text:
Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the $i$-th row and $j$-th column is equal to the complex conjugate of the element in the $j$-th row and $i$-th column, for all indices $i$ and $j$:

or in matrix form: $$A \text{ is Hermitian} \quad \iff \quad A = \overline {A^\mathsf{T}}.$$

Hermitian matrices can be understood as the complex extension of real symmetric matrices.

If the conjugate transpose of a matrix $$A$$ is denoted by $$A^\mathsf{H},$$ then the Hermitian property can be written concisely as

$$A \text{ is Hermitian} \quad \iff \quad A = A^\mathsf{H}$$

Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are $$A^\mathsf{H} = A^\dagger = A^\ast,$$ although in quantum mechanics, $$A^\ast$$ typically means the complex conjugate only, and not the conjugate transpose.

Alternative characterizations
Hermitian matrices can be characterized in a number of equivalent ways, some of which are listed below:

Equality with the adjoint
A square matrix $$A$$ is Hermitian if and only if it is equal to its conjugate transpose, that is, it satisfies $$\langle \mathbf w, A \mathbf v\rangle = \langle A \mathbf w, \mathbf v\rangle,$$ for any pair of vectors $$\mathbf v, \mathbf w,$$ where $$\langle \cdot, \cdot\rangle$$ denotes the inner product operation.

This is also the way that the more general concept of self-adjoint operator is defined.

Real-valuedness of quadratic forms
An $$n\times{}n$$ matrix $$A$$ is Hermitian if and only if $$\langle \mathbf{v}, A \mathbf{v}\rangle\in\R, \quad \text{for all } \mathbf{v}\in \mathbb{C}^{n}.$$

Spectral properties
A square matrix $$A$$ is Hermitian if and only if it is unitarily diagonalizable with real eigenvalues.'''

Applications
Hermitian matrices are fundamental to quantum mechanics because they describe operators with necessarily real eigenvalues. An eigenvalue $$a$$ of an operator $$\hat{A}$$ on some quantum state $$|\psi\rangle$$ is one of the possible measurement outcomes of the operator, which requires the operators to have real eigenvalues.

In signal processing, Hermitian matrices are utilized in tasks like Fourier analysis and signal representation. The eigenvalues and eigenvectors of Hermitian matrices play a crucial role in analyzing signals and extracting meaningful information.

Hermitian matrices are extensively studied in linear algebra and numerical analysis. They have well-defined spectral properties, and many numerical algorithms, such as the Lanczos algorithm, exploit these properties for efficient computations. Hermitian matrices also appear in techniques like singular value decomposition (SVD) and eigenvalue decomposition.

In statistics and machine learning, Hermitian matrices are used in covariance matrices, where they represent the relationships between different variables. The positive definiteness of a Hermitian covariance matrix ensures the well-definedness of multivariate distributions.

Hermitian matrices are applied in the design and analysis of communications system, especially in the field of multiple-input multiple-output (MIMO) systems. Channel matrices in MIMO systems often exhibit Hermitian properties.

In graph theory, Hermitian matrices are used to study the spectra of graphs. The Hermitian Laplacian matrix is a key tool in this context, as it is used to analyze the spectra of mixed graphs. The Hermitian-adjacency matrix of a mixed graph is another important concept, as it is a Hermitian matrix that plays a role in studying the energies of mixed graphs.

Examples and solutions
In this section, the conjugate transpose of matrix $$ A $$ is denoted as $$ A^\mathsf{H} ,$$ the transpose of matrix $$ A $$ is denoted as $$ A^\mathsf{T} $$ and conjugate of matrix $$ A $$ is denoted as $$ \overline{A} .$$

See the following example:

$$\begin{bmatrix} 0    & a - ib & c-id \\ a+ib & 1     & m-in \\ c+id    &   m+in & 2 \end{bmatrix}$$

The diagonal elements must be real, as they must be their own complex conjugate.

Well-known families of Hermitian matrices include the Pauli matrices, the Gell-Mann matrices and their generalizations. In theoretical physics such Hermitian matrices are often multiplied by imaginary coefficients, which results in skew-Hermitian matrices.

Here, we offer another useful Hermitian matrix using an abstract example. If a square matrix $$ A $$ equals the product of a matrix with its conjugate transpose, that is, $$ A = BB^\mathsf{H} ,$$ then $$ A $$ is a Hermitian positive semi-definite matrix. Furthermore, if $$ B $$ is row full-rank, then $$ A $$ is positive definite.

Main diagonal values are real
The entries on the main diagonal (top left to bottom right) of any Hermitian matrix are real.

$$

Only the main diagonal entries are necessarily real; Hermitian matrices can have arbitrary complex-valued entries in their off-diagonal elements, as long as diagonally-opposite entries are complex conjugates.

Symmetric
A matrix that has only real entries is symmetric if and only if it is a Hermitian matrix. A real and symmetric matrix is simply a special case of a Hermitian matrix.

$$

So, if a real anti-symmetric matrix is multiplied by a real multiple of the imaginary unit $$i,$$ then it becomes Hermitian.

Normal
Every Hermitian matrix is a normal matrix. That is to say, $$AA^\mathsf{H} = A^\mathsf{H}A.$$

$$

Diagonalizable
The finite-dimensional spectral theorem says that any Hermitian matrix can be diagonalized by a unitary matrix, and that the resulting diagonal matrix has only real entries. This implies that all eigenvalues of a Hermitian matrix $A$ with dimension $n$ are real, and that $A$ has $n$ linearly independent eigenvectors. Moreover, a Hermitian matrix has orthogonal eigenvectors for distinct eigenvalues. Even if there are degenerate eigenvalues, it is always possible to find an orthogonal basis of $i = j$ consisting of $n$ eigenvectors of $A$.

Sum of Hermitian matrices
The sum of any two Hermitian matrices is Hermitian.

$$

Inverse is Hermitian
The inverse of an invertible Hermitian matrix is Hermitian as well.

$$

Associative product of Hermitian matrices
The product of two Hermitian matrices $A$ and $B$ is Hermitian if and only if $C^{n}$.

$$

ABA Hermitian
If A and B are Hermitian, then ABA is also Hermitian. $$

$AB = BA$ is real for complex $A^{n}$
For an arbitrary complex valued vector $v^{H}Av$ the product $$ \mathbf{v}^\mathsf{H} A \mathbf{v} $$ is real because of $$ \mathbf{v}^\mathsf{H} A \mathbf{v} = \left(\mathbf{v}^\mathsf{H} A \mathbf{v}\right)^\mathsf{H} .$$ This is especially important in quantum physics where Hermitian matrices are operators that measure properties of a system, e.g. total spin, which have to be real.

Complex Hermitian forms vector space over $v$
The Hermitian complex $n$-by-$n$ matrices do not form a vector space over the complex numbers, $v$, since the identity matrix $ℝ$ is Hermitian, but $ℂ$ is not. However the complex Hermitian matrices do form a vector space over the real numbers $I_{n}$. In the $i I_{n}$-dimensional vector space of complex $ℝ$ matrices over $2n^{2}$, the complex Hermitian matrices form a subspace of dimension $n × n$. If $ℝ$ denotes the $n$-by-$n$ matrix with a $n^{2}$ in the $E_{jk}$ position and zeros elsewhere, a basis (orthonormal with respect to the Frobenius inner product) can be described as follows: $$E_{jj} \text{ for } 1 \leq j \leq n \quad (n \text{ matrices}) $$

together with the set of matrices of the form $$\frac{1}{\sqrt{2}}\left(E_{jk} + E_{kj}\right) \text{ for } 1 \leq j < k \leq n \quad \left( \frac{n^2-n} 2 \text{ matrices} \right) $$

and the matrices $$\frac{i}{\sqrt{2}}\left(E_{jk} - E_{kj}\right) \text{ for } 1 \leq j < k \leq n \quad \left( \frac{n^2-n} 2 \text{ matrices} \right) $$

where $$i$$ denotes the imaginary unit, $$i = \sqrt{-1}~.$$

An example is that the four Pauli matrices form a complete basis for the vector space of all complex 2-by-2 Hermitian matrices over $1$.

Eigendecomposition
If $n$ orthonormal eigenvectors $$\mathbf{u}_1, \dots, \mathbf{u}_n$$ of a Hermitian matrix are chosen and written as the columns of the matrix $U$, then one eigendecomposition of $A$ is $$ A = U \Lambda U^\mathsf{H}$$ where $$U U^\mathsf{H} = I = U^\mathsf{H} U$$ and therefore $$A = \sum_j \lambda_j \mathbf{u}_j \mathbf{u}_j ^\mathsf{H},$$ where $$\lambda_j$$ are the eigenvalues on the diagonal of the diagonal matrix $$\Lambda.$$

Singular values
The singular values of $$A$$ are the absolute values of its eigenvalues:

Since $$A$$ has an eigendecomposition $$A=U\Lambda U^H$$, where $$U$$ is a unitary matrix (its columns are orthonormal vectors; see above), a singular value decomposition of $$A$$ is $$A=U|\Lambda|\text{sgn}(\Lambda)U^H$$, where $$|\Lambda|$$ and $$\text{sgn}(\Lambda)$$ are diagonal matrices containing the absolute values $$|\lambda|$$ and signs $$\text{sgn}(\lambda)$$ of $$A$$'s eigenvalues, respectively. $$\sgn(\Lambda)U^H$$ is unitary, since the columns of $$U^H$$ are only getting multiplied by $$\pm 1$$. $$|\Lambda|$$ contains the singular values of $$A$$, namely, the absolute values of its eigenvalues.

