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Eleusinian Mysteries

The Eleusinian Mysteries (Ἐλευσίνια Μυστήρια) were initiations held every year for the cult of Demeter and Persephone based at the Panhellenic Sanctuary of Eleusis in ancient Greece. They are considered the "most famous of the secret religious rites of ancient Greece". Their basis was a Bronze Age agrarian cult, and there is some evidence that they were derived from the religious practices of the Mycenean period. The Mysteries represented the myth of the abduction of Persephone from her mother Demeter by the king of the underworld Hades, in a cycle with three phases: the descent (loss), the search, and the ascent, with the main theme being the ascent (ἄνοδος) of Persephone and the reunion with her mother. It was a major festival during the Hellenic era, and later spread to Rome. Similar religious rites appear in the agricultural societies of the Near East and in Minoan Crete.

The rites, ceremonies, and beliefs were kept secret and consistently preserved from antiquity. For the initiated, the rebirth of Persephone symbolized the eternity of life which flows from generation to generation, and they believed that they would have a reward in the afterlife. There are many paintings and pieces of pottery that depict various aspects of the Mysteries. Since the Mysteries involved visions and conjuring of an afterlife, some scholars believe that the power and longevity of the Eleusinian Mysteries, a consistent set of rites, ceremonies and experiences that spanned two millennia, came from psychedelic drugs. The name of the town, Eleusis, seems to be pre-Greek, and is likely a counterpart with Elysium and the goddess Eileithyia.

Etymology
Eleusinian Mysteries (Ἐλευσίνια Μυστήρια) was the name of the mysteries of the city Eleusis.

The name of the city Eleusis is Pre-Greek, and may be related with the name of the goddess Eileithyia. Her name Ἐλυσία (Elysia) in Laconia and Messene probably relates her with the month Eleusinios and Eleusis, but this is debated.

The ancient Greek word from which English mystery derives, mystḗrion (μυστήριον), means "mystery or secret rite" and is related with the verb myéō (μυέω), which means "(I) teach, initiate into the mysteries", and the noun mýstēs (μύστης), which means "one initiated". The word mystikós (μυστικός), source of the English mystic, means "connected with the mysteries", or "private, secret" (as in Modern Greek).

Demeter and Persephone
The Mysteries are related to a myth concerning Demeter, the goddess of agriculture and fertility as recounted in one of the Homeric Hymns (c. 650 BC). According to the hymn, Demeter's daughter Persephone (also referred to as Kore, "maiden") was assigned the task of painting all the flowers of the earth. Before completion, she was seized by Hades, the god of the underworld, who took her to his underworld kingdom. Distraught, Demeter searched high and low for her daughter. Because of her distress, and in an effort to coerce Zeus to allow the return of her daughter, she caused a terrible drought in which the people suffered and starved, depriving the gods of sacrifice and worship. As a result, Zeus relented and allowed Persephone to return to her mother.

According to the myth, during her search Demeter traveled long distances and had many minor adventures along the way. In one she taught the secrets of agriculture to Triptolemus. Finally, by consulting Zeus, Demeter reunited with her daughter and the earth returned to its former verdure and prosperity: the first spring.

Zeus, pressed by the cries of the hungry people and by the other deities who also heard their anguish, forced Hades to return Persephone. However, it was a rule of the Fates that whoever consumed food or drink in the Underworld was doomed to spend eternity there. Before Persephone was released to Hermes, who had been sent to retrieve her, Hades tricked her into eating pomegranate seeds (either six or four according to the telling), which forced her to return to the underworld for some months each year. She was obliged to remain with Hades for six or four months (one month per seed) and lived above ground with her mother for the rest of the year. This left a long period of time when Demeter was unhappy due to Persephone's absence, neglecting to cultivate the earth. When Persephone returned to the surface, Demeter became joyful and cared for the earth again.

In the central foundation document of the mystery, the Homeric Hymn to Demeter line 415, Persephone is said to stay in Hades during winter and return to her mother in the spring of the year: "This was the day [of Persephone's return], at the very beginning of bountiful springtime."

Persephone's rebirth is symbolic of the rebirth of all plant life and the symbol of eternity of life that flows from the generations that spring from each other.

However, a scholar has proposed a different version, according to which the four months during which Persephone is with Hades correspond to the dry Greek summer, a period during which plants are threatened with drought.

Mysteries

The Eleusinian Mysteries are believed to have ancient origins. Some findings in the temple Eleusinion in Attica suggest that their basis was an old agrarian cult. Some practices of the mysteries seem to have been influenced by the religious practices of the Mycenaean period, thus predating the Greek Dark Ages. Excavations showed that a private building existed under the Telesterion in the Mycenean period, and it seems that originally the cult of Demeter was private. In the Homeric Hymn is mentioned the palace of the king Keleos. One line of thought by modern scholars has been that the Mysteries were intended "to elevate man above the human sphere into the divine and to assure his redemption by making him a god and so conferring immortality upon him".

Some scholars argued that the Eleusinian cult was a continuation of a Minoan cult, and that Demeter was a poppy goddess who brought the poppy from Crete to Eleusis. Some useful information from the Mycenean period can be taken from the study of the cult of Despoina (the precursor goddess of Persephone) and the cult of Eileithyia, who was the goddess of childbirth. The megaron of Despoina at Lycosura is quite similar to the Telesterion of Eleusis, and Demeter is united with the god Poseidon, bearing a daughter, the unnamable Despoina (the mistress). In the cave of Amnisos at Crete, the goddess Eileithyia is related with the annual birth of the divine child, and she is connected with Enesidaon  (The Earth Shaker), who is the chthonic aspect of Poseidon.

At Eleusis inscriptions refer to "the Goddesses" accompanied by the agricultural god Triptolemus (probably son of Ge and Oceanus), and "the God and the Goddess" (Persephone and Plouton) accompanied by Eubuleus who probably led the way back from the underworld. The myth was represented in a cycle with three phases: the "descent", the "search", and the "ascent" (Greek anodos) with contrasted emotions from sorrow to joy which roused the mystae to exultation.

The main theme was the ascent of Persephone and the reunion with her mother Demeter. At the beginning of the feast, the priests filled two special vessels and poured them out, one towards the west and the other towards the east. The people looking both to the sky and the earth shouted in a magical rhyme "rain and conceive". In a ritual, a child was initiated from the hearth (the divine fire). The name pais (child) appears in the Mycenean inscriptions, it was the ritual of the "divine child" who originally was Ploutos. In the Homeric hymn the ritual is connected with the myth of the agricultural god Triptolemus. The goddess of nature survived in the mysteries where the following words were uttered: "Mighty Potnia bore a great son". Potnia (Linear B po-ti-ni-ja : lady or mistress), is a Mycenaean title applied to goddesses, and probably the translation of a similar title of pre-Greek origin.

The high point of the celebration was "an ear of grain cut in silence", which represented the force of the new life. The idea of immortality did not exist in the mysteries at the beginning, but the initiated believed that they would have a better fate in the underworld. Death remained a reality, but at the same time a new beginning like the plant which grows from the buried seed. A depiction from the old palace of Phaistos is very close to the image of the anodos of Persephone. An armless and legless deity grows out of the ground, and her head turns to a large flower.

According to George Mylonas, the lesser mysteries were held "as a rule once a year in the early spring in the month of flowers, the Anthesterion," while "the Greater Mysteries were held once a year and every fourth year they were celebrated with special splendor in what was known as the penteteris. Kerényi concurs with this assessment: "The Lesser Mysteries were held at Agrai in the month of Anthesterion, our February... The initiates were not even admitted to the epopteia [Greater Mysteries] in the same year, but only in September of the following year." This cycle continued for about two millennia. In the Homeric Hymn to Demeter, King Celeus is said to have been one of the first people to learn the secret rites and mysteries of her cult. He was also one of her original priests, along with Diocles, Eumolpos, Polyxeinus, and Triptolemus, Celeus' son, who had supposedly learned agriculture from Demeter.

