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Nebuchadnezzar II

Nebuchadnezzar II (Babylonian cuneiform: Nabû-kudurri-uṣur, meaning "Nabu, watch over my heir"; Biblical Hebrew:  Nəḇūḵaḏneʾṣṣar), also spelled Nebuchadrezzar II, was the second king of the Neo-Babylonian Empire, ruling from the death of his father Nabopolassar in 605 BC to his own death in 562 BC. Historically known as Nebuchadnezzar the Great, he is typically regarded as the empire's greatest king. Nebuchadnezzar remains famous for his military campaigns in the Levant, for his construction projects in his capital, Babylon, including the Hanging Gardens of Babylon, and for the role he plays in Jewish history. Ruling for 43 years, Nebuchadnezzar was the longest-reigning king of the Babylonian dynasty. By the time of his death, he was among the most powerful rulers in the world.

Possibly named after his grandfather of the same name, or after Nebuchadnezzar I ((r. undefined – undefined)c. 1125–1104 BC), one of Babylon's greatest ancient warrior-kings, Nebuchadnezzar II already secured renown for himself during his father's reign, leading armies in the Medo-Babylonian conquest of the Assyrian Empire. At the Battle of Carchemish in 605 BC, Nebuchadnezzar inflicted a crushing defeat on an Egyptian army led by Pharaoh Necho II, and ensured that the Neo-Babylonian Empire would succeed the Neo-Assyrian Empire as the dominant power in the ancient Near East. Shortly after this victory, Nabopolassar died and Nebuchadnezzar became king.

Despite his successful military career during his father's reign, the first third or so of Nebuchadnezzar's reign saw little to no major military achievements, and notably a disastrous failure in an attempted invasion of Egypt. These years of lacklustre military performance saw some of Babylon's vassals, particularly in the Levant, beginning to doubt Babylon's power, viewing the Neo-Babylonian Empire as a paper tiger rather than a power truly on the level of the Neo-Assyrian Empire. The situation grew so severe that people in Babylonia itself began disobeying the king, some going as far as to revolt against Nebuchadnezzar's rule.

After this disappointing early period as king, Nebuchadnezzar's luck turned. In the 580s BC, Nebuchadnezzar engaged in a successful string of military actions in the Levant against the vassal states in rebellion there, likely with the ultimate intent of curbing Egyptian influence in the region. In 587 BC, Nebuchadnezzar destroyed the Kingdom of Judah, and its capital, Jerusalem. The destruction of Jerusalem led to the Babylonian captivity as the city's population, and people from the surrounding lands, were deported to Babylonia. The Jews thereafter referred to Nebuchadnezzar, the greatest enemy they had faced until that point, as a "destroyer of nations" (משחית גוים, Jer. 4:7). The biblical Book of Jeremiah paints Nebuchadnezzar as a cruel enemy, but also as God's appointed ruler of the world and a divine instrument to punish disobedience. Through the destruction of Jerusalem, the capture of the rebellious Phoenician city of Tyre, and other campaigns in the Levant, Nebuchadnezzar completed the Neo-Babylonian Empire's transformation into the new great power of the ancient Near East.

In addition to his military campaigns, Nebuchadnezzar is remembered as a great builder king. The prosperity ensured by his wars allowed Nebuchadnezzar to conduct great building projects in Babylon, and elsewhere in Mesopotamia. The modern image of Babylon is largely of the city as it was after Nebuchadnezzar's projects, during which he, among other work, rebuilt many of the city's religious buildings, including the Esagila and Etemenanki, renovated its existing palace, constructed a brand new palace, and beautified its ceremonial centre through renovations to the city's Processional Street and the Ishtar Gate. As most of Nebuchadnezzar's inscriptions deal with his building projects, rather than military accomplishments, he was for a time seen by historians mostly as a builder, rather than a warrior.

Name
Nebuchadnezzar II's name in Akkadian was Nabû-kudurri-uṣur, meaning "Nabu, watch over my heir". The name was often interpreted in earlier scholarship as "Nabu, protect the boundary", given that the word kudurru can also mean 'boundary' or 'line'. Modern historians support the 'heir' interpretation over the 'boundary' interpretation in terms of this name. There is no reason to believe that the Babylonians intended the name to be difficult to interpret or to have a double meaning.

Nabû-kudurri-uṣur is typically anglicised to 'Nebuchadnezzar', following how the name is most commonly rendered in Hebrew and Greek, particularly in most of the Bible. In Hebrew, the name was rendered as נְבוּכַדְנֶאצַּר (Nəḇūḵaḏneʾṣṣar) and in Greek it was rendered as Ναβουχοδονόσορ (Nabouchodonosor). Some scholars, such as Donald Wiseman, prefer the anglicisation "Nebuchadrezzar", with an "r" rather than an "n", following the assumption that "Nebuchadnezzar" is a later, corrupted form of the contemporary Nabû-kudurri-uṣur.

The alternative anglicisation "Nebuchadrezzar" derives from how the name is rendered in the books of Jeremiah and Ezekiel, נְבוּכַדְרֶאצַּר (Nəḇūḵaḏreʾṣṣar), a more faithful transliteration of the original Akkadian name. The Assyriologist Adrianus van Selms suggested in 1974 that the variant with an "n" rather than an "r" was a rude nickname, deriving from an Akkadian rendition like Nabû-kūdanu-uṣur, which means 'Nabu, protect the mule', though there is no concrete evidence for this idea. Van Selms believed that a nickname like that could derive from Nebuchadnezzar's early reign, which was plagued by political instability.

Nebuchadnezzar II's name, Nabû-kudurri-uṣur, was identical to the name of his distant predecessor, Nebuchadnezzar I ((r. undefined – undefined)c. 1125–1104 BC), who ruled more than five centuries before Nebuchadnezzar II's time. Like Nebuchadnezzar II, Nebuchadnezzar I was a renowned warrior-king, who appeared in a time of political upheaval and defeated the forces of Babylon's enemies, in Nebuchadnezzar I's case the Elamites. Although theophoric names using the god Nabu are common in texts from the early Neo-Babylonian Empire, the name Nebuchadnezzar is relatively rare, only being mentioned four times with certainty. Though there is no evidence that Nabopolassar named his son after Nebuchadnezzar I, Nabopolassar was knowledgeable in history and actively worked to connect his rule to the rule of the Akkadian Empire, which preceded him by nearly two thousand years. The significance of his son and heir bearing the name of one of Babylon's greatest kings would not have been lost on Nabopolassar.

If Jursa's theory concerning Nabopolassar's origin is correct, it is alternatively possible that Nebuchadnezzar II was named after his grandfather of the same name, as the Babylonians employed patronymics, rather than after the previous king.

Ancestry and early life
Nebuchadnezzar was the eldest son of Nabopolassar ((r. undefined – undefined)626–605 BC), the founder of the Neo-Babylonian Empire. This is confirmed by Nabopolassar's inscriptions, which explicitly name Nebuchadnezzar as his "eldest son", as well as inscriptions from Nebuchadnezzar's reign, which refer to him as the "first" or "chief son" of Nabopolassar, and as Nabopolassar's "true" or "legitimate heir". The Neo-Babylonian Empire was founded through Nabopolassar's rebellion, and later war, against the Neo-Assyrian Empire, which liberated Babylonia after nearly a century of Assyrian control. The war resulted in the complete destruction of Assyria, and the Neo-Babylonian Empire, which rose in its place, was powerful, but hastily built and politically unstable.

As Nabopolassar never clarified his ancestry in lineage in any of his inscriptions, his origin is not entirely clear. Subsequent historians have variously identified Nabopolassar as a Chaldean, an Assyrian or a Babylonian. Although no evidence conclusively confirms him as being of Chaldean origin, the term "Chaldean dynasty" is frequently used by modern historians for the royal family he founded, and the term "Chaldean Empire" remains in use as an alternate historiographical name for the Neo-Babylonian Empire.

Nabopolassar appears to, regardless of his ethnic origin, have been strongly connected to the city of Uruk, located south of Babylon. It is possible that he was a member of its ruling elite before becoming king and there is a growing body of evidence that Nabopolassar's family originated in Uruk, for instance that Nebuchadnezzar's daughters lived in the city.

In 2007, Michael Jursa advanced the theory that Nabopolassar was a member of a prominent political family in Uruk, whose members are attested since the reign of Esarhaddon ((r. undefined – undefined)681–669 BC). To support his theory, Jursa pointed to how documents describe how the grave and body of "Kudurru", a deceased governor of Uruk, was desecrated due to the anti-Assyrian activities of Kudurru's two sons, Nabu-shumu-ukin and a son whose name is mostly missing. The desecration went so far as to drag Kudurru's body through the streets of Uruk. Kudurru can be identified with Nebuchadnezzar (Nabû-kudurri-uṣur, "Kudurru" simply being a common and shortened nickname), a prominent official in Uruk who served as its governor under the Assyrian king Ashurbanipal ((r. undefined – undefined)669–631 BC) in the 640s BC.

In Assyrian tradition, the desecration of a dead body showed that the deceased individual and their surviving family were traitors and enemies of the state, and that they had to be completely eradicated, serving to punish them even after death. The name of the son whose name is unpreserved in the letter ended with either ahi, nâsir or uṣur, and the remaining traces can fit with the name Nabû-apla-uṣur, meaning that Nabopolassar could be the other son mentioned in the letter and thus a son of Kudurru.

Strengthening this connection is that Nebuchadnezzar II is attested very early during his father's reign, from 626/625 to 617 BC, as high priest of the Eanna temple in Uruk, where he is often attested under the nickname "Kudurru". Nebuchadnezzar must have been made high priest at a very young age, considering that his year of death, 562 BC, is 64 years after 626 BC. The original Kudurru's second son, Nabu-shumu-ukin, also appears to be attested as a prominent general under Nabopolassar, and the name was also used by Nebuchadnezzar II for one of his sons, possibly honoring his dead uncle.

Nebuchadnezzar as crown prince
Nebuchadnezzar's military career began in the reign of his father, though little information survives. Based on a letter sent to the temple administration of the Eanna temple, it appears that Nebuchadnezzar participated in his father's campaign to take the city of Harran in 610 BC. Harran was the seat of Ashur-uballit II, who had rallied what remained of the Assyrian army and ruled the Neo-Assyrian rump state. The Babylonian victory in the Harran campaign and the defeat of Ashur-uballit in 609 BCE marked the end of the ancient Assyrian monarchy, which would never be restored. According to the Babylonian Chronicles, Nebuchadnezzar also commanded an army in an unspecified mountainous region for several months in 607 BC.

