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8/8/2019 Mathematics, arts and photography by Dr Marcella Lorenzi, University of Calabria
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MATHEMATICS, ART
AND PHOTOGRAPHY
(from Antiquity to Futurism)Talk at the Final Event: SCIENAR Project
The Dutch Academy of Science
Amsterdam, 15 October 2010
Marcella Giulia LORENZI
(Universit della Calabria)(in collaboration with Mauro FRANCAVIGLIA)
Part I: Geometry in Art untilXX Century
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GEOMETRY AND ART from Antiquity to Futurism
Agreement Number 2008-2254/001-001 CTU-MECOAN
SCIENtific Scenarios and theARts
Culture Project
PARTNERS
University of Calabria - Italy (Coordinator)
Institute for Computers - Romania
Virtual Image - England
Electronic Media Reporting - NL
Polytechnic School - Slovakia
www.scienar.eu/main
Project SCIENAR
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Project SCIENAR
Art and Science: they shared deep relationships over the centuries
from ancient Greek to nowadays
Interdisciplinary Approach: scientific and humanistic domains are part of
A SINGLE AND UNIQUE CULTURE
Today: Importance of communicating and diffusing Science through emotion
Possibility of involvement of public and policy makers, more funding
GEOMETRY AND ART from Antiquity to Futurism
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Katherine Hayles says that: artistic expression and Science are cultural products that,
at the same time, express and contribute to form the matrix of the culture itself out of
which they emerge.
Observing reality through the
algorithmic formulation means to
contemplate the true image ofreality, to grasp its mechanisms,
to understand its secret codes.
[] Accordingly, all constraints,
all obstacles, all bridgeless
abyssae between Art and Science
disappear (from an interview
with Haebel, i.e. AntonioDAnna, one of the major
exponents of Fractalism in Italy).
Geometry & Art - A Parallel Development I
Art & Science as a Whole
William Latham- Internal Shape
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The new relation between Art and Science has to be
understood in terms of dynamical complexity: well
established although unpredictable. One looks for a way to
escape cultural addiction, rigid and pre-established models;Fractal Geometry is at the same time an instrument and a result
for this. Art Making can be therefore realized within a pensive
and careful feeling of contemporaneity, animated by a cognitive
pull made actual by appropriate modes and means. (Giudi
Scotto Rosati - 2006).
Geometry & Art - A Parallel Development II
The Common Language of Art & Science
Haebel- Ripetitivit Incostante
A. Einstein (XX Century) Where the world ceases to be the
scene of our personal hopes and wishes, where we face it asfree beings, admiring, asking and observing, there we enter
the realm of Art and Science.
Galileo Galilei(Il Saggiatore, XVI Century)One cannot understandthe Universe if one does not learn before to know the characters by which
it is written. The Universe is written in mathematical language and its
characters are triangles, circles and other geometrical figures.
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Geometry & Art - A Parallel Development III
The Four Eras in the Geometry of Art & Space
All Geometries - the Euclidean one, the Geometry of Perspective, non-EuclideanGeometries, as well as more modern and mathematically formal ones, like Topology,
Riemannian Geometry or Fractal Geometry - share striking relations with Art:
Euclidean Geometry Interprets and describes ordinary space
for all Classical forms of Art.
Projective GeometryPainters use it as Perspective, as they want
to reproduce exactly what the eye sees.
Riemannian GeometryHas to do with XIX Century Art (Cubism,
Impressionsim) in coincidence and in full
consonance with the historical, perceptive andinterpretative developments of observed reality.
Fractal Geometry,
T o p o l o g y ,
Dynamism
Have to do with Modern and Contemporary Art,
where new research is performed on Form, Shape
and Deconstruction (Cubism, Futurism).
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Mathematics & Art in the Antiquity I
Pythagorean Arithmetic and the Beauty of Cosmos. 1
The Mathematics of Antiquity is conventionally divided into Arithmetic and Geometry.Arithmetic is the Science of Numbers it has to do with the human need of
counting. Geometry is the Science of Shapes it has to do with the human need of
measuring. The two needs are of course deeply intertwined; they are developed
together with the need of understanding and representing Space.
The Pythagorean School developsNumber Theory and
attributes to them the task ofregulating beauty.
Pythagoras of Samo
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Mathematics & Art in the Antiquity II
Pythagorean Arithmetic and the Beauty of Cosmos. 2
Astronomical observations of the three major naturalcycles(Earth, Moon, Sun) lead mankind to develop
the idea of Day, Moon Period and Year the ratio
between the approximate durations of these cycles
lead to attribute special meanings to a few Numbers,
considered as magic because of their relations with
the periodicity of Nature: twelvelunar cycles (in oneYear) and twenty-eight Days in each Lunar Cycle
(Lunar Calendars). Sinceperiodicity imposes four
periods also the Numbers three and sevenacquire
thence a special role (the Months in each Season and
the Week). The twelve Months in a Year lead
eventually to subdivide theCelestial Sphereinto
twelve parts and introduce what we call the Zodiac.
12
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Mathematics & Art in the Antiquity III
Space and Euclidean Geometry
The knowledge about the properties of Space and itsmeasures are eventually encoded into the famous
treatise The Elements (of Geometry) ofEuclid.
Euclidean Geometry describes a Space formed by
points, lines, circles and all geometrical shapes
obtained by using a ruler and a compass.
A central role is attributed to the existence ofparallel lines. They are postulated to exist, even if
vision tells us thatparallel lines are seen to converge
somewhere
Euclid of Gela
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Mathematics & Art in the Antiquity IV
Euclidean Geometry and the Dichotomy: Continuum or Discrete?
While for Euclid the point is immaterial, thePythagorean school attributes instead materiality to
the point: Pythagoreans points have a dimension.
The Greek thinkers speculate aroundInfinity andInfinitesimals; their speculations will eventually form
the basis of modern Science and still form a
challenging table of debate. Even if post-EuclideanScience will favor the idea that Geometrical Space
is Continuous the dichotomy between continuity and
discreteness will continue forever.
Democrituswill introduce theidea ofAtomism.
The Physics of XX Century will eventually revitalize the dichotomy
because of the advent of
Quantum Mechanics.
Democritus of AbderaEuclid of Gela
Pythagoras of Samo
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Mathematics & Art in the Antiquity V
Pythagoras Theorem
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Mathematics & Art in the Antiquity VI
Platonic Solids
In Ancient Greece The Theory of Proportionswas a canon for Science and Art; Mathematical Objects such as Platonic Solids were symbols of
classical beauty and harmony.
