View
217
Download
2
Embed Size (px)
Citation preview
1
Partitions of Reality
Barry Smith
http://ontology. buffalo.edu
2
Leon Battista Alberti (1404-1472)
3
Alberti (Medal)
4
Leon Battista Alberti (1404-1472)
architect and town planner
moral philosopher
cryptographer
painter
mathematician
Papal adviser and Doctor of Canon Law
land surveyor
5
Della pittura 1435–36
6
The goal of the artist:
to produce a picture that will represent the visible world
as if the observer of the picture were looking through a window
7
Panofsky:
one can properly speak of a perspectival intuition of space only wherea whole picture is as it were transformed into a “window” through which we should then believe ourselves to be looking into the space
8
Alberti’
s Grid
c.1450
9
10
11
Machines for seeingfor measuring the visible surfaces of external reality
‘reticolato’
‘grill’ (graticola)
‘veil’ (velo)
12
Dürer’s treatise on
measurement
Underweysung der Messung (1527)
13
Dürer
14
15Artist’s Grid
transparent grid
16
Practical problem of
perspective
solved by Brunelleschi in 1425
with painting of Baptistery of St. John in Florence
17
18
Peepshow
19
20
Theoretical problem of
perspectivesolved by Alberti in Book 1of Della pittura
The solution is captured in the diagram of the reticolato
… belongs to projective geometry
21
‘true’ or correct
perspective
= what is captured on a plane intersecting the visual pyramid
22
Alberti influence on
Dürer
Piero della Francesca
Leonardo da Vinci
transformed painting in realist direction, freed European art from bad geometry
23
Giotto
24
Giotto
25
Ideal City
26
The Flagellation
27
School of Athens
28
School of Athens
29
How, 1700 years after Euclid’s
geometry, did Alberti solve the
theoretical problem of linear
perspective ?
30
Rediscovery of Ptolemy’s
Geographia (c. 140 A.D.)
Greek text arrived in Florence from Constantinople in 1400
Ptolemy used regular mathematical grid system to map the entire known world
31
Florence by 1424 a center
of cartographic and
geographic study
commentaries on Florentine versions of the Geographia influenced Christopher Columbus
32
Hecataeus 6th Century B.C:
33
Ptolemaic World Map, J.
Scotus 1505
34
Ptolemy’s grid system
transformed relationship between astronomy vs. sublunar physicsfor the first time made the world below susceptible to uniform mathematical treatment
35
Ptolemaic World Map
12th-13th Century
36
Ptolemaic World Map,
13th Century
37
Ptolemaic World Map, J.
Scotus 1505
38
Ptolemy‘s Regional World
Divisions
39
Ptolemy’s grid system
not just mathematical regularity
also transparency
... the grid helps us to see the world aright
... it partitions reality
40
Periodic Table
41
Kansas
42
Alberti extended Ptolemy’s
method to pictures
Ptolemy applied his perspective construction only in the construction of maps and in stage design
43
44
Uccello: Gridded Challice c. 1450
45
Alberti’s Ontology of
Painting
Two kinds or levels of matter
linked together by projective geometry
46
Alberti’s Ontology of
Painting
1. the three-dimensional matter of the observable world (macrocosm)
composed of surfaces in three-dimensional reality
2. the two-dimensional matter of the painting (microcosm, simulacrum)
composed of marks on a flat plane
47
Two kinds of matterthe two-dimensional matter of the painting exists in the form of an istoria
constructed out of points, lines and planes (marks)
grouped together to form limbs, bodies and groups of bodies
in a way that is analogous to the logical structure of words, phrases, sentences and paragraphs in a story
48
The artist’s job
is to project the objective array of planes into the microcosm of the painting in such a way as to achieve a maximally beneficial (moral) effect
49
Rules for manipulating
the elements of an istoriadignità
varietà
modestia
verisimilitudo
together with geometry, these four principles constitute the basis of a rational art
50
Leonardo:
Non mi legga chi non e matematico.
(‘Let no one read me who is not a mathematician.’)
51
52
Rays of marvelous
subtletyqualities of color, shape and size of planes in the objective array are ‘measured with sight.’
rays that serve sight carry the form of the thing seen to the sense
‘by a certain marvelous subtlety’
they penetrate the air and ‘all thin and clear objects’
53
Rays of marvelous
subtlety... until they strike against something
dense and opaque, where they strike with a point and adhere to the mark they make.
54
„Among the ancients there was no little dispute whether these rays come from the eye or the plane. This dispute is very difficult and is quite useless for us. It will not be considered.
„We can imagine those rays to be like the finest hairs of the head, or like a bundle, tightly bound within the eye where the sense of sight has its seat.“
Rays of marvelous
subtlety
55
Intromission vs. extromission
„The rays, gathered together within the eye, are like a stalk; the eye is like a bud which extends its shoots rapidly and in a straight line on the plane opposite.”
