Tschumi’s *folies* in the Parc de la Villette begin with a basic cube, 10.8 x 10.8 x 10.8 meters, itself divided into 27 equal cubes within, 3 to the third power. The cube in each *folie* undergoes various transformations—additions, subtractions, combinations—marginally related to its program, if at all, if it has one, sometimes subverting structural function within or leaving support stranded without.

Here R4, where the cube rests on gray columns, beneath which descend stairs in one direction, continuing in descent one path; through which passes another path perpendicular, bridged, gracefully curving. The two paths do not intersect and the *folie* serves no purpose whatsoever other than to mark this crossing. We want to believe this treatment gives the intersection meaning. Just as much, we realize we are at a loss for anything to say. Still, it holds our attention and perhaps makes us think about movement, about direction, about crossing, and about containment, but also non-intersection. It asks us to linger, it pushes us to move on. Any further discussion leaves us where we started, with questions.

But take his basic cube, imagined complete. You comprehend it almost instantly—a structure of even sides, those sides divided by 3 to make the 27 small cubes packed within that of course are congruent with the large, that spread load and stress evenly. The cube sings with tautology.

Build one, however, and you become involved in what it takes to raise and hold it together, the even lengths of posts and beams, many more than you first roughly guessed; the intersections inside of six members, of three on the corners, of four on the edges and five on the faces, the different demands each makes. You look to discover patterns that can become procedures that allow repetition of the basic tasks of construction—a challenge when your pieces have odd and varied sizes that don’t match those intentions. Combinations and compromises have to be made. Yet compromises coalesce, and all analysis, all work join and return you exactly to what it is you are building, a cube.

You feel you have brought balance and order to the world, that you have enclosed something and comprehended it, that you have it in your grasp, that you have discovered a basic truth, one that has extension and, with extension, a whiff of the infinite. Just as much, however, you become aware of all that you have boxed out, excluded. Uneasiness sets in.

Then ponder R4. The top two rows together hang over the place of entry and descent, perhaps giving it formal dignity, even significance. But you also become aware of tensions you would not expect in a cube, possibly of instability, of peril, as they are suspended in air and largely kept in place in the middle by one row of beams on the left. Yet R4 does hold together, and the peril may only be an illusion, an insecurity on your part.

You latch on to the 4 x 4 part that thrusts suspended, as it fits your expectation of what a cube is supposed to be. Then you focus on the 4 x 4 part bottom left, where central members are omitted for the path, that counterweights, in part, at least in the mind, the suspension. Then you focus on the 1 x 1 row where the two 4 x 4 squares intersect, as if a point of focus, but then quickly shift to the 1 x 1 row at the bottom middle, the groin of the cube, where most weight rests. Then you discover there is no reason to remain at any of the squares, but rather you need to keep your attention moving.

And you realize you have only scratched the surface of the possibilities of R4.

When you build a model—and, I assume, the actual thing—there is the drama of peril, since, for a while, the 4 x 4 suspension is simply hanging bare, and you rush to complete the rest, the parts that hold it and pull the structure together. But when the model is completed you find it is stable enough, in fact solid.

Walking through the cube, now in reality, on the human scale, presents a different experience, another set of expectations, an additional set of assumptions for analysis, more open-ended speculation.

Only from a certain and unlikely vantage point does the basic cube present its familiar face, and the tension, maybe peril disperse. Start moving again, however, and the illusion of completeness disappears, the play of variations, the possible or projected peril resume.

Then you focus on the top row above the path, to its side, on the top edge, where you are most aware of incompletion, one square closed with two posts left standing naked, their emptiness counterpointing the suspension at the front, the missing row below it. There is no structural reason for any of these members—they are not attached to anything, except in one case to each other, support nothing except perhaps our expectations of a cube. Why this arrangement? Putting the complete square in the middle with two posts on the corners would bring dubious symmetry that undercuts the appearance of incompletion, suggesting a finality that isn’t there, in the cube. You need at least two standing posts, however, for the effect. One would not be enough. Then you are left with the question of which side the two posts should be on. Either it matters for some reason you haven’t discovered, or it simply doesn’t matter at all. You can’t decide.

There is no reason to think the complete cube is more true about anything than the one that Tschumi has designed, or than any of his other *folies*.

There is no reason to build a model of R4, or to study it, or write about it.

There is no reason not to.

But R4 helps us keep our options open, alive.

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*Folie* photos via Flickr

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