The colloquium starts with a 13 minute long movie “Physics, Jazz and Poetry”, which documents a concert by the Tomasz Stańko New York Quartet, celebrating the 20th anniversary of the Nobel Prize for the late Polish poet, Wisława Szymborska. The concert was held in Barcelona in March 2016 under the patronage of ICREA and ICFO. After the film Maciej Lewenstein introduces the concept of abstraction, first quoting Wikipedia, and then discussing abstraction in mathematics and equivalence relations. He argues that in natural sciences essentially “Modelling = Abstraction”, and illustrates this in physics, in which building of models is based on abstracting from details of reality. He discusses two examples: a pendulum and the so called quantum simulators of high Tc superconductors. He then looks at the development of the contemporary art as a process of abstraction from the rules of realism in the Western visual arts, or of harmony and tonality in the Western music. In the latter case, he bases his examples on the history of jazz from the swing era to the free improvised music of the XXIst century. The talk ends with a short 20 minute live concert of the free improvised jazz by Vasco Trilla (drums, percussion) and El Pricto (reeds).

1.
Claude Debussy:
La musique est l'arithmétique du son, comme
l'optique est la géométrie de la lumière.
Claude Debussy – Préludes, Livre I,
La fille aux cheveux de lin,
performed by Krystian Zimerman

2.
EU IP SIQS
EU STREP EQuaM
Advanced ERC Grant:
OSYRIS
John Templeton
Foundation
EU FET-Proactive
QUIC
SGR 874
Advanced ERC Grant:
QUAGATUA
FNP
Polish Science Foundation
NCN
Narodowe Centrum Nauki
AvH
Feodor
Lynen
CERCA/Program MPG
MPI
Garching
Sym
fonia
FOQUS and
FISICATEAMO
Abstraction in Science and Art:
From Quantum Simulators
to Free Improvised Jazz

3. ICFO – Quantum Optics Theory
PhD ICFO:
Samuel Mugel (QRandom Walks)
Aniello Lampo (Open Systems)
David Raventos (Gauge Fields)
Emanuelle Tirito (TNS)
Angelo Piga (TNS)
Nils-Eric Gűnther (many body)
Christos Charampoulos (Open Sys)
Noslen Suárez (Atto)
MPI Garching postdoc:
Arnau Riera (Qthermo, Qdyn)
Postdocs ICFO:
Alessio Celi (LGT, Gen. Rel.)
Pietro Massignan (Fermions, Disorder)
Miguel Angel García March (Gauge Fields)
Michał Tomża (Quant-chemistry):
Christian Gogolin (QI, D-wave computers)
Shi-Ju Ran (TNS, many body)
James Quach (many body)
Alexis Chacón (Atto)
Manab Bera (QI)
Swapan Rana (QI)
Alexandre Duaphin
Ex-members and collaborators: François Dubin (CNRS), G. John Lapeyre
(CSIC), Luca Tagliacozzo (Stathclyde), Matthieu Alloing (Paris), Tomek
Sowiński (IFPAN), Phillip Hauke (IQOQI), Omjyoti Dutta (Donostia), Christian
Trefzger (Paris); Kuba Zakrzewski (UJ, Cracow), Mariusz Gajda (IF PAN),
Boris Malomed (Haifa), Ulrich Ebling (Kyoto), Bruno Julia Díaz (UB), Christine
Muschik (IQOQI), Marek Kuś, Remigiusz Augusiak (CFT), Julia Stasińska
(IFPAN), Alexander Streltsov (FUB), Ravindra Chhajlany (UAM), Fernando
Cucchietti (MareNostrum), Anna Sanpera (UAB), Veronica Ahufinger (UAB),
Tobias Grass (JQI,UMD/NIST), Jordi Tura (MPQ)

4.
Why are we here?
A narcissistic motivation…
Barcelona Final eng sub small.mp4

5. Outline: Abstraction in Science and Art
• Abstraction in [Western] visual art
 Ideology: abstracting from “classicist art”: realism
 From realism to abstract expressionism
• Introduction
 Abstraction: definitions from Wikipedia
 Abstraction in mathematics: equivalence relations
 Modelling = Abstraction
• Abstraction in physics
 Ideology: abstracting from “classicist physics”: reality
 How do we build models? A pendulum
 High Tc superconductors
 Quantum Simulators of high Tc superconductors
• Abstraction in [Western] music - jazz
 Ideology: abstracting from “classicist music”: tonal music
 From swing to free jazz and free improvised music

