text: User talk:80.116.222.125

title: User talk:80.116.222.125


text:
Beth number

In mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written $$\beth_0, \beth_1, \beth_2, \beth_3, \dots$$, where $$\beth$$ is the Hebrew letter beth. The beth numbers are related to the aleph numbers ($$\aleph_0, \aleph_1, \dots$$), but unless the generalized continuum hypothesis is true, there are numbers indexed by $$\aleph$$ that are not indexed by $$\beth$$.

Definition
Beth numbers are defined by transfinite recursion:

 * $$\beth_0 = \aleph_0,$$
 * $$\beth_{\alpha+1} = 2^{\beth_\alpha},$$
 * $$\beth_\lambda = \sup\Bigl\{ \beth_\alpha : \alpha < \lambda \Bigr\},$$

where $$\alpha$$ is an ordinal and $$\lambda$$ is a limit ordinal.

The cardinal $$\beth_0 = \aleph_0$$ is the cardinality of any countably infinite set such as the set $$\mathbb{N}$$ of natural numbers, so that $$\beth_0 = |\mathbb{N}|$$.

Let $$\alpha$$ be an ordinal, and $$A_\alpha$$ be a set with cardinality $$\beth_\alpha = |A_\alpha|$$. Then,

 * $$\mathcal{P}(A_\alpha)$$ denotes the power set of $$A_\alpha$$ (i.e., the set of all subsets of $$A_\alpha$$),

 * the set $$2^{A_\alpha} \subset \mathcal{P}(A_\alpha \times 2)$$ denotes the set of all functions from $$A_\alpha$$ to $$\{0, 1\}$$,

 * the cardinal $$2^{\beth_\alpha}$$ is the result of cardinal exponentiation, and

 * $$\beth_{\alpha+1} = 2^{\beth_\alpha} = \left| 2^{A_\alpha} \right| = |\mathcal{P}(A_\alpha)|$$ is the cardinality of the power set of $$A_\alpha$$.

Given this definition,

 * $$\beth_0, \beth_1, \beth_2, \beth_3, \dots$$

are respectively the cardinalities of

 * $$\mathbb{N}, \mathcal{P}(\mathbb{N}), \mathcal{P}(\mathcal{P}(\mathbb{N})), \mathcal{P}(\mathcal{P}(\mathcal{P}(\mathbb{N}))), \dots$$

so that the second beth number $$\beth_1$$ is equal to $$\mathfrak{c}$$, the cardinality of the continuum (the cardinality of the set of the real numbers), and the third beth number $$\beth_2$$ is the cardinality of the power set of the continuum.

Because of Cantor's theorem, each set in the preceding sequence has cardinality strictly greater than the one preceding it. For infinite limit ordinals $$\lambda$$, the corresponding beth number is defined to be the supremum of the beth numbers for all ordinals strictly smaller than $$\lambda$$:

 * $$\beth_\lambda = \sup \Bigl\{ \beth_{\alpha} : \alpha < \lambda \Bigr\}.$$

One can show that this definition is equivalent to

 * $$\beth_\lambda = |\bigcup \Bigl\{ A_{\alpha} : \alpha < \lambda \Bigr\}|.$$

For instance:

 * $$\beth_\omega$$ is the cardinality of $$\bigcup \Bigl\{\mathbb{N}, \mathcal{P}(\mathbb{N}), \mathcal{P}(\mathcal{P}(\mathbb{N})), \mathcal{P}(\mathcal{P}(\mathcal{P}(\mathbb{N}))), \dots \Bigr\}$$.
 * $$\beth_{2\omega}$$ is the cardinality of $$\bigcup \Bigl\{\mathbb{N}, \mathcal{P}(\mathbb{N}), \mathcal{P}(\mathcal{P}(\mathbb{N})), \mathcal{P}(\mathcal{P}(\mathcal{P}(\mathbb{N}))), \dots, {A_\omega}, \mathcal{P}({A_\omega}), \mathcal{P}(\mathcal{P}({A_\omega})), \mathcal{P}(\mathcal{P}(\mathcal{P}({A_\omega}))), \dots\Bigr\}$$.
 * $$\beth_{\omega^2}$$ is the cardinality of $$\bigcup \Bigl\{\mathbb{N}, \mathcal{P}(\mathbb{N}), \mathcal{P}(\mathcal{P}(\mathbb{N})), \mathcal{P}(\mathcal{P}(\mathcal{P}(\mathbb{N}))), \dots, {A_\omega}, \mathcal{P}({A_\omega}), \mathcal{P}(\mathcal{P}({A_\omega})), \dots, {A_{2\omega}}, \mathcal{P}({A_{2\omega}}), \mathcal{P}(\mathcal{P}({A_{2\omega}})), \dots, $$ $$ {A_{3\omega}}, \mathcal{P}({A_{3\omega}}), \mathcal{P}(\mathcal{P}({A_{3\omega}})), \dots, \dots \Bigr\}$$.

This equivalence can be shown by seeing that:

 * for any set $$\mathbb{S}$$, the union set of all its members can be no larger than the supremum of its member cardinalities times its own cardinality, $$|\bigcup\mathbb{S}|\le \Bigl(|\mathbb{S}| \times \sup\Bigl\{|s|:s\in\mathbb{S}\Bigr\}\Bigr)$$
 * for any two non-zero cardinalities $$\kappa_a, \kappa_b$$, if at least one of them is an infinite cardinality, then the product will be the larger of the two, $$\kappa_a \times \kappa_b = \max\{\kappa_a, \kappa_b\}$$
 * the set $$\Bigl\{ A_{\alpha} : \alpha < \lambda \Bigr\}$$ will be smaller than most or all of its subsets for any limit ordinal $$\lambda$$
 * therefore, $$|\bigcup\Bigl\{ A_{\alpha} : \alpha < \lambda \Bigr\}|=\sup \Bigl\{ \beth_{\alpha} : \alpha < \lambda \Bigr\}$$ for any limit ordinal $$\lambda$$

Note that this behavior is different from that of successor ordinals. Cardinalities less than $$\beth_\beta$$ but greater than any $$\beth_\alpha: \alpha<\beta$$ can exist when $$\beta$$ is a successor ordinal (in that case, the existence is undecidable in ZFC and controlled by the Generalized Continuum Hypothesis); but cannot exist when $$\beta$$ is a limit ordinal, even under the second definition presented.

One can also show that the von Neumann universes $$V_{\omega+\alpha}$$ have cardinality $$\beth_{\alpha}$$.

Relation to the aleph numbers
Assuming the axiom of choice, infinite cardinalities are linearly ordered; no two cardinalities can fail to be comparable. Thus, since by definition no infinite cardinalities are between $$\aleph_0$$ and $$\aleph_1$$, it follows that
 * $$\beth_1 \ge \aleph_1.$$

Repeating this argument (see transfinite induction) yields $$\beth_\alpha \ge \aleph_\alpha$$ for all ordinals $$\alpha$$.

The continuum hypothesis is equivalent to
 * $$\beth_1=\aleph_1.$$

The generalized continuum hypothesis says the sequence of beth numbers thus defined is the same as the sequence of aleph numbers, i.e., $$\beth_\alpha = \aleph_\alpha$$ for all ordinals $$\alpha$$.

Beth null
Since this is defined to be $$\aleph_0$$, or aleph null, sets with cardinality $$\beth_0$$ include:

 * the natural numbers $$\mathbb{N}$$
 * the rational numbers $$\mathbb{Q}$$
 * the algebraic numbers $$\mathcal{A}$$
 * the computable numbers and computable sets
 * the set of finite sets of integers or of rationals or of algebraic numbers
 * the set of finite multisets of integers
 * the set of finite sequences of integers.

Beth one
Sets with cardinality $$\beth_1$$ include:

 * the transcendental numbers
 * the irrational numbers
 * the real numbers $$\mathbb{R}$$
 * the complex numbers $$\mathbb{C}$$
 * the uncomputable real numbers
 * Euclidean space $$\mathbb{R}^n$$
 * the power set of the natural numbers $$2^\mathbb{N}$$ (the set of all subsets of the natural numbers)
 * the set of sequences of integers (i.e., $$\mathbb{Z}^\mathbb{N}$$, which includes all functions from $$\mathbb{N}$$ to $$\mathbb{Z}$$)
 * the set of sequences of real numbers, $$\mathbb{R}^\mathbb{N}$$
 * the set of all real analytic functions from $$\mathbb{R}$$ to $$\mathbb{R}$$
 * the set of all continuous functions from $$\mathbb{R}$$ to $$\mathbb{R}$$
 * the set of all functions from $$\mathbb{R}$$ to $$\mathbb{R}$$ with at most countable discontinuities
 * the set of finite subsets of real numbers
 * the set of all analytic functions from $$\mathbb{C}$$ to $$\mathbb{C}$$ (the holomorphic functions)
 * the set of all functions from the natural numbers to the natural numbers ($$\mathbb{N}^\mathbb{N}$$).

Beth two
$$\beth_2$$ (pronounced beth two) is also referred to as $$2^\mathfrak{c}$$ (pronounced ''two to the power of $$\mathfrak{c}$$).

Sets with cardinality $$\beth_2$$ include:

 * the power set of the set of real numbers, so it is the number of subsets of the real line, or the number of sets of real numbers
 * the power set of the power set of the set of natural numbers
 * the set of all functions from $$\mathbb{R}$$ to $$\mathbb{R}$$ ($$\mathbb{R}^\mathbb{R}$$)
 * the set of all functions from $$\mathbb{R}^m$$ to $$\mathbb{R}^n$$
 * the set of all functions from $$\mathbb{R}$$ to $$\mathbb{R}$$ with uncountably many discontinuities
 * the power set of the set of all functions from the set of natural numbers to itself, or the number of sets of sequences of natural numbers
 * the Stone–Čech compactifications of $$\mathbb{R}$$, $$\mathbb{Q}$$, and $$\mathbb{N}$$
 * the set of deterministic fractals in $$\mathbb{R}^n$$
 * the set of random fractals in $$\mathbb{R}^n$$.

Beth omega
$$\beth_\omega$$ (pronounced beth omega) is the smallest uncountable strong limit cardinal.

Generalization
The more general symbol $$\beth_\alpha(\kappa)$$, for ordinals $$\alpha$$ and cardinals $$\kappa$$, is occasionally used. It is defined by:
 * $$\beth_0(\kappa)=\kappa,$$
 * $$\beth_{\alpha+1}(\kappa)=2^{\beth_\alpha(\kappa)},$$
 * $$\beth_\lambda(\kappa)=\sup\{ \beth_\alpha(\kappa):\alpha<\lambda \}$$ if λ is a limit ordinal.

