Abstract art can provoke wild guesses. During the press preview of "Kazimir Malevich: Suprematism" at the Guggenheim Museum, a man came up to Matthew Drutt, curator of the Menil Collection (which co-organized the exhibition), and asked, "Is Malevich's art an art of space. . . like that of Kandinsky?"

"No," replied Drutt, who said that in fact Malevich hated the art of Kandinsky.

The man persisted. "But Malevich's art is an art of infinite space. . . like Matisse and Picasso," he said.

Drutt added that Matisse's space is not infinite but "is about surface." The curator was trying to make a point, to dissuade the guy from believing that pictorial space is illusionist and thus deep, or spiritual and thus deep. The assumption that all abstraction is the same in the content of its form is no more valid than the assumption that all representation is alike.

The Guggenheim's select retrospective of Malevich's paintings, drawings and architectural ideas is intensely wrought, and it is also stunning. And clear -- which is why a viewer might well see that this focus on Suprematism from 1913 to 1931 (without much of the Cubo-Futurist preparation leading up to it), allows a lucid understanding of the visionary proposals Malevich dreamt for our world.

Think of his art as a thought process through which material dross is shed and the essence shines forth. Although this sounds utopic -- and it is -- Malevich has in mind to create a formal language for realizing radical values to inspire the modern Soviet citizen. The pictorial realism of a Peasant in Two Dimensions, Called Red Square (1915), announces this radical program. Is it abstract? Let's say it is highly condensed immanence. "Painting is only color and form," Malevich once declared.

The year 1915 was vintage for Malevich, who created an astonishing number of superb works, innovative and definitive all at once. The reductive essences, including the deservedly legendary Black Square as well as Black Cross, Black Circle, Eight Red Rectangles and Plane in Rotation, Called Black Square, show us that even within this strict mode, the artist articulated colored planes that are flat, that curve, that rotate, that fade out -- and so establish a lexicon of dynamic form.

In one year, Malevich produced a yield of abstract compositions as complex in syntax as the lexicon was simple. As shown by Suprematist Non-Objective Painting from a museum collection in Ekaterinburg, paired squares in black and red present a stable form above and against which levitating crossed lines and planes -- and black half circle -- reveal a rich and subtle dynamic.

This non-objective art is neither geometry, nor decor, but an intuited system for uniting the ideal with the real. The show and excellent catalogue essays aim to rectify the simplistic impression we have of Malevich as reductive only.

Toward this purpose, the 42 drawings on view are not studies for paintings to be executed like copycat knock-offs, but rather help establish the on-going thought process by which Malevich developed a plastic visual language for the modern age. Just to remind us that Malevich put his vision to use, the Guggenheim shows us a tea-set that Malevich designed, patterns for fabric, and other designs by the artist.

However idealized they may be, the Suprematist architectural models (which were reconstructed in 2002 from photographs) reflect back to us the image of the skyscraper, an ideal which we have long realized -- and in which we now live.

"Kazimir Malevich: Suprematism" originated at the Deutsche Guggenheim Berlin, where it was seen by 70,000 visitors. When the show closes in New York, it will travel to the Menil Collection, where it may be viewed from October 3, 2003 through January 11, 2004.