The most beautiful objects in
the Universe
(Plato)
Exahedron
Tetrahedron
Octahedron
IcosahedronDodecahedron
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The Persistence of Forms in
Geometry & Architecture II
Fractalized structures in Roman time
Bridges and in modern constructions. 1)
The Marine County Civic Center; 2)
Aqueduct on Gard River (France)
F.L. Wright- Marine County Civic Center
Aqueduct of Gard
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Even if the correct equation of catenaries was in fact derived in 1691 by Leibniz,Christiaan Huygensand Johann Bernoulli, catenaries begun early to be used in theconstruction of Mesopotamic arches (already at the time of pre-Greek and pre-Roman
Architecture). In antiquity the curvature of the (inverted) catenary was in fact
intuitively discovered and understood to be useful in the construction of stable arches
and vaults. Greeks and Romans preferred instead to use the much less efficient
curvature of the circle, both in circular arches and semi-spherical vaults. Catenaries in Taq-i Kisra in
Ctesiphon (Mesopotamia)
Parabolas and catenaries in Gaud
Architecture (XX Century)
The Persistence of Forms in Geometry & Architecture III
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Castel del Monte and its Geometry
The Persistence of Forms in Geometry & Architecture IV
Geometrical Shapes in Romanesque Architecture. 1
Photo by M.G. Lorenzi
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Castel del Monte and its Geometry
The Persistence of Forms in Geometry & Architecture V
Geometrical Shapes in Romanesque Architecture. 2
Photo by M.G. Lorenzi
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The Persistence of Forms in
Geometry & Architecture VILisbon
from Mosteiro dos Jeronimos
to Calatravas Station of Oriente
Photos by M.G. Lorenzi
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Throughout his life Gaud studied natural angles andcurves and tried to incorporated them into his
sculptured particulars, into mosaics and into the
designs of his Architecture. Hyperbolic Paraboloids from
the Exterior of the Vaults of
La Sagrada Famila
Instead of relying directly on thesimple shapes of Geometry herather mimicked Nature by subtly
combining them; rotational surfaces
having a peculiar role, such as
hyperboloids and paraboloids, were in
fact borrowed from Nature, so to
allow his work to resemble
environmental elements. He saidonce: Those who look for the laws of
Nature as a support for their new
works collaborate with God.
The Persistence of Forms in Geometry & Architecture VII
Revolution Surfaces in ModernArchitecture (Gaud)
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The Harmonic RatioTake a segment AB and divide it into two parts AC and CB, so that the whole AB
contains the larger part AC as many times as the part AC contains the smaller part CB
AB : AC = AC : CB
AB = AC + CB
implies
(AC + CB) : AC = AC : CB
(AC + CB)/AC = AC/CB
setting AC/CB =
1 + 1/ = ===> = (1 + 5)/2The Golden Mean is an Irrational Number
The Canon of Beauty: The Golden Mean IWhat is the Golden Mean?
A________________C_________B
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The Harmonic Ratio was called Golden Mean by Luca PacioliTake a segment AB and divide it into two parts AC and CB, so that the whole AB
contains the larger part AC as many times as the part AC contains the smaller part CB
AB : AC = AC : CB
AB = AC + CB
implies
(AC + CB) : AC = AC : CB
(AC + CB)/AC = AC/CB
setting AC/CB =
1 + 1/ = ===> = (1 + 5)/2Luca Paciolisaid: the Golden Mean is Divina Proportione
The Canon of Beauty: The Golden Mean IIThe Golden Mean
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The Golden Mean pervades Art since the Antiquity it is supposed to exist in the proportions of many Egyptian monuments.
Gizah (Egypt) - The Pyramids of Saqqara
The Canon of Beauty: The Golden Mean IIIThe Golden Mean in Egyptian Pyramids
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The Golden Mean pervades Art since the Antiquity as a canon of beauty it is easy to recognize it in many pieces of Art.
Athinai (Greece) - The Parthenon
The Canon of Beauty: The Golden Mean IVThe Golden Mean in Greek Architecture
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Johannes Kepler
Harmonices Mundi
Johannes Keplersaid: the Golden Mean is one among two jewels of Euclidean Geometry
The Canon of Beauty: The Golden Mean VJohannes Kepler and The Golden Mean in Cosmology
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The Golden Mean in NatureThe Golden Mean is in fact intimately related with several growth phenomena
as it was recognized byLeonardo Fibonacci. It belongs to Nature..
AB : AC = AC : CB
AB = AC + CB
implies
(AC + CB) : AC = AC : CB
(AC + CB)/AC = AC/CB
setting AC/CB =
1 + 1/ = ===> = (1 + 5)/2
The Canon of Beauty: The Golden Mean VIThe Golden Mean in Nature
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Amazingques0on:WasLowerPaleolithicMan
masteringGeometry?
Hand axes from Lower Paleolithic
Reproduced after in the Acheullian-John Feliks-University of Michigan Courtesy ofGheorghe Samoila
The Canon of Beauty: The Golden Mean VIIThe Golden Mean in Proto-Geometry. 1
Acheullian-Kilombe
hand-axes seem to
respect the proportions of
the Golden Mean
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The Canon of Beauty: The Golden Mean XThe Golden Mean in Human Proportions. 2
CourtesyofGheorgheSamoila
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Leonardo da
Vinci
Homus
Vitruvianus
The Canon of Beauty: The Golden Mean XIThe Golden Mean in Human Proportions. 3
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Symmetry, after Vitruvius, resides inthe correlation by measurement between
various elements of the plan, and between
each of these elements and the whole As
in the human body
The Canon of Beauty: The Golden Mean XIIfrom the Golden Mean to Symmetry
Itproceeds from proportion and it achieves
consonance between every part and the whole
This symmetry is regulated by the modulus, the
standard of common measure which the Greeks
called the number
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Since the antiquities, Symmetry hasplayed a fundamental role in the
construction of classical beauty - in
good Sculpture, in good Painting
and especially in good Architecture.
The old meaning of symmetry
had to do mainly with the staticnotion of proportion; the present
notion of symmetry, on the
contrary, has a dynamical
interpretation, having to do with
motions or dilatations that
allow parts to superimpose exactly
to other parts of a given object.Exactly in this sense symmetry
enters the new and more dynamical
forms of Art.
Symmetry as a Mirror Game.
This mathematical exhibit is due to the
Department of Mathematics of the
University of Milano.
Art & Symmetry - IThe Paradigm of Symmetry
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Narciso (1579-1599) by Caravaggio (1573 1610)
In this famous painting one can immediately
recognize the existence of an axial symmetry.
