An explanation of Piet Mondrian's work by Michael Sciam

Straight opposite lines?

A metaphor of duality

A relational space

In his pursuit of a new plastic art, the painter progressively identified the spiritual with the vertical and the natural with the horizontal in order to create a relational space in the two dimensions of the canvas between what he, like every human being, felt to be contrasting realities.

This should not, however, be taken as an attribution of objective value.
The vertical could function equally well as a symbol of the natural, in which case the horizontal would come to symbolize the spiritual.
Natural space is of course presented to the eye as a boundless horizontal expanse whereas the vertical aptly expresses the human desire to concentrate the variety of the physical world ideally, conceiving it as a whole. A vertical thrust expresses mankind’s atavistic propensity to imagine the spiritual as an invisible reality extending toward the ethereal space of the heavens rather than remaining bound to the everyday matter spread out before our eyes.

All this may have influenced the artist in his attribution of meaning, but not to any great extent. After all, Mondrian’s aim was to express an equivalence of opposites such as unity and multiplicity, spirit and matter, interior and exterior.
Horizontal and vertical have no inherent value in Neoplastic space. They serve as visual metaphors of the duality present in the human mind, the symbol of basic natural forces that clash and relate with one another to generate all the variety of the world.

It is not a grid

Mondrian: “Everything is expressed through relations. Color, size, and position exist only through opposition to a different color, size, and position. This is why I call the relationship the fundamental element. (…) Each thing becomes knowable only through another, as every form of wisdom teaches us.”

Humanistic and scientific thought

Time and teaching

I am afraid that time and a great deal of teaching will still be needed to make people understand the degree of mental openness and emotional transport that should actually be involved in the enjoyment of a Neoplastic composition.
The orthogonal lines and primary colors are an act of autonomy and freedom of thought with respect to nature, not an imposition. Though it might at first seem an arbitrary and restrictive choice with respect to the natural world, the Neoplastic language then strives to reformulate as exhaustively as possible the real and not merely apparent characteristics of natural space, or rather the characteristics of the relationship between thought and nature, finally treating the two aspects as essential components of a single and indissoluble process.