In the war against the Babylonians and Medes, Assyria had allied with Pharaoh Psamtik I of the Twenty-sixth Dynasty of Egypt, who had been interested in ensuring Assyria's survival so that Assyria could remain as a buffer state between his own kingdom and the Babylonian and Median kingdoms. After the fall of Harran, Psamtik's successor, Pharaoh Necho II, personally led a large army into former Assyrian lands to turn the tide of the war and restore the Neo-Assyrian Empire, even though it was more or less a lost cause as Assyria had already collapsed. As Nabopolassar was occupied with fighting Urartu in the north, the Egyptians took control of the Levant largely unopposed, capturing territories as far north as the city of Carchemish in Syria, where Necho established his base of operations.

Nebuchadnezzar's greatest victory from his time as crown prince came at the Battle of Carchemish in 605 BC, which put an end to Necho's campaign in the Levant by inflicting a crushing defeat on the Egyptians. Nebuchadnezzar had been the sole commander of the Babylonian army at this battle as his father had chosen to stay in Babylon, perhaps on account of illness. Necho's forces were completely annihilated by Nebuchadnezzar's army, with Babylonian sources claiming that not a single Egyptian escaped alive. The account of the battle in the Babylonian Chronicle reads as follows:

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The story of Nebuchadnezzar's victory at Carchemish reverberated through history, appearing in many later ancient accounts, including in the Book of Jeremiah and the Books of Kings in the Bible. It is possible to conclude, based on subsequent geopolitics, that the victory resulted in all of Syria and Israel coming under the control of the Neo-Babylonian Empire, a feat which the Assyrians under Tiglath-Pileser III ((r. undefined – undefined)745–727 BC) accomplished only after five years of protracted military campaigns. The defeat of Egypt at Carchemish ensured that the Neo-Babylonian Empire would grow to become the major power of the ancient Near East, and the uncontested successor of the Neo-Assyrian Empire.

Accession to the throne
Nabopolassar died just a few weeks after Nebuchadnezzar's victory at Carchemish. At this point in time, Nebuchadnezzar was still away on his campaign against the Egyptians, having chased the retreating Egyptian forces to the region around the city of Hamath. The news of Nabopolassar's death reached Nebuchadnezzar's camp on 8 Abu (late July), and Nebuchadnezzar quickly arranged affairs with the Egyptians and rushed back to Babylon, where he was proclaimed king on 1 Ulūlu (mid-August).

The speed in which Nebuchadnezzar returned to Babylon might be due to the threat that one of his brothers (two are known by name: Nabu-shum-lishir and Nabu-zer-ushabshi) could claim the throne in his absence. Though Nebuchadnezzar had been recognised as the eldest son and heir by Nabopolassar, Nabu-shum-lishir, Nabopolassar's second-born son, had been recognised as "his equal brother", a dangerously vague title. Despite these possible fears, there were no attempts made at usurping his throne at this time.

One of Nebuchadnezzar's first acts as king was to bury his father. Nabopolassar was laid in a huge coffin, adorned with ornamented gold plates and fine dresses with golden beads, which was then placed within a small palace he had constructed in Babylon. Shortly thereafter, before the end of the month in which he had been crowned, Nebuchadnezzar returned to Syria to resume his campaign. The Babylonian Chronicle records that "he marched about victoriously", meaning that he faced little to no resistance, returning to Babylon after several months of campaigning. The Syrian campaign, though it resulted in a certain amount of plunder, was not a complete success in that it did not ensure Nebuchadnezzar's grasp on the region. He had seemingly failed to inspire fear, given that none of the westernmost states in the Levant swore fealty to him and paid tribute.

Early military campaigns
Though little information survives concerning them, the Babylonian Chronicle preserves brief accounts of Nebuchadnezzar's military activities in his first eleven years as king. In 604 BC, Nebuchadnezzar campaigned in the Levant once again, conquering the city of Ascalon. According to the Babylonian Chronicle, Ascalon's king was captured and taken to Babylon, and the city was plundered and levelled to the ground. Modern excavations at Ascalon have confirmed that the city was more or less destroyed at this point in time. The Ascalon campaign was preceded by a campaign in Syria, which was more successful than Nebuchadnezzar's first, resulting in oaths of fealty from the rulers of Phoenicia.

In 603 BC, Nebuchadnezzar campaigned in a land whose name is not preserved in the surviving copy of the chronicle. The chronicle records that this campaign was extensive, given that the account mentions the construction of large siege towers and a siege of a city, the name of which does not survive either. Anson Rainey speculated in 1975 that the city taken was Gaza, whereas Nadav Na'aman thought in 1992 that it was Kummuh in south-eastern Anatolia. In the second half of the 5th century BC, some documents mentioned the towns Isqalanu (the name derived from Ascalon) and Hazzatu (the name possibly derived from Gaza) near the city of Nippur, indicating that deportees from both of these cities lived near Nippur, and as such possibly that they had been captured at around the same time.

In both 602 BC and 601 BC, Nebuchadnezzar campaigned in the Levant, though little information survives beyond that a "vast" amount of booty was brought from the Levant to Babylonia in 602 BC. On account of the entry for 602 BC also referring to Nabu-shum-lishir, Nebuchadnezzar's younger brother, in a fragmentary and unclear context, it is possible that Nabu-shum-lishir led a revolt against his brother in an attempt to usurp the throne in that year, especially since he is no longer mentioned in any sources after 602 BC. The damage to the text however makes this idea speculative and conjectural.

In the 601 BC campaign, Nebuchadnezzar departed from the Levant and then marched into Egypt. Despite the defeat at Carchemish in 605 BC, Egypt still had a great amount of influence in the Levant, even though the region was ostensibly under Babylonian rule. Thus, a campaign against Egypt was logical in order to assert Babylonian dominance, and also carried enormous economic and propagandistic benefits, but it was also risky and ambitious. The path into Egypt was difficult, and the lack of secure control of either side of the Sinai Desert could spell disaster.

Nebuchadnezzar's invasion of Egypt failed – the Babylonian Chronicle states that both the Egyptian and Babylonian armies suffered a huge number of casualties. Though Egypt was not conquered, the campaign did result in momentarily curbing Egyptian interest in the Levant, given that Necho II gave up his ambitions in the region. In 599 BC, Nebuchadnezzar marched his army into the Levant and then attacked and raided the Arabs in the Syrian desert. Though apparently successful, it is unclear what the achievements gained in this campaign were.

In 598 BC, Nebuchadnezzar campaigned against the Kingdom of Judah, succeeding in capturing the city of Jerusalem. Judah represented a prime target of Babylonian attention given that it was at the epicenter of competition between Babylon and Egypt. By 601 BC, Judah's king, Jehoiakim, had begun to openly challenge Babylonian authority, counting on that Egypt would lend support to his cause. Nebuchadnezzar's first, 598–597 BC, assault on Jerusalem is recorded in the Bible, but also in the Babylonian Chronicle, which describes it as follows:

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Jehoiakim had died during Nebuchadnezzar's siege and been replaced by his son, Jeconiah, who was captured and taken to Babylon, with his uncle Zedekiah installed in his place as king of Judah. Jeconiah is recorded as being alive in Babylonia thereafter, with records as late as 592 or 591 BC listing him among the recipients of food at Nebuchadnezzar's palace and still referring to him as the 'king of the land of Judah'.

In 597 BC, the Babylonian army departed for the Levant again, but appears to not have engaged in any military activities as they turned back immediately after reaching the Euphrates. The following year, Nebuchadnezzar marched his army along the Tigris river to do battle with the Elamites, but no actual battle happened as the Elamites retreated out of fear once Nebuchadnezzar was a day's march away. In 595 BC, Nebuchadnezzar stayed at home in Babylon but soon had to face a rebellion against his rule there, though he defeated the rebels, with the chronicle stating that the king "put his large army to the sword and conquered his foe." Shortly thereafter, Nebuchadnezzar again campaigned in the Levant and secured large amounts of tribute. In the last year recorded in the chronicle, 594 BC, Nebuchadnezzar campaigned in the Levant yet again.

There were several years without any noteworthy military activity at all. Notably, Nebuchadnezzar spent all of 600 BC in Babylon, when the chronicle excuses the king by stating that he stayed in Babylon to "refit his numerous horses and chariotry". Some of the years when Nebuchadnezzar was victorious can also hardly be considered real challenges. Raiding the Arabs in 599 BC was not a major military accomplishment and the victory over Judah and the retreat of the Elamites were not secured on the battlefield. It thus appears that Nebuchadnezzar achieved little military success after the failure of his invasion of Egypt. Nebuchadnezzar's poor military record had dangerous geopolitical consequences. According to the Bible, in Zedekiah's fourth year as king of Judah (594 BC), the kings of Ammon, Edom, Moab, Sidon and Tyre met in Jerusalem to deal with the possibility of throwing off Babylonian control.

Evidence that Babylonian control was beginning to unravel is also clear from contemporary Babylonian records, such as the aforementioned rebellion in Babylonia itself, as well as records of a man being executed in 594 BC at Borspippa for "breaking his oath to the king". The oath-breaking was serious enough that the judge in the trial was Nebuchadnezzar himself. It is also possible that Babylonian–Median relations were becoming strained, with records of a "Median defector" being housed in Nebuchadnezzar's palace and some inscriptions indicating that the Medes were beginning to be seen as "enemies". By 594 BC, the failure of the Egyptian invasion, and the lacklustre state of Nebuchadnezzar's other campaigns, loomed high. According to the Assyriologist Israel Ephʿal, Babylon at this time was seen by its contemporaries more like a "paper tiger" (i. e. an ineffectual threat) than a great empire, like Assyria just a few decades prior.

Destruction of Jerusalem
From his appointment as king of Judah, Zedekiah waited for the opportune moment to throw off Babylonian control. After Pharaoh Necho II's death in 595 BC, Egyptian intervention in affairs in the Levant increased once again under his successors, Psamtik II ((r. undefined – undefined)595–589 BC) and Apries ((r. undefined – undefined)589–570 BC), who both worked to encourage anti-Babylonian rebellions. It is possible that the Babylonian failure to invade Egypt in 601 BC helped inspire revolts against the Babylonian Empire. The outcome of these efforts was Zedekiah's open revolt against Nebuchadnezzar's authority. Unfortunately, no cuneiform sources are preserved from this time and the only known account of the fall of Judah is the biblical account.

