Her day begins in pre-dawn darkness. Switching on the lights, Supreme Court Associate Justice Sandra Day O'Connor dresses quickly and moves toward the kitchen. Every square foot of her highceilinged apartment is guarded. A step-down living room leads to a sunroom and outdoor balcony, three bedrooms, a study, and four baths, all secured by a private television channel through which she can identify any caller who presses the O'Connor button at street level outside a pair of locked wrought-iron doors. Over breakfast of half a grapefruit and a softboiled egg, she no longer has the time to enjoy several newspapers. Given the demands of the court, she does well to get through The Washington Post. By 7 a.m., the O'Connors ease their Honda out of the garage. She drops her husband, attorney John O'Connor, at the University Club for an early swim. At 7:30 she vanishes into the marble-pillared Supreme Court building. Ten hours later - hours of hearing arguments, writing decisions, conferring, and coping with stacks of mail - she emerges; carrying a briefcase of night reading, often tackled in the wee hours. "With Sandra O'Connor," says a former colleague in the Arizona Legislature, "there ain't no Miller time." No branch of government is more remote from public scrutiny than the Supreme Court. Absolute secrecy sunounds its deliberations. "I do not talk to reporters at any time, at any place, on any subject," Justice William J. Brennan Jr. has said. Socially, with few exceptions, the justices