Real determinant
The determinant of a Hermitian matrix is real:

$$ (Alternatively, the determinant is the product of the matrix's eigenvalues, and as mentioned before, the eigenvalues of a Hermitian matrix are real.)

Decomposition into Hermitian and skew-Hermitian matrices
Additional facts related to Hermitian matrices include:
 * The sum of a square matrix and its conjugate transpose $$\left(A + A^\mathsf{H}\right)$$ is Hermitian.
 * The difference of a square matrix and its conjugate transpose $$\left(A - A^\mathsf{H}\right)$$ is skew-Hermitian (also called antihermitian). This implies that the commutator of two Hermitian matrices is skew-Hermitian.
 * An arbitrary square matrix $C$ can be written as the sum of a Hermitian matrix $A$ and a skew-Hermitian matrix $B$. This is known as the Toeplitz decomposition of $C$. $$C = A + B \quad\text{with}\quad A = \frac{1}{2}\left(C + C^\mathsf{H}\right) \quad\text{and}\quad B = \frac{1}{2}\left(C - C^\mathsf{H}\right)$$

Rayleigh quotient
In mathematics, for a given complex Hermitian matrix $M$ and nonzero vector $j,k$, the Rayleigh quotient $$R(M, \mathbf{x}),$$ is defined as: $$R(M, \mathbf{x}) := \frac{\mathbf{x}^\mathsf{H} M \mathbf{x}}{\mathbf{x}^\mathsf{H} \mathbf{x}}.$$

For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose $$\mathbf{x}^\mathsf{H}$$ to the usual transpose $$\mathbf{x}^\mathsf{T}.$$ $$R(M, c \mathbf x) = R(M, \mathbf x)$$ for any non-zero real scalar $$c.$$ Also, recall that a Hermitian (or real symmetric) matrix has real eigenvalues.

It can be shown that, for a given matrix, the Rayleigh quotient reaches its minimum value $$\lambda_\min$$ (the smallest eigenvalue of M) when $$\mathbf x$$ is $$\mathbf v_\min$$ (the corresponding eigenvector). Similarly, $$R(M, \mathbf x) \leq \lambda_\max$$ and $$R(M, \mathbf v_\max) = \lambda_\max .$$

The Rayleigh quotient is used in the min-max theorem to get exact values of all eigenvalues. It is also used in eigenvalue algorithms to obtain an eigenvalue approximation from an eigenvector approximation. Specifically, this is the basis for Rayleigh quotient iteration.

The range of the Rayleigh quotient (for matrix that is not necessarily Hermitian) is called a numerical range (or spectrum in functional analysis). When the matrix is Hermitian, the numerical range is equal to the spectral norm. Still in functional analysis, $$\lambda_\max$$ is known as the spectral radius. In the context of C*-algebras or algebraic quantum mechanics, the function that to $ℝ$ associates the Rayleigh quotient $x$ for a fixed $M$ and $R(M, x)$ varying through the algebra would be referred to as "vector state" of the algebra.

title: Hermitian matrix


text:
HMNZS Achilles

HMNZS Achilles was a Leander-class cruiser (1931) light cruiser, the second of five in the class. She served in the Royal New Zealand Navy in the Second World War. She was launched in 1931 for the Royal Navy, loaned to New Zealand in 1936 and transferred to the new Royal New Zealand Navy in 1941. She became famous for her part in the Battle of the River Plate, alongside HMS Ajax (22) and HMS Exeter (68) and notable for being the first Royal Navy cruiser to have fire control radar, with the installation of the New Zealand-made SS1 fire-control radar in June 1940.

After Second World War service in the Atlantic and Pacific, she was returned to the Royal Navy. She was sold to the Indian Navy in 1948 and recommissioned as INS Delhi. She was scrapped in 1978.

Design
She was the second of five ships of the Leander-class light cruisers, designed as effective follow-ons to the York-class cruiser. Upgraded to Improved Leander-class, she could carry an aircraft and was the first ship to carry a Supermarine Walrus, although both Walruses were lost before the Second World War began. At one time she carried the unusual DH.82 Queen Bee which was a radio-controlled unmanned aircraft, normally used as a drone.

Service
Achilles was originally built for the Royal Navy, and was commissioned as HMS Achilles on 10 October 1933. She would serve with the Royal Navy's New Zealand Division from 31 March 1936 up to the creation of the Royal New Zealand Navy, into which she was transferred in September 1941 and recommissioned HMNZS Achilles. About 60 per cent of her crew was from New Zealand.

At the outbreak of the Second World War, Achilles began patrolling the west coast of South America looking for German merchant ships, but by 22 October 1939 she had arrived at the Falkland Islands, where she was assigned to the South American Division under Commodore Henry Harwood and allocated to Force G (with Exeter and HMS Cumberland (57)).

Battle of the River Plate
In the early morning of 13 December 1939, a force consisting of Achilles, Ajax and Exeter detected smoke on the horizon, which was confirmed at 06:16 to be a pocket battleship, thought to be the GERMAN BATTLESHIP Admiral Scheer but which turned out to be GERMAN BATTLESHIP Admiral Graf Spee. A fierce battle ensued, at a range of about 20 km. Achilles suffered some damage. In the exchange of fire, four crew were killed, her captain, WE Parry, was wounded; 36 of Graf Spee's crew were killed.

The range reduced to about 4 nmi at around 07:15 and Graf Spee broke off the engagement around 07:45 to head for the neutral harbour of Montevideo which she entered at 22:00 that night, having been pursued by Achilles and Ajax all day. Graf Spee was forced by international law to leave within 72 hours. Faced with what he believed to be overwhelming odds, the captain of Graf Spee, Hans Langsdorff, scuttled his ship rather than risk the lives of his crew. An ensign flag flown by HMS Achilles in the Battle of the River Plate was donated to Christ Church Cathedral in the Falkland Islands and is still on display hanging on the south wall of the Cathedral at Port Stanley.

Pacific theatre
Following the Atlantic battle, Achilles returned to Auckland, New Zealand, on 23 February 1940, where she underwent a refit until June. After German raider activity in the South Pacific in 1940 Achilles escorted the first Trans-Tasman commercial convoy, VK.1, composed of MV Empire Star (1935), MV Port Chalmers (1933), RMS Empress of Russia, and TSS Maunganui leaving Sydney 30 December 1940 for Auckland. After Japan entered the war, she escorted troop convoys, then joined the ANZAC Squadron in the south-west Pacific.

Achilles met HMAS Canberra (D33), flagship of Rear-Admiral John G. Crace, and HMAS Perth (D29) in December 1941 to form an escort for the Pensacola Convoy.

While operating off Guadalcanal Island with US Navy Task Force 67 on 5 January 1943, she was attacked by four Japanese aircraft. A bomb blew the top off X turret, killing 13 sailors. Between April 1943 and May 1944 Achilles was docked in Portsmouth, England for repairs and modernisation. Her single 4-inch AA guns were replaced by the dual-purpose QF 4 inch Mk XVI naval gun in four twin mountings, modern radar was fitted, and the damaged X turret was replaced by four QF 2 pom poms in a quadruple-mount. The work was delayed by a dockyard explosion that killed 14 men. Stoker William Dale was awarded the Albert Medal for Lifesaving for his actions in saving the lives of several dockyard workers.

Sent back to the New Zealand Fleet, Achilles next joined the British Pacific Fleet in May 1945 for final operations in the Pacific War.

Indian Navy
After the war, Achilles was returned to the Royal Navy at Sheerness in Kent, England on 17 September 1946. She was then sold to the Indian Navy and recommissioned on 5 July 1948 as INS Delhi (1948). She remained in service until decommissioned for scrap in Bombay on 30 June 1978. In 1968 she was present at the granting of independence to Mauritius representing the Indian Government together with the Royal Navy frigate HMS Tartar (F133) under Captain Cameron Rusby. As part of the scrapping her Y turret was removed and presented as a gift to the New Zealand government. It is now on display at the entrance of Devonport Naval Base in Auckland. On 22 January 1979, Admiral Jal Cursetji, the Indian Navy Chief of the Naval Staff, presented Achilles's builder's plaque, steering wheel and engine room telegraph to Admiral Terence Lewin, the First Sea Lord and Chief of the Naval Staff of the Royal Navy.

Achilles played herself in the film The Battle of the River Plate in 1956.

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

title: HMNZS Achilles


text:
John Taylor (classical scholar)

John Taylor (22 June 1704 – 4 April 1766), English classical scholar, was born at Shrewsbury in Shropshire, England.

