The Symbolic Number 3: its Role in the Aeneid

LA Rocme LA The Symbolic Number 3 : its Role in the Aeneid “Six is a number perfect in itself, and not because God created all things in 6 days ; rather the converse is true ; God created all things in 6 days because the number6 is perfect, and it would have been perfect even if the work of the 6 days did not exist ... We should not underestimate the significance of numbers, since, in many passages of Sacred Scriptures, numbers have a meaning for the conscientious interpreter. Not without reason has it been said in praise of God : ‘Thou hast ordered all things in measure, and number, and weight’” (St. Augustine, De Ciuitate Dei 11, 30). I believe that the same situation is true for the number 17 in many areas and especially as the key mystical number (i.e. the golden number) in the Aeneid. There is conclusive evidence that Vergil was intimately concerned with mystical numbers both explicitly and implicitly (') and that he followed a very detailed, exact overall mystical numerical scheme in writing the Aeneid. However, as a true Pythagorean he kept his intentions secret and did not confide his mystical numerical designs to anyone. Yet a close analysis of the text reveals numerous examples of mystical numerical usage based on a master plan which he followed in his two earlier works. In addition to 17 there are 3 other key mystical numbers in the Aeneid: 3, 7, and 13. However, in many cases their influence is only implicit. For example, Vergil never cites either 13 or 17 in the Aeneid but their influence is undeniable. In this case Vergil’s behavior reveals the powerful influence of the ancient concept of the “Evil Eye” which stipulated that it was bad luck and undesirable to know or state the exact number involved in any situation especially in the case of mystical numbers. The ancients believed that the envious could bring misfortune upon a person or thing only if they knew the exact number involved and so the safest course of action was to avoid stating any exact number. This popular superstition is still widespread among many eastern nations and curious traces of this belief survive in many countries. At the root of this superstition is the notion that numbers must not be misused since they contain an unknown power and, in fact, they are more powerful than words. Thus from very early times it was believed that a spell could be surely based only on some mathematically exact enumeration of particulars and so it has been considered taboo (nefas) to tell, or even to know, certain details about one’s creations or precious possessions, e.g. the exact number of one’s children, oxen, or age. (1) Cf. Larocue (article forthcoming in Phoenix) for the evidence.

This prohibition does not extend to impersonal matters (?). In the Aeneid Vergil cites 17 numbers, always excluding 1 and 2 which are of of odd numbers but only 118 citations of even numbers which yields an odd total 288 no consequence in such an investigation. In fact, the Pythagoreans did not consider 2, the dyad, a number but only as the principle of the even, as 1, the unit, was the principle of number. The 17 numbers cited occur 237 times which is very significant since there are exactly 237 citations of Aeneas in the Aeneid. In addition, Vergil’s use of these 17 numbers is not haphazard but rather based on mystical numerical considerations. Vergil cites 13 different numbers in Books I-VI (Part I of the Ameid) and then 4 numbers occur for the first time in Books VIIXII (Part II of the Aeneid) with all 17 numbers occurring in the last 6 books (cf. Appendix I). Perhaps Vergil decided to divide his mystically significant total of 12 books into 2 halves of 6 books each because of influence from the number 6, the first perfect number (discussed below) (*). Of the 4 numbers cited for the first time in Books VII-XII only one, the number 5, occurs more than once. Similarly, Vergil advances 13 even numbers in the Aeneid: 4, 10, 12, 14, 20, 30, 50, 100, 200, 300, 500, 600, and 1,000 ; and 4 odd numbers : 3, 5, 7, and 9. The number 9 is the only odd number in this work which is not also a prime number and it seems to have been included because of its great mystical power since it represents the triplication of the triple, ic. 3 x 3. Significantly, there are 119 citations of odd numbers and 118 citations of even numbers but I believe that Vergil consciously omitted one citation of 100 (discussed below) and thus there would also be 119 citations of even numbers. A total of 119 is very significant and mystical since it represents the product of 7 x 17 (in fact, 7 and 17 are the only aliquot factors of 119). Also 2 x 119 = 238 but for some reason Vergil decided to advance only 237 numerical citations which correspond to the 237 citations of Aeneas. Perhaps this anomaly can be traced to Vergil’s (and the 289 ancients’) belief in the superiority of odd numbers and so there are 119 citations of citations — 237. For example, Vergil states (Ecl. 8, 73-78) that “Three threads here I first tie around thee, marked with three different hues, and three times around these shrines I draw thy image. In an uneven number heaven delights (numero deus impare gaudet). Bring Daphnis home from town, bring him, my songs ! Weave, Amaryllis, three hues in three knots ; weave them, Amaryllis, I beg, and say, ‘Chains of love (Veneris) I weave !‘”. A very similar passage, including the statement numero deus impare gaudet, occurs at Ciris 369-373. I believe that in referring to an uneven number Vergil had in mind not only 3 but such numbers as 7, 13, and 17. Servius’ comment on this passage in the Eclogues is that according to some superstition odd numbers are immortal because they cannot be divided into 2 equal parts and even numbers are mortal. Thus the ancients attributed special power to odd numbers and especially to odd numbers that are also prime numbers : e.g. 3, 7, 13, and 17. The number 1,000, the largest number cited in the Aeneid, seems to have been especially mystical since it represents the triplication of 10, i.e. 10 cubed, which as the fetraktys was the perfect number for Pythagoras and his followers. Significantly, 1,000 is cited 13 times in Books I-VI and 17 times in Books VIIXII — a situation which corresponds exactly to the overall distribution of numbers in the Aeneid since 13 numbers occur in Books I-VI and 17 in Books VIIXIE. Also the largest and the smallest numbers in this work, 3 and 1,000, are cited the most often while 100, i.e. 10 x 10, is 3" in frequency. Furthermore, 13 symbolical totals (3, 4, 5, 7, 9, 10, 12, 20, 30, 50, 100, 300,and 1,000) are cited 4 times or more in the Aeneid while 4 numbers (14, 200, 500, and 600), with limited symbolic significance, are advanced only once or twice. The pervasive influence of 17, schematically disguised as the sum of 13 and 4 (*), is noticeable in at least 3 cases and the combined influence of 13 (2) Cf. Larocue who has treated this topic in articles on Greek and Roman literature and chronology [cf. e.g. (1972, p. 1-512) ; (1977, p. 358-368) ; (1982, p. 112-120); (1983, p. 5-25); (1986, and 17 is present in at least 2 cases. Additionally, the mystical total 119 reveals p. 31-43) ; (1995, p. 568-576); and (1998, p. 145-156). This article is based on an examination of the primary evidence, i.c. the Aeneid, with limited reliance on secondary sources dealing with the Aeneid which are, of