Monday, June 26, 2006



Seifert hits the button of hypercube unreality

In Robert A. Heinlein's classic short story, “—And He Built a Crooked House”, a cheerfully deranged architect builds a Los Angeles home shaped like a tesseract, a four dimensional hypercube.  His idea is to invent a revolutionary new building that'll save space (after all, if a home exists in four dimensions, you get a lot more square footage to work with), but an earthquake shifts the house into still another dimension.  And then things start to get strange from there.

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.)

Crooked house prototype

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.”

Direct portal to teleport entrance into The Future's Crooked House here

Vast thanks yet again to Torley, who found the house first, and told me.


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Listed below are links to weblogs that reference -- AND HE REZZED A CROOKED HOUSE:

» Heinlein-inspired tesseract house in Second Life from Boing Boing
James sez, "A Stanford math student just created a working version of a hypercube house, inspired by Robert A. Heinlein's classic "-- And He Built A Crooked House" short story. When you walk through four rooms in a straight line, or make three ninety ... [Read More]

» Expand your Dimensions from An Engine Fit For My Proceeding
If you have not already done so, I Highly Recommend that you read Hamlet Aus piece on Seifert Surfaces crooked house. This very much falls into the category of I wish Id thought of that - Mr Surface has ... [Read More]

» Non-Euclidean Geometry in Second Life from
No sooner have I re-activated my Second Life account after a long absense, do I come across this article about a hypercube construction inside a virtual world that tries very hard to emulate the real world. I'm definitely going to... [Read More]

» Brain. Hurts. from Literal Barrage
Weve been over this a million times: some people have way, way too much time on their hands. As further evidence, I present a 2D representation of a 3D representation of a 4D house, constructed entirely using the tools provided to players of the... [Read More]

» I am not a crook from TheophileEscargot from Hulver's site
Reading: A History of Britain, Jonathan Livingston Trafalgar Square Pigeon. Poll: Best recent Home Secretary? What I'm Reading Finished the audiobook of A History of Britain: At the Edge of the World? - 3000BC -AD 1603 by Simon Schama. Very go... [Read More]

» Second Life House--in 4-D! from
Incredibly insane and wonderful: Seifert Surface has taken Robert A. Heinlein's hypercube house from "--And He Built a Crooked House" and, well, made one. Granted, it's in Second Life but still: the way he put this together is pretty freaking ingen... [Read More]

» Heinleins Crooked House realized from
In one of the short stories of Robert A. Heinlein, the protagonist builds a house in the shape of a four-dimensional tesseract. Now an inhabitant of the online world Second Life has duplicated the feat. ... [Read More]

» Crooked house from VTOR - Virtual TO Reality
Crooked House via NWN:And so a graduate student in Stanford’s math department has managed to create, more than 60 years after Heinlein firs... [Read More]

» Infinite loop from VANTAN.ORG: The Daily Weblog
This dude did something awesome with his Second Life house. Technorati Tags: Second Life... [Read More]

» HeinleinLives from Farnham's Freehold
and he built a crooked house. Not the Kirk Douglas movie, but the Robert A. Heinlein short story. Now in the Social Network rez Video Game, Second Life, comes word that someone has built a Tesseract House, in 4 dimensions. Holy Escher, Batman! H... [Read More]

» Infinite loop from VANTAN.ORG: The Daily Weblog
This dude did something awesome with his Second Life house. Technorati Tags: Second Life... [Read More]


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Tao Takashi

Incredible cool!!!!!!

Laukosarg Svarog

Seifert recently gave me a tour of the house, really very cool !!
It's really funny when you take a wrong turn and end up in an upsidedown room. Masterful coding :)

Robbie D

I just had one of those, 'oh I get it', it's like, errr... 'oh no I don't' - moments, I guess I need to go vist asap, but the concept sounds truely amazing to me.

Elle Pollack

The embedded video doesn't seem to be working (least not for me), direct linkage to the video pages are and

Chalk another one up for Sei! It's much cooler than *my* home in The Future (I'm a deadbeat living in a big culvert pipe with a solar pannel and cantenna powering my computer)

Luciftias Neurocam

Nicely done, Seifert.

Joe Rybicki

Here from Boingboing, great story.

Just a point of clarification, though: In the short story, the architect builds the house as a -disassembled- hypercube, so eight cubes arranged very similarly to the outside view of this house. The earthquake causes the house to collapse into itself and turn into a true hypercube. No extra dimensions are necessary.

Sorry, Heinlein geek over here.

Vlad Bjornson

Great job Seifert - that is truly some 2nd Life architecture! Now we need an article on that animated, 3d projection of the Hypercube that you showed me a while back. I have tried to explain it to several friends, but I can't wrap my brain around it far enough to make any sense. :D

Relee Baysklef

Now that was great. XD

I had a suspicion that he was moving the rooms; either that or moving the avatars.