Under Peisistratos of Athens, the Eleusinian Mysteries became pan-Hellenic, and pilgrims flocked from Greece and beyond to participate. Around 300 BC, the state took over control of the mysteries; they were controlled by two families, the Eumolpidae and the Kerykes. This led to a vast increase in the number of initiates. The only requirements for membership were freedom from "blood guilt", meaning never having committed murder, and not being a "barbarian" (being unable to speak Greek). Men, women, and even slaves were allowed initiation.

Participants
To participate in these mysteries one had to swear a vow of secrecy.

Four categories of people participated in the Eleusinian Mysteries:
 * Priests, priestesses, and hierophants
 * Initiates, undergoing the ceremony for the first time
 * Others who had already participated at least once – they were eligible for the final category
 * Those who had attained épopteia (Greek: ἐποπτεία) (contemplation), who had learned the secrets of the greatest mysteries of Demeter

Priesthood
The priesthood officiating at the Eleusinian Mysteries and in the sanctuary was divided into several offices with different tasks.

Six categories of priests officiated in the Eleusinian Mysteries:

 * Hierophantes – male high priest, an office inherited within the Phileidae or Eumolpidae families.
 * High Priestess of Demeter or Priestess of Demeter and Kore – an office inherited within the Phileidae or Eumolpidae families.
 * Dadouchos – men serving as torch bearers, the second-highest male role next to Hierophantes.
 * Dadouchousa Priestess – a female priestess who assisted the Dadouchos, an office inherited within the Phileidae or Eumolpidae families.
 * Hierophantides – two married priestesses, one serving Demeter, and the other Persephone.
 * Panageis ('the holy') or melissae ('bees') – a group of priestesses who lived a life secluded from men.

The offices of Hierophant, High Priestess, and Dadouchousa priestess were all inherited within the Phileidae or Eumolpidae families, and the Hierophant and the High Priestess were of equal rank. It was the task of the High Priestess to impersonate the roles of the goddesses Demeter and Persephone in the enactment during the mysteries, and at Eleusis events were dated by the name of the reigning High Priestess.

Secrets
The outline below is only a capsule summary; much of the concrete information about the Eleusinian Mysteries was never written down. For example, only initiates knew what the kiste, a sacred chest, and the calathus, a lidded basket, contained.

Hippolytus of Rome, one of the Church Fathers writing in the early 3rd century AD, discloses in Refutation of All Heresies that "the Athenians, while initiating people into the Eleusinian rites, likewise display to those who are being admitted to the highest grade at these mysteries, the mighty, and marvellous, and most perfect secret suitable for one initiated into the highest mystic truths: an ear of grain in silence reaped."

Lesser Mysteries
There were two Eleusinian Mysteries, the Greater and the Lesser. According to Thomas Taylor, "the dramatic shows of the Lesser Mysteries occultly signified the miseries of the soul while in subjection to the body, so those of the Greater obscurely intimated, by mystic and splendid visions, the felicity of the soul both here and hereafter, when purified from the defilements of a material nature and constantly elevated to the realities of intellectual [spiritual] vision." According to Plato, "the ultimate design of the Mysteries ... was to lead us back to the principles from which we descended, ... a perfect enjoyment of intellectual [spiritual] good."

The Lesser Mysteries took place in the month of Anthesteria – the eighth month of the Attic calendar, falling in mid winter around February or March – under the direction of Athens' archon basileus. In order to qualify for initiation, participants would sacrifice a piglet to Demeter and Persephone, and then ritually purify themselves in the river Illisos. Upon completion of the Lesser Mysteries, participants were deemed mystai (initiates) worthy of witnessing the Greater Mysteries.

Greater Mysteries
The Greater Mysteries took place in Boedromion – the third month of the Attic calendar, falling in late summer around September or October – and lasted ten days.

The first act (on the 14th of Boedromion) was the bringing of the sacred objects from Eleusis to the Eleusinion, a temple at the base of the Acropolis of Athens.

On the 15th of Boedromion, a day called the Gathering (Agyrmos), the priests (hierophantes, those who show the sacred ones) declared the start of the rites (prorrhesis), and carried out the sacrifice (hiereía deúro, hither the victims).

The seawards initiates (halade mystai) started out in Athens on 16th Boedromion with the celebrants washing themselves in the sea at Phaleron.

On the 17th, the participants began the Epidauria, a festival for Asklepios named after his main sanctuary at Epidauros. This "festival within a festival" celebrated the healer's arrival at Athens with his daughter Hygieia, and consisted of a procession leading to the Eleusinion, during which the mystai apparently stayed at home, a great sacrifice, and an all-night feast (pannykhís).

The procession to Eleusis began at Kerameikos (the Athenian cemetery) on the 18th, and from there the people walked to Eleusis, along the Sacred Way (Ἱερὰ Ὁδός, Hierá Hodós), swinging branches called bacchoi. At a certain spot along the way, they shouted obscenities in commemoration of Iambe (or Baubo), an old woman who, by cracking dirty jokes, had made Demeter smile as she mourned the loss of her daughter. The procession also shouted "Íakch', O Íakche!", possibly an epithet for Dionysus, or a separate deity Iacchus, son of Persephone or Demeter.

Upon reaching Eleusis, there was an all-night vigil (pannychis) according to Mylonas and Kerényi. perhaps commemorating Demeter's search for Persephone. At some point, initiates had a special drink (kykeon), of barley and pennyroyal, which has led to speculation about its chemicals perhaps having psychotropic effects from ergot (a fungus that grows on barley, containing psychedelic alkaloids similar to LSD). Discovery of fragments of ergot in a temple dedicated to the two Eleusinian goddesses excavated at the Mas Castellar site (Girona, Spain) provided legitimacy for this theory. Ergot fragments were found inside a vase and within the dental calculus (plaque) of a 25-year-old man, providing evidence of ergot being consumed (Juan-Stresserras, 2002). This finding seems to support the hypothesis of ergot as an ingredient of the Eleusinian kykeon.

Inside the Telesterion
On the 19th of Boedromion, initiates entered a great hall called Telesterion; in the center stood the Palace (Anaktoron), built of ruins dating back to the Mycenaean Age, which only the hierophants could enter, where sacred objects were stored. Before mystai could enter the Telesterion, they would recite, "I have fasted, I have drunk the kykeon, I have taken from the kiste (box) and after working it have put it back in the calathus (open basket).

It is widely supposed that the rites inside the Telesterion comprised three elements:

 * dromena (things done), a dramatic reenactment of the Demeter/Persephone myth
 * deiknumena (things shown), displayed sacred objects, in which the hierophant played an essential role
 * legomena (things said), commentaries that accompanied the deiknumena

Combined, these three elements were known as the aporrheta (unrepeatables); the penalty for divulging them was death.

Athenagoras of Athens, Cicero, and other ancient writers cite that it was for this crime (among others) that Diagoras was condemned to death in Athens; the tragic playwright Aeschylus was allegedly tried for revealing secrets of the mysteries in some of his plays, but was acquitted. The ban on divulging the core ritual of the mysteries was thus absolute, which is probably why almost nothing is known about what transpired there.

Climax

As to the climax of the mysteries, there are two modern theories.

