Plimpton 322

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The Plimpton 322 clay tablet, with numbers written in cuneiform script.

Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics. It has number 322 in the G.A. Plimpton Collection at Columbia University. This tablet, believed to have been written about 1800 BC, has a table of four columns and 15 rows of numbers in the cuneiform script of the period.

This table lists two of the three numbers in what are now called Pythagorean triples, i.e., integers a, b, and c satisfying a² + b² = c². From a modern perspective, a method for constructing such triples is a significant early achievement, known long before the Greek and Indian mathematicians discovered solutions to this problem. At the same time, one should recall the tablet's author was a scribe, in his day, a professional mathematician; it has been suggested that one of his goals may have been to produce, find, and fix school problems.

There has been significant scholarly debate on the nature and purpose of the tablet. For readable popular treatments of this tablet see Robson (2002) or, more briefly, Conway & Guy (1996). Robson (2001) is a more detailed and technical discussion of the interpretation of the tablet's numbers, with an extensive bibliography.

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Provenance and dating

Plimpton 322 is partly broken, approximately 13 cm wide, 9 cm tall, and 2 cm thick. New York publisher George Arthur Plimpton purchased the tablet from an archaeological dealer, Edgar J. Banks, in about 1922, and bequeathed it with the rest of his collection to Columbia University in the mid 1930s. According to Banks, the tablet came from Senkereh, a site in southern Iraq corresponding to the ancient city of Larsa.

The tablet is believed to have been written about 1800 BC, based in part on the style of handwriting used for its cuneiform script: Robson (2002) writes that this handwriting "is typical of documents from southern Iraq of 4000–3500 years ago." More specifically, based on formatting similarities with other tablets from Larsa that have explicit dates written on them, Plimpton 322 might well be from the period 1822–1784 BC. Robson points out that Plimpton 322 was written in the same format as other administrative, rather than mathematical, documents of the period.

Content

The main content of Plimpton 322 is a table of numbers, with four columns and fifteen rows, in Babylonian sexagesimal notation. The fourth column is just a row number, in order from 1 to 15. The second and third columns are completely visible in the surviving tablet. However, the edge of the first column has been broken off, and there are two consistent extrapolations for what the missing digits could be; these interpretations differ only in whether or not each number starts with an additional digit equal to 1. With the differing extrapolations shown in parentheses, these numbers with six errors corrected are

(1) 59 00 15	1 59	2 49	1
(1) 56 56 58 14 50 06 15	56 07	1 20 25	2
(1) 55 07 41 15 33 45	1 16 41	1 50 49	3
(1) 53 10 29 32 52 16	3 31 49	5 09 01	4
(1) 48 54 01 40	1 05	1 37	5
(1) 47 06 41 40	5 19	8 01	6
(1) 43 11 56 28 26 40	38 11	59 01	7
(1) 41 33 45 14 03 45	13 19	20 49	8
(1) 38 33 36 36	8 01	12 49	9
(1) 35 10 02 28 27 24 26 40	1 22 41	2 16 01	10
(1) 33 45	45	1 15	11
(1) 29 21 54 02 15	27 59	48 49	12
(1) 27 00 03 45	2 41	4 49	13
(1) 25 48 51 35 06 40	29 31	53 49	14
(1) 23 13 46 40	56	1 46	15

It is possible that additional columns were present in the broken-off part of the tablet to the left of these columns. Conversion of these numbers from sexagesimal to decimal raises additional ambiguities, as the Babylonian sexagesimal notation did not specify the power of the initial digit of each number. The sixty sexagesimal entries are exact, no truncations or rounding off.

Interpretations

In each row, the number in the second column can be interpreted as the shortest side ${\displaystyle s}$ of a right triangle, and the number in the third column can be interpreted as the hypotenuse ${\displaystyle d}$of the triangle. The number in the first column is either the fraction ${\displaystyle \scriptstyle {\tfrac {s^{2}}{l^{2}}}}$ (if the "1" is not included) or ${\displaystyle \scriptstyle {\tfrac {d^{2}}{l^{2}}}\,=\,1+{\tfrac {s^{2}}{l^{2}}}}$ (if the "1" is included), where ${\displaystyle l}$ denotes the longer side of the same right triangle. Scholars still differ, however, on how these numbers were generated. Below is the decimal translation of the tablet.

${\displaystyle d^{2}/l^{2}}$ or ${\displaystyle s^{2}/l^{2}}$	Short Side ${\displaystyle s}$	Diagonal ${\displaystyle d}$	Row #
(1).9834028	119	169	1
(1).9491586	3,367	4,825	2
(1).9188021	4,601	6,649	3
(1).8862479	12,709	18,541	4
(1).8150077	65	97	5
(1).7851929	319	481	6
(1).7199837	2,291	3,541	7
(1).6927094	799	1,249	8
(1).6426694	481	769	9
(1).5861226	4,961	8,161	10
(1).5625	45	75	11
(1).4894168	1,679	2,929	12
(1).4500174	161	289	13
(1).4302388	1,771	3,229	14
(1).3871605	56	106	15