Hamlet Au

Thanks for the headzup, Elle, I just added direct links to the YouTube vids in the story.

Gwyneth Llewelyn

I'm confused :) This seems to much magic to my poor head, I would *never* find out what was going on without the movie from "far back".

Cool? No. This is mind-boggling!

*blows up her prim-tortured brain*

You're a math wizard, Seifert :)


very, very nice. congrats, amigo.


Ordinal Malaprop

This is quite a superb creation, and something which reminds me why I ever started studying pure maths in the first place. In my relatively advanced years I appreciate being taken back to my old level of wonder.

Gwyneth Llewelyn

Ok. Let me rephrase all that. I've just went through the weirdest experience in SL, after testing this out "in the flesh", so to speak. I was quite sure I understood what was going on, but the illusion is *perfect*.

My poor brain is simply not wired to understand how this works. I'm bedazzled and beffudled. Ack. I need a shrink to put my mind in order again. I truly hope that this doesn't become a trend; SL is getting more and more fascinatingly confusing these days; or is it confusingly fascinating? :)


Brilliant. Gives me the same other worldly feel I had as a kid reading Edwin A. Abbott's Flat Land

It would make a really good brain teasing puzzle game.

Elle Pollack

The owner of The Future recently installed a telehub in the sim, so everyone who's clicking the slurl link to get through are landing in our Grand Central Station. Just follow the signs on the ground and the transport tubes from the telehub to get to the "workshop platform" where you'll be pointed to a teleporter that will put you inside the house proper.

Elle Pollack

Almost forgot to add: this story made the Digg frontpage (over 480 diggs so far)!

John Cartan

Nice! For more information about higher dimensional hijinx, including a floorplan of Heinlein's 4-cube, a 5-cube, and even a visit to a 9-cube hotel, see the URL above.

John Cartan

Oops! I meant to say: see THIS URL:

Cartan's Triangle

Jeska "Linden"

Great find, Seifert gave me the tour last night and I have to admit I was quite disoriented!

Nicholas Lawson

You know that description of the rooms folding around each other, that could very easily be a plausible reality that surrounds us right now. We would never know if we were really on a morphing spaceship that was floating in space, if it was always set up like that for everyone ...


I have to say that the Crooked House kind of creeped me out. I couldn't escape! I yelped when I ran into another resident wandering around.

Reminded me too much of "the Cube."

Hamlet Au

Actually, there's a rumor that some other Residents have built a working cube inspired by, well, *The Cube*.


yeah, i've seen the build inspired by *the Cube* - a giant array of rooms where sometimes the cubes move about.

i believe the coding was done by a guy named Seifert Surface. you might ask him for a demo.


Hamlet Au


Senor Surface did not inform me of such!


I've been trying to find this place and I can't seem to get to it. The slurl doesn't work for me.

Dyne Talamasca

I built a disassembled and collapsed rough model of the house exterior, inspired by just that story, back around October/November, but I wasn't crazy enough (or familiar enough with SL at the time) to try to figure out how to make it functional. :)

Nebula Gray

The structure's cool, but I would imagine being on the surface of a "real" hypercube would be one of the following: if you're on the top or bottom of it, you would be floating; if you were on the sides, you'd "fall" to the bottom due to gravity. Except you wouldn't have to worry about hitting the floor--you'd just float once you got to the bottom. Then again, since we're talking about a 90 degree angle in 4-D space, you'd probably just be able to stand hovering above the door to the bottom room.

Primitive Hax

How would time pass inside a 4D hypercube?
I'm probably confused, but doesn't "time" in Einstein's 4D spacetime happen all at once?
Does this mean that if I lived in a hypercube with a (hypothetical) wife, and she asked me to clean the living room... Without lifting a finger I could nonchalantly reply "I already have or haven't dear"?

Dammit, I'm sick of being an ignorant 2D bug, doomed to blindly wander around a stretchy rubber 3D topology :(

This guy's a genius, but I hate him so.

Farnham Farrjones

Could you build "Rufo's Fold Box", from The Glory Road with this tesseract scenario? As I recall, it was a smaller, portable version of tesserocity, in which Our Hero could ask Rufo, his retainer, to extract everything from a howitzer to a banquet table, depending on the mood of the evening. To steal another quote, "Brain hurts, rest now".
Analog Guy, Farnham Farrjones

Lionel Oliva

Awesome article, clever concept! I hope to find something on Escher sometime soon.

Seifert Surface

The Crooked House has moved, it can now be found at:


What is this? I just saw a crooked house and clicked on the link in google. What is this?

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