Some hold that the priests were the ones to reveal the visions of the holy night, consisting of a fire that represented the possibility of life after death, and various sacred objects. Others hold this explanation to be insufficient to account for the power and longevity of the mysteries, and that the experiences must have been internal and mediated by a powerful psychoactive ingredient contained in the kykeon drink (see Entheogenic theories below).

Following this section of the Mysteries was an all-night feast (Pannychis) accompanied by dancing and merriment. This portion of the festivities was open to the public. The dances took place in the Rharian Field, rumored to be the first spot where grain grew. A bull sacrifice also took place late that night or early the next morning. That day (22nd Boedromion), the initiates honoured the dead by pouring libations from special vessels.

On the 23rd of Boedromion, the mysteries ended and everyone returned home.

Demise
In 170 AD, the Temple of Demeter was sacked by the Sarmatians but was rebuilt by Marcus Aurelius. Aurelius was then allowed to become the only lay person ever to enter the anaktoron. As Christianity gained in popularity in the 4th and 5th centuries, Eleusis's prestige began to fade. The last pagan emperor of Rome, Julian, reigned from 361 to 363 after about fifty years of Christian rule. Julian attempted to restore the Eleusinian Mysteries and was the last emperor to be initiated into them. The closing of the Eleusinian Mysteries in 392 AD by the emperor Theodosius I is reported by Eunapius, a historian and biographer of the Greek philosophers. Eunapius had been initiated by the last legitimate Hierophant, who had been commissioned by the emperor Julian to restore the Mysteries, which had by then fallen into decay. According to Eunapius, the last Hierophant was a usurper, "the man from Thespiae who held the rank of Father in the mysteries of Mithras". In 396, during his raiding campaign in Attica, the king of the Goths Alaric I – accompanied by Christian monks "in their dark robes" – looted the remains of the shrines.

According to historian Hans Kloft, despite the destruction of the Eleusinian Mysteries, elements of the cult survived in the Greek countryside. There, local peasants and shepherds partially transferred Demeter's rites and religious duties onto Saint Demetrius of Thessaloniki, who gradually became the local patron of agriculture and "heir" to the pagan mother goddess.

In art, literature, and culture
There are many paintings and pieces of pottery that depict various aspects of the Mysteries. The Eleusinian Relief, from the late 5th century BC, displayed in the National Archaeological Museum of Athens is a representative example. Triptolemus is depicted receiving seeds from Demeter and teaching mankind how to work the fields to grow crops, with Persephone holding her hand over his head to protect him. Vases and other works of relief sculpture, from the 4th, 5th and 6th centuries BC, depict Triptolemus holding an ear of corn, sitting on a winged throne or chariot, surrounded by Persephone and Demeter with pine torches. The monumental Protoattic amphora from the middle of the 7th century BC, with the depiction of Medusa's beheading by Perseus and the blinding of Polyphemos by Odysseus and his companions on its neck, is kept in the Archaeological Museum of Eleusis which is located inside the archaeological site of Eleusis.

The Ninnion Tablet, found in the same museum, depicts Demeter, followed by Persephone and Iacchus, and then the procession of initiates. Then, Demeter is sitting on the kiste inside the Telesterion, with Persephone holding a torch and introducing the initiates. The initiates each hold a bacchoi. The second row of initiates were led by Iakchos, a priest who held torches for the ceremonies. He is standing near the omphalos while an unknown female (probably a priestess of Demeter) sat nearby on the kiste, holding a scepter and a vessel filled with kykeon. Pannychis is also represented.

The Myth of Er, part of Plato's Republic, is thought to be a representation of the teaching of the Eleusinian Mysteries. Er, after being killed in battle and brought to the underworld, is reincarnated without drinking from the River Lethe. He retains his memories and tells the living about his experience in the underworld. He no longer has a fear of death.

In Shakespeare's Mystery Play: A Study of The Tempest, Colin Still argued that The Tempest was an allegory for initiation into the Eleusinian Mysteries. Though widely rejected, this interpretation was supported by Michael Srigley in Images of Regeneration.

Carl Gustav Jung (1875–1961) borrowed terms and interpretations from the late 19th and early 20th century classical scholarship in German and French as a source of metaphors for his reframing of psychoanalytic treatment into a spiritualistic ritual of initiation and rebirth. The Eleusinian mysteries, particularly the qualities of the Kore, figured prominently in his writings.

Dimitris Lyacos in the second book of the Poena Damni trilogy With the People from the Bridge, a contemporary, avant-garde play focusing on the return of the dead and the revenant legend combines elements from the Eleusinian mysteries as well as early Christian tradition in order to convey a view of collective salvation. The text uses the pomegranate symbol in order to hint at the residence of the dead in the underworld and their periodical return to the world of the living.

Octavio Vazquez's symphonic poem Eleusis draws on the Eleusinian Mysteries and on other Western esoteric traditions. Commissioned by the Sociedad General de Autores y Editores and the RTVE Symphony Orchestra, it was premiered in 2015 by the RTVE Orchestra and conductor Adrian Leaper at the Teatro Monumental in Madrid.

Entheogenic theories
Numerous scholars have proposed that the power of the Eleusinian Mysteries came from the kykeon's functioning as an entheogen, or psychedelic agent. The use of potions or philtres for magical or religious purposes was relatively common in Greece and the ancient world. The initiates, sensitized by their fast and prepared by preceding ceremonies (see set and setting), may have been propelled by the effects of a powerful psychoactive potion into revelatory mind states with profound spiritual and intellectual ramifications. In opposition to this idea, skeptical scholars note the lack of any solid evidence and stress the collective rather than individual character of initiation into the Mysteries.

Many psychoactive agents have been proposed as the significant element of kykeon, though without consensus or conclusive evidence. These include the ergot species Claviceps paspali, a fungal parasite of paspalum, which contains the alkaloids ergotamine, a precursor to LSD, and ergonovine. However, modern attempts to prepare a kykeon using ergot-parasitized barley have yielded inconclusive results, though Alexander Shulgin and Ann Shulgin describe both ergonovine and LSA to be known to produce LSD-like effects.

Discovery of fragments of ergot (fungi containing LSD-like psychedelic alkaloids) in a temple dedicated to the two Eleusinian Goddesses excavated at the Mas Castellar site (Girona, Spain) provided some legitimacy for this theory. Ergot fragments were found inside a vase and within the dental calculus of a 25-year-old man, providing evidence of ergot being consumed. This finding seems to support the hypothesis of ergot as an ingredient of the Eleusinian kykeon.

Psychoactive mushrooms are another candidate. Scholars such as Robert Graves and Terence McKenna, speculated that the mysteries were focused around a variety of Psilocybe. Other entheogenic fungi, such as Amanita muscaria, have also been suggested. A recent hypothesis suggests that the ancient Egyptians cultivated Psilocybe cubensis on barley and associated it with the deity Osiris.

Another candidate for the psychoactive drug is an opioid derived from the poppy. The cult of the goddess Demeter may have brought the poppy from Crete to Eleusis; it is certain that opium was produced in Crete.

Another theory is that the psychoactive agent in kykeon is DMT, which occurs in many wild plants of the Mediterranean, including Phalaris and/or Acacia. To be active orally (like in ayahuasca) it must be combined with a monoamine oxidase inhibitor such as Syrian rue (Peganum harmala), which grows throughout the Mediterranean.