Otto E. Neugebauer (1957) argued for a number-theoretic interpretation, pointing out that this table provides a list of (pairs of numbers from) Pythagorean triples. For instance, line 11 of the table can be interpreted as describing a triangle with short side 3/4 and hypotenuse 5/4, forming the side:hypotenuse ratio of the familiar (3,4,5) right triangle. If p and q are two coprime numbers, one odd and one even, then ${\displaystyle \scriptstyle (p^{2}-q^{2},\,2pq,\,p^{2}+q^{2})}$ form a Pythagorean triple, and all Pythagorean triples can be formed in this way or as multiples of a triple formed in this way. For instance, line 11 can be generated by this formula with p = 2 and q = 1. As Neugebauer argues, each line of the tablet can be generated by a pair (p,q) that are both regular numbers, integer divisors of a power of 60. This property of p and q being regular leads to a denominator that is regular, and therefore to a finite sexagesimal representation for the fraction in the first column. Neugebauer's explanation is the one followed e.g. by Conway & Guy (1996). However, as Eleanor Robson (2002) points out, Neugebauer's theory fails to explain how the values of p and q were chosen: there are 92 pairs of coprime regular numbers up to 60, and only 15 entries in the table. In addition, it does not explain why the table entries are in the order they are listed in, nor what the numbers in the first column were used for.

Buck (1980) proposed a possible trigonometric explanation: the values of the first column can be interpreted as the squared secant or tangent (depending on the missing digit) of the angle opposite the short side of the right triangle described by each row, and the rows are sorted by these angles in roughly one-degree increments. In other words, if you take the number in the first column, discounting the (1), and derive its square root, and then divide this into the number in column two, the result will be the length of the long side of the triangle. Consequently, the square root of the number (minus the one) in the first column is what we would today call the tangent of the angle opposite the short side. If the (1) is included, the square root of that number is the secant.

In contraposition with these earlier explanations of the tablet, Robson (2002) claims that historical, cultural and linguistic evidence all reveal the tablet to be more likely "a list of regular reciprocal pairs." Robson argues on linguistic grounds that Buck's trigonometric theory is "conceptually anachronistic": it depends on too many other ideas not present in the record of Babylonian mathematics from that time. In 2003, the MAA awarded Robson with the Lester R. Ford Award for her work, stating it is "unlikely that the author of Plimpton 322 was either a professional or amateur mathematician. More likely he seems to have been a teacher and Plimpton 322 a set of exercises." Robson takes an approach that in modern terms would be characterized as algebraic, though she describes it in concrete geometric terms and argues that the Babylonians would also have interpreted this approach geometrically.

Robson bases her interpretation on another tablet, YBC 6967, from roughly the same time and place. This tablet describes a method for solving what we would nowadays describe as quadratic equations of the form, ${\displaystyle \scriptstyle x-{\tfrac {1}{x}}=c}$, by steps (described in geometric terms) in which the solver calculates a sequence of intermediate values v₁ = c/2, v₂ = v₁², v₃ = 1 + v₂, and v₄ = v₃^1/2, from which one can calculate x = v₄ + v₁ and 1/x = v₄ - v₁.

Robson argues that the columns of Plimpton 322 can be interpreted as the following values, for regular number values of x and 1/x in numerical order:

v₃ in the first column,

v₁ = (x - 1/x)/2 in the second column, and

v₄ = (x + 1/x)/2 in the third column.

In this interpretation, x and 1/x would have appeared on the tablet in the broken-off portion to the left of the first column. For instance, row 11 of Plimpton 322 can be generated in this way for x = 2. Thus, the tablet can be interpreted as giving a sequence of worked-out exercises of the type solved by the method from tablet YBC 6967, and reveals mathematical methods typical of scribal schools of the time, and that it is written in a document format used by administrators in that period. Therefore, Robson argues that the author was probably a scribe, a bureaucrat in Larsa. The repetitive mathematical set-up of the tablet, and of similar tablets such as BM 80209, would have been useful in allowing a teacher to set problems in the same format as each other but with different data. In short, Robson suggests that the tablet would probably have been used by a teacher as a problem set to assign to students.

So what does any of this have anything to do with the occult? Simple mathematics being one of the 7 sciences encompasses what we know as the occult. 

Tosca Cake

Tosca cake is a Scandinavian favorite, thought to be named for Puccini's opera. It's a delicate sponge, crowned with a caramelized almond, praline-like topping. It's luscious enough on its own, but it also makes a great accompaniment for a pile of tiny new summer strawberries.

Makes about 8 servings

Cake Layer

1 1/4 cups all-purpose flour
1 teaspoon baking powder
1/2 teaspoon coarse salt
1 stick butter (8 tablespoons), melted and cooled
1 teaspoon vanilla extract
1/3 cup milk
3 large eggs
3/4 cup sugar

Tosca Topping

1/2 stick butter (4 tablespoons)
2/3 cup sugar
1/4 cup whipping cream
2 tablespoons all-purpose flour
Pinch salt
1 cup sliced/flaked almonds (you can substitute slivered almonds if desired, though I think the thin-sliced almonds make a more delicate topping)
1/4 teaspoon almond extract
1/4 teaspoon vanilla extract

Preheat oven to 350 degrees, and butter and flour a 9-inch springform pan. Line the bottom of the pan with a circle of parchment, and butter that as well.

