| DANTE'S 55 & THE PLATONIC LAMBDA
Peter Y. Chou
for Professor John Freccero's Dante's Paradiso
INTRODUCTION
The study of numbers was a religious exercise for Pythagoreans. Iamblichus (250-330 AD)
says that “if we wish to study mathematics in a Pythagorean manner, we ought to pursue
zealously its God-inspired, anagogic, cathartic and initiatory process.”
1
For Iamblichus, mathematics revealed divine mysteries of the soul's descent and return.
2
As Proclus (411-485 AD) put it, in the performance of mathematics
“the soul becomes at the same time seeing and seen.”
3
In this paper we will show through the significance of the number 55 that Dante was a
Pythagorean and Platonic philosopher at heart. Dante scatters the word "star" 55 times
in his Commedia, and uses the Platonic Lambda's number 55 as a vehicle for the soul's
ascent to the stars. In examining Dante's conscious placements of key passages in lines 55
of his Commedia, we discover secret doors that open the path to our cosmic soul.
These studies will help us to participate more fully in Dante's and our spiritual pilgrimage
to paradise.
DANTE'S HOMAGE TO PYTHAGORAS (580 B.C.-500 B.C.)
Dante mentions Pythagoras 8 times— 7 times in his Convivio and once in the De Monarchia.
Dante also cites his followers, the Pythagoreans, in the Convivio once.
4
Lansing lists Pythagoras & Pythagoreans 7 times in his index.
5
A word search at the Princeton Dante Project web site
6
for "Pittagora" in Dante's Convivio yielded 8 citations— 7 "Pittagora" & 1 "Pittagorici".
They are listed in Table 1 with
Lansing's translation7
of Dante's Convivio, Dante's sources according to Toynbee, and Prue Shaw's translation
8 of Dante's Monarchia.
It is clear from his Convivio citations that Dante holds Pythagoras in high regard calling him
"a very noble philospher" (Convivio 3.11.3) who considers "all things are number" (Convivio 2.13.18).
Dante notes that Pythagoras coined the word "philosopher" meaning "lover of wisdom" to show humility rather than
arrogance (Convivio 3.11.5). Dante confesses that after his first love (Beatrice), he was enamored by
“the most beautiful and honorable daughter of the Emperor of the universe, to whom Pythagoras gave the name
of Philosophy.” (Convivio 3.11.5). Since Dante names Pythagoras as the first philosopher
and places him "almost at the beginning of the foundation of Rome" (Convivio 3.11.3), Hopper says:
“the combination of priority and proximity to the foundation of Rome was in Dante's mind tantamount
to divine approval.”9
If Dante holds Pythagoras in such high esteem, why is Pythagoras not mentioned at all in his Commedia?
My guess is that sometime between the writing of the Convivio (1303-1308) and the latter part of the
Commedia, Dante was sworn to a vow of silence by the secret brotherhood of the Pythagoreans in Italy.
According to Iamblichus's De Vita Pythagorica, Pythagoras was born in Samos but journeyed to Croton,
Italy, where he established a school with some 600 followers.
10
Legend has it that Pythagoras' soul was sent down to humans under Apollo's guidance, and that his birth
was prophesied by Pythian Apollo.
11
Because of this, it is agreed that no one used his personal name, but that all called him "divine".
12
In accord with the "silence" legislated for them by Pythagoras, the students engaged in divine mysteries
and methods of instruction forbidden to the unintitiated, and through symbols, they protected their talks
with one another and their treatises. One of their dictims was “Do not talk about Pythagorean matters
without light.”
13
That Dante does not disclose the Pythagorean secrets openly shows that he observes the vow of
"Pythagorean silence."14
DANTE'S HOMAGE TO PLATO (428 B.C.-347 B.C.)
In the Commedia, Dante cites Plato three times and Timaeus once.
15
These citations are summarized in Table 2.
In his Epistle to Can Grande(13.84),
Dante says that “[Plato] saw many things with the light of his mind which he was not able
to express in his own words.”
16
hinting at his own inadequacy in describing the cosmic vision
Paradiso 33.121— “Oh quanto è corto il dire e come fioco al mio concetto!”
