I When we look, we count

For Dom Hans Van der Laan, order is the underlying principle of everything. Nature, as God’s creation, is unfathomable. Its forms have countless sizes. Architecture, as the fundamental HABITUS is there to surround us like clothing and to make our environment readable. As such, it is closely linked to our process of knowing. Van der Laan defines ‘to inhabit’ as being able to enter into a relationship with a space, being able to measure that space.

This is the EXPRESSIVENESS of architecture.

When we measure, we round off to whole numbers and we count. We intuitively estimate the size of something by choosing a yardstick in space, using it as a foundation for counting that space.

II 7 = 3 + 4

There are two ways of READING space: COUNTING and MEASURING. When confronted with two measures of the same size, one COUNTS. In the case of unequal parts, one MEASURES or compares. In order for space to be clearly readable, architecture makes measuring as straightforward as counting.

To enable this, Van der Laan asks himself the question: what is the minimum difference between two sizes, so that we can differentiate them clearly, in other words, so that we can count or name the difference?

The answer is 3:4.

So Van der Laan does not start from 10 and divides this in equal parts, he starts from 7 and divides this in 3 and 4. This opens up a whole new world of designing through relations and compositions beyond mirror symmetry.

III 3:4 in a building composition

In Dom van der Laan’s buildings, everything is interrelated through 3:4.

‘This is what the Ancients called symmetry; not in the sense of two identical halves, but in the sense of the proportion between the sizes of the parts of a building, from the smallest to the whole.’ (VDL, AS IX 6)

A beautiful example of these 3:4 compositions is the entrance of Roosenberg Abbey.

IV Proportional Continuity

The Plastic Number 1,325… has a continuous growth pattern. This growth occurs three-dimensionally.

Moreover: the Plastic Number represents the smallest proportional growth of three-dimensional objects.

1 + a = a3

V The Plastic Number and the Golden Section

With the Plastic Number, Dom Van der Laan found a proportion that allowed all six segments produced by two subdivisions to be a continuous ratio, forming an additive geometric progression.

The discovery of the Plastic Number grew out of a dissatisfaction with the Golden Section. Dom van der Laan claimed that this proportion did not allow for a certain harmonious progressive subdivision of a measure. When subdividing the largest measure according to the Golden Section ratio, one ends up with two equal parts. This is the first definition of the Plastic Number, as explained by Dom Van der Laan in his first lecture series in Leiden, on 16 January 1943.

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