Sift together the flour, baking powder and salt. Set aside. Mix together the butter, vanilla and milk, and set aside (it should be warm enough that the butter is liquid, but not too hot).

With an electric mixer, beat together the eggs and sugar on a high speed until pale and thick. Add the flour mixture and the milk mixture in turns, mixing after each addition until just barely combined, ending with the dry ingredients. Do not overmix (it's better to err on the side of undermixing to ensure a tender cake). Pour into the springform pan and place in the oven to bake for 20 to 25 minutes, until the top is just barely set.

While the cake is baking, prepare the topping. Combine the butter, sugar, cream, flour and salt in a saucepan. Place over a medium-high flame and stir to combine as the butter melts. When the mixture has combined, add the almonds and allow the mixture to come to a simmer. Let simmer 1 minute, then turn off the heat. Stir in the extracts and set aside.

When the cake has baked for 20 to 25 minutes and is just barely set, gently remove it from the oven. Raise the oven temperature to 400. Gently spread the topping on the cake. Place the cake back in the oven, and bake an additional 15 minutes or so, until the topping is golden brown. Allow to cool before slicing.

A bit of history of the Summer Solstice

The summer solstice is the longest day of the year, and the shortest night. In the Northern Hemisphere it takes place between June 20 and 22, depending on the year. (The reverse is true in the Southern Hemisphere, where the longest day of the year occurs between December 20 and 22.) Humans may have observed the summer solstice as early as the Stone Age. Cultures around the world still celebrate the day with feasts, bonfires, picnics and songs.

According to some ancient Greek calendars, the summer solstice marked the start of the New Year. The summer solstice also marked the one-month countdown to the opening of the Olympic games.

Kronia, a festival celebrating Cronus, the god of agriculture, was also held around this time. The Greeks’ strict social code was temporarily turned on its head during Kronia, with slaves participating in the merriment as equals or even being served by their masters.

In the days leading up to the summer solstice, the ancient Romans celebrated Vestalia, a religious festival in honor of Vesta, goddess of the hearth. During Vestalia, married women could enter the temple of Vesta and leave offerings to the goddess in exchange for blessings for their families.

In ancient China, the summer solstice was associated with “yin,” the feminine force. Festivities celebrated Earth, femininity, and the “yin” force.

Before Christianity, ancient Northern and Central European pagans (including Germanic, Celtic and Slavic groups) welcomed Midsummer with bonfires. It was thought that bonfires would boost the sun’s energy for the rest of the growing season and guarantee a good harvest for the fall.

Bonfires also were associated with magic. It was believed that bonfires could help banish demons and evil spirits and lead maidens to their future husbands. Magic was thought to be strongest during the summer solstice.

Midsummer was a crucial time of year for the Vikings, who would meet to discuss legal matters and resolve disputes around the summer solstice.

Many Native American tribes took part in solstice rituals, some of which are still practiced today. The Sioux, for instance, performed a ceremonial sun dance around a tree while wearing symbolic colors.

Some scholars believe that Wyoming’s Bighorn Medicine Wheel, an arrangement of stones built several hundred years ago by Plains Indians that aligns with the summer solstice sunrise and sunset, was the site of that culture’s annual sun dance.


In agrarian times, Midsummer celebrations in Sweden were held to welcome summertime and the season of fertility. In some areas people dressed up as ‘green men’, clad in ferns. They also decorated their houses and farm tools with foliage, and raised tall, leafy maypoles to dance around, probably as early as the 1500s. Midsummer was primarily an occasion for young people, but it was also celebrated in the industrial communities of central Sweden, where all mill employees were given a feast of pickled herring, beer and schnapps. It was not until the 1900s, however, that this became the most Swedish of all traditional festivities.

Ever since the 6th century AD, Midsummer bonfires have been lit around Europe. In Sweden, they were mainly found in the southern part of the country. Young people also liked to visit holy springs, where they drank the healing water and amused themselves with games and dancing. These visits were a reminder of how John the Baptist baptised Christ in the River Jordan.

Midsummer Night is the lightest of the year and was long considered a magical night, as it was the best time for telling people’s futures. Girls ate salted porridge so that their future husbands might bring water to them in their dreams, to quench their thirst. You could also discover treasures, for example by studying how moonbeams fell.

Also that night, it was said, water was turned into wine and ferns into flowers. Many plants acquired healing powers on that one night of the year.

Interested in learning about some of the history behind Litha? 

Many cultures have honored gods and goddesses of the sun, so let's look at some of the Deities of the Summer Solstice. There's also a seasonal legend of the battle between the Oak King and the Holly King.

There's a ton of solar magic and myths and legend out there, and many cultures have worshiped the sun as part of religious practice throughout time. In Native American spirituality, the Sun Dance is an important part of ritual.

The summer solstice is also associated with festivals such as the Vestalia, in ancient Rome, and with ancient structures like the stone circles found all over the world.