Art & Symmetry - IIThe Paradigm of Symmetry in Painting
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Symmetry is present in an essential and practically universal way in Architecture, starting fromMesopotamic, Egyptian, Greek and Roman buildings; it helped in structural calculations and
contributed to construct elegantly and in a structurally stable way.
Town of Palmanova
Unusual 9-folded symmetry
Art & Symmetry - IIIThe Paradigm of Symmetry in Architecture
Bramante - San Pietro Planimetry
Example of 4-folded or 8-folded symmetry
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Ahlambra in Granada
Art & Symmetry IVSymmetry in Arab Architecture. 1
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Art & Symmetry VSymmetry in Arab Architecture. 2
Ahlambra in Granada
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Rosettes represent invariance groups of geometrical figures, that do not contain: i)
rotations of exact sub-multiples of 2 (cyclic groups); ii) rotations and reflections(diedral groups).
Rosettes existing in some Medieval Churches
Art & Symmetry VIRosettes
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Friezes are infinite sets of forms that repeat and show invariance with respect to
translations in a single direction.
The 7 types of Friezes
Art & Symmetry VIIFriezes
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Mosaics i.e. crystallographic groups of
the plane (forming a family of exactly 17
elements) - are infinite groups of forms that
repeat by showing a translational invariance
in two or more independent directions.
Mosaic in Via Tiberti (Cesena)
Art & Symmetry VIIIMosaics
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Knots in Mathematics: they are
images of a circle, i.e. closed
curves embedded into 3-
dimensional Euclidean Space.
Art & Symmetry IXKnots. 1
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Examples ofKnots in Art1) Isis Knot;
2) Savoia Knot;
3) Longobard Knot;
4) An example ofQuipu.1
2
3
4
Art & Symmetry XKnots. 2
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Other Tessellations of the Euclidean Plane.
Art & Symmetry XIITessellations. 2
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Examples ofColored Tessellations in the Plane.
Art & Symmetry XIIITessellations. 3
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Examples ofTessellations
of curved compact and
non-compact surfaces.
Art & Symmetry XIVTessellations. 4
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Symmetries in the Euclidean Plane
Symmetry in Advertising?Andy Warhol
Art & Symmetry XVSymmetry in Modern Art
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Aprimordial form of Perspective
already existed in Greek and Roman
Painting, as well as in Gothic:
inMasaccio (1401-1428) (frescoes ofCappella del Carmine, in
Firenze);
in Giotto (frescoes ofCappella degliScrovegni, in Padova, as well as in
Madonne in Trono).
In a sense an elementary perspective
was adopted, with more than one point
at infinity; it is like having more than
one point of observation in the painting,
each one corresponding to a different
viewpoint
From the V Postulate of Euclid
to Perspective and Projective Geometry - I
Several convergence lines,
more than one point at infinity
Perspective in Giotto is not exactly
codified and there is no single point of
convergence
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A primordial form of Perspective
already existed in Greek and Roman
Painting, as well as in Gothic:
inMasaccio (1401-1428) (frescoes ofCappella del Carmine, in
Firenze);
in Giotto (frescoes ofCappella degliScrovegni, in Padova, as well as in
Madonne in Trono).
In a sense an elementary perspective
was adopted, with more than one point
atinfinity; it is like having more than
one point of observation in the painting,
each one corresponding to a different
viewpoint
From the V Postulate of Euclid
to Perspective and Projective Geometry - II
While in Renaissance, Painters and
Mathematicians begin to abandon empirism
and look for general methods, that later one
will be codified in systematical treatises on
Perspective (rules for Buona Pittura).
Thanks to Filippo Brunelleschi, LeonBattista Alberti (in Architecture) and Piero
della Francesca (in Painting), the Theory of
Good Proportions becomes a general
instrument, giving to painters rules that he
has to follow to obtain that what is seen is also
painted.
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From the V Postulate of Euclid
to Perspective and Projective Geometry - III
While in Renaissance, Painters and
Mathematicians begin to abandon empirism
and look for general methods, that later one
will be codified in systematical treatises on
Perspective (rules for Buona Pittura).
Thanks to Filippo Brunelleschi, LeonBattista Alberti (in Architecture) and Piero
della Francesca (in Painting), the Theory of
Good Proportions becomes a general
instrument, giving to painters rules that he
has to follow to obtain that what is seen is also
painted.
Perspective in Piero della
Francesca: one point at infinity.
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Geometry is recognized as an essential tool for Artists.
() E sappi che cosa niuna dipinta mai parr pari alla vera, dove non sia certadistanza a vederle. ()
Pertanto affermo sia necessario al pittore imprendere geometria. ()
Perch ho dicto dato lochi, se intende essere posto al vedere in quelloluogho, dove tu vai stare a vedere il piano assegnato
Leon Battista Alberti
Piero Della Francesca
De prospectiva pingendi
(a mathematical treatise with
good rules for painting).
From the V Postulate of Euclid
to Perspective and Projective Geometry - IV
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??.
From the V Postulate of Euclid
to Perspective and Projective Geometry - IV
Several convergence lines,
more than one point at infinity
Perspective in Giotto is not exactly
codified and there is no single point of
convergence
Perspective in Piero della
Francesca: one point at infinity.
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??.
From the V Postulate of Euclid
to Perspective and Projective Geometry - IV
Several convergence lines,
more than one point at infinity
Perspective in Giotto is not exactly
codified and there is no single point of
convergence
Perspective in Piero della
Francesca: one point at infinity.
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Botticelli Piero dellaFrancesca Leonardo da Vinci
Painting in Renaissance
Symmetry, Perspective and Proportions - I
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This famous masterpiece by Raffello
Sanzio is essentially based on a
clever use of both Perspective and
the Golden Mean.
The Painting occupies a Golden
Rectangle; in the square at the basis
of this rectangle there is a circle,
that inscribes two squares to form
an octagon. Prolonging its sides one
can determine the radius of two
further inscribed circles.
Raffaello Sanzio - La Trasfigurazione
Painting in Renaissance
Symmetry, Perspective and Proportions - II
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Leonardo da Vinci -Mona Lisa (Harmonic Analysis)
Painting in Renaissance
Symmetry, Perspective and Proportions - III
CourtesyofGheorgheSamoila
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Twohorizontalsuperposedgoldenrectangles.Goldensec0ondividestherectanglesatleFandright.
Parallelswithgoldenrectanglesdiagonalsaredrawn.
Athalfthebase,ameridianmarksLedasbodywhichisperfectlyframedbytheGoldensec0onmarkers.