course, very numerous. For the tions of odd numbers in the Aeneid ; 2) excluding the 13 citations of 1,000, the secondary bibliography, cf. R. D. WiLLiams (1967), DonLan (1978), and reviews in Vergilius. I have made free use of the standard Vergilian commentators and I am enormously indebted , directly or indirectly, to them : viz. Servius, Henry, Paige, Mackail, Clausen, Conway, Austin, Mynors, Thomas, R. D. Williams, and especially John Conington. This constitutes my acknowledgement of indebtedness to them. The Vergilian text which I have followed is that of Mynors (OCT, 1969) and all transinfluence from 17 and this total occurs in at least 3 cases : 1) there are 119 citaother 12 numbers advanced in Books I-VI are cited 119 times (cf. the number 7 is also cited 13 times in Books I-VI ; thus 7 and 1,000 are each cited 13 times in these books and there are 13 numbers advanced in Books I-VI providing 3 instances which reveal influence from the number 13) ; and 3) there are 90 citations of 3 in all and 29 of 100 for a combined total of 119 citations while the lations are from the LCL series. I have also relied on Warwick (1975) whose work is based on Mynors’ text which for numbers is the same as the LCL text. In fact, there is no alternate reading in either the OCT or the LCL text for a number in the Aeneid. (3) The number 6 is not cited explicitly in the Aeneid or, for that matter, in Vergil, but only as a factor of 12 (as bis sex or a form of bis seni) on 7 occasions and so perhaps this is the third number that is hidden in the text of the Aeneid: viz. 6, 13, and 17. However, influence from 6 is not extensive in the Aeneid: |) the 12 books are divided into 2 sections of 6 books each ; and 2) Book VI, a key book and a focal point of the Aeneid, has 901 verses = 17 x 53 (both prime numbers). (4) The division of 17 into units of 13 and 4 could reveal influence from Greek and Pythagorean musical theory in which 4, 5, and 8 represent the 3 harmonies (guquwviat) of ancient Greek music : the fourth, fifth, and octave |cf. Kraus (1943, p. 207-209) for further information on this topic]. In this case, the numbers 4, 5, and 8 are combined as follows : 4 = 4 and 5 + 8 = 13. However, these 3 numbers were more often combined as follows : 4 + 5 = 9 and 8 = 8 which yields the ratio 9:8.

other 15 numbers are cited 118 times (of course, an even neater arrangement language in Hesiod's Works and Days — in the same context) (’). The number 290 291 would involve 90 citations of 3, the smallest number, and 29 citations of 1,000, 13 is not cited explicitly by Vergil. Both 13 and 17 had ambivalent connotations the largest number, since then the total number of citations for the largest and the in antiquity. In Roman times 17 was often feared because XVII could also be interpreted as VIXI= mortuus sum and 13, representing 12 + 1, often had a nesmallest number would be 119). gative connotation. However, at times both 13 and 17 were considered to be ausThe Number 17 picious numbers evidently because they represent the sum of 10 + 3 and 10 +7 respectively. In the religious epics of the Anatolian Turks and in the Islamic tradition the At this point a brief overview of important symbolic/mystical numbers in number 17 has”an almost magical quality. In fact, the mystical Shiites from a antiquity and especially of Pythagoras and his influence on ancient number thevery early time worshipped the number 17 (*). They believed that the shape or ory is appropriate. form (sura) of everything in the world was 17. Some believe that this veneration A symbolic/mystical number is one which suggests something in addition to among the Shiites stems from the ancient Pythagorean speculations based on the in this alphabet (*). However, I believe that most probably there are 17 consothe number per se by reason of association, convention, etc. Such a number makes no specific reference to the actual quantity involved. Rather it is the visible sign of something invisible, such as an idea or a quality, and, in fact, it is a nants and 7 vowels in the ancient Greek alphabet because of influence from the symbol. It is necessary to distinguish between the arithmetical and the symbolic letters of the ancient Greek alphabet since there are 17 consonants and 7 vowels mystical numbers 7 and 17 and not vice-versa. number ; the former defines an object by its quantity but says nothing about its The number 17 has many mystical aspects : 1) it represents the sum of 2 very nature, whereas the latter expresses an inner link with the object it defines by important mystical numbers — 7 and 10 ; 2) it is the 7* prime number according virtue of a mystic relationship between what is enumerated and the number to the following classification which I believe existed at some time in antiquity itself. Religious numerical values vary with longitude and latitude and it is posalthough there is no surviving documentation of this fact : 1, 3, 5, 7, 11, 13, and sible to identify many different numbers which were, and in many cases still are, 17 ; later Aristotle and Euclid replaced 1 by 2 as the first, and only, even prime number ; 3) the decimal 8ystem of counting had a mysterious importance for the invested with occult significance in different places and at different times. From very ancient times numbers have represented symbolic ideas and the Pythagoreans and they believed that the numbers over 10 were simply a repetiinterpretation of numbers is one of the oldest symbolical science. Also “the pecution of the first 10 numbers and so 17 = 7 ; 4) according to the Pythagoreans only liar fascination which numbers as individuals have exerted on the mind of man 17 souls would be resurrected at the end of the world and each soul would from time immemorial was the main obstacle in the way of developing a collective theory of numbers, i.e. an arithmetic” (*). For example, the Pythagoreans and the Greeks were very much preoccupied with the symbolism of numbers and Plato regarded number as the essence of harmony, and harmony as the basis of receive one of the 17 letters (the 17 consonants ?) of the ancient Greek alphabet which spelled out the perfect name of God ; and 5) the Pythagoreans attributed special importance to 17 since it represents the sum of 4 + 5 (= 9) + 8, the 3 key numbers in their music theory and in their theory about the harmony of the spheres — the ratio 9:8 constantly recurs in ancient Pythagorean and Greek arithmetical speculations on grammatical, musical, and cosmological questions. (7) Cf. Hesıop (Works and Days, 805) who assigns such activities to the 7* day of midmonth Apparently the fear of such mystically powerful numbers as 13 (cf. the super- (uécoy 6 '¿Bóouárp), i.e. the 7* day after the 10*. Such usage is due to the Greek practice of divistition labeled “triskaidekaphobia”) and 17 influenced Vergil not to cite them explicitly in the Aeneid but their implicit influence is unquestionable. The only ding each month into 3 “weeks”, i.e. periods, of 10 days. The present citation is as close as Vergil ever comes to citing the number 17, which implicitly is, I believe, the most important, i.e. his signature, number in the Aeneid, but he chooses in this case to specify that total in terms of 2 other very reference to 17 in Vergil, be it veiled, occurs at Georgics 1, 284 where the Moon important mystical numbers- 7 and 10. Such circumlocution graphically illustrates Vergil's great preherself