6. Introduction

7. Introduction
Abstraction: definition from Wikipedia:
Abstraction is a process by which concepts are derived
from the usage and classification of literal ("real" or
"concrete") concepts, first principles, or other methods.
"An abstraction" is the product of this process—a
concept that acts as a super-categorical noun for all
subordinate concepts, and connects any related concepts
as a group, field, or category.
Abstractions may be formed by reducing the information
content of a concept or an observable phenomenon,
typically to retain only information which is relevant for
a particular purpose.
For example, abstracting a leather soccer ball to the
more general idea of a ball retains only the information
on general ball attributes and behavior, eliminating the
other characteristics of that particular ball”.

8. Abstraction in mathematics
• Definition from Wikipedia:
“Abstraction in mathematics is the process of extracting the
underlying essence of a mathematical concept, removing any
dependence on real world objects with which it might originally
have been connected, and generalizing it so that it has wider
applications or matching among other abstract descriptions of
equivalent phenomena”.

9. Abstraction in mathematics
• Equivalence relations:
• A given binary relation ~ on a set X is said to be an
equivalence relation if and only if it is reflexive,
symmetric and transitive. Equivalently, for all a, b
and c in X:
• a ~ a. (Reflexivity)
• if a ~ b then b ~ a. (Symmetry)
• if a ~ b and b ~ c then a ~ c. (Transitivity)
• Equivalence classes, or classes of abstraction:
• The equivalence class, or class of abstraction of a
under ~, denoted [a], is defined as [a]={b in X such
that b ~ a}
• Fundamental concept of math and phys: Examples
include quotient spaces in linear algebra, quotient
spaces in topology, quotient groups, homogenous
spaces, quotient rings, quotient monoids, and the
quotient categories. In physics gauge potentials and
gauge fields!

10. Introduction
• Modelling in science:
ML dixit: is the process of extracting the underlying essence of
a real world phenomenon by abstracting from irrelevant details.
• Ergo, Modelling = Abstraction

11. Abstraction in Physics

12. Abstraction in physics
Ideology: abstracting from “classicist model”: reality
Reality is very complex and complicated. If we are interested in the
essence of things, phenomena etc. we should avoid to try to faithfully
describe reality. We should focus on relevant aspects, i.e. abstract
from irrelevant ones…

13. Abstraction in physics: How do we build models?
Interesting phenomenon: A pendulum
From its discovery in around
1602 by Galileo Galilei, the
regular motion of pendulums was
used for timekeeping, and was
the world's most accurate time-
keeping technology until the ‘30s.

14. Interesting quantum phenomenon:
Superconductivity
Superconductors are “ideal” conductors,
they conduct electric currents without
resistance.
They conduct strong currents without losses.
They can generate strong
magnetic fields outside of them,
but due to the Meissner-
Ochsenfeld effect, they do not
let magnetic fields enter them!
Unfortunately, superconductors exist only at
low temperatures: normally close to absolute
zero, -270º Celcius, “high temperature SC”
at T>-166º (boiling of liquid nitrogen)
The Awesome Levitating Train.

15. Superconductivity:
Theory
We (some of us) believe there exist a
simple model that captures the phenomenon
of high Tc superconductivity, the Hubbard
model
Unfortunately, even this simple model is far to hard
to simulate, and hard to understand with
existing computers.
So, why not trying to mimick it
with atoms…

16. Simple Hubbard model
First band
Tunneling On site interactions
(Fermi) Hubbard model
∑−+∑
><
+−
↑↓
∑=
,,
..
,2
1
si
isnch
sij
s
b
s
bJ
i
n
i
n
i
UH µ

17. Quantum Simulators: Ideology
There exist many interesting quantum
phenomena (such as superconductivity)
 Maybe we can use another, simpler and better
controllable quantum system to simulate, understand and
control these phenomena (R.P. Feynman)? Such a system
would thus work as quantum computer of special purpose,
i.e.
These phenomena may have important
applications!
These phenomena are often difficult to describe
and understand with the help of standard computers
QUANTUM SIMULATOR

18. 3D Lattice Potential (by courtesy of M. Greiner,
O. Mandel, T. Esslinger, I. Bloch, and T. Hänsch)
•Resulting potential consists of a simple cubic
lattice
•BEC coherently populates more than 100,000
lattice sites
V0 up to 22 Erecoil
wr up to 2p ´ 30 kHz
n ⊕ 1-5 atoms on
average per site