In 589 BC, Zedekiah refused to pay tribute to Nebuchadnezzar, and he was closely followed in this by Ithobaal III, the king of Tyre. In 587 BC, Ammon, Edom and Moab likewise rebelled. In response to Zedekiah's uprising, Nebuchadnezzar conquered and destroyed the Kingdom of Judah in 586 BC, one of the great achievements of his reign. The campaign, which probably ended in the summer of 586 BC, resulted in the plunder and destruction of the city of Jerusalem, a permanent end to Judah, and it led to the Babylonian captivity, as the Jews were captured and deported to Babylonia. Archaeological excavations confirm that Jerusalem and the surrounding area was destroyed and depopulated. It is possible that the intensity of the destruction carried out by Nebuchadnezzar at Jerusalem and elsewhere in the Levant was due to the implementation of something akin to a scorched earth-policy, aimed at stopping Egypt from gaining a foothold there.

Some Jewish administration was allowed to remain in the region under the governor Gedaliah, governing from Mizpah under close Babylonian monitoring. According to the Bible, and the 1st-century AD Jewish historian Flavius Josephus, Zedekiah attempted to flee after resisting the Babylonians, but was captured at Jericho and suffered a terrible fate. According to the narrative, Nebuchadnezzar wanted to make an example out of him given that Zedekiah was not an ordinary vassal, but a vassal directly appointed by Nebuchadnezzar. As such, Zedekiah was supposedly taken to Riblah in northern Syria, where he had to watch his sons being executed before having his eyes gouged out and sent to be imprisoned in Babylon.

Per the Books of Kings in the Bible, the campaign against Judah was longer than typical Mesopotamian wars, with the siege of Jerusalem lasting 18–30 months (depending on the calculation), rather than the typical length of less than a year. Whether the unusual length of the siege indicates that the Babylonian army was weak, unable to break into the city for more than a year, or that Nebuchadnezzar by this time had succeeded in stabilising his rule in Babylonia and could thus wage war patiently without being pressured by time to escalate the siege, is not certain.

Later military campaigns
It is possible that the Egyptians took advantage of the Babylonians being preoccupied with besieging Jerusalem. Herodotus describes Pharaoh Apries as campaigning in the Levant, taking the city of Sidon and fighting the Tyrians, which indicates a renewed Egyptian invasion of the Levant. Apries is unlikely to have been as successful as Herodotus describes, given that it is unclear how the Egyptian navy would have defeated the superior navies of the Phoenician cities, and even if some cities had been taken, they must have shortly thereafter fallen into Babylonian hands again. Tyre had rebelled against Nebuchadnezzar at around the same time as Judah, and Nebuchadnezzar moved to retake the city after his successful subduing of the Jews.

The biblical Book of Ezekiel describes Tyre in 571 BC as if it had been recently captured by the Babylonian army. The supposed length of the siege, 13 years, is only given by Flavius Josephus, and is subject to debate among modern scholars. Josephus's account of Nebuchadnezzar's reign is obviously not entirely historic, as he describes Nebuchadnezzar as, five years after the destruction of Jerusalem, invading Egypt, capturing the Pharaoh and appointing another Pharaoh in his place. A stele from Tahpanhes uncovered in 2011 records that Nebuchadnezzar attempted to invade Egypt in 582 BC, although Apries' forces managed to repel the invasion.

Josephus states that Nebuchadnezzar besieged Tyre in the seventh year of "his" reign, though it is unclear whether "his" in this context refers to Nebuchadnezzar or to Ithobaal III of Tyre. If it refers to Nebuchadnezzar, a siege begun in 598 BC and lasting for thirteen years, later simultaneously with the siege of Jerusalem, is unlikely to have gone unmentioned in Babylonian records. If the seventh year of Ithobaal is intended, the beginning of the siege may conjecturally be placed after Jerusalem's fall. If the siege lasting 13 years is taken at face value, the siege would then not have ended before 573 or 572 BC. The supposed length of the siege can be ascribed to the difficulty in besieging the city: Tyre was located on an island 800 metres from the coast, and could not be taken without naval support. Though the city withstood numerous sieges, it would not be captured until Alexander the Great's siege in 332 BC.

In the end, the siege was resolved without a need of battle and did not result in the Tyre being conquered. It seems Tyre's king and Nebuchadnezzar came to an agreement for Tyre to continue to be ruled by vassal kings, though probably under heavier Babylonian control than before. Documents from Tyre near the end of Nebuchadnezzar's reign demonstrate that the city had become a centre for Babylonian military affairs in the region. According to later Jewish tradition, it is possible that Ithobaal III was deposed and taken as a prisoner to Babylon, with another king, Baal II, proclaimed by Nebuchadnezzar in his place.

It is possible that Nebuchadnezzar campaigned against Egypt in 568 BC, given that a fragmentary Babylonian inscription, given the modern designation BM 33041, from that year records the word "Egypt" as well as possibly traces of the name "Amasis" (the name of the then incumbent Pharaoh, Amasis II, (r. undefined – undefined)570–526 BC). A stele of Amasis, also fragmentary, may also describe a combined naval and land attack by the Babylonians. Recent evidence suggests that the Babylonians were initially successful during the invasion and gained a foothold in Egypt, but they were repelled by Amasis' forces. If Nebuchadnezzar did campaign against Egypt again, he was unsuccessful again, given that Egypt did not come under Babylonian rule.

Nebuchadnezzar's campaigns in the Levant, most notably those directed towards Jerusalem and Tyre, completed the Neo-Babylonian Empire's transformation from a rump state of the Neo-Assyrian Empire to the new dominant power of the ancient Near East. Still, Nebuchadnezzar's military accomplishments can be questioned, given that the borders of his empire, by the end of his reign, had not noticeably increased in size and that he had not managed to conquer Egypt. Even after a reign of several decades, Nebuchadnezzar's greatest victory remained his victory over the Egyptians at Carchemish in 605 BC, before he even became king.

Building projects
The Babylonian king was traditionally a builder and restorer, and as such large-scale building projects were important as a legitimising factor for Babylonian rulers. Nebuchadnezzar extensively expanded and rebuilt his capital city of Babylon and the most modern historical and archaeological interpretations of the city reflect it as it appeared after Nebuchadnezzar's construction projects. The projects were made possible through the prospering economy during Nebuchadnezzar's reign, sustained by his conquests. His building inscriptions record work done to numerous temples, notably the restoration of the Esagila, the main temple of Babylon's national deity Marduk, and the completion of the Etemenanki, a great ziggurat dedicated to Marduk. Extensive work was also conducted on civil and military structures. Among the most impressive efforts was the work done surrounding the city's northern ceremonial entrance, the Ishtar Gate. These projects included restoration work on the South Palace, inside the city walls, the construction of a completely new North Palace, on the other side of the walls facing the gate, as well as the restoration of Babylon's Processional Street, which led through the gate, and of the gate itself. The ruins of Nebuchadnezzar's North Palace are poorly preserved and as such its structure and appearance are not entirely understood. Nebuchadnezzar also constructed a third palace, the Summer Palace, built some distance north of the inner city walls in the northernmost corner of the outer walls.

The restored Ishtar Gate was decorated with blue and yellow glazed bricks and depictions of bulls (symbols of the god Adad) and dragons (symbols of the god Marduk). Similar bricks were used for the walls surrounding the Processional Street, which also featured depictions of lions (symbols of the goddess Ishtar). Babylon's Processional Street, the only such street yet excavated in Mesopotamia, ran along the eastern walls of the South Palace and exited the inner city walls at the Ishtar Gate, running past the North Palace. To the south, this street went by the Etemenanki, turning to the west and going over a bridge constructed either under the reign of Nabopolassar or Nebuchadnezzar.

Some of the bricks of the Processional Street bear the name of the Neo-Assyrian king Sennacherib ((r. undefined – undefined)705–681 BC) on their underside, perhaps indicating that construction of the street had begun already during his reign, but the fact that the upper side of the bricks all bear the name of Nebuchadnezzar suggests that construction of the street was completed under Nebuchadnezzar's reign. Glazed bricks such as the ones used in the Procession Street were also used in the throne room of the South Palace, which was decorated with depictions of lions and tall, stylised palm trees.

Nebuchadnezzar also directed building efforts on the city of Borsippa, with several of his inscriptions recording restoration work on that city's temple, the Ezida, dedicated to the god Nabu. Additionally, Nebuchadnezzar also restored the ziggurat of the Ezida, the E-urme-imin-anki, and also worked on the temple of Gula, Etila, as well as numerous other temples and shrines in the city. Nebuchadnezzar also repaired Borsippa's walls.

Other great building projects by Nebuchadnezzar include the Nar-Shamash, a canal to bring water from the Euphrates close to the city of Sippar, and the Median Wall, a large defensive structure built to defend Babylonia against incursions from the north. The Median Wall was one of two walls built to protect Babylonia's northern border. Further evidence that Nebuchadnezzar believed the north to be the most likely point of attack for his enemies comes from that he fortified the walls of northern cities, such as Babylon, Borsippa and Kish, but left the walls of southern cities, such as Ur and Uruk, as they were. Nebuchadnezzar also began work on the Royal Canal, also known as Nebuchadnezzar's Canal, a great canal linking the Euphrates to the Tigris which in time completely transformed the agriculture of the region, but the structure was not completed until the reign of Nabonidus, who ruled as the last king of the Neo-Babylonian Empire from 556 to 539 BC.

Death and succession
Nebuchadnezzar died at Babylon in 562 BC. The last known tablet dated to Nebuchadnezzar's reign, from Uruk, is dated to the same day, 7 October, as the first known tablet of his successor, Amel-Marduk, from Sippar. Amel-Marduk's administrative duties probably began before he became king, during the last few weeks or months of his father's reign when Nebuchadnezzar was ill and dying. Having ruled for 43 years, Nebuchadnezzar's reign was the longest of his dynasty and he would be remembered favourably by the Babylonians.