Life
His father was a barber, and, by the generosity of one of his close customers, the son, having received his early education at the grammar school of his native town, was sent to St John's College, Cambridge. In 1732, he was appointed librarian, and in 1734 Registrary of the university. Somewhat late in life he took orders and became rector of Lawford in Essex in 1751, Archdeacon of Buckingham in 1753, canon of St Paul's in 1757. He died in London on 4 April 1766, aged 61 and was buried in St Paul's Cathedral.

He is also shown as Prebendary of Aylesbury from 1745 to 1747 and again from 1750 to 1756.

Taylor is best known for his editions of some of the Greek orators, chiefly valuable for the notes on Attic law, e.g. Lysias (1739); Demosthenes' Contra Leptinem (1741) and Contra Midiam (1743, with Lycurgus' Contra Leocratem), intended as specimens of a proposed edition, in five volumes, of the orations of Demosthenes, Aeschines, Dinarchus, and Demades, of which only vols. ii and iii were published.

Taylor also published (under the title of Marmor Sandvicense) a commentary on the inscription on an ancient marble brought from Greece by Lord Sandwich, containing particulars of the receipts and expenditures of the Athenian magistrates appointed to celebrate the festival of Apollo at Delos in 374 BC. His Elements of Civil Law (1755) also deserves notice. It was severely attacked by William Warburton in his Divine Legation of Moses, professedly owing to a difference of opinion in regard to the persecution of the early Christians, in reality because Taylor had spoken disparagingly of his scholarship.

title: John Taylor (classical scholar)


text:
Hugues de Payens

Hugo de Paganis, better known by the French translation Hugues de Payens or Payns (c. 1070 – 24 May 1136), was the co-founder and first Grand Master of the Knights Templar. In association with Bernard of Clairvaux, he created the Latin Rule, the code of behavior for the Order.

Name
The majority of the primary sources of information for his life are presented in medieval Latin, French or Italian. Latin sources call him Hugo de Paganis. Some of his earliest appearances in documents are under the part-Latin, part-French name Hugo de Peans (1120–1125; details below), then in Italian as Ugo de' Pagani or Ugo dei Pagani. In later French works his name usually appears as Hugues de Payens or Payns, often translated into English as Hugh de Payns.

Origin and early life
There is no known early biography of Hugo de Paganis in existence, nor do later writers cite such a biography. None of the sources on his later career give details of his early life. Information is therefore scanty and uncertain; embellishments depend partly on documents that may not refer to the same individual, partly on histories written decades or even centuries after his death.

There is long-dated claim that Hugo de Paganis (Ugo de' Pagani) came from Nocera de' Pagani in Campania, Southern Italy, historically supported by authors like Carlo Sigonio, Heinrich Pantaleon, Scipione Mazzella, Filiberto Campanile, Marco Antonio Guarini, Frans Mennens, Antonino Amico, Costantino Gaetani, Blaise François de Pagan, Pierre Dupuy, Bernardo Giustinian and Johann Jacob Hofmann. Mentions of Nocera as his birthplace also appear in Baedeker's ''Italy: handbook for travellers. Part 3'' (1869) and in the Old Catholic Encyclopedia (Volume 11) published by Robert Appleton Company in 1911. Two Italian writers have stated that this claim is supported by a letter Hugo supposedly wrote from Palestine in 1103, in which he talked of writing to "my father in Nocera" to tell him of the death of his cousin Alessandro.

The earliest source that details a geographical origin for the later Grand Master is the Old French translation of William of Tyre's History of Events Beyond the Sea, dated to c. 1200. The Latin text actually calls him simply Hugo de Paganis, but the French translation by Paulin Paris, dated to 1879, describes him as Hues de Paiens delez Troies ("Hugh of Payens near Troyes"), a reference to the village of Payns, about 10 km from Troyes, in Champagne (eastern France).

In early documents of that region Hugo de Pedano, Montiniaci dominus is mentioned as a witness to a donation by Count Hugh of Champagne in a document of 1085–90, indicating that the man was at least sixteen by this date—a legal adult and thus able to bear witness to legal documents—and so born no later than 1070. The same name appears on a number of other charters up to 1113 also relating to Count Hugh of Champagne, suggesting that Hugo de Pedano or Hugo dominus de Peanz was a member of the Count's court. By the year 1113 he was married to Elizabeth de Chappes, who bore him at least one child, Thibaud, later abbot of the Abbaye de la Colombe at Sens. The documents span Hugues' lifetime and the disposition of his property after his death.

The one belated statement that the founder of the Knights Templars came from "Payns near Troyes" has some circumstantial confirmation. Bernard of Clairvaux, who favoured the Order and helped to compose its Latin Rule, also had the support of Hugh of Champagne. The Latin Rule of the Order was confirmed at the Council of Troyes in 1129. A Templar commandery was eventually built at Payns. Some scholars have however looked for Hugues' origins elsewhere. There was an early claim that he came from the Vivarais (the district of Viviers in the modern département of Ardèche). Hugues has also been identified with Hug de Pinós, third son of Galceran I, lord of Pinós in Catalonia; however, Galceran married only in 1090, far too late a date for him to be the father of the founder of the Knights Templars.

The foundation of the Order
Hugh, Count of Champagne made a pilgrimage to the Holy Land in 1104–07 and visited Jerusalem for a second time in 1114–16. It is probable that he was accompanied by Hugues de Payens, who remained there after the Count returned to France as there is a charter with "Hugonis de Peans" in the witness list from Jerusalem in 1120 and again in 1123. In 1125 his name appears again as a witness to a donation, this time accompanied by the title "magister militum Templi" ("Master of the Knights of the Temple"). He most likely obtained approval for the Order from King Baldwin II of Jerusalem and Warmund, Patriarch of Jerusalem at the Council of Nablus in 1120.

One early chronicler, Simon de St. Bertin, implies that the Knights Templar originated earlier, before the death of Godfrey of Bouillon in 1100: "While he [Godfrey] was reigning magnificently, some had decided not to return to the shadows of the world after suffering such dangers for God's sake. On the advice of the princes of God's army they vowed themselves to God's Temple under this rule: they would renounce the world, give up personal goods, free themselves to pursue purity, and lead a communal life wearing a poor habit, only using arms to defend the land against the attacks of the insurgent pagans when necessity demanded."

Later chroniclers write that Hugues de Payens approached King Baldwin II of Jerusalem (whose reign began in 1118) with eight knights, two of whom were brothers and all of whom were his relatives by either blood or marriage, in order to form the Order of the Knights Templar. The other knights were Godfrey de Saint-Omer, Payen de Montdidier, Archambaud de St. Amand, André de Montbard, Geoffrey Bison, and two men recorded only by the names of Rossal and Gondamer. Baldwin approved the foundation of the Order and entrusted the Temple of Jerusalem to its care.

Count Hugh of Champagne himself joined the Knights Templar on his third visit to the Holy Land in 1125.

In the late 1120s, Hugues, along with several other Templars, went on a diplomatic mission to western Europe on behalf of Baldwin II. They met with nobles and kings in an attempt to encourage warriors to come to the Kingdom of Jerusalem and join an attack on Damascus Baldwin was planning.

As Grand Master, Hugues de Payens led the Order for almost twenty years until his death, helping to establish the Order's foundations as an important and influential military and financial institution. On his visit to England and Scotland in 1128, he raised men and money for the Order, and also founded their first House in London and another near Edinburgh at Balantrodoch, now known as Temple, Midlothian. The Latin Rule laying down the way of life of the Order, attributed to Hugues de Payens and Bernard of Clairvaux, was confirmed in 1129 at the Council of Troyes over which a papal legate, sent by Pope Honorius II, presided.

Death
Hugues de Payens died in 1136. The circumstances and date of his death are not recorded in any chronicle, though the Templars commemorated him every year on 24 May, and it's presumed he died of old age. The 16th century historian Marco Antonio Guarini claimed that Hugues was buried in the Church of San Giacomo in Ferrara. He was succeeded as Grand Master by Robert de Craon.

In popular culture
It has recently been claimed that the wife of Hugues de Payens was Catherine St. Clair within the context of the alternative history of Rosslyn, such as in the pseudohistory of the Dossiers Secrets d'Henri Lobineau and the conspiracy theory of The Holy Blood and the Holy Grail.

Hugues is the main protagonist of the Jack Whyte novel Knights of the Black and White.

Hughes is mentioned on the TV series Knightfall in season 2, chapter 5.

title: Hugues de Payens


text:
David Ruhnken

David Ruhnken (2 January 1723 – 14 May 1798) was a Dutch classical scholar of German origin.

Origins
Ruhnken was born in Bedlin (today Bydlino) near Stolp, Pomerania Province, (today Słupsk, Poland). After he had attended Latin school at Königsberg (1737–1741), his parents wanted him to enter the church, but after two years at the University of Wittenberg he determined to live the life of a scholar. At Wittenberg, Ruhnken studied with two distinguished professors, Johann Daniel Ritter and Johann Wilhelm von Berger. To them he owed a thorough grounding in ancient history and Roman antiquities and literature; and from them he learned a pure and vivid Latin style. At Wittenberg, Ruhnken also studied mathematics and Roman law.