Goldensec0onrectanglediagonalsareDrawn.Theircrossingmarksimportantfocal
pointsofthecomposi0on.
Ahorizontallinemarkstheheadschin.Theeyelineismarkedbythesideofthetrianglebuilthavingthepreviouslineasheightand
Mediator.
*ReproducedaFerMa0laGhykaTheGeometryofArtandLife(1)
Painting in Renaissance
Symmetry, Perspective and Proportions - III
CourtesyofGheorgheSamoila
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K. F. Gauss
(1827, Disquisitiones
supra Superficies Curvas)
B. Riemann (1854, On the Hypotheses that lie at the bases of
Geometry, published postmously in 1866)
If the independence of bodies from position does not exist, we
cannot draw conclusions from metric relations of the great to
those of the infinitely small; in that case the curvature at each
point may have an arbitrary value in three directions, provided
that the total curvature of every measurable portion of space does
not differ sensibly from zero [] The question of the validity of
the hypotheses of geometry in the infinitely small is bound up with
the question of the ground of the metric relations of space.
From Linearity to Curvature in XIX Century
Non-Euclidean Geometry
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The discussion about the validity of Euclids fifth postulate lead, however, also to
Hyperbolic Geometry and, in the artistic field, that paved the way for the development
of Impressionism. It turns out, in fact, that our visual space is hyperbolic rather thanEuclidean (Lunemberg, 1947), so that it is not surprising that artists in the XIX Century
begun to represent what the eye actually sees rather than what the eye ispretendedto see
in a fully Euclidean world. The XIX and XX Century will finally see the introduction of
time as a fourth sensibile dimension alongside and on equal footing with height,
lenght and depth (Einsteins Theory of General Relativity is at the top of this line of
thought); motion and curvature become part of the World and not something which is
embedded into the World. This will form the subject of the second half of this Lecture.
From Linearity to Curvature in XIX Century
Non-Euclidean Geometry, Impressionism and Fourth Dimension
MATHEMATICS ART
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MATHEMATICS, ART
AND PHOTOGRAPHY
(from Antiquity to Futurism)Talk at the Final Event: SCIENAR ProjectThe Dutch Academy of Science
Amsterdam, 15 October 2010
Marcella Giulia LORENZI
(Universit della Calabria)(in collaboration with Mauro FRANCAVIGLIA)
Part II: Space, Time and Motion in XX Century Art
A & S i i XX C R d I i 1
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At the end of XIX Century and during the XX Century Science becomes in a number of
occasions a source of inspiration for Art.
Examples begin with the Impressionists desire to decompose colors according to their light
decomposition in fundamental components (Divisionism, Pointillism)
Later on Picasso and Braque with Cubism will introduce different viewpoints into painting,
destroying classical perspective and letting extra dimensions enter the scene of Art
The need of representing dynamism and motion will lead Futurists to their ideasEventually motion will be captured by Cinema and later on by Computer Graphics
Art Nouveau will introduce new geometric shapes in all forms of Art, from Painting to
Architecture to all Arts Decoratifs
Geometric Forms and also Fractals will be used as subjects for Art
Photography and Digital Photography will produce new forms of Art
in which Science can play a predominant role
Art & Science in XX Century a Renovated Interaction. 1
A & S i i XX C R d I i 2
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Dynamics is impossibile to represent in just two
dimensions, yet artists (e.g., Balla, Boccioni,
Duchamp) tried to provide pictorialrepresentations of movement. Dynamism in
Modern Art is achieved through the moving
camera and Cinema, but the idea of time-flowing
sections may be also used in figurative arts (think
of Picasso or Dal, a 4-dimensional hypercube
that opens up in 3-dimensional space). The new
Mathematics of the XX Century is also the
Mathematics of Manifoldness, Curvature,
Discreteness, Fractals and Chaos, and some
modern ways of painting reflect these new ideas
(Picasso, Pollock). Also the famous artist Escher,
the unchallenged inventor of impossibile objects
and imaginary world, was influenced by theMathematics of Poincar and Penrose in creating
his striking pieces of Art. The connection existing
between Art and Mathematics is universally
recognized and needs no more examples.
Picasso - Still LifeThe substantial monochromy of theensemble, the unususally elliptic shape
(shared by other works of the Cubist
period) and the simple rope used as aframe represent an intentional recalling
of shape that transfigures in matter,
matter thakes new shapes, which do
n o t b e l o n g t o i t s o w n
nature(Itinerario nell'arte. vol. III).
Art & Science in XX Century a Renovated Interaction. 2
A t & S i i XX C t I i i d P i tilli
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Seurat
Le pont de
Courbevoie
Notice thepersistence
of the
Golden
Mean
Impressionism generated in XIX Century a great innovation in composition
in particular, studies on the decomposition of colors lead to Pointillism
Art & Science in XX Century - Impressionism and Pointillism
Th D t ti f P ti I
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Perspective - so long looked for inRenaissance, in order to reproduce exactly
reality, by respecting the mechanisms of
vision - was rejected in the XIX Century Art:
With Post-Impressionism Artists create paintingsin which different parts respect a rigorous
perspective, although several different viewing angles
are mixed-up together;
In a sense, Perspective gets deformed but notcompletely abandoned by Artists.
With Impressionism Artists begun to renounce theolder rules of good painting, by first deforming and
later cancelling totally the fundamental principles of
Renaissance perspective canons;
House of the Hung Man Paul Czanne
The Big Bathers Paul
Czanne
The Deconstruction of Perspective - I
Paul Czanne
Th D t ti f P ti II
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Pablo Picasso - demolishes Perspective and paintsfragments of reality as seen from different angles or in
different planes, later mixed-up
Many elements of Euclidean Geometry and Optics arerejected;
Euclidean Distance looses its meaning with stronginfluence on the final result: particulars that are far from
each other are seen to be near, whilst particulars that are
not near appear to be contiguous in the painting.
The represented reality cannot be always detected directly; one has to recognize different
pieces, glueing them together in its own perception - as in a Manifold or in a Kaleidoscope.
The artistic message is thus reconstructed in an independent way by each onlooker. The
Artistic piece becomes thus a Topological Manifold, that can be reconstructed only by
chart glueing.
Ambroise Voilard - Picasso
The Deconstruction of Perspective - II
Picasso and Cubism Manifolds and Fourth Dimension. 1
Th D t ti f P ti III
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Guernica -PicassoThe famous painting Guernica is formed by several independent portions, that intersectand overlap without an apparently clear and immediate logical order. Looking carefully at
this painting, however, one can realize that the painting is in fact formed by an Atlas,
Is it a Manifold or a Piece of Art..?
