COLUMNS MAKE ORDER OUT OF CHAOS AND SHAPE PUBLIC SPACES; AN EXHIBITION

Defying gravity; defining architecture; decoding space; gracing facades; groveling in ruins; rising upright and alone; surrounding and shaping the complete urban space in pairs; flattened on textiles or rounded for candlesticks; austere or adorned; severe or fluted; of marble, granite, stone, terra cotta, plaster, wood, or metal, the column has been architecture's primary element.

Anciently, Vitruvius says, men lived in woods and inhabited caves; but in time, perhaps following the example of the birds that build their nests with great skill, men made their shelters of upright tree trunks.

Across the trunks went roofs, and the result was called a building.

Such was the origin of columns, bases, and capitals, as described by William Chambers in the vintage book on the ''Origin of Building'' on view here with other aspects of ''The Column: Structure and Ornament'' through Aug. 22.

This show of objects and graphics, largely drawn from the Smithsonian Institution, is on view at the Cooper-Hewitt Museum of the National Museum of Design.

The definition of the column is obvious. ''A slender, upright post consisting of a nearly cylindrical shaft, with a base and capital and used as a support or ornament in building,'' according to ''American Shelter'' (Lookout Press).

Ionic, Doric, and Corinthian describe the dominant orders, as any student of architecture knows. (Tuscan and Composite complete the five orders of the Western world.)

Making order out of chaos, a column can transform the bland line of the horizon into the orderly segments of a shaped public space.

A column can have many non-architectural uses as the show demonstrates in some of its five rooms. It can become the legs on furniture, the upright curve of andirons, the framing form for a chimney piece, or an ornament for interiors. (The Cooper-Hewitt itself displays that use.)

It can, and has, also become a code of building behavior in America.

Frank Lloyd Wright's Johnson Wax plant in Racine, Wis., carried this requirement to the utmost extreme. The authorities insisted that it needed more columns to hold aloft the structure. The architect argued he needed less support and stopped some of the columns just short of the ceiling.

Wright won and the columns held.

''That heroic slender stem, standing up there and a graceful thing on tiptoe, '' the architect exulted, ''standing straight and true until 60 tons instead of the 12 tons required were on top of a shaft nine inches in diameter at the top.''

Wright's flat capitals, like the plan of a waiter supporting a tray, suggest the free-play columns of our own century. These imaginative columns comprise the most delightful aspect of an often-dry exhibition.

In this modernist half century we have added to the zest of the staple form. Even a building itself can stand in for a column; witness Adolf Loos' design for the Chicago Tribune competition, which looks less like a skyscraper than a swelled base, shaft, and capital.

Although the show supplies Egyptian-faced capitals, wheat shafts, balls, and dogheaded capitals in Wedgwood vases, our own era offers still more appealing works of whimsy. A major architect (Charles Moore) can recharge the column form with humorous content (the ''Order of the Deli'') in a public setting of major impact (the Piazza d'Italia in New Orleans).

Unfortunately, this post-modernist or neo-historical work of the 20th century - the wry use of tradition - doesn't get enough space here. Colored columns are few; the black-and-white works do not show the exuberance possible in the shafting form, and the show does not venture far enough afield from its own collection to amplify the idea by showing the full range of execution.

However, the most lively, if skimpy, section of the show does highlight some contemporary re-uses of the column: the silverized ionic capital of Moore's Piazza; the asymmetrical orange-and-green house, columns to the forefront, by Thomas Gordon Smith; the French and Company facade by Michael Graves.

A work of Hans Holbein hangs here - his fanciful, palm-shaped-column form for the Viennese travel bureau - it only suggests the physical support and showmanship that could have helped update this exhibition.

Drawing from its own collection, the Cooper-Hewitt overdid the graphics and objects, where they might have shown how historical motifs or forms can serve new functions of humor, wit, elegance.

Even before today's post-modernist parodies and replays of the past, architects were adorning state capitols with state mottoes or images (corn was one motif).

Neither antique architecture nor the exhibitors at the Cooper-Hewitt show the treatment of the column as part of a stage setting. Its theatrical effects are amply illustrated as are its ancient uses from palace to prison.

But to make architecture as sprightly a show as the lively entourage of buttons and baskets that the museum has shown through the years, the Cooper-Hewitt organizers needed to extend themselves more to discover eclectic, contemporary, and spry artifacts.

''Like many things of apparently simple purpose, columns are actually complex ,'' the catalogue notes.

A more orderly and organized exhibition could have divided and amplified political purposes, too. A more dramatic collection of architectural objects could have isolated the columnar form from its architectural origins and freshened our outlook on the past.

As it is, the exhibition lacks the variety and vitality necessary for most visitors to see beyond an academic exhibition to its engaging idea of a physically supporting element that is an aesthetically inviting one as well.