M. C. Escher: Visions of Symmetry (Doris Schattschneider)

M. C. Escher: Visions of Symmetry

D'avance assassinés...

Samuel Jessurun de Mesquita and his wife were killed in Auschwitz. His son Jaap perished in the concentration camp at Theresienstadt.
The french poet Robert Desnos also died, very ill, in the concentration camp at Theresienstadt shortly after its liberation. First, he was arrested by the Gestapo and sent to a concentration camp located in Compiègne, France.

Robert Desnos: «Robert Desnos est un poète français, né le 4 juillet 1900 à Paris et mort du typhus le 8 juin 1945 au Camp de concentration de Theresienstadt, en Tchécoslovaquie à peine libérée du joug de l'Allemagne nazie.»

Robert le diable

Tu portais dans ta voix comme un chant de Nerval
Quand tu parlais du sang jeune homme singulier
Scandant la cruauté de tes vers réguliers
Le rire des bouchers t'escortait dans les Halles
Tu avais en ces jours ces accents de gageure
Que j'entends retentir à travers les années
Poète de vingt ans d'avance assassiné
Et que vengeaient déjà le blasphème et l'injure

Je pense à toi Desnos qui partis de Compiègne
Comme un soir en dormant tu nous en fis récit
Accomplir jusqu'au bout ta propre prophétie
Là-bas où le destin de notre siècle saigne

Debout sous un porche avec un cornet de frites
Te voilà par mauvais temps près de Saint-Merry
Dévisageant le monde avec effronterie
De ton regard pareil à celui d'Amphitrite
Enorme et palpitant d'une pâle buée
Et le sol à ton pied comme au sein nu l'écume
Se couvre de mégots de crachats de légumes
Dans les pas de la pluie et des prostituées

Je pense à toi Desnos qui partis de Compiègne
Comme un soir en dormant tu nous en fis récit
Accomplir jusqu'au bout ta propre prophétie
Là-bas où le destin de notre siècle saigne

Et c'est encore toi sans fin qui te promènes
Berger des longs désirs et des songes brisés
Sous les arbres obscurs dans les Champs-Elysées
Jusqu'à l'épuisement de la nuit ton domaine
O la Gare de l'Est et le premier croissant
Le café noir qu'on prend près du percolateur
Les journaux frais les boulevards pleins de senteur
Les bouches du métro qui captent les passants

Je pense à toi Desnos qui partis de Compiègne
Comme un soir en dormant tu nous en fis récit
Accomplir jusqu'au bout ta propre prophétie
Là-bas où le destin de notre siècle saigne

La ville un peu partout garde de ton pasaje
Une ombre de couleur à ses frontons salis
Et quand le jour se lève au Sacré-Cœur pâli
Quand sur le Panthéon comme un équarissage
Le crépuscule met ses lambeaux écorchés
Quand le vent hurle aux loups dessous le Pont-au-Change
Quand le soleil au Bois roule avec les oranges
Quand la lune s'assied de clocher en clocher

Je pense à toi Desnos qui partis de Compiègne
Comme un soir en dormant tu nous en fis récit
Accomplir jusqu'au bout ta propre prophétie
Là-bas où le destin de notre siècle saigne

(Louis Aragon)

Video: Robert le diable, poème d'Aragon mis en musique par Jean Ferrat

Samuel Jessurun de Mesquita (16 June 1868, Amsterdam - 11 February 1944 (?), Auschwitz) and M. C. Escher

«These days, Jessurun de Mesquita (1868-1944) is known principally for his association with one of his pupils, M.C. Escher. He is also well-known in the Netherlands for his crisp woodcuts of animals in Amsterdam’s Artis zoo. But De Mesquita’s surviving oeuvre is far more varied and innovative than is generally assumed. This first major retrospective in twenty years illustrates the point with drawings, water colours, woodcuts, etchings, paintings and examples of the applied arts.
Samuel Jessurun de Mesquita grew up in the closed world of Amsterdam’s Portuguese(*) Jewish community. He trained at the city’s school of applied arts and state teachers’ training college.»

