Metaphysics
and geometry of the line in the engravings of
Claude Mellan's moon
Instituto de investigaciones Estéticas UNAM
Hall Francisco de la Maza
Coordination: Nydia Pérez
February 1, 2019
The
relationship between the macrocosm and the microcosm is a metaphysical paradigm
that attempts to solve the question of why the universe, its measurable and
symbolic reasons. With the sight man understands his world and with it, he
recognizes himself in it. See to understand and compare to compare and
consolidate, is to perceive. The foundations of Western thought, established
from the pre-Socratic thought of Pythagoras, where the measurability of the
world through geometry, which is based on the determination that mathematics is
the means to justify nature; of the relation of the geometric bodies with the
natural elements; reinforced in the Renaissance, especially in the sixteenth
century with German geometrists such as Albrecht Dürer, Walter Hermann Ryff,
Jamnitzer, Lautensack and Lencker; for the treaties of Italians such as
Vitruvio, Leon Batista Alberti and Leonardo Da Vinci; as well as the
contemporary vision of the application of geometry to formal and aesthetic
reasons in the images of Jay Hambidge, an American researcher studied and
applied by José Clemente Orozco in the mural The struggle in the west of 1931
at the New School for Social Research In New York; and Douglas Hofstadter, who
implies the formal reasons as a geometric paradigm that relates to the
geometric and symbolic harmony, widely explained in his book Gödel, Escher,
Bach: an eternal golden braid, of 1979, are just a starting point.
Returning
to the central point, which tries to justify the geometric, optical and
metaphysical relationships with the line in the engravings and with it,
sustainable reasons for its physical and symbolic relationship with the
observation of the celestial bodies, we must consider that the theoretical
paradigms, both geometric , as symbolic and aesthetic, they have been and
always deserve a practical corroboration, otherwise they manage mythological
monsters that wallow in narrow daring. However, the reaffirmation that the
world is what it is because it is perceived, interpreted and consequently
represented and re-perceived and interpreted, begins with optical science, but
not only in its volitional reasons, but in the evident consciousness in the
engravings that represent it, which is by itself, a cognitive reason of the
trade of engraving.
With
the sight a line of focus is drawn, with the thoughts interconnected
interconnections and volitional, cognitive and sensitive structures, linear
too. The eye is an instrument that transits its perception in two angles: one
of focus, which in optical science is called the optical axis; and another that
perceives indirectly, called visual field. In both cases, the perceptual
linearity has to do with attention, which is the allocation of visual and
mental interest. However, the angle of focus of the optical axis is so reduced
compared to the visual field, that it allows to interpret the visual trace as a
gradient line that starts from the eye at a point and opens with the distance
at a minimum angle. This is a purely optical phenomenon and because it is
measurable, it is geometric.
The construction of graphic solutions for
the representation of shapes, volumes, spaces, light conditions and textures
are human inventions that conform to a perceptive and interpretative reality to
be credible. The most common way in which the line represents images is the
outline. The envelopment of the objects upon seeing them and touching them to
identify and reaffirm their morphology is linear inasmuch as their physical and
spatial limitations, that is, their contours, are thus linear. Every time we
look or touch the objects we reaffirm their linear circumstances as far as
their physical and visual limits. To see the objects or to touch them is to
wrap them, is to reaffirm or restore their descriptive linearity. One more to
this representative modulation of the line is that which arises in the
circumstance of bodies: by movement, position, size, superposition or touch
generate variable directions according to their strength and internal or
external circumstance of the context in which They are registered. This, in the
visual representation is called composition or organization of the space. The
reasons that determine the conjugation of these formal trousseau have to do
with the relationship between man and his space; that is, with the priority of
balance, stability and movement of the body, as well as the relationship of the
objects in its environment with a physical and visual logic.
In
the images made with engravings, the line is the first paradigm in the
representation of the universe. With straight lines flat surfaces are described;
with curved lines, round, concave or convex surfaces. Vertical and horizontal
lines describe the spaces that interrelate and reaffirm the position of bodies.