(How incomplete is speech, how weak, when set against my thought!)
17
Dante places Plato along with Socrates and Aristotle in Limbo (Inferno 4.134-136) because to
grant these pagan philosophers a place in heaven would amount to heresy. Dante expresses doubt in
Plato's teaching that "the souls return to the stars" (Paradiso 4.22-24). But Beatrice tells
him that Plato's words are "not to be derided" (Paradiso 4.55-57) and that Plato's "arrow reaches
something true" (Paradiso 4.60). Why is Dante putting these words in Beatrice's mouth instead of
his own? In 1302, while Dante was in Rome on a peace mission, the Black Guelfs assumed power in Florence.
They charged Dante of fraud and corruption in office and exiled him and if caught would burn him at the stake.
18
Was Dante afraid that Pope Boniface VIII will come after him for heresy?
Cecco d'Ascoli, a professor of astrology at the University of Bologna was burned at the stake by the
Inquisition at Florence in 1327.
19
Others burned at the stake for heresy by the Church include Joan of Arc in Rouen (1431), Savonarola in Florence (1498),
and Giordano Bruno in Rome (1600).
20
However Dante was fearless in his condemnation of the city of Florence when at the
height of his cosmic vision he tells how he came “from the human to the divine,
from time to eternity, and from Florence to a people just and sane" (Paradiso 31.39).
He was equally ruthless with Pope Boniface VIII having Saint Peter proclaim in the Eighth Heaven
of the Fixed Stars that "my place, my place, my place is empty." (Paradiso 27.22-24).
I believe that Dante placed Plato in paradise not overtly but covertly in accord with the silence
of the Pythagorean school. Paget Toynbee
21
notes that Dante cites Plato 18 times in his works—
3 times in his Commedia and 15 times in his Convivio. When we examine the citations
in Table 3, we see that Dante's regard for Plato is similar
to that of Pythagoras. He calls Plato "a most eminent man" (Convivio 2.4.4) and "possessed
a supremely excellent nature" (Convivio 4.24.6). Is it synchronicity that Dante placed Plato's
name in the Convivio and Paradiso both at 4.24? The word "Platone" at Paradiso 4.24
occurs on line 444 of Paradiso: "Plato taught that the souls return to the stars"
(Paradiso 4.22-24). Here, the number 444 represents the 4 circles & 3 crosses (Paradiso 1.39),
and the sum of 4+4+4 = 12 symbolizes the 12 hours, 12 months, 12 signs of the Zodiac. So outwardly,
Dante doubts the Platonic philosophy to Beatrice, but inwardly, he honors Plato by planting him at line 444
of Paradiso. Dante pays further tribute to Plato by comparing him to Christ:
“I believe that if Christ had not been crucified and had lived out the term which his life could have
encompassed according to its nature, he would have undergone the change from mortal body to immortal
in his 81st year.” (Convivio 4.24.6). Since Christ lived to the age 33 and Plato to 81,
let us see what is at line Paradiso 33.81:
While Plato's Republic was not translated during Dante's lifetime, he had certainly read the Timaeus (Paradiso 4.49). The continuity of the Platonic tradition during the Middle Ages has been documented by Klibansky. 23 Copies of Plato's Meno, Phaedo, and Timaeus belonging to Gérard d'Abbeville, the adversary of St. Thomas and Bonaventura in the University of Paris, were bequeathed to the Sorbonne, and were accessible to scholars after 1271. Before his death in 1286, the Dominican friar William of Moerbeke translated Proclus's Commentary on Plato's Parmenides. If Dante had studied at the Sorbonne "in the Street of Straw" (Paradiso 10.137), he may have had access to these works. PLATONIC LAMBDA: THE COSMIC SOUL
“Now God did not make the soul after the body, although we are speaking of them in this order; for having brought them together he would never have allowed that the elder should be ruled by the younger... First of all, he took away one part of the whole [1], and then he separated a second part which was double the first [2], and then he took away a third part which was half as much again as the second and three times as much as the first [3], and then he took a fourth part which was twice as much as the second [4], and a fifth part which was three times the third [9], and a sixth part which was eight times the first [8], and a seventh part which was twenty-seven times the first [27]. After this he filled up the double intervals [i.e. between 1, 2, 4, 8] and the triple [i.e. between 1, 3, 9, 27] cutting off yet other portions from the mixture and placing them in the intervals” “This entire compound he divided lengthways into two parts, which he joined to one another at the centre like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side to the right, and the motion of the diverse diagonally to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two-and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three [Sun, Mercury, Venus] he made to move with equal swiftness, and the remaining four [Moon, Saturn, Mars, Jupiter] to move with unequal swiftness to the three and to one another, but in due proportion.”
