In September 1901, Leon Czolgosz ruined almost any chance you have of high-fiving the leader of the free world.

It was a zanier time. Top hats weren’t ironic, no one laughed at having an international fair in Buffalo, and electric lights were as sexy as the iPad. You could still count on the president for a few ribbon-cuttings, so McKinley was glad-handing at the Pan-American Exposition, surrounded by thousands of yokels in the Temple of Music. The 1901 equivalent of Ke$ha was probably warbling nearby.

And then Leon shot him point blank in the name of anarchy, instantly becoming the most daunting spelling challenge in American history. There’s a lovely, watermelon-sized rock in the middle of a median strip commemorating all this, in the middle of the lovely middle-class neighborhood where the Temple once stood. The shirtless guy mowing his lawn on my visit was not lovely, but visit in the colder months and you might miss him.

That killing was the third strike for president-hating whackadoos. Secret Service protection was finally escalated, even though Teddy Roosevelt would have preferred catching bullets with his teeth. These days, if you try to chest-bump our leader—maybe he just finished a small air war, or you just won bar trivia by correctly spelling Czolgosz—you’re going to be crippled in the effort, which is a shame. The whole point of this stupid country is that we don’t have royalty: if you’re motivated and patient you should be allowed to hug the president, because the president belongs to us.

Thomas Jefferson got it. In 1800, with America still in its acne-laden tweens, people were still worried about monarchy. Modern tiffs about health care or bailouts are friendly disagreements; back then, factions of the opposition party would plan on breaking off large parts of the country and installing a dictator (usually Aaron Burr). That is partisanship.

In that happy context, the nation’s leading anti-monarchist adopted an open door policy. If you showed up at the White House and he was at least partially dressed, you got to share a cheeseboard with the POTUS, regardless of your status. It wasn’t even BYOB. It’s not as ballsy as it sounds—until 1840 or so, D.C. was two mud roads and a chicken coop, so tourism was light. But the sentiment counts. In America, the president is just one of the guys, and you should be allowed to get close to him.

Plantation etiquette would have given you a shot at fist-bumping a few of the Founders. Mount Vernon was a motel—almost anyone could pull up on their horse and expect a meal and a room, sending the bill to the Father of Our Country. Washington used the back staircase to get from his bedroom to his often-locked office, probably to avoid open-robed freeloaders in the hall. But he had to eat eventually, and then you’d have your chance. Up top, George. Then maybe you could steal his hand towels.

And there were times when you might have bumped into the president on the street. John Quincy Adams used to skinny dip in the Potomac—get closer at your own risk—and James Buchanan took afternoon strolls until impending war made him into Hester Prynne. When at his Georgia retreat, FDR liked to ditch the Secret Service, drive the back roads in his polio-mobile and see how the Depression was going. Guys who left office didn’t have much security until the 1960s; if you could keep up with Harry Truman (120 steps per minute) then he might have led you around Independence on his daily stroll past boyhood homes and old schools. They honor Harry’s habit with a walking tour today, and you can imagine the only man in history to order a nuclear strike stopping by the courthouse to tousle the hair of a seven-year-old neighborhood kid.

Today? Those windows of opportunity, nudged downward in 1901, are just about closed. For the president to go to Olive Garden, it takes 27 armored vehicles and snipers on the roof of the Chuck-E-Cheese across the way. You might arrange to touch the man—I shook Clinton’s hand in a receiving line. But you aren’t going to get close—he never told me a dirty joke, when you know he has tons. The president was never going to be your best friend, but increased security, celebrity and time constraints have eroded the potential for him to interact with the poor slobs of the world much beyond a photo op.

Instead, if you’re hankering for that rare combination of physical proximity with a president and a chance to connect, you have to think inside the box. The heavy, stone box.

Only the very enthusiastic or disturbed will succeed in high-fiving a dead president. Everyone else can settle on that happy medium of standing by their grave, thanking them for their service, reflecting on their struggles and wanting to punch the text-messaging fourteen-year-olds nearby. Though Eisenhower defeated Hitler, I am sad to report from graveside that he made no landing on the beaches of Verizon.

Still, you can get surprisingly close even without a crowbar. A few graves and tombs are fenced off, either to keep souvenir seekers out or keep zombie William Henry Harrison in. Others are under a few feet of dirt. But in the vault of United First Parish Church (Quincy, Mass.), a few inches of stone sarcophagus is all that’s separating you and whatever’s left of presidents No. 2 and 6. There’s more of a connection, as though they could actually hear your heartfelt review of the HBO miniseries. Any lover of facial hair owes Chester Arthur a word of thanks, and his outdoor sarcophagus in Albany—adorned with an angel statue as elegant as his whiskers—gives you a chance to do it up close.

If that’s not enough, you have one last recourse. In 1893 Grover Cleveland had a secret surgery on a yacht in the East River to remove a cancerous growth from his mouth; he didn’t want word of his illness to unsettle the financial markets. The doctor held on to what he removed, and so chunks of Grover Cleveland are now on display at Philadelphia’s Mutter Museum, an excellent repository of gross medical oddities. If you put your face up against the case while pondering Uncle Jumbo and the great leveling force of mortality, I wager that’s as close as you’ll get to a president without immediate tackling.

When they eventually drag you out, be sure to flip the bird to two other Mutter displays: the thorax of John Wilkes Booth (strike one) and a decent sized chunk of Charles Guiteau’s brain (strike two). If not for them and Leon, you could still dream of that high five. Maybe even on the flip side.