Digging into Complexity

Project Description |

Nowadays, architectural designers are chasing complex geometries to create more ample spatial experiences. By looking at the plans, sections,  elevations and models architects produced in the CAD tools, these geometries are extremely complex. However, they can be even more complex, way complex. The reason is that the complexity of geometry is not explored completely yet, once architects realize how complex actually a simple square can be, the design process will be tweaked.

For instance, Sol Lewitt's work, "Untitled, 1976", demonstrated a way to access the complexity of geometry. In this work, the geometry looks very simple, a square with 4 lines inside. What Sol Lewitt did is to manipulate the number of the lines in the square, and plotted all the possible combinations of the lines. Therefore, there are 4 possible ways to select only one line in the square, six ways to select two lines in the square, 4 ways to select three lines in the square and 1 way to select four lines and zero line in the square. In total, there are 16 variations created by this simple geometry. Now, let's expand Sol Lewitt's work a little bit. We take the square into account, thus there are 8 lines (maximal lines) in total. And, let's ask a question: How many ways to select three lines without touching each other? The answer is 186 possible ways to select this combination, shown as below.

Figure 1 - Three lines without touching each other, page 1

Figure 2 - Three lines without touching each other, page 2

Figure 3 - Three lines without touching each other, page 3

We can ask more, such as: How many ways to select a "T" and an "L" without touching each other? The answer is 28. And, we can go further, there are 220 ways to select a polygon with three segments (such as an "N" or a "Z" or a "C"). There are 32 ways to select a "flag" shape (like a triangle with an extended edge). Actually, we can have a simple calculation to show the total number of variations this geometry can provide: 2^16 = 65536 variations. This calculation is familiar because it is just like the bar code system we are using. Each line segment can be show or not show, 1 or 0, thus, there are 65536 variations for a 16-segment shape. It is not difficult to imagine that a simple geometry can provide more than sixty thousand shapes, however, it is difficult to "grasp" meaningful shapes from this big pool. In the previous demonstration, we described how the shape look like to identify the shape, for instance: "three lines without touching each other", "a T and an L without touching each other", "a polygon with three segments", and so on. The only reason that we can "touch" the shape is that we can describe it. The shape has describable features for our language system. If we are working in digital infrastructure, the shape should have the describable features fitting to the digital system (data or information). The complexity of geometry is under estimated because we don't have a tool to grasp meaningful sets from the pool of complexity. A tougher question is that: can we calculate all the possible combinations in this geometry?

Variations and  Identities |

In the previous section, we mentioned bar code system in our daily life. Bar code is a efficient system to create variations by manipulating the presence and absence of each "bar". Because of the extremely large number of variations, bar code is used to give identity to object. In other words, the object can thus be given a "name". Once the shape has a name, it can be put into our knowledge system, and we can use it. The classification system for shapes is still naive nowadays, it is easy to count all the classes we are using now such as “square”, “triangle”, "rectangle", "quadrilateral", etc. These classes are not able to capture all the shapes we will be using, and we don't even talk about those shapes which never exist. By looking at the examples we generated in the previous section, each selection can be a small architecture with an identity, yes, just like bar code. In other words, it is a efficient way to create tons of various architectures, if we want to give each building an identity. This exhibition is to demonstrate the ability of complexity of geometry, and the possibility of turning these shapes into buildings. 

Since we have ARGO to access the complexity pool, the next question we can ask is: what shape looks like an "architecture"? For example, the selections of a "T" and an "L" without touching each other look very like architectures. But, the selections of two triangles sharing one edge (just like a "B") look not like architectures, instead, they look more like the configurations of five long buildings with two courtyards inside. It is interesting how to make selections to let these selected results look like architectures. Furthermore, which selections look like Mies' buildings? Which selections look like Frank Lloyd Wright? Which selections look like Louis I. Kahn? One continuous poly line looks more like the plan by Christian Kerez, "one T plus three floating lines" looks like Mies' building. This brief discussion reveals that the complexity of geometry is possible to be a bed for typology research.