The Platonic Lambda diagram was first attributed to Crantor of Soli (335-275 BC). It is shown
in Cornford's commentary
24 on the Timaeus,
as well as references.25-33
but not in the references of Jowett,
34
Thomas Taylor
35
and the other commentaries.
36-38
While the even (double) series of 1, 2, 4, 8, and odd (triple) series of 1, 3, 9, 27 are cited
often, none of these commentators mention the sum of the two series adds up to 55 as shown below:
The Soul of the Universe is the sum of the two series (Timaeus 35b):
ON THE NUMBER 55
In her book The Mystery of Numbers, Schimmel writes “Fifty-five is not considered
a particularly important number today... it is interesting from an arithmetical viewpoint as the sum
of all integers between 1 and 10; it can also be divided into different elements, such as the sum
of 28 + 12 + 10 + 5."
39
In his Medieval Number Symbolism, Hopper
9 covers astrological numbers,
Christian numbers, Dante's use of numbers, elementary number symbolism, Gnostic numbers, medieval number philosophy,
Pagan number symbols, and Pythagorean numbers. A search through his index listing these categories of
numbers do not show 55 among them. Macqueen's Numerology has a chapter on "Plato: The Harmonic Soul of the Universe"
40 and Butler's Number Symbolism opens
with a chapter on "The Greek Origins of Number Symbolism."
41
Both authors quote Plato's Timaeus on the "World Soul" and even draw the Platonic Lambda diagram.
They arranged the numerical series sequentially as 1, 2, 3, 4, 8, 9, 27. However neither bothered to add
them up to yield 54 or as the double & triple series (1, 2, 4, 8) and (1, 3, 9, 27) to yield 55.
Isaacs' Jewish Book of Numbers compiles number symbolisms in the Bible, in Rabbinic thought, and
in Jewish life, but 55 is not cited.
42
Allen's Nuptial Arithmetic lists two pages of numbers from 1 to 33,550,336 with insightful
commentaries by Ficino. There are even 11 pages in the index referring to the Platonic Lambda,
but no mention of 55.
43
Likewise, Hardt's
44 Die Zahl in der Divina Commedia
and Guzzardo's45
Dante's Numerological Studies do not mention 55 in their studies and compilations.
The above survey of books on numbers and numerology show a dearth on the number 55. Even Plato in his
Timaeus does not mention 55 as the sum of the double & triple series that make up the soul of the
universe. No wonder none of the Timaeus commentators
24-38 delved into this sacred number.
Nevertheless, 55 was known to the ancient sage-kings of China in the I Ching (circa 1000 B.C.)
