THEY'RE FLYING magic carpets again at the Textile Museum. The latest show, embracing five centuries of Oriental rugs, is a brain-teaser as well as an eye-pleaser.

Presenting rare old carpets as puzzles, curator Carol Bier has set up an intriguing quiz while putting across a fundamental difference in the way patterns are perceived in the Orient and the Occident.

To the Western eye a border fences a design and marks its end. Our minds come to the edge and stop. To their weavers, however, the intricately executed borders of these carpets are simply arbitrary overlays on infinitely repeating patterns, Bier says. Though the fingers are stopped by the edges of the loom, in the weaver's mind the margins fade forever and forever. All is one under the eyes of Allah.

The designs may run at right angles and/or diagonals or may radiate from one or several centers. Many carpets contain patterns within patterns within patterns, flashing forward and backward until reels the mind.

Westerners can be slow to pick up the patterns, Bier says, because "we're much more familiar with the representational traditions of Western art focused on systems of proportion related to the human form."

It's hard for the unpracticed eye even to decide whether a design is floral or geometric, much less to puzzle out the overall scheme. Some backgrounds are so richly textured that the eye periodically promotes them to the foreground, like those puzzle-page cubes that turn themselves inside-out as you stare at them.

"I've been studying them for years and they still fool me," Bier says.

A carpet may contain several full repeats of a pattern composed of small elements; others reveal only part or even a single section of the design, which must play itself out in the imagination. Usually the area within the borders is symmetrical, but sometimes the border slashes through the heart of a repeat.

Study a pattern long enough and you may begin to develop a sense of the weaver. A 17th-century pile carpet from Persia seems to have been created by a poet, or perhaps a plotter: The floral design radiates and ramifies in whirls and swirls that somehow always lead the eye back to the point of beginning.

A sense of humor is suggested by a diagonal design pile carpet woven by a 19th-century Yomud Turkman (Central Asia). Although the oval elements repeat in regular array, somehow they seem to skitter around like water drops on a hot skillet, and you can't help but smile.

Darker musings -- even hallucinations -- may be stimulated by a 17th-century Anatolian design that seems to presage current events in the Middle East. The pattern of the central field is so damnably dense that the eye, defeated, retreats to the border, which itself repeats and suggests nothing so much as double rows of concertina wire and tank traps defining a no man's land.