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Hans van der Laan: Playing With Proportions in 3D

The Benedictine monk and sometime architect Hans van der Laan (1904–1991) is hardly a household name outside his native Holland. Architect Tiziana Proietti and her theologian co-author, Kees den Biesen, have released a new book on van der Laan’s theories of architecture that strives to give him his due as an innovator among modern architects. Hans van der Laan’s Instruments of Thought: Proportion, Architecture and Analogy (Routledge 2025) is rather unusual in its means of argument. Readers are not only given tutelage in some complex ideas tied to mathematics, but are also invited to play games with several wooden “tools” invented by van der Laan for use by his students. The book has over 50 pages of visual exercises that may, if successfully completed, allow someone with little knowledge of proportion to judge the shape, size, and disposition of geometric solids in space.

Van der Laan worked largely outside the architectural profession, living in a monastery in Oosterhout and teaching church design in Breda with his brother Nico, also an architect, just after World War II. During the latter half of his career, he designed several churches and monastic buildings, as well as a house for a friend, which tested his somewhat arcane theories of “architectonic space.” He also published extensively in Dutch and French, bringing him some attention in Europe. Today his followers have created an extensive, easy-to-navigate online archive of van der Laan’s theories and practice.

St. Benedictusberg Abbey, Vaals, Netherlands. Photo by Jeroen Verrecht, courtesy of Dom Hans van der Laan, Caroline Voet, and van der Laan Archives.

 

His buildings have some characteristics of Italian Neo-Rationalism, resembling the work of Mario Botta and Aldo Rossi, but also the minimalism of Swiss architects like Peter Zumthor. Perhaps the rather abstract, planar characteristics of his mainly masonry architecture have brought him a larger audience during the past decade. One hopes so, and this book provides some compelling reasons to look closely at his design work, as it encompassed not just architecture but furniture, liturgical artifacts, and vestments.

Unlike many of his modernist colleagues, van der Laan believed that architecture should be conceived of as inhabited communal space, defined by walls and carefully proportioned openings. He used geometry more literally than many contemporaries—an important exception being Louis Kahn, who employed a much richer palette of materials in his mature buildings and relied more on indirect sources of light. The Dutch master was steeped in Neo-Platonic philosophy as a result of his early education in the Rule of Saint Benedict and the precepts of Plotinus and St. Augustine. Like a medieval master mason, van der Laan believed that God’s divine hand was found in nature and that architecture should emulate its forms and laws. Den Biesen provides an excellent introduction to these key ideas—but, alas, it’s in the book’s final chapter rather than its opening one. The book’s main weakness is the lack of integration between the two authors’ quite different expertise and points of view. We hear their voices together only in the introductory chapter. The lengthy second and third chapters are about architecture and perception, seasoning van der Laan’s ideas with many polemical assertions.

Both authors go to great lengths to explain Plastic Number Theory, a geometric system that resembles those that employ Pythagorean principles, the Fibonacci Series, and the Golden Mean. Though not strictly invented by van der Laan (we learn this in an appendix of the book), the theory formed the basis of both his teaching and his practice over decades. Using a number series based on √3 rather than √2, the Plastic Number ρ (1.324) is smaller than ϕ (1.618), and thus its series increases in smaller increments over its length than that popularized by Fibonacci. The eight divisions are indeed easy to perceive. For van der Laan, who believed that the human visual system favored these smaller increments when judging distance or size, his “new” proportional system was superior to that of the ancients, despite centuries of teaching that used the latter method. He spent much of his life trying to prove his theories, and a few loyal followers have continued the quest. Today, both systems are well understood and could be equally useful for designers. 

 

At the University of Oklahoma, where she teaches, Proietti and her neuroscience colleague Sergei Gepshtein, of the Salk Institute for Biological Studies, did experiments using van der Laan’s system that attempted to test whether subjects did indeed “see” proportion in three dimensions through these small increments. Though results are at present inconclusive, Proietti developed a series of visual exercises, included in this book, that may ingrain the recognition of Plastic Number rectangular solids in those who master them. In order to play the games, a reader is required to build one of two complex wooden block sets, a 2D abacus or a 3D morphotheque—a requirement not easily met by most students or even practicing architects. Though I have a wood shop, I have not yet tried it out. It looks like a lot of fun.

There is no reason to doubt that architecture students can learn to see proportional ratios in three dimensions, though not using computer aided design software. Block sets have long been employed for this, including the famous Froebel Blocks that Frank Lloyd Wright played with as a child. Young designers have been taught to do so for centuries under classical and Beaux Arts pedagogy, which I know from 40 years’ experience of teaching and practice. Most experienced architects who learned to draw by hand can accurately render circles, squares, cubes, equilateral triangles, tetrahedrons, and other figures accurately. Many who use graphic scales also have the ability to judge height-to-width-to-depth ratios without any special tutelage or prompts. Moreover, experiments now under way in Parma have indicated that when viewing classical sculpture and paintings, untutored subjects can distinguish the Golden Ratio, preferring it to other ratios on a male torso, in highly rendered 3D models. I welcome any research that promotes the study of proportion. Tying these studies to what we know about visual perception is critical, and this book makes a persuasive case for doing so. Since we know from theories of 4E cognition that perception is not merely visual but tied to the body and the environment, any research should avoid only visual modalities.

Spiritual teachers such as van der Laan are not often compelled to divorce their theological ideas from abstract mathematical or formal precepts related to designing buildings. Abbot Suger did not do so when he built San Denis in Paris, nor King Solomon when he erected his temple. It is difficult to ascertain, reading the interpretation of an architect and a learned theologian, how van der Laan reconciled this tension in his life and work. He may well have felt differently about the architectural profession at various times in his long life, and changed his writings accordingly.

At a number of points in the book we learn that the monk-architect was committed to aesthetics based upon part/whole relationships and “the special datum of nature.” But he apparently did not push his students hard to produce work according to his fixed formulas, one mark of a good teacher. In 1988–89 he wrote that the “form of the whole that is intended must then, along with the forms of other artifacts, be integrated into created nature to elevate it into a human environment.” Unfortunately, as in other parts of the book, the authors argue unpersuasively that their protagonist did not accept the old, Neo-Platonic truths about proportion, symmetry, rhythm, and harmonic ratios because such canons of beauty were discredited by modernists in the 1950s. Look at his buildings and I believe you will think otherwise. Like most spiritually grounded designers, he did not always hew strictly to his own theories. Louis Kahn and Abbot Suger certainly didn’t.

This handsomely produced book will fascinate anyone interested in visual design in three dimensions or curious to explore unusual ideas about how humans perceive space and form. In order to use it, they will have to enlarge the small, delicate line drawings 200%–300% in order to see them, a problem the publisher could have addressed with a larger trim size. But, like many texts that push a particular theory at the expense of other, more established ones, Hans van der Laan’s Instruments of Thought often skews its arguments toward proselytizing for an unsung hero, albeit a compelling one. 

Feature image: St. Benedictusberg Abbey, Vaals, Netherlands, begun in 1956. Photo by Jeroen Verrecht, courtesy of Dom Hans van der Laan, Caroline Voet, and van der Laan Archives.

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