Lectures: A history of the Taweez the talisman or magic square

The magic square has a rich history, which most likely journeyed from China to India, then to the Arab countries and after that to Europe.

The earliest appearance dates back to China around 2200 B.C. A Chinese legend claimed that while the Chinese Emperor Yu was walking along the Yellow River, he became aware of a tortoise with a unique diagram on its shell. The Emperor decided to call the unusual numerical pattern lo shu. 

Magic Squares can be traced in Chinese literature as far back as 2800 B.C.

The legend of "Lo Shu" or "scroll of the river Lo" tells the story of a huge flood that destroyed crops and land. The people offered a sacrifice to the river god for one of the flooded rivers, the Lo river, to calm his anger.

Every time the river flooded, there emerged a turtle that would walk around the sacrifice. It was not until a child noticed a unique pattern on the turtles shell (Figure 2) that told the people how many sacrifices to make for the river god to accept their sacrifice.

There were circular dots of numbers that were arranged in a 3-by-3 grid pattern such that the sum of the numbers in each column, row, and diagonal equaled the same sum: fifteen.

Fifteen became the number of sacrifices needed in order to make the river god happy. This number is equal to the number of days in each of the 24 cycles of the Chinese solar year.

The oldest magic square of order four was found inscribed in Khajuraho, India dating to the eleventh or twelfth century. This magic square is also known as the diabolic or panmagic square, where, in addition to the rows, columns, and diagonals the broken diagonals also have the same sum. 

History

Iron plate with an order 6 magic square in Eastern Arabic numerals from China,
dating to the Yuan Dynasty(1271–1368).

The third order magic square was known to Chinese mathematicians as early as 190 BCE, and explicitly given by the first century of the common era. 

By the end of 12th century, the general methods for constructing magic squares were well established. Around this time, some of these squares were increasingly used in conjunction with magic letters, as in Shams Al-ma'arif, for occult purposes. 

In India, all the fourth order pandiagonal magic squares were enumerated by Narayana in 1356. 

Magic squares were made known to Europe through translation of Arabic sources as occult objects during the Renaissance, and the general theory had to be re-discovered independent of prior developments in China, India, and Middle East. 

China

While ancient references to the pattern of even and odd numbers in the 3×3 magic square appears in the I Ching, the first unequivocal instance of this magic square appears in a 1st century book Da Dai Liji (Record of Rites by the Elder Dai). 

These numbers also occur in a possibly earlier mathematical text called Shushu jiyi (Memoir on Some Traditions of Mathematical Art), said to be written in 190 BCE. 

This is the earliest appearance of a magic square on record; and it was mainly used for divination and astrology. The 3×3 magic square was referred to as the "Nine Halls" by earlier Chinese mathematicians. 

The identification of the 3×3 magic square to the legendary Luoshu chart was only made in the 12th century, after which it was referred to as the Luoshu square. The oldest surviving Chinese treatise on the systematic methods for constructing larger magic squares is Yang Hui's Xugu zheqi suanfa (Continuation of Ancient Mathematical Methods for Elucidating the Strange) written in 1275. 

The contents of Yang Hui's treatise were collected from older works, both native and foreign; and he only explains the construction of third and fourth order magic squares, while merely passing on the finished diagrams of larger squares. 

He gives a magic square of order 3, two squares for each order of 4 to 8, one of order nine, and one semi-magic square of order 10. He also gives six magic circles of varying complexity.

The order 5 square is a bordered magic square, with central 3×3 square formed according to Luo Shu principle.

The order 9 square is a composite magic square, in which the nine 3×3 sub squares are also magic.

After Yang Hui, magic squares frequently occur in Chinese mathematics such as in Ding Yidong's Dayan suoyin (circa 1300), Chen Dawei's Suanfa tongzong (1593), Fang Zhongtong's Shuduyan (1661) which contains magic circles, cubes and spheres, Zhang Chao's Xinzhai zazu (circa 1650), who published China's the first magic square of order ten, and lastly Bao Qishou's Binaishanfang ji (circa 1880), who gave various three dimensional magic configurations.

However, despite being the first to discover the magic squares and getting a head start by several centuries, the Chinese development of the magic squares are much inferior compared to the Islamic, the Indian, or the European developments.

The high point of Chinese mathematics that deals with the magic squares seems to be contained in the work of Yang Hui; but even as a collection of older methods, this work is much more primitive, lacking general methods for constructing magic squares of any order, compared to a similar collection written around the same time by the Byzantine scholar Manuel Moschopoulos.

This is possibly because of the Chinese scholars' enthrallment with the Lo Shu principle, which they tried to adapt to solve higher squares; and after Yang Hui and the fall of Yuan dynasty, their systematic purging of the foreign influences in Chinese mathematics.

Middle East: Persia, Arabia, North Africa, Muslim Iberia

Although the early history of magic squares in Persia and Arabia is not known, it has been suggested that they were known in pre-Islamic times. It is clear, however, that the study of magic squares was common in medieval Islam, and it was thought to have begun after the introduction of chess into the region.

The first datable appearance of magic square of order 3 occur in the alchemical works of Jābir ibn Hayyān (fl. c. 721– c. 815). 

While it is known that treatises on magic squares were written in the 9th century, the earliest extant treaties we have date from the 10th-century: one by Abu'l-Wafa al-Buzjani (circa 998) and another by Ali b. Ahmad al-Antaki (circa 987).

These early treatise were purely mathematical, and the Arabic designation for magic squares is wafq al-a'dad which translates as harmonious disposition of the numbers.

By the end of 10th century, the Islamic mathematicians had understood how to construct bordered squares of any order as well as simple magic squares of small orders (n ≤ 6) which were used to make composite magic squares.

The first datable instance of the fourth order magic square occur in 587 CE in India. Specimens of magic squares of order 3 to 9 appear in an encyclopedia from Baghdad circa 983, the Rasa'il Ikhwan al-Safa (the Encyclopedia of the Brethren of Purity). The Brethren of Purity ‎were a secret society of philosophers in Basra, Iraq, in the 8th century A.D. 

The 11th century saw the finding of several ways to construct simple magic squares for odd and evenly-even orders; the more difficult case of evenly-odd case (n = 4k + 2) was solved by Ibn al-Haytham with k even (circa 1040), and completely by the beginning of 12th century, if not already in the latter half of the 11th century.

