THE RELIANCE ON THE ARCHITECTONINCS OF SIMPLE GEOMETRIC FORM

JORJ PAPAS


 
 

Name: Jorj Papas, Artist, (b. Toronto, Ontario, Canada, 1965).

E-mail: krisjorj@hotmail.com

Fields of interest: Geometric and Gestural Abstract Painting (Philosophy: Phenomenology, Aesthetics; Mathematics: Geometry; Fine Art History).

Awards: Experimental Arts Faculty Award, 1994; Experimental Arts Faculty Award, 1993; D.L. Stevenson & Son Award, 1992.

Exhibitions: 

SOLO EXHIBITIONS: 

*1998 (May), "Untitled", The Empty Box, 801 King St. West, Suite 1125, Toronto, Ontario.

*1997 (April), "Abstraction Untitled" - Executive Outcome, The Empty Box. 801 King St. West, Suite 1125, Toronto, Ontario

1996 (Nov.), "The Corporate Horse", 220 King St. West, 4th Floor, Toronto, Ontario. 

1992 (Nov.), "Jorj Papas: Recent Paintings", The Bartello Gallery, 121 Ave. Rd. Toronto, Ontario

GROUP EXHIBITIONS; Organization, Selection, Curation and Participation of Fine Art Exhibitions;

1997 (June), "Hugh Alcock & Jorj Papas - Untitled", Empty Box, 801 King St. West, Suite 1125, Toronto, Ontario

*1996 (May), "C.1996", 525 Adelaide St. West, Toronto, Ontario

*1995 (Oct.), "Installations & Hangings", The Cable Street Gallery, 56 Cable Street, Whitechapel, London, England.

*1995 (Feb.), "Between Eye & Hand: Contemporary Drawing", 96 Spadina Ave., 5th Floor, Toronto, Ontario.

1994 (Nov.), "Dead Industry", 388 Carlaw Ave., Toronto, Ontario.

1992 (April), "Hey Baby Spit Me A Kiss", (Sponsorship BPK Communications), 209 Adelaide St. East, Toronto, Ontario.
 
 

Abstract: Both Artistic and Scientific approaches to phenomena have a similar basis in the axiomatic method. As such, the methodology of both practices have been dependent upon a form of reasoning that leads to the truth or falsity of a given proposition or hypothesis. As the axiomatic method has its roots in Euclidean Geometry, Artistic and Scientific practice can be traced back to this particular geometric discourse, which has as its impetus an approach to phenomena of which is to acquire coherent relationships of exact and specific spatial forms. I will give a brief exegesis of geometry and geometric reasoning in the lineage following Plato, Euclid, Kant and Non-Euclidean forms.
 
 

1. PAINTING AND THE EMPLOYMENT OF GEOMETRIC FORM

The following discussion is to explicate and clarify the nature of geometry and geometric form and its possible relation to painting as an art-form. The use of this geometric system and its relationship of form in painting, is an approach of employing architectonic (first) principles of a universal order. The implicit goal of this study is to enable the mind to process through manifested form the immaterial a priori universal(s) that is (are) hidden from sensory perception. This vision of geometric universal order has its roots in an assumption that the phenomenal world and the perception of this world (bodily existence) are understood as systems of geometric structures of forms, which exist innately as a priori form without a material/matter correlate. 

The distinction between the perceptual appearance of the world and its true, mathematical structure is the Platonic interpretation of geometry as embodying the ideal of true knowledge - geometry is the ideal/universal by performing as the original model. The manifested particular form as representation, is assumed to be inferior and explained in terms by the not manifest idea of the higher order.

The Platonic sense of geometry with the distinction between the two realms of the material and ideal can be paralleled to Euclidean Geometry and the advent of the number "Zero". Previous to Euclidean Geometry, there were no a priori axioms/assumptions. The advent of "Zero" allowed arithmetical / geometrical functions to represent ideas which had no material manifestation. Euclidean Geometry and its use of the axiomatic method necessitates that the fundamental propositions and methods of construction are explicitly specified. This Euclidean system, is based on five postulates (assumed statements for the avoidance of circularity), and five axioms (common notions) as general principles. While the first four postulates contain a self-evident certainty, the fifth postulate (referred to as the parallel postulate) does not have the simplicity and the immediate self-evident certainty that the first four possess of which is required for the axiomatic method.