Alternatively, J. Nigro Sansonese (1994), using the mythography supplied by Mylonas, hypothesizes that the Mysteries of Eleusis were a series of practical initiations into trance involving proprioception of the human nervous system induced by breath control (similar to samyama in yoga). Sansonese speculates that the kisté, a box holding sacred objects opened by the hierophant, is actually an esoteric reference to the initiate's skull, within which is seen a sacred light and are heard sacred sounds, but only after instruction in trance practice. Similarly, the seed-filled chambers of a pomegranate, a fruit associated with the founding of the cult, esoterically describe proprioception of the initiate's heart during trance.

Notable participants

 * Aeschylus (525/524–456/455 BC)
 * Plato (428/427 or 424/423–348/347 BC)
 * Augustus (63 BC–AD 14)
 * Plutarch (c. AD 46–after 119)
 * Hadrian (76–138)
 * Antinous (c. 111–130)
 * Marcus Aurelius (121–180)
 * Commodus (161–192)
 * Gallienus (c. 218–268)
 * Julian (331–363)

title: Eleusinian Mysteries


text:
Gero von Wilpert

Gero von Wilpert (13 March 1933 – 24 December 2009) was a German author, a senior lecturer in German at the University of New South Wales and, from 1980, Professor of German at the University of Sydney.

Life and career
Wilpert was born in Tartu (Dorpat), Estonia. Like all Baltic Germans, he was forced to leave Estonia after the Molotov–Ribbentrop Pact and the takeover of the country by the Soviet Union (1939–40).

From 1953 to 1957 he studied at the University of Heidelberg, where he was at times a docent. He then settled near Stuttgart to work as independent author and lecturer.

Wilpert published several editions of an encyclopedia of literary descriptions Sachwörterbuch der Literatur. He also wrote a comprehensive Lexikon der Weltliteratur [Lexicon of World Literature] and earlier had published his Deutsche Literatur in Bildern [German Literature in Pictures] and a journal on Schiller.

He was a member of the Australian Academy of the Humanities.

Wilpert died in Sydney.

Books

 * Sachwörterbuch der Literatur. Kröner, 1955; 8th revised edition, 2001, ISBN 3-520-23108-5.
 * Lexikon der Weltliteratur. Kröner, 1963; 4th edition, 2004.
 * Erstausgaben deutscher Dichtung. Joint author: Adolf Gühring. 1967; 2nd revised edition, 1992, ISBN 3-520-80902-8.
 * Moderne Weltliteratur. Die Gegenwartsliteraturen Europas und Amerikas. Joint author: Ivar Ivask. Kröner, 1972, ISBN 3-520-43001-0.
 * Deutsche Literatur in Bildern. Kröner, 1957; 2nd revised edition, 1975.
 * Der verlorene Schatten. Kröner, 1978, ISBN 3-520-70101-4.
 * Deutsches Dichterlexikon. Kröner, 1988, ISBN 3-520-28803-6.
 * Die deutsche Gespenstergeschichte. Kröner, 1994, ISBN 3-520-40601-2.
 * Goethe-Lexikon. Kröner, 1998, ISBN 3-520-40701-9.
 * Schiller-Chronik. Sein Leben und Schaffen. 2000, ISBN 3-15-018060-0.
 * Deutschbaltische Literaturgeschichte. C.H. Beck, München 2005, ISBN 3-406-53525-9.
 * Die 101 wichtigsten Fragen: Goethe. C.H. Beck, München 2007, ISBN 978-3-406-55872-6.
 * Die 101 wichtigsten Fragen: Schiller. C.H. Beck, München 2009, ISBN 978-3-406-58687-3.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Gero von Wilpert


text:
223

Year 223 (CCXXIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Maximus and Aelianus (or, less frequently, year 976 Ab urbe condita). The denomination 223 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Asia

 * Battle of Dongkou: The Chinese state of Cao Wei is defeated by Eastern Wu.

Births

 * Ji Kang, Chinese poet and philosopher (d. 262)
 * Wang Hun, Chinese general and politician (d. 297)

Deaths

 * May 6 – Cao Ren (or Zixiao), Chinese general (b. 168)
 * June 10 – Liu Bei, Chinese warlord and emperor (b. 161)
 * August 1 – Cao Zhang, Chinese prince and warlord
 * August 11 – Jia Xu, Chinese official and politician (b. 147)
 * Xing Yong (or Zi'ang), Chinese official and politician
 * Zhang Ji (or Derong), Chinese official and politician

title: 223


text:
224

Year 224 (CCXXIV) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Iulianus and Crispinus (or, less frequently, year 977 Ab urbe condita). The denomination 224 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Parthia

 * April 28 – Battle of Hormozdgan: King Ardashir I defeats Artabanus V, destroying the Parthian Empire, and establishing the Sassanid Dynasty. Artabanus V's brother Vologases VI will continue to rule, with Armenian and Kushan support, over outlying parts of Parthia.

Births

 * Jungcheon of Goguryeo, Korean ruler (d. 270)
 * Liu Xuan (or Wenheng), Chinese prince (d. 264)
 * Marcus Aurelius Carus, Roman emperor (d. 283)
 * Mercurius, Christian saint and martyr (d. 250)
 * Pei Xiu, Chinese official and politician (d. 271)
 * Sun He (or Zixiao), Chinese prince (d. 253)

Deaths

 * April 28 – Artabanus IV, king of Parthia
 * Du Ji, Chinese official and politician
 * Yang Biao, Chinese politician (b. 141)
 * Ji Yan, Chinese official and politician
 * Zhu Zhi, Chinese general and politician (b. 156)

title: 224


text:
225

Year 225 (CCXXV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Fuscus and Domitius (or, less frequently, year 978 Ab urbe condita). The denomination 225 for this year has been used since the early medieval period when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Empire

 * Emperor Alexander Severus marries Sallustia Orbiana, and possibly raises her father Seius Sallustius to the rank of Caesar.

Art and Science

 * The first Christian paintings appear in Rome, decorating the Catacombs.

Births

 * January 20 – Gordian III, Roman emperor (d. 244)
 * December 31 – Lawrence, Christian martyr (d. 258)
 * Trieu Thi Trinh, Vietnamese female warrior (d. 248)
 * Zhong Hui, Chinese general and politician (d. 264)

Deaths

 * Gaius Vettius Gratus Sabinianus, Roman consul
 * Gong Lu, Chinese official and politician (b. 195)
 * Sun Shao, Chinese official and chancellor (b. 163)
 * Xiahou Shang, Chinese general and politician

title: 225


text:
226

Year 226 (CCXXVI) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Marcellus (or, less frequently, year 979 Ab urbe condita). The denomination 226 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

China

 * A merchant from the Roman Empire, called "Qin Lun" by the Chinese, arrives in Jiaozhi (modern Hanoi), and is taken to see King Sun Quan of Eastern Wu, who requests him to make a report on his native country and people. He is given an escort for the return trip, including a present of ten male and ten female "blackish-colored dwarfs." However, the officer in charge of the Chinese escort dies, and Qin Lun has to continue his journey home alone.

Persian Empire

 * Ctesiphon, until now capital of the Parthian Empire, falls into the hands of the Sasanian Empire, who also make it their capital, after putting an end to the Parthian Dynasty in Iran.

Births

 * Lu Kang, Chinese general and politician (d. 274)
 * Wang Bi (or Fusi), Chinese philosopher (d. 249) saint valentine (d.269)

Deaths

 * June 29 – Cao Pi, Chinese emperor (b. 187)
 * Farn-Sasan, king of the Parthian Kingdom
 * Shi Xie, Chinese politician and warlord (b. 137)
 * Xiahou Shang (or Boren), Chinese general

title: 226


text:
227

Year 227 (CCXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Senecio and Fulvius (or, less frequently, year 980 Ab urbe condita). The denomination 227 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Empire

 * Seius Sallustius is executed for the attempted murder of his son-in-law, Emperor Alexander Severus. Sallustius' daughter, as well as Alexander's wife, Sallustia Orbiana, is exiled to Libya.