So
 * $$\beth_\alpha=\beth_\alpha(\aleph_0).$$

In Zermelo–Fraenkel set theory (ZF), for any cardinals $$\kappa$$ and $$\mu$$, there is an ordinal $$\alpha$$ such that:

 * $$\kappa \le \beth_\alpha(\mu).$$

And in ZF, for any cardinal $$\kappa$$ and ordinals $$\alpha$$ and $$\beta$$:

 * $$\beth_\beta(\beth_\alpha(\kappa)) = \beth_{\alpha+\beta}(\kappa).$$

Consequently, in ZF absent ur-elements, with or without the axiom of choice, for any cardinals $$\kappa$$ and $$\mu$$, the equality

 * $$\beth_\beta(\kappa) = \beth_\beta(\mu)$$

holds for all sufficiently large ordinals $$\beta$$. That is, there is an ordinal $$\alpha$$ such that the equality holds for every ordinal $$\beta \geq \alpha$$.

This also holds in Zermelo–Fraenkel set theory with ur-elements (with or without the axiom of choice), provided that the ur-elements form a set which is equinumerous with a pure set (a set whose transitive closure contains no ur-elements). If the axiom of choice holds, then any set of ur-elements is equinumerous with a pure set.

Borel determinacy
Borel determinacy is implied by the existence of all beths of countable index.

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

title: Beth number


text:
Chinese People's Liberation Army Forces Hong Kong Building

The Chinese People's Liberation Army Forces Hong Kong Building is the headquarters building of the People's Liberation Army Hong Kong Garrison, located on Lung Wui Road, Admiralty, Hong Kong.

It is a 113-metre (371 ft) tall, 28-floor building located within the former HMS Tamar naval base. The building is also known by its former name the Prince of Wales Building.

History
Constructed in 1979, the building was named the Prince of Wales Building. It housed the head office of the Royal Navy stationed in Hong Kong until the territory's handover to the People's Republic of China on 1 July 1997 when it was made the head office of the PLA Hong Kong Garrison. In May 2000, the Legislative Council of Hong Kong passed the Military Installations Closed Areas (Amendment) Order 2000, which renamed the former Prince of Wales Barracks to Central Barracks, and the Prince of Wales Building to the Chinese People's Liberation Army Forces Hong Kong Building. After the base became the Central Barracks, the old name of the building remained visible in large raised letters along the bottom of the tower for several years. The building underwent a 20-month full renovation, completed in 2014, during which most of the troops were transferred to the Stonecutters Island base.

Due to its distinctive shape, likened to a wineglass, the building stands out from the rest of the Admiralty waterfront buildings. Architects attribute the shape of the building to passive protection, its narrow stem with the protruding upper storeys, supposedly makes it difficult to climb or attack. It is also informally known as 'the upside-down Gin bottle' due to its shape resembling a bottle of Gordon's Gin. The corner of the building at the podium level which faces east (towards Admiralty MTR station) used to be a chapel under British use of the barracks. There used to be a crucifix visible on the exterior—however, during external refurbishment (including replacing the 'Prince of Wales Building' inscription in English with its current name in Chinese) in 2001, the cross was removed. This was despite initial claims the cross would be retained.

People's Liberation Army in Hong Kong
The PLA maintains a number of garrisons in the Hong Kong Special Administrative Region. In addition to the PLA Forces Hong Kong Building, there are notable garrisons at the Stonecutters Island, and at Stanley Fort. Soldiers located at these three garrisons are considered to be the élite of the PLA. The soldiers are not permitted to leave their compounds, even during off-duty times to mingle with the local populace. As a restricted area, the PLA Forces Hong Kong Building is heavily guarded by soldiers with automatic rifles.


text:
Historia Augusta

The Historia Augusta (English: Augustan History) is a late Roman collection of biographies, written in Latin, of the Roman emperors, their junior colleagues, designated heirs and usurpers from 117 to 284. Supposedly modeled on the similar work of Suetonius, The Twelve Caesars, it presents itself as a compilation of works by six different authors, collectively known as the Scriptores Historiae Augustae, written during the reigns of Diocletian and Constantine I and addressed to those emperors or other important personages in Ancient Rome. The collection, as extant, comprises thirty biographies, most of which contain the life of a single emperor, but some include a group of two or more, grouped together merely because these emperors were either similar or contemporaneous.

The true authorship of the work, its actual date, its reliability and its purpose have long been matters for controversy by historians and scholars ever since Hermann Dessau, in 1889, rejected both the date and the authorship as stated within the manuscript. Major problems include the nature of the sources that it used, and how much of the content is pure fiction. For instance, the collection contains in all about 150 alleged documents, including 68 letters, 60 speeches and proposals to the people or the senate, and 20 senatorial decrees and acclamations.

By the second decade of the 21st century, the consensus supported the position that there was only a single author, who wrote either in the late 4th century or the early 5th century, who was interested in blending contemporary issues (political, religious and social) into the lives of the 3rd century emperors. There is further consensus that the author used the fictitious elements in the work to highlight references to other published works, such as to Cicero and Ammianus Marcellinus, in a complex allegorical game. Despite the conundrums, it is the only continuous account in Latin for much of its period and so is continually being re-evaluated. Modern historians are unwilling to abandon it as a unique source of possible information, despite its obvious untrustworthiness on many levels.

Title and scope
The name Historia Augusta originated with Isaac Casaubon, who produced a critical edition in 1603, working from a complex manuscript tradition with a number of variant versions. The title as recorded on the Codex Palatinus manuscript, written in the 9th century, is Vitae Diversorum Principum et Tyrannorum a Divo Hadriano usque ad Numerianum Diversis compositae ("The Lives of various Emperors and Tyrants from the Divine Hadrian to Numerian by Various Authors"). It is assumed that the work may have been originally called de Vita Caesarum or Vitae Caesarum ("Lives of the Caesars").

How widely the work was circulated in late antiquity is unknown, but its earliest known use was in a Roman History composed by Quintus Aurelius Memmius Symmachus in 485. Lengthy citations from it are found in authors of the 6th and 9th centuries, including Sedulius Scottus who quoted parts of the Marcus Aurelius, the Maximini and the Aurelian within his Liber de Rectoribus Christianis, and the chief manuscripts also date from the 9th or 10th centuries. The six Scriptores – "Aelius Spartianus", "Julius Capitolinus", "Vulcacius Gallicanus", "Aelius Lampridius", "Trebellius Pollio", and "Flavius Vopiscus (of Syracuse)" – dedicate their biographies to Diocletian, Constantine and various private persons, and so ostensibly were all writing around the late 3rd and early 4th century. The first four scriptores are attached to the lives from Hadrian to Gordian III, while the final two are attached to the lives from Valerian to Numerian.

The biographies cover the emperors from Hadrian to Carinus and Numerian. A section covering the reigns of Philip the Arab, Decius, Trebonianus Gallus, Aemilian and all but the end of the reign of Valerian is missing in all the manuscripts, and it has been argued that biographies of Nerva and Trajan have also been lost at the beginning of the work, which may suggest the compilation might have been a direct continuation of Suetonius' The Twelve Caesars. It has been theorized that the mid-3rd-century lacuna might actually be a deliberate literary device of the author or authors, saving the labour of covering Emperors for whom little source material may have been available.

Despite devoting whole books to ephemeral or in some cases non-existent usurpers, there are no independent biographies of the factual, but short reigns of Emperors Quintillus and Florian, whose reigns are merely briefly noted towards the end of the biographies of their respective predecessors, Claudius Gothicus and Tacitus. For nearly 300 years after Casaubon's edition, though much of the Historia Augusta was treated with some scepticism, it was used by historians as an authentic source – Edward Gibbon used it extensively in the first volume of the Decline and Fall of the Roman Empire. However, "in modern times most scholars read the work as a piece of deliberate mystification written much later than its purported date, however the fundamentalist view still has distinguished support. (...) The Historia Augusta is also, unfortunately, the principal Latin source for a century of Roman history.  The historian must make use of it, but only with extreme circumspection and caution."

Textual transmission
Existing manuscripts and witnesses of the Historia Augusta fall into three groups:

 * 1) A manuscript of the first quarter of the ninth century, Vatican Pal. lat. 899 (Codex Palatinus), known as P, and its direct and indirect copies. P was written at Lorsch in Caroline minuscule. The text in this manuscript has several lacunae marked with dots indicating the missing letters, a confusion in the order of the biographies between Verus and Alexander, and the transposition of several passages: two long ones which correspond to a quire of the original which became loose and was then inserted in a wrong place, and a similar transposition in Carus. P is also distinguished by a succession of six centuries of editorial corrections, beginning with the original scribe, and includes such worthies as Petrarch and Poggio Bracciolini; none of these editors betray any knowledge of any other witness.
 * 2) A group of 15th-century manuscripts, designated as Σ. Not only are the lives rearranged in chronological order, but the corruptions present in P have been subjected to drastic emendations or omitted altogether. Beginning with Ernst Hohl, some have asserted that the improvements in the text come from a source independent of P. Although admitting that "this question still remains to be answered definitively", author Peter Marshall noted that research undertaken through to the 1980s had improved scholarly knowledge concerning the methods and abilities of early Italian humanists, and concludes by saying that "the Σ manuscripts nowhere provide readings which are beyond the powers of the humanists active at the time.
 * 3) Three different sets of excerpts, one of which Theodor Mommsen suggested was possibly the work of Sedulius Scottus. How any are related to P is unclear.

In Marshall's opinion, the best scholarly editions are those by H. Peter (Teubner, 2nd ed. 1884), and E. Hohl (Teubner, 1971, reissue of 1965 revised by Ch. Samberger & W. Seyfarth).

A copy of the Codex Palatinus (possibly the one made for Petrarch in 1356) was the basis of the editio princeps of the History, published in Milan in 1475. A subsequent printed version (the Aldine edition) was published at Venice in 1516, and this was followed closely by an edition edited by Desiderius Erasmus, and published by Johann Froben in Basel in 1518.

Debates on dating
In 1776, Gibbon observed that there was something wrong with the numbers and names of the imperial biographers, and that this had already been recognised by older historians who had written on that subject. A clear example was the referencing of the biographer 'Lampridius' (who was apparently writing his biographies after 324) by 'Vopiscus', who was meant to be writing his biographies in 305–306. Then, in 1889, Hermann Dessau, who had become increasingly concerned by the large number of anachronistic terms, Vulgar Latin vocabulary, and especially the host of obviously false proper names in the work, proposed that the six authors were all fictitious personae, and that the work was in fact composed by a single author in the late 4th century, probably in the reign of Theodosius I. Among his supporting evidence was that the life of Septimius Severus appeared to have made use of a passage from the mid-4th-century historian Aurelius Victor, and that the life of Marcus Aurelius likewise uses material from Eutropius.