The Deconstruction of Perspective - III
Picasso and Cubism Manifolds and Fourth Dimension. 2
Breaking the Euclidean Symmetries
G t I i ti f M d A t I
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Golden Mean and Brancusis works
25 ofBrncuis ovoid works respect the rule of the Golden Mean. Out of
these, 5 display the ratios of 0,617 and 0,620, which compare with theideal ratio of 0,618. Other 13 display this ratio with a slight variation of
1%, and in only 4 there is a deviation of 2-3% from the nominal
value. (taken from a note oftefan Georgescu Gorjan)
Geometry as an Inspiration for Modern Art - I
The Golden Mean in Brncui
CourtesyofGheorgheSamoila
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Salvador Dali - Leda
Persistence of the Golden
Mean
Internetimage
Geometry as an
Inspiration for Modern
Art - II
Salvador Dali. 1
CourtesyofGheorgheSamoila
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An hypercube in four dimensions can be constructed out of 8 ordinary 3-dimensionl cubes in ordinary Euclidean Space, in much the same way in which anordinary cube in three dimensions can be constructed out of 6 ordinary squares (thatare ordinary cubes in 2-dimensional Euclidean Space) and an ordinary square can beconstructed out of 4 ordinary cubes in 1-dimensional Space, i.e. four segments.
This construction was adopted bySalvador Dal to represent a skillful
Crucifixion, in which the Holy Cross is infact the 3-dimensional representation of anhypercube. This introduces de facto anextra dimension in the painting, which -in a sense - acquires also an extension intime, to represent the flow of events thathas accompanied the Passion of Christ.
Geometry as an Inspiration for Modern Art - III
Salvador Dali. 2
Geometry as an Inspiration for Modern Art IV
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The beginning of XX Centurymarks the eve of new forms of
Art. Art Nouveau is one of the
most important ones (also called
LibertyorJugendstil)
One of the most importantcharacteristics of thisNew Style
resides in its continuous
reference to Nature, from which
the structural elements are
derived and given dynamical
undulate contours.
The clever use of geometrical structures inspired by such curves would produce
shapes in the form of trees and flowers, a reason for which the Style was also
called Floral. Some of the curved lines used became clichs, to be adopted by
artists worldwide.
G. Klimt The Tree of Life
Geometry as an Inspiration for Modern Art - IV
Art Nouveau and Geometrical Forms
Geometry as an Inspiration for Modern Art V
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Fig. 2 La Sagrada Famila, photo byMarcella Giulia Lorenzi
Geometry as an Inspiration for Modern Art - V
Art & Mathematics in Antoni Gauds Architecture. 1
La Sagrada Famlia
Geometry as an Inspiration for Modern Art VI
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Cubic Elements for the Pinnacles of LaSagrada Famila, in the Museum of the
Church,
photo by Marcella Giulia Lorenzi
Geometry as an Inspiration for Modern Art - VI
Art & Mathematics in Antoni Gauds Architecture. 2
Geometrical Forms for La Sagrada Famlia (1)
Geometry as an Inspiration for Modern Art - VII
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Platonic Solids and otherGeometrical Shapes for the
Pinnacles of La Sagrada
Famila, in the Museum of
the Church,photo by Marcella
Giulia Lorenzi
Geometry as an Inspiration for Modern Art - VII
Art & Mathematics in Antoni Gauds Architecture. 3
Geometrical Forms for La Sagrada Famlia (2)
Geometry as an Inspiration for Modern Art - VIII
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Other Elements for the Pinnacles of La Sagrada Famila,
in the Museum of the Church,
photo by Marcella Giulia Lorenzi
Geometry as an Inspiration for Modern Art - VIII
Art & Mathematics in Antoni Gauds Architecture. 4
Geometrical Forms for La Sagrada Famlia (3)
Geometry as an Inspiration for Modern Art - IX
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photo by Marcella
Giulia Lorenzi
Geometry as an Inspiration for Modern Art - IX
Art & Mathematics in Antoni Gauds Architecture. 5
The Geometrical Columns of La Sagrada Famlia. (4)
Geometry as an Inspiration for Modern Art - X
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Columns resemble Trees,from the Museum of the
Church,photo by Marcella
Giulia Lorenzi
Geometry as an Inspiration for Modern Art - X
Art & Mathematics in Antoni Gauds Architecture. 6
The Geometrical Columns of La Sagrada Famlia (5)
Geometry as an Inspiration for Modern Art - XI
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F.A. Alsbachs Disced field at down - Harmonic Analysis
Reproducedwithar0stspermission
Geometry as an Inspiration for Modern Art XI
The Golden Mean in Modern Painting. 1
CourtesyofGheorgheSamoila
Geometry as an Inspiration for Modern Art - XII
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IdousetheGoldenMeanasastar1ngpointandtoarriveatbasicdimensions.The
designbeginswiththeGoldenMean,butIalsoplayedwiththeGeometrysomehow
asIpainted.FloydAlsbachEvening Canticle
Reproducedwithar0stspermission
Geometry as an Inspiration for Modern Art XII
The Golden Mean in Modern Painting. 2
CourtesyofGheorgheSamoila
Geometry as an Inspiration for Modern Art - XIII
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Vassily Kandinski- Black Square (1923)
In the Peinture ofXX Century some artistic movements begun to use Geometryas a mean to construct pieces of Art. Among the great names of these currents
we may just quote Vassili Kandinsky or Max Bill, but many others could be
recalled. In their paintings and sculptures the presence ofGeometry (Euclidean
or not) is not accidental but represents in fact an artistic theme.
Max Bill- Endless Ribbon
Geometry as an Inspiration for Modern Art XIII
Patterns and Topological Forms. 1
Geometry as an Inspiration for Modern Art - XIV
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Numeri innamoratiG. Balla
Disco Simultaneo -Robert Delaunay
Geometry as an Inspiration for Modern Art XIV
Patterns and Topological Forms. 2
Geometry as an Inspiration for Modern Art - XV
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Emblematic examples of broken symmetry
may be found in the sculptures ofArnaldo
Pomodoro, that are placed along the streets of
the Swiss town ofLugano: they represent objects
that are symmetric only if seen from suitable
angles or positions.
Geometry as an Inspiration for Modern Art XV
Patterns and Topological Forms. 3
From Order to Disorder - I
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One of the most fascinating conquers of XX Century is the notion ofFractal. Introduced at the end of XIX Century as curves that fill-upportion of the plane and have an intermediate dimension larger
than one but smaller than two (e.g., the Peano Curve or the Koch
Curve), they represent stimulating objects related with iteration and
self-similarity at scales smaller and smaller (coasts, mountains,
vegetation, nervous system are good examples).