Samuel Jessurun de Mesquita on gemeentemuseum.nl
(*) Father: Josua Jessurun de Mesquita. Mother: Judith Mendes da Costa

«With Nazi Germany’s invasion of the Netherlands in May, 1940, de Mesquita, already in poor health, was forced to lead a secluded life, limiting his work largely to sketches. In the winter of 1944, on either January 31 or February 1, the occupying German forces entered the home of the de Mesquita family in Watergraafsmeer, now part of Amsterdam, and apprehended him, his wife Elisabeth, and their only son Jaap. Transported to Auschwitz, Samuel Jessurun and Elisabeth were sent to the gas chambers within days of their arrival on February 11; Jaap perished in the concentration camp at Theresienstadt on March 20. Escher and some of Jaap’s friends were successful in rescuing some of the works that had remained in the de Mesquita home.» Samuel Jessurun de Mesquita (Wikipedia)

«Still trying to pursue a career in architecture, M.C. Escher next moved to Haarlem and began studies as the School for Architecture and Decorative Arts. After on a week in the city, he met the artist Jessurun de Mesquita. After seeing Escher's drawings, Mesquita and the school's director advised him to continue with them. He began full-time study of "the graphic and decorative arts" in the fall of 1919. Also at this time, he acquired a white cat as a present from his land-lady. (...) The Nazi persecution of the Jews touched Escher in a very personal way. His old teacher, Samuel de Mesquita, a Jew, was taken away by the Nazis in January of 1944, and was killed. Escher helped to transfer Mesquita's works at the Stedelijk Museum in Amsterdam. He kept for himself a sketch that bore the imprint of a German boot, and kept it with his drawing supplies for the rest of his life. In 1946, he organized a memorial showing for Mesquita at the Stedelijk. Immediately after the war ended, Escher participated in a show of works by artists who had refused to collaborate with the Nazi regime. Afterwards, he earned several new commissions, including one to make 400 copies of one of his prints for distribution to schools.»

«In September 1920 Maurits moved to Haarlem in a final attempt to try follow his father's wish that he study architecture and he enrolled at the School for Architecture and Decorative Arts. A chance meeting with Samuel Jesserum de Mesquita, a graphic arts teacher, proved a landmark event in Escher's life and he became convinced that a graphic arts programme would be better suited to his skills. De Mesquita taught the eager Escher all he knew of woodcut printing techniques, gave him space to experiment, and encouraged him to experiment widely in order to develop his skills.»
Maurits Cornelius Escher

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Listen Escher about the influence that Mesquita had in his change from architecture to graphic art: Interview part 2 (listen also: Interview part 1 Interview part 3)

Interviews from The Official M.C. Escher Website

The Fantastic World of M. C. Escher

The Fantastic World of MC Escher - Part 1/5
The Fantastic World of MC Escher - Part 2/5
The Fantastic World of MC Escher - Part 3/5
The Fantastic World of MC Escher - Part 4/5
The Fantastic World of MC Escher - Part 5/5
(A film by Michele Emmer, with music by Ennio Morricone)

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IMDb: The Fantastic World of M.C. Escher (1980)
The Fantastic World of M.C. Escher

Nexus 2010: Relationships Between Architecture and Mathematics

Nexus 2010

Relationships Between Architecture and Mathematics

13-15 June 2010, Porto, Portugal

Akira Kurosawa: Dersu Uzala (Дерсу Узала)

1/15 , 2/15 , 3/15 , 4/15 , 5/15
6/15 , 7/15, 8/15 , 9/15 , 10/15
11/15 , 12/15 , 13/15 , 14/15 , 15/15

Akira Kurosawa (23 March 1910 – 6 September 1998)

Akira Kurosawa: a hundred years of human dreams

Akira Kurosawa (黒澤 明 or 黒沢 明, Kurosawa Akira, 23 March 1910 – 6 September 1998)

Video: Crows or Crows (Akira Kurosawa Dreams, 1990)

A arte matemática de M. C. Escher

M.C. Escher Self-Portrait 1929 Lithograph
*
Video, here:
The Mathematical Art Of M. C. Escher

or here:

Matemática de M. C. Escher
***
Biography of M.C. Escher

***

Interview part 1 Interview part 2 Interview part 3

Dia Mundial da Poesia / World Poetry Day

Inventario galante

Tus ojos me recuerdan
las noches de verano,
negras noches sin luna,
orilla al mar salado,
y el chispear de estrellas
del cielo negro y bajo.
Tus ojos me recuerdan
las noches de verano.
Y tu morena carne,
los trigos requemados
y el suspirar de fuego
de los maduros campos.
(…)
De tu morena gracia,
de tu soñar gitano,
de tu mirar de sombra
quiero llenar mi vaso.
Me embriagaré una noche
de cielo negro y bajo,
para cantar contigo,
orilla al mar salado,
una canción que deje
cenizas en los labios...
De tu mirar de sombra
quiero llenar mi vaso.
(…)