In the decades following Dessau, many scholars argued to preserve at least some of the six Scriptores as distinct persons and in favour of the first-hand authenticity for the content. As early as 1890, Theodor Mommsen postulated a Theodosian 'editor' of the Scriptores' work, an idea that has resurfaced many times since. Hermann Peter, editor of the Historia Augusta and of the Historicorum Romanorum reliquiae, proposed a date of 330 for when the work was written, based upon an analysis of style and language. Others, such as Norman H. Baynes, abandoned the early 4th-century date but only advanced it as far as the reign of Julian the Apostate, useful for arguing the work was intended as pagan propaganda.

In the 1960s and 1970s, Dessau's original arguments received powerful restatement and expansion from Sir Ronald Syme, who devoted three books to the subject and was prepared to date the writing of the work closely in the region of AD 395. Other recent studies also show much consistency of style, and most scholars now accept the theory of a single author of unknown identity, writing after 395. Although it was believed that the Historia Augusta did not reference any material from Ammianus Marcellinus' history, which was finished before 391 and which covered the same period, this has now been shown not to be the case, and that the Historia Augusta does in fact make reference to Ammianus' history.

Not all scholars have accepted the theory of a forger working around the last decades of the 4th century or the beginning of the 5th. Arnaldo Momigliano and A. H. M. Jones were the most prominent 20th century critics of the Dessau-Syme theory amongst English-speaking scholars. Momigliano, summarizing the literature from Dessau down to 1954, defined the question as "res iudicanda" (i.e. "a matter to be decided") and not as "res iudicata" ("a matter that has been decided"). Momigliano reviewed every book published on the topic by Sir Ronald Syme, and provided counter arguments to most if not all of Syme's arguments.

For instance, the reference in the Life of Probus about the emperor's descendants which has been taken to refer to Sextus Claudius Petronius Probus (consul in 371) and his family may, in the opinion of Momigliano, equally refer to the earlier members of the family, which was prominent throughout the 4th century, such as Petronius Probinus (consul in 341) and Petronius Probianus (consul in 322). Momigliano's opinion was that there was insufficient evidence to dismiss a composition date of the early 4th century, and that any post-Constantinian anachronisms could be explained by an editor working on the material at a later date, perhaps during the reigns of Constantius II or Julian.

Other opinions included H Stern's, who postulated that the History was composed by a team of writers during the reign of Constantius II after the defeat of Magnentius on behalf of the senatorial aristocracy who had supported the usurper. In the 21st century, Alan Cameron rebutted a number of Syme's and Barnes' arguments for a composition date c. 395–400, suggesting a composition date between 361 and the 380s.

Authorship debate
Linked to the problem of dating the composition of the History is the question about the authorship of the work. Taking the History at face value, there is clearly a division between the authors named prior and after the presence of the interrupting lacuna. For the first half of the History, four scriptores are present, and the biographies are divided in a remarkably erratic fashion:
 * Aelius Spartianus (7 lives): Hadrian, Aelius, Didius Julianus, Severus, Niger, Caracalla and Geta.
 * Julius Capitolinus (9 lives): Antoninus, Marcus, Lucius Verus, Pertinax, Albinus, Macrinus, The Maximini, The Gordiani, and Maximus and Balbinus.
 * Vulcacius Gallicanus (1 life): Avidius Cassius.
 * Aelius Lampridius (4 lives): Commodus, Diadumenus, Heliogabalus and Severus Alexander.

Of these four, Spartianus and Gallicanus claim to be undertaking a complete set of imperial biographies from Julius Caesar onwards, while Lampridius' stated intention was to write a collection of biographies that would deal with the Gordians, Claudius II, Aurelian, Diocletian, Maximian and the four rivals of Constantine. Capitolinus also implied that he was writing more biographies than are present in the History.

The second half of the History is divided between two scriptores. Unlike the first half, the emperors tackled in this section are grouped logically, and are divided roughly in half between the two scriptores in chronological sequence:
 * Trebellius Pollio (4 lives): Valerian, Gallienus, Tyranni Triginta and Claudius.
 * Flavius Vopiscus Syracusanus (5 lives): Aurelian, Tacitus, Probus, Quadrigae Tyrannorum and Carus, Carinus and Numerian.

In terms of any acknowledgement of the mutual existence between the scriptores, only Flavius Vopiscus, ostensibly writing in 305 or 306, refers to any of the other authors, specifically Trebellius Pollio, Julius Capitolinus and Aelius Lampridius. None of the other five demonstrate any awareness of the existence of any of their 'colleagues'. However, these references cause difficulties when these authors also address Constantine in their dedications, as Vopiscus was also doing. For instance, Capitolinus mostly addresses Diocletian, but in the Albinus, Maximini and Gordiani he addresses Constantine in a fashion that suggests he is writing after 306.

The theory that there was a single author, as initially postulated by Hermann Dessau, is based on the difficulties inherent in having a single work comprising a number of individuals but without any textual evidence of an editor who brought the material together. This is especially evident in that the text has examples of stated intentions by an author to write a life of one of the emperors, only for that life to be completed by another of the scriptores. If those statements are true, and those additional lives were completed, then an editor must have been involved in the project in order to select one scriptor's life over another's.

The presence of a post-Constantinian editor, as originally postulated by Theodor Mommsen, still has notable support, most recently articulated by Daniel Den Hengst, who suggests that the editor was the author of the second half of the History, operating under the pseudonyms of Pollio and Vopiscus. Further, that this editor not only wrote the secondary lives in the first half, but he was responsible for the insertions into the primary lives in that series. He takes the view that the vast stylistic differences between the two halves of the History means they cannot have been written by the same author.

If the validity of six independent authors is accepted, there are still issues, as the way they approached their work shows similar themes and details. All six not only provide biographies for the emperors, but also for the Caesars and usurpers. They describe their work and approach in very similar language, and quote otherwise unknown historians and biographers, such as Junius Cordus. They collectively share many errors, such as calling Diadumenianus "Diadumenus". They share much idiosyncratic content and similar language, with particular focus on women, wine and military discipline, and were fixated on poor-quality plays on words ascribing personality traits to certain emperors, for instance Verus was truthful, while Severus was a severe individual.

The authors shared certain stylistic characteristics that has been suggested would not naturally occur between individuals writing separately. For instance, the authors all happen to use the word occido with respect to killing, a total of 42 occurrences, but only once do any of them use the alternative word of interficio. This ratio is not found with any other writers in this time period and for this genre. Each of the six scriptores authored fictional lives for some of their biographies, all of them using fake sources, documents and acclamations.

It has been postulated that the names of the scriptores themselves are a form of literary playfulness, not only mocking both legitimate authors and historians, but the narrative itself. The names Trebellius Pollio and Flavius Vopiscus are sourced in various ways from Cicero's writings, as is the name Capitolinus. The word vopiscus is a rare Latin term, referring to a twin who survives, while its sibling died in utero. This has been interpreted to refer to "Flavius Vopiscus" as being the final one to survive from the six authors of the History. Vulcacius is believed to be a mockery of Volcatius Sedigitus, who was a historical literary critic with some association with humor. The meanings behind the other two scriptores, Spartianus and Lampridius, have eluded interpretation.

It should also be noted that the results of recent computer-assisted stylistic analysis concerning the single vs multiple authorship have proven to be inconclusive: "'Computer-aided stylistic analysis of the work has, however, returned ambiguous results; some elements of style are quite uniform throughout the work, while others vary in a way that suggests multiple authorship. To what extent this is due to the fact that portions of the work are obviously compiled from multiple sources is unclear. Several computer analyses of the text have been done to determine whether there were multiple authors. Many of them conclude that there was but a single author, but disagree on methodology. However, several studies done by the same team concluded there were several authors, though they were not sure how many.'"

Primary and secondary Vitae
A unique feature of the Historia Augusta is that it purports to supply the biographies not only of reigning Emperors, called "primary lives" by modern scholars, but also "secondary lives" of their designated heirs, junior colleagues, and usurpers who unsuccessfully claimed the supreme power. Thus among the biographies of 2nd-century and early 3rd-century figures are included Hadrian's heir Aelius Caesar, and the usurpers Avidius Cassius, Pescennius Niger and Clodius Albinus, Caracalla's brother Geta and Macrinus' son Diadumenianus. None of these pieces contain much in the way of solid information: all are marked by rhetorical padding and obvious fiction. The biography of Marcus Aurelius' colleague Lucius Verus, which Mommsen thought 'secondary', is rich in apparently reliable information and has been vindicated by Syme as belonging to the 'primary' series.

The 'secondary' lives allowed the author to exercise freedom in the invention of events, places and people without the need to conform to authentic historical facts. As the work proceeds the author's inventiveness undergoes an increasing degree of elaboration as legitimate historical sources begin to run out, eventually composing largely fictional accounts such as the "biographies" of the "Thirty Tyrants", whom the author claimed had risen as usurpers under Gallienus. After the biography of Caracalla the 'primary' biographies, of the emperors themselves, begin to assume the rhetorical and fictive qualities previously confined to the 'secondary' ones, probably because the secondary lives were written after the Life of Caracalla.

The biography of Macrinus is notoriously unreliable, and after a partial reversion to reliability in the Life of Elagabalus, the Alexander Severus, one of the longest biographies in the entire work, develops into a kind of exemplary and rhetorical fable on the theme of the wise philosopher king. Clearly the author's previous sources had given out, but also his inventive talents were developing. He still makes use of some recognized sources – Herodian up to 238, and probably Dexippus in the later books, for the entire imperial period the Enmannsche Kaisergeschichte as well as Aurelius Victor, Eutropius, Ammianus Marcellinus and Jerome – but the biographies are increasingly tracts of invention in which occasional nuggets of fact are embedded.

Even where recognisable facts are present, their use in the History cannot be taken at face value. In the Life of Alexander Severus, the History makes the claim at 24.4 that Alexander had considered banning male prostitution but had decided against making it illegal, although the author added that the emperor Philip later banned the practice. Although the claim about Alexander is false, the note about Philip is true – the source of this is Aurelius Victor (28.6–7, and who sourced it from the Kaisergeschichte), and the History even copies Victor's style of moralising asides, which were not in the Kaisergeschichte. Normally, this anecdote would have been included in a Life of Philip, but its absence saw the author include it in another life. This is taken as evidence that the mid-work lacuna is deliberate, as the author was apparently reluctant to abandon any useful material that could be gleaned from the Kaisergeschichte.

Genre and purpose
Interpretations of the purpose of the History also vary considerably, some considering it a work of fiction or satire intended to entertain (perhaps in the vein of 1066 and All That), others viewing it as a pagan attack on Christianity, the writer having concealed his identity for personal safety. Under this anti-Christianity theory, the lacuna covering the period from Philip the Arab through to the end of Valerian's reign is seen as deliberate, as it freed the author from addressing Philip's reign, as by the late 4th century, Philip was being claimed as a Christian emperor, as well as not discussing Decius and Valerian's reigns, as they were well known persecutors of the Church. It avoided dealing with their fates, as Christians saw their ends as divine retribution for their persecutions.