Around the same time, pandiagonal squares were being constructed. Treaties on magic squares were numerous in the 11th and 12th century. These later developments tended to be improvements on or simplifications of existing methods.

From the 13th century on wards, magic squares were increasingly put to occult purposes.

However, much of these later texts written for occult purposes merely depict certain magic squares and mention their attributes, without describing their principle of construction, with only some authors keeping the general theory alive.

One such occultist was the Egyptian Ahmad al-Buni(circa 1225), who gave general methods on constructing bordered magic squares; another one was the 18th century Nigerian al-Kishnawi.

The magic square of order three was described as a child-bearing charm since its first literary appearances in the alchemical works of Jābir ibn Hayyān (fl. c. 721– c. 815) and al-Ghazālī (1058–1111) and it was preserved in the tradition of the planetary tables.

The earliest occurrence of the association of seven magic squares to the virtues of the seven heavenly bodies appear in Andalusian scholar Ibn Zarkali's (known as Azarquiel in Europe) (1029–1087) Kitāb tadbīrāt al-kawākib (Book on the Influences of the Planets).

A century later, the Egyptian scholar Ahmad al-Buni attributed mystical properties to magic squares in his highly influential book Shams al-Ma'arif (The Book of the Sun of Gnosis and the Subtleties of Elevated Things), which also describes their construction.

This tradition about a series of magic squares from order three to nine, which are associated with the seven planets, survives in Greek, Arabic, and Latin versions.

There are also references to the use of magic squares in astrological calculations, a practice that seems to have originated with the Arabs.

India

The 3×3 magic square has been a part of rituals in India since ancient times, and still is today. For instance, the Kubera-Kolam, a magic square of order three, is commonly painted on floors in India. 

It is essentially the same as the Lo Shu Square, but with 19 added to each number, giving a magic constant of 72 (below, square on the left). 

The 3×3 magic square first appears in India in Gargasamhita by Garga, who recommends its use to pacify the nine planets (navagraha). 

The oldest version of this text dates from 100 CE; however passage on planets could not have been written earlier than 400 CE. 

The first datable instance of 3×3 magic square in India occur in a medical text Siddhayog (ca. 900 CE) by Vrnda, which was prescribed to women in labor in order to have easy delivery. 

The earliest unequivocal occurrence of magic square is found in a work called Kaksaputa, composed by the alchemist Nagarjuna around 1st century CE. All of the squares given by Nagarjuna are 4×4 magic squares, and one of them is called Nagarjuniya after him. Nagarjuna gave a method of constructing 4×4 magic square using a primary skeleton square, given an odd or even magic sum. Incidentally, the special Nagarjuniya square cannot be constructed from the method he expounds.

The Nagarjuniya square is a pan-diagonal magic square, where the broken diagonals (e.g. 16+22+34+28, 18+24+32+26, etc) sum to 100. It is also an instance of a most perfect magic square, where every 2×2 sub-square, four corners of any 3×3 sub-square, four corners of the 4×4 square, the four corners of any 2×4 or 4×2 sub-rectangle, and the four corners of oblong diagonals (18+24+32+26 and 10+16+34+40) all sum to 100.

Furthermore, the corners of eight trapezoids (16+18+32+34, 44+22+28+6, etc) all sum to 100. The Nagarjuniya square is made up of two arithmetic progressions starting from 6 and 16 with eight terms each, with a common difference between successive terms as 4.

When these two progressions are reduced to the normal progression of 1 to 8, we obtain the adjacent square.

The oldest datable magic square in the world is found in an encyclopaedic work written by Varahamihira around 587 CE called Brhat Samhita.

The magic square is constructed for the purpose of making perfumes using 4 substances selected from 16 different substances. Each cell of the square represents a particular ingredient, while the number in the cell represents the proportion of the associated ingredient, such that the mixture of any four combination of ingredients along the columns, rows, diagonals, and so on, gives the total volume of the mixture to be 18.

Although the book is mostly about divination, the magic square is given as a matter of combinatorial design, and no magical properties are attributed to it.



The square of Varahamihira as given above has sum of 18. Here the numbers 1 to 8 appear twice in the square. It is a pan-diagonal magic square. It is also an instance of most perfect magic square. Four different magic squares can be obtained by adding 8 to one of the two sets of 1 to 8 sequence.

This magic square is remarkable in that it is a 90 degree rotation of a magic square that appears in the 13th century Islamic world as one of the most popular magic squares.

 His book also contains a method for constructing a magic square of order four when a constant sum is given. It also contains the Nagarjuniya square.

Around 12th-century, a 4×4 magic square was inscribed on the wall of Parshvanath temple in Khajuraho, India. Several Jain hyms teach how to make magic squares, although they are undatable.

As far as is known, the first systematic study of magic squares in India was conducted by Thakkar Pheru, a Jain scholar, in his Ganitasara Kaumudi (ca. 1315). This work contains a small section on magic squares which consists of nine verses. Here he gives a square of order four, and alludes to its rearrangement; classifies magic squares into three (odd, evenly even, and oddly even) according to its order; gives a square of order six; and prescribes one method each for constructing even and odd squares.[28] For the even squares, Pheru divides the square into component squares of order four, and puts the numbers into cells according to the pattern of a standard square of order four.[28] For odd squares, Pheru gives the method using horse move or knight's move. Although algorithmically different, it gives the same square as the De la Loubere's method.[28] 

Below is Pheru's square of order six.

The next comprehensive work on magic figures was taken up by Narayana Pandit, who in the fourteenth chapter of his Ganita Kaumudi (1356) gives general methods for the constructions of all sorts of magic squares with the principles governing such constructions. It consists of 55 verses for rules and 17 verses for examples. 

Narayana gives the method to make a magic squares of order four using knight's move; enumerates the number of pan-diagonal magic squares of order four, 384, including every variation made by rotation and inversion; three general methods for squares having any order and constant sum when a standard square of the same order is known; two methods each for constructing evenly even, oddly even, and odd squares when the sum is given. 

While Narayana recounts some older methods of construction, his folding method seems to be his own invention, which was later re-discovered by De la Hire. In the last section, he conceives of other figures, such as circles, rectangles, and hexagons, in which the numbers may be arranged to possess properties similar to those of magic squares.