19. Ultracold atoms in optical lattices: Simulating quantum many-body physics
M. Lewenstein, A. Sanpera, V. Ahufinger, Oxford University Press (2012),
reprint-paperback (2017)
Quantum simulators

20. Abstraction in Visual Art

21. Abstraction in visual art
Ideology: abstracting from “classicist art” - realism
Modern and contemporary art is to a great extend characterized by a
departure from classicist art. Reality is very complex and complicated.
If we are interested in the essence of things, phenomena etc. we
should avoid the faithful reproduction of reality. We should focus on
relevant aspects, i.e. abstract from irrelevant ones…

22. Abstraction in visual art: Realism
Leonardo Da Vinci (1452-1519)
“La Dama con l’Ermellino” (Lady with
Ermine) – a portrait of Cecilia Gallerani, a
mistress of Ludovico Sforza il Moro, Duke
of Milan, painted in 1488, «quando Ludovico
ricevette il prestigioso titolo onorifico di
cavaliere dell'Ordine dell'Ermellino dal re di
Napoli». In Greek ermellino=galée...
This is the only work of Leonardo da Vinci
in Poland – in the collection of Muzeum
Książąt Czartoryskich in Cracow.

23. Abstraction in visual art: Impressionism
Ideology: abstracting from “classicist art”
-impressionism
“Impressionist painting characteristics include relatively small, thin,
yet visible brush strokes, open composition, emphasis on accurate
depiction of light in its changing qualities (often accentuating the
effects of the passage of time), ordinary subject matter, inclusion of
movement as a crucial element of human perception and experience,
and unusual visual angles”.

24. Abstraction in visual art: Impressionism
Claude Monet (1840-1926)
“Impression, soleil levant” – dated 1872, its subject is the harbour of Le Havre in
France, using very loose brush strokes that suggest rather than delineate it. The name
of the art movement came from this. Now in Musée Marmottan Monet, Paris

25. Abstraction in visual art: Cubism
Ideology: abstracting from “classicist art” - Cubism
In Cubist artwork, objects are analyzed, broken up and reassembled in
an abstracted form—instead of depicting objects from one viewpoint,
the artist depicts the subject from a multitude of viewpoints to
represent the subject in a greater context.

26. Abstraction in visual art: Cubism
George Braque
(1882-1963)
Georges Braque's 1908
“Maisons à l’Estaque” (Houses
at L’Estaque) (and related
works) prompted the critic
Louis Vauxcelles to refer to
bizarreries cubiques (cubic
oddities). Now in Kunstmuseum,
Bern.

27. Abstraction in visual art: Cubism
Pablo Picasso
(1881-1973)
Picasso’s, Les Demoiselles
d'Avignon, 1907, considered to
be a major step towards the
founding of the Cubist
movement. The work portrays
five nude female prostitutes
from a brothel on Carrer
d'Avinyó (Avinyó Street) in
Barcelona. Now in MoMA.

28. Abstraction in visual art: Cubism
Pablo Picasso
(1881-1973)
Gertrude Stein referred to
landscapes made by Picasso in
1909, such as Reservoir at
Horta de Ebro, as the first
Cubist paintings. Now in MoMA.

29. Abstraction in visual art: Abstract Art
Ideology: abstracting from “classicist art” –
abstract art
“Abstract art uses a visual language of form, color and line to create
a composition which may exist with a degree of independence from
visual references in the world”.

30. Abstraction in visual art: Abstract Art
Piet Mondrian
(1872-1944)
Pieter Cornelis "Piet" Mondriaan,
after 1906 Mondrian, was a Dutch
painter. He was an important
contributor to the De Stijl art
movement and group, which was
founded by Theo van Doesburg. He
evolved a non-representational form
which he termed neoplasticism. This
consisted of white ground, upon
which was painted a grid of vertical
and horizontal black lines and the
three primary colors.
Composition with Yellow, Blue, and
Red, painted between 1937–42, is
now in Tate Modern, London.

31. Abstraction in visual art: Abstract Art
Kazimir Malevich
(1879-1935)
Kazimir Severinovich Malevich was a
Russian painter and art theoretician. He
was a pioneer of geometric abstract art
and the originator of the avant-garde,
Suprematist movement.
His parents, Ludwika and Seweryn
Malewicz, were ethnic Poles. His native
languages were Russian and Polish. In
1927, Malevich traveled to Warsaw
where he was given a hero's welcome.
Here he met with artists and former
students Władysław Strzemiński and
Katarzyna Kobro, whose own movement,
Unism, was highly influenced by Malevich
Black Square, painted after 1916, is
now in State Russian Museum, St.
Petersburg.