Amel-Marduk's accession does not appear to have gone smoothly. He was not the eldest living son of Nebuchadnezzar and the reason why he was picked as crown prince is not known. The choice is especially strange given that some sources suggest that the relationship between Nebuchadnezzar and Amel-Marduk was particularly poor, with one surviving text describing both as parties in some form of conspiracy and accusing one of them (the text is too fragmentary to determine which one) of failing in the most important duties of Babylonian kingship through exploiting Babylon's populace and desecrating its temples. Amel-Marduk also at one point appears to have been imprisoned by his father, possibly on account of the Babylonian aristocracy having proclaimed him as king while Nebuchadnezzar was away. It is possible that Nebuchadnezzar intended to replace Amel-Marduk as heir with another son, but died before doing so.

In one of Nebuchadnezzar's late inscriptions, written more than forty years into his reign, he wrote that he had been chosen for the kingship by the gods before he was even born. Mesopotamian rulers typically only stressed divine legitimacy in this fashion when their actual legitimacy was questionable, a method often employed by usurpers. Given that Nebuchadnezzar at this point had been king for several decades and was the legitimate heir of his predecessor, the inscription is very strange, unless it was intended to help legitimize Nebuchadnezzar's successor, Amel-Marduk, who as a younger son and a former conspirator could be seen as politically problematic.

Family and children
No surviving contemporary Babylonian documents provide the name of Nebuchadnezzar's wife. According to Berossus, her name was Amytis, daughter of Astyages, king of the Medes. Berossus writes that '[Nabopolassar] sent troops to the assistance of Astyages, the tribal chieftain and satrap of the Medes in order to obtain a daughter of Astyages, Amyitis, as wife for his son [Nebuchadnezzar]'. Though the ancient Greek historian Ctesias instead wrote that Amytis was the name of a daughter of Astyages who had married Cyrus I of Persia, it seems more likely that a Median princess would marry a member of the Babylonian royal family, considering the good relations established between the two during Nabopolassar's reign.

Given that Astyages was still too young during Nabopolassar's reign to already have children, and was not yet king, it seems more probable that Amytis was Astyages's sister, and thus a daughter of his predecessor, Cyaxares. By marrying his son to a daughter of Cyaxares, Nebuchadnezzar's father Nabopolassar likely sought to seal the alliance between the Babylonians and the Medes.

According to tradition, Nebuchadnezzar constructed the Hanging Gardens of Babylon, one of the Seven Wonders of the Ancient World, featuring exotic shrubs, vines and trees as well as artificial hills, watercourses and knolls, so that Amytis would feel less homesick for the mountains of Media. No archaeological evidence for these gardens has yet been found.

Nebuchadnezzar had six known sons. Most of the sons, with the exceptions of Marduk-nadin-ahi and Eanna-sharra-usur, are attested very late in their father's reign. It is possible that they might have been the product of a second marriage and that they could have been born relatively late in Nebuchadnezzar's reign, possibly after his known daughters. The known sons of Nebuchadnezzar are:

Three of Nebuchadnezzar's daughters are known by name:
 * Marduk-nadin-ahi (Akkadian: Marduk-nādin-aḫi) – the earliest attested of Nebuchadnezzar's children, attested in a legal document, probably as an adult as he is described as being in charge of his own land, already in Nebuchadnezzar's third year as king (602/601 BC). Presumably Nebuchadnezzar's firstborn son, if not eldest child, and thus his legitimate heir. He is also attested very late in Nebuchadnezzar's reign, named as a "royal prince" in a document recording the purchase of dates by Sin-mār-šarri-uṣur, his servant, in 563 BC.
 * Eanna-sharra-usur (Akkadian: Eanna-šarra-uṣur) – named as a "royal prince" among sixteen people in a document at Uruk from 587 BC recorded as receiving barley "for the sick".
 * Amel-Marduk (Akkadian: Amēl-Marduk), originally named Nabu-shum-ukin (Nabû-šum-ukīn) – succeeded Nebuchadnezzar as king in 562 BC. His reign was marred with intrigues and he only ruled for two years before being murdered and usurped by his brother-in-law, Neriglissar. Later Babylonian sources mostly speak ill of his reign. Amel-Marduk is first attested, notably as crown prince, in a document 566 BC. Given that Amel-Marduk had an older brother in Marduk-nadin-ahi, alive as late as 563 BC, why he was named crown prince is not clear.
 * Marduk-shum-usur (Akkadian: Marduk-šum-uṣur or Marduk-šuma-uṣur) – named as a "royal prince" in documents from Nebuchadnezzar's 564 BC and 562 BC years, recording payments by his scribe to the Ebabbar temple in Sippar.
 * Mushezib-Marduk (Akkadian: Mušēzib-Marduk) – named as a "royal prince" once in a contract tablet from 563 BC.
 * Marduk-nadin-shumi (Akkadian: Marduk-nādin-šumi) – named as a "royal prince" once in a contract tablet from 563 BC.

It is possible that one of Nebuchadnezzar's daughters married the high official Nabonidus. Marriage to a daughter of Nebuchadnezzar could explain how Nabonidus could become king, and also explain why certain later traditions, such as the Book of Daniel in the Bible, describe Nabonidus's son, Belshazzar, as Nebuchadnezzar's son (descendant). Alternatively, these later traditions might instead derive from royal propaganda.
 * Kashshaya (Akkadian: Kaššaya) – attested in several economic documents from Nebuchadnezzar's reign as "the king's daughter". Her name is of unclear origin; it might be derived from the word kaššû (kassite). Kashshaya is attested from contemporary texts as a resident of (and landowner in) Uruk. Kashshaya is typically, although speculatively, identified as the daughter of Nebuchadnezzar who married Neriglissar.
 * Innin-etirat (Akkadian: Innin-ēṭirat) – attested as "the king's daughter" in a 564 BC document which records her granting mār-banûtu status ("status of a free man") to a slave by the name Nabû-mukkê-elip. The document in question was written at Babylon, but names including the divine prefix Innin are almost unique to Uruk, suggesting that she was a resident of that city.
 * Ba'u-asitu (Akkadian: Ba'u-asītu) – attested as the owner of a piece of real estate in an economic document. The precise reading and meaning of her name is somewhat unclear. Paul-Alain Beaulieu, who in 1998 published the translated text which confirms her existence, believes that her name is best interpreted as meaning "Ba'u is a/the physician". The document was written at Uruk, where Ba'u-asitu is presumed to have lived.

The ancient Greek historian Herodotus names the "last great queen" of the Babylonian Empire as "Nitocris", though that name, nor any other name, is not attested in contemporary Babylonian sources. Herodotus's description of Nitocris contains a wealth of legendary material that makes it difficult to determine whether he uses the name to refer to Nabonidus's wife or mother. In 1982, William H. Shea proposed that Nitocris may tentatively be identified as the name of Nabonidus's wife and Belshazzar's mother.

Assessment by historians
Because of the scarcity of sources, assessment by historians of Nebuchadnezzar's character and the nature of his reign have differed considerably over time. He has typically been regarded as the greatest and most prestigious king of the Neo-Babylonian Empire.

Since military activity was not a major issue described in the inscriptions of any Neo-Babylonian king regardless of their actual military accomplishments, in sharp contrast to the inscriptions of their Neo-Assyrian predecessors, Nebuchadnezzar's own inscriptions record very little about his wars. Out of the fifty or so known inscriptions by the king, only a single one deals with military action, and in this case only small-scale conflicts in the Lebanon region. Many Assyriologists, such as Wolfram von Soden in 1954, thus initially assumed that Nebuchadnezzar had mainly been a builder-king, devoting his energy and efforts to building and restoring his country.

A major change in evaluations of Nebuchadnezzar came with the publication of the tablets of the Babylonian Chronicle by Donald Wiseman in 1956, which cover the geopolitical events of Nebuchadnezzar's first eleven years as king. From the publication of these tablets and onwards, historians have shifted to perceiving Nebuchadnezzar as a great warrior, devoting special attention to the military achievements of his reign.

According to the historian Josette Elayi, writing in 2018, Nebuchadnezzar is somewhat difficult to characterise on account of the scarcity of Babylonian source material. Elayi wrote, about Nebuchadnezzar, that "[h]e was a conqueror, even though reservations can be had about his military capabilities. There was no lack of statesmanlike qualities, given his success in building the Babylonian Empire. He was a great builder, who restored a country that for a long time had been devastated by war. That is roughly all we know about him because the Babylonian Chronicles and other texts say little about his personality."

In Jewish and biblical tradition
The Babylonian captivity initiated by Nebuchadnezzar came to an end with the fall of Babylon to the Achaemenid king Cyrus the Great in 539 BC. Within a year of their liberation, some exiled Jews returned to their homeland. Their liberation did little to erase the memory of five decades of imprisonment and oppression. Instead, Jewish literary accounts ensured that accounts of the hardship endured by the Jews, as well as of the monarch responsible for it, would be remembered for all time. The Book of Jeremiah calls Nebuchadnezzar a "lion" and a "destroyer of nations".

Nebuchadnezzar's story thus found its way into the Old Testament of the Bible. The Bible narrates how Nebuchadnezzar destroyed the Kingdom of Judah, besieged, plundered and destroyed Jerusalem, and how he took away the Jews in captivity, portraying him as a cruel enemy of the Jewish people. The Bible also portrays Nebuchadnezzar as the legitimate ruler of all the nations of the world, appointed to rule the world by God. As such, Judah, through divine ruling, should have obeyed Nebuchadnezzar and should not have rebelled. Nebuchadnezzar is also depicted as carrying out death sentences pronounced by God, slaying two false prophets. Nebuchadnezzar's campaigns of conquest against other nations are portrayed as being in-line with God's will for Nebuchadnezzar's dominance.

Despite Nebuchadnezzar's negative portrayal, the Book of Jeremiah notably refers to him using the epithet 'my servant' (i.e. God's servant) in three passages:

 * Nebuchadnezzar's attack on the Kingdom of Judah is theologically justified in the Book of Jeremiah on account of Judah's populace's disobedience of God, and the king is called "Nebuchadnezzar the king of Babylon, my servant".
 * The Book of Jeremiah also states that God has made all the Earth and given it to whom it seemed proper to give it to, deciding upon giving all of the lands of the world to "Nebuchadnezzar the king of Babylon, my servant".
 * The Book of Jeremiah also prophesies Nebuchadnezzar's victory over Egypt, stating that "Nebuchadnezzar the king of Babylon, my servant" will invade Egypt and "deliver to death those appointed for death, and to captivity those appointed for captivity, and to the sword those appointed for the sword".