is said to have ordained that the 17* day of the month be lucky for plantoccupation with mystical numbers in general and especially with the number 17, In fact, there is no ing the vine (septima post decimam: the choice of terms is significant: the other example in Vergil of such numerical circumlocution and this citation is very important in 7% day after the 10" rather than simply stating the 17°, septendecim, day of the month; admittedly septendecim is a rare term in Latin; cf. also the similar helping us understand his overall numerical philosophy. (8) Cf. Dantzic (1954, p. 56 and in general Chapter 111 “Number-Lore"). The reader should consult any standard work on symbolism for additional information and illustrative examples of statements made in this paper about symbols, including symbolic numbers. In the present investigation I have especially relied on the following sources : Hopper (1938) ; ALLENDY (1948) ; Guenon (1949) ; (5) Cf. Méuixorr (1962, p. 435-445) for the documentation. Du (1952); Etiape: 1952); Guyka (1952); PaneTH (1953) ; Jung (1954); Brac (1994); and (6) Cf. ChevaLier et GHEERBRANT (1973, Il, p. 203-204), s.v. “dix-sept”. especially CirLor (1962) and ChevaLiER and GHEERBRANT (1973).

the cosmos and of man. Plato was particularly interested in the mysticism of numbers and in the Republic (8, 546) he speaks in an obscure fashion of a certain mystical number but he does not explicit state what this number is. The solutions proposed to date for this mystical Platonic number, e.g. 60 to the 4* power, are unsatisfactory. According to Cicero in the Tusculan Disputations (1, 17) Plato traveled to Italy to become acquainted with the Pythagoreans and there he met Archytas and Timaeus from whom he learned all the tenets of the Pythagoreans. Some commentators believe that the mystical Platonic number played an important part in the mysticism of the Hindus and the Babylonians and that perhaps Pythagoras found it on the banks of the Euphrates, if he really studied there, and that he took it with him to Crotona, passing it along to his disciples who finally revealed it to Plato and his followers (°). Additionally, Plato states in the Republic (7, 525f.) that the study of numbers has a great and elevating effect since it compels the mind to reason about abstract numbers and that a philo- Pythagoras (fl. 540-510 B.C. ; born at Samos and then settled at Crotona in southern Italy) was similar to the philosophers of the Ionic school who undertook 292 293 to solve by means of a single primordial principle the problem of the origin and the constitution of the universe as a whole. His predilection for mathematical studies led him to trace the origin of everything to numbers (') and his theory was suggested and confirmed by his observation of various numerical relationships in the phenomena of the universe (cf. especially the recurring presence of the golden number). Mathematical, especially numerical, relations were essential in mystical speculations and in the interpretation of the world. As a result, there was extensive Pythagorean influence on Platonic doctrines and on later literature. Musical principles played almost as important a role in the Pythagorean system as did mathematical and numerical concepts. Running throughout the system is the belief that order, or harmony of relation, is the regulating principle of the whole universe. For example, the intervals between the heavenly bodies sopher should also be an arithmetician. Pythagoras was especially interested in the mystical quality of numbers and professed a mysticism of numbers that is very similar to that found earlier in were said to have been determined according to the laws and relations of musical harmony — hence the doctrine of the harmony of the spheres. Pythagorean Babylon. He maintained that everything is disposed according to number and scientific theory was intimately connected with their number theory. that number is the universal measure of everything. Pythagoras believed that the The religious element was the predominant one in the character of Pythagoras and he chiefly labored to obtain religious ascendancy in connection with a mysessence of everything is number and that number rules the universe and is the key to fully understanding the world. The mystic number worship of the Pythagoreans with all its magic and superstition was the forerunner of the theory of numbers and number worship found its supreme expression in the mathematical philosophy of the Pythagoreans whose whole system was cosmological in nature and who believed that the real world was composed of numbers. They Apollo. By practicing divination and prophecy he revealed a way of life to his followers that was calculated to raise them above the level of mankind. At maintained that the nature of the universe could only be grasped through number Crotona he had a brotherhood of 300 (evidently 300, i.e. 3 x 100, was a special tic religious system. It was this religious element which profoundly influenced his contemporaries, and later ages as well, and so they considered him to be very closely related to the gods. Some, e.g. the Crotoniats, even identified him with and form. Their mystic philosophy classified all numbers in a variety of ways Pythagorean number) who were bound to him and to each other by a vow to including perfect and prime numbers ('°). Thus the theory of integers was born in devote themselves to religious and ascetic matters. Everything that was done or religious mysticism and it passed through an erratic period of puzzle-solving taught among the 300 was kept a profound secret. It was a Pythagorean maxim before it acquired the status of a science. Gradually, over the course of centuries, that everything was not to be revealed equally to everyone and so even within the the natural numbers lost their association with mysticism. Pythagorean number brotherhood there were gradations to distinguish the mere listeners from the speculations created many strange notions about numbers as, for example, the more advanced esoteric students. Members of the brotherhood were very closefact that 1 is not a number but simply the source of numbers and that even numly devoted to each other and they held in contempt those who were not in their bers are feminine and thus soluble and ephemeral but odd numbers are mascuranks. They had secret symbols, e.g. the pentagram, by which members of line and so indissoluble and celestial. The golden number, the divine proportion, the brotherhood could recognize each other even if they were from different the golden section, i.e. 618, was very important to the Pythagoreans (*'). clubs since brotherhoods of 300 were also established in Tarentum, Metapontum, etc. They shared common meals in companies of 10 (30 groups of 10 — both (9) Cf. Sm (1958, I, p. 89). (10) For a clear explanation of these categories and illustrative examples, cf. Dantzic (1954, p. 40-45) : also THomas (1957, I, p. 67-141). (11) Some, e.g. DuckwortH (1962, p. 1f.), have proposed that the Aeneid has a mathematical structure based on the Pythagorean golden section. (12) The following is a list of the main mystical/symbolical numbers favored in antiquity and in most cases Greek and Roman authors favored Pythagorean mystical numbers : i.e. 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 17, and 30. For a detailed discussion of these Greek and Roman mystical numbers, cf.