Ireland

 * The rule of High King Cormac mac Airt begins (approximate).

Persian Empire

 * King Ardashir I annexes his new empire from the east to the northwest. He conquers, with his army, the provinces of Chorasmia, Sistan and the island Bahrain in the Persian Gulf. The kings of the Kushan Empire and Turan recognize Ardashir as their overlord.

Asia

 * Dongcheon becomes ruler over the Korean kingdom of Goguryeo.

Births

 * Herennius Etruscus, Roman emperor (d. 251)
 * Sima Zhou, Chinese prince and general (d. 283)
 * Zhuge Zhan, Chinese general and official (d. 263)

Deaths

 * Han Dang (or Yigong), Chinese general
 * He Qi (or Gongmiao), Chinese general
 * Seius Sallustius, Roman usurper (Caesar)
 * Shi Hui, Chinese official and general (b. 165)
 * Xu Huang (or Gongming), Chinese general

title: 227


text:
Shiritori

Shiritori (しりとり; 尻取り) is a Japanese word game in which the players are required to say a word which begins with the final kana of the previous word. No distinction is made between hiragana, katakana, and kanji. "Shiritori" literally means "taking the end" or "taking the rear".

Rules
There are various optional and advanced rules, which the players must agree on before the game begins.

Standard rules

 * Two or more people take turns to play.
 * Only nouns are permitted.
 * A player who plays a word ending in the mora "N" (ん) loses the game, as almost no Japanese word begins with that character, except for some loanwords and proper nouns such as ンジャメナ (N'Djamena).
 * Words may not be repeated.
 * Phrases connected by no (の; meaning roughly "of") are permitted, but only in those cases where the phrase is sufficiently lexicalized to be considered a "word".

Example:"sakura (さくら) → rajio (ラジオ) → onigiri (おにぎり) → risu (りす) → sumou (すもう) → udon (うどん)."The player who used the word udon lost this game, because the word ends in N (ん).

Optional rules

 * The first word of the game is shiritori, the name of the game itself.
 * Dakuten and handakuten may be ignored or added. Thus suupu (スープ) may be followed by furo (ふろ), and sato (さと) may be followed by dorayaki (どら焼き).
 * A long vowel may either be ignored or considered as a vowel. Mikisaa (ミキサー/みきさあ) can be followed by either sakura (さくら) or aki (あき).
 * Common pronouns and place names may be permitted. Example: Edo jou (えどじょう, lit. 'Edo Castle'), is acceptable.
 * Two words spelled with the same kana but different kanji may be permitted. For example, su (す) can either be spelled as "巣" (lit. 'a bird's nest') or "酢" (lit. 'vinegar').

Advanced rules

 * Words are limited to a certain genre.
 * Instead of using only the last kana, the final two kana must be used again. In this case only the first kana may not be the mora "N" (ん).
 * The length of a word must be three or more syllables.

English shiritori
A version of Shiritori using only English words was invented to help people learn English. Most rules are the same, yet there are several original and optional rules that are used.

 * For students of English, any words - including nouns, verbs, and adjectives - can be used.
 * Players cannot use different tenses of previously used verbs unless they have nonstandard conjugation. For example, a player may use "be", "was", and "is", but not both "kick" and "kicked".
 * When a word ends in a silent vowel, like "life", one may either use the vowel in another word or use the preceding consonant instead.

Similar games

 * In English, the closest game is word chain.

 * Similar Russian word games include "A Game of Words" (Игра в слова), where players are required to say a noun that begins with the final letter of the previous word, and "A Game of Cities" (Игра в города), where players are required to say a name of a city or town that begins with the final letter of the previous word.

 * In Chinese languages, a similar game is known as jielong (接龍), where players start new words with the last hanzi of the preceding word. Another variant of the game is known as tzuchuan (字串), which utilises adding, removing or replacing of one of the character's components to form another character. The most popular variant of the game is known as chengyu jielong (成語接龍), which involves four character idioms instead.

 * There is also a similar South Slavic game called Kalodont, in which players continue the chain by beginning with last two letters of the previous word.

 * In Korean, a similar game is kkeunmaritgi (끝말잇기), in which players must say a word that starts with the last Hangul letter of the previous word.

 * In Romanian, there is a game called "Fazan" ("Pheasant"), in which players must say a word that starts with the last two letters of the previous word.

Examples from popular culture

 * In the Japanese version of Tomodachi Life, there is an event called Shiritori Tournament, which was changed into Word chain in the European version and kkeunmaritgi in the Korean version; the North American version lacks the game, although there is a similar event called Rap Battle.
 * In episode 6 of the anime Nichijou, the characters Yūko Aioi and Mio Naganohara play a picture version of the game.
 * In episode 2 of the anime Miss Kobayashi's Dragon Maid, the characters Miss Kobyashi, Tohru, and Kanna play the game (and lose by using the word dragon).
 * In episode 6 of No Game No Life, Shiro and Sora face off against Jibril in materialization Shiritori, where objects appear or disappear when that object is named.
 * In episode 3 of Non Non Biyori, the sisters Komari and Natsumi play Shiritori to pass time after running from home.
 * In episode 2 of The Quintessential Quintuplets, Miku Nakano challenges Futaro Uesugi to a game of shiritori using names of Sengoku warlords.
 * In episode 7 of Chronicles of the Going Home Club, Sakura challenges Natsuki to a game of shiritori using taboo cards on which words are written that cannot be said by either player.
 * The Japanese ending theme of Pokémon Journeys is "Pokémon Shiritori", which features the game being played with names of Pokémon.

title: Shiritori


text:
User:A.J.Armitage

My main interests are political philosophy, history, and theology.

title: User:A.J.Armitage


text:
Proper motion

Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars.

The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μα) and of declination (μδ). Their combined value is computed as the total proper motion (μ). It has dimensions of angle per time, typically arcseconds per year or milliarcseconds per year.

Knowledge of the proper motion, distance, and radial velocity allows calculations of an object's motion from the Solar System's frame of reference and its motion from the galactic frame of reference – that is motion in respect to the Sun, and by coordinate transformation, that in respect to the Milky Way.

Introduction
Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. As examples, both Ursa Major in the northern sky and Crux in the southern sky, look nearly the same now as they did hundreds of years ago. However, precise long-term observations show that such constellations change shape, albeit very slowly, and that each star has an independent motion.

This motion is caused by the movement of the stars relative to the Sun and Solar System. The Sun travels in a nearly circular orbit (the solar circle) about the center of the galaxy at a speed of about 220 km/s at a radius of 8,000 pc from Sagittarius A* which can be taken as the rate of rotation of the Milky Way itself at this radius.

Any proper motion is a two-dimensional vector (as it excludes the component as to the direction of the line of sight) and it bears two quantities or characteristics: its position angle and its magnitude. The first is the direction of the proper motion on the celestial sphere (with 0 degrees meaning the motion is north, 90 degrees meaning the motion is east, (left on most sky maps and space telescope images) and so on), and the second is its magnitude, typically expressed in arcseconds per year (symbols: arcsec/yr, as/yr, ″/yr, ″ yr−1) or milliarcseconds per year (symbols: mas/yr, mas yr−1).

Proper motion may alternatively be defined by the angular changes per year in the star's right ascension (μα) and declination (μδ) with respect to a constant epoch.