The celestial bodies represent, under this association of geometric and linear
characters, an enveloping perceptual solution. The invention of the line works
as an interlocutor between perception and theories. Metrology and a theory
about measurements developed partially in this study, help to understand how
the lines in the engravings have an eloquent language to discuss representative
optics. The distance between the eye that looks and the object in which it
fixes its focus results in an angle that corresponds with the human eye nature
and with the metrological science, a situation applied or applicable to the
distances predisposed in the lines in the engravings.
The linear solutions of the engravings of
the moon (1635-1636) of Claude Mellan, are part of a geometric code that comes
from the heritage of German Renaissance engraving, where Dürer defined with
great precision the way in which perception and representation , as well as
intuition and reflection, can function as a reconstructive whole of the world.
The size of these engravings (21 x 23 cm approximately), plus the distance between
lines (between 750 and 900 micrometers), the thickness of the lines (variable
and gradient in each of them between 200 and 500 micrometers) and the
interrelation between these, whose formal solution is given horizontally with
variables of length according to the terrain of the moon and the light
modulation of each area, generate a positive and convincing propositive image.
Although the lines in this case are horizontal straight lines and the body they
describe is spherical, their enveloping emphasis is manifested in the
thicknesses of each line and as a whole, where the thick and thin lines
respectively define the depth and relief of the terrain of the Moon. This
linear tuning in Mellan's engravings seems a contribution to the linear
descriptive spectrum in the engravings, but in fact it is not more than one of
the options that conform to the geometric linear and perceptual treatment of
the forms translated into lines and that has to be see with a perceptive
metaphysics. For example, the discovery of the elliptical translation
attributed to Kepler was already represented in the preceding astronomical
engravings, which describe the trajectory of the celestial bodies and the
spatial layers in the armillary spheres when the rings or armillas should be
represented as circles in perspective, that is, as ellipses.
The
use of lenses to enhance eye perception seeks to adapt to their reasons for
study. In the engraving, seeing through a lens is for the engraver (in addition
to an approach to the crumbling microcosm), a way of splicing it with its
macrocosm. The faculties of the engraver have to do with the sensitive tuning
that is projected in the lines that trace when they are looked at closely, that
is, with their expressive character; that is why they must be seen as poetic
and nomothetic ribs, in reason first and respectively, of their creative
potentiality and aesthetic eloquence; and second, by the geometric
determination in the interrelation of the lines, which must respond to an
indissoluble geometrical parameter, which also responds to its technical and
formal nature.
To
represent what is far away and what is nearby, the engraver runs between the
visual world and the metaphysical world. He fuses the reasons to understand
with his eyes what he must represent and make others understand with his
engravings.
Although the relativity on physical and
metaphysical reasons of the engravings made with lines has to do with the
conceptualization between the distances, between the microcosm and the
macrocosm and between the technical possibilities in the processes; and
although the astronomical representation of the seventeenth century depended on
partially corroborating and soluble reasons, as well as symbolic intersections,
the engraver relates the elements he perceives and how he perceives them with a
way of representing them. The variables of linear solution in the engravings
have to do with the technical capacity of the engraver, with the knowledge he
has of the physical and metaphysical world, where the correspondences between
what is seen and what is represented are in the engraver and in the others that
they look at their engravings; and with the way in which the cognitive
construction of the time determines statutory modes of representative
validation. The connection between what is seen, is represented and the
agreements reached between those who see the visual reality and the one
represented is, of course, a cognitive epithet. The discrepancies between these
parts arise when the symbolic world, which is iconographic and therefore
statutory, goes hand in hand with its perceptive and visual interpretation
capabilities. Here we enter again into this metaphysical dissertation. The
images of Mellan's moon are not the moon but a representation of it. What we see
in the engravings are linear interrelationships in different intensities and
formal particularities that allow us to define a symbolic unit altogether. The
lenses to see the moon in the sky and those used to make and see the engravings
work as metaphysical reaffirmations of this symbolic world that is seen and
represented. In order for the engraver to make a consensual interpretation of
what he requires, he must first identify a perceptive and symbolic connection
in those around him and in himself in order to be valid, otherwise he would be
describing pure abstractions.
Héctor Morales
