Piet Mondriaan, Composition no. 1, III (1927)
The line of a perfect circle is not perfection of the first order. The line of a perfect circle is perfect as a line. But it is not perfect without limitations, it is not perfect as an unending line, it is not perfection of the first order, it is not the perfect line.
The perfect straight line is the perfect line. Why? Because it is the only perfection of the first order. Likewise its ray, the perfect eternal ray, is perfection of the first order. The perfect eternal ray is also the perfect ray. For only it is as ray a perfection of the first order.
The figure which objectifies the concept of this pair of perfections of the first order is the figure of the perfect right-angledness, or, in other words, the cross-figure. This is the figure that represents a ray-and-line reduced to perfection of the first order. It characterizes the relationship between perfections of the first order as a perfect right-angled relationship, a “cross” relationship. This figure is actually “open.”
In those days, Piet Mondrian sent a message that he was in Holland and that he could not return to Paris. Mrs. Hannaert invited him to stay, and when one afternoon I arrived, he was sitting with her at the table. He made a curious impression upon me, because of his hesitating way of speaking and the nervous motions of his mouth. During the summer of 1915 he stayed in Laren and rented a small atelier in the Noolse Street. In the evenings we would go to Hamdorf, because Piet loved dancing. Whenever he made a date (preferably with a very young girl), he was noticeably good-humoured. He danced with a straight back, looking upwards as he made his “stylized” dance steps. The artists in Laren soon began to call him the “Dancing Madonna”!
In ‘29 I was with him one afternoon in Paris and met the Hoyacks in his atelier. After a while, without saying anything, he put on a small gramophone (which stood as a black spot on a small white table under a painting of which it seemed to be the extension) and began quietly and stiffly, with Madame Hoyack, to step around the atelier. I invited him to dine with me as we used to do in the old days. Walking on the Boulevard Raspail, suddenly I had the feeling that he had shrunk. It was a strange sensation. In the metro we said goodbye; when we heard the whistle, he placed his hand on my arm and embraced me. I saw him slowly walking to the exit, his head slightly to one side, lost in himself, solitary, and alone. That was our last meeting.
A “cross” relationship.
This figure is really “open.”
We can prolong it on any side as long as we wish without changing its essential character, and however far we prolong this figure, it never attains a perimeter. It never becomes “closed” thereby; it is thereby totally and utterly boundless: it excludes all boundaries. Because this figure is born from itself in our conception, it characterizes the concept of perfect opposites of the first order, as a concept of the essential “open,” the actual and real “unbounded.”
· M. H. J. Schoenmaekers, Beginselen der beeldende wiskunde (‘Principles of Visual Mathematics’) (1916)
· M. Van Domselaer-Middelkoop, Herinneringen aan Piet Mondriaan (‘Memories of Piet Mondrian’) (1959/1960)