important Pythagorean mystical numbers). If Pythagoras ever wrote anything, his writings perished with him or not long after. But in all probability he wrote nothing and relied on the oral tradition. His disciple Philolaus was the first to publish the Pythagorean doctrines. Significantly, most of the 17 numbers cited in the Aeneid occur a mystically significant number of times: e.g. 9, 12, and 30 are each cited 7 times; the expression “3 times” and the number 1,000 are advanced 30 times but 100 only occurs 29 times (this discrepancy is discussed below); 5, 20, and 50 occur 4 times. All in all, Vergil's use of numbers in the Aeneid is very deliberate and schematic and I am convinced that he had an overall plan in mind concerning his use of numbers in his 3 works as I have argued elsewhere concerning his use of numbers in the Eclogues and the Georgics ("). There is no random, haphazard citation of numbers in Vergil and, in fact, at times he changes a numerical total found in another author, Homer for example, in order to suit his own specific numerical scheme. Also in many cases Vergil’s repetition of a numerical total reveals influence from the literary technique of ring-composition which in an epic poem is simply thematic anticipation used for structural purposes (9. 1 believe that thematic numerical anticipation is an important structural element in Vergil, especially in the Aeneid, and that its importance has not been noticed to date. This important Vergilian stylistic trait frequently serves to foreshadow events. In other words, most of the numbers advanced in Vergil’s works are nei- 295 Aeneas kills 27, i.e. 3 cubed, Latins and significantly Turnus is the 27* victim (10, 312f. and 12, 505f.), etc. In the following pages I will analyze the role of the symbolic number 3 in the Aeneid while pointing out evidence of both explicit and implicit symbolical numerical influence. The number 3 is cited 90 times As would be expected, by far the most common symbolical number cited in the Aeneid is 3 — a universal magical number. In fact, it occurs 90 times and so accounts for nearly 40% of all numerical citations. Significan tly, the magical expression 3 times occurs 30 times and the number 3, including the expression 3 times, occurs 90 times, i.e. 3 x 30. The number 3 is the only figure (always excluding 1 and 2) which is advanced in every book of the Aeneid — 56 times in Books I-VI and 34 times in Books VII-XII (always as a form of tres, tria ; tertius, a, um ; tridens ; or triuia). The number 3 is advanced 10 times in Book I and 9 of the first 14 numerical citations involve 3: 1-10: 1,94; 1, 108; 1, 110; 1, 184; 1, 116; 1, 265; 1, 226; 1, 483 ; 1, 138; and 1, 145 : the very first words spoken by Aeneas in the Aeneid, which contain the 2% and 3" numerical citations in this work, are “O thrice and four times blest, whose lot it was ...” ; a set, formulaic expression of ther historical, nor random, figures but rather arbitrary, schematic totals selected great antiquity with definite Homeric overtones which is fittingly according to his overall numerical plan. by Vergil at key spots in the narrative and always in connection | Implicit influence from mystical numbers can often be detected in the Aeneid. cited 3 times with death and twice the impending death of a main character — Dido (4, 589) and Turnus For example, it is certainly not fortuitous that Vergil cites the name of Aeneas 155). This expression is simply synonymous for “O very happy are those 237 times and that there are exactly 237 numerical citations in this masterpiece. should be noted that a climax is usually expressed in many languages Also the magical expression “3 times” occurs 30 times, 3 times in each of the first 4 books, and there are 3 expressions that specify how many times something happens : 3,4, and 9. Furthermore, the number 3, including the expression “3 times”, occurs 90, i.e. 3 x 30, times. The number 7 is the 7* number cited, it occurs in 7 books, and it is the last number advanced in the Aeneid (cf. the first number cited is 14, i.e, 2 x 7, thus revealing influence from 7). Also many, if not all, of the books of the Aeneid are divided into 3 parts, a person is often accompanied by 3 attendants (cf. e.g. Camilla at 12, 655-656), 7 heroines are named (6, 445f.) before Dido’s introduction, 7 contestants are mentioned (5, 294f.) by name followed by the expression multi praeterea, etc. Often the number of enemy killed by a hero/heroine, though not cited explicitly, is significant (often 3): Camilla kills 12 men (11, 666f.), Turnus slays 18 opponents (9, 696f.), (13) Cf. Larocue (article forthcoming in Phoenix) for the evidence. (14) Cf. WitLiams (1983, p. 75f.). (12, ...”. It by thrice, but Greek and Latin authors sometimes added the expression 4 times for still greater emphasis. Aeneas speaks the aforementioned words in a 7 '/, verse address while mourning for himself and his comrades at the onset of the fierce Aeolean storm. He states that the Trojan heroes who died before the eyes of the fathers beneath the walls of Troy were very fortunate indeed (cf. Odyssey 5, 306312 for a similar 7-verse speech by Ulysses : “three times and four times blessed are the Danaans who perished in broad Troy then, doing the pleasure of the sons of Atreus”). During the great cosmic storm at sea, 3 ships are driven on the rocks and subsequently 3 other ships crash on the shoals — both magical references which serve as thematic numerical anticipation for the following reference to 3 stags grazing, i.e. one stag per ship in either group. In fact, in Book I in at least 6 cases there is a specific numerical correspondence between a group of animals and either people or various objects such as ships. The ship of Orontes is whirled around 3 times before disappearing in the sea-evidently because it was the unlucky 13% ship in the group. The malevolent associations of the number

