Annus Platonicus: A Study of World Cycles in Greek, Latin and Arabic Sources

303 Pages·1996·5.352 MB·English

by  Godefroid de Callataÿ

ANNUS PLA TONICUS
A STUDY OF WORLD CYCLES IN GREEK,
LATIN AND ARABIC SOURCES

PUBLICATIONS DE L'INSTITUT ORIENTALISTE DE LOUVAIN
47
Godefroid DE C-A-LLATA Y
ANNUS PLATONICUS
A STUDY OF WORLD CYCLES IN GREEK,
LATIN AND ARABIC SOURCES
UNIVERSITE CATHOLIQUE DE LOUVAIN
INSTITUT ORIENTA LISTE
LOUVA IN-LA-NEUVE
1996
© lnstitut Orientaliste de l'Universite Catholique de Louvain
College Erasme
Place Blaise Pascal. I
B-1348 Louvain-la-Neuve
© Peeters Press Louvain-Paris
Orders should be sent to:
Peeters Press, P.O.B. 41. B-3000 Louvain
ISSN 0076-1265
ISBN 90-6831-876-4 (Peeters Leuven)
ISBN 2-87723-303-0 (Peeters France)
TABLE OF CONTENTS
Prologue: Instruments of Time........................................................ VII
CHAPTER 1: The Foundation Stones from Classical Antiquity ... .
A. The Perfect Year of Plato .......................................................... l
I. The Manifold Meaning of the teA.eo<;e viaut6<; ................ 2
II. The Number of Divine Begettings ...................................... 9
Ill. Floods, Conflagrations and the Ages of the World ............ 15
B. In Search of Aristotle's Greatest Year........................................ 32
I. The Lost Protrepticus .......................................................... 33
II. The Aristotelian Analogy with the Solsticial Year.............. 37
C. Cicero on the Truly Revolving Year.......................................... 42
I. Cicero's magna quaestio ...................................................... 42
II. The Reconstruction of a Rational Universe ........................ 54
CHAPTER n: Periodic Returns and Astral Determinism .............. 59
A. Endless Recurrence of Worlds in Early Stoicism...................... 59
I. The Fragments .............................................................., . . .. . . . 61
II. The Babylonian Great Year of Berosus .............................. 66
B. Censorinus's List of Conjunctional Great Years........................ 68
C. The Lumber-Room of Astrological Speculations ................. ..... 72
I. The Sothic Period and the Life Span of the Phoenix.......... 74
II. The Vain Demonstrations of the Greeks.............................. 76
III. The Babylonian Naros in Josephus...................................... 78
IV. The Ambiguity of Ptolemy's Tetrabiblos ............................ 79
CHAPTER m: The First Opponents of the Doctrine ... ...... ....... ...... 81
A. An Absurdity: The Epicurean Great Year ................................ 81
B. Scepticism or the Questioning of Astronomical Observations .. 84
C. The Growing Hostility of the Christians.................................... 88
I. The Pagan Distortion of the Bible ...................................... 88
II. The Attack on Astrology .................. ..... ................. ..... ... . . . .. . 91
CHAPTER IV: The Commentators .............. .. .... .......... .............. ... . . . .. 99
A. Middle-Platonism and the Remnants of the Stoa ...................... 99
B. The Perpetuation of the Timaeus via Calcidius.......................... 106
VI TABLE OF CONTENTS
C. Proclus on the Scientific Way to Compute the Perfect Year.... 108
D. The Peripatetics on Aristotle's Greatest Year............................ 116
E. A Foretaste of the Precessional Great Year in Macrobius . .. ... .. 120
CHAPTER v: The World Year in Islam .......................................... 129
A. Abu Ma'shar and the Cycle of the Persians .............................. 129
B. The Ikhwan al-~afa' on Precession and General Conjunctions. 137
I. Between the Almagest and the Zfj al-Sindhind.................... 138
II. Precession and the Periodic Interchanges on Earth .... ... .. ... 143
III. Two Allegories on the Conjunctional Great Year .............. 145
C. Arabic Material in Latin Translation .......... .. .................... ..... .. . .. 149
CHAPTER v1: Astrology and Computus in the Western Middle
Ages............................................................................ 163
A. Conjunctionism ...... ... .. ..... .... .. .......... ................. ....... .. .. .. .... .. . ... .. 163
B. Sacrobosco and the Ever-Growing Fortune of Macrobius ........ 168
C. The Two Zodiacs of Pietro d'Abano.......................................... 174
CHAPTER vu: The Condemnation by the Christians .. ... .. .. ... .. ...... 183
A. The Reaction of Scholasticism .................................................. 183
B. Oresme on the lncommensurability of Celestial Revolutions.... 189
C. In the Footsteps of Oresme .. .. .... .... .... .. . ....... .. ................. .... ... .. .. 204
CHAPTER vm: The Last Sigh of the Annus Platonicus .................. 213
A. Ficino or a New Attempt at Understanding Plato...................... 213
B. The Ten Propositions by Francesco Piccolomini ...................... 219
Appendix 1 : Original Texts.............................................................. 227
Appendix 2: Great Cycles................................................................ 253
Index of Sources . . ... . .. . ... ... . .... . . ... . ... ... ... . ... ... . ... .. . . . . . . . . . . . . . . . .. . .. . ... . .. . .. 259
Index of Names ................................................................................ 263
Index of Topics ................................................................................ 267
Bibliography...................................................................................... 269
PROLOGUE
INSTRUMENTS OF TIME
Let us consider an ordinary analog clock. It has a dial divided into
twelve regular portions (numbered from I to 12) and two hands of
unequal length to mark the hours and the minutes. The minute-hand goes
twelve times faster than the hour-hand, which means that the former
completes twelve revolutions around the dial while the latter completes
only one. Let us now suppose that it is noon, so that both hands are on
the number 12. It is plain to anyone that these two hands will not be
together again on the number 12 before midnight, i.e. twelve hours (or
60 x 12 = 720 minutes) later. But at the same time everyone reckons that
both hands will be together a certain number of times before midnight.