Given that Nebuchadnezzar was the enemy of what the Bible proclaims as God's chosen people, possibly the worst enemy they had faced until this point, there must be a special reason for referring to him with the epithet "my servant". Other uses of this epithet are usually limited to some of the most positively portrayed figures, such as the various prophets, Jacob (the symbol of the chosen people) and David (the chosen king). Klaas A. D. Smelik noted in 2004 that "in the Hebrew Bible, there is no better company conceivable than these; at the same time, there is no candidate less likely for this title of honour than the Babylonian king Nebuchadnezzar".

It is possible that the epithet is a later addition, as it is missing in the Septuagint version of the Old Testament, perhaps added after Nebuchadnezzar began to be seen in a slightly more favourable light than immediately after Jerusalem's destruction. Alternatively, possible theological explanations include Nebuchadnezzar being seen, despite his cruelty, as an instrument in fulfilling God's universal plan; or perhaps that designating him as a "servant" of God was to show that readers should not fear Nebuchadnezzar, but his true master, God.

In the Book of Daniel, considered by scholars to be a work of historical fiction, the figure of Nebuchadnezzar differs considerably from his portrayal in the Book of Jeremiah. He is for the most part depicted as a merciless and despotic ruler. The king has a nightmare, and asks his wise men, including Daniel and his three companions Shadrach, Meshach and Abednego, to interpret the dream, but refuses to state the dream's contents. When the servants protest, Nebuchadnezzar sentences all of them, including Daniel and his companions, to death.

By the end of the story, when Daniel has successfully interpreted the dream, Nebuchadnezzar shows much gratitude, showering Daniel with gifts, appointing him the governor of the "province of Babylon" and making him the chief of the kingdom's wise men. A second story again casts Nebuchadnezzar as a tyrannical and pagan king, who, after Shadrach, Meshach and Abednego refuse to worship a newly erected golden statue, sentences them to death through being thrown into a fiery furnace. They are miraculously delivered, and Nebuchadnezzar then acknowledges God as the "lord of kings" and "god of gods".

Though Nebuchadnezzar is also mentioned as acknowledging the Hebrews' God as the true god in other passages of the Book of Daniel, it is apparent that his supposed conversion to Judaism does not change his violent character, given that he proclaims that anyone who speaks amiss of God "shall be cut in pieces and their houses shall be made a dunghill". In a third story, Daniel interprets another dream as meaning that Nebuchadnezzar will lose his mind and live like an animal for seven years before being restored to his normal state (Daniel 1-4). The Nebuchadnezzar in the Book of Daniel, a fickle tyrant who is not particularly consistent in his faith, contrasts with the typical "servant of God" in other books of the Bible.

Given that Nebuchadnezzar is referred to as the father of Belshazzar in the Book of Daniel, it is probable that this portrayal of Nebuchadnezzar, especially the story of his madness, was actually based on Belshazzar's actual father, Nabonidus, the last king of the Neo-Babylonian Empire ((r. undefined – undefined)556–539 BC). Separate Jewish and Hellenistic traditions exist concerning Nabonidus having been mad, and it is likely that this madness was simply reattributed to Nebuchadnezzar in the Book of Daniel through conflation.

Some later traditions conflated Nebuchadnezzar with other rulers as well, such as the Assyrian Ashurbanipal ((r. undefined – undefined)669–631 BC), the Persian Artaxerxes III ((r. undefined – undefined)358–338 BC), the Seleucids Antiochus IV Epiphanes ((r. undefined – undefined)175–164 BC) and Demetrius I Soter ((r. undefined – undefined)161–150 BC) and the Armenian Tigranes the Great ((r. undefined – undefined)95–55 BC). The apocryphal Book of Judith, which probably applies the name "Nebuchadnezzar" to Tigranes the Great of Armenia, refers to Nebuchadnezzar as a "king of the Assyrians", rather than of the Babylonians, and demonstrates that Nebuchadnezzar was still viewed as an evil king, responsible for destroying Jerusalem, looting its temple, taking the Jews hostage in Babylon, and for the various misdeeds ascribed to him in later Jewish writings.

Other
Nebuchadnezzar is referred to as (بخت نصر) in works of the mediaeval scholar al-Ṭabarī, where he is credited with conquering Egypt, Syria, Phoenicia and Arabia. The historical Nebuchadnezzar never conquered Egypt, and it appears that al-Ṭabarī transferred to him the achievements of the Assyrian king Esarhaddon ((r. 681 – 669)). In similar fashion Strabo, citing Megasthenes, mentioned in a list of mythical and semi-legendary conquerors, a Nabocodrosor as having led an army to the Pillars of Hercules and being revered by the Chaldaeans.

Titles
In most of his inscriptions, Nebuchadnezzar is typically only titled as "Nebuchadnezzar, king of Babylon, son of Nabopolassar, king of Babylon" or "Nebuchadnezzar, king of Babylon, the one who provides for Esagil and Ezida, son of Nabopolassar, king of Babylon". In economic documents, Nebuchadnezzar is also ascribed the ancient title "king of the Universe", and he sometimes also used the title "king of Sumer and Akkad", used by all the Neo-Babylonian kings. Some inscriptions accord Nebuchadnezzar more elaborate version of his titles, including the following variant, attested in an inscription from Babylon:

""

title: Nebuchadnezzar II


text:
Talk:Fasces

Cincinnatus
I've added the image of Cincinnatus, but I'm not sure if it is too much for the page -- some people don't like multiple pictures in a small article. I thought it was a good illustration of the object; what do you think? Rdikeman 23:02, Apr 16, 2004 (UTC)

Cincinnatus is important.
I think the inclusion of Cincinnatus is important. What about including a link to or information about the Society of the Cincinnati ? — Preceding unsigned comment added by 151.203.183.119 (talk • contribs) 12:08, 11 June 2005 (UTC)

 * Some text about the occasion in Cincinnatus' career and the significance of the portrayed gesture is essential. Anyone want to give this a paragraph? The connection between Roman Cincinnatus and the Society of the Cincinnati should be explained at Society of the Cincinnati, but not here at Fasces: too peripheral. --Wetman 18:34, 11 Jun 2005 (UTC)

Alternative Fasces
I remember seeing an illustration of a fasces used as a papal symbol. It was from a book on the history of Christianity, whose name I have forgotten, but it was part of a frieze. The interesting this about this fasces was that it used a candle in place of an axe... Anyone know anything else about this? — Preceding unsigned comment added by 203.217.34.107 (talk • contribs) 03:48, 22 May 2006 (UTC)

List of Symbols Containing the Fasces
In the interest of keeping the main un-cluttered would it be a good idea to make a seperate article called "List of Symbols Containing Fasces"? I think it would be immensely helpful for resaerchers of symbolism to have a list of images containing the fascses (or any symbol for that matter), as a reference and also to be able to compare and contrast different usages. 24.18.35.120 01:52, 2 July 2006 (UTC)

It would keep the main page uncluttered. The Mace of the United States House of Reprensentatives is one historical example. GuitarTesseract (talk) 23:01, 10 May 2022 (UTC)

RIC IVa 422A
Hey there! I have yet another question about coins. Brennan, in Fasces (2022), cites the sestertius which shows the redesigned fasces as RIC IVa 422A (id at p 229 n 37; formatting verbatim). Do you know if we have an image of it? Happy holidays! Ifly6 (talk) 22:18, 20 December 2022 (UTC)

 * Added picture. T8612  (talk) 15:10, 21 December 2022 (UTC)
 * Fantastic. Ifly6 (talk) 18:37, 21 December 2022 (UTC)

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

title: Talk:Fasces


text:
Gaspar Corte-Real

Gaspar Corte-Real (1450–1501) was a Portuguese explorer who, alongside his father João Vaz Corte-Real and brother Miguel, participated in various exploratory voyages sponsored by the Portuguese Crown. These voyages are said to have been some of the first to reach Newfoundland and possibly other parts of eastern Canada.

Early life
Gaspar was born into the noble Corte-Real family on Terceira in the Azores Islands, the youngest of three sons of Portuguese explorer João Vaz Corte-Real (c. 1420–1496). Gaspar accompanied his father on expeditions to North America. His brothers were explorers as well.

Careers
In 1498, King Manuel I of Portugal took an interest in western exploration, likely believing that the lands recently discovered by John Cabot (the coast of North America) were within the realm of Portuguese control under the Treaty of Tordesillas. Corte-Real was one of several explorers to sail west on behalf of Portugal.

In 1500, Corte-Real reached Greenland, believing it to be east Asia (as Christopher Columbus had regarded the New World), but was unable to land. He set out on a second voyage in 1501, taking three caravels. The expedition was again prevented from landing at Greenland due to frozen seas. They changed course, and landed in a country of large rivers, pine trees, and berries, believed to be Labrador. There it is believed they captured 57 indigenous people, who were taken back to Portugal to be sold into slavery to assist in financing the voyage. Two of the expedition's three ships made the return trip to Portugal, but the ship carrying Corte-Real was lost.

Nothing more was heard of Gaspar Corte-Real after 1501. His brother Miguel attempted to find him in 1502, but he too got lost.

Legacy
There is debate amongst historians about the relative importance of Corte-Real. Memorial University of Newfoundland historian Jeff Webb stated in 2017 that "He is a minor figure about whom very, very little is known with confidence." The 20th-century myth-building of Corte-Real was largely the work of historian-diplomat Eduardo Brazao, the former National Secretary of Portugal's propaganda ministry, the Secretariado Nacional de Informação, Cultura Popular e Turismo,  during the regime of António de Oliveira Salazar.

A statue of Corte-Real was erected in front of the Confederation Building in St. John's, Newfoundland and Labrador in 1965, and has more recently been the subject of controversy. A street in Mount Pearl is named for the explorer. A building at Memorial University of Newfoundland's St. John's campus was formerly named after him. In December 2019, the Board of Regents voted to change its name to the Global Learning Centre, after prompting by the Internationalization Office that the building presently houses.

