SYNTAGM I 23...31
Both this and earlier print are the result of my research over more than twenty years on a problem that presents itself in the two ways as theorized by Mondrian and Van Doesburg.
Mondrian wrote in 1943: "In his later works Doesburg tries to destroy static expression by diagonal position of his lines. But in this way the feeling of physic equilibrium which is necessary to enjoy a work of art is lost. The relationship with architecture of vertical and horizontal position is broken." The second way derives more from mathematical philosophy and, if I may use the term, mathematical politics regarding the relative status of contradictory attributes of infinite collections.
Prompted by Fritz Glarner's commentary on the Mondrian/Van Doesburg problem - his use of tapering forms arising from slight deviations from an implicit orthogonal substructure - I discovered that if two such structures are allowed to interfere with each other in a strictly regulated way the whole field becomes nuanced, at the moment of maximum coherence, by a secondary re-ticulation which is diagonally oriented with regard to the original lattice.
Syntagm IV 23....31 was developed from a page of my 1980 research notes. The four vectors of the secondary reticulation are denoted by the presence of colored elements which sweep the Euclidean plane at seven different stages of its articulation. Each of these stages is the product of a binary summation of two sets of positive/negative (white/black) elements from a logically precedent stage.
It seems possible that some of the well-known paradoxes associated with Georg Cantor's treatment of the problem of infinite collections may be explicable in terms of slippage of linguistic reference amongst different forms of topological connectivity. In this instance quasi-paradoxical phenomena result from the simultaneous attribution to the surface of the properties of a Euclidean plane and of a torus.
Increasing topological compactness is realized as the summations accumulate.