The only thing that made him want to leave Wittenberg was a desire to explore Greek literature. Neither at Wittenberg nor at any other German university was Greek being seriously studied at the time. It was taught to students in divinity for the sake of the Greek New Testament and the early fathers of the church. Friedrich August Wolf was the real creator of Greek scholarship in modern Germany, and Richard Porson's gibe that "the Germans in Greek are sadly to seek" had some truth in it.

University of Leiden
Ruhnken followed the advice of his friends at Wittenberg and early in 1744 went to the University of Leiden, where, stimulated by the influence of Richard Bentley, Tiberius Hemsterhuis had founded the only real school of Greek learning on the Continent since the days of Joseph Justus Scaliger and Isaac Casaubon. Hemsterhuis and Ruhnken were close friends during the twenty-three years between Ruhnken's arrival in the Netherlands in 1743 and the death of Hemsterhuis in 1766. Ruhnken and Valckenaer were the two pupils of the great master on whom his inheritance must devolve.

As Ruhnken's reputation spread, many efforts were made to attract him back to Germany, but after settling in Leiden, he only left the country once, when he spent a year in Paris, ransacking the public libraries (1755). For work achieved, this year of Ruhnken may compare even with the famous year which Ritschl spent in Italy.

In 1757 Ruhnken was appointed lecturer in Greek, to assist Hemsterhuis, and in 1761 he succeeded Oudendorp, with the title of "ordinary professor of history and eloquence", as Latin professor. This promotion attracted the enmity of some native Netherlanders, who deemed themselves more worthy of the chair of Latin. Ruhnken's defence was to publish works on Latin literature which eclipsed and silenced his rivals.

In 1766 Valckenaer succeeded Hemsterhuis in the Greek chair. The intimacy between the two colleagues was only broken by Valckenaer's death in 1785, and stood the test of common candidature for the office (an important one at Leiden) of 12th Librarian of Leiden University, in which Ruhnken was successful. Ruhnken's later years were clouded by severe domestic misfortune, and by the political commotions which, after the outbreak of the war with England in 1780, troubled the Netherlands without ceasing, and threatened to extinguish the University of Leiden.

Character
Soon after his Ruhnken's death, his pupil Wyttenbach wrote his biography. He wrote that Ruhnken was not a recluse or a pedant, but  was sociable and cared nothing for rank. Wyttenbach said of him in his early days that he knew how to sacrifice to the Sirens without proving traitor to the Muses. Life in the open air had a great attraction for him; he was fond of sport, and would sometimes devote to it two or three days in the week. In his bearing towards other scholars Ruhnken was generous and dignified, distributing literary aid with a free hand, and meeting onslaughts for the most part with a smile. In the records of learning he occupies an important position, as a principal link in the chain which connects Bentley with the modern scholarship of the European Continent. The spirit and the aims of Hemsterhuis, the great reviver of Continental learning, were committed to his trust, and were faithfully maintained. He greatly widened the circle of those who valued taste and precision in classical scholarship. He powerfully aided the emancipation of Greek studies from theology. Ruhnken was one of the first scholars of the 18th century to study and interpret Plato's writings in ancient Greek rather than interpreting Plato's works through the prisms of translations by others.

Works
Ruhnken's principal works are editions of:
 * 1) Timaeus's Lexicon of Platonic Words (1st ed. 1754 with commentary; 2nd ed. 1789; there appeared a revision of the second edition by Georg Aenotheus Koch in 1828)
 * 2) Thalelaeus and other Greek commentators on Roman law
 * 3) Rutilius Lupus and other grammarians
 * 4) Velleius Paterculus
 * 5) the works of Muretus.

He also occupied himself much with the history of Greek literature, particularly the oratorical literature, with the Homeric hymns, the scholia or, Plato and the Greek and Roman grammarians and rhetoricians. A discovery famous in its time was that in the text of the work of Apsines on rhetoric a large piece of a work by Longinus was embedded. Modern views of the writings attributed to Longinus have lessened the interest of this discovery without lessening its merit.

title: David Ruhnken


text:
Baphomet

Baphomet is a deity which the Knights Templar were accused of worshipping that subsequently became incorporated into various occult and Western esoteric traditions. The name Baphomet appeared in trial transcripts for the Inquisition of the Knights Templar starting in 1307. It first came into popular English usage in the 19th century during debate and speculation on the reasons for the suppression of the Templar order. Baphomet is a symbol of balance in various occult and mystical traditions, the origin of which some occultists have attempted to link with the Gnostics and Templars, although occasionally purported to be a deity or a demon. Since 1856 the name Baphomet has been associated with the "Sabbatic Goat" image drawn by Éliphas Lévi, composed of binary elements representing the "symbolization of the equilibrium of opposites": half-human and half-animal, male and female, and good and evil. Lévi's intention was to symbolize his concept of balance, with Baphomet representing the goal of perfect social order.

History
The name Baphomet appeared in July 1098 in a letter about the siege of Antioch by the French Crusader Anselm of Ribemont:

Raymond of Aguilers, a chronicler of the First Crusade, reports that the troubadours used the term Bafomet for Muhammad, and Bafumaria for a mosque. The name Bafometz later appeared around 1195 in the Provençal poems Senhors, per los nostres peccatz by the troubadour Gavaudan. Around 1250, a Provençal poem by Austorc d'Aorlhac bewailing the defeat of the Seventh Crusade again uses the name Bafomet for Muhammad. De Bafomet is also the title of one of four surviving chapters of an Occitan translation of Ramon Llull's earliest known work, the Libre de la doctrina pueril.

Baphomet was allegedly worshipped as a deity by the medieval order of the Knights Templar. King Philip IV of France had many French Templars simultaneously arrested, and then tortured into confessions in October 1307. The name Baphomet appeared in trial transcripts for the Inquisition of the Knights Templar that same year. Over 100 different charges had been leveled against the Templars, including heresy, homosexual relations, spitting and urinating on the cross, and sodomy. Most of them were dubious, as they were the same charges that were leveled against the Cathars and many of King Philip's enemies; he had earlier kidnapped Pope Boniface VIII and charged him with nearly identical offenses. Yet Malcolm Barber observes that historians "find it difficult to accept that an affair of such enormity rests upon total fabrication". The "Chinon Parchment suggests that the Templars did indeed spit on the cross", says Sean Martin, and that these acts were intended to simulate the kind of humiliation and torture that a Crusader might be subjected to if captured by the Saracens, where they were taught how to commit apostasy "with the mind only and not with the heart". Similarly, Michael Haag suggests that the simulated worship of Baphomet did indeed form part of a Templar initiation rite:

"The indictment (acte d'accusation) published by the court of Rome set forth ... 'that in all the provinces they had idols, that is to say, heads, some of which had three faces, others but one; sometimes, it was a human skull ... That in their assemblies, and especially in their grand chapters, they worshipped the idol as a god, as their saviour, saying that this head could save them, that it bestowed on the order all its wealth, made the trees flower, and the plants of the earth to sprout forth.'"

The name Baphomet comes up in several of these dubious confessions. Peter Partner states in his 1987 book The Knights Templar and their Myth: "In the trial of the Templars one of their main charges was their supposed worship of a heathen idol-head known as a Baphomet (Baphomet = Mahomet)." The description of the object changed from confession to confession; some Templars denied any knowledge of it, while others, who confessed under torture, described it as being either a severed head, a cat, or a head with three faces. The Templars did possess several silver-gilt heads as reliquaries, including one marked capud m, another said to be St. Euphemia, and possibly the actual head of Hugues de Payens. The claims of an idol named Baphomet were unique to the Inquisition of the Templars. Karen Ralls, author of the Knights Templar Encyclopedia, argues that it is significant that "no specific evidence [of Baphomet] appears in either the Templar Rule or in other medieval period Templar documents."

"Gauserand de Montpesant, a knight of Provence, said that their superior showed him an idol made in the form of Baffomet; another, named Raymond Rubei, described it as a wooden head, on which the figure of Baphomet was painted, and adds, 'that he worshipped it by kissing its feet, and exclaiming, 'Yalla', which was', he says, 'verbum Saracenorum', a word taken from the Saracens. A templar of Florence declared that, in the secret chapters of the order, one brother said to the other, showing the idol, 'Adore this head—this head is your god and your Mahomet.'"

The name Baphomet came into popular English usage in the 19th century during debate and speculation on the reasons for the suppression of the Templars. Modern scholars agree that the name of Baphomet was an Old French corruption of the name "Mohammed", with the interpretation being that some of the Templars, through their long military occupation of the Outremer, had begun incorporating Islamic ideas into their belief system, and that this was seen and documented by the Inquisitors as heresy. Alain Demurger, however, rejects the idea that the Templars could have adopted the doctrines of their enemies. Helen Nicholson writes that the charges were essentially "manipulative"—the Templars "were accused of becoming fairy-tale Muslims". Medieval Christians believed that Muslims were idolatrous and worshipped Muhammad as a god, with mahomet becoming mammet in English, meaning an idol or false god (see also Medieval Christian views on Muhammad). This idol-worship is attributed to Muslims in several chansons de geste. For example, one finds the gods Bafum e Travagan in a Provençal poem on the life of St. Honorat, completed in 1300. In the Chanson de Simon Pouille, written before 1235, a Saracen idol is called Bafumetz.