Where mentioned, both Decius and Valerian are viewed very positively by the author of the History. It is noted that the History also parodies Christian scripture. For instance, in the Life of Alexander Severus there is: "It is said that on the day after his birth a star of the first magnitude was visible for the entire day at Arca Caesarea", while "where, save at Rome, is there an imperial power that rules an empire?" is considered to be a response to 2 Thessalonians 2:6–7.

Syme argued that it was a mistake to regard it as a historical work at all and that no clear propaganda purpose could be determined. He theorized that the History is primarily a literary product – an exercise in satire produced by a 'rogue scholiast' catering to, and making fun of or parodying, the antiquarian tendencies of the Theodosian age, in which Suetonius and Marius Maximus were fashionable reading and Ammianus Marcellinus was producing sober history in the manner of Tacitus. The History implausibly makes the Emperor Tacitus (275–276) a descendant and connoisseur of the historian.

In a passage on the Quadriga tyrannorum – the 'four-horse chariot of usurpers' said to have aspired to the purple in the reign of Probus – the History itself accuses Marius Maximus of being a producer of 'mythical history': homo omnium verbosissimus, qui et mythistoricis se voluminibis implicavit ('the most long-winded of men, who furthermore wrapped himself up in volumes of historical fiction'). The term mythistoricis occurs nowhere else in Latin. Of considerable significance in this regard is the opening section of the life of Aurelian, in which 'Flavius Vopiscus' records a supposed conversation he had with the City Prefect of Rome during the festival of Hilaria in which the Prefect urges him to write as he chooses and invent what he does not know.

Other examples of the work as a parody can be taken from the names of the Scriptores themselves. It has been suggested that "Trebellius Pollio" and "Flavius Vopiscus Syracusius" were invented, with one theory arguing that their origins are based on passages in Cicero's letters and speeches in the 1st century BC. With respect to "Trebellius Pollio", this is a reference to Lucius Trebellius, a supporter of Mark Antony who was mentioned in the Philippics (Phil, 11.14), and another reference to him in Epistulae ad Familiares along with the term "Pollentiam" reminded the History's author of Asinius Pollio, who was a fellow plebeian tribune alongside Lucius Trebellius and a historian as well.

This is reinforced by noted similarities between the fictitious criticism of "Trebellius Pollio" by "Flavius Vopiscus" at the start of the Life of Aurelian, with similar comments made by Asinius Pollio about Julius Caesar's published Commentaries. Significantly, Lucius Trebellius adopted the cognomen Fides for his actions as Plebeian Tribune in 47 BC to resist laws that would abolish debts. Later when he fell into debt himself and began supporting debt abolishment, Cicero used his cognomen as a method of abuse and ridicule. According to this theory it is no coincidence that, in selecting the name "Trebellius Pollio", the author is playing with the concepts of fides and fidelitas historica at the precise point in the lives that are assigned to "Trebellius Pollio" and "Flavius Vopiscus Syracusius".

In the case of "Flavius Vopiscus Syracusius", it was argued that it too was inspired by the Philippics' reference to "Caesar Vopiscus" (Phil, 11.11), with Cicero's reference to Vopiscus immediately preceding his reference to Lucius Trebellius. The cognomen "Syracusius" was selected because Cicero's In Verrem is filled with references to "Syracusae" and "Syracusani". Further, in Cicero's De Oratore, Cicero refers to Strabo Vopiscus as an authority on humour, during which he refers to the reputation of Sicilians when it came to humour, and Syracuse was one of the principal cities of Sicily.

Such references were intended as a "knowing wink" to the readers of the History, who would recognise the mockery of the historical material by the author. This corresponds with David Rohrbacher's view of the History, who maintains that the author has no political or theological agenda; rather that the History is the equivalent of a literary puzzle or game, with the reader's understanding and enjoyment of the numerous elaborate and complicated allusions contained within it being the only purpose behind its existence.

In support of this theory, Rohrbacher provides an example with respect to Ammianus Marcellinus' work. In one passage (Amm. 19.12.14), Ammianus describes the Christian emperor Constantius II's attempts to prosecute cases of magic under treason laws, in particular the death penalty applied to those men who were condemned simply for wearing an amulet to ward off diseases: "si qui remedia quartanae vel doloris alterius collo gestaret" ("For if anyone wore on his neck an amulet against the quartan ague or any other complaint"). There is a very similar imperial ruling described in the Life of Caracalla (5.7), which makes no sense in Caracalla's time, and is worded in almost exactly the same way: "qui remedia quartanis tertianisque collo adnexas gestarent" ("wearing them around their necks as preventives of quartan or tertian fever").

Other theories include André Chastagnol's minimalist opinion that the author was a pagan who supported the Senate and the Roman aristocracy and scorned the lower classes and the barbarian races, while François Paschoud proposed that the last books of the History are in fact a type of alternative historical narrative, with events and the personalities of recent 4th century emperors woven into the fabric of a series of 3rd century emperors. According to Paschoud, the representation of the emperor Probus is in fact a version of Julian, with Carus substituting for Valentinian I and Carinus for Gratian.

Historical value
From the sixth century to the end of the 19th century, historians had recognized that the Historia Augusta was a flawed and not a particularly reliable source, and since the 20th century modern scholars have tended to treat it with extreme caution. Older historians, such as Edward Gibbon, not fully aware of its problems with respect to the fictitious elements contained within it, generally treated the information preserved within it as authentic. For instance, in Gibbon's account of the reign of Gallienus, he uncritically reproduces the Historia Augusta's biased and largely fictional account of that reign. So when Gibbon states "The repeated intelligence of invasions, defeats, and rebellions, he received with a careless smile; and singling out, with affected contempt, some particular production of the lost province, he carelessly asked, whether Rome must be ruined, unless it was supplied with linen from Egypt, and arras cloth from Gaul", he is reworking the passage in The Two Gallieni:

"I am ashamed to relate what Gallienus used often to say at this time, when such things were happening, as though jesting amid the ills of mankind. For when he was told of the revolt of Egypt, he is said to have exclaimed 'What! We cannot do without Egyptian linen!' and when informed that Asia had been devastated both by the violence of nature and by the inroads of the Scythians, he said, 'What! We cannot do without saltpetre!' and when Gaul was lost, he is reported to have laughed and remarked, 'Can the commonwealth be safe without Atrebatic cloaks?' Thus, in short, with regard to all parts of the world, as he lost them, he would jest, as though seeming to have suffered the loss of some article of trifling service."

Gibbon then noted after this passage: "This singular character has, I believe, been fairly transmitted to us. The reign of his immediate successor was short and busy; and the historians who wrote before the elevation of the family of Constantine could not have the most remote interest to misrepresent the character of Gallienus." Modern scholars now believe that Gallienus' reputation was posthumously maligned, that he was one of the main architects of the later Roman imperial structure, and that his reforms were built upon by succeeding emperors.

Nevertheless, it is unwise to dismiss it altogether as it is also the principal Latin source regarding a century of Roman history. For example, scholars had assumed that Veturius Macrinus, mentioned in the Life of Didius Julianus, was an invention of the author, like so many other names. However, an inscription was uncovered which confirmed his existence and his post as praetorian prefect in 193. Likewise, the information that Hadrian's Wall was constructed during Hadrian's reign and that the Antonine Wall was built during the reign of Antoninus Pius are recorded by no other extant ancient writer apart from the Historia Augusta, the veracity of which has been confirmed by inscriptions.

False documents and authorities
A peculiarity of the work is its inclusion of a large number of purportedly authentic documents such as extracts from Senate proceedings and letters written by imperial personages. In all it contains around 150 alleged documents, including 68 letters, 60 speeches and proposals to the people or the senate, and 20 senatorial decrees and acclamations. Records like these are quite distinct from the rhetorical speeches often inserted by ancient historians – it was accepted practice for the writer to invent these himself – and on the few occasions when historians, such as Sallust in his work on Catiline or Suetonius in his Twelve Caesars, include such documents, they have generally been regarded as genuine. Almost all those found in the Historia Augusta have been rejected as fabrications, partly on stylistic grounds, partly because they refer to military titles or points of administrative organisation which are otherwise unrecorded until long after the purported date, or for other suspicious content.

The History cites dozens of otherwise unrecorded historians, biographers, letter-writers, knowledgeable friends of the writers, and so on, most of whom must be regarded as expressions of the author's creative imagination. For example, the biographer "Cordus" is cited twenty-seven times in the History. Long considered to be a real, but lost, biographer until midway into the 20th century, with a couple of minor exceptions where material claimed to be sourced from Cordus is in reality from Suetonius or Cicero, every other citation is fake, providing details which have been invented and ascribed to Cordus. Cordus is mentioned almost exclusively in those Vitae where the History used Herodian as the primary source, and his appearances vanish once Herodian's history comes to an end.

The author also misattributes material taken from a legitimate historian and ascribe it to a fictitious author. For instance, Herodian is used more often than he is explicitly referenced in the History. In addition to the ten times he is correctly cited, three times his material is cited as "Arrianus", probably to multiply the author's sources. Not only does the author copy from Herodian without citation, either direct lifts, abbreviations or supplementations, he often distorts Herodian, to suit his literary objective.

Then there is the deliberate citation of false information which is then ascribed to legitimate authors. For instance, at a minimum, five of the History's sixteen citations of Dexippus are considered to be fake, and Dexippus appears to be mentioned, not as a principal source of information, but rather as a contradictory author to be contrasted against information sourced from Herodian or the Enmannsche Kaisergeschichte. In addition Quintus Gargilius Martialis, who produced works on horticulture and medicine, is cited twice as a biographer, which is considered to be another false attribution.