Asparagus Stuffed Chicken

Serves: 6

Ingredients:

6 small boneless chicken breast halves
6 stalks asparagus
3 ounces Colby or Colby Jack cheese
1 cup plain bread crumbs
1/2 cup grated parmesan cheese
1/2 cup pignoli nuts -- finely chopped
3 eggs
salt and pepper -- to taste
6 ounces pesto sauce
1 Cup heavy cream

Directions:

Pound chicken breasts to a 1/4 inch thickness and set aside. Snap off tough bottoms of asparagus. Place in boiling water and cover for 1 minute. Drain, rinse with cold water; then pat dry. Cut asparagus from tip down stalk into 3 inch lengths. Cut cheese into sticks 1/2 inch high x 1/2 inch wide by 3 inches long. Set aside. Combine bread crumbs, parmsean and pine nuts in a bowl. In another bowl beat eggs.

Season chicken breasts with salt and pepper. Place a stick of cheese and an asparagus spear next to one long edge of each breast.

Roll breast around ingredients tucking in ends to form a neat package. Secure with a toothpick. Dip each piece in egg and then in breadcrumb mixture. Make a double coating by dipping again into egg then crumbs. Place packages in a baking dish and bake for 20 to 25 minutes at 400F degrees. While the chicken is baking combine pesto and cream in a small saucepan. Bring to a boil and reduce 2 minutes until lightly thickened. Serve pesto cream sauce over chicken.

If you want you can make these ahead of time and freeze. These freeze very well.

Juno, Roman Goddess and Queen

The Roman Goddess Juno. 

Bust. First half of 2nd century A.C. 

Marble. Carlsberg Glyptotek Museum. 

Copenhagen. Denmark. 

Juno (Latin: IVNO, Iūnō [ˈjuːnoː]) is an ancient Roman goddess, the protector and special counselor of the state. A daughter of Saturn, she is the wife of Jupiter and the mother of Mars, Vulcan, Bellona and Juventas. She is the Roman equivalent of Hera, queen of the gods in Greek mythology; like Hera, her sacred animal was the peacock. Her Etruscan counterpart was Uni, and she was said to also watch over the women of Rome. As the patron goddess of Rome and the Roman Empire, Juno was called Regina ("Queen") and was a member of the Capitoline Triad (Juno Capitolina), centered on the Capitoline Hill in Rome; it consisted of her, Jupiter, and Minerva, goddess of wisdom.

Juno's own warlike aspect among the Romans is apparent in her attire. She is often shown armed and wearing a goatskin cloak. The traditional depiction of this warlike aspect was assimilated from the Greek goddess Athena, who bore a goatskin, or a goatskin shield, called the 'aegis'.

Etymology

The name Juno was also once thought to be connected to Iove (Jove), originally as Diuno and Diove from *Diovona. At the beginning of the 20th century, a derivation was proposed from iuven- (as in Latin iuvenis, "youth"), through a syncopated form iūn- (as in iūnix, "heifer", and iūnior, "younger"). This etymology became widely accepted after it was endorsed by Georg Wissowa.

Iuuen- is related to Latin aevum and Greek aion (αιών) through a common Indo-European root referring to a concept of vital energy or "fertile time". The iuvenis is he who has the fullness of vital force. In some inscriptions Jupiter himself is called Iuuntus, and one of the epithets of Jupiter is Ioviste, a superlative form of iuuen- meaning "the youngest". Iuventas, "Youth", was one of two deities who "refused" to leave the Capitol when the building of the new Temple of Capitoline Jove required the exauguration of deities who already occupied the site. Juno is the equivalent to Hera, the Greek goddess for love and marriage. Juno is the Roman goddess of love and marriage. Ancient etymologies associated Juno's name with iuvare, "to aid, benefit", and iuvenescendo, "rejuvenate", sometimes connecting it to the renewal of the new and waxing moon, perhaps implying the idea of a moon goddess.

Roles and epithets

Punishment of Ixion: in the center is Mercury holding the caduceus and on the right Juno sits on her throne. Behind her Iris stands and gestures. On the left is Vulcan (blond figure) standing behind the wheel, manning it, with Ixion already tied to it. Nephele sits at Mercury's feet; a Roman fresco from the eastern wall of the triclinium in the House of the Vettii, Pompeii, Fourth Style (60-79 AD).

Juno Roman Goddess Statue 

Louvre Museum Paris 

Juno's theology is one of the most complex and disputed issues in Roman religion. Even more than other major Roman deities, Juno held a large number of significant and diverse epithets, names and titles representing various aspects and roles of the goddess. In accordance with her central role as a goddess of marriage, these included Pronuba and Cinxia ("she who looses the bride's girdle"). However, other epithets of Juno have wider implications and are less thematically linked.

While her connection with the idea of vital force, fullness of vital energy, eternal youthfulness is now generally acknowledged, the multiplicity and complexity of her personality have given rise to various and sometimes irreconcilable interpretations among modern scholars.

Juno is certainly the divine protectress of the community, who shows both a sovereign and a fertility character, often associated with a military one. She was present in many towns of ancient Italy: at Lanuvium as Sespeis Mater Regina, Laurentum, Tibur, Falerii, Veii as Regina, at Tibur and Falerii as Regina and Curitis, Tusculum and Norba as Lucina. She is also attested at Praeneste, Aricia, Ardea, Gabii. In five Latin towns a month was named after Juno (Aricia, Lanuvium, Laurentum, Praeneste, Tibur). Outside Latium in Campania at Teanum she was Populona (she who increase the number of the people or, in K. Latte's understanding of the iuvenes, the army), in Umbria at Pisaurum Lucina, at Terventum in Samnium Regina, at Pisarum Regina Matrona, at Aesernia in Samnium Regina Populona. In Rome she was since the most ancient times named Lucina, Mater and Regina. It is debated whether she was also known as Curitis before the evocatio of the Juno of Falerii: this though seems probable.