Alternative etymologies
While modern scholars and the Oxford English Dictionary state that the origin of the name Baphomet was a probable Old French version of "Mahomet", alternative etymologies have also been proposed.

According to Pierre Klossowski in Le Baphomet (1965, Editions Mercure de France, Paris; translated into English by Sophie Hawkes and published as The Baphomet in 1988 by Eridanos Press): "The Baphomet has diverse etymologies ... the three phonemes that constitute the denomination are also said to signify, in coded fashion, Basileus philosophorum metaloricum: the sovereign (basileus) of metallurgical philosophers, that is, of the alchemical laboratories that were supposedly established in various chapters of the Temple. The androgynous nature of the figure apparently goes back to the Adam Kadmon of the Chaldeans, which one finds in the Zohar" (pages 164–165).

In the 18th century, speculative theories arose that sought to tie the Knights Templar with the origins of Freemasonry. Bookseller, Freemason and Illuminatus Christoph Friedrich Nicolai (1733–1811), in Versuch über die Beschuldigungen welche dem Tempelherrenorden gemacht worden, und über dessen Geheimniß (1782), was the first to claim that the Templars were Gnostics, and that "Baphomet" was formed from the Greek words βαφη μητȢς, baphe metous, to mean Taufe der Weisheit, "Baptism of Wisdom". Nicolai "attached to it the idea of the image of the supreme God, in the state of quietude attributed to him by the Manichaean Gnostics", according to F. J. M. Raynouard, and "supposed that the Templars had a secret doctrine and initiations of several grades", which "the Saracens had communicated ... to them". He further connected the figura Baffometi with the Pythagorean pentacle:

"What properly was the sign of the Baffomet, 'figura Baffometi', which was depicted on the breast of the bust representing the Creator, cannot be exactly determined ... I believe it to have been the Pythagorean pentagon (Fünfeck) of health and prosperity: ... It is well known how holy this figure was considered, and that the Gnostics had much in common with the Pythagoreans. From the prayers which the soul shall recite, according to the diagram of the Ophite-worshippers, when they on their return to God are stopped by the Archons, and their purity has to be examined, it appears that these serpent-worshippers believed they must produce a token that they had been clean on earth. I believe that this token was also the holy pentagon, the sign of their initiation (τελειας βαφης μετεος)."

Émile Littré (1801–1881) in Dictionnaire de la langue francaise asserted that the word was cabalistically formed by writing backward ''tem. o. h. p. ab'', an abbreviation of templi omnium hominum pacis abbas, "abbot, or father of the temple of peace of all men". His source is the "Abbé Constant", which is to say, Alphonse-Louis Constant, the real name of Eliphas Lévi.

Hugh J. Schonfield (1901–1988), one of the scholars who worked on the Dead Sea Scrolls, argued in his book The Essene Odyssey that the word "Baphomet" was created with knowledge of the Atbash substitution cipher, which substitutes the first letter of the Hebrew alphabet for the last, the second for the second last, and so on. "Baphomet" rendered in Hebrew is (bpwmt); interpreted using Atbash, it becomes  (šwpy‘, "Shofya'"), which can be interpreted as the Greek word Sophia, meaning "wisdom". This theory appears as an important plot point in the novel The Da Vinci Code, although it was recently questioned by the French historian Thierry Murcia, who challenges the method of calculation used by Schonfield.

Joseph Freiherr von Hammer-Purgstall

In 1818, the name Baphomet appeared in the essay by the Viennese Orientalist Joseph Freiherr von Hammer-Purgstall, Mysterium Baphometis revelatum, seu Fratres Militiæ Templi, qua Gnostici et quidem Ophiani, Apostasiæ, Idoloduliæ et Impuritatis convicti, per ipsa eorum Monumenta ("Discovery of the Mystery of Baphomet, by which the Knights Templars, like the Gnostics and Ophites, are convicted of Apostasy, of Idolatry and of moral Impurity, by their own Monuments"), which presented an elaborate pseudohistory constructed to discredit Templarist Masonry and, by extension, Freemasonry. Following Nicolai, he argued, using as archaeological evidence "Baphomets" faked by earlier scholars and literary evidence such as the Grail romances, that the Templars were Gnostics and the "Templars' head" was a Gnostic idol called Baphomet:

"His chief subject is the images which are called Baphomet ... found in several museums and collections of antiquities, as in Weimar ... and in the imperial cabinet in Vienna. These little images are of stone, partly hermaphrodites, having, generally, two heads or two faces, with a beard, but, in other respects, female figures, most of them accompanied by serpents, the sun and moon, and other strange emblems, and bearing many inscriptions, mostly in Arabic ... The inscriptions he reduces almost all to Mete[, which] ... is, according to him, not the Μητις of the Greeks, but the Sophia, Achamot Prunikos of the Ophites, which was represented half man, half woman, as the symbol of wisdom, unnatural voluptuousness and the principle of sensuality ... He asserts that those small figures are such as the Templars, according to the statement of a witness, carried with them in their coffers. Baphomet signifies Βαφη Μητεος, baptism of Metis, baptism of fire, or the Gnostic baptism, an enlightening of the mind, which, however, was interpreted by the Ophites, in an obscene sense, as fleshly union ... the fundamental assertion, that those idols and cups came from the Templars, has been considered as unfounded, especially as the images known to have existed among the Templars seem rather to be images of saints."

Hammer's essay did not pass unchallenged, and F. J. M. Raynouard published an Étude sur 'Mysterium Baphometi revelatum' in Journal des savants the following year. Charles William King criticized Hammer, saying that he had been deceived by "the paraphernalia of ... Rosicrucian or alchemical quacks", and Peter Partner agreed that the images "may have been forgeries from the occultist workshops". At the very least, there was little evidence to tie them to the Knights Templar—in the 19th century some European museums acquired such pseudo-Egyptian objects, which were cataloged as "Baphomets" and credulously thought to have been idols of the Templars.

Éliphas Lévi

Later in the 19th century, the name of Baphomet became further associated with the occult. Éliphas Lévi published Dogme et Rituel de la Haute Magie (Dogma and Rituals of High Magic) as two volumes (Dogme 1854, Rituel 1856), in which he included an image he had drawn himself, which he described as Baphomet and "The Sabbatic Goat", showing a winged humanoid goat with a pair of breasts and a torch on its head between its horns (see the illustration). This image has become the best-known representation of Baphomet. Lévi considered the Baphomet to be a depiction of the absolute in symbolic form and explicated in detail his symbolism in the drawing that served as the frontispiece:

"The goat on the frontispiece carries the sign of the pentagram on the forehead, with one point at the top, a symbol of light, his two hands forming the sign of occultism, the one pointing up to the white moon of Chesed, the other pointing down to the black one of Geburah. This sign expresses the perfect harmony of mercy with justice. His one arm is female, the other male like the ones of the androgyne of Khunrath, the attributes of which we had to unite with those of our goat because he is one and the same symbol. The flame of intelligence shining between his horns is the magic light of the universal balance, the image of the soul elevated above matter, as the flame, whilst being tied to matter, shines above it. The beast's head expresses the horror of the sinner, whose materially acting, solely responsible part has to bear the punishment exclusively; the soul is insensitive according to its nature and can only suffer when it materializes. The rod standing instead of genitals symbolizes eternal life, the body covered with scales: the water, the semi-circle above it: the atmosphere, the feathers following above: the volatile. Humanity is represented by the two breasts and the androgyne arms of this sphinx of the occult sciences."

Witches' Sabbath
Lévi's depiction of Baphomet is similar to that of The Devil in the early Tarot. Lévi, working with correspondences different from those later used by S. L. MacGregor Mathers, "equated the Devil Tarot key with Mercury", giving "his figure Mercury's caduceus, rising like a phallus from his groin". The symbol is said to have originated when Mercury / Hermes once attempted to stop a fight between two snakes by throwing his rod at them, whereupon they twined themselves around the rod. The word Caduceus is from the Greek root meaning "herald’s wand" and was also a badge of diplomatic ambassadors and became associated with commerce, eloquence, alchemy, thievery, and lying. The etymology of Caduceus is from Doric Greek κᾱρύκειον karukeion, from the Greek κῆρυξ kērux meaning "herald".

