The Star of the Magi

Courtney Roberts, M.A.

   The Eighth Sphere: Trepidation & Precession   

     Issac Newton had one significant advantage over his many predecessors in the pursuit of meaningful religious chronologies: he actually understood the nature of precession and had accurately calculated its annual rate.

In fact, Newton is credited with the first full theoretical explanation of the precession of the equinoxes. 

     In Book III of his Principia (prop. xxxix, problem xx), Newton published both his theoretical explanations and his computations, which set the annual rate of precession at 50" 00"' 12iv (Manuel, 1963, 67); a most welcome scientific achievement, and long overdue.

          In one of his early New College manuscripts, Newton summarized the work of other contemporary astronomers who, living and working in the aftermath of the Copernican heliocentric revolution, had calculated similar rates:

"Now recconing (sic) with astronomers that the Equinox moves backwards about 50". Tycho Kepler & Bullialdus reccon 51", Hevelius 50"52"', Ricciolus in his Almagewst 50" 00"' and afterwards in his Astronomia reformata 50" 4-"'.  Vindelinus Petavius & some later astronomers (in a round number) 50" per annum or one degree in 72 years" (Manuel, 1963, 67).

     Before Copernicus, even though most astronomers operated within the reigning geocentric cosmology with its system of nested, interlocking, planetary spheres, they were still fully aware of the precessional motion.  It was impossible to undertake any kind of systematic observation and not notice that the so-called 'fixed stars' were moving. However, this was generally believed to be a result of the motion of the fabulous ‘eighth sphere.’  This 'eighth sphere,' in the geocentric cosmology, revolved somewhere beyond the seven planetary spheres, and was believed to be the home of the fixed stars of the constellations.

         While astronomers had long known about this apparent motion of the eighth sphere, at least since the time of Hipparchus (approx. 128 B.C.) if not before, the calculation of the exact rate of this precessional motion had been a source of great contention.

     The conflicting values for the rate of precession apparently began with Ptolemy, who, in the Almagest, VII.2. claims to quote Hipparchus himself from his On the Precession of Solstitial and Equinoctial Points (no longer extant), for a series of observations of the star Spica. These observations would have yielded a precessional rate of 1 degree in a little over 75 years, had Ptolemy bothered to check the math.

     However, Ptolemy, whose influence has always exceeded his importance, instead went on to quote yet another work by Hipparchus, On the Magnitude of the Solar Year (no longer extant) (North, 1976, 253).  From this book, Ptolemy concluded that the rate of precession is closer to 1 degree in 100 years. This latter value was accepted by Theon of Alexandria, and hung around for centuries, while the former, and more accurate value had to be rediscovered many times over before it was finally accepted (North, 1976, 253). 

     There were perceptive astronomers who came closer to the real figure in their calculations.  Albategni (d. 929 A.D.) believed the rate of precession was approximately 1 degree in 66 years, and Al-Biruni (d. 1048 A.D.) calculated it to 1 degree in 68 years (North, 1976, 254). Among the many astronomico-chronological schemes discussed by Petro d'Abano throughout his work, he refers to the duration of the complete cycle of the stars which al-Battani (Albategni) set at 23,760 years and to the precessional cycle of  'Azolphi"  (25,200 years), which is even closer to the accurate rate (North, 1989, 108).

     Still, much of the work of the intervening centuries quotes Ptolemy's nice, round figure of 100 years.  For instance, the Sphaera mundi of Rabbi Abraham bar Hiyya, published in 1546, contains a history of the theories of the eighth sphere and opens with the assertion that it moves 1 degree in 100 years, and makes a complete rotation in 36,000 years (North, 1976, 265).  Edward Grant notes that:

“During the Middle Ages, numerous periods were proposed for the Great Year, the most popular being 36,000 and 49,000 years.  The former was derived from Ptolemy’s Almagest, based upon a value of precession of the equinoxes of 1 degree in 100 years.” (Grant, 1996, 498)

     Further adding to the confusion was the development of the theory of trepidation which held that the eighth sphere not only precessed at a regular pace, but that it also periodically reversed itself and went back in the other direction, at varying intervals!  North adds, in his Richard of Wallingford:

"It is currently de riguer to maintain...that it is greatly to the credit of a medieval astronomer that he was not led astray by the 'imaginary phenomenon' of trepidation.  The fact is that most of the best astronomers of the time believed that Arabic writers had established the reality of the phenomenon beyond doubt...(and were) not sufficiently careful readers of Ptolemy's Almagest to appreciate the source of the fallacy..."(North, 1976, 238)

            If Ptolemy had gotten the precessional rate right in the Almagest, the theory of trepidation might have never come into play, for it was a necessary adjustment astronomers had to make as they tried to square their own observations with Ptolemy's fictitious precessional rate.

     The most widely used theory of trepidation during the Middle Ages was that of the ninth-century Arab astronomer, Thabit ibn Qurra, and was introduced in his On the Motion of the Eighth Sphere. While Thabit is credited with first postulating this theory of the progressive and regressive motion of the stars, also known as access and recess, it is possible that he may have been drawing on earlier sources (Neugebauer, 1975, 340).