Haebel- Isole
From Order to Disorder I
Fractals in Mathematics. 1
From Order to Disorder - II
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Worthwhile to mention is the revolutionary idea that continuity anddimension may be different from the notions that resisted since the time of
Greeks, through their advent.
B. Mandelbrot
Fractals
Peano Curve
Fractals in Mathematics. 2
Koch Curves
From Order to Disorder - III
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Mandelbrot Sets
The Mandelbrot Sets aredefined starting
from a Julia set, by the recursive formula
(x,y) (x 2 - y2+ x, 2xy + y)
Fractals in Mathematics. 3
From Order to Disorder - IV
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The advent of computer has certainlygiven a great impetus to Fractal
Painting - also called Fractalism - but
also the literary tradition of XX Century
had a propositive role. Mandelbrot
speaks of representations of infinitythrough finite and of non integer
dimensions. In parallel, several artists
of XX Century had liberated themselves
from predetermined models and have
focused their activity on the search of
unpractioned and unexperienceddimensions, so determining new
viewpoints and new models through
which one can experiment reality.
Paolo Barlusconi-Ineffabili Stati dellEssere
Fractalism in Art. 1
From Order to Disorder - V
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Haebel states moreover about Fractal Art:The scientific component is present only at
the level of study [] the creative act is by
no means mortified [] and it remains the
undiscussed protagonist [] it would be
impossible to repeat a painting, while
repetitivity is a founding value of scientific
work.
Haebel-Attrattore in Espansione
Again with Haebel we can say that: Fractal Geometry
configures a new theoretical and methaphorical field. The
rigid boundaries that have traditionally separated Art from Science are falling down one by one.
Interdisciplinarity is extremely open minded: it has no
limits, no boundaries, it is infinite as Fractal Geometry is.
Gianni DAnna-Fleur Fractal
Fractalism in Art. 2
F.L. Wright - From Order to Disorder - VI
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Fractalized structures in Roman time
Bridges and in modern constructions. 1)
The Marine County Civic Center; 2)
Aqueduct on Gard River (France)
F.L. Wright Marine County Civic Center
Acqueduct of Gard
Fractals in Architecture. 1
D. Libeskind- V & A Museum, London From Order to Disorder - VII
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Fractalized structures are often encountered inModern Architecture, as these examples show(below, a view of Guggenheim Museum at
Bilbao; on the left, the Victoria & Albert
Museum; below, a modern structure at an
exhibition centre in Denver. But also in
relatively older buildings or even in Roman
constructions, as in the next slide.
Daniel Libeskind-Art Museum, Denver F.O. Gehry - Guggenheim Museum, Bilbao
Fractals in Architecture. 2
From Order to Disorder - VIII
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Escher found inspiration in Alhambras Mosaics and realized tessellations of theplane through symmetrical schemes taken from Geometry (later replaced by Angels,
Demons, Ghosts, Reptiles, Fishes and Imaginary Beasts so creating unique artworks
based on Non-Euclidean Geometry or even Impossibile Geometries. The following
images live in the so-called Poincare Disk.
The dimension of reptiles decrease movingtowards the centre
The dimension of reptiles increase movingtowards the centre
Fractals and Hyperbolic Geometry in Eschers Art. 1
From Order to Disorder - IX
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Escher and Poincar Disk
From Order to Disorder IX
Fractals and Hyperbolic Geometry in Eschers Art. 2
Time and Motion in Modern Art - I
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Dynamics of a dog on a landGiacomo Balla
Nude descending
a staircase Marcel Duchamp
As we said, across XIX and XX Century: The idea ofSpace changes, together with its description; Non-Euclidean Geometries are introduced; Time becomes a fourth
sensible dimension; Technology grows rapidly; Velocity becomesessential
Artists of XX Century begin trying to represent motion pictorially
The Futurism. 1
Time and Motion in Modern Art - II
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The Futurism is an Art movement that started in Milano, 100 years ago(in 2009)
Futurists concept of movementand their attempts to capture a sense ofmovement in painting, sculpture and photography.
The Futurism. 2
Time and Motion in Modern Art - III
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The Aesthetic of Velocity generates a prevalence of truly dynamical
elements; motion involves both the object depicted and the space in
which motion takes place.
Trains, Cars, Airplanes are peculiar subjects, but also human figures
(dogs, dancers, children) animated by multicolored and polyphonic
brush touches, aimed at putting into evidence the propulsive push of
moving forms. The difference of velocity (higher or lower) is usually
represented by using either broken and rough-edged lines or more
harmonious and fluid linear brushstrokes.
Futurism is well described by the own words ofBoccioni(1913):
I want to render the fusion of a head with its environment.I want to render the prolongation of objects in space.I want to model light and the atmosphere.I want to transfix the human form in movement.I want to synthesize the unique forms of continuity in space.
The Futurism and the Aesthetic of Velocity
Time and Motion in Modern Art IV
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At the same time in which Marinetti, Tato, Boccioni, Balla,
Bragaglia, etc. where trying to insert movement in their
art, including photography
Muybridge used photography as ascientific instrumentto
study animal and human movement imperceptible to the
human eye
Futurism and Photography
Time and Motion in Modern Art V
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The Fotodinamismo of Futurists. 1
Time and Motion in Modern Art VI
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Manifesto della Fotografia Futurista
The Fotodinamismo of Futurists. 2
Time and Motion in
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Modern Art VII
The Fotodinamismo of
Futurists. 3
Time and Motion in Modern Art VIII
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Time and Motion in Modern Art - IX
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Generative Artis a new method of making Art. The term refers to how the Artis made, and does not take into account why it was made or what the content of theartwork is: Artworks, in Generative Art, can be identified in the creative processes
and not only in the results. Painting with Light: it is a form of Generative Art that through DigitalPhotography allows one the setting in motion of the fourth dimension
Generative Art Painting with Light
photo by Marcella
Giulia Lorenzi
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Future of Futurism Project
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On the 100th anniversary of the Futurist art movement whichstarted in Milano, we want to examine the aims and ideasof Futurist imagery, then proceed to a discussion of howtoday's digital photography can achieve many of the goalsof the Futurist artists.
Digital photography can record pictures that are very similarto the Futurists' vision of depicting a world that is alwaysin motion.
An Installation/Exhibition was held in Milano in 2009 and inBratislava in 2010; it will be expanded and presented in
other cities (Buenos Aires, Bucharest, etc.)
