True Grid. Barry Smit h http://ontology.buffalo.edu/smith. 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. Leon Battista Alberti (1404-1472).
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
True Grid • Barry Smith • http://ontology.buffalo.edu/smith
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
Leon Battista Alberti (1404-1472) Alberti’s grid
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
Dürer Underweysung der Messung (1525) the problem of measuring the surfaces of reality
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
‘true’ or correct perspective = what is captured on a plane intersecting the visual pyramid
‘true’ or correct perspective = what is captured by a transparent grid
Practical problem of perspective • solved by Brunelleschi in 1425 • with a painting of the Baptistery of St. John in Florence
Theoreticalproblem of perspective solved by Alberti in Book 1of Della pittura The solution, captured in the diagram of the reticolato, … belongs to projective geometry
How did Alberti solve the theoretical problem of linear perspective ?
And why did mankind have to wait 1700 after Euclid’s Geometry and Optics for this solution?
Ptolemy’s Geographia (c. 140 A.D.) • uses a regular mathematical grid system to map the entire known world
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
The Rediscovery of Ptolemy’s Geographia • Greek text arrived in Florence from Constantinople in 1400
Florence by 1424 a center of cartographic and geographic study • commentaries on Florentine versions of the Geographia influencedColumbus
Ptolemy’s grid system • not just mathematical regularity • also transparency • ... the grid helps us to see the world aright
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.
Ideal City (Grid)
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
the result of this selection is perfectly objective • compare what happens on the stage in the theater • selection does not imply distortion
Degen’s Law • If a well-formed diagram is transparent to reality, then so are all its well-formed parts From:
Mereological fallacies • Inferring that a part is the whole • Concluding, given a true representation, that truth implies completeness
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
Selection implies distortion • only if the mistake is made of assuming that the selected part is identical with the whole
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)
How to Tell the Truth with Maps • There are maps of different scales • There are transparent grids of different granularities
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
… containing labeled and non-labeledcells formed by: • linear and non-linear icons • icons representing spatial regions
Most maps contain two grids of cells • projecting simultaneously onto the same underlying reality
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?
The theory of transparent grids can help us to understand how intentional directedness works selection, foregrounding, labeling, classification