Ronald Reagan thinks he can run the world. But maybe he should learn first how to run Richard Nixon.

It happened that the day after Nixon had won his war for respectability, the entire White House staff was at Yorktown, the site of the final American victory, fending off inquiries about who told what to whom and when about the foreign mission of the discredited ex-president.

The unmistakable note of irritation and defensiveness was clearly heard over the din of the mock battle. The Reagan White House was obviously getting its first bitter lesson in the presumptuousness of its fellow Californian, who--using the amenities of the U.S. Embassy in Paris--was issuing instructions on the proper conduct of our foreign policy, something that Ronald Reagan had thought he was in charge of.

The State Department says that Deputy Secretary William P. Clark, the president's good friend from California, was told on the telephone by Nixon, who "couldn't find Al" (Secretary of State Alexander M. Haig Jr.), that he had decided to "split off" from the official delegation and embark on a Middle Eastern tour. That was Thursday, two days before the funeral, at 10 a.m. Nixon requested the updating due all former presidents, and Clark promised to have the material at planeside. Nixon assured Clark that there would be "no press" on his peregrinations.

Haig's spokesman, Dean Fischer, told the press that Clark then informed the deputy White House chief of staff, Michael K. Deaver.

Deaver, however, told a press pool on his way to Yorktown that he recalled receiving no such call.

So Fischer took it back. According to another State Department source, Clark informed Haig of Nixon's plans Thursday noon. But Fischer says that Haig learned from Nixon just before the plane took off that he was extending his funeral portfolio to do a little foreign-policy making in the Middle East.

All parties are agreed on one point. Nixon told Reagan he was planning to pick up a number of "long-standing invitations" from four Mideast leaders. The president seems to have forgotten it.

But before it was established that Nixon had gone to the top, the fabled White House paranoia about his former underling, Alexander Haig, had been activated, and staff members were telling the press over the weekend that Haig had plotted secretly with Nixon about the trip--and had provided a special briefing by Vernon Walters, the ambassador-at-large, another alumnus of the Nixon days.

What makes it all so farcical is that the worthies at the White House, who pride themselves on management mastery, have been making exceptionally pompous statements about their foreign policy skills:

Here is Edwin Meese III, talking to The New York Times: "We have a highly centralized but participatory decision-making system for policy, and a decentralized system for policy implementation with specific responsibility and accountability."

Where did the "specific responsibility and accountability" begin in the Nixon case? Who, in other words, made the fateful decision to send him to Cairo as the official representative of the U.S. president?

That's a bigger question than who told whom what and when.

As one Democrat cackled, "They didn't need him. They had two ex-presidents, one Democrat and one Republican. They should have known what would happen."

A State Department official who does not wish to be identified gives this explanation:

"There was some feeling here that perhaps Nixon's presence would confuse issues, but then we determined that he was planning to go by commercial plane and be there on his own, so it seemed the charitable thing to include him."

There was no confusion in Nixon's mind. He had a round-trip ticket to respectability. In Paris, having thoughtfully advised all U.S. papers and wire services of what he was about to depose, he called for a boycott of Libya and gave Israel counsel about the Palestinians.

Maybe it was Reagan himself who decided to give the only unindicted co-conspirator in the history of the American presidency what Nixon has wanted most since the helicopter took off from the White House lawn in August, 1975--to be treated just like any other former president.

For Nixon, it is triumph. It was child's play for him to muscle his way onto the delegation, to make innocents abroad believe he spoke for the government, to add to the "cacophony of voices" which his old underling, the secretary of state, so deplored in a recent interview with The Washington Post, to make headlines and to end the hated obscurity of his exile in New Jersey.

He has done it all at the expense of Ronald Reagan, who wants to stand tall in the western world. Nixon can run rings around the crowd in the White House, which is what he wanted to prove. Alexander Haig tried to make the point several times and got slapped down. Nixon is nimbler, as the White House now knows to its sorrow.