On December 13, 2011, Paul Allen, the reclusive billionaire and cofounder of Microsoft, stood in front of a group of reporters in Seattle and told them about his wild new plan.

Wearing the tech-Brahmin uniform of navy blazer, dress shirt, and conspicuously absent tie, Allen made some introductory remarks and then rolled a video simulation of a strange beast of an aircraft leaving an oversize hangar. This was Strato­launch. It would be the largest airplane, by wingspan, ever created. The twin-fuselage, catamaran-style aircraft would be a flying launchpad, its purpose to heave a half-million-pound rocket ship to cruising altitude and then drop it, whereupon the rocket would ignite its engines for a fiery ascent into space. Allen’s hope was that this extraordinary bird would be able to do quick laps between the ground and the stratosphere, making access to space no more exotic than a New York–to–Boston commuter flight.

Burt Rutan took the microphone next. Rutan, a gregarious designer of exotic aircraft, wore a light-blue work shirt and sported huge Elvis-style muttonchops. He was the original architect of the outlandish endeavor and the person who had sold Allen on the project. “Right here in front of us is a very large mistake,” he said, landing heavily on the word mistake and jabbing his finger at a model of the plane. The problem, he explained, was that no one in the room could possibly grasp how friggin’ big Stratolaunch would be. For them to have any sense, they’d have to understand that even a Boeing 747 would seem like a Tinkertoy in comparison. Rutan’s devilish grin said it all: This would be a plane to defy the imagination. The plane, he and Allen said, would take its first flight in 2015.

Three years past that target date, the plane finally exists, and as Rutan promised, it is one big mama. As I discovered, nothing—not even a Rutan-approved scale model—can prepare you for an encounter with it.

This past December I traveled to the Mojave Air and Space Port, a desert city of giant industrial structures in Southern California, where Stratolaunch was built. The plane’s facility on the eastern edge of the port stands out among the other structures. After walking through some drab offices, I was escorted into the approximately 100,000-square-foot hangar. The gleaming white Stratolaunch didn’t just fill the expanse; it reached into every corner of it. There was no way to take in the monster with a single glance. Starting near its tail, I walked through and around it, craning my neck and stretching on my tiptoes to gather mental snapshots of the two fuselages and the white drag strip of a wing and stitch them together into one panoramic picture.

Everything about Stratolaunch is supersized. It has six screaming Pratt & Whitney turbofan jet engines, salvaged from three 747s. Its maximum takeoff weight is 1.3 million pounds. It’s got more than 80 miles of wiring. Most astounding is its 385-foot wingspan, the spec that puts Stratolaunch in the history books. That number may not seem remarkable, but on a single airplane wing 385 feet is an eternity. It’s a football field plus the end zones and a little bit more. If the Wright brothers had begun their initial Kitty Hawk flight at the tip of one Stratolaunch wing, they could have completed the journey and done it twice more before they reached the other end.

Though the two fuselages look identical, only the right one has a cockpit, largely preserved from one of the 747s, with a throttle, foot pedal, and even some analog displays that a commercial pilot working in the 1970s might find familiar. One of the seats is covered by a sheepskin-like cushion of the type often found in New York City taxis. Looking out the window, the second fuselage is so far away that it looks like a plane sitting on an adjacent runway.