Other epithets of hers that were in use at Rome include Moneta and Caprotina, Tutula, Fluonia or Fluviona, Februalis, the last ones associated with the rites of purification and fertility of February.

Her various epithets thus show a complex of mutually interrelated functions that in the view of Georges Dumézil and Vsevolod Basanoff(author of Les dieux Romains) can be traced back to the Indoeuropean trifunctional ideology: as Regina and Moneta she is a sovereign deity, as Sespeis, Curitis (spear holder) and Moneta (again) she is an armed protectress, as Mater and Curitis (again) she is a goddess of the fertility and wealth of the community in her association with the curiae.

The epithet Lucina is particularly revealing since it reflects two interrelated aspects of the function of Juno: cyclical renewal of time in the waning and waxing of the moon and protection of delivery and birth (as she who brings to light the newborn as vigor, vital force). The ancient called her Covella in her function of helper in the labors of the new moon. The view that she was also a Moon goddess though is no longer accepted by scholars, as such a role belongs to Diana Lucifera: through her association with the moon she governed the feminine physiological functions, menstrual cycle and pregnancy: as a rule all lunar deities are deities of childbirth. These aspects of Juno mark the heavenly and worldly sides of her function. She is thus associated to all beginnings and hers are the kalendae of every month: at Laurentum she was known as Kalendaris Iuno (Juno of the Kalends).

At Rome on the Kalends of every month the pontifex minor invoked her, under the epithet Covella, when from the curia Calabra announced the date of the nonae. On the same day the regina sacrorum sacrificed to Juno a white sow or lamb in the Regia. She is closely associated with Janus, the god of passages and beginnings who after her is often named Iunonius.

Some scholars view this concentration of multiple functions as a typical and structural feature of the goddess, inherent to her being an expression of the nature of femininity. Others though prefer to dismiss her aspects of femininity and fertility and stress only her quality of being the spirit of youthfulness, liveliness and strength, regardless of sexual connexions, which would then change according to circumstances: thus in men she incarnates the iuvenes, word often used to design soldiers, hence resulting in a tutelary deity of the sovereignty of peoples; in women capable of bearing children, from puberty on she oversees childbirth and marriage. Thence she would be a poliad goddess related to politics, power and war. Other think her military and poliadic qualities arise from her being a fertility goddess who through her function of increasing the numbers of the community became also associated to political and military functions.

Festivals

Juno; Vatican, Rome. Brooklyn Museum Archives, Goodyear Archival Collection

All festivals of Juno were held on the kalendae of a month except two (or, perhaps, three):

The Nonae Caprotinae on the nonae of July, the festival of Juno Capitolina on September 13, because the date of these two was determined by preeminence of Jupiter.

Perhaps a second festival of Juno Moneta was held on October 10, possibly the date of the dedication of her temple. This fact reflects the strict association of the goddess with the beginning of each lunar month.

Every year, on the first of March, women held a festival in honor of Juno Lucina called the Matronalia. Lucina was an epithet for Juno as "she who brings children into light." On this day, lambs and cattle were sacrificed in her honor in the temple of her sacred grove on the Cispius.

The second festival was devoted to Juno Moneta on June 1.

Following was the festival of the Nonae Caprotinae ("The Nones of the Wild Fig") held on July 7.

The festival of Juno Regina fell on September 1, followed on the 13 of the same month by that of Juno Regina Capitolina.

October 1 was the date of the Tigillum Sororium in which the goddess was honoured as Juno Sororia.

Last of her yearly festivals came that of Juno Sospita on February 1.

It was an appropriate date for her celebration since the month of February was considered a perilous time of passage, the cosmic year coming then to an end and the limits between the world of the living and the underworld being no longer safely defined.

Hence the community invoked the protection (tutela) of the warlike Juno Sospita, "The Saviour".

Juno is the patroness of marriage, and many people believe that the most favorable time to marry is June, the month named after the goddess. 

The Capitoline Triad - Juno, Jupiter and Minerva 

Juno in the Capitoline triad

The first mention of a Capitoline triad refers to the Capitolium Vetus. The only ancient source who refers to the presence of this divine triad in Greece is Pausanias X 5, 1-2, who mentions its existence in describing the Φωκικόν in Phocis. The Capitoline triad poses difficult interpretative problems. It looks peculiarly Roman, since there is no sure document of its existence elsewhere either in Latium or Etruria. A direct Greek influence is possible but it would be also plausible to consider it a local creation. Dumézil advanced the hypothesis it could be an ideological construction of the Tarquins to oppose new Latin nationalism, as it included the three gods that in the Iliad are enemies of Troy. It is probable Latins had already accepted the legend of Aeneas as their ancestor. Among ancient sources indeed Servius states that according to the Etrusca Disciplina towns should have the three temples of Jupiter, Juno and Minerva at the end of three roads leading to three gates. Vitruvius writes that the temples of these three gods should be located on the most elevated site, isolated from the other. To his Etruscan founders the meaning of this triad might have been related to peculiarly Etruscan ideas on the association of the three gods with the birth of Herakles and the siege of Troy, in which Minerva plays a decisive role as a goddess of destiny along with the sovereign couple Uni Tinia.