46
It will be noted that the sum of the odd heavenly numbers and even earthly numbers = 25 + 30 = 55 from the I Ching is obtained differently from that of Plato's Timaeus whose Cosmic Soul is the sum of the double and triple series = 15 + 40 = 55. The I Ching hexagram 55 "Fêng / Abundance (Fullness)" shows trigrams "thunder" above "flame" with the Judgment:
The commentary notes “Only a man who is inwardly free of sorrow and care can lead in a time of abundance. He must be like the sun at midday, illuminating and gladdening everything under heaven.” 47 The tetraktys is the legendary oath of the Pythagoreans where the decad is produced from the sum of the first four numbers (1 + 2 + 3 + 4 = 10): “Lo! what thou thinkest four is ten, and a perfect triangle, and our oath.” 48 Butler shows how the Pythagoreans invented the triangular numbers using pebbles to build successive rows of dots in an arithmetical progress. 49
It is easy to see how the Pythagoreans found 10 as the 4th triangular number, and by means of this progression will deduce 55 as the 10th triangular number. However, the number 55 is not cited in Pythagorean literature, perhaps owing to their oath of silence. We find the number 55 in Aristotle (384-322 B.C.) who postulated a complex arrangement of 55 concentric spheres. 50 Aristotle writes in Metaphysics 1074a6 (Bk XII or Book Lambda) 51
It is interesting that Aristotle arranged 55 heavenly spheres in his Book Lambda of Metaphysics perhaps in honor of his mentor Plato, where he learned about 55 and the Platonic Lambda— the World Soul. Next we come to Leonardo Fibonacci of Pisa (1170-1250). He discovered a series of numbers that describes a logarithmic spiral: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. Each number is the sum of the two before it, so that the 10th Fibonacci number is 21 + 34 = 55. We find Fibonacci numbers everywhere in nature— sunflowers, artichokes, pineapples, branches on trees, reproduction rate of rabbits, and spiral galaxies. 52 It is fascinating to note that Thomas Taylor who translated Plato from Greek to English in five volumes (1804), called his book 55 Dialogues of Plato. A close examination of Taylor's work 53 reveals that he called each of the ten books of The Republic a separate dialogue to come up with the magic number of 55. In one of the few books that cites 55, Kozminsky 54 says that “the number 55 is symbolised as The Sword signifying energy and triumph. It denotes mental penetration which pierces the darkness of ignorance as a sharp sword pierces a dense body. We'll keep this sword image in mind when reading Dante's Commedia. A summary of other numbers on 55 is shown in Table 4. 55 55 STARS IN DANTE'S COMMEDIA When Halley's Comet returned in 1986, Science News reported that the comet will make its closest approach to the sun (perihelion) on February 9, 1986 at a distance on only about 55 million miles.” 56 Yeoman's Comet Halley Handbook records that “the velocity of Halley's Comet at perihelion is 55 kilometers per second.” 57 The conjunction of these numbers 55 with respect to Comet Halley's position and velocity at perihelion sparked something in me. Never mind that the dimensions of miles and kilometers were not in sync or that Heisenberg's Uncertainty Principle says that one cannot measure the precise position and momentum of an electron at the same time. All I heard is Comet Halley's whisper: “Remember 55— the Platonic Lambda— the soul's return to the stars.” I recalled Singleton's lecture at Cornell's "Dante's 700th Birthday Symposium" that "Dante ended each of his cantiche of the Inferno, Purgartorio, and Paradiso with the word "stelle" (stars). I found my copy of Wilkins' Concordance to the Divine Comedy and began counting the stars under "stelle": 58 11 in Inferno, 13 in Purgatorio, and 31 in Paradiso. with the line Paradiso 28.21 containing two stars: Ah! 55 stars Dante scattered in his Commedia— Did Dante know about the Platonic Lambda? Did he add up the double & triple series to get 55? Was this accidental or a conscious decision of Dante's to use Plato's Cosmic Soul number of 55 as the number of stars in his cosmic drama? To answers these questions, we need to examine the lines of the Commedia and see whether Dante has incorporated the number 55 in his poem. When Freccero told me that Wilkins compiled his Concordance using index cards, I was concerned of possible manual errors in such a compilation. Two other concordances were examined that of Fay (1888) 59 and Lovera (1975). 