Incidentally, Narayana states that the purpose of studying magic squares is to construct yantra, to destroy the ego of bad mathematicians, and for the pleasure of good mathematicians. The subject of magic squares is referred to as bhadraganita and Narayana states that it was first taught to men by god Shiva.

Latin Europe

Athanasius Kircher's Oedipus Aegyptiacus (1653)

belongs to a treatise on magic squares 

and shows the Sigillum Iovis associated with Jupiter

Unlike in Persia and Arabia, we have better documentation of how the magic squares were transmitted to Europe. Around 1315, influenced by Islamic sources, the Greek Byzantine scholar Manuel Moschopoulos wrote a mathematical treatise on the subject of magic squares, leaving out the mysticism of his Muslim predecessors, where he gave two methods for odd squares and two methods for evenly even squares. 

Moschopoulos was essentially unknown to the Latin Europe until the late 17th century, when Philippe de la Hire rediscovered his treatise in the Royal Library of Paris. 

However, he was not the first European to have written on magic squares; and the magic squares were disseminated to rest of Europe through Spain and Italy as occult objects. The early occult treaties that displayed the squares did not describe how they were constructed. 

Thus the entire theory had to be rediscovered.Magic squares had first appeared in Europe in Kitāb tadbīrāt al-kawākib (Book on the Influences of the Planets) written by Ibn Zarkali of Toledo, Al-Andalus, as planetary squares by 11th century. 

The magic square of three was discussed in numerological manner in early 12th century by Jewish scholar Abraham ibn Ezra of Toledo, which influenced later Kabbalists. Ibn Zarkali's work was translated as Libro de Astromagia in the 1280s, due to Alfonso X of Castille.

 In the Alfonsine text, magic squares of different orders are assigned to the respective planets, as in the Islamic literature; unfortunately, of all the squares discussed, the Mars magic square of order five is the only square exhibited in the manuscript.

Magic squares surface again in Florence, Italy in the 14th century. A 6×6 and a 9×9 square are exhibited in a manuscript of the Trattato d'Abbaco (Treatise of the Abacus) by Paolo Dagomari. 

It is interesting to observe that Paolo Dagomari, like Pacioli after him, refers to the squares as a useful basis for inventing mathematical questions and games, and does not mention any magical use. Incidentally, though, he also refers to them as being respectively the Sun's and the Moon's squares, and mentions that they enter astrological calculations that are not better specified. 

As said, the same point of view seems to motivate the fellow Florentine Luca Pacioli, who describes 3×3 to 9×9 squares in his work De Viribus Quantitatis by the end of 15th century.

Europe after 15th century

The planetary squares had disseminated into northern Europe by the end of 15th century. For instance, the Cracow manuscript of Picatrix from Poland displays magic squares of orders 3 to 9. The same set of squares as in the Cracow manuscript later appears in the writings of Paracelsus in Archidoxa Magica (1567), although in highly garbled form. 

In 1514 Albrecht Dürer immortalized a 4×4 square in his famous engraving Melencolia I. Paracelsus' contemporary Heinrich Cornelius Agrippa von Nettesheim published his famous book De occulta philosophia in 1531, where he devoted a chapter to the planetary squares. 

The same set of squares given by Agrippa reappear in 1539 in Practica Arithmetice by Girolamo Cardano. The tradition of planetary squares was continued into the 17th century by Athanasius Kircher in Oedipi Aegyptici (1653). 

In Germany, mathematical treaties concerning magic squares were written in 1544 by Michael Stifel in Arithmetica Integra, who rediscovered the bordered squares, and Adam Riese, who rediscovered the continuous numbering method to construct odd ordered squares published by Agrippa. 

However, due to the religious upheavals of that time, these work were unknown to the rest of Europe.

In 1624 France, Claude Gaspard Bachet described the "diamond method" for constructing Agrippa's odd ordered squares in his book Problèmes Plaisants. 

In 1691, Simon de la Loubère described the Indian continuous method of constructing odd ordered magic squares in his book Du Royaume de Siam, which he had learned while returning from a diplomatic mission to Siam, which was faster than Bachet's method. 

In an attempt to explain its working, de la Loubere used the primary numbers and root numbers, and rediscovered the method of adding two preliminary squares. 

This method was further investigated by Abbe Poignard in Traité des quarrés sublimes (1704), and then later by Philippe de La Hire in Mémoires de l’Académie des Sciences for the Royal Academy (1705), and by Joseph Sauveur in Construction des quarrés magiques (1710). 

In Divers ouvrages de mathematique et de physique published posthumously in 1693, Bernard Frenicle de Bessy demonstrated that there were exactly 880 distinct magic squares of order four. 

De la Hire also introduced concentric bordered square in 1705, while Sauveur introduced magic cubes and lettered squares, which was taken up later by Euler in 1776, who is often credited for devising them. 

In 1750 d'Ons-le-Bray rediscovered the method of constructing doubly even and singly even squares using bordering technique. 

By this time the earlier mysticism attached to the magic squares had completely vanished, and the subject was treated as a part of recreational mathematics.

In the 19th century, Bernard Violle gave the most comprehensive treatment of magic squares in his three volume Traité complet des carrés magiques (1837—1838), which also described magic cubes, parallelograms, parallelopipeds, and circles. 

Pandiagonal squares were extensively studied by Andrew Hollingworth Frost, who learned it while in the town of Nasik, India, (thus calling them Nasik squares) in a series of articles: On the knight's path (1877), On the General Properties of Nasik Squares (1878), On the General Properties of Nasik Cubes (1878), On the construction of Nasik Squares of any order (1896). 

He showed that it is impossible to have normal singly-even pandiagonal magic square. 

Frederick A.P. Barnard constructed inlaid magic squares and other three dimensional magic figures like magic spheres and magic cylinders in Theory of magic squares and of magic cubes(1888). 

In 1897, Emroy McClintock published On the most perfect form of magic squares, coining the words pandiagonal square and most perfect square, which had previously been referred to as perfect, or diabolic, or Nasik.

This iron plate, inscribed with Arabic numbers in a six by six grid was excavated from beneath the cornerstone of the palace of Prince Anxi in the eastern suburbs of Xi’an, China (1275 A.D.)