     However, Thabit’s theory of the trepidation of the eighth sphere was originally conceived of as an alternative, or substitute theory for the precession of the equinoxes.  Nevertheless, it soon became common practice for astronomers to treat both trepidation and precession as two separate and distinct motions (Grant, 1996, 315).

     In the ceaseless, and ultimately, thankless efforts to refine the notion of trepidation, not only were various values proposed for the rate, and various intervals designated as recessional, or backwards periods, but also, whole new spheres were eventually required; the ninth, the tenth, the eleventh, ad infinitum, to account for these varying degrees of motion.

            Albertus Magnus, in his Metaphysics, book 2, attributed three separate motions to the eighth sphere of the fixed stars: 1) the obvious east-to-west motion observed every night  2) the precession of the equinoxes and 3) the trepidation, or motion of accession and recession described by Thabit (Grant, 1996, 315).

     However, other astronomers disagreed, and believed that extra spheres, or orbs, were necessary to explain such complicated motion. Peter of Abano in his Lucidator, argued for nine spheres; assigning the daily, east-to-west motion of the fixed stars to the eighth sphere and the precession of the equinoxes to the ninth sphere (Grant, 1996, 316).

     Further, a major contingent believed in the three separate motions of the fixed stars and fell in behind the idea of ten spheres, including Albert of Saxony, Roger Bacon, Themon Judaeus, and Pierre d’Ailly.  Albert of Saxony assigned precession to the eighth sphere, trepidation to the ninth, and the daily motion to the tenth sphere (Grant, 1996, 315).

      Nevertheless, in describing the work of the 14h century astronomer/historian, Walter of Odington, J. D. North maintains that:

 " would have been appropriate to include a discussion of precession and trepidation in a work on the age of the world; first, it was widely thought that vicissitudes of the world's history were linked with the periodicities of trepidation - notice how Alfonsine trepidation had a turning point near the time of Incarnation. '  (North, 1976, III,  262)

     So while there was great confusion over the nature and the rate of precession and trepidation, the idea that significant intervals in those movements coincided with turning points in world history continued to flourish.

       Consider, for example, how the theory of trepidation was used by the 16th century French astronomer, Pierre Turrel.  Lynn Thorndike quotes his work (Thorndike, 1941, V, 310-11) from an obscure French manuscript, the English title of which translates as: The Period, that is to say, the End of the World, containing the disposition of terrestrial things by the virtue and influence of the celestial bodies. Turrel used a regular precessional movement in which the entire sky revolved once in 49,000 years, (North, 1989,106) against a periodic, or trepidational movement of 7,000 years. Turrel believed that there were four stations in the trepidational period, occurring quarterly, or every 1750 years, and to these pivotal stations he assigned the Flood, Exodus, the destruction of Jerusalem, and the end of the world.

            Thorndike maintains that Turrel probably derived his methods from the earlier, 15th century work of Jean de Bruges, De veritate astronomiae(Thorndike, 1941, V, 311)  De Bruge, in turn, may have been influenced by the Summa astrologie of John Ashenden, which also discusses trepidation and the theories of the highly influential Thabit ibn Qurra. (North, 1989,106)

       So by all accounts, the precession of the equinoxes and its medieval concomitant, trepidation, were widely used in Christian astrology to apportion history.  Certainly Newton and his post-Copernican contemporaries had a great advantage in their understanding of the true nature and rate of precession, but that did not stop their predecessors from trying.

      J. D. North quotes from the Lucidator and Conciliator of Petro d'Abano (Bodleian MS Ashmole 802, f.86) the following tale in which the diminishing life span of man is linked to an ill-defined movement through the constellations of the zodiac.

"The wordle (sic) is divided into 3 partes.  The firste from the Creation unto Noah his flod and after then untille 2000 years...' The age to which a man might live was supposed to reduce in steps from 1200 years (and that begane in the head of [Sagittarius]') to a mere 75.'  The top of the page has been torn away, and this might have given some clue as to what 'it' was which was supposed to move steadily around the zodiac, starting at the head of Sagittarius at the Creation, occupying each sign for 500 years, and finishing at the end of Scorpio at the end of the world, Anno Mundi 6000." (North, 1989, 108) 

      Another famous 14th century astrologer, Cecco d'Ascoli (d. 1327 A.D., at the stake), in his commentary of the Sphaera of Sacrobosco, quotes from a work falsely attributed to Hipparchus, De hierarchiis spirituum, in order to relate a strange story about the incubi and sucubi who reside at the colures (the great circles on the celestial sphere which pass through the north and south poles and define the solstices and equinoxes).

      Cecco recounts that at pivotal moments in world history, these spirits combine to produce great men "as of the Godhead" (Thorndike, 1949, 387-8).  J.D. North describes how:

"Cecco then goes on to relate a similar account from a "pseudo-Zoroastrian work...entitled Liber de dominio quartarum octave spere.  A quadrant of the eighth sphere is said to dominate every historical period of 12,000 years and the turning points of which men of divine attributes are born of incubi and succubi..." (North, 1989, 85)

     North makes an intriguing reference to the work of Bouche-LeClercq,  
(North, 1989, 105) saying that he "writes of a system claimed as Tuscan but found again in Mazdean cosmogony, in which each sign of the zodiac was supposed to rule the world for a thousand years."  

     In tracing back this reference, we need to leave Christian Europe behind and delve into the roots of Islamic astrology.

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