Examples of false historical events and personages
The untrustworthiness of the History stems from the multifarious kinds of fraudulent, as opposed to simply inaccurate, information that run through the work, becoming ever more dominant as it proceeds. The various biographies are ascribed to different invented 'authors', and continue with the dedicatory epistles to Diocletian and Constantine, the quotation of fabricated documents, the citation of non-historical authorities, the invention of persons, extending even to the subjects of some of the minor biographies, presentation of contradictory information to confuse an issue while making a show of objectivity, deliberately false statements, and the inclusion of material which can be shown to relate to events or personages of the late 4th century rather than the period supposedly being written about. For example:
 * The biography of Geta states he was born in Mediolanum on 27 May. The year is not specified but it was 'in the suffect consulships of Severus and Vitellius'. He was actually born in Rome on 7 March 189. There was no such pair of suffect consuls in this or any other year. It has been suggested that the names for these persons be amended to be Severus and Vettulenus, and that these men were suffect consuls sometime before 192.
 * In the Vita Commodi, the biography on emperor Commodus, there is much doubt about the authenticity of the sources used and cited. Lampridius, the pseudonym the author works with here, claims to have used Marius Maximus on multiple occasions for his work. One instance forms a case in point: Lampridius supposedly quotes the senatorial speeches in Maximus’ work which were held after Commodus’ death. It is unclear whether the references to Maximus are genuine or made up by the author to give himself a sense of authority and expertise. Baldwin thinks that the senatorial speeches are probably a figment of Lampridius’ imagination. Molinier-Arbo believes in their authenticity. She suggests that the full report of the acta senatus (lit. acts of the senate) was handed down in the acta urbis (a kind of city gazette). Marius Maximus could have used this report for his work and Lampridius could have used it later on.
 * A letter of Hadrian written from Egypt to his brother-in-law Servianus is quoted at length, and was accepted as genuine by many authorities well into the 20th century. Servianus is saluted as consul, and Hadrian mentions his adopted son Lucius Aelius Caesar: but Hadrian was in Egypt in 130, Servianus' consulship fell in 134, and Hadrian adopted Aelius in 136. The letter is said to have been published by Hadrian's freedman Phlegon, with the letter's existence not mentioned anywhere except in the History, in another suspect passage. A passage in the letter dealing with the frivolousness of Egyptian religious beliefs refers to the Patriarch, head of the Jewish community in the Empire. This office only came into being after Hadrian put down the Jewish revolt of 132, and the passage is probably meant in mockery of the powerful late 4th-century Patriarch, Gamaliel.
 * Decius revives the office of Censor; the Senate acclaims Valerian as worthy to hold it in a decree dated 27 October 251. The decree is brought to Decius, on campaign against the Goths, and he summons Valerian to bestow the honour. The revival of the censorship is fictitious, and Decius had been dead for several months by the date stated.
 * Valerian holds an imperial council in Byzantium, attended by several named dignitaries, none of them otherwise attested and some holding offices not known to exist until the following century, at which the general 'Ulpius Crinitus', a name apparently chosen to evoke the military glories of the Emperor Trajan, takes the young Aurelian, destined to be another military Emperor, as his adopted son. There are no grounds to believe this is anything other than invention.

 * In the Tyranni Triginta, the author 'Trebellius Pollio' sets out to chronicle 'the 30 usurpers who arose in the years when the Empire was ruled by Gallienus and Valerian'. The number 30 is evidently modelled on the notorious 'Thirty Tyrants' who ruled Athens after the end of the Peloponnesian War. The chapter contains 32 mini-biographies. They include two women, six youths, and seven men who never claimed the imperial power, one usurper of the reign of Maximinus Thrax, one of the time of Decius, and two of the time of Aurelian, and a number who are not historical personages: Postumus the Younger, Saturninus, Trebellianus, Celsus, Titus, Censorinus, and Victorinus Junior.
 * In the Life of Tacitus, the emperor is acclaimed by the Senate, meeting in the Curia Pompiliana, which never existed. The History then lists a number of individuals, all of whom are invented by the author: the consul 'Velius Cornificius Gordianus', 'Maecius Faltonius Nicomachus', the Prefect of the City 'Aelius Cesettianus', and the Praetorian Prefect 'Moesius Gallicanus'. Private letters commending Tacitus are quoted from the senators 'Autronius Tiberianus' and 'Claudius Sapilianus', both of whom are assumed to be non-historical personages. Most of the 'Maecii' and 'Gallicani' in the History are believed to be inventions of the author.
 * In the Quadrigae Tyrannorum (Four tyrants: The Lives of Firmus, Saturninus, Proculus and Bonosus), the author includes Firmus, said to have been a usurper in Egypt under Aurelian. There is no certainty that this person ever existed. There was a Corrector named Claudius Firmus stationed in Egypt in 274, about the time Zosimus states that Aurelian was dealing with some trouble in that province. Nevertheless, the History's wealth of detail about him is considered to be completely invented. For example, he would eat an ostrich a day, he had a carriage drawn by ostriches, he would swim among crocodiles, he built himself a house fitted with square panels of glass.
 * In the Life of Probus, the author 'Flavius Vopiscus of Syracuse' states that the Emperor's descendants (posteri) fled from Rome and settled near Verona. There a statue of Probus was struck by lightning, a portent according to soothsayers 'that future generations of the family would rise to such distinction in the senate they all would hold the highest posts', though Vopiscus, supposedly writing under Constantine, says this prophecy has not yet come to pass. This is one of the strongest indications of the History's late 4th-century date, as it seems to be a fairly transparent allusion to the rich and powerful senator Sextus Claudius Petronius Probus (consul in 371) whose two sons held the consulship together in 395. Petronius Probus was born in Verona.

Marius Maximus or 'Ignotus'?
Certain scholars have always defended the value of specific parts of the work. Anthony Birley, for instance, has argued that the lives up to Septimius Severus are based on the now-lost biographies of Marius Maximus, which were written as a sequel to Suetonius' Lives of the Twelve Caesars. As a result, his translation of the History for Penguin Books covers only the first half, and was published as Lives of the Later Caesars, Birley himself supplying biographies of Nerva and Trajan (these are not part of the original texts, which begin with Hadrian).

His view (part of a tradition that goes back to J. J. Müller, who advanced Marius' claims as early as 1870, and supported by modern scholars such as André Chastagnol) was vigorously contested by Ronald Syme, who theorized that virtually all the identifiable citations from Marius Maximus are essentially frivolous interpolations into the main narrative source, which he postulated was a different Latin author whom he styled 'Ignotus ("the unknown one"), the good biographer'.

His theory argued, firstly, that as Marius wrote a sequel to the Lives of the Twelve Caesars, his work covered the reigns from Nerva to Elagabalus; consequently, this would not have included a biography of Lucius Verus, even though the biography of that Princeps in the History is mainly of good quality. Secondly, that 'Ignotus' only went up to Caracalla, as is revealed by the inferior and mostly fictitious biography of Macrinus.

Finally, that the composer of the Historia Augusta wrote the lives of the emperors through to the Life of Caracalla, including Lucius Verus, using Ignotus as his main source, and supplementing with Marius Maximus on occasion. It was only when the source failed that he turned to other less reliable sources (such as Herodian and Maximus), as well as his own fertile imagination, and it was at this juncture that he composed the first five minor lives, through to the Life of Geta.

A similar theory to Syme's has been put forward by François Paschoud, who claimed that Maximus was probably a satirical poet, in the same vein as Juvenal and not an imperial biographer at all. His argument rests on the point that, outside of the mentions in the History, the only extant referencing of Marius' work is always in the context of Juvenal, and that the History's description of him as a historian cannot be taken at face value, given how it invents or distorts so many other citations. This theory is rejected by historians such as Anthony Birley and David Rohrbacher.

Literary value
The Historia Augusta has been described by Ronald Syme as "the most enigmatic work that Antiquity has transmitted". Although much of the focus of study throughout the centuries has been on the historical content, since the 20th century there has also been an assessment of the literary value of the work. For much of that time the assessment has been critical, as demonstrated by the analysis put forward by David Magie:

"The literary, as well as the historical, value of the Historia Augusta has suffered greatly as a result of the method of its composition. In the arrangement in categories of the historical material, the authors did but follow the accepted principles of the art of biography as practised in antiquity, but their narratives, consisting often of mere excerpts arranged without regard to connexion or transition, lack grace and even cohesion. The over-emphasis of personal details and the introduction of anecdotal material destroy the proportion of many sections, and the insertion of forged documents interrupts the course of the narrative, without adding anything of historical value or even of general interest. Finally, the later addition of lengthy passages and brief notes, frequently in paragraphs with the general content of which they have no connexion, has put the crowning touch to the awkwardness and incoherence of the whole, with the result that the oft-repeated charge seems almost justified, that these biographies are little more than literary monstrosities."

M. L. W. Laistner was of the opinion that "even if the Historia Augusta was propaganda disguised as biography, it is still a wretched piece of literature", while Ronald Syme noted that with respect to the author's Latin prose:

"He was not an elegant exponent. His normal language is flat and monotonous. But uneven, and significantly so. For this author is erudite, a fancier of words, and a collector. Hence many rarities, or even inventions ... first, when depicting the measures of a military disciplinarian, he brings in technical terms redolent of the camp. Second, archaism, preciosity, and flowery words."

Further, the work shows evidence of its having been put together in a very haphazard and hasty fashion, with little to no subsequent editing of the material to form a cohesive narrative. Birley sees an example of the carelessness with which the author approached the work in the construction of Marcus Aurelius' biography, where midway through the Life of Marcus Aurelius the author found himself in a muddle, probably because he had historical material in excess of what he required, and because he had already used up much of his source to write separate biographies of Lucius Verus and Avidius Cassius, whose lives intersected with Marcus'.

The answer he came up with was to use Eutropius as his source for a brief overview of Marcus' principate following the death of Lucius Verus. However, he found that in doing so, the narrative's ending was too abrupt and so, after including some gossip about Commodus not being his son, he once again began an account of Marcus' reign after the death of Verus.

Although these criticisms still form the prevailing view on the History's literary worth, modern scholars such as Rohrbacher have begun to argue that, while it is poorly written and not a stylistic or polished work, its use of allusion as a vehicle for parodying popular late 4th century biographical and historiographical works means that the very features which were once a cause for intense criticism (such as the inclusion of irrelevant or contradictory inventions alongside traditionally sourced material) are actually an intentional and integral part of the work, making it one of the most unusual pieces of literature to emerge from the ancient world.

title: Historia Augusta


text:
Oakwood

Oakwood may refer to:

Places

 * in Australia
 * Oakwood, Queensland, a locality in the Bundaberg Region

 * in Canada
 * Oakwood, Ontario
 * Oakwood-Vaughan, Toronto, Ontario, a neighbourhood
 * Oakwood Collegiate Institute, a public high school in the southern end of the Oakwood-Vaughan neighbourhood

 * in the United Kingdom
 * Oakwood, Derbyshire, a housing estate in Derby, England
 * Oakwood, Leeds, area of the city
 * Oakwood, London, part of Enfield
 * Oakwood tube station
 * Oakwood, Warrington, a neighbourhood in Birchwood, Warrington, Cheshire
 * Oakwood Park, Essex
 * Oakwood Theme Park in Pembrokeshire, Wales
 * Oakwood (HM Prison), a prison near Wolverhampton

 * in the United States (by state)
 * Oakwood University, located in Huntsville, Alabama
 * Oakwood, a neighborhood in Venice, Los Angeles
 * Oakwood, Georgia
 * Oakwood, Illinois
 * Oakwood, LaPorte County, Indiana
 * Oakwood, Steuben County, Indiana
 * Oakwood Estate, a historic house in Winchester, Kentucky also known as Oakwood, listed on the National Register of Historic Places (NRHP)
 * Oakwood, Maryland
 * Oakwood (Harwood, Maryland), NRHP-listed in Anne Arundel County
 * Oakwood, Missouri
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 * Oakwood (Wrightstown, New Jersey), NRHP-listed in Burlington County
 * Oakwood, Staten Island, New York, a neighborhood in New York City
 * Historic Oakwood, North Carolina, a neighborhood in Raleigh
 * Oakwood, Cuyahoga County, Ohio
 * Oakwood, Montgomery County, Ohio
 * Oakwood, Paulding County, Ohio
 * Oakwood, Oklahoma
 * Oakwood, an incorporated area in Lawrence County, Pennsylvania
 * Oakwood, a neighborhood in Pittsburgh, Pennsylvania
 * Oakwood, Texas
 * Oakwood, Virginia
 * Oakwood, Milwaukee County, Wisconsin
 * Oakwood, Winnebago County, Wisconsin

title: Oakwood


text:
Giessen (disambiguation)

Giessen is a town in Hesse, Germany.