Such plates were buried in the corner of the foundation to ward off evil spirits. 

In India the 3×3 magic square has been a part of rituals in India since Vedic times, and still is today. Magic squares were used in the conventional mathematical context, alchemical and medicinal recipes as well as a magical means. In Vrnda’s medical work Siddhayoga, 900 A.D. he prescribes a magic square the order of three to be employed by a woman in labor to ease childbirth.2 There is also a well known 10th century 4×4 magic square on display in the Parshvanath Jain temple in Khajuraho.

In the Islamic Arabic speaking nations, the mathematical properties of magic squares were already developed by the 9th and 10th century A.D. The magic square (known in Arabic as waqf) appeared in Islamic literature at around 9th century A.D. It was attributed to the writings of Jabir ibn Hayyan, in the Jabirean corpus, and used as a charm to ease childbirth.

Thabit Ibn Qurra was a famous Harranian Sabian Arab mathematician, astronomer, physician, and philosopher. He translated many Greek texts in Baghdad, under the Abbasid caliphate and soon wrote original works on the magic square in latter half of the 9th century A.D.

The science of magic squares reached its pinnacle in the 11th and 12th centuries. From the 13th century, magical and divinatory applications began to replace the mathematical study of the magic square.

The Arab mathematician and sufi mystic Ahmad ibn ‘Ali al-Buni, attributed magical properties to the square with references to the use of magic squares in astrological calculations in his 13th century treaties, The Shams al-Ma’arif. The Shams al-Ma’arif is a manual on Arabic magic and for achieving esoteric mysticism through magic squares, numerology, astrology, alchemy and amulets. Al-Buni combined the magic square with astrology and assigned them with the planets. Al Buni’s work is still very much a point of reference for taweez makers in the Indian subcontinent, North Africa, the Yoruba healers of Nigeria and also the Arab countries today.

Pages from Al Buni’s occult manuscript, Shams al-Ma’arif 

In West Africa there was also substantial interest in magic squares, which were interwoven throughout West African culture. The squares held particular religious importance and were adorned on clothing, masks, and religious artifacts. In the early 18th century, Muhammad ibn Muhammad, a well-known astronomer, mathematician, mystic, and astrologer in Muslim West Africa, took an interest in magic squares. In one of his manuscripts, he gave examples of, and explained how to construct, odd order magic squares.

Abraham ben Meir bin Ezra (c. 1090-1167), a Jewish philosopher and astrologer, was born in Toledo during the Golden Age of Muslim Spain. He translated many Arabic works into Hebrew and had a deep interest in magic squares and numerology in general. He traveled widely throughout Italy and beyond, and may have been the one of the people responsible for the introduction of magic squares into Europe.

Magic squares were introduced into Europe in 1300 AD by Manuel Moschopoulos, Greek Byzantine scholar. He wrote a mathematical treatise on the subject of the magic squares, building on the work of Al-Buni who preceded him. In contrast, his work was purely mathematical to that of the Arabic manuscripts.

The Italian mathematician and Franciscan friar, Luca Pacioli wrote De viribus quantitatis (On The Powers Of Numbers) between 1496 and 1508, which contains a large collection of examples of magic squares. With Pacioli there is a move towards the western mystical practice concerning magic squares.

Heinrich Cornelius Agrippa (1486 – 1535) was an influential writer of renaissance esoterica. In his work “de occulta philosophia, Book II ” he constructed magic squares from orders 3 to 9. A Magic Square is given for each planet, and sigils are drawn using the square to represent the Angel (Intelligence), Demon (Spirit), and the Seal of each Planet.

The most famous European work involving magic squares in art is Albrecht Durer’s engraving ‘Melancolia’, from 1514 which contains a heavily coded 4 x4 magic square influenced by alchemical ideas and symbolism.

Food and the role it played in Greek Thought

Food and the act of eating played an important part in the Greek mind. 

Ancient Greek cuisine was characterized by its frugality, reflecting agricultural hardship. It was founded on the "Mediterranean triad": wheat, olive oil, and wine.

Meals

The Greeks had three to four meals a day. Breakfast (ἀκρατισμός akratismos) consisted of barley bread dipped in wine (ἄκρατος akratos), sometimes complemented by figs or olives. 

They also ate pancakes called τηγανίτης (tēganitēs), ταγηνίτης(tagēnitēs) or ταγηνίας(tagēnias), all words deriving from τάγηνον (tagēnon), "frying pan". The earliest attested references on tagenias are in the works of the 5th century BC poets Cratinus and Magnes.

Tagenites were made with wheat flour, olive oil, honey and curdled milk, and were served for breakfast. 

Another kind of pancake was σταιτίτης (staititēs), from σταίτινος (staitinos), "of flour or dough of spelt", derived from σταῖς (stais), "flour of spelt". Athenaeus in his Deipnosophistae mentions staititas topped with honey, sesame and cheese.

A quick lunch (ἄριστον ariston) was taken around noon or early afternoon. 

Dinner (δεῖπνον deipnon), the most important meal of the day, was generally taken at nightfall. 

An additional light meal (ἑσπέρισμα hesperisma) was sometimes taken in the late afternoon.Ἀριστόδειπνον / aristodeipnon, literally "lunch-dinner", was served in the late afternoon instead of dinner.

Men and women took their meals separately. When the house was too small, the men ate first, the women afterwards. Slaves waited at dinners. Aristotle notes that "the poor, having no slaves, would ask their wives or children to serve food." Respect for the father who was the breadwinner was obvious.

The ancient Greek custom of placing terra cotta miniatures of their furniture in children's graves gives us a good idea of its style and design. The Greeks normally ate while seated on chairs; benches were used for banquets. The tables, high for normal meals and low for banquets, were initially rectangular in shape.

By the 4th century BC, the usual table was round, often with animal-shaped legs (for example lion's paws). Loaves of flat bread could be used as plates, but terra cotta bowls were more common.

Dishes became more refined over time, and by the Roman period plates were sometimes made out of precious metals or glass. Cutlery was not often used at the table: use of the fork was unknown; people ate with their fingers. Knives were used to cut the meat. 

Spoons were used for soups and broths. Pieces of bread (ἀπομαγδαλία apomagdalia) could be used to spoon the food or as napkins to wipe the fingers.