would seem to have influenced the placing of the first citation of Karthago as the first word in verse 13 whereas Roma is cited for the first time as the last word in verse 7 and the next reference to Roma under the form Romanam gentem occurs in verse 33. | Aeneas is destined to found a city, Lavinium, 3 years, i.e. 3 summers, after landing in Italy — a magical total similar to the reference to the La summer to specify the duration of Aeneas’ wanderings before landing in Carthage. According to Vergilian mystical chronology, which is not the standard one, the first settlementof the Trojans in Italy, i.e. in their armed camp, lasted for 3 years, then Lavinium lasted for 30 years before the founding of Alba Longa, and finally Alba Longa existed for 300 years before the founding of Rome — overall a period of 333 years. But Vergilian chronology is nebulous and sketchy at best and, in fact, Vergil is much more concerned with individual, discrete, non-cumulative mystical periods of time rather than with a consistent chronology that is mathematically correct. For example, he tends to telescope the 3-yearperiod that the Trojans spent in their fortified camp and the 30-year period spent in Lavinium. For emphasis, Vergil states that after defeating the Rutuli the Trojans spent 3 winters in camp before founding Lavinium — so they spent 3 winters and 3 summers in Italy before founding Lavinium. There is a neat progression in Book I from 3 ships, to 3-stags, to 3 years and similarly from 7 ships, to 7 stags, to 7 years — quite a striking arrangement which certainly is not fortuitous. According to Vergil, Achilles dragged Hector’s body 3 times around the walls of Troy — a magical number of times with heightened effect because of the concomitant use of concentric circles. However, more exactly according to Homer (Iliad 24, 478f.), Hector was chased around the walls but his body was dragged around the tomb of Patroclus. Therefore, the magical expression 3 times is cited 3 times in Book I, also in Books II, IH, and IV, for a combined total of 12 citations in the first 4 books — definitely a schematic, deliberate arrangement by Vergi da are 2 references to a trident in Book I — a magical symbol because of its 3 points. The trident with its 3 prongs can either bring help or destruction and so it has some of the same attributes as Mercury’s caduceus, his magical wand. Evidently, anything with 3 prongs, whether natural or man-made, is endowed with magical power. In fact, many infernal beings that are base counterparts of the ternary are 3-headed like Cerberus or Hecate, or else they wield 3-pronged weapons such as the trident. The final 2 references to a trident in the Aeneid occur at 2, 418 and 2, 610 and in 3 cases it is a question of Neptune’s trident and once that of Nereus (2.418). | î 11-16 : 2, 174; 4 475 ; 2, 792 ; 2, 793; 2, 418 ; and 2, 610: the Palladium leaps (emicuit) from the ground 3 times — a magical event as indicated by the expression mirabile dictu. For the early agricultural Romans the ritualistic act of jumping over the crops was done in sympathetic magic and closely associated 297 with Mars (an early agricultural deity) and later traces of this practice survived in the ritualistic jumpings of the Salii, especially over bridges. In the present case, the special significance of the leaping is intensified by the presence of the magical number 3. The mention of the 3-forked tongue (trisulcis linguis) of a snake is certainly reminiscent of the 3-pronged trident but, in fact, snakes only have a 2-forked tongue. Subsequently, Aeneas tries 3 times to embrace the phantom of Creusa and 3 times the form escapes from his hands — cf. the magical significance of repeating an action 3 times with the clear expectation that the 3" time will be the charm, that the 3“ time never fails, but the 3” event can also be negative. These 2 verses (2, this is not always so since 792-2, 793) are repeated verbatim at 6, 700-6, 701 when Aeneas tries unsuccessfully to grasp the shade of Anchises and they have definite Homeric overtones since Odysseus (Odyssey 11, 204f.) grasping at the shade of his mother says : “3 times I sprang towards her and my heart bade me to clasp her, and 3 times she flitted from my arms like a shadow or a dream”. The expression 3 times is cited at the beginning of each of the verses mentioned and, as is often the case, Vergil advances a very close Latin translation of the corresponding Greek Homeric trident in this book are discussed above. passage. The 2 references to a 17-2 : 3, 421 4 ; 3, 566 ; 3, 567 ; 3, 37; 3, 117 ; 3, 645 ; 3, 203 ; and 3, 467: Charybdis is said to suck in the vast waves 3 times into her abyss and then to cast them upward again — cf. the magical power of repeating an action 3 times. Once again Vergil is following Homer very closely and he even adopts the expression 3 times from him — cf. Odyssey 12, 73f. for the statement that “Charybdis does this (i.e. suck in the water) 3 times a day” ; also at 12, 105 “3 times a day Charybdis belches forth the water and 3 times she sucks it down”. Subsequently, Vergil mentions that the cliffs of Charybd is utter a cry 3 times as Aeneas and his men mount up to heaven and then sink down to the depths of Hell with the receding wave and that the followers of Aeneas see the Spray and the dripping stars 3 times. Once again ter is cited as the first word in both verses (566-567). Some commentators believe that ter in this case has no reference to the 3 ingurgitations of Charybdis at 3, 421 but I disagree. Apparently, Aeneas and his men were sent up to the sky 3 times by Charybdi s after descending 3 times to the depths of Hell — cf. the popular belief that a person drowns after going down 3 times. Also on 3 occasion in Book III it is a question of the occurrenc e of a 3" event. First, Aeneas pulls on a 3“ cluster of shafts, i.e. shoots, and this time a groan is heard from the ground, i.e. from Polydorus. This magical event is appropriately flagged by the expression mirabile dictu (3, 26) and it provides further evidence that the 3" time never fails. Next, the 3" dawn brings Aeneas and his men to Crete — a sacred, magical period of time as found in a triduum for religious purposes and ultimately revealing Homeric influence (cf. e.g. day we might reach Phthia”). Finally, Achaemenides Iliad 9, 363 for “on the 3" states that the horns of the