56
Extromissionism
57
Intromissionism
rays of light
come into the eye
58
The laws of optics are the same
whether intromissionism or extromissionism is true
59
we perceive through the intromission of bodies (Democritus)
we perceive through the intromission of spirits/forms/species (Aristotle)
Intromissionism
60
Extromissionism
We perceive through the extromission of rays (Empedocles, Pythagorians, Euclid, Stoics, Ptolemy, Galen)
61
Extromissionism
Euclid’s geometry and optics relates not to rays of light in the physical sense but to extromissionist ‘visual rays’
Galen: the eye’s crystalline lens is a transmitter of visual force
62
Euclid:
rays are sent out of the observer’s eyes to apprehend the object observed
63
Atomist argument for
extromissionismThe effluxes of, say, a camel or a mountain could not very well pass through the tiny pupil of the eye
How could every point on so large a visual surface be transmitted simultaneously to the eye, with its finite compass, via atoms of light?
64
The intromissionist
answerAlhazen:
refraction and the curvature of the lens of the eye work to filter out excess information in the light,
every point on the surface of an object can convey its form to the seat of vision within the eye – in an exact one-for-one, place-for-place proportionate way.
65
Lux gratiae
Robert Grosseteste, Roger Bacon and John Pecham:
the new optical theories of the transmission of light provide a model of how God spreads the light of grace to his subjects in the world.
66
Physics and physiology are
nowadays thoroughly
intromissionist
67
Yet extromissionism lives
on,
through the arrow of intentionality
in phenomenology
68
Intentionality
69
corrected
content, meaningrepresentations
70
Frege
referent
expression
sense
intentionality Fregeanized
71
concepts, contents, meanings belong here
they are not isolated
but form complex grids
72
concepts, contents, meanings belong here
and they are transparent
they form partitions of reality
73
Intentional directedness
… is effected via partitions/grids
we reach out to objects because partitions are transparent
74
Foreground/Background
with the help of grids we determine what is foreground, what is background
75
Transparent partitions
are involved in simple acts of naming, classifying, seeing, recognizing, mapping
76
Intentionality can be Many-
Rayed‘people’
‘my three sons’
‘Benelux’
‘die Deutschen’
77
1 2 3 4
Counting
with the help of grids weare able to count
78
Intentionality is
foregroundedsingle-rayed or many-rayedmediated via partitions of reality
79
J. J. Gibson’s Dual
Extromissionist-
Intromissionist ViewThere is information in the light, which comes in from the outside
We are pre-tuned to grasp this information with the help of the grids which we project outwards onto reality
80
Partitions of reality can
be good and bad
81
The Empty Mask
(Magritte)mama
mouse
milk
Mount Washington
82
The DER-DIE-DAS partition
DER
(masculine)
moon
lake
atom
DIE
(feminine)
sea
sun
earth
DAS
(neuter)
girl
firedangerous
thing
83
the Spinoza partition
84
Universe
85
Intentional directedness
… is effected via partitions
we reach out to the objects themselves because partitions are transparent
86
A transparent partition is
like an open window
a window on reality
87
Panofsky
perspective is not a true theory of the way light is projected by three-dimensional surfaces onto a two-dimensional plane
rather: it is a system of conventions bound to a certain time and culture.
Perspective as Symbolic Form 1927
88
Against the veridicality of
intentionality
partitions, concepts, contents are not transparent
Midas-touch epistemology
89
Windowless monads
post Duchamp: visual arts are freed from connection to everyday life (and to beauty and harmony)
recontextualized in the museum
90
The Domain of Arnheim
91
The Fair Captive
92
After Duchamp
No place for talk of ‘correct’ perspectival representation, with its implication to the effect that there is some single detached master point of view
no method of painting can be ‘true’ or ‘correct’ for there is no single notion of reality against which its results could be matched
93
Pipe
94
The realist response to
Panofskyeven granting the simplifying assumptions of geometrical optics, perspective paintings correspond to the way we see the world around us with a very high degree of approximation.
best explanation for this: the mathematical forms captured in the geometry of perspective are out there in the world
95
The realist response
the strange fascination which perspective had for the Renaissance mind ‘was the fascination of truth.’ (Pirenne 1952)
96
The geometry of
perspective is purely
objectivethe geometrical relationship between an object and its image on the picture plane obtains independently of whether there is an eye at the vanishing point
(cf. laser-guided missiles)
the laws of perspective hold independently of the existence of subjects, observers, artists or cultures
97
How to Tell the Truth with
MapsA good map casts a transparent net over the surface of the earth
Alberti’s reticolato casts its transparent net over the array of planes out there in objective reality in such a way as to cast into relief a visual scene.
98
Optical Projection
99
Cartographic Projection
100
EVERY MAP MUST HAVE SOME SCALE
EVERY MAP MUST USE SOME METHOD OF PROJECTION
EVERY MAP MUST INVOLVE SOME SELECTION FROM THE WHOLE OF REALITY
THEREFORE: EVERY MAP IS FALSE
A bad argument
101
Therefore: No ‘God’s eye
perspective’ No ‘view from
nowhere’Therefore: every single one of the myriad perspectives we enjoy embodies a false view of reality
This inference from partiality to falsehood would be valid only in a world without windows.
102
Grids of Reality (Mercator
1569)
103
The railway tracks on the Circle
Line are not in fact yellow:
104
Every projection system is
correctthe point is merely to use it properlyintelligence of the projective technique vs. stupidity of the interpreter(maps do not lie)
105
Almost all of our
partitionsare transparentintentional directedness
succeeds
fit happens
106
THE END
THE END