A 4D experience: The Crooked House

The amazing Crooked House in SL

The marvelous Crooked House in SL

The Crooked House is another classic in Second Life. I will summarize its story here, but my point is to look further into the ways and means of a 4D simulation in a virtual (3D) world. If you want to read further on the house itself, you can check the excellent description of it and of how it was built, written by Hamlet Au/Wagner James Au for New World Notes (just do not try to find it at the slurl there, for the house has moved to a new sim – actually, twice), or Natalia Zelmanov’s account of her visit to it on her Mermaid Diaries (again, old slurl), or Bixyl Shuftan’s post for the SL Newser – Places blog (the slurl there doesn’t work anymore) or a more recent text by the amazing Honour McMillan, posted on her Honour’s Post Menopausal View (of Second Life) blog (yay, now the slurl works!). I should only mention that the building, by Seifert Surface, is inspired by a story by  Robert A. Heinlein called “-And He Built A Crooked House”. It is designed as a 3D projection of a four-dimensional analog of the cube and has been in the grid since 2006 – though it has moved from sim to sim, which also shows how people have been trying to save it from disappearing.

The Crooked House in SL: closer view of some rooms

The Crooked House in SL: closer view of some rooms

Cube projection

By linking two squares, we have a cube. This is also a 2D projection of a cube. (Image from Wikipedia)

A projection of a cube centered by one of its faces

2D projection of a cube centered by one face: we see a square. (Image from Wikipedia)

Did I say the house takes the form of a 4D projection? Actually, it is a bit different. Our understanding of a 4D environment comes as an analogy of what happens with the transition from 2D to 3D spaces (and from 1D to 2D spaces, as well). So, if you link two 2D figures – let’s say, two squares – in a certain way, you can have a 3D object – a cube, for instance. But the projection of a cube on a 2D surface is still a 2D image. Furthermore, a projection of a cube on a 2D surface at 90 degrees is… a square! Let me explain it in other words: imagine you have a cube right in front of you, not at an angle. What you will see is one of its faces, the other faces being “hidden” behind it by perspective. So, you will actually see a square, a 2D square. Well, but if you “unfold” a cube… we all have seen that: if you draw on a piece of paper (a 2D surface) four squares in a row, from top to bottom, and, to the left and to the right of the second square, you draw another two squares, you will have an “unfolded” cube. If you cut that shape with scissors and start folding the squares along their adjoining edges, you will build a cube, a 3D object.

An "unfolded" cube

An “unfolded” cube (which is a 3D figure) is made of six squares (which are 2D figures). (Image from Wikipedia)

How to create a 4D hypercube

How to create a 4D hypercube: first, you link two points (0D objects) to form a segment (1D object); then, you connect two segments to form a square (2D object); third, you connect two squares to form a cube (3D object); finally, you can link two cubes to form a 4D hypercube. (Image from Wikipedia)

Now, let’s move to the 4D world.  By extension, if you link two 3D objects in a certain way, you will have a 4D object. So, if you link the correspondent vertices of two cubes, then you will have… a hypercube. The problem is that we cannot “see” the hypercube. We are too used to imagining the space around us as a 3D environment (and maybe we cannot do it differently). So, what we see when we build a hypercube like that is a projection of such a hypercube on a 3D “surface”. In other words, we still see a 3D object. When we see a cube drawn on a piece of paper, we can imagine how it would look in a 3D space, because we have enough references to do so. But when we see a hypercube projected on the 3D world, we cannot really picture the hypercube in our minds, because we lack the necessary references there. Still, even if we cannot “see” the hypercube in our minds, we can “understand” it in abstracto, theoretically. And in order to make things easier to conceive, many have suggested analogies between the 2D, the 3D and the 4D worlds.

An animated projection of a 4D hypercube

An animated projection of a 4D hypercube: an 8-cell object performing a rotation. (Image from Wikipedia)

A 4D hypercube unfolded

An unfolded 4D hypercube would be made of 8 cubes. (Image from Wikipedia)

Following those analogies, since we can “unfold” a cube and have an image made of six squares on a 2D surface, we could also “unfold” a hypercube and have an image made of eight cubes on a 3D surface (four cubes in a row, from top to bottom, and another four cubes surrounding the second one). Note that, as the unfolded cube is not the same as a projected cube (an unfolded cube is made of 6 squares, and a projected cube could be, as we saw, just one square), also the unfolded hypercube is not the same as a projected hypercube (which, again by analogy, could even be seen as just one cube if we “looked” at it at 90 degrees).