Giessen may also refer to:

 * Giessen (district), district of Hesse, Germany
 * Giessen (region), region of Hesse, Germany
 * Giessen, Netherlands, a village in the municipality of Altena
 * The former German name of what is today the town of Jeże, Lubusz_Voivodeship, Poland

title: Giessen (disambiguation)


text:
Emil Constantinescu

Emil Constantinescu (born 19 November 1939) is a Romanian professor and politician, who served as the President of Romania, from 1996 to 2000.

After the Romanian Revolution of 1989, Constantinescu became a founding member and vice president of the Civic Alliance (AC). In addition, he also served as the acting president of the Democratic Romanian Anti-Totalitarian Forum, the first associative structure of the democratic opposition in post-1989 Romania, which was later transformed into a centre-right political and electoral alliance known as the Romanian Democratic Convention (CDR). He had also subsequently presided the People's Action (AP) party from the early 2000s until it merged into the National Liberal Party (PNL) in 2008. Nowadays, Constantinescu remains involved in Romanian politics solely to a limited extent.

Early life and education
Emil Constantinescu was born on November 19, 1939, in Tighina, Tighina county (today, Republic of Moldova). His mother, Maria Georgeta Colceag, was born in Ploiești on April 24, 1916, and, after graduating from high school, was a student at the Bucharest Conservatory in the harp class, but gave up her career in music to follow her husband, Ion Constantinescu. He was originally from Oltenia, he had 8 brothers, and after becoming an agronomist engineer, he was assigned to Bessarabia. The Constantinescu family took refuge in 1943 in Brădetu village, Argeș County where Emil Constantinescu spent his childhood. His sister, Marina, was born in 1942, and in 1946, his brother, Cristian, was born.

In the period 1953–1956 Emil Constantinescu was a student of the "Nicolae Bălcescu" High School in Pitești (currently Colegiu IC Bratianu) and obtained his Matriculation Diploma on July 19, 1956, in the same year he enrolled at the Faculty of Law of the University Bucharest. He obtained a Diploma in Legal Sciences in 1960 and after completing his military internship in Piatra Neamț, he began his work as a trainee judge at the Pitesti Regional Court, economic section. The political climate causes him to give up this position and become a student at the Faculty of Geology – Geography, between 1961 and 1966. He holds a PhD in Geology from the University of Bucharest and a Doctor of Sciences from Duke University, US. In 1963, he married Nadia Ileana, a lawyer, who was his colleague at the Faculty of Law in Bucharest. His father died in 1991 and his mother died at Elias Hospital on November 25, 2011.

Professional career
He went through all stages of his university career as an assistant and lecturer at the Faculty of Geology (1966–1990). Since 1991 onwards, he is a professor of Mineralogy at the University of Bucharest. He was also a visiting professor at Duke University in the United States between 1991 and 1992. He was elected vice-rector (1990–1992) and rector (1992–1996) of the University of Bucharest; president of the National Council of Rectors from Romania (1992–1996); member of the Permanent Committee of the Association of European Universities – CRE (1992–1993; 1994–1998); member of the International Association of University Presidents – IAUP (1994–1996).

He is the author of 12 books and over 60 studies in the field of geology, published in prestigious scientific journals in the country and abroad. He is also Honorary Member and Elected Member of the Geological and Mineralogical Societies of the United Kingdom, Germany, US, Greece, and Japan; of the Geographical Society of France and the National Geographic Society of the USA.

He gave lectures at the Universities of Tübingen, Oxford, Stanford, Harvard, Berkeley, Columbia – New York, Georgetown – Washington, Indiana – Bloomington, Rio de Janeiro, Sydney, Prague, Turku, Cairo, Lublin. He was awarded the Romanian Academy Award for scientific contributions in the field of geology (1980); Palmas Academicas, awarded by the Brazilian Academy of Letters, Rio de Janeiro (2000); gold and honorary medals of the Comenius University in Bratislava; Charles University in Prague and University of São Paulo; Arthur Bertrand Medal, awarded by the Academy of Sciences, Institut de France; medals awarded by the National Institute of Sciences and Arts of France, the University of Paris–Sorbonne and the University of Amsterdam.

Political activity (1990–1996)
After the fall of the communist dictatorship, he engaged along with other university colleagues and renowned Romanian intellectuals in the effort to re-democratize Romania, in the defense of fundamental human rights and freedoms as well as in the establishment of the civil society. He was one of the personalities who protested against the anti-democratic actions of the new authorities during a 42-day rally, between April and May 1990, in Bucharest's University Square.

After the bloody violence committed by the miners who, at the call of the then president Ion Iliescu, invaded Bucharest in June 1990, he founded, together with his colleagues, professors, and students, the association Solidaritatea Universitară (i.e. Academic Solidarity).

He was also a founding member and vice-president of the Civic Alliance (1990), the most important non-governmental organization in the country, and president of the Civic Academy. These associations joined the opposition democratic parties and together formed the Romanian Democratic Convention (or CDR for short) in 1991. At the proposal of the Academic Solidarity, supported by the Civic Alliance (PAC), Emil Constantinescu was designated the CDR candidate in the presidential elections of 1992. He entered the second round and obtained 38% of the votes in the confrontation with then incumbent president Ion Iliescu who was supported by the Democratic National Salvation Front (FDSN). After this first important political experience, the CDR elected, in 1992, its president and sole candidate for the presidential elections of 1996 (which was represented by Constantinescu). He continued to act to strengthen the democratic opposition throughout this period of time from 1992 until 1996, alongside other notable CDR political leaders.

Presidency (1996–2000)
In 1996, he competed once again for the presidency as the CDR's candidate and managed to defeat Iliescu in the second round, securing a victory by a margin of roughly 10%. CDR's success in the 1996 general election marked the first peaceful transition of power in post-1989 Romania. On the day he took office, he suspended his membership from the PNȚ-CD, as the Constitution precludes a president holding formal membership of a political party during his term(s).

Throughout his sole four-year term, Constantinescu struggled with the ineffective implementation of the processes of privatization, which, bogged down by excessive bureaucracy, increased unemployment and poverty in the short term. After another two Mineriads which took place in 1999 (one in January and the other in February), culminating with the arrest of Miron Cozma, the remainder of his term suffered a political crisis between the majority parties that, at the time, formed the governing coalition (i.e. CDR, PD, PSDR, and UDMR/RMDSZ). The country was further damaged by a drought in 2000. At the end of his term in 2000, he decided not to run for re-election, stating that the system had defeated him.

One of the last gestures made as president of Romania was the pardon of Ion Coman, the one who had led the repression of the 1989 revolution in Timișoara.

Post-presidency

Constantinescu's presidency along with CDR's governance were marred by an economic recession. Despite this, his presidency has been eventually credited with putting an end to the Mineriads, a reform of the banking system as well as with the attraction of the first major foreign investments in Romania after 1989. With dashed expectations of an immediate improvement in daily life, Romanians exhibited strong disillusionment with the major parties and politicians of the CDR at the end of the 1996–2000 legislature, with the Greater Romania Party (PRM) subsequently gaining the second place in the 2000 legislative election.

A disenchanted Emil Constantinescu, who lost popularity and had failed to fulfil his reformist agenda announced on 17 July 2000 that he would not run for a second term. He temporarily withdrew from political life at the end of his term in November 2000. Constantinescu's direction in foreign affairs continued however after the comeback of Ion Iliescu in 2000. Eventually, Romania joined NATO in 2004 and the European Union (EU) three years later, in 2007, alongside Bulgaria.

The former president returned to the political scene in 2002 as head of the People's Action (AP; Acţiunea Populară) party, which subsequently merged within the National Liberal Party (PNL) in 2008.

Constantinescu had occasionally criticized the policies of the 2004–2014 president, Traian Băsescu, accusing him of authoritarian tendencies, and supported Crin Antonescu in the first round of the 2009 presidential elections.

Nowadays, he still remains heavily involved in politics through working for many NGOs, both in Romania and internationally. Emil Constantinescu is the current president of the Association of Citizenship Education, of the Romanian Foundation for Democracy and also the founding president of the Institute for Regional Cooperation and Conflict Prevention (INCOR).

A frequent speaker at the Oslo Freedom Forum, in 2010 he presented the OFF with a presidential medal. He is also a member of the international advisory council of the Victims of Communism Memorial Foundation.

National honours

 * 🇷🇴 Romania:
 * Order of the Star of Romania, 1st Class
 * Emblema de Onoare a Armatei României ("The Romanian Army's Badge of Honor") – 24 October 2012

Foreign honours

 * 🇦🇹 Austria: Grand Star of the Decoration of Honour for Services to the Republic of Austria (1999)
 * 🇭🇷 Croatia: Recipient of the Grand Order of King Tomislav (2000)
 * 🇩🇰 Denmark: Knight of the Order of the Elephant (2000)
 * 🇫🇮 Finland: Grand Cross with Collar of the Order of the White Rose of Finland (1998)
 * 🇵🇪 Peru: Grand Cross with Diamonds of the Order of the Sun of Peru (2 September 1998)
 * 🇳🇴 Norway: Grand Cross of the Order of St. Olav (1999)
 * 🇵🇹 Portugal: Grand Collar of the Order of Prince Henry (2000)
 * 🇸🇰 Slovakia: Grand Cross (or 1st Class) of the Order of the White Double Cross (2000)
 * 🇹🇷 Turkey: Order of the State of Republic of Turkey (1999)
 * 🇺🇦 Ukraine: First Class of the Order of Prince Yaroslav the Wise (2000)
 * 🇬🇧 United Kingdom: Honorary Knight Grand Cross of the Order of St Michael and St George (2000)

title: Emil Constantinescu


text:
Graham scan

Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald Graham, who published the original algorithm in 1972. The algorithm finds all vertices of the convex hull ordered along its boundary. It uses a stack to detect and remove concavities in the boundary efficiently.