moon are now filling with the 3“ light (tertia lumine) since he has been living among the Cyclopes, i.e. it has been a period of 3 months — another sacred period of time expressed poetically. Aeneas and his men wander on the deep for 3 days (soles) and as many nights (totidem) — a period similar to the sacred biblical interval of 3 days and 3 nights — and they sight land on the 4* day. Therefore, it is almost as if they rose from the dead after a period of 3 days and 3 nights — a stock, traditional concept. In one case Helenus orders a 3-threaded (trilicem) breastplate with hooks of gold to be brought to the ships of the Trojans. Trilix refers to a kind of armor, perhaps chain mail, which no doubt resembled the pattern of cloth which was designated by the same term. Cloth was called either bilix or trilix according to the number of leashes employed in weaving it. The expression trilicem, cited 3 times in the Aeneid, has a magical connotation because it has 3 parts. matter of 3 x 3 = 9). Once again the number of animals corresponds to the 25-30 : 4, 511; 4, 511 : 4, 589 ; 4, 609 ; 4, 690; and 4, 691 : after mentioning 300, i.e. 3 x 100, gods Vergil then refers to 3-fold (tergeminam) Hecate and to triple-faced (tria hora) Diana. Thus the idea of tripleness, which is fitting in such a magical, ritualistic ceremony, occurs 3 times in successive verses (4, 5104, 511). In fact, Hecate, Diana, and Artemis are but 3 aspects of the same divinity (cf. 6, 247). Similarly, Geryon is called tergeminus (6, 287). Following the report that Dido struck her breast 3 and 4 times — symbolic, I 299 number of ships (cf. Book I for similar examples). Also one of the prizes is a coat of chain mail with hooks of triple (trilicem) gold and then the 3” prize is mentioned — a pair of brazen cauldrons. In the 2* contest, a foot race, Aeneas declares that the first 3 finishers will receive a prize. This is the same arrangement specified for the ship race and evidently the custom of rewarding only the first 3 finishers in a contest is very ancient and once again reflects the strong pervasive influence of such magical numbers as 3. Subsequently, Aeneas announces that the 3" place finisher will receive an Argive helmet and at one point in the race Euryalus is in 3" place but he eventually wins the race with Helymus second and Diores 3”. In the archery contest, Eurytion is selected as the 3” participant to shoot. Then 3 troops of horses are mentioned with their 3 riding captains (cf. the 3 centuries of equites mentioned by Livy, A.V.C. 1, 13, 8) and the 3 troops break up the columns for a manoeuvre, Finally, Aeneas orders 3 steers to be sacrificed to Eryx — a magical number to ensure a safe trip. Noticeably, there is no citation of the expression 3 times in this book. 46-56 : 6, 229 ; 6, 289 ; 6, 417 ; 6, 421 ; 6, 355 ; 6, 484 ; 6, 506 ; 6, 549 ; 6, 700 ; 6, 701 ; and 6, 859 : Corynaeus performs a lustration by encircling his companions 3 times to cleanse them — combining the mystical power of 3 and of believe, of her impending death and a traditional sign of mourning — Dido readily admits that she is about to die (4, 604 : quem metui moritura). Then there concentric circles as part of a religious, ritualistic act. Circumambulation is a is a notice that Hecate is invoked at night at the crossroads of the city (triuiis) — the only citation of triuia in the Aeneid but Hecate is invoked as the goddess Triuia on 9 occasions. It is appropriate that a 3-fold goddess be invoked at the juncture of 3 roads since there is a certain magical connotation associated with crossroads which represent a strange, mysterious location (cf. e.g. Oedipus Rex ; also Cirlot, s.v. “crossroads”). Finally, Dido, after throwing herself on a sword, 3 times tries to lift herself and 3 times she rolls back on the couch — cf. the magical quality associated with the triple repetition of an action (cf. 2, 792-2, 793 ; and 6, 700-6, 701). In this monies. Vergil was certainly familiar with the special magical power of 3 (cf. e.g. case, the 3“ time is the end and not the charm. Once again, ter is cited as the first word in each verse. . 31-45 : , 119 ; 5, 120; 5, 143; 5, 247 ; 5, 259; 5, 266; 5, 308 ; 5, 314; 5, 322; 5, 337; 5, 495; 5, 560; 5, 560; 5, 580; and 5, 772: the Chimaera is manned by Dardan youths in triple tier (for versus = a tier of oars, cf. Livy, A.V.C, 23, 30) with oars rising in triple rank. However, in this case Vergil is guilty of an anachronism since triremes were not invented until approximately 700 B.C. Undoubtedly, he selected a 3-tiered ship because of the magical qualities of 3. Similarly, he later mentions the triple-pointed beaks of the ships. Cloanthus is told to choose and take away 3 bullocks as a gift for each ship (evidently only for the first 3 to finish since the 4* was presumed lost ; so it isa universal magical ritual especially associated with lustrations and death cerehis statement, discussed above, at G. 8, 73-78 that “three threads here I first tie around thee, marked with three different hues, and three times round these shrines I draw thy image. In an uneven number heaven delights”). The reference to triple-bodied Geryon and to Cerberus with his 3 throats (trifaux — a hapax legomenon) reveal the strong magical power of triplication. A more standard reference to Cerberus occurs when he is described as having 3 mouths (tria guttura). However, according to Hesiod (Theog. 