1 Partitions of Reality Barry Smith buffalo.edu

2 Leon Battista Alberti ( )

3 Alberti (Medal)

4 Leon Battista Alberti ( ) 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 where a 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

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11 Machines for seeing for measuring the visible surfaces of external reality ‘reticolato’ ‘grill’ (graticola) ‘veil’ (velo)

12 Dürer’s treatise on measurement Underweysung der Messung (1527)

13 Dürer

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15 Artist’s Grid transparent grid

16 Practical problem of perspective solved by Brunelleschi in 1425 with painting of Baptistery of St. John in Florence

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18 Peepshow

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20 Theoretical problem of perspective solved by Alberti in Book 1 of 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 physics for 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

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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 matter the 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 istoria dignità 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.’)

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52 Rays of marvelous subtlety qualities 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 extromissionism The 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 answer Alhazen: 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, meaning representations

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’

Counting with the help of grids we are able to count

78 Intentionality is foregrounded single-rayed or many-rayed mediated via partitions of reality

79 J. J. Gibson’s Dual Extromissionist- Intromissionist View There 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 fire dangerous 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 Panofsky even 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 objective the 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 Maps A 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 correct the point is merely to use it properly intelligence of the projective technique vs. stupidity of the interpreter (maps do not lie)

105 Almost all of our partitions are transparent intentional directedness succeeds fit happens

106 THE END