What is further developed from this standpoint is that, since the fifth postulate was not dependent on the four preceding postulates - a necessary pre-requisite for the axiomatic method - the Euclidean system was not the only answer to the questions of geometry. The proven consistency of Non-Euclidean systems liberates geometry from the initial starting points and with it the notions of Form as universal(s) / ideal(s) as necessary conditions. Hence, the "postulates of geometry become mere hypotheses where physical truth or falsity are of no concern...., as long as they are consistent with one another, any number of postulates may coincide to develop an alternative geometry." 

In this way, "a postulate has nothing to do with self-evidence". 

This stance has an implicit effect on the presumed notions of space as an ideal, a priori universal entity in the work of Kant. For Kant, space in its manifested form, is a representation of an a priori intuition and a conception. Space existing prior to sensuous experience, is directed toward the external manifest world and not the reverse. Hence, this a priori intuition is the foundation of any and all intuitions of the manifest world. The phenomena of sensuous presence are conditioned by this a priori condition, and space is therefore, not dependent upon phenomena of the manifest world. Not dependent upon these phenomena, space cannot be deduced upon the relations of things in space, therefore, empirical intuition is possible only through a priori intuitions of space.

The practice of constructing conceptions from intuitions given prior to experience, deals only with the a priori prototypes of the existence of things in intuition as relations of quantity. Geometry (constructing descriptions) in its relation to painting therefore, develops merely expressions of diagrammatic, representational images from a priori intuition about physical space, not succeeding the purpose to establish the universality of the principles of geometry in the Platonic - Euclidean - Kantian systems.

The development of geometric construction as a way of measuring spatial order is now derived from the external experience of the sensuous world. This is in contra-distinction to geometrical figures being understood as ideal entities. As ideal entities, the spatial shapes and constructions in perceptual experience are compared to the ideal entities as imitations with the consequence of the experienced manifest world idealized to quantitative relationships. 

Since the construction of universals with geometric quantification cannot be achieved out of sensations via the physical processes of the body, a distinction arises. This distinction is the "sensation" of color and the "being" of color. The sensation of color becomes an image in the perceiverís mind creating a dichotomy between an external and sub-ordinate internal world, i.e. a relapse into empiricism. The sensation is removed from the phenomenon and placed in the mind as an independent image.

Being already in the situation of which is to be measured, the figures in the sensuous realm are apprehended as forms of a material given with specific sense qualities (e.g. color). This awareness of color and space is an immediate apprehension as opposed to an actuality hidden behind the appearance of solids in the manifest world as pre-conceptions of ideal entities. Hence, geometrical space and perceptual space are two different structures.

What is distinguished is a qualification of conceptual, perceptual and physical space. For the predecessors of Non-Euclidean geometry this distinction did not arise as the sensuous manifest world was only appearance and therefore could not distinguish between its aspects of perceptual, physical and conceptual.

Geometry becomes a tool used to construct the distinctions between perceptual, conceptual and physical space as it is experienced by redirecting the geometrical perspective as a preconceived conceptual constructive system of quantification, to the systematization of perceptual construction by the placement of the embodied consciousness in the center of experience. This allowing the focus onto the consciousness of abstraction in the painting activity and the objects of that act. The painting activity in its relation to the manipulation of geometric form is a way of making marks to explore the connections between conception, perception and physicality. In this sense, when the material of painting consists not only in physical manipulations but also visual, somatic and tactile perception are tied up in the making of the marks along with the ideas that reside in the artistís approach. 

Upon speculation it can ascertained that the ascension of universals by way of abstraction in the painting activity dealing with the qualitative aspects of sense-perception and the manipulating of geometric form/construction begins in the distinction of the different aspects of space. 
 
 

References 

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