An art-ificial history of mathematicsetopia.sintlucas.be/3.14/DoReMath SintL.pdf · Afrika + 2 Kunst der Füge 1) Douglas Hofstadter: “Gödel, Escher, Bach, an eternal golden braid”

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An art-ificial history of

mathematics

An art-ificial history of mathematics

Dirk HuylebrouckDepartment for Architecture Sint-Lucas Brussels BELGIUM

"Show" of African music and mathematics

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Kunst der Füge

1) Douglas Hofstadter: “Gödel, Escher, Bach, an eternal golden braid”

M.C. Escher's "Reptiles," modified for quilts by Kay Parker in herbook "Contem-porary Quilts".

Kunst der Füge


Kunst der Füge


Kunst der Füge

Picture of the UN in NY inspired by Escher


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Footprints in ash and pumice dated to 385,000 to 325,000 years ago on the slopes of the Roccamonfina volcano in southern Italy.

2) Dawn

43000 - 82000 years old

Neanderthal flute, Slovenia

2) Dawn

43000 - 82000 years old


Tiny 77000-years-old stone from the Lebombo Mountains in South Africa

2) Dawn

43000 - 82000 years old


France's "Grotte Chauvet" up to 32,000 years ago (horses).

2) Dawn

43000 - 82000 years old


25000 years old “key-pattern” from Mezin, Ukraine

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3) From Africa over the Middle East to Greece

Structural propertiesmusic inAfrica:1 Hemiola2 Additive rhythm3 Gestalt

RujindiriRwanda



RujindiriRwanda

Proportions?



RujindiriRwanda



RujindiriRwanda

“Ostrakas" in what is now called ‘Iraq’

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Delphi stone with music notation of the hymn.

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81:644:33:2

27:16243:128

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4) Greece: Euclide, Parthenon, Cithar


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Roger Herz-Fischler 1987; George Markowsky, 1992

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deffisgabccisd'

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32:2781:64

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27:1616:9

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5) Fibonacci, cathedrals, kyries

Stacking up tones in the medieval tone "system" or … working without it.

deffisgabccisd'

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Stacking up tones in the medievaltone "system" or … working without it.

deffisgabccisd'

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32:2781:64

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deffisgabccisd'

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6) Pacioli, Brunelleschi, simplified ratios

Simplifying ratios in tackling the Pythagorean commaproblem

Filippo Brunelleschi, San Lorenzo, 1440.

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Dutch artistsVredeman de Vries ±1550

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Borromini gallery, as a transportable"blow up 'play' castle"

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Rembrandt, The Night Watch, 1642 (Amsterdam).

7) Newton, Vermeer, Bach

Music studies in centre of attention:mean tone scales, etcmusic geometry

doremi…

11.118… = √5/2 1.25 = (√5/2)2



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11.118… = √5/2 1.25 = (√5/2)2

Aldert Mantje & Jan Maris: Night Watch Research Project

www.verbekefoundation.com/



doremi…

11.118… = √5/2 1.25 = (√5/2)2

Johannes Vermeer 1632 - 1675 Girl with a pearl earring



doremi…

11.118… = √5/2 1.25 = (√5/2)2

The Anatomy Lesson of Dr. Nicolaes Tulp(Rembrandt)

Influence science & technology:linseed (flax seed) replaces egg tempera paint; lenses and mirrors: chiaroscuro (clairobsur), geometric composition ...

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doremifasollasido

11.122…=22/12

1.259…=24/12

1.334…=25/12

1.498…=27/12

1.681…=29/12

1.887…=211/12

2

8) Gauss, J-F Millet, 21/12 relation.

One mathematical rule explains all music notes

John Constable, Dedham Vale 1802

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1.259…=24/12

1.334…=25/12

1.498…=27/12

1.681…=29/12

1.887…=211/12

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Jacques-Louis David, La mort de Socrate 1787

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11.122…=22/12

1.259…=24/12

1.334…=25/12

1.498…=27/12

1.681…=29/12

1.887…=211/12

2



Adolph von Menzel, Flötenkonzert 1850-52

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1.259…=24/12

1.334…=25/12

1.498…=27/12

1.681…=29/12

1.887…=211/12

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Jean-François Millet, The Gleaners (1857), a realistic painting, applying all known techniques before photography.

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261.63 Hz293.66 Hz329.63 Hz349.23 Hz

392 Hz440 Hz

493.88 Hz523.25 Hz

9) Cantor, Seurat, Hertz.

Some label AntonWebern’s “Concerto for Nine Instruments” pointillist.Georges Seurat, Sunday Afternoon on the Island of La

Grande Jatte 1886

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261.63 Hz293.66 Hz329.63 Hz349.23 Hz

392 Hz440 Hz

493.88 Hz523.25 Hz


Some label AntonWebern’s “Concerto for Nine Instruments” pointillist.

Theodoor van Rysselberghe,

Portrait of Alice Sethe, 1888

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261.63 Hz293.66 Hz329.63 Hz349.23 Hz

392 Hz440 Hz

493.88 Hz523.25 Hz


Some label AntonWebern’s “Concerto for Nine Instruments” pointillist.Georges Seurat, Sunday Afternoon on the Island of La

Grande Jatte 1886Georges Seurat, La Parade, 1889

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261.63 Hz293.66 Hz329.63 Hz349.23 Hz

392 Hz440 Hz

493.88 Hz523.25 Hz


Some label AntonWebern’s “Concerto for Nine Instruments” pointillist.