St. John's statue
In May 1963, Brazao, then the Portuguese Ambassador to Canada, visited St. John's to meet with premier Joseph Smallwood. Following conversations with Brazao, Smallwood announced on 28 May 1963 that the Portuguese fishing fleet "with the hearty approval of the government of Portugal" would commission "a famous Portuguese sculptor" to create a statue that would depict both Gaspar Corte-Real and his brother Miguel. Following their meeting, Brazao invited Smallwood to Portugal, where Smallwood met with Salazar in October of that year.

Two years later, a statue of Corte-Real (minus Miguel) was presented under the banner of the Canadian Portuguese Fisheries Organisation in 1965 to commemorate the hospitality of Newfoundlanders towards Portuguese Grand Banks fishermen.

In early 1999, a car, apparently chauffeured by a speeding tourist, slammed into the pedestal that supports the statue. The statue itself was unscathed, but its base was mangled. Later that year, Ottawa bronze restoration specialist Craig Johnson subcontracted local foundry sculptors to undertake the repairs while Johnson himself repainted the statue. According to local sculptor Will Gill, who did some of the work, no scars remain from the accident and the statue was returned to its original condition.

In 2020, it was noted that the statue, designed by Estado Novo propagandist Martins Correa, was erected as part of a behind-the-scenes fisheries rights conflict between Salazar and Spain's Francisco Franco. In 1968, Smallwood had announced that "Generalissimo Franco is to present a statue to the province" which would have been erected beside the statue of Corte-Real; this second statue was never delivered.

On June 11, 2020, Newfoundland and Labrador Premier Dwight Ball was quoted as saying the government would review politically sensitive provincial statues. Author Edward Riche noted on June 20, 2020, "If enough people now see the statue of Corte-Real as memorializing a character who enslaved Indigenous people during his imperial ventures, we have a problem."

On June 28, 2020, it was reported that Todd Russell, president of NunatuKavut, which represents Inuit in central and southern Labrador, "doesn't need any more consultation — he wants it taken down." On July 8, 2020, it was reported that the statue had been spray-painted with the phrases "Slaver" and "Why is this guy still here?" Various opinion pieces and letters to the editor called for the statue's removal. The statue was further vandalized in July 2021, following the discovery of unmarked graves of Indigenous children on properties part of the Canadian Indian residential school system. A government working group made recommendations on the statue in February 2022; no action had been taken by July 2023.

title: Gaspar Corte-Real


text:
Ogimachi

Ogimachi may refer to:
 * Emperor Ōgimachi, the 106th Emperor of Japan
 * Ōgimachi Station (Osaka), a station of the Sakaisuji Line of Osaka Municipal Subway
 * Ōgimachi Station (Kanagawa), a station of the JR Tsurumi Line
 * Ogimachi Village, included in Historic Villages of Shirakawa-gō and Gokayama

title: Ogimachi


text:
Trinity College

Trinity College may refer to:

Australia

 * Trinity Anglican College, an Anglican coeducational primary and secondary school in, New South Wales
 * Trinity Catholic College, Auburn, a coeducational school in the inner-western suburbs of Sydney, New South Wales
 * Trinity Catholic College, Goulburn, a coeducational school in the Southern Tablelands, New South Wales
 * Trinity Catholic College, Lismore, a coeducational school in northeastern New South Wales
 * Trinity College Queensland, a theological college of the Uniting Church in Australia, in Auchenflower, Brisbane
 * Trinity College, Beenleigh, a Roman Catholic coeducational school in Queensland
 * Trinity College, Gawler, a coeducational multi-school college in South Australia
 * Trinity College, Melbourne, a residential college of the university of Melbourne
 * Trinity College, Perth, a Roman Catholic boys' school in Western Australia
 * Trinity Lutheran College (Queensland), a coeducational school in Ashmore, on the Gold Coast
 * Trinity Residential College, a residential college of the University of Western Australia in Perth
 * Trinity Theological College, Perth, an evangelical Christian college in Western Australia

Canada

 * Trinity College, Toronto, a federated college of the University of Toronto, in Ontario
 * Trinity College School, in Port Hope, Ontario
 * Trinity Western College, former name of Trinity Western University in Langley, British Columbia

Ireland

 * Trinity College Dublin, the sole constituent college of the University of Dublin

New Zealand

 * Trinity Catholic College, Dunedin, a school in Dunedin, New Zealand

United Kingdom
In the UK, Trinity College is generally used as a term to refer to the colleges at one of the English ancient universities:

 * Trinity College, Cambridge, a constituent college of the University of Cambridge
 * Trinity College, Oxford, a constituent college of the University of Oxford

It may also refer to:
 * Trinity College, Bristol, an Anglican theological college
 * Trinity College, Carmarthen, former name of Trinity University College, now merged into the University of Wales Trinity Saint David
 * Trinity College, Glasgow, a Church of Scotland institution within the University of Glasgow supervising candidates for ministry
 * Trinity College, Glenalmond, former name of Glenalmond College in Perthshire
 * Trinity College London, an examination board formerly associated with Trinity College of Music
 * Trinity College Kirk, also known as Trinity College Church, the remnants of a medieval collegiate foundation in Edinburgh
 * Trinity College of Music, in Greenwich, Greater London, now merged into Trinity Laban Conservatoire of Music and Dance
 * Trinity Catholic College, Middlesbrough, a school in North Yorkshire

United States

 * Trinity Baptist College, in Jacksonville, Florida
 * Trinity Bible College and Graduate School, in Ellendale, North Dakota
 * Trinity Christian College, in Palos Heights, Illinois
 * Trinity College and University, former name of Bronte International University, previously based in South Dakota
 * Trinity College (Connecticut), a liberal arts college in Hartford
 * Trinity College of Arts and Sciences in Durham, North Carolina; Duke University's undergraduate liberal arts college ("Trinity College" was the former name of the entire university)
 * Trinity College of the Bible and Theological Seminary, in Newburgh, Indiana
 * Trinity College of Florida, a Bible college in New Port Richey
 * Trinity College of Vermont, formerly a women's college in Burlington
 * Trinity College, former name of Trinity Washington University in Washington, D.C.
 * Trinity College, the undergraduate school of Trinity International University, Deerfield, Illinois
 * Trinity College, in Miami, Florida, now merged into Trinity International University as its Florida campus
 * Trinity Lutheran College (Washington), in Seattle
 * Trinity School (Athens, Alabama), a historical school for African Americans

Other locations

 * Trinity College and University, former name of Bronte International University, based in Tortola, British Virgin Islands
 * Trinity College Foochow, the precursor of Fuzhou Foreign Language School, in Fujian, China
 * Trinity College Nabbingo, a secondary school in the Central Region of Uganda
 * Trinity College of Quezon City, former name of Trinity University of Asia in the Philippines
 * Trinity College Rancagua, a high school in Cachapoal Province, Chile
 * Trinity College Rome Campus, in Italy, an overseas residential programme of the Trinity College in Connecticut, U.S.
 * Trinity College, Kandy, a secondary school in Sri Lanka
 * Trinity College, Leuven, formerly a college of the old University of Leuven, in Brabant, modern-day Belgium
 * Trinity College, Moka, a secondary school in Maraval, Trinidad and Tobago
 * Trinity Theological College, Singapore, an ecumenical Christian college
 * Trinity International College, a college in Kathmandu, Nepal

title: Trinity College


text:
German Museum of Technology

Deutsches Technikmuseum Berlin (German Museum of Technology) in Berlin, Germany is a museum of science and technology, and exhibits a large collection of historical technical artifacts. The museum's main emphasis originally was on rail transport, but today it also features exhibits of various sorts of industrial technology. In 2003, it opened both maritime and aviation exhibition halls in a newly built extension. The museum also contains a science center called Spectrum.

History
The Museum of Traffic and Technology (Museum für Verkehr und Technik) was founded in 1982 and assumed the tradition of the Royal Museum of Traffic and Construction (Königliches Verkehrs- und Baumuseum) which was opened in the former Hamburger Bahnhof station building in 1906. The present-day museum is located on the former freight yard attached to the Anhalter Bahnhof in the Kreuzberg district of Berlin, including two historic roundhouses and several office buildings.

Renamed Deutsches Technikmuseum in 1996, the exhibition area was gradually expanded. An adjacent new building complex was inaugurated in 2003, topped by a prominent US Air Force Douglas C-47B "Raisin Bomber", which can be seen with ease from the top of the Fernsehturm and formerly at the Tempelhof Airport.

Locomotives

An extensive railway collection opened in 1987/88 in the rebuilt 19th century roundhouses of the Anhalter Bahnhof locomotive depot (Bahnbetriebswerk) that had lain derelict for about 30 years. The 33 tracks illustrate the history of rail transport, including the deportations of Jews and others by the Deutsche Reichsbahn in The Holocaust. The exhibition also features a H0 scale model of the Anhalter Bahnhof track installations.

Locomotives on display include:

Steam

 * 17 008, a Prussian S 10, which has been sectioned.
 * 50 001 of DRB Class 50

Other

 * E 19 01, one of four members of DRG Class E 19 (1938)
 * 118 075 of DR Class V 180
 * V 200 018, of DB Class V 200 (1957)
 * 202 003-0, one of three Henschel-BBC DE2500 prototypes (1971 or 1974)

Aircraft
A large aviation section beside the C-47 houses numerous aircraft from the single Jeannin Stahltaube to a Lufthansa Junkers Ju 52 (Spanish aircraft built by CASA under license) and an Arado Ar 79. The museum addresses the flight enthusiasm of the early 20th century and its abuse in the German re-armament building up the Luftwaffe, documented by an Arado Ar 96, a wrecked Junkers Ju 87 Stuka dive bomber and the current restoration of a Focke-Wulf Fw 200 Condor as well as by one of three preserved Messerschmitt Bf 110, a Flak cannon, and a V-1 flying bomb built by Mittelbau-Dora concentration camp inmates at the Mittelwerk site. Post-war aircraft including a VFW-Fokker 614 and the Cessna 172P that Mathias Rust flew to the Moscow Red Square during the Cold War have also been added to the exhibition.

The remains of Avro Lancaster B III JA914 are displayed. This aircraft served with 57 Squadron as DX-O. It was shot down over Berlin in September 1943 and crashed into a lake opposite Zahrensdorf.

Computers

On 15 May 2002, a special exhibition opened which featured the inventions of computer pioneer Konrad Zuse, including a replica of the Z1 and several other Zuse computers.