Lévi believed that the alleged devil worship of the medieval Witches' Sabbath was a perpetuation of ancient pagan rites. A goat with a candle between its horns appears in medieval witchcraft records, and other pieces of lore are cited in Dogme et Rituel:

"Below this figure we read a frank and simple inscription—THE DEVIL. Yes, we confront here that phantom of all terrors, the dragon of all theogonies, the Ahriman of the Persians, the Typhon of the Egyptians, the Python of the Greeks, the old serpent of the Hebrews, the fantastic monster, the nightmare, the Croquemitaine, the gargoyle, the great beast of the Middle Ages, and—worse than all these—the Baphomet of the Templars, the bearded idol of the alchemist, the obscene deity of Mendes, the goat of the Sabbath. The frontispiece to this 'Ritual' reproduces the exact figure of the terrible emperor of night, with all his attributes and all his characters ... Yes, in our profound conviction, the Grand Masters of the Order of Templars worshipped the Baphomet, and caused it to be worshipped by their initiates; yes, there existed in the past, and there may be still in the present, assemblies which are presided over by this figure, seated on a throne and having a flaming torch between the horns. But the adorers of this sign do not consider, as do we, that it is a representation of the devil; on the contrary, for them it is that of the god Pan, the god of our modern schools of philosophy, the god of the Alexandrian theurgic school and of our own mystical Neoplatonists, the god of Lamartine and Victor Cousin, the god of Spinoza and Plato, the god of the primitive Gnostic schools; the Christ also of the dissident priesthood ... The mysteries of the Sabbath have been variously described, but they figure always in grimoires and in magical trials; the revelations made on the subject may be classified under three heads—1. those referring to a fantastic and imaginary Sabbath; 2. those which betray the secrets of the occult assemblies of veritable adepts; 3. revelations of foolish and criminal gatherings, having for their object the operations of black magic."

Lévi's Baphomet may have been partly inspired by grotesque carvings on the Templar churches of Lanleff in Brittany and Saint-Merri in Paris, which depict squatting bearded men with bat wings, female breasts, horns and the shaggy hindquarters of a beast.

Socialism, romanticism, and magnetism
Lévi's references to the School of Alexandria and the Templars can be explained against the background of debates about the origins and character of true Christianity. It has been pointed out that these debates included contemporary forms of Romantic socialism, or Utopian socialism, which were seen as the heirs of the Gnostics, Templars, and other mystics. Lévi, being himself an adherent of these schools since the 1840s, regarded the socialists and Romantics (such as Alphonse de Lamartine) as the successors of this alleged tradition of true religion. In fact, his narrative mirrors historiographies of socialism, including the Histoire des Montagnards (1847) by his best friend and political comrade Alphonse Esquiros. Consequently, the Baphomet is depicted by Lévi as the symbol of a revolutionary heretical tradition that would soon lead to the "emancipation of humanity" and the establishment of a perfect social order.

In Lévi's writings, the Baphomet does not only express a historical-political tradition, but also occult natural forces that are explained by his magical theory of the Astral Light. He developed this notion in the context of what has been called "spiritualist magnetism": theories that stressed the religious implications of magnetism. Often, their representatives were socialists that believed in the social consequences of a "synthesis" of religion and science that was to be achieved by the means of magnetism. Spiritualist magnetists with a socialist background include the Baron du Potet and Henri Delaage, who served as main sources for Lévi. At the same time, Lévi polemicized against famed Catholic authors such as Jules-Eudes de Mirville and Roger Gougenot des Mousseaux, who regarded magnetism as the workings of demons and other infernal powers. The paragraph just before the passage cited in the previous section has to be seen against this background:

"Let us state now for the edification of the vulgar, for the satisfaction of M. le Comte de Mirville, for the justification of the demonologist Bodin, for the greater glory of the Church, which persecuted Templars, burnt magicians, excommunicated Freemasons, &c. let us state boldly and precisely that all the inferior initiates of the occult sciences and profaners of the great arcanum, not only did in the past, but do now, and will ever, adore what is signified by this alarming symbol."

Goat of Mendes
Mendes is the Greek name for the ancient Egyptian city of Djedet. Lévi equates his image with "The Goat of Mendes", possibly following the account by Herodotus that the god of Mendes was depicted with a goat's face and legs. Herodotus relates how all male goats were held in great reverence by the Mendesians, and how in his time a woman publicly copulated with a goat. The chief deities of Mendes were the ram deity Banebdjedet (lit. Ba of the Lord of Djedet), who was the Ba of Osiris, and his consort, the fish goddess Hatmehit.

E. A. Wallis Budge writes:

"At several places in the Delta, e.g. Hermopolis, Lycopolis, and Mendes, the god Pan and a goat were worshipped; Strabo, quoting (xvii. 1, 19) Pindar, says that in these places goats had intercourse with women, and Herodotus (ii. 46) instances a case which was said to have taken place in the open day. The Mendisians, according to this last writer, paid reverence to all goats, and more to the males than to the females, and particularly to one he-goat, on the death of which public mourning is observed throughout the whole Mendesian district; they call both Pan and the goat Mendes, and both were worshipped as gods of generation and fecundity. Diodorus compares the cult of the goat of Mendes with that of Priapus, and groups the god with the Pans and the Satyrs."

The link between Baphomet and the pagan god Pan was also observed by Aleister Crowley as well as Anton LaVey:

"Many pleasures revered before the advent of Christianity were condemned by the new religion. It required little change-over to transform the horns and cloven hooves of Pan into a most convincing devil! Pan's attributes could neatly be changed into charged-with-punishment sins, and so the metamorphosis was complete."

Aleister Crowley
The Baphomet of Lévi was to become an important figure within the cosmology of Thelema, the mystical system established by Aleister Crowley in the early 20th century. Baphomet features in the Creed of the Gnostic Catholic Church recited by the congregation in The Gnostic Mass, in the sentence: "And I believe in the Serpent and the Lion, Mystery of Mysteries, in His name BAPHOMET."

In Magick (Book 4), Crowley asserted that Baphomet was a divine androgyne and "the hieroglyph of arcane perfection", seen as that which reflects: "What occurs above so reflects below, or As above so below":

"The Devil does not exist. It is a false name invented by the Black Brothers to imply a Unity in their ignorant muddle of dispersions. A devil who had unity would be a God... 'The Devil' is, historically, the God of any people that one personally dislikes ... This serpent, SATAN, is not the enemy of Man, but He who made Gods of our race, knowing Good and Evil; He bade 'Know Thyself!' and taught Initiation. He is 'The Devil' of The Book of Thoth, and His emblem is, the Androgyne who is the hieroglyph of arcane perfection ... He is therefore Life, and Love. But moreover his letter is ayin, the Eye, so that he is Light; and his Zodiacal image is Capricornus, that leaping goat whose attribute is Liberty."

For Crowley, Baphomet is further a representative of the spiritual nature of the Spermatozoon, while also being symbolic of the "magical child" produced as a result of sex magic. As such, Baphomet represents the Union of Opposites, especially as mystically personified in Chaos and Babalon combined and biologically manifested with the sperm and egg united in the zygote.

Crowley proposed that Baphomet was derived from "Father Mithras". In his Confessions he describes the circumstances that led to this etymology:

"I had taken the name Baphomet as my motto in the O.T.O. For six years and more I had tried to discover the proper way to spell this name. I knew that it must have eight letters, and also that the numerical and literal correspondences must be such as to express the meaning of the name in such a way as to confirm what scholarship had found out about it, and also to clear up those problems which archaeologists had so far failed to solve ... One theory of the name is that it represents the words βαφὴ μήτεος, the baptism of wisdom; another, that it is a corruption of a title meaning 'Father Mithras'. Needless to say, the suffix R supported the latter theory. I added up the word as spelt by the Wizard. It totalled 729. This number had never appeared in my Cabbalistic working and therefore meant nothing to me. It however justified itself as being the cube of nine. The word κηφας, the mystic title given by Christ to Peter as the cornerstone of the Church, has this same value. So far, the Wizard had shown great qualities! He had cleared up the etymological problem and shown why the Templars should have given the name Baphomet to their so-called idol. Baphomet was Father Mithras, the cubical stone which was the corner of the Temple."

Modern interpretations and usage

Lévi's Baphomet is the source of the later tarot image of the Devil in the Rider–Waite design. The concept of a downward-pointing pentagram on its forehead was enlarged upon by Lévi in his discussion (without illustration) of the Goat of Mendes arranged within such a pentagram, which he contrasted with the microcosmic man arranged within a similar but upright pentagram. The actual image of a goat in a downward-pointing pentagram first appeared in the 1897 book La Clef de la Magie Noire, written by the French occultist Stanislas de Guaita. It was this image that was later adopted as the official symbol—called the Sigil of Baphomet—of the Church of Satan, and continues to be used among Satanists.

Baphomet, as Lévi's illustration suggests, has occasionally been portrayed as a synonym of Satan or a demon, a member of the hierarchy of Hell. Baphomet appears in that guise as a character in James Blish's The Day After Judgment. Christian evangelist Jack T. Chick claimed that Baphomet is a demon worshipped by Freemasons, a claim that apparently originated with the Taxil hoax. Lévi's Baphomet was depicted on the cover of Les Mystères de la franc-maçonnerie dévoilés, Léo Taxil's lurid paperback "exposé" of Freemasonry, which, in 1897, he revealed as a hoax intended to ridicule the Catholic Church and its anti-Masonic propaganda.

In 2014, The Satanic Temple commissioned an 8.5 ft statue of Baphomet to stand alongside a monument of the Ten Commandments at the Oklahoma State Capitol, citing "respect for diversity and religious minorities" as reasons for the monument. (The Oklahoma Supreme Court ultimately declared religious displays illegal.) The Baphomet statue was unveiled in Detroit on 25 July 2015, as a symbol of the modern Satanist movement. The Satanic Temple transported the Baphomet statue to Little Rock, Arkansas, where another 10 Commandments monument had been recently installed; the statue was publicly displayed during a Temple demonstration on 16 August 2018.