The components of proper motion by convention are arrived at as follows. Suppose an object moves from coordinates (α1, δ1) to coordinates (α2, δ2) in a time Δt. The proper motions are given by:
 * $$\mu_{\alpha} = \frac{\alpha_2 - \alpha_1}{\Delta t}, $$
 * $$\mu_{\delta}= \frac{\delta_2-\delta_1}{\Delta t} \ .$$

The magnitude of the proper motion μ is given by the Pythagorean theorem:
 * $$\mu^2 = {\mu_\delta}^2 + {\mu_\alpha}^2 \cdot \cos^2 \delta \, $$
 * technically abbreviated:
 * $$\mu^2 = {\mu_\delta}^2 + {\mu_}^2 \ . $$

where δ is the declination. The factor in cos2δ accounts for the widening of the lines (hours) of right ascension away from the poles, cosδ, being zero for a hypothetical object fixed at a celestial pole in declination. Thus, a co-efficient is given to negate the misleadingly greater east or west velocity (angular change in α) in hours of Right Ascension the further it is towards the imaginary infinite poles, above and below the earth's axis of rotation, in the sky. The change μα, which must be multiplied by cosδ to become a component of the proper motion, is sometimes called the "proper motion in right ascension", and μδ the "proper motion in declination".

If the proper motion in right ascension has been converted by cosδ, the result is designated μα*. For example, the proper motion results in right ascension in the Hipparcos Catalogue (HIP) have already been converted. Hence, the individual proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions.

The position angle θ is related to these components by:

 * $$\mu \sin \theta = \mu_\alpha \cos \delta = \mu_ \ ,$$
 * $$\mu \cos \theta = \mu_\delta \ . $$

Motions in equatorial coordinates can be converted to motions in galactic coordinates.

Examples
For most stars seen in the sky, the observed proper motions are small and unremarkable. Such stars are often either faint or are significantly distant, have changes of below 0.01″ per year, and do not appear to move appreciably over many millennia. A few do have significant motions, and are usually called high-proper motion stars. Motions can also be in almost seemingly random directions. Two or more stars, double stars or open star clusters, which are moving in similar directions, exhibit so-called shared or common proper motion (or cpm.), suggesting they may be gravitationally attached or share similar motion in space.

Barnard's Star has the largest proper motion of all stars, moving at 10.3″ yr−1. Large proper motion usually strongly indicates an object is close to the Sun. This is so for Barnard's Star, about 6 light-years away. After the Sun and the Alpha Centauri system, it is the nearest known star. Being a red dwarf with an apparent magnitude of 9.54, it is too faint to see without a telescope or powerful binoculars. Of the stars visible to the naked eye (conservatively limiting unaided visual magnitude to 6.0), 61 Cygni A (magnitude V=5.20) has the highest proper motion at 5.281″ yr−1, discounting Groombridge 1830 (magnitude V=6.42), proper motion: 7.058″ yr−1.

A proper motion of 1 arcsec per year 1 light-year away corresponds to a relative transverse speed of 1.45 km/s. Barnard's Star's transverse speed is 90 km/s and its radial velocity is 111 km/s (perpendicular (at a right, 90° angle), which gives a true or "space" motion of 142 km/s. True or absolute motion is more difficult to measure than the proper motion, because the true transverse velocity involves the product of the proper motion times the distance. As shown by this formula, true velocity measurements depend on distance measurements, which are difficult in general.

In 1992 Rho Aquilae became the first star to have its Bayer designation invalidated by moving to a neighbouring constellation – it is now in Delphinus.

Usefulness in astronomy
Stars with large proper motions tend to be nearby; most stars are far enough away that their proper motions are very small, on the order of a few thousandths of an arcsecond per year. It is possible to construct nearly complete samples of high proper motion stars by comparing photographic sky survey images taken many years apart. The Palomar Sky Survey is one source of such images. In the past, searches for high proper motion objects were undertaken using blink comparators to examine the images by eye. More modern techniques such as image differencing can scan digitized images, or comparisons to star catalogs obtained by satellites. As any selection biases of these surveys are well understood and quantifiable, studies have confirmed more and inferred approximate quantities of unseen stars – revealing and confirming more by studying them further, regardless of brightness, for instance. Studies of this kind show most of the nearest stars are intrinsically faint and angularly small, such as red dwarfs.

Measurement of the proper motions of a large sample of stars in a distant stellar system, like a globular cluster, can be used to compute the cluster's total mass via the Leonard-Merritt mass estimator. Coupled with measurements of the stars' radial velocities, proper motions can be used to compute the distance to the cluster.

Stellar proper motions have been used to infer the presence of a super-massive black hole at the center of the Milky Way. This black hole is suspected to be Sgr A*, with a mass of 4.2 × (solar masses).

Proper motions of the galaxies in the Local Group are discussed in detail in Röser. In 2005, the first measurement was made of the proper motion of the Triangulum Galaxy M33, the third largest and only ordinary spiral galaxy in the Local Group, located 0.860 ± 0.028 Mpc beyond the Milky Way. The motion of the Andromeda Galaxy was measured in 2012, and an Andromeda–Milky Way collision is predicted in about 4.5 billion years. Proper motion of the NGC 4258 (M106) galaxy in the M106 group of galaxies was used in 1999 to find an accurate distance to this object. Measurements were made of the radial motion of objects in that galaxy moving directly toward and away from Earth, and assuming this same motion to apply to objects with only a proper motion, the observed proper motion predicts a distance to the galaxy of $7.2 Mpc$.

History
Proper motion was suspected by early astronomers (according to Macrobius, c. AD 400) but a proof was not provided until 1718 by Edmund Halley, who noticed that Sirius, Arcturus and Aldebaran were over half a degree away from the positions charted by the ancient Greek astronomer Hipparchus roughly 1850 years earlier.

The lesser meaning of "proper" used is arguably dated English (but neither historic, nor obsolete when used as a postpositive, as in "the city proper") meaning "belonging to" or "own". "Improper motion" would refer to perceived motion that is nothing to do with an object's inherent course, such as due to Earth's axial precession, and minor deviations, nutations well within the 26,000-year cycle.

Stars with high proper motion
The following are the stars with highest proper motion from the Hipparcos catalog. It does not include stars such as Teegarden's Star, which are too faint for that catalog. A more complete list of stellar objects can be made by doing a criterion query at the SIMBAD astronomical database.

The figure for HIP 67593 is almost certainly an error, probably because the star has a relatively nearby brighter visual binary companion; the movement between the DSS2 and SDSS9 images is less than it. Gaia measured a much smaller proper motion for its Data Release 2, yet a 15-fold parallax between it and its likely common-proper-motion companion HIP 67594. Reconciling its distance and motion will have to wait for Data Release 3 expected to analyse well very high proper motion objects.

title: Proper motion


text:
W. T. Tutte

William Thomas Tutte OC FRS FRSC (14 May 1917 – 2 May 2002) was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a major Nazi German cipher system which was used for top-secret communications within the Wehrmacht High Command. The high-level, strategic nature of the intelligence obtained from Tutte's crucial breakthrough, in the bulk decrypting of Lorenz-enciphered messages specifically, contributed greatly, and perhaps even decisively, to the defeat of Nazi Germany. He also had a number of significant mathematical accomplishments, including foundation work in the fields of graph theory and matroid theory.

Tutte's research in the field of graph theory proved to be of remarkable importance. At a time when graph theory was still a primitive subject, Tutte commenced the study of matroids and developed them into a theory by expanding from the work that Hassler Whitney had first developed around the mid-1930s. Even though Tutte's contributions to graph theory have been influential to modern graph theory and many of his theorems have been used to keep making advances in the field, most of his terminology was not in agreement with their conventional usage and thus his terminology is not used by graph theorists today. "Tutte advanced graph theory from a subject with one text (D. Kőnig's) toward its present extremely active state."