Buildings
The museum has two windmills (one German, one Dutch), a brewery, and a forge powered by a water wheel.

title: German Museum of Technology


text:
Eroticism

Eroticism is a quality that causes sexual feelings, as well as a philosophical contemplation concerning the aesthetics of sexual desire, sensuality, and romantic love. That quality may be found in any form of artwork, including painting, sculpture, photography, drama, film, music, or literature. It may also be found in advertising. The term may also refer to a state of sexual arousal or anticipation of such – an insistent sexual impulse, desire, or pattern of thoughts.

As French novelist Honoré de Balzac stated, eroticism is dependent not just upon an individual's sexual morality, but also the culture and time in which an individual resides.

Definitions
Because the nature of what is erotic is fluid, early definitions of the term attempted to conceive eroticism as some form of sensual or romantic love or as the human sex drive (libido); for example, the Encyclopédie of 1755 states that the erotic "is an epithet which is applied to everything with a connection to the love of the sexes; one employs it particularly to characterize...a dissoluteness, an excess". Libertine literature such as those by John Wilmot, 2nd Earl of Rochester evoked eroticism to the readers.

Because eroticism is wholly dependent on the viewer's culture and personal tastes pertaining to what, exactly, defines the erotic, critics have often confused eroticism with pornography, with the anti-pornography activist Andrea Dworkin saying, "Erotica is simply high-class pornography; better produced, better conceived, better executed, better packaged, designed for a better class of consumer." This confusion, as Lynn Hunt writes, "demonstrate[s] the difficulty of drawing... a clear generic demarcation between the erotic and the pornographic": "the history of the separation of pornography from eroticism... remains to be written".

Audre Lorde recognises eroticism and pornography as “two diametrically opposed uses of the sexual”, defining the erotic as “a measure between the beginnings of our sense of self and the chaos of our strongest feelings.” In her 1978 essay, Uses of the Erotic: The Erotic as Power, Lorde identifies the erotic as a source of creative power that is deeply rooted in a spiritual plane of unrecognised or unexpressed feeling and sensation.

Psychoanalytical approach
Influenced by Sigmund Freud, psychotherapists have turned to Greek philosophy for an understanding of eros' heightened aesthetic. For Plato, Eros takes an almost transcendent manifestation when the subject seeks to go beyond itself and form a communion with the object/other: "the true order of going...to the things of love, is to use the beauties of earth as steps...to all fair forms, and from fair forms to fair actions, and from fair actions to fair notions, until from fair notions he arrives at the notion of absolute beauty".

French philosophy
Modern French conceptions of eroticism can be traced to the Age of Enlightenment, when "in the eighteenth century, dictionaries defined the erotic as that which concerned love...eroticism was the intrusion into the public sphere of something that was at base private". This theme of intrusion or transgression was taken up in the twentieth century by the French philosopher Georges Bataille, who argued that eroticism performs a function of dissolving boundaries between human subjectivity and humanity, a transgression that dissolves the rational world but is always temporary, as well as that, "Desire in eroticism is the desire that triumphs over the taboo. It presupposes man in conflict with himself". For Bataille, as well as many French theorists, "Eroticism, unlike simple sexual activity, is a psychological quest...eroticism is assenting to life even in death".

Non-heterosexual
Queer theory and LGBT studies consider the concept from a non-heterosexual perspective, viewing psychoanalytical and modernist views of eroticism as both archaic and heterosexist, written primarily by and for a "handful of elite, heterosexual, bourgeois men" who "mistook their own repressed sexual proclivities" as the norm.

Theorists like Eve Kosofsky Sedgwick, Gayle S. Rubin and Marilyn Frye all write extensively about eroticism from a heterosexual, lesbian and separatist point of view, respectively, seeing eroticism as both a political force and cultural critique for marginalized groups, or as Mario Vargas Llosa summarized: "Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual's sovereignty".

Audre Lorde, a lesbian Caribbean-American writer and outspoken feminist, called the erotic a source of power specifically identified with the female, often corrupted or distorted by oppression, since it poses the challenge of change. "For women, this has meant a suppression of the erotic as a considered source of power and information within our lives". In "The Uses of the Erotic" within Sister Outsider, she discusses how the erotic comes from the sharing of joy, "whether physical, emotional, psychic, or intellectual" and provides the basis on which understanding provides a foundation for acknowledging difference. Lorde suggests that if we suppress the erotic rather than recognize its presence, it takes on a different form. Rather than enjoying and sharing with one another, it becomes objectifying, which she says translates into abuse as we attempt to hide and suppress our experiences.

title: Eroticism


text:
Imaginary unit

The imaginary unit or unit imaginary number ($i$) is a solution to the quadratic equation $x + 1 = 0.$ Although there is no real number with this property, $i$ can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of $i$ in a complex number is $2 + 3i.$

Imaginary numbers are an important mathematical concept; they extend the real number system $$\mathbb{R}$$ to the complex number system $$\mathbb{C},$$ in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square.

There are two complex square roots of $−1:$ $i$ and $−i$, just as there are two complex square roots of every real number other than zero (which has one double square root).

In contexts in which use of the letter $i$ is ambiguous or problematic, the letter $i$ is sometimes used instead. For example, in electrical engineering and control systems engineering, the imaginary unit is normally denoted by $j$ instead of $j$, because $i$ is commonly used to denote electric current.

Terminology
Square roots of negative numbers are called imaginary because in early-modern mathematics, only what are now called real numbers, obtainable by physical measurements or basic arithmetic, were considered to be numbers at all – even negative numbers were treated with skepticism – so the square root of a negative number was previously considered undefined or nonsensical. The name imaginary is generally credited to René Descartes, and Isaac Newton used the term as early as 1670. The $i$ notation was introduced by Leonhard Euler.

A unit is an undivided whole, and unity or the unit number is the number 1|one ($1$).

Definition
The imaginary unit $i$ is defined solely by the property that its square is −1: $$i^2 = -1.$$

With $i$ defined this way, it follows directly from algebra that $i$ and $−i$ are both square roots of −1.

Although the construction is called "imaginary", and although the concept of an imaginary number may be intuitively more difficult to grasp than that of a real number, the construction is valid from a mathematical standpoint. Real number operations can be extended to imaginary and complex numbers, by treating $i$ as an unknown quantity while manipulating an expression (and using the definition to replace any occurrence of $i$ with $−1$). Higher integral powers of $i$ are thus $$\begin{alignat}{3} i^3 &= i^2 i &&= (-1) i &&= -i, \\[3mu] i^4 &= i^3 i &&= \;\!(-i) i &&= \ \,1, \\[3mu] i^5 &= i^4 i &&= \ \, (1) i &&= \ \ i, \end{alignat}$$ and so on, cycling through the four values $1$, $i$, $−1$, and $−i$. As with any non-zero real number, $i = 1.$

As a complex number, $i$ can be represented in rectangular form as $0 + 1i$, with a zero real component and a unit imaginary component. In polar form, $i$ can be represented as $1 × e$ (or just $e$), with an absolute value (or magnitude) of 1 and an argument (or angle) of $$\tfrac\pi2$$ radians. (Adding any integer multiple of $2π$ to this angle works as well.) In the complex plane, which is a special interpretation of a Cartesian plane, $i$ is the point located one unit from the origin along the imaginary axis (which is orthogonal to the real axis).

i vs. −i
Being a quadratic polynomial with no multiple root, the defining equation $x = −1$ has two distinct solutions, which are equally valid and which happen to be additive and multiplicative inverses of each other. Although the two solutions are distinct numbers, their properties are indistinguishable; there is no property that one has that the other does not. One of these two solutions is labelled $+i$ (or simply $i$) and the other is labelled $−i$, though it is inherently ambiguous which is which.

The only differences between $+i$ and $−i$ arise from this labelling. For example, by convention $+i$ is said to have an argument of $$+\tfrac\pi2$$ and $−i$ is said to have an argument of $$-\tfrac\pi2,$$ related to the convention of labelling orientations in the Cartesian plane relative to the positive $i$-axis with positive angles turning anticlockwise in the direction of the positive $i$-axis. Despite the signs written with them, neither $+i$ nor $−i$ is inherently positive or negative in the sense that real numbers are.

A more formal expression of this indistinguishability of $+i$ and $−i$ is that, although the complex field is unique (as an extension of the real numbers) up to isomorphism, it is not unique up to a unique isomorphism. That is, there are two field automorphisms of the complex numbers $$\C$$ that keep each real number fixed, namely the identity and complex conjugation. For more on this general phenomenon, see Galois group.

Matrices
Using the concepts of matrices and matrix multiplication, complex numbers can be represented in linear algebra. The real unit $1$ and imaginary unit $x$ can be represented by any pair of matrices $y$ and $i$ satisfying $I = I,$ $IJ = JI = J,$ and $J = −I.$ Then a complex number $a + bi$ can be represented by the matrix $aI + bJ,$ and all of the ordinary rules of complex arithmetic can be derived from the rules of matrix arithmetic.

The most common choice is to represent $1$ and $I$ by the $2 × 2$ identity matrix $J$ and the matrix $i$,

$$ I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \quad J = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}.$$

Then an arbitrary complex number $a + bi$ can be represented by:

$$aI + bJ = \begin{pmatrix} a & -b \\ b & a \end{pmatrix}.$$

More generally, any real-valued $2 × 2$ matrix with a trace of zero and a determinant of one squares to $−I$, so could be chosen for $I$. Larger matrices could also be used; for example, $1$ could be represented by the $4 × 4$ identity matrix and $J$ could be represented by any of the Dirac matrices for spatial dimensions.

Root of $x^{2} + 1$
Polynomials (weighted sums of the powers of a variable) are a basic tool in algebra. Polynomials whose coefficients are real numbers form a ring, denoted $$\R[x],$$ an algebraic structure with addition and multiplication and sharing many properties with the ring of integers.

The polynomial $$x^2 + 1$$ has no real-number roots, but the set of all real-coefficient polynomials divisible by $$x^2 + 1$$ forms an ideal, and so there is a quotient ring $$\reals[x] / \langle x^2 + 1\rangle.$$ This quotient ring is isomorphic to the complex numbers, and the variable $$x$$ expresses the imaginary unit.

