JF Ptak Science Books  Post 1079

In a world constructed of nothing but right angles in horizontals and verticals,  how would a diagonal fare?

Would it be like extraordinary confusion and then recognition of a sphere in a flat two dimensional world (as in Edwin Abbott’s Flatland), or would it be an astonishing moment of discovery like Robert Hooke’s Micrographia images, or a creeping, sweeping acknowledgment of first-seen perspective in Paolo Uccello? 

In the case of the cubist Piet Mondrian, it would be revulsion and disgust.  Mondrian helped establish¹ De Stijl (1917or thereabouts), with a philosophy of using lines to transform artistic thought onto canvas, and the lines were all horizontal or vertical, with square and rectangular shapes. These would represent the pure harmonies of expression, along with the primary colors as well as black and white. 
 

Mondrian wrote “:… this new plastic idea will ignore the particulars of appearance, that is to say, natural form and colour. On the contrary, it should find its expression in the abstraction of form and colour, that is to say, in the straight line and the clearly defined primary colour.”

Stijl co-founder, popularist, artist and editor of the movement’s journal, Theo van Doesburgh and his work (1924) introduced diagonals into the horizontal/vertical field in his painting “Arithmetische Compositie” and Mondrian quits the group.Van Doesburgh felt that the diagonal was more vital and important than the vertical and horizontal.  Mondrian felt that this was wrong, and clearly raked the original ideals of De Stijl, and so quit the movement, which he felt to be compromised by one of its co-founders.

I can certainly appreciate Mondrian’s need to go; though, honestly, what the debate and reticence reminds me of is an episode from the original Star Trek series, “Let That Be Your Last Battlefield” (1969).  The story is about an intractable difference between two seemingly identical factions of the planet Cheron²–it turns out that the differences between the two sides is a physical one that was inconsequential to the crew of the Enterprise, but of all-consuming importance to the Cheronites.  They were both white and back, their skin color cleanly halving  their bodies on the vertical.  But the “inconsequential” difference was that one person was black on the right side and white on the left; the other was the opposite.  It was this difference that led to their planet-wide schism and abandonment of each other. 

Its no wonder that the writers of that episode chose the name “Cheron”, which is another accepted spelling of “Charon”, the Greek ferryman who transports the dead to Hades.

That’s where this particular schism falls to me, though to those involved I’ve no doubt that the differences were as significant as 2D vs. 3D and flat perspective vs. real perspective, the blatant if not micrographic differences looming mighty small to everyone but those involved. 
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Notes

1. In 1917 it was Mondrian who coined the term Nieuwe Beelding (“the New Plastic”) , or Neo-Plasticism, from which De Stijl took its meaning.  He set out the philosophy of the group in that same year in a series of twelve articles in the group’s journal, De Stijl

2. From Wikia Entertainment:  “Cheron is a Class M planet located in the southern region of the galaxy near the Coalsack, which once supported a humanoid civilization of Cheron natives. In the 23rd century, the area of space was largely unexplored by Starfleet, so the race was previously unknown to the Federation.”