In popular culture
In Sartor Resartus (1833–34) by Thomas Carlyle, protagonist Diogenes Teufelsdröckh describes his spiritual rebirth as a "Baphometic Fire-baptism". Clive Barker's novel Cabal (1988) and its film adaption, Nightbreed (1990), Baphomet is depicted as the god worshipped by the Night Breed creatures.

An interpretation of Baphomet, referred to as The Sword of Baphomet, forms part of the main plot in the 1996 point-and-click adventure game Broken Sword: The Shadow of the Templars developed by Revolution Software. It is the first game in the Broken Sword series. The player assumes the role of George Stobbart, an American tourist in Paris, as he attempts to unravel a conspiracy, much of which is influenced by and includes factual and fictional references and narrative devices relating to the history of the Knights Templar.

Baphomet appears as a recurring antagonist in the long-running German novel series Geisterjäger John Sinclair, in which he is the master of Vincent van Akkeren and his cult of renegade Knights Templar. The horror novels by author Jason Dark portray Baphomet as one of the three entities that form the unholy trinity of Lucifer, with the other two being Asmodis and Beelzebub.

The 2016 audio drama Robin of Sherwood: The Knights Of The Apocalypse (based on the TV show Robin of Sherwood), has Robin and his companions come into conflict with the titular Knights. The Knights of the Apocalypse are depicted as a cult which worships Baphomet; the Knights are also depicted as a splinter group from the Knights Templar.

The 2018 Netflix series Chilling Adventures of Sabrina has a large statue of Baphomet displayed at the Academy of Unseen Arts. The Satanic Temple accused the show of plagiarizing their statue of Baphomet, though later settled out of court.

title: Baphomet


text:
User:Jimmer

=How long is a chromosome?= Chromosome 1 is the longest human chromosome at 245,203,898 base pairs (bp) according to the published sequence. And the distance between base pairs along the sugar-phosphate backbone of DNA is about 0.33 nanometers (nm). Thus the total length

$$ = \frac{0.33\mathrm{nm}}{\mathrm{bp}} \times 0.25 \times 10^9 \mathrm{bp} \times \frac{\mathrm{m}}{10^9 \mathrm{nm}} = 0.08 \mathrm{m} $$

So the largest human chromosome is almost almost ten centimeters in length!

title: User:Jimmer


text:
The Battle of the River Plate (film)

The Battle of the River Plate (a.k.a. Pursuit of the Graf Spee in the United States) is a 1956 British war film in Technicolor and VistaVision by the writer-director-producer team of Michael Powell and Emeric Pressburger. The film stars John Gregson, Anthony Quayle, Bernard Lee and Peter Finch. It was distributed worldwide by Rank Film Distributors Ltd.

The film's storyline concerns the Battle of the River Plate, an early World War II naval engagement in 1939 between a Royal Navy force of three cruisers and the German pocket battleship GERMAN CRUISER Admiral Graf Spee.

Plot
In the early months of the Second World War, Nazi Germany's Kriegsmarine sends out merchant raiders to attack Allied shipping. The British Royal Navy responds with hunting groups whose mission is to stop these attacks. In time, the German battleship Admiral Graf Spee is discovered in the Atlantic, just off South America, by a trio of British cruisers. With its speed and destructive firepower, Graf Spee is a formidable menace. Nevertheless, the British go straight into attack, closing swiftly to minimise the Graf Spee's substantial advantage in gun range. The British use their superior numbers to split her fire by attacking from different directions. But Graf Spee, under Captain Hans Langsdorff (Peter Finch), inflicts much damage on her foes. One of them, HMS Exeter, is particularly hard hit and is forced to retire to the Falklands for repair.

For her own part, the Graf Spee sustains some damage and takes refuge in the neutral port of Montevideo, Uruguay, for repairs. According to international law, the ship may remain in a neutral harbour only long enough to repair for seaworthiness, not to refit for battle; any overstay will lead to the ship and its crew being interned for the duration of the war. The British initially demand the Uruguayan authorities send Graf Spee out to sea within 24 hours, but once they recognise that reinforcements can arrive for an impending second battle they change strategy and lobby for an extension for the Germans. In reality the most powerful British ships are still extremely distant, but local media spreads false reports that more Royal Navy warships have arrived, including battleships and aircraft carriers; in fact, only three cruisers (Exeter having been replaced by HMS Cumberland (57)) lie in wait.

Taken in by the ruse, Langsdorff takes his ship out with a skeleton crew aboard. As the onlookers watch from shore, she heads down the River Plate for the open sea and then bursts into flames from a series of explosions. It is obvious that Langsdorf has ordered that his ship be scuttled. This is a relief to the Royal Navy fleet, which reports, "Many a life has been saved today". At story's end, Langsdorff is personally complimented by the British for his humane decision.

At sea

 * Peter Finch as Captain Hans Langsdorff, GERMAN CRUISER Admiral Graf Spee
 * Bernard Lee as Captain Patrick Dove, MS Africa Shell
 * Andrew Cruickshank as Captain William Stubbs, SS Doric Star
 * Peter Dyneley as Captain John Robison, SS Newton Beech
 * Anthony Quayle as Commodore (later Rear-Admiral) Henry Harwood, HMS Ajax (22)
 * Ian Hunter as Captain Charles Woodhouse, HMS Ajax
 * Julian Somers as Quartermaster of Admiral Graf Spee
 * Patrick Macnee as Lieutenant Commander Ralph Medley, HMS Ajax
 * John Gregson as Captain Frederick "Hookie" Bell, HMS Exeter (68) (Gregson served in the Royal Navy during the War)
 * Jack Gwillim as Captain Edward Parry, HMS Achilles (70) (Gwillim served 20 years in the Royal Navy, rising to the rank of Commander)
 * John Le Mesurier as the Chaplain of HMS Exeter (minor role)
 * Donald Moffat as Able Seaman Swanston, HMS Ajax (uncredited)
 * Barry Foster as Able Seaman Roper, HMS Exeter (uncredited)

Ashore

 * Lionel Murton as Mike Fowler, American radio reporter in Montevideo
 * Christopher Lee as Manolo, bar owner in Montevideo harbour
 * Edward Atienza as Pop, Mike Fowler's gaucho assistant
 * April Olrich as Dolores (singing voice by Muriel Smith)
 * Anthony Bushell as Eugen Millington-Drake, the British Minister in Uruguay
 * Michael Goodliffe as Captain Henry McCall, British Naval Attaché in Buenos Aires
 * Peter Illing as Dr Alberto Guani, Uruguayan Foreign Minister
 * William Squire as Ray Martin, British SIS agent in Montevideo
 * John Chandos as Dr Otto Langmann, the German Minister in Uruguay
 * Douglas Wilmer as M. Desmoulins, the French Minister in Uruguay
 * Roger Delgado as Captain Varela, Uruguayan Navy

 * Cast notes
 * Future director John Schlesinger has a small part as the German naval officer escorting Dove at the beginning of the film, as does Captain Patrick Dove of Africa Shell, who is himself portrayed by Bernard Lee.
 * Anthony Newley has a small part as a radio operator. Donald Moffat and Barry Foster, both uncredited, were making their film debuts, as was Jack Gwillim.

Production
The Battle of the River Plate had its genesis in an invitation to Michael Powell and Emeric Pressburger to attend a film festival in Argentina in 1954. They decided they could not afford to take the time from their schedules unless it was a working holiday, and used the trip to research the defeat of GERMAN CRUISER Admiral Graf Spee. They came across the "hook" for their story when one of the surviving British naval officers gave Pressburger a copy of Captain Patrick Dove's book I Was Graf Spee's Prisoner, published in 1940., which became the basis of the human story of the film.

Principal photography began on 13 December 1955, the 16th anniversary of the battle. The HMS Ajax and River Plate Association reportedly sent a message to the producers: "Hope your shooting will be as successful as ours". Location shooting for the arrival and departure of Admiral Graf Spee took place at the port of Montevideo, using thousands of locals as extras. However, the scenes showing Admiral Graf Spee sailing from Montevideo were shot in the Grand Harbour at Valletta in Malta, and the launch taking McCall out to HMS Ajax was filmed in Mġarr harbour on Gozo, Malta's northern island.

Two songs written by composer Brian Easdale were used in the film, "Dolores' Song" and "Rio de la Plata". Both were acted by April Olrich as "Dolores", with singing voice dubbed by Muriel Smith.