As with modern dinner parties, the host could simply invite friends or family; but two other forms of social dining were well documented in ancient Greece: the entertainment of the all-male symposium, and the obligatory, regimental syssitia.

Symposium

The symposium (Greek: συμπόσιον symposion or symposio, from συμπίνειν sympinein, "to drink together") was a part of a banquet that took place after the meal, when drinking for pleasure was accompanied by music, dancing, recitals, or conversation.

 Literary works that describe or take place at a symposium include two Socratic dialogues, Plato's Symposium and Xenophon's Symposium, as well as a number of Greek poems such as the elegies of Theognis of Megara. Symposia are depicted in Greek and Etruscan art that shows similar scenes.

It consisted of two parts: the first dedicated to food, generally rather simple, and a second part dedicated to drinking. However, wine was consumed with the food, and the beverages were accompanied by snacks (τραγήματα tragēmata) such as chestnuts, beans, toasted wheat, or honey cakes, all intended to absorb alcohol and extend the drinking spree.

The second part was inaugurated with a libation, most often in honor of Dionysus, followed by conversation or table games, such as kottabos. The guests would recline on couches (κλίναι klinai); low tables held the food or game boards. 

Dancers, acrobats, and musicians would entertain the wealthy banqueters. A "king of the banquet" was drawn by lots; he had the task of directing the slaves as to how strong to mix the wine.

With the exception of courtesans, the banquet was strictly reserved for men. It was an essential element of Greek social life. Great feasts could only be afforded by the rich; in most Greek homes, religious feasts or family events were the occasion of more modest banquets. 

The banquet became the setting of a specific genre of literature, giving birth to Plato's Symposium, Xenophon's work of the same name, the Table Talk of Plutarch's Moralia, and the Deipnosophists (Banquet of the Learned) of Athenaeus.

Setting and social occasion

Plato's Symposium, depiction by Anselm Feuerbach

The Greek symposium was a key Hellenic social institution. It was a forum for men of respected families to debate, plot, boast, or simply to revel with others. They were frequently held to celebrate the introduction of young men into aristocratic society. Symposia were also held by aristocrats to celebrate other special occasions, such as victories in athletic and poetic contests. They were a source of pride for them.

Banquet scene from a Temple of Athena (6th century BC relief).

Symposia were usually held in the andrōn (ἀνδρών), the men's quarters of the household. The participants, or "symposiasts", would recline on pillowed couches arrayed against the three walls of the room away from the door. 

Due to space limitations, the couches would number between seven and nine, limiting the total number of participants to somewhere between fourteen and twenty seven (Oswyn Murray gives a figure of between seven and fifteen couches and reckons fourteen to thirty participants a "standard size for a drinking group"). 

If any young men took part, they did not recline but sat up. However, in Macedonian symposia, the focus was not only on drinking but hunting, and young men were allowed to recline only after they had killed their first wild boar.

Food and wine were served. Entertainment was provided, and depending on the occasion could include games, songs, flute-girls or boys, slaves performing various acts, and hired entertainment.

Symposia often were held for specific occasions. The most famous symposium of all, described in Plato's dialogue of that name (and rather differently in Xenophon's) was hosted by the poet Agathon on the occasion of his first victory at the theater contest of the 416 BC Dionysia. According to Plato's account, the celebration was upstaged by the unexpected entrance of the toast of the town, the young Alcibiades, dropping in drunken and nearly naked, having just left another symposium.

The men at the symposium would discuss a multitude of topics—often philosophical, such as love and the differences between genders.

Drinking

A symposium would be overseen by a "symposiarch" who would decide how strong the wine for the evening would be, depending on whether serious discussions or merely sensual indulgence were in the offing. The Greeks and Romans customarily served their wine mixed with water, as the drinking of pure wine was considered a habit of uncivilized peoples.

 However, there were major differences between the Roman and Greek symposia. 

A Roman symposium (convivium) served wine before, with and after food, and women were allowed to join. In a Greek symposium, wine was only drunk after dinner, and women were not allowed to attend. 

A female aulos-player entertains men at a symposium on this Attic red-figure bell-krater, c. 420 BC

The wine was drawn from a krater, a large jar designed to be carried by two men, and served from pitchers (oenochoe). Determined by the Master of Ceremonies, the wine was diluted to a specific strength and was then mixed.

 Slave boys would manage the krater, and transfer the wine into pitchers. They then attended to each man in the symposium with the pitchers and filled their cups with wine. Certain formalities were observed, most important among which were libations, the pouring of a small amount of wine in honor of various deities or the mourned dead.

 In a fragment from his c. 375 BC play Semele or Dionysus, Eubulus has the god of wine Dionysos describe proper and improper drinking:

For sensible men I prepare only three kraters: one for health (which they drink first), the second for love and pleasure, and the third for sleep. After the third one is drained, wise men go home. 

The fourth krater is not mine any more - it belongs to bad behavior; the fifth is for shouting; the sixth is for rudeness and insults; the seventh is for fights; the eighth is for breaking the furniture; the ninth is for depression; the tenth is for madness and unconsciousness.

In keeping with the Greek virtue of moderation, the symposiarch should have prevented festivities from getting out of hand, but Greek literature and art often indicate that the third-krater limit was not observed.

Classicist John Wilkins notes that "in the Odyssey for example, good men are distinguished from bad and Greeks from foreigners partly in terms of how and what they ate. Herodotus identified people partly in terms of food and eating".

Up to the 3rd century BC, the frugality imposed by the physical and climatic conditions of the country was held as virtuous. The Greeks did not ignore the pleasures of eating, but valued simplicity. The rural writer Hesiod, as cited above, spoke of his "flesh of a heifer fed in the woods, that has never calved, and of firstling kids" as being the perfect closing to a day. Nonetheless, Chrysippus is quoted as saying that the best meal was a free one.

Culinary and gastronomical research was rejected as a sign of oriental flabbiness: the inhabitants of the Persian Empire were considered decadent due to their luxurious taste, which manifested itself in their cuisine. 

The Greek authors took pleasure in describing the table of the Achaemenid Great King and his court: Herodotus, Clearchus of Soli, Strabo and Ctesias were unanimous in their descriptions.