Early life and education
Tutte was born in Newmarket in Suffolk. He was the younger son of William John Tutte (1873–1944), an estate gardener, and Annie (née Newell; 1881–1956), a housekeeper. Both parents worked at Fitzroy House stables where Tutte was born. The family spent some time in Buckinghamshire, County Durham and Yorkshire before returning to Newmarket, where Tutte attended Cheveley Church of England primary school in the nearby village of Cheveley. In 1927, when he was ten, Tutte won a scholarship to the Cambridge and County High School for Boys. He took up his place there in 1928.

In 1935 he won a scholarship to study natural sciences at Trinity College, Cambridge, where he specialized in chemistry and graduated with first-class honours in 1938. He continued with physical chemistry as a graduate student, but transferred to mathematics at the end of 1940. As a student, he (along with three of his friends) became one of the first to solve the problem of squaring the square, and the first to solve the problem without a squared subrectangle. Together the four created the pseudonym Blanche Descartes, under which Tutte published occasionally for years.

Second World War

Soon after the outbreak of the Second World War, Tutte's tutor, Patrick Duff, suggested him for war work at the Government Code and Cypher School at Bletchley Park (BP). He was interviewed and sent on a training course in London before going to Bletchley Park, where he joined the Research Section. At first, he worked on the Hagelin cipher that was being used by the Italian Navy. This was a rotor cipher machine that was available commercially, so the mechanics of enciphering was known, and decrypting messages only required working out how the machine was set up.

In the summer of 1941, Tutte was transferred to work on a project called Fish. Intelligence information had revealed that the Germans called the wireless teleprinter transmission systems "Sägefisch" ('sawfish'). This led the British to use the code Fish for the German teleprinter cipher system. The nickname Tunny (tunafish) was used for the first non-Morse link, and it was subsequently used for the Lorenz SZ machines and the traffic that they enciphered.

Telegraphy used the 5-bit International Telegraphy Alphabet No. 2 (ITA2). Nothing was known about the mechanism of enciphering other than that messages were preceded by a 12-letter indicator, which implied a 12-wheel rotor cipher machine. The first step, therefore, had to be to diagnose the machine by establishing the logical structure and hence the functioning of the machine. Tutte played a pivotal role in achieving this, and it was not until shortly before the Allied victory in Europe in 1945, that Bletchley Park acquired a Tunny Lorenz cipher machine. Tutte's breakthroughs led eventually to bulk decrypting of Tunny-enciphered messages between the German High Command (OKW) in Berlin and their army commands throughout occupied Europe and contributed—perhaps decisively—to the defeat of Germany.

Diagnosing the cipher machine
On 31 August 1941, two versions of the same message were sent using identical keys, which constituted a "depth". This allowed John Tiltman, Bletchley Park's veteran and remarkably gifted cryptanalyst, to deduce that it was a Vernam cipher which uses the Exclusive Or (XOR) function (symbolised by "⊕"), and to extract the two messages and hence obtain the obscuring key. After a fruitless period during which Research Section cryptanalysts tried to work out how the Tunny machine worked, this and some other keys were handed to Tutte, who was asked to "see what you can make of these". At his training course, Tutte had been taught the Kasiski examination technique of writing out a key on squared paper, starting a new row after a defined number of characters that was suspected of being the frequency of repetition of the key. If this number was correct, the columns of the matrix would show more repetitions of sequences of characters than chance alone. Tutte knew that the Tunny indicators used 25 letters (excluding J) for 11 of the positions, but only 23 letters for the other. He therefore tried Kasiski's technique on the first impulse of the key characters, using a repetition of 25 × 23 = 575. He did not observe a large number of column repetitions with this period, but he did observe the phenomenon on a diagonal. He therefore tried again with 574, which showed up repeats in the columns. Recognising that the prime factors of this number are 2, 7 and 41, he tried again with a period of 41 and "got a rectangle of dots and crosses that was replete with repetitions".

It was clear, however, that the first impulse of the key was more complicated than that produced by a single wheel of 41 key impulses. Tutte called this component of the key $$\chi_1$$ (chi1). He figured that there was another component, which was XOR-ed with this, that did not always change with each new character, and that this was the product of a wheel that he called $$\psi_1$$ (psi1). The same applied for each of the five impulses ($\chi_1 \chi_2 \chi_3 \chi_4 \chi_5$ and $\psi_1 \psi_2 \psi_3 \psi_4 \psi_5$). So for a single character, the whole key K consisted of two components: $$K = \chi \oplus \psi$$

At Bletchley Park, mark impulses were signified by x and space impulses by •. For example, the letter "H" would be coded as ••x•x. Tutte's derivation of the chi and psi components was made possible by the fact that dots were more likely than not to be followed by dots, and crosses more likely than not to be followed by crosses. This was a product of a weakness in the German key setting, which they later eliminated. Once Tutte had made this breakthrough, the rest of the Research Section joined in to study the other impulses, and it was established that the five chi wheels all advanced with each new character and that the five psi wheels all moved together under the control of two mu or "motor" wheels. Over the following two months, Tutte and other members of the Research Section worked out the complete logical structure of the machine, with its set of wheels bearing cams that could either be in a position (raised) that added x to the stream of key characters, or in the alternative position that added in •.

Diagnosing the functioning of the Tunny machine in this way was a truly remarkable cryptanalytical achievement which, in the citation for Tutte's induction as an Officer of the Order of Canada, was described as "one of the greatest intellectual feats of World War II".

Tutte's statistical method
To decrypt a Tunny message required knowledge not only of the logical functioning of the machine, but also the start positions of each rotor for the particular message. The search was on for a process that would manipulate the ciphertext or key to produce a frequency distribution of characters that departed from the uniformity that the enciphering process aimed to achieve. While on secondment to the Research Section in July 1942, Alan Turing worked out that the XOR combination of the values of successive characters in a stream of ciphertext and key emphasised any departures from a uniform distribution. The resultant stream (symbolised by the Greek letter "delta" Δ) was called the difference because XOR is the same as modulo 2 subtraction.

The reason that this provided a way into Tunny was that although the frequency distribution of characters in the ciphertext could not be distinguished from a random stream, the same was not true for a version of the ciphertext from which the chi element of the key had been removed. This was the case because where the plaintext contained a repeated character and the psi wheels did not move on, the differenced psi character ($$\Delta\psi$$) would be the null character (' / ' at Bletchley Park). When XOR-ed with any character, this character has no effect. Repeated characters in the plaintext were more frequent both because of the characteristics of German (EE, TT, LL and SS are relatively common), and because telegraphists frequently repeated the figure-shift and letter-shift characters.

To quote the General Report on Tunny:"Turingery introduced the principle that the key differenced at one, now called ΔΚ, could yield information unobtainable from ordinary key. This Δ principle was to be the fundamental basis of nearly all statistical methods of wheel-breaking and setting."

Tutte exploited this amplification of non-uniformity in the differenced values and by November 1942 had produced a way of discovering wheel starting points of the Tunny machine which became known as the "Statistical Method". The essence of this method was to find the initial settings of the chi component of the key by exhaustively trying all positions of its combination with the ciphertext, and looking for evidence of the non-uniformity that reflected the characteristics of the original plaintext. Because any repeated characters in the plaintext would always generate •, and similarly $$\Delta\psi_1 \oplus \Delta\psi_2$$ would generate • whenever the psi wheels did not move on, and about half of the time when they did – some 70% overall.

