There is virtually no relationship between the normal reality of the everyman and the corresponding reality in Phil Mickelson’s head. What goes on in that vast space under his visor is often inexplicable, ranging from cunning to creative to downright crazy. It is a factory that can take someone else’s “You’re gonna do what?” and turn it into a shrug of the shoulders, a sighing “ho-hum.”

So it was Mickelson who prepared for the U.S. Open, a tournament about which he professes to care enormously, by taking two cross-continental flights — the second a red-eye — so he could attend his eldest daughter’s eighth-grade graduation. Wheels went up in Carlsbad, Calif., around 8 p.m. Wednesday and came down in Philadelphia at 3:30 a.m. Thursday, some sleep wedged in between. He arrived at Merion Golf Club at 5:37 a.m., teed off at 7:11, endured a 3-hour 32-minute rain delay — which bought him a nap — propped himself up with caffeine, hit a wall with two holes to go and still shot a brilliant 67 that gave him the clubhouse lead at day’s end, 3 under par.

“This is not that out of the ordinary,” Mickelson said.

In Phil’s world, in Phil’s mind, maybe not. Still, in a field of 156 — with so many Type-A personalities, so many borderline obsessive-compulsives — Mickelson is likely the only character who could have solved Merion under such circumstances. England’s Luke Donald, the former world No. 1, birdied his final three holes to get to 4 under through 13 at 8:16 p.m., when play was halted. Adam Scott, the Masters champ, got to 3 under through 11 when the horn blew. Both will rise to face Merion’s daunting five-hole finishing stretch. Mickelson is already done with it.

Half the field must resume play at 7:15 a.m. Friday — including Tiger Woods, who was 2 over through 10. By that point, Woods had twice hit shots out of the rough that caused him to wince, and he shook his left wrist after each — including on 11, where he marked his ball on the green and will stand over a par putt Friday morning.

Those final minutes created questions about Woods’s fitness to contend here — particularly with 25 holes to play Friday. “Hopefully I can play a little better than I did today,” Woods said. The questions about Merion’s fitness to host this championship, however, seem to be answered.

Only two players who completed their rounds — Mickelson and Nicolas Colsaerts, who shot 69 — left Merion under par. Thirteen others joined them, each with at least five holes left.

None of the others performed their preparation on a plane. No sleep? No matter. Three-putt the first hole? Get the one mistake out of the way early. For Mickelson, four birdies and 13 pars followed.

“I was as anxious as anybody to see what he would do,” said veteran Steve Stricker, who played with Mickelson. “When he three-putted the first hole, I thought, ‘Here we go.’ . . . But he’s such a competitor. He thinks he can do anything.”

That could include slinging a shot from behind a tree at Augusta National, as he did to win the most recent of his three Masters in 2010. It could be trying to will an approach through trees and tents on the final hole, as he did to lose the 2006 U.S. Open. It is why Thursday he could talk about the Open — in which he has been runner-up five times — and call it “heartbreaking” if he never won one but still say, “I believe I will.”

That he is in such a position at Merion — where he is not even carrying a driver but instead put five different wedges in his bag — might seem surprising. The course is listed at 6,996 yards, the first major championship layout under 7,000 yards in nine years.

But the number, it would appear, serves as a beard. It certainly provides an overly simplistic basis for analysis. The rough here approaches the bottom of shins and for much of Thursday was wet and heavy. Miss the fairway and hold on. Merion hasn’t hosted an Open since 1981. Some assumed it was because it had become obsolete, anachronistic. It hasn’t.

“I think that anybody in that commentary box has never given this golf course enough respect,” said England’s Ian Poulter, who opened with three straight birdies before the morning delay, then shot 71. “They were joking around, laughing at [the possibility of] 63s and 62s — and just look at the [leader] board. I mean, they need to respect this golf course. It’s brutal.”

In those conditions, Mickelson was his most magical self. After beginning his round at No. 11, he made up for his opening bogey with a birdie at the tiny, 102-yard 13th. He then rolled in a 30-footer for birdie at 1, hit a 9-iron to tap-in range for a birdie at 7 and curled in a 25-footer at 9 to take the outright lead.

The key to his round, though, may have come at 5, where he hit his tee shot down an embankment near a creek, and 6, where he ended up in a greenside bunker facing a dastardly shot. He made a seven-footer to save the first par and an eight-footer to save the second.

“Those are the momentum builders that are important in the rounds at the U.S. Open,” Mickelson said. “They actually give you more of a boost than birdies do.”

On Thursday, with all that flying behind him, he needed a boost. He said he told his daughter Amanda — who delivered a speech at the ceremony — “I want to be there.” So he was. He pointed out, too, that he plays after such red-eye flights perhaps half a dozen times a year.

Those trips, though, are for corporate outings. This is the U.S. Open.

“It might be abnormal,” he conceded. “But it actually worked out really well.”