*
Video:
Inventario Galante (Tus ojos me recuerdan), Antonio Machado

Dia Mundial da Poesia / World Poetry Day

Les Poètes, Extraits de Prologue

Je ne sais ce qui me possède
Et me pousse à dire à voix haute
Ni pour la pitié ni pour l'aide
Ni comme on avouerait ses fautes
Ce qui m'habite et qui m'obsède

Celui qui chante se torture
Quels cris en moi quel animal
Je tue ou quelle créature
Au nom du bien au nom du mal
Seuls le savent ceux qui se turent

Machado dort à Collioure
Trois pas suffirent hors d'Espagne
Que le ciel pour lui se fît lourd
Il s'assit dans cette campagne
Et ferma les yeux pour toujours

Au-dessus des eaux et des plaines
Au-dessus des toits des collines
Un plain-chant monte à gorge pleine
Est-ce vers l'étoile Hölderlin
Est-ce vers l'étoile Verlaine

Marlowe il te faut la taverne
Non pour Faust mais pour y mourir
Entre les tueurs qui te cernent
De leurs poignards et de leurs rires
A la lueur d'une lanterne

Étoiles poussières de flammes
En août qui tombez sur le sol
Tout le ciel cette nuit proclame
L'hécatombe des rossignols
Mais que sait l'univers du drame

La souffrance enfante les songes
Comme une ruche ses abeilles
L'homme crie où son fer le ronge
Et sa plaie engendre un soleil
Plus beau que les anciens mensonges

Je ne sais ce qui me possède
Et me pousse à dire à voix haute
Ni pour la pitié ni pour l'aide
Ni comme on avouerait ses fautes
Ce qui m'habite et qui m'obsède

(Louis Aragon)

Videos:
Jean Ferrat - Les poètes
JEAN FERRAT - LES POÈTES
Jean Ferrat - Les Poètes

Symmetry / Simetria (14)

In each of these photos one can see one of the six natural solutions of the dodecahedron (2) puzzle. This solution is easily recognized because it has the number 1 assigned to orthogonal edges. See Symmetry / Simetria (10).

In all these photos the dodecahedron in the middle is obtained from the one in the left hand side using a reflection and the dodecahedron in the right hand side is obtained from the one in the middle using a permutation of the numbers.

Vidro côncavo

Tenho sofrido poesia
como quem anda no mar.
Um enjoo. Uma agonia.
Sabor a sal. Maresia.
Vidro côncavo a boiar.

Dói esta corda vibrante.
A corda que o barco prende
à fria argola do cais.
Se vem onda que a levante
vem logo outra que a distende.
Não tem descanso jamais.

(António Gedeão, in Movimento Perpétuo, 1956)

Symmetry / Simetria (13)

In this first photo: the dodecahedron in the middle is obtained from the one in the left hand side using a reflection and the permutation (24)(35) of the numbers and the dodecahedron in the right hand side is obtained from the one in the middle using the permutation (12)(35) of the numbers.
In this second photo: the dodecahedron in the middle is obtained from the one in the left hand side using a reflection and the dodecahedron in the right hand side is obtained from the one in the middle using the permutation (12)(35) of the numbers
In this third photo: the dodecahedron in the middle is obtained from the one in the left hand side using a reflection and the dodecahedron in the right hand side is obtained from the one in the middle using the permutation (12)(35) of the numbers

In each of these photos one can see two of the six natural solutions of the dodecahedron (2) puzzle that belong to the same equivalence class. These solutions are easily recognized because they have the number 1 (the two solutions in the l.h.s.) and the number 2 (solution in the r.h.s) assigned to orthogonal edges. See Symmetry / Simetria (10).

A history of symmetry (Ian Stewart)

Ian Stewart (Wikipedia)
*

Vídeo:
A history of symmetry

Symmetry / Simetria (12)

In these first three photos: the right hand side is obtained from the left hand side using the identity permutation of the numbers

In this fourth photo: the right hand side is obtained from the left hand side using the permutation (13)(24) of the numbers

In this fifth photo: the right hand side is obtained from the left hand side using a reflection and the permutation (14)(23) of the numbers

In this sixth photo: the right hand side is obtained from the left hand side using a reflection and the permutation (134) of the numbers

In this seventh photo: the right hand side is obtained from the left hand side using the permutation (123) of the numbers

In this eighth photo: the right hand side is obtained from the left hand side using the permutation (123) of the numbers

In each of these photos one can see one of the six natural solutions of the dodecahedron (2) puzzle. This solution is easily recognized because it the number 5 assigned to orthogonal edges. See Symmetry / Simetria (10).

