In Robert A. Heinlein's classic short story, “—And He Built a Crooked
House”, a cheerfully deranged architect builds a
Things get odd in the crooked house of Seifert Surface, located hundreds of meters up above an island called, appropriately enough, The Future. But it doesn't require an earthquake. To enter the hyper-dimensionality of Seifert’s home, all that’s necessary is to push the big button on the marble table in the foyer. From that point, you’re sucked into its warped, infinite reality.
Watch the video, and see what happens after Seifert hits the button.
And so a graduate student in Stanford’s math department has managed to create, more than 60 years after Heinlein first conceived it, a home that seems to exist in more than three dimensions, a kind of multi-directional Mobius strip. (Metaphysics in the metaverse?)
After the break, a chat with the architect of unreality on the theory and implementation of his crooked house.
Seifert’s house seems normal enough, when you first enter it. (Other than being suspended high up the sky, that is, for reasons that’ll soon be obvious.)
The strangeness sets in when you push the button and go from room to room-- through doors, up ladders, sometimes through hatches-- and realize that you are somehow walking in circles. And that you’re also in a house that seems to have been designed by Escher.
“It’s the eight cube sides of a four dimensional hypercube,” Seifert explains. “Just like a normal 3D cube has six square sides, and a normal 2D square has four line sides, so the sequence continues. And just like if you were an ant walking on the faces of a cube, if you go four times in one direction, you end up back where you started. Also, if you make three ninety degree turns, you come back where you started.”
Essentially, he finishes, “I want the avatar to walk around and see what you would see if you were walking through the cube faces of a hypercube, like the ant sees what it sees, walking around on the square faces of a cube.”
That’s the theory, but how is this possible? Rather than write out the explanation, maybe it’s better to first move our camera back, outside the house. Now watch Seifert Surface walking through his crooked house. You'll see Seifert begin his reality-warping journey in the doorway of the center room (direct video link here):
So the crooked house is quite crooked— programmed to literally move rooms into place, so that the person inside is always in the hypercube.
“When you step into a room,” Surface tells me, “the other rooms cluster around it so that they’re always connected together the right way. But it only works for one focus.”
In other words, it’s all relative: click the Focus button, and stay in the reality of the tesseract. Don’t, and remain in the basic Second Life reality of 3D objects that more or less operate according to Newtownian physics.
So if you’re sitting in the crooked house while someone else takes the focus, the house spins and rotates to adjust, to maintain the illusion. (Unless you’re sitting down, you’re liable to get unceremoniously booted out in mid-air.)
To chart out the algorithm of shifting rooms, Seifert Surface created a much smaller prototype. “[B]asically the focus cube tells all the rest that it’s [the] focus, and where it is, and what its rotation is. And the other cubes move to match up.” From there, it was mostly a matter of creating the human-sized version, building a 19th century era interior with textures and furniture provided by Desmond Shang, and taking advantage of a Linden Script Language coding hack released on the Forum by Keknehv Psaltery, which helped him speed up the movement of the rooms past LSL's default maximum velocity for moving objects.
Though he’s a grad student of three dimensional topology and geometry at Stanford, and his real life studies inspired this project (along with other mathematical condunrums he’s created in Second Life) they aren’t part of his day-to-day studies, which are pure math on the most abstract order.
“It’s the kind of thing that might be useful in 200 years time,” he shrugs, “who knows.”
Which may explain why it’s so difficult for him to explain the concept of the tesseract to me, even when he creates an impromptu 2D model of a cube splayed out on the ground. I finally give up and describe it as a 3D Mobius strip.
“Yeah,” he allows, “that’s a pretty good way to think about it, except Mobius strips have a twist. And this doesn’t.”
“Well, the 'twist' is you moving all the rooms around behind our back!”
He laughs in the foyer of his crooked house. “Well, the formal term would be "orientability". The Mobius strip is non-orientable, this thing is orientable.”
“That's a nice way to say ‘F***-ing with a dude's head’," I observe.
Seifert Surface grins. “It’s one of my favorite past times in Second Life.”