Jupiter and Juno (detail), Peter Paul Rubens

Juno and Jupiter

The divine couple received from Greece its matrimonial implications, thence bestowing on Juno the role of tutelary goddess of marriage (Iuno Pronuba).

The couple itself though cannot be reduced to a Greek apport. The association of Juno and Jupiter is of the most ancient Latin theology. Praeneste offers a glimpse into original Latin mythology: the local goddess Fortuna is represented as nursing two infants, one male and one female, namely Jove (Jupiter) and Juno. It seems fairly safe to assume that from the earliest times they were identified by their own proper names and since they got them they were never changed through the course of history: they were called Jupiter and Juno. These gods were the most ancient deities of every Latin town. Praeneste preserved divine filiation and infancy as the sovereign god and his paredra Juno have a mother who is the primordial goddess Fortuna Primigenia. Many terracotta statuettes have been discovered which represent a woman with a child: one of them represents exactly the scene described by Cicero of a woman with two children of different sex who touch her breast. Two of the votive inscriptions to Fortuna associate her and Jupiter: " Fortunae Iovi puero..." and "Fortunae Iovis puero..."

However, in 1882 R. Mowat published an inscription in which Fortuna is called daughter of Jupiter, raising new questions and opening new perspectives in the theology of Latin gods. Dumézil has elaborated an interpretative theory according to which this aporia would be an intrinsic, fundamental feature of Indoeuropean deities of the primordial and sovereign level, as it finds a parallel in Vedic religion. The contradiction would put Fortuna both at the origin of time and into its ensuing diachronic process: it is the comparison offered by Vedic deity Aditi, the Not-Bound or Enemy of Bondage, that shows that there is no question of choosing one of the two apparent options: as the mother of the Aditya she has the same type of relationship with one of his sons, Dakṣa, the minor sovereign who represents the Creative Energy, being at the same time his mother and daughter, as is true for the whole group of sovereign gods to which she belongs. Moreover, Aditi is thus one of the heirs (along with Savitr) of the opening god of the Indoiranians, as she is represented with her head on her two sides, with the two faces looking opposite directions. The mother of the sovereign gods has thence two solidal but distinct modalities of duplicity, i.e. of having two foreheads and a double position in the genealogy. Angelo Brelich has interpreted this theology as the basic opposition between the primordial absence of order (chaos) and the organisation of the cosmos.

Mosaic of two-faced figure, the god Janus, with opened and closed books 

Juno and Janus

The relationship of the female sovereign deity with the god of beginnings and passages is reflected mainly in their association with the kalendae of every month, which belong to both, and in the festival of the Tigillum Sororium of October 1.

Janus as gatekeeper of the gates connecting Heaven and Earth and guardian of all passages is particularly related to time and motion. He holds the first place in ritual invocations and prayers, in order to ensure the communication between the worshipper and the gods. He enjoys the privilege of receiving the first sacrifice of the new year, which is offered by the rex on the day of the Agonium of January as well as at the kalendae of each month: These rites show he is considered the patron of the cosmic year. Ovid in his Fasti has Janus say that he is the original Chaos and also the first era of the world, which got organized only afterwards. He preserves a tutelary function on this universe as the gatekeeper of Heaven. His nature, qualities and role are reflected in the myth of him being the first to reign in Latium, on the banks of the Tiber, and there receiving god Saturn, in the age when the Earth still could bear the gods. The theology of Janus is also presented in the Carmen Saliare. According to Johannes Lydus the Etruscans called him Heaven. His epithets are numerous Iunonius is particularly relevant, as the god of the kalendae who cooperates with and is the source of the youthful vigour of Juno in the birth of the new lunar month. His other epithet Consivius hints to his role in the generative function.

The role of the two gods at the kalendae of every month is that of presiding over the birth of the new moon. Janus and Juno cooperate as the first looks after the passage from the previous to the ensuing month while the second helps it through the strength of her vitality. The rites of the kalendae included the invocations to Juno Covella, giving the number of days to the nonae, a sacrifice to Janus by the rex sacrorum and the pontifex minor at the curia Calabra and one to Juno by the regina sacrorum in the Regia: originally when the month was still lunar the pontifex minor had the task of signalling the appearance of the new moon. While the meaning of the epithet Covella is unknown and debated, that of the rituals is clear as the divine couple is supposed to oversee, protect and help the moon during the particularly dangerous time of her darkness and her labours: the role of Juno Covella is hence the same as that of Lucina for women during parturition. The association of the two gods is reflected on the human level at the difficult time of labours as is apparent in the custom of putting a key, symbol of Janus, in the hand of the woman with the aim of ensuring an easy delivery, while she had to invoke Juno Lucina. At the nonae Caprotinae similarly Juno had the function of aiding and strengthening the moon as the nocturnal light, at the time when her force was supposed to be at its lowest, after the Summer solstice.