As well as applying differencing to the full 5-bit characters of the ITA2 code, Tutte applied it to the individual impulses (bits). The current chi wheel cam settings needed to have been established to allow the relevant sequence of characters of the chi wheels to be generated. It was totally impracticable to generate the 22 million characters from all five of the chi wheels, so it was initially limited to 41 × 31 = 1271 from the first two. After explaining his findings to Max Newman, Newman was given the job of developing an automated approach to comparing ciphertext and key to look for departures from randomness. The first machine was dubbed Heath Robinson, but the much faster Colossus computer, developed by Tommy Flowers and using algorithms written by Tutte and his colleagues, soon took over for breaking codes.

Doctorate and career
In late 1945, Tutte resumed his studies at Cambridge, now as a graduate student in mathematics. He published some work begun earlier, one a now famous paper that characterises which graphs have a perfect matching, and another that constructs a non-Hamiltonian graph.

Tutte completed a doctorate in mathematics from Cambridge in 1948 under the supervision of Shaun Wylie, who had also worked at Bletchley Park on Tunny. His thesis An Algebraic Theory of Graphs was considered ground breaking and was about the subject later known as matroid theory.

The same year, invited by Harold Scott MacDonald Coxeter, he accepted a position at the University of Toronto. In 1962, he moved to the University of Waterloo in Waterloo, Ontario, where he stayed for the rest of his academic career. He officially retired in 1985, but remained active as an emeritus professor. Tutte was instrumental in helping to found the Department of Combinatorics and Optimization at the University of Waterloo.

His mathematical career concentrated on combinatorics, especially graph theory, which he is credited as having helped create in its modern form, and matroid theory, to which he made profound contributions; one colleague described him as "the leading mathematician in combinatorics for three decades". He was editor in chief of the Journal of Combinatorial Theory until retiring from Waterloo in 1985. He also served on the editorial boards of several other mathematical research journals.

Research contributions
Tutte's work in graph theory includes the structure of cycle spaces and cut spaces, the size of maximum matchings and existence of k-factors in graphs, and Hamiltonian and non-Hamiltonian graphs. He disproved Tait's conjecture, on the Hamiltonicity of polyhedral graphs, by using the construction known as Tutte's fragment. The eventual proof of the four colour theorem made use of his earlier work. The graph polynomial he called the "dichromate" has become famous and influential under the name of the Tutte polynomial and serves as the prototype of combinatorial invariants that are universal for all invariants that satisfy a specified reduction law.

The first major advances in matroid theory were made by Tutte in his 1948 Cambridge PhD thesis which formed the basis of an important sequence of papers published over the next two decades. Tutte's work in graph theory and matroid theory has been profoundly influential on the development of both the content and direction of these two fields. In matroid theory, he discovered the highly sophisticated homotopy theorem and founded the studies of chain groups and regular matroids, about which he proved deep results.

In addition, Tutte developed an algorithm for determining whether a given binary matroid is a graphic matroid. The algorithm makes use of the fact that a planar graph is simply a graph whose circuit-matroid, the dual of its bond-matroid, is graphic.

Tutte wrote a paper entitled How to Draw a Graph in which he proved that any face in a 3-connected graph is enclosed by a peripheral cycle. Using this fact, Tutte developed an alternative proof to show that every Kuratowski graph is non-planar by showing that K5 and K3,3 each have three distinct peripheral cycles with a common edge. In addition to using peripheral cycles to prove that the Kuratowski graphs are non-planar, Tutte proved that every simple 3-connected graph can be drawn with all its faces convex, and devised an algorithm which constructs the plane drawing by solving a linear system. The resulting drawing is known as the Tutte embedding. Tutte's algorithm makes use of the barycentric mappings of the peripheral circuits of a simple 3-connected graph.

The findings published in this paper have proved to be of much significance because the algorithms that Tutte developed have become popular planar graph drawing methods. One of the reasons for which Tutte's embedding is popular is that the necessary computations that are carried out by his algorithms are simple and guarantee a one-to-one correspondence of a graph and its embedding onto the Euclidean plane, which is of importance when parameterising a three-dimensional mesh to the plane in geometric modelling. "Tutte's theorem is the basis for solutions to other computer graphics problems, such as morphing."

Tutte was mainly responsible for developing the theory of enumeration of planar graphs, which has close links with chromatic and dichromatic polynomials. This work involved some highly innovative techniques of his own invention, requiring considerable manipulative dexterity in handling power series (whose coefficients count appropriate kinds of graphs) and the functions arising as their sums, as well as geometrical dexterity in extracting these power series from the graph-theoretic situation.

Tutte summarised his work in the Selected Papers of W.T. Tutte, 1979, and in Graph Theory as I have known it, 1998.

Positions, honours and awards
Tutte's work in World War II and subsequently in combinatorics brought him various positions, honours and awards: Tutte served as Librarian for the Royal Astronomical Society of Canada in 1959–1960, and asteroid 14989 Tutte (1997 UB7) was named after him.
 * 1958, Fellow of the Royal Society of Canada (FRSC);
 * 1971, Jeffery–Williams Prize by the Canadian Mathematical Society;
 * 1975, Henry Marshall Tory Medal by the Royal Society of Canada;
 * 1977, A conference on Graph Theory and Related Topics was held at the University of Waterloo in his honour on the occasion of his sixtieth birthday;
 * 1982, Isaak-Walton-Killam Award by the Canada Council;
 * 1987, Fellow of the Royal Society (FRS);
 * 1990–1996, First President of the Institute of Combinatorics and its Applications;
 * 1998, Appointed honorary director of the Centre for Applied Cryptographic Research at the University of Waterloo;
 * 2001, Officer of the Order of Canada (OC);
 * 2001, CRM-Fields-PIMS prize.
 * 2016, Waterloo Region Hall of Fame
 * 2017, Waterloo "William Tutte Way" road naming

Because of Tutte's work at Bletchley Park, Canada's Communications Security Establishment named an internal organisation aimed at promoting research into cryptology, the Tutte Institute for Mathematics and Computing (TIMC), in his honour in 2011.

In September 2014, Tutte was celebrated in his hometown of Newmarket, England, with the unveiling of a sculpture, after a local newspaper started a campaign to honour his memory.

Bletchley Park in Milton Keynes celebrated Tutte's work with an exhibition Bill Tutte: Mathematician + Codebreaker from May 2017 to 2019, preceded on 14 May 2017 by lectures about his life and work during the Bill Tutte Centenary Symposium.

Personal life and death
In addition to the career benefits of working at the new University of Waterloo, the more rural setting of Waterloo County appealed to Bill and his wife Dorothea. They bought a house in the nearby village of West Montrose, Ontario where they enjoyed hiking, spending time in their garden on the Grand River and allowing others to enjoy the beautiful scenery of their property.

They also had an extensive knowledge of all the birds in their garden. Dorothea, an avid potter, was also a keen hiker and Bill organised hiking trips. Even near the end of his life Bill still was an avid walker. After his wife died in 1994, he moved back to Newmarket (Suffolk), but then returned to Waterloo in 2000, where he died two years later. He is buried in West Montrose United Cemetery.

Books

 * . Also
 * Volume I: ISBN 978-0-969-07781-7
 * Volume II: ISBN 978-0-969-07782-4
 * Reprinted by Cambridge University Press 2001, ISBN 978-0-521-79489-3
 * Reprinted 2012, ISBN 978-0-19-966055-1
 * Volume II: ISBN 978-0-969-07782-4
 * Reprinted by Cambridge University Press 2001, ISBN 978-0-521-79489-3
 * Reprinted 2012, ISBN 978-0-19-966055-1

title: W. T. Tutte