Presidential press secretary James S. Brady, who had a large part of his brain shot away Monday afternoon, was soon moving one side of his body almost normally, breathing without the aid of a machine, counting, and answering when asked his name.

Predictions of his future range from 100 percent recovery of his mental functions to possible death if he suffers severe infection. How can this be?

The answer is three-fold, beginning with the fact that the brain is an extraordinarily complex, regenerative -- and unpredictable organ.

First. The bullet allegedly fired by John W. Hinckley Jr. destroyed some of Brady's brain cells. It damaged others, by causing swelling, bruising, bleeding and complicated metabolic and biochemical imbalances. It also simply shocked the brain cells.

No one can predict how severe the permanent damage to Brady's brain will be, and it appeared yesterday that medical spokesmen were trying to modify somewhat the White House's optimistic reports.

But some of the temporary damage and shock apparently have begun to recede. "When there's a gunshot wound the whole brain becomes unconscious," one neurosurgeon said yesterday. "We now see some return of consciousness."

Second. The right half of the brain exercises most control over the motor activity -- the movement -- of the left side of the body. The left half of the brain mainly controls the right side.

The bullet passed only through the tip of his left frontal lobe. So he is moving his right side "very well, close to normally," one source said.

But the bullet then did extensive damage to the right frontal lobe and less damage to other structures as it continued its course. "So he has some, but still very little, voluntary movement of his left side," this source continued. "And it is too early to say what may happen in future days or months."

Many neurosurgeons believe they see "adaptive mechanisms taking over" in patients with brain damage caused by strokes or injuries. But this process takes months and would not account for any of Brady's improvement so far.

Others think this "taking over" does not really happen in adults, that what we see is "just a system healing, a system that wasn't really gone," in the words yesterday of one prominent neuroscientist, Dr. Michael Gazzaniga of Cornell University.

Those who subscribe to the "takeover" theory point out that the brain's two halves, even though they do different jobs, have millions of interconnecting nerve fibers and really work together in dimly understood ways. They say that only a "taking over" can explain the amazing return of some functions after unmistakable damage in vital regions of the brain.

Third. It is much too early to tell what personality changes or ability changes Brady will undergo. He could continue improving; he could stay the same, or he could suddenly get worse, dangerously worse, especially if infection sets in or swelling resumes, instead of continuing to subside.

However, said Gazzaniga, "if you have to have damage to part of your brain, the right frontal lobe -- in a right-handed person -- is generally the part where damage is least disruptive."

In 99 percent of right-handed males," he said, "all the major language and speech functions are localized mainly in the left hemisphere, and then not in the frontal lobe. The left brain is also essential for logical and mathematical abilities, in fact, everything that has to do with life in an intelligent behavior sense. So Brady should be able to comprehend and carry out commands and do logical problems, if all we've heard is true.

"This is not to say serious harm may not be done by right hemisphere damage. The right brain is very important in spatial localization, in orienting ourselves.

"It may be that right side lesions may have a flattening effect on personality [a loss of strong emotions]. But all these are questions people are still arguing about and trying to learn about."

With a little luck, brain experts say, Brady could wind up with some physical weakness, possible limited activity on his left side and 100 percent of his former mental abilities. But this, or any of many other possible forecasts, are still guesses.

There were differing reports on Brady's actual condition yesterday.

The White House said in the morning: he continues to improve, as he remains in critical condition, but he is able to speak," can "move his left arm and leg," in addition to his much better right-side motion, and "may be able to sit up" in a few days. "During Mrs. Brady's visit [Tuesday] night, she and Mr. Brady played catch . . . in spite of his weakened condtion." He is "breathing well without the assistance of a respirator," and his "physicians continue to be cautiously optimistic."

An informed source said his physicians are indeed more confident because of his easy breathing. But he merely "moved his left side during the night and does not yet move it spontaneously or purposefully," and the "catch" game just consisted of being able to toss a ball of gauze toward his wife on command.

His eyes are still closed because of swelling, it was learned, but he can see when someone opens them for him. His speech so far consists of answering questions with only a few words. But he stated his name and, when asked to count, repsonded, "One, two, three."

The outlook, the source said, should be cautious but guarded optimism.