Lewis Carroll was wrong on one point: at 7 1/2 Alice was too old to believe in looking-glass houses.

But a French psychologist has found that younger children share Alice's belief. Even after they have learned to recognized their reflections, they believe that the space beyond the mirror is real. In fact, they go Alice one better. They also seem to think that their image is real.

"It's as if for several months the child believes himself to be ubiquitous: he is here and at the other side of themirror at the same time," psychologist Rene Zazzo said.

Dr. Zazzo, professor at the University of Paris at Nanterre, has found that children don't recognize themselves in the mirror until they're about two and a half - considerably older than previous studies had indicated. And they don't understant that the space in the mirror is just an illusion for several more months.

Carrying the previous studies into seemingly uncharted areas, Zazzo believes that this behavior with mirrors reveals much about how a child acquires a sense of who he is.

"It can teach us about the stages by which a child acquires a sense of identity, and also about his uncertainty and hesitations," he said.

"Adults generally underestimate children's ability in practical matters, but overestimated their intelligence."

Even at 5 or 6, the child's understanding can be shaken. Seeing himself on a television screen, with right and left sides reversed, he will stoutly deny that he is the child on the screen. Image and Reality

ZAZZO'S interest in children and mirrors was aroused years ago when his small son, whom he was holding in his arms, caught sight of his reflection in a mirror and began to wall.

"I interpreted his fear as a sign that he had recognized himself, especially when a few days later he used the word 'I' for the first time," Zazzo recalled. "But I wasn't satisfied."

More than 25 years later, in 1972, he hit on an idea for studying the process. He would compare the reactions of identical twins as they looked at themselves in a mirror or through a pane of glass at their twin.

"That way the only difference is that the child commands the movements of his reflection but not those of his twin."

He and co-worker Anne-Marie Fontaine were surprised by their findings. They had expected that the child would identify his reflection as soon as he realized that he controlled the movements of his image. "That turned out to be false," Zazzo said.

The children showed signs of noticing that they controlled their reflections as young as 12 months. First they played with their hands, comparing their movements with those of the hands in the mirror. Then, beginning at 16 months, they showed signs of fear and fascination. Put before a mirror, they studiously avoided looking at it, except to steal an occasionaly sideways glance.

But it wasn't until the age of 26 months that most of the children recognized themselves, according to the "paint dab" test. In this test, the child's nose was unobtrusively dabbed with paint. If he rubbed his own nose when he saw a spot on the nose of the mirror child, it was evidence that he identified with the reflection.

But what Zazzo found "the most surprising and unexpected" was that for three to six months after success with the paint dab, the children were still confused about the space in the mirror. When a blinking light was shown in the mirror, they looked for its source in the mirror, not behind them.

Like Alice who held her kitten up to the glass, "that it might see how sulky it was," they recognized reflections. But like her, they still believed that the space in the mirror was real. Two of the children even grabbed a mirror and ran with it, as if trying to catch their image.[*] "It's Not Me"

BY ABOUT 3 this confusion vanished, both for the 18 pairs of twins and for 180 other children Zazzo studied later. But curiously, the self-recognition of older children could still be shaken. When children 3 or 4 years old saw themselves on a television screen, with right and left sides reversed, they weren't fazed by the difference.

"But from 5 to 6 years old children all deny that they are the children on the screen," Zazzo said. "They say, 'it' not 'me', 'it'sa friend of mine,' or 'it's a child that looks like me.' Some even tell you when and where they met the child.

"It's an age of terrible logic, when children insist on splitting hairs. They say, 'Since it doesn't move like me, it's not me."

This last bastion of childish doubts falls about age 7 - Alices age. The child now blames the television. "It's not a real television," they would tell Zazzo. Or "your television is broken, you should get it fixed."

And finally one child got up and twirled before the researchers to show how his right arm became his "left" by changing directions. He lacked the words to express the adult concept, but he had understood.

Mirrors give us a handy but false image of ourselves. Television, which "reverses" right and left, lets us quite literally "see ourselves as others see us."