In consequence of this cult of frugality, and the diminished regard for cuisine it inspired, the kitchen long remained the domain of women, free or enslaved.

 In the classical period, however, culinary specialists began to enter the written record. Both Aelian and Athenaeus mention the thousand cooks who accompanied Smindyride of Sybaris on his voyage to Athens at the time of Cleisthenes, if only disapprovingly. 

In contrast, Greeks as a whole stressed the austerity of their own diet. Plutarch tells how the king of Pontus, eager to try the Spartan "black gruel", bought a Laconian cook; 'but had no sooner tasted it than he found it extremely bad, which the cook observing, told him, "Sir, to make this broth relish, you should have bathed yourself first in the river Eurotas"'. 

According to Polyaenus, on discovering the dining hall of the Persian royal palace, Alexander the Great mocked their taste and blamed it for their defeat. Pausanias, on discovering the dining habits of the Persian commander Mardonius, equally ridiculed the Persians, "who having so much, came to rob the Greeks of their miserable living".

Plato in Gorgias, mentions "Thearion the cook, Mithaecus the author of a treatise on Sicilian cooking, and Sarambos the wine merchant; three eminent connoisseurs of cake, kitchen and wine." Some chefs also wrote treatises on cuisine.

Over time, more and more Greeks presented themselves as gourmets. From the Hellenistic to the Roman period, the Greeks — at least the rich — no longer appeared to be any more austere than others. The cultivated guests of the feast hosted by Athenaeus in the 2nd or 3rd century devoted a large part of their conversation to wine and gastronomy.

They discussed the merits of various wines, vegetables, and meats, mentioning renowned dishes (stuffed cuttlefish, red tuna belly, prawns, lettuce watered with mead) and great cooks such as Soterides, chef to king Nicomedes I of Bithynia (who reigned from the 279 to 250 BC). 

When his master was inland, he pined for anchovies; Soterides simulated them from carefully carved turnips, oiled, salted and sprinkled with poppy seeds.

Bread

Woman kneading bread, c. 500–475 BC, National Archaeological Museum of Athens

Cereals formed the staple diet. The two main grains were wheat (σῖτος sitos) and barley (κριθή krithe).

In ancient Greece, bread was served with accompaniments known as opson ὄψον, sometimes rendered in English as "relish".[30] This was a generic term which referred to anything which accompanied this staple food, whether meat or fish, fruit or vegetable.

Wheat

Wheat grains were softened by soaking, then either reduced into gruel, or ground into flour (ἀλείατα aleiata) and kneaded and formed into loaves (ἄρτος artos) or flatbreads, either plain or mixed with cheese or honey. Leavening was known; the Greeks later used an alkali (νίτρον nitron) and wine yeast as leavening agents. Dough loaves were baked at home in a clay oven (ἰπνός ipnos) set on legs.

Bread wheat, difficult to grow in Mediterranean climates, and the white bread made from it, were associated with the upper classes in the ancient Mediterranean, while the poor ate coarse brown breads made from emmer wheat and barley.

A simpler baking method involved placing lighted coals on the floor and covering the heap with a dome-shaped lid (πνιγεύς pnigeus); when it was hot enough, the coals were swept aside, and dough loaves were placed on the warm floor. The lid wasthen put back in place, and the coals were gathered on the side of the cover. (This method is still traditionally used in Serbia and elsewhere in the Balkans, where it is called crepulja or sač). The stone oven did not appear until the Roman period. Solon, an Athenian lawmaker of the 6th century BC, prescribed that leavened bread be reserved for feast days. By the end of the 5th century BC, leavened bread was sold at the market, though it was expensive.

Barley

Barley was easier to produce but more difficult to make bread from. It provided a nourishing but very heavy bread. Because of this it was often roasted before milling, producing a coarse flour (ἄλφιτα alphita) which was used to make μᾶζα maza, the basic Greek dish. Many recipes for maza are known; it could be served cooked or raw, as a broth, or made into dumplings or flatbreads. Like wheat breads, it could also be augmented with cheese or honey.

In Peace, Aristophanes employs the expression ἐσθίειν κριθὰς μόνας, literally "to eat only barley", with a meaning equivalent to the English "diet of bread and water".

Fruit and vegetables

In ancient Greece, fruit and vegetables were a significant part of the diet, as the ancient Greeks consumed much less meat than is usual today. Legumes would have been important crops, as their ability to replenish exhausted soil was known at least by the time of Xenophon. As one of the first domesticated crops to be introduced to Greece, lentils are commonly found at archaeological sites in the region from the Upper Paleolithic.

Vegetables were eaten as soups, boiled or mashed (ἔτνος etnos), seasoned with olive oil, vinegar, herbs or γάρον gáron, a fish sauce similar to Vietnamese nước mắm. In the comedies of Aristophanes, Heracles was portrayed as a glutton with a fondness for mashed beans. Poor families ate oak acorns (βάλανοι balanoi). Raw or preserved olives were a common appetizer.

In the cities, fresh vegetables were expensive, and therefore, the poorer city dwellers had to make do with dried vegetables. Lentil soup (φακῆ phakē) was the workman's typical dish. Cheese, garlic, and onions were the soldier's traditional fare. In Aristophanes' Peace, the smell of onions typically represents soldiers; the chorus, celebrating the end of war, sings Oh! joy, joy! No more helmet, no more cheese nor onions! Bitter vetch (ὄροβος orobos) was considered a famine food.

Fruits, fresh or dried, and nuts, were eaten as dessert. Important fruits were figs, raisins, and pomegranates. In Athenaeus' Deipnosophistae, he describes a dessert made of figs and broad beans. Dried figs were also eaten as an appetizer or when drinking wine. In the latter case, they were often accompanied by grilled chestnuts, chick peas, and beechnuts.

Fish and meat

Sacrifice; principal source of meat for city dwellers
here a boar; tondo of an Attickylix by the Epidromos Painter,
c. 510–500 BC, Louvre.

The consumption of fish and meat varied in accordance with the wealth and location of the household; in the country, hunting (primarily trapping) allowed for consumption of birds and hares. Peasants also had farmyards to provide them with chickens and geese. Slightly wealthier landowners could raise goats, pigs, or sheep. In the city, meat was expensive except for pork. In Aristophanes' day a piglet cost three drachmas, which was three days' wages for a public servant. Sausages were common both for the poor and the rich. Archaeological excavations at Kavousi Kastro, Lerna, and Kastanas have shown that dogs were sometimes consumed in Bronze Age Greece, in addition to the more commonly-consumed pigs, cattle, sheep, and goats.