60 Both gave 29 "stella" and 26 "stelle" for a total of 55 stars. A web search program by Williams 61 "Concordance: Dante's Divine Comedy" also yielded the same results of 29 "stella" and 26 "stelle." Having ascertained that Dante did indeed use 55 stars in his Commedia, I began compiling a table similar to Singleton 62 and Logan. 63 Singleton had discovered the amazing symmetry at the center of Dante's Purgatorio from Canto 14-20: 151, 145, 145, 139, 145, 145, 151. Logan had found additional symmetry in the sums of the lines at Cantos 11-23 in Purgatorio: 7, 1, 1, 7, 1, 1, 4, 1, 1, 7, 1, 1, 7 and Paradiso: 4, 1, 7, 4, 4, 1, 7, 1, 4, 4, 7, 1, 4. An examination of Table 5 will show an Inferno symmetry at its center in Cantos 15-19 with the sums of canto lines = 7, 1, 1, 1, 7 as well as symmetries at Cantos 8-12 with sums = 4, 7, 1, 7, 4 and Cantos 29-33 with sums = 4, 4, 1, 4, 4. Additional symmetries can be discerned at the beginnings of Purgatorio Cantos 1-7 with sums = 1, 7, 1, 4, 1, 7, 1 and Paradiso Cantos 1-9 with sums = 7, 4, 4, 7, 4, 7, 4, 4, 7. These symmetries are outlined in bold in Table 5 with the central Canto underlined. A recent study of canto-length sums were made by Vanderwielen. 64 She notes that the symmetric Inferno Cantos 15-19 with sums = 7, 10, 10, 10, 7 adds to 44. The symmetric Purgatorio Cantos 11-23 sums = 121 and the symmetric Paradiso Cantos 11-23 sums = 139. Since Vanderwielen did not reduce the 10 and 13 further to 1 and 4 respectively, the additional four symmetries noted above were not observed. Table 6 shows the total lines in Dante's Inferno, Purgatorio, and Paradiso. This study was undertaken to facilitate calculations of the line occurrences of the 55 star citations as well as the distance between these stars as shown in Table 7. Since Fibonacci (1170-1250) died only 15 years before Dante (1265-1321) was born, did Dante used the spiral patterns of the Fibonacci series in the structure of his Commedia? Being such a cosmic visionary, did Dante scatter his stars like the spiral galaxies. A glance at Table 7 does not show any discernible Fibonacci patterns. What is striking is the symbolism of 11 stars in the Inferno, 13 in Purgatorio and 31 in Paradiso that Dante distributed in these cantiche. The number 11 may be reduced to "2" symbolising duality, which is the root of evil according to Pythagoras cited by Dante in his Monarchia 1.15.2 (see Table 1). Also the German word for doubt is zweifel which is etymologically related to zwei,the number two. When the mind is in doubt, we're in a state of confusion or hell because our action is frozen like Satan and those thousand faces in ice (Inferno 32.70-72). Also the number 11 (undici) is used in the Commedia only once 65 by Dante— the 11 miles circumference of the 10th bolgia in the 8th circle of Hell (Inferno 30.86). On the other hand the 13 stars in Purgatorio remind us of the One-in-Three of the Trinity: "che tiene una sustanza in tre persone" (taken by One Substance in Three Persons) 66 in Purgatorio 3.36 and "vidi una porta, e tre gradi di sotto" (saw a gate with three steps beneath) 67 in Purgatorio 9.76. Finally the 31 stars in Paradiso reinforces the idea of the Three-in-One of the Trinity. The following translations are from Mandelbaum. 68
The star citations in the Inferno (Table 8), Purgatorio (Table 9), and Paradiso (Table 10) in Italian with Mandelbaum's translations were compiled using the Columbia University's Digital Dante web site. 69 It will be noted that two of the Inferno star citations occur on line 55 (Platonic Lambda sum):
In the first instance, Dante compares Beatrice's eyes as surpassing the splendor of stars. In the second instance, Dante's former mentor Brunetto Latini tells Dante to follow his star to reach a splendid harbor. As Frecerro elucidated in his lectures, Brunetto's harbor may have been a tenure position at the University in Florence, but Dante's harbor was paradise. Within these star terzinas we find images of descent in Inferno 7.98 and 26.127 (Table 8) as well as Purgatorio 6.100 and 31.106 (Table 9). Ascent and return images are found in Paradiso 4.23, 4.52, 12.29, 14.86, and 18.68 (Table 10). Two books on Dante's stars may be studied with much illumination— Orr's 70 Dante and the Early Astronomers and Kay's71 Dante's Christian Astrology. As the titles suggest, the first covers Dante's stars from an astronomical point of view, and the second from an astrological point of view. In this present study, we see that for Dante, the stars are but a memory in the Inferno, a compass guide for the pilgrim in Purgatory, and a celebratory dance and feast in Paradise.