32. Abstraction in visual art: Abstract Art
Katarzyna Kobro (1898-1951) was a Polish sculptor of Russian, Latvian and German origin. Under the
influence of Constructivism she rejected individualism, subjectivism and expressionism, and instead
postulated the absolute objectivism of form. Her main aim was to build an abstract work of art,
based on universal and objective rules discovered through experimentation and analysis. Present &
Correct, from the 1920s, is now in Muzeum Sztuki (Museum of Art) in Łódź.

33. Abstraction in visual art: Abstract Art
Władysław Strzemiński (1893-1952)
was a Polish constructivist and avant-
garde painter of international renown.
During the 1920s he formulated his
theory of Unism (Unizm in Polish). His
Unistic paintings inspired the unistic
musical compositions of the Polish
composer Zygmunt Krauze. He is an
author of a revolutionary book titled
"The theory of vision.“
Kompozycja unistyczna 14 (Unist
Composition 14), painted in 1934, is in
Muzeum Sztuki in Łódź.
The last movie of the late great
Polish film director, Andrzej Wajda,
“Powidoki”, tells the story of
Władysław Strzemiński struggling
against socrealism in the communist
Poland,

34. Abstraction in visual art
Ideology: abstracting from
“classicist art”
– Abstract Expressionism
Abstract Expressionism is an
American post–World War II art movement in
American painting, developed in New York
in the 1940s. It was the first specifically American movement.
In Abstract Expressionism the artist expresses himself purely through
the use of form and color. It is non-representational, or non-
objective, art, which means that there are no actual objects
represented. Technically, it has emphasis on spontaneous, automatic or
subconscious creation – see Jackson Pollock's dripping paint onto a
canvas laid on the floor.
Pollock painting (1950).mp4

35. Abstraction in visual art: Abstract Expressionism
Paul Jackson Pollock (1912-1956) known as Jackson Pollock, was an influential American
painter and a major figure in the Abstract Expressionist movement. He was well known for his
unique style of drip painting.
Autumn Rhythm, painted in 1950, is in Metropolitan Museum of Art.

36. Abstraction in visual art: Abstract Expressionism
Mark Rothko (Latvian:
Markus Rotkovičs, Marcus
Yakovlevich Rothkowitz;
1903- 1970) was an
American painter of Latvian
Jewish descent. He is
generally identified as an
Abstract Expressionist,
although he himself rejected
this label and even resisted
classification as an "abstract
painter." With Jackson
Pollock and Willem de
Kooning, he is one of the
most famous postwar
American artists.
Magenta, Black, Green on
Orange, painted in 1953, is
in MoMA.

37. Abstraction in Music - Jazz

38. Abstraction in music
Ideology: abstracting from “classicist music” –
tonal and harmonic music
Modern and contemporary music is to a great extend characterized by
a departure from tonal and harmonic music. Reality is very complex and
complicated. If we are interested in the essence of things, phenomena
etc. We should avoid the rules of tonality and harmony. We should
focus on relevant aspects, i.e. abstract from irrelevant ones…

39. Abstraction in music
Ideology: abstracting from “classicist music” –
tonal and harmonic music
Tonality is a system/language of music in which specific hierarchical
pitch relationships are based on a key "center"—and the root of the
tonic triad; that is, on hierarchical relationships between the roots of
triads.
In music, harmony is the use of simultaneous pitches (tones, notes), or
chords. The study of harmony involves chords and their construction
and chord progressions and the principles of connection that govern
them. Harmony is often said to refer to the "vertical" aspect of
music, as distinguished from melodic line, or the "horizontal" aspect

40. Abstraction in music: Classicist jazz - Swing
Swing music, or simply Swing, is a form of American jazz that developed in the early
1930s and became a distinctive style by 1940. Swing uses a strong rhythm section of
double bass and drums as the anchor for a lead section of brass instruments such as
trumpets and trombones, reeds including saxophones and clarinets, and sometimes
stringed instruments such as violin and guitar, medium to fast tempos, and a "lilting"
swing time rhythm. The name swing came from the phrase ‘swing feel’ where the
emphasis is on the off–beat or weaker pulse in the music (unlike classical music). Swing
jazz bands featured soloists who would improvise on the melody over the arrangement.
Elements of swing:
•Tonality
•Harmony
•Melody (frequently based in Black American folk – blues, gospels, spirituals)
•Rhythm
•Swing feeling
•Syncopation, a musical effect caused by a syncope, missed beat or off-the-beat stress
•Improvisations, respecting the chords progression
Alvin “Junior” Raglin on bass
Duke Ellington - C Jam Blues (1942).mp4