In the 8th century BC Hesiod describes the ideal country feast in Works and Days:

“But at that time let me have a shady rock and Bibline wine, a clot of curds and milk of drained goats with the flesh of a heifer fed in the woods, that has never calved, and of firstling kids; then also let me drink bright wine…”

Meat is much less prominent in texts of the 5th century BC onwards than in the earliest poetry, but this may be a matter of genre rather than real evidence of changes in farming and food customs. Fresh meat was most commonly eaten at sacrifices, though sausage was much more common, consumed by people across the economic spectrum.

Spartans primarily ate a soup made from pigs' legs and blood, known as melas zōmos (μέλας ζωμός), which means "black soup". According to Plutarch, it was "so much valued that the elderly men fed only upon that, leaving what flesh there was to the younger". It was famous amongst the Greeks. "Naturally Spartans are the bravest men in the world," joked a Sybarite, "anyone in his senses would rather die ten thousand times than take his share of such a sorry diet". It was made with pork, salt, vinegar and blood. The dish was served with maza, figs and cheese sometimes supplemented with game and fish. The 2nd–3rd century author Aelian claims that Spartan cooks were prohibited from cooking anything other than meat.

In the Greek islands and on the coast, fresh fish and seafood (squid, octopus, and shellfish) were common. They were eaten locally but more often transported inland. Sardines and anchovies were regular fare for the citizens of Athens. They were sometimes sold fresh, but more frequently salted. A stele of the late 3rd century BC from the small Boeotian city of Akraiphia, on Lake Copais, provides us with a list of fish prices. The cheapest was skaren (probably parrotfish) whereas Atlantic bluefin tuna was three times as expensive. Common salt water fish were yellowfin tuna, red mullet, ray, swordfish or sturgeon, a delicacy which was eaten salted. Lake Copais itself was famous in all Greece for its eels, celebrated by the hero of The Acharnians. Other fresh water fish were pike-fish, carp and the less appreciated catfish. In classical Athens, eels, conger-eels, and sea-perch (ὈρΦὸς) were considered to be great delicacies, while sprats were cheap and readily available.

Eggs and dairy products

Greeks bred quails and hens, partly for their eggs. Some authors also praise pheasant eggs and Egyptian Goose eggs, which were presumably rather rare. Eggs were cooked soft- or hard-boiled as hors d'œuvre or dessert. Whites, yolks and whole eggs were also used as ingredients in the preparation of dishes.

Country dwellers drank milk (γάλα gala), but it was seldom used in cooking. Butter (βούτυρον bouturon) was known but seldom used either: 

Greeks saw it as a culinary trait of the Thracians of the northern Aegean coast, whom the Middle Comic poet Anaxandrides dubbed "butter eaters". 

Yet Greeks enjoyed other dairy products. Πυριατή pyriatē and Oxygala (οξύγαλα) were curdled milk products, similar to cottage cheese or perhaps to yogurt. 

Most of all, goat's and ewe's cheese (τυρός tyros) was a staple food. Fresh and hard cheese were sold in different shops; the former cost about two thirds of the latter's price.

Cheese was eaten alone or with honey or vegetables. It was also used as an ingredient in the preparation of many dishes, including fish dishes. The only extant recipe by the Sicilian cook Mithaecus runs: "Tainia: gut, discard the head, rinse and fillet; add cheese and olive oil".

However, the addition of cheese seems to have been a controversial matter; Archestratus warns his readers that Syracusan cooks spoil good fish by adding cheese.

Drink

Attic Rhyton, c. 460–450 BC, National Archaeological Museum of Athens.

The most widespread drink was water. Fetching water was a daily task for women. Though wells were common, spring water was preferred: it was recognized as nutritious because it caused plants and trees to grow, and also as a desirable beverage. Pindar called spring water "as agreeable as honey".

One of the comic poet Antiphanes's characters claimed that he could recognize Attic water by taste alone. Athenaeus states that a number of philosophers had a reputation for drinking nothing but water, a habit combined with a vegetarian diet (cf. below). Milk, usually goats' milk, was not widely consumed, being considered barbaric.

The usual drinking vessel was the skyphos, made out of wood, terra cotta, or metal. Critias[81] also mentions the kothon, a Spartan goblet which had the military advantage of hiding the colour of the water from view and trapping mud in its edge. The ancient Greeks also used a vessel called a kylix (a shallow footed bowl), and for banquets the kantharos (a deep cup with handles) or the rhyton, a drinking horn often moulded into the form of a human or animal head.

Wine

The Greeks are thought to have made red as well as rosé and white wines. Like today, these varied in quality from common table wine to valuable vintages. It was generally considered that the best wines came from Thásos, Lesbos and Chios.

Cretan wine came to prominence later. A secondary wine made from water and pomace (the residue from squeezed grapes), mixed with lees, was made by country people for their own use. The Greeks sometimes sweetened their wine with honey and made medicinal wines by adding thyme, pennyroyal and other herbs. By the first century, if not before, they were familiar with wine flavoured with pine resin (modern retsina). Aelian also mentions a wine mixed with perfume. Cooked wine was known, as well as a sweet wine from Thásos, similar to port wine.

Wine was generally cut with water. The drinking of akraton or "unmixed wine", though known to be practised by northern barbarians, was thought likely to lead to madness and death. Wine was mixed in a krater, from which the slaves would fill the drinker's kylix with an oinochoe (jugs). Wine was also thought to have medicinal powers. Aelian mentions that the wine from Heraia in Arcadia rendered men foolish but women fertile; conversely, Achaean wine was thought to induce abortion.

Outside of these therapeutic uses, Greek society did not approve of women drinking wine. According to Aelian, a Massalian law prohibited this and restricted women to drinking water. Sparta was the only city where women routinely drank wine.

Wine reserved for local use was kept in skins. That destined for sale was poured into πίθοι pithoi, (large terra cotta jugs). From here they were decanted into amphoras sealed with pitch for retail sale. Vintage wines carried stamps from the producers or city magistrates who guaranteed their origin. This is one of the first instances of indicating the geographical or qualitative provenance of a product.

