1 True Grid Barry Smith .
-
date post
22-Dec-2015 -
Category
Documents
-
view
214 -
download
0
Transcript of 1 True Grid Barry Smith .
2
Leon Battista Alberti (1404-1472)
author of Della pittura (1435-36)
the first scientific manual of painting
and simultaneously a contribution to the ontology of visual representation
4
Leon Battista Alberti (1404-1472)
The goal of the artist
is to produce a picture that
will represent the visible world
as if the observer of the picture
were looking through a window
6
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
9
Practical problem of perspective
solved by Brunelleschi in 1425
with a painting of the Baptistery of St. John in Florence
12
Theoretical problem of perspective
solved by Alberti in Book 1of Della pittura
The solution, captured in the diagram of the reticolato,
… belongs to projective geometry
16
Ptolemy’s Geographia (c. 140 A.D.)
uses a regular mathematical grid system to map the entire known world
20
Ptolemy’s grid system
transformed the relationship between astronomy and sublunar physics
... this made the world below for the first time susceptible to uniform mathematical treatment
21
The Rediscovery of Ptolemy’s
Geographia
Greek text arrived in Florence from Constantinople in 1400
22
Florence by 1424 a center of
cartographic and geographic study
commentaries on Florentine versions of the Geographia influenced Columbus
24
Ptolemy’s grid system
not just mathematical regularity
also transparency
... the grid helps us to see the world aright
26
Alberti extended Ptolemy’s method
to pictures
Alberti: the veil affords the greatest assistance in executing your pictures,
since you can see any object that is round and in relief, represented on the flat surface of the veil.
30
Alberti’s Ontology of Painting
1. The grid of the reticolato and the grid of the objective reality beyond are linked together by a projective relation
2. The grid effects a selection, from the totality of surfaces in objective reality, of those parts which will be foregrounded in the painting
31
the result of this selection is
perfectly objective
compare what happens on the stage in the theater
selection does not imply distortion
32
Degen’s Law
If a well-formed diagram is transparent to reality, then so are all its well-formed parts
24
The Flagellation
From:
34
Mereological fallacies
Inferring that a part is the whole
Concluding, given a true representation, that truth implies completeness
35
Algebra
Algebraic ontologists are correct: the world contains processes;
they err only when they add: and nothing else
Field ontologists are correct: the world contains fields;
they err only when they add: and nothing else
36
Selection implies distortion
only if the mistake is made of assuming that the selected part is identical with the whole
37
The world contains fields
Evidence: this assumption supports successful predictions
The world contains only fields and nothing else
This conclusion rests on a mereological fallacy (and also on a mistaken understanding of the role of granularity)
38
How to Tell the Truth with Maps
There are maps of different scales
There are transparent grids of different granularities
39
How to Tell the Truth with Maps
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.
A good map casts its transparent net over reality in such a way as to cast into relief a certain portion of the surface of the earth
43
… containing labeled and non-labeled
cells formed by:linear and non-linear icons
icons representing spatial regions
45
The analogy between maps and pictures
– has nothing to do with perspective
– but rather with the highly general concept of a transparent grid and with an associated highly general notion of projection
But how are we to understand this notion of projection?
57
selection, foregrounding,
labeling, classification
The theory of transparent grids can help us to
understand how intentional directedness works
58
Intentional directedness
… is effected in every case via something like an Albertian grid: a cognitive artifact which we shall call a granular partition
… we can reach out to objects because partitions are transparent
59
and such partitions
are always granular:
when we perceive a frog we do not perceive the molecules in the frog’s skin
when we think about Mary, we do not think about the molecules in Mary’s nose
60
Vagueness comes to awareness
through ontological zooming (from coarse-grained to fine-grained partitions)
61
This granularity of our partitions
explains also (how we are able to cope with) the phenomenon of vagueness
when we think about Mary, we do not think about the molecules in Mary’s nose
when we think about Mount Everest, we do not think about where, precisely, the mountain begins or ends in its foothills
62
Foreground/Background
granular partitions are involved wherever there is a division of reality into foreground and background
63
That granular partitions have multiple cells
corresponds to the fact that intentionality can be
many-rayed
‘people’
‘my three sons’
‘Benelux’
‘the Germans’
‘COSIT participants’
65
Granular partitions
are involved in simple acts of naming, classifying, seeing, recognizing, mapping
All (veridical) databases and information systems involve granular partitions
66
Intentional directedness
… is effected via partitions
we reach out to the objects themselves because our partitions are transparent
67
A granular partition is like an
open window
we use partitions because they help us to see the world aright
68
Some would deny the veridicality of
intentionality
partitions, concepts, contents are not transparent, they say ...
we can never see objects as they really are, they say ...
because we must always use those human artifacts called partitions (concepts, ideas, words, metaphors, image schemata ...)
69
Against the veridicality of
intentionality
and whenever we grasp an object by means of a concept we somehow change the object,
hence we can never know how the object really is in itself
call this: „Midas-touch epistemology“
70
After Duchamp
there is 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
71
The realist response
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 accuracy.
The best explanation for this is: the mathematical forms captured in the geometry of perspective are out there in the world
72
The realist response
even granting the simplifying assumptions involved when we use a grid of cells of a certain granularity, our intentional reference gives us access to the world around us with a very high degree of accuracy.
The best explanation for this is: our granular partitions are transparent to the structures out there in the world
74
Fit happens
There are structures out there in the world accessible at different levels of granularity
(There are maps of different scales)
75
Every one of the standard map
projection systems is correct
the point is merely to use them properly
maps do not lie (but they may be old, or embody local errors)
intelligence of the projective technique vs. stupidity of the interpreter
77
There is no ‘God’s eye perspective’
– no ‘view from nowhere’
No super-partition encapsulating the entirety of human knowledge
But this does not mean that every one of the myriad perspectives we enjoy embodies a false view of reality
Rather, it means that we must take distinct (granular) perspectives together
78
There is super-partition encapsulating
the entirety of human knowledge
Yet the claims of the scientific method to yield knowledge of reality still stand
– the mistake would be to claim that we can know reality only through science
(or through Haskell-programming, or whatnot)
79
Almost all of our partitions
are transparentintentional directedness succeeds
... our job is to understand it