312) Cerberus had 50 heads. Palinurus is driven along for 3 nights on the ocean (cf. Odysseus at Odyssey 5, 388f. who reportedly floats for 2 days and nights and then sights land on the 3” day), i.e. for a sacred period of time. This is but one example of a magical, traditional sacred period of time similar to periods of 3 months, 3 years, etc. Subsequently, the 3 sons of Antenor are mentioned — again a mystical number of sons (cf. Iliad 11, 59 : also Aen. 10, 351 for references to 3 sons : 10, 518 for 4 sons ; 12, 270 for 9 sons ; and 10, 329 for 7 sons). Aeneas calls the spirit of Deiphobus 3 times — the stock, traditional, magical number of invocations necessary to insure that a person was in fact dead and a practice at least as old as Homer (cf. Odyssey 9, 65 where Odysseus calls the spirits of his dead companions 3 times ; cf. also 6, 229 and 3, 68 in the Aen. which are discussed above). In fact, most of the rituals associated with death involve some form of triplica-

301 tion as, for example, the necessity of throwing 3 handfuls of dirt on a corpse to mother at birth (horrendum dictu) 3 lives and 3-fold armor to wear meaning that guarantee a proper burial. he had to be killed 3 times and on that day Turnus stripped him of his armor In the Underworld, Aeneas sees a castle surrounded bya triple wall, a concept which combines the magical connotations of 3 and of concentric circles, and such an arrangement occurs earlier in Hesiod (cf. Theog. 726). The 3 walls surrounding the castle represent the same basic idea as the act of circumambulation : a circle is a magical concept and 3 circles are that much more effective and powerful. Aeneas tries 3 times to'hug his father’s phantom and 3 times he fails. Such an action is analogous to the triple invocation made to attempt to recapture a dead person’s spirit and it should be compared to Dido’s behavior at 4, 690-691 and to Aeneas’ earlier action at-2, 792-793. The final numerical citation in this book occurs when a 3" set of arms is hung up to Father Quirinus, i.e. deified Romulus. According to Roman tradition the spolia opima, i.e. the spoils captured by a Roman general upon slaying the general of the enemy, had been won on only 3 occasions (evidently reflection the magical power of 3) : by Romulus, Cossus, and now Marcellus. This detail should be compared to the so-called triple triumph of Augustus at 8, 715. life for each of his bodies and evidently he served as the prototype for Erulus (cf. influence from folktales, for example the popular belief that cats have 9 lives). Following a second reference to the triple-pointed beaks of the ships (cf. 5, 143 for the same verse), Augustus is said to enter Rome in triple triumph : viz. for his victories in Dalmatia, at Actium, and at Alexandria — definitely a schematic, deliberate arrangement reflecting the strong attraction of the mystical number 3 (cf. the 3 spolia opima discussed above), 72-73 : 9, 329 and 9, 587 : Nisus kills 3 attendants and Mezentius whirls his sling 3 times around his head before shooting — a magical act as is the killing of 3 soldiers. However, slingers were advised (cf. Veget. 2, 23) to whirl the sling only once since the repetition of the movement consumed too much time and thus a slinger had to learn to put as much force as possible into a single whirl. Therefore, the use of 3 in this context does not reflect standard usage but is rather In Book VI the expression 3 times is cited 4 times for a total of 16 citations in Books I-VI — noticeably, one additional citation of ter in these books and one fewer in Books VII-XII would yield yet a 3" example of a 17-13 distribution pattern in the Aeneid. an anomaly reflecting the great power of 3 and especially of the expression 3 times — 3 is the last number advanced in this book as it is in Books 6 and 7. 74-84: 10, 175 ; 10, 202; 10, 350 ; 10, 351 ; 10, 685 ; 10, 685; 10, 784 ; 10, 784 ; 10, 873; 57-59 : 7, 141 ; 7, 689; and 7, 785 : ominous thunder is heard 3 times in a clear sky — a portent. The triple repetition of the thunder greatly intensifies the preternatural character of this natural phenomenon. There is a 3" and final reference to a coat-of-mail tripled-linked with gold. As in Book VI, the last number cited in this book is 3 when Turnus’ helmet is described as being triple-plumed evidently 3 for good luck. 3 times (totidem). According to Aeschylus (Agam. 869f.) Geryon had a separate i 8, 60-71 : 8, 202 ; 8, 230; 8, 231 ; 8, 232; 8, 429; 8, 429; 8, 430; 8, 564; 565 ; 8, 566 ; 8, 690 ; and 8, 715 : there is a 3" and final reference to tripled-bodied Geryon and then 3 consecutive citations of the expression 3 times when Hercules crosses the Aventine Hill 3 times, he tries 3 times to open the cave of Cacus, and 3 times he sinks in weariness. Such deliberate triple repetition of ter, cited once in each verse, greatly intensifies the magical aspect of Hercules” actions. This is an unusual and striking usage of ter. In an other case there are 3 consecutive citations of 3 when the Cyclopes add 3 rays of twisted hail, 3 of watery cloud, and 3 of ruddy flame to a thunderbolt which they are forging (cf. 7, 141) — apparently Vergil intends to represent the thunderbolt as being composed of 3 different elements of a storm. Again the triple repetition of 3 heightens the overall magical effect of the scene which is modeled on an episode in Appolonius Rhodius (cf. 1, 731f.). In one case there are 6 consecutive citations of 3 with 3 references occurring in 3 consecutive verses when it is reported that King Erulus received from his 10, 885 ; and 10, 886: Asilas is named as the 3" leader of the Etruscan forces followed by a reference to the 3 clans of Mantua. Subsequently, Clausus kills 3 Thracians and the 3 sons of Ilas