Kykeon

Hecamede preparing kykeon for Nestor, kylix by the Brygos Painter,
ca. 490 BC, Louvre

The Greeks also drank kykeon (κυκεών, from κυκάω kykaō, "to shake, to mix"), which was both a beverage and a meal. It was a barley gruel, to which water and herbs were added. In the Iliad, the beverage also contained grated goat cheese. In the Odyssey, Circe adds honey and a magic potion to it. In the Homeric Hymn to Demeter, the goddess refuses red wine but accepts a kykeon made of water, flour, and pennyroyal.

Used as a ritual beverage in the Eleusinian Mysteries, kykeon was also a popular beverage, especially in the countryside: Theophrastus, in his Characters, describes a boorish peasant as having drunk much kykeon and inconveniencing the Assemblywith his bad breath. It also had a reputation as a good digestive, and as such, in Peace, Hermes recommends it to the main character who has eaten too much dried fruit.

Cultural beliefs about the role of food

Food played an important part in the Greek mode of thought. Classicist John Wilkins notes that "in the Odyssey for example, good men are distinguished from bad and Greeks from foreigners partly in terms of how and what they ate. Herodotus identified people partly in terms of food and eating".

Up to the 3rd century BC, the frugality imposed by the physical and climatic conditions of the country was held as virtuous. The Greeks did not ignore the pleasures of eating, but valued simplicity. 

The rural writer Hesiod, as cited above, spoke of his "flesh of a heifer fed in the woods, that has never calved, and of firstling kids" as being the perfect closing to a day. Nonetheless, Chrysippus is quoted as saying that the best meal was a free one.

Culinary and gastronomical research was rejected as a sign of oriental flabbiness: the inhabitants of the Persian Empire were considered decadent due to their luxurious taste, which manifested itself in their cuisine. 

The Greek authors took pleasure in describing the table of the Achaemenid Great King and his court: Herodotus, Clearchus of Soli,Strabo and Ctesias were unanimous in their descriptions.

Fresh fish, one of the favorite dishes of the Greeks, platter with red figures,
 c. 350–325 BC, Louvre

In contrast, Greeks as a whole stressed the austerity of their own diet. Plutarch tells how the king of Pontus, eager to try the Spartan "black gruel", bought a Laconian cook; 'but had no sooner tasted it than he found it extremely bad, which the cook observing, told him, "Sir, to make this broth relish, you should have bathed yourself first in the river Eurotas"'.

According to Polyaenus, on discovering the dining hall of the Persian royal palace, Alexander the Great mocked their taste and blamed it for their defeat. Pausanias, on discovering the dining habits of the Persian commander Mardonius, equally ridiculed the Persians, "who having so much, came to rob the Greeks of their miserable living".

In consequence of this cult of frugality, and the diminished regard for cuisine it inspired, the kitchen long remained the domain of women, free or enslaved. In the classical period, however, culinary specialists began to enter the written record. 

Both Aelian and Athenaeus mention the thousand cooks who accompanied Smindyride of Sybaris on his voyage to Athens at the time of Cleisthenes, if only disapprovingly. 

Plato in Gorgias, mentions "Thearion the cook, Mithaecus the author of a treatise on Sicilian cooking, and Sarambos the wine merchant; three eminent connoisseurs of cake, kitchen and wine." Some chefs also wrote treatises on cuisine.

Over time, more and more Greeks presented themselves as gourmets. From the Hellenistic to the Roman period, the Greeks — at least the rich — no longer appeared to be any more austere than others. The cultivated guests of the feast hosted by Athenaeus in the 2nd or 3rd century devoted a large part of their conversation to wine and gastronomy. 

They discussed the merits of various wines, vegetables, and meats, mentioning renowned dishes (stuffed cuttlefish, red tuna belly, prawns, lettuce watered with mead) and great cooks such as Soterides, chef to king Nicomedes I of Bithynia (who reigned from the 279 to 250 BC). When his master was inland, he pined for anchovies; Soterides simulated them from carefully carved turnips, oiled, salted and sprinkled with poppy seeds. 

Suidas (an encyclopaedia from the Byzantine period) mistakenly attributes this exploit to the celebrated Roman gourmet Apicius (1st century BC) — which may be taken as evidence that the Greeks had reached the same level as the Romans.

Vegetarianism

Triptolemus received wheat sheaves from Demeter and blessings from Persephone,
5th century BC relief, National Archaeological Museum of Athens

Orphicism and Pythagoreanism, two common ancient Greek religions, suggested a different way of life, based on a concept of purity and thus purification (κάθαρσις katharsis) — a form of asceticism in the original sense: ἄσκησις askēsis initially signifies a ritual, then a specific way of life. Vegetarianism was a central element of Orphicism and of several variants of Pythagoreanism.

Empedocles (5th century BC) justified vegetarianism by a belief in the transmigration of souls: who could guarantee that an animal about to be slaughtered did not house the soul of a human being? However, it can be observed that Empedocles also included plants in this transmigration, thus the same logic should have applied to eating them. Vegetarianism was also a consequence of a dislike for killing: "For Orpheus taught us rights and to refrain from killing".

The information from Pythagoras (6th century BC) is more difficult to define. The Comedic authors such as Aristophanes and Alexis described Pythagoreans as strictly vegetarian, with some of them living on bread and water alone. Other traditions contented themselves with prohibiting the consumption of certain vegetables, such as the broad bean, or of sacred animals such as the white cock or selected animal parts.

It follows that vegetarianism and the idea of ascetic purity were closely associated, and often accompanied by sexual abstinence. In On the eating of flesh, Plutarch (1st–2nd century) elaborated on the barbarism of blood-spilling; inverting the usual terms of debate, he asked the meat-eater to justify his choice.

The Neoplatonic Porphyrius (3rd century) associates in On Abstinence vegetarianism with the Cretan mystery cults, and gives a census of past vegetarians, starting with the semi-mythical Epimenides. For him, the origin of vegetarianism was Demeter's gift of wheat to Triptolemus so that he could teach agriculture to humanity. His three commandments were: "Honour your parents", "Honour the gods with fruit", and "Spare the animals".