This turns out to be eleven times, which is perhaps not the figure we
would have thought of instinctively.
Above all, the different places at which they appear together are not
precisely those which many of us would have expected them to be. It is
tempting to assume that the first conjunction (after the starting position
on 12) would take place at 1.05 pm, the second at 2.10 pm, the third at
3.15, and so on until one reaches 12 again. But the intrinsic flaw in the
reasoning appears here, for this extrapolation does not add up to 12, but
only to 11.55 pm; so we are left five indispensable minutes short.
Our visual recollection of dials is misleading, as is the apparent facil
ity of the problem. In fact, the first conjunction does not .take place at
1.05 pm, but rather at 1.05 plus 27 sec. and 3/11; and this is, of course,
the interval that we find between every other subsequent conjunction of
the hands. The figure of 1 hour 5 min. 27 sec. 3/11 may look strangely
unsatisfactory if compared with any of the integral numbers we might
have anticipated. Yet one has no trouble justifying the validity of this
result. The important thing to realize is that our present problem is a
matter of addition (or substraction) prior to being one of multiplication.
To note that the minute-hand completes twelve revolutions of the dial
while the hour-hand performs only one is fair enough, but this consider
ation does not lead us very far. What we have to compute instead is the
number of revolutions that the faster hand will need in addition to the
VIII PROLOGUE
one performed by the slower in order to come back into exact conjunc
tion at the end of that unique revolution, i.e. after twelve hours. In the
example of the ordinary clock, this number is eleven, since 11 + 1 = 12.
Only when this addition (or substraction) has been performed can we
proceed to the following multiplication: 1 hour 5 min. 27 sec. 3/11 x 11
= 12 hours.
The question of how to determine the recurrence of a specific con
junction of two planets must have been raised and contemplated by the
ancients in very much the same way. Let us thus project ourselves back
to a time when the Earth was believed to be the geometrical centre of the
universe and when all planets were assumed to revolve in perfect circles
and with absolutely regular speeds. To those past observers of the heavens
it certainly was a serious matter of concern to settle, for instance, when
and where the Moon and the Sun were due to come back into conjunction.
It so happens that these two bodies complete their revolutions through
the zodiacal signs with speeds that are remarkably similar in proportion
to those of the minute-hand and the hour-hand of our clock. For the
Moon only needs one month to complete its journey through the signs,
while it takes the Sun twelve months to perform an entire revolution
along the ecliptic.
The ancients - like ourselves - would not have had to face insur
mountable obstacles had this proportion of I to 12 actually corresponded
to the respective speeds of the Sun and the Moon. But Nature does not
allow herself to be bound by such rudimentary laws, and we need not be
very advanced in astronomy to understand that twelve lunar months do
not match one solar year exactly. To make matters worse, neither the
revolution of the Moon (about 29.53 days) nor that of the Sun (about
365.24 days) consists of an integral number of days. These were the
inherent difficulties which led the ancients to look for ever more accu
rate luni-solar cycles, that is, periods embracing integral numbers of
days, months and years at the same time. Most famous in this respect
was the 19-year cycle devised in 432 BC by the Greek mathematician
Meton - a period which corresponds to 235 lunations or 6940 days -
but many others, sometimes considerably longer than the Metonic cycle,
were also used.
The doctrine of the Great Year provides us with this mathematical
problem but on a larger scale. Plato defined this Perfect Year as the
period of time required for all seven planetary spheres to come into a
perfect conjunction with the eighth one, namely, the starry sphere.