are cited — simply magical totals (cf. the tendency to have triplets fight as representatives of the entire group, as, for example, the legendary 3 Horatii and 3 Curiatii ; also the attraction of citing a magical number of sons). Turnus tries 3 times to commit suicide and 3 times Juno intervenes (cf. Iliad 1, 188f. and especially 8, 169 for Diomedes). Aeneas reportedly hurls a spear througha shield of 3-fold brass and through the inwoven work of triple bull hides — cf. the similar magical use of 7 at 8, 448 and 12, 925. Mezentius calls Aeneas 3 times in loud tones — a magical act usually reserved for death invocations (cf. e.g. 6, 506). Then he rides 3 times around him, a magical circumambulation generally associated with death rituals, and finally 3 times Aeneas carries around with him the spears on his shield. Therefore, the expression 3 times occurs 5 times in this book, including 3 successive citations at the end of the book, and 7 of the last 8 numerical citations involve 3, the last number cited in this book. 85-88: 11, 188; 11, 189; 11, 210; and 11, 631 : Aeneas and Tarchon run around the blazing funeral pyres 3 times — another example of circumambulation as part of a death ritual — and then they circle the funeral fire 3 times on horseback while wailing thus revealing combined magical influence from the act of circumambulation and from the custom of shouting a dead person’s name 3

times to ensure that that person is really dead. In the present case there is an unusual double circumambulation, i.e. 3 times on foot and 3 times on horseback, and this practice has definite Homeric overtones (cf. e.g. Iliad 23, 13 ; also the Roman custom of having soldiers march around the general’s pile). Then the bones are removed from the pyres at the 3“ dawn, i.e. after a suitable magical period of time (cf. Servius’ comment: mos enim tertia die ossa crematorum legi). As is the case with a 9-day period of mourning, i.e. 3 x 3, a 3-day interval also represents a sacred period of time. It is noteworthy that there are once again 3 consecùtive citations of the number 3 and that the only number advanced in verses 398-915 is 3 when there is a reference to a 3% encounter between the Etruscans and the Rutulians. Therefore, once again 3 is the last number cited in this book as it is in Books 6, 7, 9, and 10. 89-90 : 12, 155 and 12, 514: Juturna strikes her breast 3 and 4 times (discussed above) — a ritualistic, formulaic expression. Finally, Aeneas kills 3 Latins — a magical total. THE SYMBOLIC NUMBER 3 numerical designs in the Aeneid that Vergil either 303 implemented or was in the process of implementing at the time of his death that presently escape us. However, we can make a start by analyzing his work as it ing in mind that it is not in its final form. now stands while keep- The present investigation, which is part of a more extensiv e work in progress which examines all the numbers cited in the Aeneid, offers the reader valuable insight into Vergil's literary technique and the opportu nity to examine the Aeneid from a fresh Perspective. It also provides guidelines to help interpret problematic passages in this work that involve numerical citations (cf. e.g. 2, 263) according to Vergilian numerical practice. Such a study has serious implications for textual criticism involving the use of numbers, both implicitl y and explicitly, in the Aeneid as well as numerical questions in general. Albany Academy, Albany - New York. Roland A. Larocue. Conclusions Very little in the Aeneid is left to chance and, to paraphrase Pythagoras, I Appendix I believe that “Number rules the Aeneid” and that mystical numbers provide the Numbers Cited in the Aeneid underpinning, the foundation for this masterpiece. Vergil was very much influenced by Pythagorean humerical mysticism as is clearly indicated by an analysis of his use of numbers, both explicitly and implicitly, in the Aeneid as well as Number Found in Book(s) in the Eclogues and the Georgics. Citations in Citations in Books I-VI Books VII-XII Total Citations During the Renaissance Vergil was venerated as the classical exemplar of per- 3 fect artistic form. With good reason since the Aeneid, and indeed his entire opus, In all books 56 34 4 90 In I-VIIL,X,XII 12 10 22 represents an harmonious whole based on a detailed, precise mystical numerical plan which encompasses the numbers cited, the chronology, etc. The most important mystical numbers in his overall plan are 3, 7, 13, and 17. The single most important mystical number overall is 17, although 3 is also very influential, but 17 is never cited explicitly (nor is 13). This previously undetected dimension of the Aeneid helps to reveal starkly Vergil’s genius and his very great degree of originality based on his own mystical numerical scheme. The Aeneid is thus quintessentially Roman. The Aeneid, which has 55 incomplete verses (but in only one case, at 3, 340, is the meaning also incomplete) and some stop-gap passages, at the time of Vergil’s death was undergoing continuous revision and rewriting. It is possible that one of Vergil’s main concerns was the difficulty that he was experiencing in fully implementing his very ambitious mystical numerical scheme which permeates every aspect of this masterpiece. Perhaps he was encountering nearly 5 In VII and XII 0 4 7 4 In LV,VLVII-X,XU 13 5 9 18 In 1,V, VI XI 6 1 10 7 In I,VIILIX,XI 2 3 5 12 In I,V,EX,XLXI 2 5 14 7 In I and IX 1 20 30 50 100 200 300 500 600 1,000 1 In 1,1X,X1 In 1,18, VIII In 1,11, VI,X In I-IV, VI,VILIX-XI In VII In L,IV,VH-IX In X In X In 1-11, IV-XII 2 2 2 3 18 0 2 0 0 13 2 3 1 11 1 5 J 1 17 4 5 4 29 1 7 1 1 30 Total number of citations: insurmountable obstacles in his endeavor and thus he declared that he needed 3 more years to complete this epic. There are undoubtedly many other mystical

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