antique source connects the exaltations with stars. As far as known, the exaltations were conceived of as astrologically significant longitudes without any suggestion that they correspond to, or originate from, stellar positions. This is consistent with the fact that the Babylonian longitudes of the Normal Stars were assigned to the exaltations without any adaptation to the coordinate framework used by Greco-Roman scholars such as Claudius Ptolemy. The Babylonian longitudes were appropriated while their association with stars was discarded. The end result was a system of exaltation longitudes without any connection to stars.