41. Abstraction in music: Bebop
Bebop or bop is a style of jazz characterized by fast tempo, instrumental
virtuosity, and improvisation based on the combination of harmonic structure and
melody. It was developed in the early and mid-1940s.
Elements of bebop:
•Tonality
•Advanced harmonies (blue notes, flatted fifth)
•Complex melody
•Fast rhythm
•Rhythmic phrasing (weak beats and off beats, ending phrases on the second half
of the fourth beat)
•Complex syncopation
•Improvisations, respecting altered chords, and chord substitutions
”Billie’s Bounce” (1945): Charlie Parker (as); Miles Davis (t);
Dizzy Gillespie (p); Curly Russell (b); Max Roach (dr)

42. Abstraction in music: Modal Jazz
In music, a scale is any set of musical notes ordered by fundamental frequency or
pitch. A scale ordered by increasing pitch is an ascending scale, while descending
scales are ordered by decreasing pitch. Some scales contain different pitches when
ascending than when descending (for instance, Chromatic scale and Melodic minor
scale).
Modal jazz is jazz that uses musical modes (scales) rather than chord progressions
as a harmonic framework. Originating in the late 1950s and 1960s, modal jazz is
epitomized by Miles Davis's "Milestones" (1958), “Kind of Blue” (1959), and John
Coltrane's classic quartet from 1960–64.
Elements of modal jazz:
•Tonality
•Departure from harmony: scales instead of chords
•Complex melody
•Complex rhythm
•Complex syncopation
•Improvisations, respecting scales, rather than chords

43. Abstraction in music: Free Jazz
Free jazz is an approach to jazz music that was first developed in the 1950s and
1960s. Though the music produced by free jazz composers varied widely, the
common feature was a dissatisfaction with the limitations of bebop, hard bop, and
modal jazz, which had developed in the 1940s and 1950s. Each in their own way,
free jazz musicians attempted to alter, extend, or break down the conventions of
jazz, often by discarding hitherto invariable features of jazz, such as fixed chord
changes or tempos. While usually considered experimental and avant-garde, free
jazz has also oppositely been conceived as an attempt to return jazz to its
"primitive", often religious roots, and emphasis on collective improvisations.
Elements of modal jazz:
•Departure from tonality
•Departure from harmony: collective improvisation
•Complex themes, if any
•Complex rhythm and syncopation - pulsation
•Improvisations, not respecting any rules, totally free; often collective
Freddie Hubbard – trumpet, Dewey Johnson – trumpet, Marion Brown – alto saxophone, John Tchicai – alto
saxophone, John Coltrane – tenor saxophone, Pharoah Sanders – tenor saxophone, Archie Shepp – tenor saxophone
McCoy Tyner – piano, Art Davis – bass, Jimmy Garrison – bass, Elvin Jones – drums

44. Abstraction in music: Free Improvised Jazz/Music
Free improvisation or free music is improvised music without any rules
beyond the logic or inclination of the musician(s) involved. The term can
refer to both a technique (employed by any musician in any genre) and as a
recognizable genre in its own right.
Free improvisation, as a genre of music, developed in the U.S. and Europe
in the mid to late 1960s, largely as an outgrowth of free jazz and modern
classical music. None of its primary exponents can be said to be famous
amongst the general public; however, in experimental circles, a number of
free musicians are well known, including saxophonists Evan Parker, Anthony
Braxton, John Zorn and Peter Brötzmann, trombonist George Lewis,
guitarist Derek Bailey and the improvising groups The Art Ensemble of
Chicago and AMM. More recently, Barry Guy, Ken Vandermark, … Agustí
Fernández is one of the world leaders.
Elements of free improvised jazz:
•Total freedom
BARRY GUY AUGUSTI FERNÁNDEZ
RAMÓN LÓPEZ TRIO - Rec. by DTS Studio.mp4

45. ICFO-QOT
Progress Status Workshop
Barcelona
18-20 March 2015
Miscellanea

46. The Concert - Free Improvised Music
Vasco Trilla
El Pricto