THE chairman of the Joint Chiefs of Staff, Adm. William J. Crowe Jr. collects hats for a hobby. On his recent trip to the Soviet Union, Admiral Crowe was given handsome examples of Russian military headgear, including a swooping 19th-century cavalry officer's hat and a Crimean War hat that was worn during the siege of Sevastopol. ``Looks like a fireman's cap,'' he says of the Crimean model.
Crowe also brought back numerous souvenir lacquered boxes - and a vastly richer understanding of the Soviet Union and the problems and promise of leader Mikhail Gorbachev's reform efforts.
Where top US military leaders usually paired the words ``Soviet'' and ``threat,'' Crowe now talks about a better atmosphere, improved communications, and airing of differences.
But the admiral is not yet ready to call the superpowers ``partners,'' as Mr. Gorbachev has. ``We're just two big nations competing in the international arena,'' Crowe says.
During his unprecedented visit the admiral saw everything from a strategic-missile base to a bomber cockpit to the inside of a nuclear submarine.
He traveled by helicopter to a Kirov-class missile cruiser and stepped aboard as a Soviet honor guard struck up the ``Star Spangled Banner.''
Crowe says that as a young Navy officer he had been told Soviet ships sacrificed crew comfort for weapons space, but that the ships he saw belied that axiom.
He also was surprised, he says, by the relative youth of much of the Soviet top command.
``The commander of the cruiser I was on was only 34 years old,'' he says.
That is an age at which US counterparts might still be second or even third in command, he adds.
The Soviets showed Crowe exercises designed to demonstrate that their doctrine is now oriented to defense, not offense.
But the top US military officer says he told the Soviets that it isn't training or types of weapons that makes forces offensive, so much as it is sheer size. Reduce your overwhelming superiority in conventional forces and you'll be defensive, he said.
If completely carried out, the unilateral force reductions announced by Gorbachev could ``eliminate their surprise-attack capability,'' says Crowe. Large reductions, such as those now being discussed in the conventional arms talks, could require new military strategies on both sides, the admiral says.
Although some Western experts say that NATO forces cannot fall below a certain level and remain an adequate defense, Crowe says that ``if we get parity and can't manage that situation, something's wrong.''
At war memorials, at meetings with Soviet citizens - all over the country - Crowe says he felt the weight of Soviet history, the continued emphasis on the heroic sacrifice of repelling the Nazis. ``Every general I met lives in World War II,'' he says.
But the highlights of the visit were still his long conversations with top Soviet military leaders, Crowe says.
They spoke frankly of the problems facing their country in its struggle for economic reform - such as their worries about finding jobs for 100,000 officers laid off by force reductions.
Soviet leaders grumbled about politics intruding into the military arena, to which Crowe, thinking of Congress, said, ``Join the club.'' They talked openly about the great tragedies of their history, specifically Stalin's executions of millions.
Crowe says that while he may not have seen the seamy side of Soviet life, ``I heard them talk about it at great length.''
``They're trying hard to shed their history,'' says Crowe.