A ti, maravillosa disciplina... dodecaedro azul...

Frieze with dancers (Madrid, 1920)

A LA DIVINA PROPORCIÓN

A ti, maravillosa disciplina,
media extrema razón de la hermosura
que claramente acata la clausura
viva en la malla de tu ley divina.

A ti, cárcel feliz de la retina,
áurea sección, celeste cuadratura,
misteriosa fontana de mesura
que el Universo armónico origina.

A ti, mar de los sueños angulares,
flor de las cinco formas regulares,
dodecaedro azul, arco sonoro.

Luces por alas un compás ardiente.
Tu canto es una esfera transparente.
A ti, divina proporción de oro.

(Rafael Alberti, A LA PINTURA (Poema del color y la línea), 1945-1967)

Ver
Fundación Rafael Alberti

«Sua mítica vida está ligada, durante quase um século, aos acontecimentos culturais, políticos e sociais mais destacados da Espanha. Desde sua afiliação ao Partido Comunista, seu trabalho na Aliança de Intelectuais Antifascistas durante a Guerra Civil, sua colaboração durante a disputa junto a Maria Teresa León e outros intelectuais no salvamento de importantes obras de arte do patrimônio cultural espanhol - "Las Meninas" de Velázquez, "Carlos V" de Tiziano -, até sua presidência honorária com Dolores Ibárruri nas primeiras Cortes Democráticas... Tudo isso faz de Alberti um personagem singular da história espanhola mais recente.»

Symmetry / Simetria (11)

In this first photo: the right hand side is obtained from the left hand side using the permutation (15423) of the numbers
In this second photo: the right hand side is obtained from the left hand side using a reflection and the permutation (354) of the numbers
In this third photo: the right hand side is obtained from the left hand side using a reflection and the permutation (354) of the numbers

In this fourth photo: the right hand side is obtained from the left hand side using a reflection and the permutation (15432) of the numbers

In this fifth photo: the right hand side is obtained from the left hand side using the permutation (12354) of the numbers

In each of these photos one can see two of the six natural solutions of the dodecahedron (2) puzzle. These solutions are easily recognized because they have the number 5 (solution in the l.h.s.) and the number 4 (solution in the r.h.s) assigned to orthogonal edges. See Symmetry / Simetria (10).

A vida de ninguém estava em condições de continuar a ser uma paz podre...

(...) As coisas que tinham acontecido — arrastando toda a gente para uma realidade crua e imediata — impediam que todos continuassem calmamente a ser, com inocência ou sem ela, o que tinham sido até aí. A Guerra Civil espanhola fizera isso. As minhas motivações, as dos meus tios, as dos Ramos e dos Macedos, do Almeida, de todos, eram perfeitamente secundárias. Todas elas haviam convergido num envolvimento geral que a guerra precipitara de dois modos: como repercussão, e como charneira decisiva. A vida de ninguém estava em condições de continuar a ser uma paz podre. Não seria também uma paz limpa. Era uma guerra, com tudo o que ela implica de podridão e de lixo. A minha guerra, como a dos que tinham partido (se é que tinham), começava agora. Contra quem? E em favor de quê? Isso não me aparecia claramente, mas sem dúvida do meu direito, e o dos outros, de ser neles e por eles, reciprocamente. Mas contra quem? Contra a exigência de ser, pura e simplesmente, uma unidade ideal e fictícia. (...)

(Jorge de Sena, Sinais de Fogo, Capítulo XXVII)

Symmetry / Simetria (10)

The dodecahedron (2) puzzle

This puzzle has 6 natural solutions and 2 equivalence classes that can be distinguished in the following form. Consider two opposite dodecahedron edges. There are other four that are orthogonal to these two. The six edges are over the faces of a virtual cube where the dodecahedron is inscribed. There are five such cubes. The first equivalence class (with only one element / natural solution, see Symmetry / Simetria (9)) has the same number associated to the edges that belong to the faces of each cube. The second equivalence class (with five elements / natural solutions) has the same number associated to the edges that belong to the faces of one of the fives cubes.
The first class group is of order 120 and the second class group is of order 24.