Ships used

 * GERMAN CRUISER Admiral Graf Spee played by heavy cruiser USS Salem (CA-139) which retained its USN bow number, 139, for the film. This was explained by Captain Langsdorff as part of its camouflage to confuse other ships. One of three heavy cruisers of the Des Moines-class cruiser, she is now a museum ship in Massachusetts.
 * Supply ship GERMAN TANKER Altmark played by the fleet oiler RFAUX Olna (A216)
 * HMS Ajax (22), flagship, played by HMS Sheffield (C24)
 * HMS Exeter (68) played by HMS Jamaica (44)
 * HMNZS Achilles played by herself (at the time in service with the Indian Navy as INS Delhi (1948))
 * HMS Cumberland (57) played by herself when she joins the British squadron after the battle, (and by HMS Jamaica in the final scenes off Montevideo)
 * German freighter Tacoma, which took the crew off Admiral Graf Spee before scuttling, played by RFAUX Fort Duquesne (A229)
 * Gunboat Uruguay, boarding the Tacoma, was played by a British Ton-class minesweeper
 * HMS Birmingham (C19) used for the firing of some of the guns, and to depict the explosions on the foredeck of Exeter, and as Admiral Graf Spee during the replenishment scene with Altmark, as well as the scene on the deck of Admiral Graf Spee showing the flag-draped coffins of dead German sailors laid out for burial in Montevideo
 * Destroyers HMS Battleaxe (D118) and USS William R. Rush (DD-714) used as camera ships. The latter remained in service for many decades after the film, not being scrapped until 2016 after being transferred to the South Korea Navy in 1978.

Most of the action of the battle and prior to it takes place on real ships at sea. The producers had the advantage of having elements of the Mediterranean Fleet of the Royal Navy available for their use, and USS Salem to play the part of Admiral Graf Spee, although she had a different number of main turrets. The producers did make use of a 23 ft model of Salem (with details only on the side being shot) in a 6 ft-deep tank at Pinewood Studios for scenes depicting hits during the battle, and also for the blowing-up of Admiral Graf Spee, which was assembled from multiple takes from different angles.

In an early scene, it is claimed that Admiral Graf Spee is being disguised by the ship's carpenters – using features such as a false funnel – as an American cruiser, a trick typical of commerce raiders. The US Navy would not allow any Nazi insignia to be displayed on Salem so the wartime German flag being hoisted and flown was filmed on a British ship. This is also the explanation as to why the crew of Admiral Graf Spee are seen wearing US Navy pattern helmets rather than German "Coal Scuttles" – whilst the filmmakers wanted to achieve an accurate impression and use German helmets they were refused permission. This aspect is sometimes described as a "goof" on the part of the filmmakers, but was in fact a circumstance beyond their control. Mention is made of Graf Spee's sister ships, Admiral Scheer and Deutschland. Admiral Scheer capsized after an air raid in 1945 and the remains of the wreck buried under a new harbor. Deutschland was renamed Lutzow in 1940 and sunk as a target in 1947.

Two of the original ships, HMNZS Achilles and HMS Cumberland were available for filming 15 years after the events depicted. Cumberland was a disarmed trial ship without her 8-inch gun turrets at this time and was refitted with lattice masts, but is recognizable as the last of the three-funneled heavy cruisers to remain in service. (In the final scenes, Jamaica represented Cumberland as one of the British trio waiting off Montevideo). This use of real warships was in line with an Admiralty policy of co-operation with film-makers, which saw the corvettes HMS Coreopsis and HMS Portchester Castle (K362) reactivated in 1952 for the film version of The Cruel Sea; the cruiser HMS Cleopatra (33) and the minelayer HMS Manxman (M70) used in the 1953 film Sailor of the King, and the destroyer HMS Teazer (R23) and frigate HMS Amethyst (F116) used in the 1955 film Yangtse Incident: The Story of H.M.S. Amethyst.

Achilles had been sold to the newly formed Indian Navy in 1948, becoming INS Delhi. The flagship HMS Ajax was her sister ship, and would have looked identical to Achilles, while the original HMS Exeter was a two-funnelled half-sister of Cumberland. HMS Sheffield and HMS Jamaica, which played Ajax and Exeter, had higher superstructures and more guns, which were mounted in triple turrets. Though different from the ships they represented, both these light cruisers had played a major part in the wartime campaign against the large German surface raiders which began at the Battle of the River Plate, including GERMAN BATTLESHIP Bismarck in 1941, GERMAN CRUISER Admiral Hipper in 1942, GERMAN BATTLESHIP Scharnhorst in 1943, and GERMAN BATTLESHIP Tirpitz in 1944.

Historical details
The use of real ships allows the film to pay particular attention to detail even though Admiral Graf Spee was portrayed by the American heavy cruiser USS Salem, which mounted 3" smaller main guns, is considerably greater in tonnage, 100' longer, and quite visually distinct (in bow, shearline, and having two forward triple turrets instead of the single forward turret of the Deutschland-class cruiser s) from the German Pocket Battleship. This emphasis on realism includes the warning bells ringing before each salvo, the scorching on the gun barrels after the battle, and the accurate depiction of naval procedures. The film depicts Admiral Graf Spee and Altmark using the complex procedure of alongside refueling; actually the Germans used the slower but safer method of astern refuelling, but the alongside method is much more dramatic for film purposes, and by 1955 was standard procedure for the British ships involved (see list above). Similarly, although the scene when Harwood meets with his captains on board Ajax is fictional, it was created for the movie in order to explain the tactical situation to the audience. The battle is seen from the perspective of the British ships, and that of the prisoners captured from nine merchantmen and held in Admiral Graf Spee.

The film devotes nearly 20 minutes to the battle, which actually lasted a little more than an hour before becoming a chase into Montevideo. The initial minutes from the spotting of Admiral Graf Spee at 0614, to her opening fire at 0618, and the British ships returning fire from 0620 are depicted in real time. In reality German gunfire did not "straddle" Exeter until 0623, after three salvoes, and her main armament fire was not "split" between the British ships until 0630, although these events are shown happening immediately. Exeter's bridge and forward turrets were knocked out at 0630, but at this point the film begins to telescope the sequence of events.

Commodore Harwood is shown wearing the sleeve rings of a rear admiral from the start, although he was only promoted to this rank after the battle. This is historically correct, as 'Commodores of the first class' wore those insignia at the time. Exeter's chaplain is also correctly depicted wearing a civilian dark suit and clerical collar; it was not until later in the war that naval chaplains adopted military uniform as a security measure.

The Battle of the River Plate only obliquely hints at one aspect of the story: the death of Captain Hans Langsdorff after he scuttled his ship. In the film Langsdorff is shown as subdued and depressed afterwards. In reality he was taken ashore to the Naval Hotel in Buenos Aires, where he wrote letters to his family and superiors. He then lay atop Admiral Graf Spees battle ensign and shot himself, forestalling allegations that he had avoided further battle action through cowardice; another motivation was his desire, as Admiral Graf Spees captain, to symbolically go down with his ship. He was talked out of this by his officers, who convinced him that his leadership was still needed in seeking amnesty for his crew. Once their fate was decided, Langsdorff took his own life.

Captain Langsdorff was buried in the German section of the La Chacarita Cemetery in Buenos Aires, Argentina and was honoured by both sides in the battle for his honourable conduct. Prior to the destruction of the Graf Spee, the German crew were seen rowing away from the ship whereas in reality they were taken off by an Argentine tugboat. Also not shown is the use of certain captured merchant vessels as prizes, sailed by crews from Graf Spee to carry captured sailors, which were later sunk. In addition a Norwegian merchant ship reported the Graf Spee heading for South America before being spotted by lookouts but this is omitted. Furthermore the British Government secretly arranged for French and British merchant ships to leave Montevideo harbour every 24 hours to delay Graf Spee's departure. Also omitted is Graf Spee attempting to force a merchant ship to stop while she herself was being pursued by the British cruisers.

Release and reception
When The Battle of the River Plate was completed and screened for executives at the Rank Organisation, it was received so well that it was decided to hold the release of the film for a year, so that it could be chosen as part of the next year's Royal Film Performance (in 1956), since 1955's film had already been selected. The royal premiere was held at the Empire Theatre, Leicester Square (now Cineworld) on 29 October 1956 in the presence of Queen Elizabeth II, Princess Margaret, Marilyn Monroe, and Victor Mature.

Box office
The film performed very well at the box office, being the fourth most popular film in Britain in 1957, after High Society, Doctor at Large and The Admirable Crichton.

Critical opinion
At the time of The Battle of the River Plate's release, F. Maurice Speed writing in What's On In London described it as "Long, meticulous in its Naval detail, a little confusing sometimes to the landlubber like myself, [but] wonderfully photographed", adding that "some of the best scenes are the earlier quieter ones between Capt. Langsdorff (Graf Spee) and his prisoner Captain Dove (Bernard Lee). Finch, Lee, John Gregson (Capt. of the gallant "Exeter") and Anthony Quayle (of the "Ajax") all give performances above the average."

Stanley Kauffmann of The New Republic described The Battle of the River Plate as "almost unrelievedly dreadful".

Honours
The Battle of the River Plate was nominated for three BAFTA Awards in 1957, for "Best British Film", "Best British Screenplay" and "Best Film From Any Source".

Book
In 1956 Powell published Graf Spee with Hodder and Stoughton, a.k.a. Death in the Atlantic (Rinehart, US), retelling the story of the film in more detail. In 1976, a second edition was released by White Lion Publishers with the amended title, The Last Voyage of the Graf Spee.

title: The Battle of the River Plate (film)