After Georges Seurat, La Parade, 1889

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10) Einstein, Picasso, Grisey.

Pablo Picasso, The Bull lithographies, 1945.

Helmholtz: consonance = overlap overtones,in ear of observer.

Applied by composer Gérard Grisey founder of spectralism.


Pablo Picasso,, Les Demoiselles d'Avignon, 1907




Georges Braque, Violin and Candlestick, 1910.






Einstein formuleerde de bijzondere relativiteitstheorie (1905) weliswaar vóór het kubisme tot bloei kwam (1910-11), maar deze bloei werd uiteraard voorafgegaan door een ontluiking. De nieuwe, relativistische wijze van zien tekent zich in de schilderkunst reeds twintig jaar eerder af, met name in het werk van Cézanne. Bovendien maakt de bijzondere relativiteitstheorie de werkelijkheid nog niet kenbaar als een complex energetisch veld. Deze opvatting van de werkelijkheid, die in het kubisme van 1910 gestalte krijgt, vindt haar wetenschappelijke formulering pas in de algemene relativiteitstheorie, die Einstein in 1916 voltooide.

Uit “Aldo Van Eyck”: […] Hieruit hoeft echter niet geconcludeerd te worden dat het kubisme beïnvloed werd door de relativiteitstheorie.

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Vasarely, Stri Neu. Some speak of colloïdal art, and make comparisons with chemical topics

11) Russell, Vasarelly, sound illusion.

Sound illusions

perception

Bridget Riley,Movement in Squares, 1961.


Sound illusions

perception


Sound illusions

perception


Sound illusions

perception

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Xenakis’ musical pavilion in Brussels (1958) and stochastic music.

Jack The Dripper.

12) Schrödinger, Pollock, Xenakis.


Jackson Pollock, Lavender Mist 1950.



CD collection jazz Pollock allegedly listened to while painting. Is it art?




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13) Finite geometry, minimal art, discrete-tones

Jean-Marie Dendoncker (Belgium) is a carpenter – mathematician, who makes wooden models, for, for instance, an arrangement of 7

points on 7 lines, 3 by 3.

Twelve tone symmetry

Xenakis's Bohor layout


ISISTihany2004Bukowsky




Carlo Sequin's (Berkeley) Minimal Trefoil






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14) Romanticism

Young van Beethoven; Beethoven's third symphony = “good romantic style”

J.M.W. Turner, The fighting Téméraire tugged to her last Berth to be broken, 1839.

14) Romanticism

Young van Beethoven; Beethoven's third symphony = “good romantic style”Francisco de Goya y Lucientes, The Third of

May, 1808.

Egide Charles Gustave Wappers, Episode of the Belgian Revolution of 1830, painted in 1834.

14) Romanticism


Francisco de Goya y Lucientes, The Third of May, 1808.

14) Romanticism


Théodore Géricault, Raft of the Medusa, 1839.

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15) Impressionism

In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.

Edgar Degas, La Classe de Danse, 1874

15) Impressionism

In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.Pierre-Auguste Renoir, Le Moulin de la

Galette, 1876

15) Impressionism

In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.Claude Monet, Impression, soleil levant, 1872

15) Impressionism

In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.

Monet’s Sunset changed to grey values: the disk of the sun had to be added.

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Tatlin Tower. Model of the Monument to the Third Interna-tional

16) Constructivism

Alexander Mosolov’s “Steel Foundry” introduced mechanical sounds.

16) Constructivism


Rodchenko, Stairway, 1930.

16) Constructivism


Constructivists designed of posters for every-thing from film to propa-ganda; here: photo-montage by Gustav Klutsis.

16) Constructivism


Tatlin’s tribute to the working class.

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17) Expressionism

Schoenberg’ s opera “Erwartung” (1909) is called expressionist because of “screaming emotions” of the main character.Constant Permeke, The Daily Bread

17) Expressionism

Schoenberg’ s opera “Erwartung” (1909) is called expressionist because of “screaming emotions” of the main character.

Edvard Munch, The Scream, 1893; forerunner of expressi-onism.

17) Expressionism

Schoenberg’ s opera “Erwartung” (1909) is called expressionist because of “screaming emotions” of the main character.El Greco, View of Toledo, 1595-1610 resembles 20th

cent. expressionism (art-historically: “mannerism”).

17) Expressionism

Schoenberg’ s opera “Erwartung” (1909) is called expressionist because of “screaming emotions” of the main character.

Above: painting by Schoenberg’s friend Kandinsky; left: painting by the composer

Schoenberg.

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18) Continued?* Gödel Escher Bach in recent times?

Popular music?

J. Cage, 1952:4’33”

… of silence

abstract artAd Reinhardt, Painting, 1960

new realism Luc Tuymans The Perfect Table Setting, 2004

Some music is difficult to put in a box and so used here …

* education?

Going by the books? Or …

… learning intuitively, as if it were a game?

18) Continued?

Documents

An art-ificial history of mathematicsetopia.sintlucas.be/3.14/DoReMath SintL.pdf · Afrika + 2 Kunst der Füge 1) Douglas Hofstadter: “Gödel, Escher, Bach, an eternal golden braid”