The Tigillum Sororium was a rite (sacrum) of the gens Horatia and later of the State. In it Janus Curiatius was associated to Juno Sororia: they had their altars on opposite sides of the alley behind the Tigillum Sororium. Physically this consisted of a beam spanning the space over two posts. It was kept in good condition down to the time of Livy at public expenses. According to tradition it was a rite of purification that served at the expiation of Publius Horatius who had murdered his own sister when he saw her mourning the death of her betrothed Curiatius. Dumézil has shown in his Les Horaces et les Curiaces that this story is in fact the historical transcription of rites of reintegration into civil life of the young warriors, in the myth symbolized by the hero, freed from their furor (wrath), indispensable at war but dangerous in social life. What is known of the rites of October 1 shows at Rome the legend has been used as an aetiological myth for the yearly purification ceremonies which allowed the desacralisation of soldiers at the end of the warring season, i.e. their cleansing from the religious pollution contracted at war. The story finds parallels in Irish and Indian mythologies. These rites took place in October, month that at Rome saw the celebration of the end of the yearly military activity. Janus would then the patron of the feria as god of transitions, Juno for her affinities to Janus, especially on the day of the kalendae. It is also possible though that she took part as the tutelary goddess of young people, the iuniores, etymologically identical to her. Modern scholars are divided on the interpretation of J. Curiatius and J. Sororia. Renard citing Capdeville opines that the wisest choice is to adhere to tradition and consider the legend itself as the source of the epithets.

M. Renard advanced the view that Janus and not Juppiter was the original paredra or consort of Juno, on the grounds of their many common features, functions and appearance in myth or rites as is shown by their cross coupled epithets Janus Curiatius and Juno Sororia: Janus shares the epithet of Juno Curitis and Juno the epithet Janus Geminus, as sororiusmeans paired, double. Renard's theory has been rejected by G. Capdeville as not being in accord with the level of sovereign gods in Dumézil's trifunctional structure. The theology of Janus would show features typically belonging to the order of the gods of the beginning. In Capdeville's view it is only natural that a god of beginnings and a sovereign mother deity have common features, as all births can be seen as beginnings, Juno is invoked by deliverers, who by custom hold a key, symbol of Janus.

Junon Allaitant Hercule (Juno Nursing Hercules)

 Peter Paul Rubens (1577-1640) 

Royal Museums of Art, Brussels, Belgium

Juno and Hercules

Even though the origins of Hercules are undoubtedly Greek his figure underwent an early assimilation into Italic local religions and might even preserve traces of an association to Indoiranian deity Trita Apya that in Greece have not survived. Among other roles that Juno and Hercules share there is the protection of the newborn. Jean Bayet, author of Les origines de l'Arcadisme romain, has argued that such a function must be a later development as it looks to have superseded that of the two original Latin gods Picumnus and Pilumnus.

The two gods are mentioned together in a dedicatory inscription found in the ruins of the temple of Hercules at Lanuvium, whose cult was ancient and second in importance only to that of Juno Sospita. In the cults of this temple just like in those at the Ara maxima in Rome women were not allowed. The exclusion of one sex is a characteristic practice in the cults of deities of fertility. Even though no text links the cults of the Ara maxima with Juno Sospita, her temple, founded in 193 BC, was located in the Forum Holitorium near the Porta Carmentalis, one of the sites of the legend of Hercules in Rome. The feria of the goddess coincides with a Natalis Herculis, birthday of Hercules, which was celebrated with ludi circenses, games in the circus. In Bayet's view Juno and Hercules did supersede Pilumnus and Picumnus in the role of tutelary deities of the newborn not only because of their own features of goddess of the deliverers and of apotropaic tutelary god of infants but also because of their common quality of gods of fertility. This was the case in Rome and at Tusculum where a cult of Juno Lucina and Hercules was known. At Lanuvium and perhaps Rome though their most ancient association rests on their common fertility and military characters. The Latin Junos certainly possessed a marked warlike character (at Lanuvium, Falerii, Tibur, Rome). Such character might suggest a comparison with the Greek armed Heras one finds in the South of Italy at Cape Lacinion and at the mouth of river Sele, military goddesses close to the Heras of Elis and Argos known as Argivae. In the cult this Hera received at Cape Lacinion she was associated with Heracles, supposed the founder of the sanctuary. Contacts with Central Italy and similarity would have favoured a certain assimilation between Latin warlike Junos and Argive Heras and the association with Heracles of Latin Junos. Some scholars, mostly Italians, recognize in the Junos of Falerii, Tibur and Lavinium the Greek Hera, rejecting the theory of an indigenous original cult of a military Juno. Renard thinks Dumézil's opposition to such a view is to be upheld: Bayet's words though did not deny the existence of local warlike Junos, but only imply that at a certain time they received the influence of the Heras of Lacinion and Sele, fact that earned them the epithet of Argive and a Greek connotation. However Bayet recognized the quality of mother and of fertility deity as being primitive among the three purported by the epithets of the Juno of Lanuvium (Seispes, Mater, Regina).