Book catalogue and scientific and historical hints
Future of Futurism Project
Doble, Francaviglia and Lorenzi
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Youll find more in Rick Dobles new book
EXPERIMENTAL DIGITAL ART PHOTOGRAPHY
Lark Books, April 2010
The Art Work of Rick Doble10 Years On The Internet
The Culmination Of Almost 40 Years Of A Life In Art
---- 2000+ Images ----
Including 1500+ Digital Photos
Plus Experiments, Art/Science Images, Essays, Lifestory,More
F i
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Futurism
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F t f F t i
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Future of Futurism
Photo Lorenzi
F t f F t i
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Future of Futurism
Photo Lorenzi
F t f F t i
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Future of Futurism
Photo Lorenzi
F t f F t i
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Future of Futurism
Photo Lorenzi
F t f F t i
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Future of Futurism
Photo Lorenzi
Future of Futurism
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Future of Futurism
Photo Lorenzi
Optics and photography
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p p g p y
Camera Oscura is an optical instrument theprinciples of which are at the base of Photography andCinematography. Light is a physical phenomenon of electromagneticnature; emitted by some sources (for example, the Sun,fire, lamps, etc.) it propagates into transparent media
and is reflected, diffused or absorbed by matter.
Starting from the laws of Visual Perception, from theanathomy and physiology of the eye to the cerebral
cortex and the elementary laws of Optics, several
devices using these properties have been built.
photo by M.G. Lorenzi
The spectrum of irradiating energy is usually divided into families that overlap at the
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The spectrum of irradiating energy is usually divided into families, that overlap at the
extremes, called microwaves, ultraviolet, infrared, etc.; Human retina is sensibile to
electromagnetic waves in a short interval: the term light is usually referred to
electromagnetic wave-frequencies within it. Thus visibile light is a very small region of the
electromagnetic spectrum.
A light wave, irradiating into space at the constant velocity of about 300.000 kilometers per
second, can therefore energetically interact with a detector, that could be a film, a retina
or a photoelectric device.
Photography: its all about light
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g p y g
Many people do not realize and even
experienced photographers can forget, that
Photography is all about light.
The word Photography comes from two
Greek words, Photos (light) and Graphos
(writing, painting), so drawing with the light.
Photography is not about objects or people orscenery, rather it is about how the light reveals
those things. The action of light on a light-
sensitive material (film or electronic devices)
creates the image. An object can be lighted so
that it almost disappears or so that it is virtually
three -dimensional.
I often think the night is
more alive and more
richly coloured than the
day."
Vincent van Gogh, 1888
photo by M.G. Lorenzi
Color photography is a relatively recent invention,
so it is not only the intensity of the light but also
Digital photography could
be a major art form in the
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so it is not only the intensity of the light, but also
the color of the light that creates the image. This
complicates things: for example, a scene may
include different light sources which have their
own particular color (color temperatures and wavelengths) and subtleties of color that may be seen
differently by the camera than by the human eye.
1950s: single lens reflex (SLR) camera
For the first time the photographer could see
exactly what the lens saw.
1990s: Digital Photography
artist see what the camera is seeing in "real time"
on a LCD screen (approximation).
be a major art form in the
next century. It may be the
culmination of the
development of
photography. Digitalcameras may give us the
power to set photography
loose.
Rick Doble
photo by M.G. Lorenzi
The photograph can be used to record a
passage though time, a movement
"I'm an eye. A mechanical eye. I, the
machine, show you a world the way only I
can see it I free myself for today and
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passage though time, a movement
through a space, even an emotion
characterized by the movement of the
camera.
The elusive change of light, the fleeting
expression, the ephemeral form all
could be captured by the camera, an
instrument for working both in time and
space as the English painter John Piperpointed out.
Indeed taking pictures needs some
devices and a particular process in Space
and Time.
can see it. I free myself for today and
forever from human immobility. I'm in
constant movement. I approach and pull
away from objectsThis is I, the machine,
manoeuvring in the chaotic movements,recording one movement after another in the
most complex combinations.
Freed from the boundaries of time and
space, I co-ordinate any and all points of
the universe, wherever I want them to be.
My way leads towards the creation of a
fresh perception of the world. Thus I explain
in a new way the world unkown to you."
Dziga Vertov, 1923
Today scientists no longer limit themselves
to the three dimensions of Euclid TheAccording to Albert Einstein the basic
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to the three dimensions of Euclid. The
painters have been led quite naturally, one
might say by intuition, to preoccupy
themselves with the new possibilities of
spatial measurement which, in the languageof modern studios, are designated by the
term: the fourth dimension.
Regarded from the plastic point of view, the
fourth dimension appears to spring from the
three known dimensions: it represents the
immensity of space eternalizing itself in all
directions at any given moment. It is space
itself, the dimension of the infinite.
Guillaume Apollinaire, 1913
structure of our world is SpaceTime and
things exist in a spacetime continuum, a
world of four dimensions: height, width,
depth and time.
A generative process is usually referred to
as setting in motion. Motion is the
essence of Life. To be alive is to move.
It seems that both Cubism and Futurism
were deeply affected by Einstein's Special
Theory of Relativity, which was published
in 1905. The goal of the Futurists was to
include motion (and therefore Time) in a
painted image, much like the cubist
wanted to include multidimensions in a
portrait.
Photography may be the visual Art
best suited to creating still images
f bj i i Thi i b
Photography, and Digital Photography in
particular is uniquely capable of
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of subjects in time. This is because a
photograph is made by recording an
object (via the lens) over time (by
opening the shutter for a specific
d u r a t i o n ) . T h e r e f o r e , a
photographic exposure is a
combination of space and time, a
recording of space and time Rick
Doble
particular, is uniquely capable of
recording a space/time image.
Yet to photograph a space/time image is
quite complex. For example, the correct
shutter speed to depict motion varies
considerably depending on the motion of
the subject and the artistic intentions of
the photographer. In addition there are
many other variables to movement. And
to record this kind of imagery
successfully, the photographer must have
a tool that allows instant display of the
imagery just taken so that adjustments
can be made based on that feedback -
which is the very powerful capability
provided by Digital Photography.
photo by M.G. Lorenzi
Digital photography and
Futurism
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The artist and the scientist
each substitute a self-created
world for the experiential one,
with the goal of transcendence
Albert Einstein
Futurism
Digital photographers who are interested in
the depiction of movement have tried to addto the Futurist idea of an algebra of
movement. The craft of Photography
defines two fundamental kinds of movement:
subject movement and camera
movement. It also adds a third kind of
movement which is the combination ofsubject and camera movement such as
panning a camera with a moving subject.