The Crooked House and its model: an unfolded hypercube

The Crooked House and its model: an unfolded hypercube

Why am I saying all this? Because here lies an important difference between the crooked house imagined by Heinlein and the one built by Seifert Surface in SL. In Heinlein’s story, an architect builds a house as an unfolded hypercube. In other words, he builds a house made of eight cubes. One day, an earthquake “folds” the hypercube and, when the architect visits the house again, what he sees, from outside it, is a single cube – the other seven cubes being “hidden behind it by perspective”. Only when he gets in the house does he realize that the other rooms – the missing cubes – are there. Nonetheless, Seifert Surface’s house in SL keeps looking, all the time, like an unfolded hypercube, not a projected one. It is not a demerit, it just shows the difficulties we have to represent a 4D idea in a 3D world. Having said that, it only increases the marvel of Seifert Surface’s realization, for, despite the limitations he found, he could, in many aspects, give a certain concreteness (even if a virtual concreteness) to what Heinlein imagined.

Inside the house, at some point the rooms start appearing i different orientations

Inside the house, at some point the rooms start appearing in different orientations

Here is the game: get into The Crooked House in SL. There, you will find a button to “drive” the house focus to yourself. Hit the button and, after that, try to leave the house without teleporting, just walking left or right, climbing stairs, jumping through trapdoors… And keep trying, it is funny. You will realize that, at some point, you will arrive at the same room you were when you started. Maybe it will be upside-down. It doesn’t matter, there is always a way to leave the room you are in. Nonetheless, you are only leaving it to enter another room, you are not leaving the house itself. Of course, you will realize that there are only eight rooms, you will be visiting them again and again, as if they formed a loop – just as in Heinlein’s story.

The house in its original position

The house in its original position

The house starts moving

The house starts moving

The idea is that, when transformed into a hypercube, the house gets “folded”. On a cube, each face – or each square – leads to another face (actually, to another four faces). In a hypercube, each cube – or each room of the house – would lead to another cube – or to another room. Though there is a limited number of rooms (or cubes), they can be visited again and again infinitely just by walking forward (or backward, or to the left, or to the right, or up, or down). It happens both in Heinlein’s story and at Seifert Surface’s Crooked House in SL.

The house keeps changing

The house keeps changing

The house changes further

The house changes further

The trick, in Seifert Surface’s creation, is a script that allows the house, once it focuses on you, to rearrange itself as you move inside it, from room to room. Whenever you enter a new room, the other rooms move, in order to follow you. Some will say this is just a way to cheat and create an illusion. Well, of course it is an illusion. Second Life, as far as I know, behaves as a 3D space, not a 4D one, and so The Crooked House can only be a simulation, or a representation, but not a “true” 4D object. Still, there is something “true” about it, as an experience.

Where did The Crooked House go?

Where did The Crooked House go?

Uff, the house is coming back

Uff, the house is coming back

The house seen from above

The house seen from above

Imagine you are a creature that can only see the world in 2D. Even if you walk in a 3D world, what you will see is a succession of 2D planes. The third dimension will be experienced as “time”: you were on a certain plane at moment t1, on a second plane at moment t2, on a third plane at moment t3; or, another way to understand it, the same plane would “change” from t1 to t2 and from t2 to t3 and so on, but you would keep seeing a plane. Now, as a person that sees in 3D, imagine you are transported from one point to another in a 4D space. Probably, the same thing would happen, you would experience the way as a succession of 3D spaces, or as one 3D space that would change over time. So, a house rearranging itself, changing over time, seems to me, actually, a good way to show in a 3D world what a 4D house would be. For all that, The Crooked House in SL is an amazing creation. Certainly, its furniture looks old (and I don’t mean antique), given the way SL has evolved since 2006, with sculpties and now mesh. Maybe the textures used in the house will also look too “last decade”. Nevertheless, visiting The Crooked House is still a powerful experience: it is the one of being transported into a new dimension.

The Crooked House seen from below

The Crooked House seen from below

8 thoughts on “A 4D experience: The Crooked House

  1. An amazing idea! As soon as I heard the description, I immediately thought of Heinlein’s classic story. I just can’t imagine actually being build, even in SL. This is someplace I will have to check out!

    • It is definitely worth visiting. It does not work *exactly* as Heinlein’s house, but it goes pretty close – and it is so cool to see it working!

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