Magna Graecia and Lanuvium mixed their influence in the formation of the Roman Hercules and perhaps there was a Sabine element too as is testified by Varro, supported by the find of the sanctuary of Hercules Curinus at Sulmona and by the existence of a Juno Curitis in Latium.

The mythical theme of the suckling of the adult Heracles by Hera, though being of Greek origin, is considered by scholars as having received its full acknowledgement and development in Etruria: Heracles has become a bearded adult on the mirrors of the 4th and 3rd centuries BC. Most scholars view the fact as an initiation, i.e. the accession of Heracles to the condition of immortal. Even though the two versions coexisted in Greece and that of Heracles infant is attested earlier Renard suggests a process more in line with the evolution of the myth: the suckling of the adult Heracles should be regarded as more ancient and reflecting its original true meaning.

Winged genius facing a woman with a tambourine and mirror, 

from southern Italy, circa 320 BC 

Juno and Genius

The view that Juno was the feminine counterpart to Genius, i.e. that as men possess a tutelary entity or double named genius, so women have their own one named juno, has been maintained by many scholars, lastly Kurt Latte. In the past it has also been argued that goddess Juno herself would be the issue of a process of abstraction from the individual junos of every woman. According to Georg Wissowa and K. Latte Genius (from the root gen-, whence gigno bear or be born, archaic also geno) would design the specific virile generative potency, as opposed to feminine nature, reflected in conception and delivery, under the tutelage of Juno Lucina. Such an interpretation has been critically reviewed by Walter F. Otto.

While there are some correspondences between the ideas about genius and juno, especially in the imperial age, the relevant documentation is rather late (Tibullus mentions it first). Dumézil also remarks from these passages one could infer every woman has a Venus too. As evidence of the antiquity of the concept of a juno of women, homologous to the genius of men, is the Arval sacrifice of two sheep to the Juno Deae Diae ("the juno of goddesses named Dea Dia"), in contrast to their sacrifice of two cows sacrificed to Juno (singular). However both G. Wissowa and K. Latte allow that this ritual could have been adapted to fit theology of the Augustan restoration. While the concept of a Juno of goddesses is not attested in the inscriptions of 58 BC from Furfo, that of a Genius of gods is, and even of a Genius of a goddess, Victoria. On this point it looks remarkable that also in Martianus Capella's division of Heaven a Juno Hospitae Genius is mentioned in region IX, and not a Juno: the sex of this Genius is feminine.

Romans believed the genius of somebody was an entity that embodied his essential character, personality, and also originally his vital, generative force and raison d' être. However the genius had no direct relationship with sex, at least in classical time conceptions, even though the nuptial bed was named lectus genialis in honour of the Genius and brides on the day of marriage invoked the genius of their grooms.

This seems to hint to a significance of the Genius as the propagative spirit of the gens, of whom every human individual is an incarnation: Censorinus states: "Genius is the god under whose tutelage everyone is born and lives on", and that "many ancient authors, among whom Granius Flaccus in his De Indigitamentis, maintain that he is one and the same with the Lar", meaning the Lar Familiaris. Festus calls him "a god endowed with the power of doing everything", then citing an Aufustius: "Genius is the son of the gods and the parent of men, from whom men receive life. Thence is he named my genius, because he begot me". Festus's quotation goes on saying: "Other think he is the special god of every place", a notion that reflects a different idea. In classic age literature and iconography he is often represented as a snake, that may appear in the conjugal bed, this conception being perhaps the issue of a Greek influence. It was easy for the Roman concept of Genius to expand annexing other similar religious figures as the Lares and the Greek δαίμων αγαθός.

The genius was believed to be associated with the forehead of each man, while goddess Juno, not the juno of every woman, was supposed to have under her jurisdiction the eyebrows of women or to be the tutelary goddess of the eyebrows of everybody, irrespective of one's sex.

Juno in Martianus Capella's division of Heaven

Martianus Capella's collocation of gods into sixteen different regions of Heaven is supposed to be based on and to reflect Etruscan religious lore, at least in part. It is thence comparable with the theonyms found in the sixteen cases of the outer rim of the Piacenza Liver. Juno is to be found in region II, along with Quirinus Mars, Lars militaris, Fons, Lymphae and the dii Novensiles. This position is reflected on the Piacenza Liver by the situation of Uni in case IV, owing to a threefold location of Tinia in the first three cases that determines an equivalent shift.

The Map of Macrobius before 1100
By Alfred Hiatt Imago Mundi,
Vol. 59:2 (2007)

An entity named Juno Hospitae Genius is to be found alone in region IX. Since Grotius (1599) many editors have proposed the correction of Hospitae into Sospitae. S. Weinstock has proposed to identify this entity with one of the spouses of Neptune, as the epithet recurs below used in this sense.

In region XIV is located Juno Caelestis along with Saturn. This deity is the Punic Astarte_Tanit, usually associated with Saturn in Africa. Iuno Caelestis is thence in turn assimilated to Ops and Greek Rhea. Uni is here the Punic goddess, in accord with the identification of Pyrgi. Her paredra was the Phoenician god Ba'al, interpreted as Saturn. Capdeville admits of being unable to explain the collocation of Juno Caelestis among the underworld gods, which looks to be determined mainly by her condition of spouse of Saturn.