The right size
As children we build huts without drawing them first, but when we are older we make drawings before we build. The drawings help us discover the right sizes for our rooms and the materials we use to make them.
Do we determine our measures solely based on use, on practical considerations? Do certain measures help us feel more at home in a room, a building, a town?
Experiencing different measures
Since Napoleon we measure with the metric system. Wherever we are, the size of the metre does not vary. But how does our body and how do our eyes relate to measures in the metric system? When do we perceive differences in size? Which relations of length, width, and height continue to please us?
The plastic number
These are the questions Dom van der Laan asked. Through experiments with pebbles and then with building materials, he discovered a ratio he called the plastic number. The basis for the plastic number is the relationship between measures belonging to a group of measures. They increase or decrease according to the ratio four to three. The parallel in music is the ratio that relates whole and half notes to each other within an octave. The analogy between the plastic number and music goes even further: in music we can play chords, combinations of tones; with the plastic number we can compose walls and rooms and spaces that are in harmony with each other because they relate to each other as objectively as the tones within a musical key. The plastic number is not a particular measure: it disciplines the relationship between the measures we choose.
Dom van der Laan leads us back to our own experience: You climb a sand dune and look out first over the immense beach and then further to the vast and measureless sea. For a moment you lose yourself. How can you regain your place in the world, a world that has meaning for you because your body can relate to it? We concentrate on only a limited segment of space, concluded Van der Laan; and in that space we ourselves form the centre.
We can differentiate different kinds of space: first the space we live and dwell in; next the space further away, the space we walk through; and finally the wider space we can see but not yet feel as a place for our body. When we build we can give form to the differentiation we experience. Perforated walls on either side of a space bring that space experientially to life. We start according to Van der Laan with the spatial cell—a room. Then we move on to the court—a house and its yard. Finally we reach the domain—a district or town quarter.
How can we bring the three modules of space in relation to each other? How, in other words, can we build a world that literally makes space for our body in a way we can perceive and feel? Van der Laan answers with the experience of neighbourhood, or nearness.
Van der Laan begins with an intimate experience. If you hug someone, you contain him: it feels as though he comes inside you—at any rate inside a very clear segment of space. If you see a row of trees, you can approach them till you’re in their neighbourhood; when you walk away you know at which point you’re no longer in their neighbourhood. A tree welcomes you in its neighbourhood more effectively than a stone or a bush do. Conclusion? Our experience of neighbourhood depends on the size and the form of our potential neighbour, together with our distance from it. And if this is our experience, then we can ask our architecture to make the world be built neighbourly, and therefore knowable and meaningful.
With two stones we can mark the beginning of a path. If we pile more stones on top of them, we get columns. If the columns remain in each other’s neighbourhood, they form a gate; if they are too far away from each other, they stand alone as objects. The same thing happens with the walls we build. When we can perceive them as standing in each other’s neighbourhood, the space between them comes to life and becomes a knowable space for our body. But our perception of a space between walls at just the right distance from each other demands walls whose thickness we can experience. If the walls are mere surfaces, they have only two dimensions. Our body can’t engage with them as with a neighbour.
Walls can allow the space between them to be born only if we can experience the measures of the walls in the measure of the space they create. Our experience has led us to a new understanding of proportion. In terms of neighbourhood, proportion is not an abstract recipe but a concrete reality. It all boils down to human perception.
Dom van der Laan conducted experiments to discover how and when we perceive changes in the size of a building block. We don’t measure with a measuring tape but with our eyes and with our body. If we experience two blocks or elements as having the same size, we know through measuring them later on that they differ from each other to a small degree. But within a particular margin, we don’t perceive them as differing.
When do we say that the two elements no longer have the same size? When they differ by a ratio of four to three, concluded Van der Laan. And since architecture is the craft that involves three dimensions, the Golden Section (which expresses a relationship between two measures only) is not adequate to our perception of space. Via mathematical study Van der Laan arrived at the same ratio of change as in his empirical experiments: 4:3. He christened the proportion the plastic number, thus stressing the fact that architecture comprises spatial—and therefore plastic—forms.
Types and orders of size
Imagine sorting fruit or eggs into groups whose pieces are more or less the same size. Without measuring we can distinguish quite easily which pieces of fruit or which eggs have more or less the same size. Dom van der Laan called them types of size. If we use the plastic number to determine the boundary between one size and the next, then we are left with some elements that are a bit smaller and others that are a bit larger than the perfect measure. We ignore such small differences in our initial sorting of types of size.
What happens when the differences in size are so large that we can no longer perceive by how much they differ? How can we relate a matchstick to a skyscraper? The plastic number gives us an answer.
We can determine as many groups of size as we wish. But, discovered Van der Laan, the sizes of the constituent parts can only remain in relation to each other if the difference between the largest element and the next-largest element does not exceed the size of the smallest element in the group.
How many elements should there be in a group? Van der Laan determined that with seven elements a cohesive group results. The seven elements comprise in Van der Laan’s terminology an order of size. If we made the group larger than seven elements, the relation of the elements to each other would suffer. The evidence comes again from music: an octave comprises seven different notes before the eighth, which begins the next octave. Architects can make music of their spaces by attending to measures that relate to each other in a way we can easily perceive.