The state-owned art of Mexico - which goes on view today at the Smithsonian Institution - is both wonderful and strange.

Pulsing in these objects is something wholly unfamiliar - a symbolbogy, a richness, a kind of teeming violence - that most of us will never fully comprehend.

Philisopher Octavio Paz calls it "the otherness" of Mexico. For though we share a border, and much more than a border, we look upon these carvings, paintings and cerramics, across a gap of comprehensin that the art we know best, that if Western Europe, cannot help us bridge.

Dr. Armand Hammer, the art-collecting oil man whose charitable foundatin is spending $750,000 on the Mexican display, had brogt to the Smithsonian not one show, but two.

"Treasures of Mexico: From the Mexican National Museums," at the Museum of Natural Hisotry, includes a superb selection of Precolumbian objects as well as more than 50 statues, prints, and paintings produced between the Conquest and 1892. The passionate, poltical 20th-century pictures of the painters known as "Los Tres Grandes," Mexico's big three, meanwhile will be displayed in 'Orozco, Rivera, Siqueiros: A Selection From the Mexican National Collections" at the Hirshorn Museum and Sculpture Garden just across the Mall.

Because the big three all were muralists, and because murals cannot travel, the show of older treasures is the more impressive. The oldest piece on view - and the oldest sculpture yet discovered on this continent - shows what seems to be the head of a coyote. The bone that it was carved from was taken from an animal, related to the camel, that has long been extinct. This amazing work is dated 10,000 B.C. The newest work displayed is a picture of Zapata painted by David Alfaro Siqueiros on 1966.

Though cultures, of course, change in 12,000 years, something in these shows - a preference for bright color, a strong, earth-bound stolidity, and a love of public violence - links the old and new.

The soldiers of Cortes, although well accustomed to butchery and murder, were nonetheless astonished by the human sacrifices, and the cannibalism, of the Aztecs. They were told, for instance, that at the dedication of the Pyramid of Tenochtitlan in 1487, "four lines of prisoners stretching for two miles each were sacrificed by a team of executioneers who worked night and day for four days." More than 14,000 humans were killed, and later eaten, in that celebration.

Rituals of that sort apparently were not unusual. Bernal Diaz, a Spaniard, wrote in the 16th Century that in the plaza of Xocotlan "there were piles of human skulls so regularly arranged that one could count them, and I estimated them at more than 100,000. I repeat again there were more than 100, . . ."

Other kinds of death, as public and as bloody, are suggested by a number of objects on display.

Some of these are ancient. One, a 1,300-year-old ceramic of a "Ball Player," wears a thickly padded garment, and not for decoration. In the Mayan's ball games, the ball used was so hard, and thrown with such velocity, that players often died.

Among the newer works on view is a 17th-century figure, made of painted maize paste, of Christ upon the Cross. In most European Crucifixions Christ bleeds with decorum, but in this one his blood pours not only from his hands and feet, but from his shoulders, back, and knees.

Jose Guadalupe Posada (1852-1913), a popular printmaker, also filled his influential, inexpensive pictures with images of death - grinning skeletons, corpses, and spiders that eat men. The murals of the big three also show us butchery, evil aristocrats, murderous soldiers, death.

But, oddly, all this violence is often shown with humor. Posada's skeletons dance, so do Orozco's whores and fascists, and many of the bad guys in the big three's murals are, despite their badness, high-spirited cartoons.

Another sort of gaiety also is apparent in the colors in these shows.

Though the bright hues of the Precolumbian pieces have faded with the years, Olga Hammer (no relation to the doctor), who helped to select them, says, "you have to think of Pre-Conquest Mexico as being enormously colorful - think of all the colored stones, and capes made of bird feathers, and everything was painted, the pyramids, the murals, most of the ceramics. They painted their bodies, too."

The Olmecs, the Mayans and the Aztecs, had no beasts of burden, no wheels and no carts. Though Mexico's first inhabitants probably survived by hunting, by 300 B.C., when the Olmec culture rose, all the larger wild animals, the mammoths and the camels, had been killed off. Some anthropologists believe that the countless victims who were forced to climb the pyramids were killed not just to propitiate the gods, but to provide much-needed meat.

Perhaps it is not surprising that beneath the passion, the bright flash and the humor of so many of these objects, ther e is a mood of patience, stolidity and quiet, running through these shows.

One sees it in the blockiness of these pre-Columbian objects. Feathered serpents, spirals, all sorts of designs writhe and intertwine on the shallowly carved surfaces of these heavy stones. (One reason that this touring show will cost Dr. Hammer so much money is that these exhibits weigh 64,000 pounds.)

But beneath their active surfaces, many of these objects are massive, squarish, still, though there are exceptions - the "Ball Player," for instance, or the twisting Colima dog, or the famous Olmec "Wrestler" of perhaps 800 B.C. - most of the old works shown are peculiarly static. And figures just as heavy, lines of thick-limbed soldiers, rounded, squatting peasants, fill the paintings and the murals done in our own time.

Though pre-Columbian Mexico no longer exists - the Spaniards and the blacks they introduced as slaves forever changed the culture - something very ancient runs throughout this show. When it is submerged, by the teachings of the Church or of the 19th century's art academies, the art produced in Mexico seems almost Spanish, European.But in the new works at the Hirshhorn, that nation's gory, glorious past reappears again.

This is the second time that Dr. Hammer has brought an art exhibit to the rather unlikely setting of the Museum of Natural History. He showed by a hard-bound 205-page cata-

The Mexican shows are accompanied bya hard-bound 205-page catalogue with many color plates which he personally arranged with Jose Lopez Portillo the president of that nation. They will visit Knoedler's, Dr. Hammer's commercial New York gallery, and the Los Angeles County Museum of Art, which he serves as a trustee, after closing on the Mall on May 14.