Plato's Great Year most probably implies the perfect alignment of all
INSTRUMENTS OF TIME IX
planets with respect to one particular point of the starry sphere. Our
comparison with the analog clock remains valid, but one must speak of
a clock with no less than seven different hands, each one travelling at a
different speed. Needless to say, the problem of finding the periodicity
of that general conjunction of the planets was often presented as a difficult
matter to solve. Still the solution was generally not believed by the
ancients to be out of reach because most of them assumed all celestial
movements to be perfectly regular and measured by strictly commensu
rable periods of time. In fact, the difficulty of this mathematical issue
turns out to depend almost exclusively on the interpretation of the defi
nition itself, as well as on the more or less rigorous method one agrees
to follow in the computation of the values involved. There is a considerable
difference between understanding the Great Year, on the one hand, as
the mere gathering of the planets in one particular zodiacal sign and, on
the other hand, as the perfect alignment of these planets in such a way
that an imaginary straight line would traverse all their centres. As for the
method of computation, it will clearly appear, for instance, that the simple
multiplication of periods expressed by integral numbers of years is a
great deal easier than the search for the least common multiple of periods
that are expressed by fractional numbers of days.
It comes as no surprise, therefore, that the measurement of the Great
Year was hotly debated in Antiquity and that the controversy still rever
berated until well into the Renaissance. To give but a single example,
one may still catch a glimpse of the debate in the De annis by the
humanist Lilio Giraldi, a treatise on the measurement of time composed
around the same year as Copemicus's famous De revolutionibus orbium
caelestium. In the translation of the relevant section, I have inserted,
between square brackets, the references to the works probably used by
the Italian compiler:
Now we must distinguish between the Great Years according to their num
ber and variety. Diverse and manifold is the range - so far observed - of
those Years that are called Great, as is shown by the authorities. Indeed,
Aristotle, with whom I should begin, called Greatest rather than Great this
Year which is completed by the circuits of the Sun, the Moon and the five
planets when they are brought back together to the same sign in which they
once were [= CENSORINUDS,e die nat., 18, 11]. And Cicero gives almost
the same (definition) in the De finibus bonorum et malorum [= CICEROD, e
fin., II, 102). We find the same (definition) again in what is said in the sixth
book of the Republic by Scipio: people, he says, only measure the year by
the return of the Sun, i.e. of one single star; but, when all stars have come
back to the same (sign) in which they once started to move, and have
reverted, after long intervals, to the same configuration of the whole heaven,
X PROLOGUE
then this can truly be called a Revolving Year. This, as Macrobius writes,
natural philosophers assume to occur when 15,000 years have been com
pleted, and this is what one calls the World Year[= MACR0BIUSi,n Somn.,
Il, 11, 11). But Plato in the Timaeus names it the Perfect Year[= CALCIDIUS,
Tim., 39d]. Now the greatest winter of this Year is the 'cataclysmus',
which we (Latins) call the flood or deluge. The summer is the 'ecpyreosis',
which is the conflagration of the world. For according to the alternation of
these periods the world appears to change now into fire and now into water
- to use Censorinus's words. This year Aristarchus reckoned to consist of
2,484 revolving years; Aretes of Dyrrachion assigned it 5,552 (years).
Herodotus (sic; read: Heraclitus) and Linus 10,800, Dio 13,984 (sic; read:
10,884), Orpheus 120 (sic; read: 120,000), Cassandrus 3,600,000 [= CEN
S0RINUSD, e die nat., 18, t t ]. Our Cicero (assigned it) 12,954 (years) [=
TACITUSD, ial., 16; SERVIUSi,n Aen., I, 269; III, 284); Josephus the Jew, in
the first book of the Antiquitates, only 600 [= BEDET HE VENERABLED, e
temp. rat., 36). Julius - also named Vilius - Firmicus completed it by a
circuit of 1,461 years [= FIRMICUSM ATERNUSM, ath., l, Proem., 5). Some
people write that the return of this year coincides with the life of the
phoenix bird[= SouNus, Collect., 33, 13]. Other people have thought that
it was infinite and that it never came back [= CENS0RINUSD, e die nat., 18,
11) . Others have assumed for this Great Year a much shorter interval:
some made it consist of two revolving years. some of three, others of five
or more1• (my own trdllslation)
One should no doubt rank the doctrines of the Great Year amongst
those which Neugebauer used to call sympathetically the 'wretched sub
jects'. It is, indeed, a fine example of an inextricable mixture of elements
that take their roots from fields of knowledge as diverse as astronomy
and astrology, mathematics and arithmology, physics and metaphysics,
chronology and millenarianism, philosophy and faith, to name but a few
of them. Dealing briefly with some of these great cycles in his A History
of Ancient Mathematical Astronomy, Neugebauer noted that 'the diffi
culty with the term "great year" lies in its ambiguity. Almost any period
can be found sometime or somewhere honored with this name. One has
"great years" ranging from one or two years to huge sexagesimal or
decimal round numbers - usually without any astronomical signifi
cance2. ' Then, having listed a few examples, he concluded in the fol
lowing way: 'Obviously the first step in dealing with such material
should consist in a classification according to origin and purpose as well
as to time and geographical provenance. Unfortunately such indispens
able preliminary work has not been done. On the contrary far reaching
1 GIRALDI. De wm .. Basel, 1541, pp. 15-16 (Original text in Appendix I).
~ 0. NEllGEBAUER, HAMA, 11, p. 618.