As the above terzinas show, the stars are no longer outside of Dante but in his heart glowing from within. This mystic vision occurs when the spiritual aspirant purifies his mind and heart so that divine energy flows through. Lu Hsiang-shan (1139-1193), the Chinese sage of Elephant Mountain, proclaimed: “The four directions plus upward and downward constitute space. What has gone by in the past and what is to come in the future constitute time. The universe is my mind and my mind is the universe.” 72 This is similar to Dante's vision when he saw “within a single volume bounded by love, I saw the scattered leaves of all the universe” (Paradiso 33.86-87). CANTO LINES 55 IN THE INFERNO Having explored the 55 star citations in the Commedia, let's turn our attention to lines 55 in Dante's poem. If Dante had great reverence for Plato, and learned about the Platonic Lambda number 55 as the Cosmic Soul, surely he would place important ideas and messages at this line. The 19th terzina of each canto beginning with line 55 in the Inferno (Table 11), Purgatorio (Table 12), and Paradiso (Table 13) were compiled for further study. We have already discussed the two terzinas of Inferno where the word stella appears in 2.55 and 15.55.
We see that Dante places Adam (our first father) at 4.55, the theme of turn, return, and climbing are described in 9.55 and 24.55, and prayer is mentioned in 27.55. Since 4, 9, and 27 are numbers in the Platonic Lambda, Dante's placements at these cantos may be carefully designed rather than accidental. LUCIA AT PURGATORIO 9.55 Scanning through the canto lines 55 in Purgatorio (Table 12), the following terzinas stood out: eyes looking below and then above (3.55 and 4.55), repenting and forgiving bring peace with God (5.55), climbing up (7.55 and 27.55), turning (28.55 and 29.55), returning (6.55), wings uplifted (31.55), and divine spirit “conducting us to the upward path” (17.55) But perhaps the most important terzinas in Purgatorio are “I am Lucia” (9.55) and “Dante, though Virgil's leaving you” (30.55):
Gallagher 73 calls Purgatorio 9 a transitional canto that takes Dante & Virgil from the first to the second of the three divisions of Mount Purgatory “that cures by being climbed.” Dante dreamt of being carried by a golden eagle to heaven's Sphere of Fire (9.19-33). Upon waking, Virgil informs him that Saint Lucia carried the sleeping Dante up the mountain to Purgatory's Golden Gate (9.49-57). Ciardi notes that allegorically Lucia represents Divine Light. Her name in Italian suggest luce (light) and she is the patron saint of eyesight. Also Lucia is an anagram for acuila "eagle." 74 Dante alerts his readers that “my theme is now more exalted so I must write with greater art” (9.70-72). That is, we must be attentive to more symbolism at the allegorical and anagogic levels. The three steps leading to the gate of God's angel are colored, in order, white, deep purple (black), and red (9.95-103). Freccero 75 notes that Christ's “blood was shed so that man could take the final step of regeneration... and when that step is completed, it will be white.” He then quotes medieval theologians that this is the spiritual ascent of the pilgrim from penance to purification to passion and glory. Dante compares himself with Ganymede in his dream, being snatched up to Mount Olympus by Jupiter's eagle. Since Ganymede became the cupbearer to the gods, 74 after Dante's purification by fire, his poem is exalted so that he's bearing a spiritual message from the gods to the reader. Beatrice, Lucia, and Mary are the three blessed ladies aiding Dante's pilgrimage to paradise (Inferno 2.124), so Dante places Lucia at Purgatorio 9.55 because of the importance of his spiritual ascent in this canto. The symbolism of 9 as the square of the Trinity as well as Beatrice's number (La Vita Nuova 29) 76 and 55 as Plato's Cosmic Soul number are perfectly fitting for Lucia— “the eagle of light” carrying Dante upward toward paradise. DANTE'S NAME AT PURGATORIO 30.55 The appearance of "Dante" at Purgatorio 30.55 is striking in that it is the only place in the Commedia where his name is mentioned. 77 Except in certain letters and in one lyric, Dante never mentions his name in all his works. 78 In Convivio I.2.3, Dante writes “The rhetoricians grant no one the right to speak of himself, except in the case of necessity.” 79 So Dante apologizes profusely for its unique occurrence because Beatrice had uttered it— so he is reporting what truly took place (Purgatorio 30.61-63). It is interesting that 9 lines after Beatrice utters his name, Dante sees “the lady who first appeared to me” (30.64). The reader will recall that Dante first met Beatrice when he was 9 years old and then again when he was 18 years old (La Vita Nuova II & III). We find Beatrice proclaiming her name (Purgatorio 30.73) exactly 18 lines after she calls out Dante's name (Purgatorio 30.55). Students of numerology will be fascinated in finding "Dante" & "la donna" & "Beatirce" at lines 55, 64, and 73. All three numbers add up to 10 = 1 + 9 = 12 + 32 = Squares of Unity & Trinity.