In this first photo: the right hand side is obtained from the left hand side using the permutation (123) of the numbers

In this second photo: the right hand side is obtained from the left hand side using the permutation (25)(34) of the numbers
In this third photo: the right hand side is obtained from the left hand side using the permutation (12354) of the numbers
In this fourth photo: the right hand side is obtained from the left hand side using the permutation (12345) of the numbers

In this fifth photo: the right hand side is obtained from the left hand side using the permutation (123) of the numbers

In each of these photos one can see two of the six natural solutions of the dodecahedron (2) puzzle. These solutions are easily recognized because they have the number 2 (solution in the l.h.s.) and the number 3 (solution in the r.h.s) assigned to orthogonal edges.

Por que razão os tigres têm listras e os leopardos têm manchas?

Female tiger, caged in Chitwan National Park, Sauraha, Nepal

***

[PPT] Turing Patterns in Animal Coat
Why do animals' coats have patterns like spots, or stripes?
Understanding Why Leopards Can't Change Their Spots
«The leopard cannot change its spots, nor can the tiger change its stripes, but a new research report published in the January 2010 issue of the journal Genetics tells us something about how cats end up with their spots and stripes. It demonstrates for the first time that at least three different genes are involved in the emergence of stripes, spots, and other markings on domestic cats.»
Nature's numbers : discovering order and pattern in the universe, Ian Stewart
Why do many flowers have five or eight petals, but very few have six or seven? Why do snowflakes have sixfold symmetry? Why do tigers have stripes but leopards have spots? This book takes the reader on a mathematical sightseeing tour of the natural world.

[PDF] Pourquoi le léopard est-il tacheté et le tigre rayé ?

Le pelage des animaux

Symmetry / Simetria (9)

In this first photo: the right hand side is obtained from the left hand side using the identity permutation of the numbers
In this second photo: the right hand side is obtained from the left hand side using the permutation (25)(34) of the numbers
In this third photo: the right hand side is obtained from the left hand side using the permutation (13)(24) of the numbers

In this fourth photo: the right hand side is obtained from the left hand side using the permutation (354) of the numbers

Dodecahedron (2) puzzle

In each of these photos one can see one of the six natural solutions of the dodecahedron (2) puzzle. This solution is easily recognized because it has the same numbers assigned to orthogonal edges. It is symmetric by a reflection or a central symmetry (here colours do not matter, only numbers matter). This is a symmetry of this solution. This symmetry belongs to the group of this solution. If you exchange (an even permutation) of the numbers you obtain the same natural solution that belongs also to its group. It is the icosahedron's group and it has 120 elements. We just saw a simple way of showing an isomorphism between the icosahedron/dodecahedron's group and the group generated by the reflections and the even permutations of {1,2,3,4,5}: {-1,1}xA5.

Mesmo que dois e dois já não sejam quatro...

Richard II Quarante

Ma patrie est comme une barque
Qu'abandonnèrent ses haleurs
Et je ressemble à ce monarque
Plus malheureux que le malheur
Qui restait roi de ses douleurs

Vivre n'est plus qu'un stratagème
Le vent sait mal sécher les pleurs
II faut haïr tout ce que j'aime
Ce que je n'ai plus donnez-leur
Je reste roi de mes douleurs

Le cœur peut s'arrêter de battre
Le sang peut couler sans chaleur
Deux et deux ne fassent plus quatre
Au Pigeon-Vole des voleurs
Je reste roi de mes douleurs

Que le soleil meure ou renaisse
Le ciel a perdu ses couleurs
Tendre Paris de ma jeunesse
Adieu printemps du Quai-aux-Fleurs
Je reste roi de mes douleurs

Fuyez les bois et les fontaines
Taisez-vous oiseaux querelleurs
Vos chants sont mis en quarantaine
C'est le règne de l'oiseleur
Je reste roi de mes douleurs

II est un temps pour la souffrance
Quand Jeanne vint à Vaucouleurs
Ah coupez en morceaux la France
Le jour avait cette pâleur
Je reste roi de mes douleurs

(Louis Aragon, Le Crève-coeur, 1941)


"My Crown I am, but still my griefs are mine:
You may my glories and my state depose,
But not my griefs ; still am I King of those."
William SHAKESPEARE, Richard the Second, Act Four, Scene One.

Colette Magny - Richard II Quarante

Symmetry / Simetria (8)

Icosidodecahedron puzzle