Algorithm
The first step in this algorithm is to find the point with the lowest y-coordinate. If the lowest y-coordinate exists in more than one point in the set, the point with the lowest x-coordinate out of the candidates should be chosen. Call this point P. This step takes O(n), where n is the number of points in question.

Next, the set of points must be sorted in increasing order of the angle they and the point P make with the x-axis. Any general-purpose sorting algorithm is appropriate for this, for example heapsort (which is O(n log n)).

Sorting in order of angle does not require computing the angle. It is possible to use any function of the angle which is monotonic in the interval $$[0,\pi]$$. The cosine is easily computed using the dot product, or the slope of the line may be used. If numeric precision is at stake, the comparison function used by the sorting algorithm can use the sign of the cross product to determine relative angles.

If several points are of the same angle, either break ties by increasing distance (Manhattan or Chebyshev distance may be used instead of Euclidean for easier computation, since the points lie on the same ray), or delete all but the furthest point.

The algorithm proceeds by considering each of the points in the sorted array in sequence. For each point, it is first determined whether traveling from the two points immediately preceding this point constitutes making a left turn or a right turn. If a right turn, the second-to-last point is not part of the convex hull, and lies 'inside' it. The same determination is then made for the set of the latest point and the two points that immediately precede the point found to have been inside the hull, and is repeated until a "left turn" set is encountered, at which point the algorithm moves on to the next point in the set of points in the sorted array minus any points that were found to be inside the hull; there is no need to consider these points again. (If at any stage the three points are collinear, one may opt either to discard or to report it, since in some applications it is required to find all points on the boundary of the convex hull.)

Again, determining whether three points constitute a "left turn" or a "right turn" does not require computing the actual angle between the two line segments, and can actually be achieved with simple arithmetic only. For three points $$P_1 = (x_1,y_1)$$, $$P_2 = (x_2,y_2)$$ and $$P_3 = (x_3,y_3)$$, compute the z-coordinate of the cross product of the two vectors $$\overrightarrow{P_1P_2}$$ and $$\overrightarrow{P_1P_3}$$, which is given by the expression $$(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)$$. If the result is 0, the points are collinear; if it is positive, the three points constitute a "left turn" or counter-clockwise orientation, otherwise a "right turn" or clockwise orientation (for counter-clockwise numbered points).

This process will eventually return to the point at which it started, at which point the algorithm is completed and the stack now contains the points on the convex hull in counterclockwise order.

Time complexity
Sorting the points has time complexity O(n log n). While it may seem that the time complexity of the loop is O(n2), because for each point it goes back to check if any of the previous points make a "right turn", it is actually O(n), because each point is considered at most twice in some sense. Each point can appear only once as a point $$(x_2,y_2)$$ in a "left turn" (because the algorithm advances to the next point $$(x_3,y_3)$$ after that), and as a point $$(x_2,y_2)$$ in a "right turn" (because the point $$(x_2,y_2)$$ is removed). The overall time complexity is therefore O(n log n), since the time to sort dominates the time to actually compute the convex hull.

Pseudocode
The pseudocode below uses a function ccw: ccw > 0 if three points make a counter-clockwise turn, ccw < 0 if clockwise, and ccw = 0 if collinear. (In real applications, if the coordinates are arbitrary real numbers, the function requires exact comparison of floating-point numbers, and one has to beware of numeric singularities for "nearly" collinear points.)

Then let the result be stored in the.

let points be the list of points let stack = empty_stack find the lowest y-coordinate and leftmost point, called P0 sort points by polar angle with P0, if several points have the same polar angle then only keep the farthest for point in points: # pop the last point from the stack if we turn clockwise to reach this point while count stack > 1 and ccw(next_to_top(stack), top(stack), point) <= 0: pop stack push point to stack end

Now the stack contains the convex hull, where the points are oriented counter-clockwise and P0 is the first point.

Here,  is a function for returning the item one entry below the top of stack, without changing the stack, and similarly,   for returning the topmost element.

This pseudocode is adapted from Introduction to Algorithms.

Numerical robustness
Numerical robustness is an issue to deal with in algorithms that use finite-precision floating-point computer arithmetic. A 2004 paper analyzed a simple incremental strategy, which can be used, in particular, for an implementation of the Graham scan. The stated goal of the paper was not to specifically analyze the algorithm, but rather to provide a textbook example of what and how may fail due to floating-point computations in computational geometry. Later D. Jiang and N. F. Stewart elaborated on this and using the backward error analysis made two primary conclusions. The first is that the convex hull is a well-conditioned problem, and therefore one may expect algorithms which produce an answer within a reasonable error margin. Second, they demonstrate that a modification of Graham scan which they call Graham-Fortune (incorporating ideas of Steven Fortune for numeric stability ) does overcome the problems of finite precision and inexact data "to whatever extent it is possible to do so".

title: Graham scan


text:
Statue Square

Statue Square (lit. "Empress' Statue Square") is a public pedestrian square in Central, Hong Kong. Built entirely on reclaimed land at the end of the 19th century, Statue Square consists of two parts separated by Chater Road into a northern and a southern section. It is bordered by Connaught Road Central in the north and by Des Voeux Road Central in the south.

The name is a reference to the statues, mainly of British royalty, which stood on the square until the Japanese occupation of Hong Kong during World War II. Today, the only statue on the square is the one of Sir Thomas Jackson, 1st Baronet, an early HSBC banker.

History
The square was built at the end of the nineteenth century on land reclaimed by the Praya Reclamation Scheme. The idea of a square of statues dedicated to royalty was conceived by Sir Catchick Paul Chater. Initially named "Royal Square", it gradually became known as "Statue Square", as it originally contained the statue of Queen Victoria, in commemoration of the Queen's Golden Jubilee in 1887. The statue of the Queen should have been made not in bronze but in marble, an error that was not discovered until the bronze statue was almost completed. It was officially unveiled at the centre of the square on 28 May 1896, the day officially appointed for the celebration of the 77th birthday of the Queen.

A statue of Sir Thomas Jackson, 1st Baronet, the chief manager of the Hongkong and Shanghai Banking Corporation was unveiled in 1906. Apart from Jackson's statue and the two bronze lions in front of the HSBC building, the rest of the statues were displaced to Japan to be melted by the Japanese occupiers during World War II.

The Cenotaph, a replica of the Cenotaph in Whitehall, London, was unveiled on 24 May 1923 (Empire Day) by the Governor Sir Reginald Edward Stubbs. It was built on the northeastern section of Statue Square, facing the Hong Kong Club Building. This area is now only uncommonly referred to as part of Statue Square.

After the war, some of the statues were brought back to Hong Kong. Sir Thomas Jackson's now stands roughly in the middle of the square, facing the Court of Final Appeal Building. Queen Victoria's statue was placed in Victoria Park, and the two HSBC lions returned to the front of the HSBC building. The bronze statue of George V, also removed by the Japanese, was lost and never replaced after the war.

Since the 1980s, it has been a tradition for thousands of Filipina domestic workers to congregate in and around Statue Square every Sunday, their usual rest day of the week. A parallel tradition has since been developed in Victoria Park for Indonesian domestic helpers in Hong Kong.

Surrounding buildings
The HSBC Hong Kong headquarters building is located along the southern side of the square, across Des Voeux Road Central. The site was previously occupied by the old City Hall (built 1869, demolished 1933) and smaller earlier generations of the HSBC Hong Kong headquarters building. Several buildings with names reminiscent of British royalty were built on the western side of the square. Prince's Building and Queen's Building were built directly along the square (southern section and northern section respectively), while the others were built further west. The square was initially bordered by Victoria Harbour on its northern side, but following land reclamation, it is now separated from it by Edinburgh Place, which housed the Star Ferry pier, among others, until 2007.
 * South
 * East
 * Legislative Council Building, along the eastern side of the southern section of the square
 * Hong Kong Club Building, along the eastern side of the northern section of the square
 * West
 * Prince's Building 1904–1963, replaced by the current Prince's Building (1965)
 * Queen's Building 1899–1961, replaced by the Mandarin Oriental, Hong Kong hotel (1963)
 * King's Building 1905–1958, home to Marconi Wireless and now part of the footprint for Chater House
 * St George's Building (聖佐治大廈) 1904–1966, home to Millington Limited and replaced by the current St. George's Building office tower (1969)
 * Alexandra Building (亞歷山大行) 1904–1950, named for Princess of Wales, later Queen Alexandra, replaced by modernist Alexandra Building (1952–1974) and now Alexandra House (歷山大廈) (1976)
 * North

The statues
Today, the only freestanding statue on the Square is the statue of Sir Thomas Jackson. Additionally, a 2.7 m high blind-folded statue of Themis, the Greek Goddess of Justice and Law, stands on top of the pediment of the Court of Final Appeal Building, and is facing the Square. The statues that have been historically on display on the square include:
 * Statue of Queen Victoria. Unveiled on 28 May 1896. Taken by the Japanese during World War II and returned to Hong Kong in 1952. It is now in Victoria Park.
 * Statue of Prince Albert, added before 1902.
 * Statue of the Duke of Connaught. Donated by Catchick Paul Chater and erected in 1902. It was moved to the waterfront at Connaught Road Central and Pedder Street in 1907, near Blake Pier.
 * Statue of Sir Thomas Jackson, 1st Baronet, the chief manager of the Hongkong and Shanghai Banking Corporation. Unveiled on 24 February 1906 by the Governor Sir Matthew Nathan.
 * Statue of Edward VII. Bronze statue created by George Edward Wade. Donated by Catchick Paul Chater and unveiled on 6 February 1907 by the Duke of Connaught.
 * Statue of the Prince of Wales who later became King George V. Donated by John Bell-Irving, a director of Hongkong Electric Company and unveiled on 6 February 1907 by the Duke of Connaught.
 * Statue of Queen Alexandra. Bronze statue created by George Edward Wade. Unveiled on 25 November 1909. It was removed during the Japanese occupation.
 * Statue of Mary of Teck, Princess of Wales and future Queen Mary. Bronze statue created by George Edward Wade. Donated by Hormusjee Naorojee Mody as "a genuine token of the loyalty and esteem of the Parsis for their King and Queen". Unveiled on 25 November 1909. It was removed during the Japanese occupation.
 * Statue of Sir Henry May, 15th Governor of Hong Kong. Unveiled on 3 May 1923.
 * The HSBC World War I memorial statue, "Fame". Unveiled on 24 May 1923.