Even more amazing is Dante's placement of his name at 30.55. This study began when it was noted that Dante scattered 55 stars in his Commedia. Now he places his own name at line 55— the Platonic Lambda number for the Cosmic Soul. When Beatrice reproaches Dante for daring to approach the mountain— could she be referring to the shape of the Greek letter Lambda that resembles a mountain? After Dante's passage through Hell and Purgatory, he needs further purification to ascend the mountain of the Cosmic Soul. In Ifrah's 80 From One to Zero: A Universal History of Numbers, we learn that the Greek alphabetic numeration is similar to that of the Hebrew numeral letters. The 12th Hebrew letter Lamed = 30 and the 11th Greek letter Lambda = 30. So in all of Dante's writings, the only place his name appears is at Purgatorio 30.55 or "Lambda-55". Dante is purifying himself— ready for his flight to the stars, but also realizing that his individual soul and the Cosmic Soul are One. CANTO LINES 55 IN THE PARADISO Looking through the canto lines 55 of Paradiso (Table 13), we find images of God (6.55, 7.55, 10.55, 15.55, 19.55, 20.55, 26,55, 27.55), love (8.55, 12.55,13.55, 17.55), rising (11.55, 30.55), and turning (5.55, 24.55, 26.55, 31.55). But the "arrows of amazement" (2.55) that struck me were the following terzinas:
"Plato's ideas which is not to be derided" is placed at 4.55 to honor the "4" of Pythagoras' tetraktys and "55" of the Platonic Lambda. The Living Light that pours out (13.55) is the Word emanating from God as light. All our thoughts are flowing to us from God, as 5 and 6 flow from the One (15.55). Both Singleton and Mandelbaum comments that all numbers are derived from one. But why does Dante mentions specifically 5 and 6? If we look at the numbers flowing out of the Platonic Lambda, we notice that 2 and 3 flow out from the One. Now 2 + 3 = 5 and 2 x 3 = 6 or if we add the first three numbers 1 + 2 + 3 = 6. So Dante's use of 5 and 6 from the One shows that he's familiar with the Platonic Lambda or triangular numbers. This is evidenced by Dante quoting the opening lines in Plato's Timaeus: “One, two, three— but where is the fourth?” in his Paradiso 14.28 to celebrate the Trinity:
We find Beatrice's name at Paradiso 24.55 for she represents wholeness— 24 hours represents a complete day and 55 represents the Cosmic Soul. Now she's initiating Dante by baptising him with the words of Christ: “From within him, there shall flow rivers of living water.” When the pilgrim is thus purified, divine energy flows through him and he's made whole in the image of the Creator. Such a rapture is experienced in Dante when we read in 30.55 how he was rising beyond his power to drink in the flood of cosmic light and delight. PLATONIC LAMBDA: EVEN & ODD NUMBERS
SOUL'S ASCENT IN THE COMMEDIA: 55 & 139 Can we ascend the Platonic Lambda mountain from the "Good" right side of 27, 9, 3, back to the One? The number 27 is the cube of 3 and there are 27 Books in the New Testament Bible. There are 9 heavenly spheres moved by the angelic choir and 9 muses which bring inspiration to the artist and poet. Toynbee notes that Dante invokes the muses at the beginning of his description of Hell (Inferno 2.7), before his account of circle 9 of Hell (Inferno 32.10-11), at the beginning of his description of purgatory (Purgatorio 1.8), before his account of the mystical Procession in the Earthly Paradise (Purgatorio 29.37-42). He was under the inspiration of the muses and that of Apollo and Minerva at the start of his journey to Heaven (Paradiso 2.8-9), and invokes them again before his account of the evolutions of the spirits in the Sphere of Jupiter (Paradiso 18.82). Polyhymnia "the Muse of the Sublime Hymn" is cited in the terzina Paradiso 23.55, the number of the Platonic Lambda (see Table 13). The number 3 is used by Dante in his 3 cantiche each with 33 cantos with an introductory one for the Inferno to reflect the 33 years of Christ's life. Each terzina contains 3 lines with 33 syllables, a kind of cosmic tercet to remind us of Christ. 83 So we can see how Dante's use of these numbers 9 and 3 brings us back to the One. Freccero pointed out Singleton's commentary at the end of Paradiso 26.142 that the last 7 cantos of Paradiso marked a new beginning framing the first 7 cantos of Inferno. Looking at the beginning of Paradiso 27, we find:
Such a beautiful invocation as the blessed souls sing a hymn of praise to the Holy Trinity. So through prayer and song, our soul is lifted to heaven through the door of Canto 27. In Professor Freccero's last lecture on "Dante's Paradiso" (June 5, 2001), he quoted Paradiso 32.139 saying that even high up in heaven amidst the stars and angels, Dante brings us back to earth with the homely image of the "good tailor." He then mentioned other "tailor images"— Virginia Woolf's Mrs. Ramsay knitting her brown stocking that's not going to fit the boy (To the Lighthouse) and in Dante's Commedia— the spinning of Penelope (Inferno 26.93) and Arachne (Inferno 17.18) as well as Brunetto Latini squinting at Dante like an old tailor (Inferno 15.19-21). During the break, I told Freccero that he forgot another tailor. When he asked me which one, I pointed to Line 139 of the Paradiso— Plato's God who had woven the soul of the universe with two mathematical strips: 1, 2, 4, 8 and 1, 3, 9, 27 (Timaeus 35b). Freccero was pleasantly surprised that Dante may have placed Plato's "Cosmic Tailor" in the Empyrean. If the left side of the Platonic Lambda 1, 2, 4, 8 represents the descent of the soul from the One to our earthly body (8 symbolizes the points of the cube), then the right side 1, 3, 9, 27 represents the ascent of the soul back to the One. Since 1x3x9 = 27, Saint Bernard is exhorting Dante and us to "turn our vision to the Primal Love"— to gaze at that One who is full of radiance. Afterwards I checked line 139 at the end of Purgatorio and was surprised to find another tailor image. Here it's Dante the poet, weaving on his loom (ordite), finishing his tapestry of his second cantica of the Commedia. The last line of the Inferno occurs at line 139— Here Dante & Virgil climb back into the bright world, emerging from the darkness to see once more the stars. These three terzinas of lines 139 are summarized in Table 14. If Dante's usage of 55 stars in his Commedia to depict the Platonic Lambda as the "Cosmic Soul" were accidental, then his placements of "ascent" images in Lines 139 near the end of his canticas appear well designed for a master poet who had declared his Commedia as a sacred poem (Paradiso XXV.1). CONCLUSION Dante's Commedia is a garden of cosmic delights. He offers the reader a sumptuous feast of Pythagorean-Platonic philosophy, Christian theology, astronomical wonders, allegorical symbolisms, hidden numerical gems, but above all— beautiful poetry. In this paper we have shown how Dante uses the Platonic Lambda "55" as a marker to alert us to the important messages and gifts he's bearing from the gods to his reader. Singleton in his classic paper "The Poet's Number at the Center" 62 referred to the number "7" as Dante's poet number. Here we suggest the number "55" as Dante's pilgrim number. By drinking from both fountains, we are treated indeed to the bread of angels. We journey along with Dante to the outermost and innermost reaches of the cosmos, enjoying the vistas in all its height and depth, experiencing heaven on earth right here and now, right in our heart.
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In Plato's Timaeus, we find that God created the Cosmic Soul using two mathematical
strips of 1, 2, 4, 8 and 1, 3, 9, 27. These two strips have the shape of an inverted "V" or
the "Platonic Lambda" since it resembles the shape of the 11th letter of the Greek alphabet
"Lambda". Here's Benjamin Jowett's translation
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