The Futurist's notion of absolute and relative
movement is part of subject movement and
works very nicely with other photographic
considerations when it comes to taking
pictures of a subject in motion.
photo by M.G. Lorenzi
The eyes within the camera
shift and capture each moment.Some digital photographers have added other
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shift and capture each moment.
This act of perception trasmutes
and trasfigures each object
perceived creating a montage of
unique and pivotal images.
Yulla
aspects of subject movement to their ideas.
For example, one of us (RD) defined these
different types of subject movement:
Regular movement: Some movement is
unchanging, like that of a train; it moves at a fairly
steady pace in a predetermined direction. A cars
movement is also regular but with some variables,
such as swerving a bit to the left or right and
slowing down or speeding up.
Predictable movement: Less precise than regular
movement is predictable movement. A car heading
down the road will continue to head in that
direction; a car with its right turn signal blinking
will turn right. A dancer doing a traditional dance
will repeat the same steps but not in exactly thesame spot.
photo by M.G. Lorenzi
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Left: Le mani del Violinista, by G. Balla
Right: Violinist, subject movement, photo byRick Doble
Irregular movement: Some movement repeats but in an irregular fashion, such
as a dancer who moves in a free-form manner. Nevertheless, this dancer will
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repeat many of the same motions and, after a while, a photographer might gain a
sense of how that particular dancer is likely to move.
Erratic movement: The movement of a singer on a stage or a child playingwith a dog can be hard to predict, however, scenes such as these can yield
exciting and unusual imagery.
Left/right: Photodynamic portraits of Dee Dee Bridgewater singing and dancing with a
green fan during a Jazz concert. Photos by M.G. Lorenzi
Can an art form, which has
been committed to creatingCamera Movement
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g
high resolution images of the
real world, find happiness as a
contemporary art form that
includes things thatphotography has been avoiding
up to now, such as blurriness,
overexposure, underexposure,
camera movement, subject
movement, graininess and long
exposures in which the
unexpected happens?
Rick Doble
Camera movement, by itself, depicts
motion from the photographers point-of-
view. This type of imagery has been
called Painting with Light and also
camera painting.
It is essentially a new Art form that has
only been made practical with the advent
of Digital Photography and leads to
dynamic abstract imagery much like theabstract work of the Futurists.
NOTE: while this imagery was
technically possible with film
photography, not much work was done in
this area due to the high cost and largeamount of effort that was required.
photo by M.G. Lorenzi
I was by myself
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In addition camera and subject
movement together add
powerful techniques in thedepiction of movement as well
as providing considerable
individual artistic control.
Combined camera and subjectmovement can record the most
dynamic imagery where the
world seems to be rushing to fill
the picture.
My Wife Driving, subject and camera movement combined, photo by Rick Doble
I was by myself
action painting
with a camera
Rick Doble
The vital instant is the
decisive moment of
The New Digital Photographic
Capabilities
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decisive moment of
snapping the shutter
Henri Cartier-Bresson
Capabilities
The capabilities of Digital Photography can make
use of all of these ideas about movement in afashion that the Futurists could only dream about.
LCD Monitor: To begin, digital photographers can
see a rapid thumbnail photograph immediately
after taking a photograph. The instant image on the
LCD monitor gives digital photographers theessential tool they need - since photographing
motion is so complex and requires a good deal of
trial and error. Yet the LCD monitor allows the
accomplished photographer to hone his or her
imagery in real time and to take pictures both in the
studio and in the streets to record the vital pulse ofLife.
photo by M.G. Lorenzi
Low Cost: prohibitive cost of film and
pr c ssing in th past Taking pict r s f
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Camera movement
combined with a slow
shutter speed can
create fluid images
full of energy.
processing in the past. Taking pictures of
movement, by necessity, requires a lot of
test shots and shots that are not the best.
Digital photographers can now shoothundreds of pictures without worrying
about the cost.
Stabilizing Control: The new stabilizing
feature on most digital cameras allows
photographers to handhold shots at verylow shutter speed such as 1/2 second with
no camera shake. This means that
photographs of subject movement by
itself, for example, can be accurately shot
without any camera shake or with minimal
camera shake. And this is a new featureonly now available with digital
technology.
photo by M.G. Lorenzi
EXIF Data: Also important is the EXIF
d t th t i d d b t
I suppose I am interested,
above all in investigating the
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exposures data that is recorded by most
digital cameras and embedded in the
photographic image. This invaluable new
digital tool lets a photographer go back andreview the settings, such as shutter speed, that
were used with different photographs and
then allows the photographer to learn from
and to build on that information.
Expressive Control: And while DigitalPhotography is a technical craft, it is also an
expressive medium. Different photographers
can make very different images that reflect
their personalities and their artistic visions.
As a result the world in motion can be both
accurately recorded and also depicted in anexpressive and individual manner.
above all, in investigating the
golden ability of the artist to
achieve a metamorphosis of
quite ordinary things into
something wonderful and
extraordinary
Eduardo Paolozzi, 1959
photo by Rick Doble
Selecting particular initial conditions,
adding a fourth dimension andThe artist and the scientist
each substitute a self-created
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photographing motion by means of
randomised generative processes can
give rise to very expressionistic results,
in full agreement with Galantersdefinition of Generative Art.
Rick Doble proposed a new term for
this Photography, namely photo
expressionism. Generally speaking the
most interesting effects will occur atextremes, because it is at these "edges"
that the normal relationship between
light and film/CCD breaks down and
something unusual happens.
each substitute a self-created
world for the experiential one,
with the goal of transcendence
Albert Einstein
photo by M.G. Lorenzi
Real context Light painting
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photos by M.G. Lorenzi
Real context Light paintingphotos by M.G. Lorenzi
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Future of Futurism
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Future of Futurism
Future of Futurism
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Future of Futurism
Photo Doble
Future of Futurism
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Future of Futurism
Future of Futurism
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Future of Futurism
Photo Doble
Future of Futurism
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Future of Futurism
Future of Futurism
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Future of Futurism
Photo Doble
Future of Futurism
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Future of Futurism
Future of Futurism
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Future of Futurism
Photo Doble
Future of Futurism
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utu e o utu s
Photo Lorenzi
Future of Futurism
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Photo Lorenzi
Future of Futurism
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Future of Futurism
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Photo Lorenzi
Thank you for your attention!
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Contacts:
rick_doble@yahoo.com
marcella.lorenzi@unical.it
mauro.francaviglia@unito.it
The artist and the scientist
each substitute a self-created
world for the experiential one,
photo by M.G. Lorenzi
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