In addition, statues of royalty and colonial administrators located outside of Statue Square included:
 * Statue of Sir Arthur Kennedy, in the Botanical Gardens (picture). Erected by public subscription following his death at sea in 1883, it was unveiled in November 1887 by the newly arrived Governor William Des Vœux and stood "above the second terrace looking down on the fountain". It was removed during the Japanese occupation, and never recovered.
 * Statue of King George VI, in Hong Kong Zoological and Botanical Gardens. Erected in 1941 and still standing.

In popular culture
This location was the "Pit Stop" for the tenth episode of The Amazing Race 17.

title: Statue Square


text:
Tang, County Westmeath

Tang is a village and a 'half-parish' in County Westmeath, on the N55 national secondary road between Athlone and Ballymahon, County Longford. Tang forms part of the ecclesiastical parish of Drumraney. It is in County Westmeath but on the border with County Longford from which it is separated by the Dungorman River which flows into Lough Ree 3 km downstream via the River Inny. The village is 15 km north-east of Athlone

title: Tang, County Westmeath


text:
Admiralty, Hong Kong

Admiralty is the eastern extension of the central business district (adjacent to, but separate from, Central) on the Hong Kong Island of Hong Kong. It is located on the eastern end of the Central and Western District, bordered by Wan Chai to the east and Victoria Harbour to the north.

The name of Admiralty refers to the former Admiralty Dock in the area which housed a naval dockyard. The dock was later demolished when land was reclaimed and developed northward as the naval base HMS Tamar (shore station). The Cantonese name, Kam Chung (金鐘), lit. "Golden Bell", refers to a gold-coloured bell that was used for timekeeping at Wellington Barracks.

History
The area was developed as a military area by the British military in the 19th century. They built the Wellington Barracks, Murray Barracks, Victoria Barracks and Admiralty Dock at the site. Following the urbanisation of the north shore of Hong Kong Island, the military area split the urban area. The Hong Kong Government tried many times to get the land from the British military to connect the two urban areas, but the military refused. It was not until the 1970s that the land was gradually returned to government and changed to commercial buildings and gardens.

The Admiralty station of the MTR was built on the former site of the Hong Kong dockyards which was built in 1878 and demolished in the 1970s. After its completion, the area became increasingly known as Admiralty, rather than Central.

During the 2014 Hong Kong protests (aka "Umbrella Revolution"), substantial tracts of the area were occupied by suffragists, who dubbed it Umbrella Square.

Admiralty was also a focal point in the 2019 Hong Kong extradition law protests.

Features
Buildings in Admiralty consist primarily of office buildings, government buildings, shopping malls and hotels. There are also several parks in the area: Hong Kong Park, Tamar Park and Harcourt Garden.

The main development of the area in recent years has been the development of the Tamar site into the Central Government Complex, which started operating in 2011. Facing Victoria Harbour, the complex houses the Office of the Chief Executive, the Legislative Council Complex and the Central Government Offices.

As one of the main financial areas in Hong Kong, there are plenty of Grade-A commercial buildings in Admiralty including: Cheung Kong Centre II
 * Admiralty Centre
 * Asia Society Hong Kong Centre, housed in the former Former Explosive Magazine of the Victoria Barracks
 * Bank of America Tower
 * British Consulate General Hong Kong
 * Chinese People's Liberation Army Forces Hong Kong Building
 * CITIC Tower
 * Far East Finance Centre
 * High Court Building
 * Lippo Centre, which houses the Taipei Economic and Cultural Office
 * Pacific Place, a complex featuring a shopping mall, several hotels and office towers, that opened in Admiralty in phases between 1988 and 1991. The complex is connected to the MTR Admiralty station via an underground walkway. A later phase, Three Pacific Place, is located in Wan Chai
 * Queensway Government Offices
 * Queensway Plaza, a shopping centre located above Admiralty station
 * United Centre

Transport
Queensway and Harcourt Road are the major roads in the area. Both roads run from west to east and connect Central to Wan Chai. Other streets include Rodney Street and Tim Mei Avenue. Trams are running across Admiralty along Queensway. Most of the buildings of the area are connected through the Central Elevated Walkway, an extensive footbridge network which extends to the western part of Central.

The area is served by the peaktram and Admiralty station of the MTR. It is an interchange station between Island line, Tsuen Wan line, South Island line and East Rail line. The Admiralty (East) Public Transport Interchange, a major bus terminus, is located above the station.

Economy
Corporations headquartered in Admiralty include:
 * Everbright International, in the Far East Finance Centre
 * Lippo Ltd, in the Lippo Centre
 * CITIC Pacific Ltd, in the CITIC Tower
 * Culturecom (formerly Jademan), in the Far East Finance Centre

title: Admiralty, Hong Kong


text:
Luo Binwang

Luo Binwang (, ca. 619–684?), courtesy name Guanguang (觀光/观光), was a Chinese poet of the Tang dynasty. His family was from Wuzhou, modern Yiwu, Zhejiang, but he was raised in Shandong. Luo is grouped with Lu Zhaolin, Wang Bo, and Yang Jiong as the Four Paragons of the Early Tang, the most outstanding poets of their time.

Early career
It was said that Luo Binwang could recite poetry when he was six years old. In adulthood, after a period serving on the staff of Li Yuanqing (李元慶) Prince of Dao, an uncle of then-ruling Emperor Gaozong, Luo worked in the central government in Chang'an from 665. In 670, he was exiled to Xinjiang, after which he travelled to Yunnan with the army. He later served on staff of the prominent general Pei Xingjian (裴行儉) while Pei was serving as the commandant at Tao Prefecture (洮州, roughly modern Haidong Prefecture, Qinghai), and was in charge of the military correspondences, but he did not have a good relationship with Pei, who also disapproved of the other three greater writers grouped with Luo — Wang, Yang, and Lu, instead favoring the talents of Wang Bo's brother Wang Ju (王勮) and Su Weidao. Eventually, Luo became a secretary at the county government of Chang'an County — one of the two counties making up the capital Chang'an — a low position that was however considered fairly prestigious due to its location at the capital.

Participation in Li Jingye's rebellion
In 678, Luo Binwang was dismissed and imprisoned for criticising Wu Zetian, but was released the following year. After Emperor Gaozong's death and the subsequent takeover of Emperor Gaozong's wife Empress Dowager Wu (later known as Wu Zetian) as regent over initially their son Emperor Zhongzong, whom she quickly deposed, and then Emperor Ruizong, Luo made a number of suggestions to her, which she did not accept, and he was in turn demoted to the post of secretary general of Linhai County in 684. He and a number of similarly demoted officials met at Yang Prefecture (揚州, roughly modern Yangzhou, Jiangsu), and they, supporting Li Jingye the Duke of Ying as their leader, rose against Empress Dowager Wu at Yang Prefecture, claiming as their goal Emperor Zhongzong's restoration. Luo was in charge of the resistance forces' correspondences, and he wrote a particularly sharp-worded declaration against Empress Dowager Wu:

"The wrongfully ruling Lady Wu has a disagreeable temper and a dishonorable ancestry. When she was serving as one of the ladies in Emperor Taizong's palace, she had once taken the opportunity, while Emperor Taizong was changing, to consummate a relationship with him. Later, her lack of virtue polluted the spring palace [i.e., the palace of then-crown prince Emperor Gaozong].  She secretly hid the fact that she had sexual relations with Emperor Taizong to treacherously receive the emperor's love.  Once she got in the palace, she would not yield even in her brows; she falsely implicated others, and she used her fox-like charms to delude the emperor.  She finally was able to put on an empress' clothes and put our emperor in position of committing incest.  She has a heart similar to a snake and a lizard, and a disposition similar to a wolf.  She is close to insidious individuals and murders the faithful and the good. She killed her sister, slaughtered her brothers, murdered her emperor, and poisoned her mother. Both gods and men hate her, and heaven and earth cannot allow her to exist. She continues to harbor a treasonous heart, seeking to steal the symbols of sovereignty. She put the emperor's beloved son under house arrest in another palace, while giving the relatives of thieves important responsibilities. Alas! There is no Huo Guang present, and the Marquess of Zhuxu has already been wiped out. When a swallow poked at an imperial prince, Han's rule was known to be at an end; when the dragons mated before the emperor, Xia's court was known to be failing."

"Jingye is an old subject of imperial Tang, and a progeny of duke and marquess. He had seen the accomplishment of past emperors, and received great grace from this dynasty. The sadness of Weizi of Song was not without cause; were Yuan Junshan's tears to be for nought?  Therefore, he gathered his anger and resolved to secure the empire.  As the people of the realm are disappointed, and the state hopes for changes, he raises his flag of righteousness to clear away the evil."

"We will connect with the Yue peoples to the south and conscript from the Yellow River region to the north. The iron-like horses will be gathered, and the jade-like wagon axles will connect with each other. The red rice from Hailing [海陵, in modern Taizhou, Jiangsu] will fill the storage, and as the yellow flag rises from the banks of the Yangtze, how distant can the Restoration be?  As the sounds of the horses start, so does the north wind; and as the swords are drawn, the fighting sounds to the south cease.  Even if we drone quietly the mountains will crumble, and if we yell out, the winds and clouds will change.  As we use these to attack the enemy, what enemy will not be destroyed?  As we seek to accomplish great things with these, what accomplishment is out of reach?"

"You, dukes, may be living in Han lands [i.e., in the central region of the state]; or you may be relations of the Zhou [i.e., related to the imperial clan]; or you may have been entrusted by word; or you may be asked to look after the imperial house. Your words are still ringing in your ears, so how can you forget your faithfulness? The soil on the new imperial tomb is not yet dry, and to whom can the two-meter-tall orphan be entrusted?  If you can turn disaster into fortune, put things in the past, accomplish the Restoration together, and not forget about the will of the deceased emperor, your titles and rewards will be as permanent as the mountains and the rivers.  If you hold your cities out against us and hesitate on the wrong path, disregarding the signs of the future, you will surely be executed.  Look around the realm.  Who is its actual ruler?"

It was said that when Empress Dowager Wu read the declaration, she smiled and laughed at what he wrote. However, when she reached the portion that read, "The soil on the new imperial tomb is not yet dry, and to whom can the two-meter-tall orphan be entrusted?" she turned solemn, and she commented, "It is the fault of the chancellors that we lost this man's service." After Li Jingye's defeat later that year, Luo was also killed, and Empress Dowager Wu, impressed with his writing, sent people to gather them and publish them.

Style
In prose, he was a master of the ornate pianwen 駢文 "parallel prose" style. His poetry (mostly gushi) is often similarly complex. Among his works is a long, autobiographical verse narrative, but he is best known for his poem "Ode to the Goose", said to have been written when he was seven years old. His "Ode to the Cicada" is also of great renown and influence.

title: Luo Binwang