Graphic representation
The complex numbers can be represented graphically by drawing the real number line as the horizontal axis and the imaginary numbers as the vertical axis of a Cartesian plane called the complex plane. In this representation, the numbers $1$ and $J$ are at the same distance from $0$, with a right angle between them. Addition by a complex number corresponds to translation in the plane, while multiplication by a unit-magnitude complex number corresponds to rotation about the origin. Every similarity transformation of the plane can be represented by a complex-linear function $$z \mapsto az + b.$$

Geometric algebra
In the geometric algebra of the Euclidean plane, the geometric product or quotient of two arbitrary vectors is a sum of a scalar (real number) part and a bivector part. (A scalar is a quantity with no orientation, a vector is a quantity oriented like a line, and a bivector is a quantity oriented like a plane.) The square of any vector is a positive scalar, representing its length squared, while the square of any bivector is a negative scalar.

The quotient of a vector with itself is the scalar $1 = u/u$, and when multiplied by any vector leaves it unchanged (the identity transformation). The quotient of any two perpendicular vectors of the same magnitude, $J = u/v$, which when multiplied rotates the divisor a quarter turn into the dividend, $Jv = u$, is a unit bivector which squares to $−1$, and can thus be taken as a representative of the imaginary unit. Any sum of a scalar and bivector can be multiplied by a vector to scale and rotate it, and the algebra of such sums is isomorphic to the algebra of complex numbers. In this interpretation points, vectors, and sums of scalars and bivectors are all distinct types of geometric objects.

More generally, in the geometric algebra of any higher-dimensional Euclidean space, a unit bivector of any arbitrary planar orientation squares to $−1$, so can be taken to represent the imaginary unit $i$.

Proper use
The imaginary unit was historically written $\sqrt{-1},$ and still is in some modern works. However, great care needs to be taken when manipulating formulas involving radicals. The radical sign notation $\sqrt{x}$ is reserved either for the principal square root function, which is defined for only real $x ≥ 0,$ or for the principal branch of the complex square root function. Attempting to apply the calculation rules of the principal (real) square root function to manipulate the principal branch of the complex square root function can produce false results: $$-1 = i \cdot i = \sqrt{-1} \cdot \sqrt{-1} \mathrel{\stackrel{\mathrm{fallacy}}{=}} {\textstyle \sqrt{(-1) \cdot (-1)}} = \sqrt{1} = 1 \qquad \text{(incorrect).}$$

Generally, the calculation rules $\sqrt{x\vphantom{ty}} \cdot\! \sqrt{y\vphantom{ty}} = \sqrt{x \cdot y\vphantom{ty}}$ and $\sqrt{x\vphantom{ty}}\big/\!\sqrt{y\vphantom{ty}} = \sqrt{x/y}$ are guaranteed to be valid for real, positive values of $i$ and $i$ only.

When $x$ or $y$ is real but negative, these problems can be avoided by writing and manipulating expressions like $i \sqrt{7}$, rather than $\sqrt{-7}$. For a more thorough discussion, see the articles Square root and Branch point.

Properties
As a complex number, the imaginary unit follows all of the rules of complex arithmetic.

Imaginary integers and imaginary numbers
When the imaginary unit is repeatedly added or subtracted, the result is some integer times the imaginary unit, an imaginary integer; any such numbers can be added and the result is also an imaginary integer:

$$ai + bi = (a + b)i.$$

Thus, the imaginary unit is the generator of a group under addition, specifically an infinite cyclic group.

The imaginary unit can also be multiplied by any arbitrary real number to form an imaginary number. These numbers can be pictured on a number line, the imaginary axis, which as part of the complex plane is typically drawn with a vertical orientation, perpendicular to the real axis which is drawn horizontally.

Gaussian integers
Integer sums of the real unit $1$ and the imaginary unit $i$ form a square lattice in the complex plane called the Gaussian integers. The sum, difference, or product of Gaussian integers is also a Gaussian integer:

$$\begin{align} (a + bi) + (c + di) &= (a + c) + (b + d)i, \\[5mu] (a + bi)(c + di) &= (ac - bd) + (ad + bc)i. \end{align}$$

Quarter-turn rotation
When multiplied by the imaginary unit $x$, any arbitrary complex number in the complex plane is rotated by a quarter turn ($\tfrac12\pi$ radians or $90°$) anticlockwise. When multiplied by $−i$, any arbitrary complex number is rotated by a quarter turn clockwise. In polar form:

$$i \, re^{\varphi i} = re^{(\varphi + \pi/2)i}, \quad -i \, re^{\varphi i} = re^{(\varphi - \pi/2)i}.$$

In rectangular form,

$$ i(a + bi) = -b + ai, \quad -i(a + bi) = b - ai.$$

Integer powers
The powers of $y$ repeat in a cycle expressible with the following pattern, where $i$ is any integer:

$$ i^{4n} = 1, \quad i^{4n+1} = i, \quad i^{4n+2} = -1, \quad i^{4n+3} = -i.$$

Thus, under multiplication, $i$ is a generator of a cyclic group of order 4, a discrete subgroup of the continuous circle group of the unit complex numbers under multiplication.

Written as a special case of Euler's formula for an integer $i$,

$$ i^n = {\exp}\bigl(\tfrac12\pi i\bigr)^n = {\exp}\bigl(\tfrac12 n \pi i\bigr) = {\cos}\bigl(\tfrac12 n\pi \bigr) + {i \sin}\bigl(\tfrac12 n\pi \bigr). $$

With a careful choice of branch cuts and principal values, this last equation can also apply to arbitrary complex values of $n$, including cases like $n = i$.

Roots
Just like all nonzero complex numbers, $i = e^{\pi i/ 2}$ has two distinct square roots which are additive inverses. In polar form, they are $$\begin{alignat}{3} \sqrt{i} &= {\exp}\bigl(\tfrac12{\pi i}\bigr)^{1/2} &&{}= {\exp}\bigl(\tfrac14\pi i\bigr), \\ -\sqrt{i} &= {\exp}\bigl(\tfrac14{\pi i}-\pi i\bigr) &&{}= {\exp}\bigl({-\tfrac34\pi i}\bigr). \end{alignat}$$

In rectangular form, they are

$$\begin{alignat}{3} \sqrt{i} &= \ (1 + i)\big/ \sqrt2 &&{}= \phantom{-}\tfrac{\sqrt{2}}{2} + \tfrac{\sqrt{2}}{2}i, \\[5mu] -\sqrt{i} &= -(1 + i)\big/ \sqrt2 &&{}= - \tfrac{\sqrt{2}}{2} - \tfrac{\sqrt{2}}{2}i. \end{alignat}$$

Squaring either expression yields $$ \left( \pm \frac{1 + i}{\sqrt2} \right)^2 = \frac{1 + 2i - 1}{2} = \frac{2i}{2} = i. $$

The three cube roots of $i$ are

$$ \sqrt[3]i = {\exp}\bigl(\tfrac16 \pi i\bigr) = \tfrac{\sqrt{3}}{2} + \tfrac12i, \quad {\exp}\bigl(\tfrac56 \pi i\bigr) = -\tfrac{\sqrt{3}}{2} + \tfrac12i, \quad {\exp}\bigl({-\tfrac12 \pi i}\bigr) = -i. $$

For a general positive integer $n$, the $n$-th roots of $i$ are, for $(x + iy)2 = i$ $$ \exp \left(2 \pi i \frac{k+\frac14}{n} \right) = \cos \left(\frac{4k+1}{2n}\pi \right) + i \sin \left(\frac{4k+1}{2n}\pi \right). $$ The value associated with $x + 2ixy - y = i.$ is the principal $x$-th root of $y$. The set of roots equals the corresponding set of roots of unity rotated by the principal $x$-th root of $x$. These are the vertices of a regular polygon inscribed within the complex unit circle.

Exponential and logarithm
The complex exponential function relates complex addition in the domain to complex multiplication in the codomain. Real values in the domain represent scaling in the codomain (multiplication by a real scalar) with $x - y + 2ixy = 0 + i.$ representing multiplication by $y$, while imaginary values in the domain represent rotation in the codomain (multiplication by a unit complex number) with $i$ representing a rotation by $2xy = 1$ radian. The complex exponential is thus a periodic function in the imaginary direction, with period $k = 0, 1, ..., n − 1,$ and image $k = 0$ at points $1$ for all integers $i$, a real multiple of the lattice of imaginary integers.

The complex exponential can be broken into even and odd components, the hyperbolic functions $1$ and $2πi$ or the trigonometric functions $1$ and $2kπi$:

$$\exp z = \cosh z + \sinh z = \cos(-iz) + i\sin(-iz)$$

Euler's formula decomposes the exponential of an imaginary number representing a rotation:

$$\exp i\varphi = \cos \varphi + i\sin \varphi.$$

The quotient $cosh$ with appropriate scaling, can be represented as an infinite partial fraction decomposition as the sum of reciprocal functions translated by imaginary integers: $$ \pi \coth \pi z = \lim_{n\to\infty}\sum_{k=-n}^n \frac{1}{z + ki}. $$

Other functions based on the complex exponential are well-defined with imaginary inputs. For example, a number raised to the $i$ power is: $$x^{n i} = \cos(n\ln x) + i \sin(n\ln x ).$$

Because the exponential is periodic, its inverse the complex logarithm is a multi-valued function, with each complex number in the domain corresponding to multiple values in the codomain, separated from each-other by any integer multiple of $sinh$ One way of obtaining a single-valued function is to treat the codomain as a cylinder, with complex values separated by any integer multiple of $cos$ treated as the same value; another is to take the domain to be a Riemann surface consisting of multiple copies of the complex plane stitched together along the negative real axis as a branch cut, with each branch in the domain corresponding to one infinite strip in the codomain. Functions depending on the complex logarithm therefore depend on careful choice of branch to define and evaluate clearly.

For example, if one chooses any branch where $$\ln i = \tfrac12 \pi i$$ then when $i$ is a positive real number, $$ \log_i x = -\frac{2i \ln x }{\pi}.$$

Factorial
The factorial of the imaginary unit $n$ is most often given in terms of the gamma function evaluated at $sin$:

$$i! = \Gamma(1+i) = i\Gamma(i) \approx 0.4980 - 0.1549\,i.$$

The magnitude and argument of this number are:

$$ \arg{\Gamma(1+i)} \approx -0.3016. $$
 * \Gamma(1+i)| = \sqrt{\frac{\pi}{ \sinh \pi}} \approx 0.5216, \quad

title: Imaginary unit