The search for the fourth dimension.

Henk van Putten-Lunenburg



In my booklet from 2006 I stated that it is ‘sheer vanity’ To seek after the fourth dimension, but that striving for it could bring me into the neighborhood of that “something” I am looking for.


Since that time it keeps me busy, and I know in the meantime that an explanation of the fourth dimension by mathematicians is theory. A real concrete image is never given. Nevertheless, I have a strong idea, and automatically am driven to develop my own vision. In this light I will first give a more detailed introduction of myself.

I am not an artist.
I am a constructor. 

I construct geometrical elements and put them in a certain order. These elements are squares, circles, triangles and all the related forms such as ellipses, cylinders and so on.
These geometrical shapes are not created by me. They are simply available, and I only borrow them. This is what is called the “sacred geometry”.
An artist creates, I construct.


In 2014 I finished the construction of twelve black granite pieces. Heavy solid severe shapes. I love the material because it can be polished so nicely!
After polishing it is hard to stop stroking them! (like I stroke my cat).


Then, pondering, strongly appeared the longing for more information.
These sculptures are very nice, but also at the same time so introverted. What are they hiding? All of a sudden I wanted to see their soul!
That was the beginning of re- discovering my idea of the fourth dimension.


In my booklet “Limitation or addition”? already I doubted extensively the three dimensionality of certain sculptures.
Light and shadow are phenomena that prescribe how spacious a work appears to be. A drawing or a painting can be more spatial than for instance a sculpture made of wire. If light and shadow have little chance of interacting the three dimensional sculpture remains flat like a drawing.


The models of my experiment are made of black granite. Is that coincidental or conscious chosen? White carrara marble perhaps would have been better, because light and shadow give more expressiveness on white.
But here, in India, we have nice black granite, and the radiance of this material I consider absolutely very special and nice. Shadow and light form a subtle play.
And, on top of that, the darkness of the stone intensifies its severity and mysteriousness. Something cryptic, hidden, is inside. Exactly this I like to discover.


Again I have to give an explanation. I work in many different materials.
My workshop is quite a chaotic mass, first I am chaotic, and second, because I work with all these different materials and each material needs special tools.
I am not equipped for stone. So I make my designs first in wood. That gives a rather different approach to working directly in stone: the shape is constructed and not hewn.


The series of twelve granite sculptures are strongly related. It is one close-knit family of dark stones, but very shiny and lovable. Modest and introverted.
It is almost indecent to transform the shapes in transparent cages displaying their inner world and revealing their souls. Their souls, almost always a triangle or rhombus, are reproduced in strong red or blue to emphasis the importance of the part.


But, you could say, what has that to do with the fourth dimension? To discover another dimensionality one has to search, to try, to experiment. It is my believe that only a thorough investigation of the spatial shape can possibly result in any light in this difficult matter. Only deep digging can be a guide towards a conclusion.
A conclusion anyway will be a compromise.


Considering all my transparent transformations of the solid granite sculptures, I got the humble idea that I can formulate something more concrete than mathematic formulas. After all, I was searching for a tangible image. Let me say that I found something “on the way”.
A conjecture.


I transformed the sold granite pieces in open transparent constructions.
Like a drawing, I used only the outline of the shape. Certain surfaces are being shaded with parallel lines to indicate the form. The open inner space is now revealing the core, the center, the soul. I want to emphasize that by this translation from granite to steel the same identical shapes are used. Everything is geometric and exact.
But, how different is the dimension!


Looking at the transparent pieces from several angles Is rather confusing. Even trained eyes are in quandary and loose control about the shape. This is definitely not the third dimension.
I do not claim the fourth dimension but surely it is another dimension.


My conjecture is present: it only needs a name. By transforming the pieces in only rods, another process of visibility is appearing. Light has now entrance inside the sculpture. The eye has to work to get the image under control.
There is a sense of confusion. There is also a sense of conclusion: From severe geometric simplicity to ordered, but informative chaos.




Henk van Putten



Figure 1 ‘Borsalino’

Abstract: It is said, especially in constructive art, that “less is more”. The ideal would be a simple, strong, shape, well made and of interesting construction. For the past forty years I have been trying to makesuch work, but I still struggle with contradictory considerations: leaving things out (like surfaces) can lead to objects which do not look simpler, but, on the contrary, more complex. Presenting a geometrical idea in a beautiful way sits in the way of presenting it in an understandable way. These days, I notice that considerations of ‘beauty’ are of less concern to me then they used to be; it is the geometrical idea, the play with newly discovered ratios, which takes precedence. One such idea, which led to many objects in very different materials, I will discuss here as an example.


Keywords: constructivism, geometric art.







figure 2 ellipses
Figure 2
Figure 3 Knot
Figure 3 ‘Knot’

When creating a new sculpture, I look for new and interesting ways to arrange the all-time basic geometrical forms. By manipulating these given elements in a certain way, surprising and interesting new shapes can be created. For this to be possible, all the elements should have planes of similar form and size. For instance, if the circle elements were cut from a ring with a rectangular cross section, it is only possible to fit two elements together in two ways: continuing the circle, or, by turning one of the elements a half-turn, reversing the circle form. But by using a square cross section, one can join them in 4 ways: a quarter turn will also make them fit.

During the design of the Borsalino (figure 1), I discovered one more “fitting” possibility: under certain conditions it is possible to reverse the whole element (see the sketch, figure 2). This only works with the right proportions: if the ring has a square diameter of 1 x 1, then the radius of the outer circle should be 1.707. This optimal fitting enabled me to build ‘the knot’, the kernel of the Borsalino sculpture (figure 3). Only three half circle elements would be needed to complete the sculpture into the Borsalino shape.


Since the discovery of this optimal fitting element, I use these proportions always in my new works.

Even if the sculpture is not as “severe” looking as this one, but rather “playful”, the overall harmony of the piece is more perfect.
The sculpture “Contrapunctus No 14, a completion” (figure 4) is made of 33 pieces. 21 eighth-part circles, 10 half circles and two quarter circles.

Here the reversing of the eighth-part circle elements is everywhere visible. The continuation of the squared shape seems endless.








figure 4 contrapuntus
Figure 4 ‘Contrapunctus’
figure 5 strength granite
Figure 5 ‘Strength’, a ‘zero’ form.

Being a sculptor, one is always busy investigating the three-dimensional effect. Form, size and material together determine the monumentality of a sculpture. Always, I use a very limited scale of basic forms. The circle, the square and the triangle are my basic tools. I try to realize a metamorphosis in the shape and especially in the spaciousness of a basic form by using very different materials and ‘translating’ the basic concept into different expressions or ‘descriptions’ of one basic form. Figures 5 through 8 may illustrate what I mean by this. In the nineteen-eighties I made a series of paintings of my sculptures and found that sometimes the painting looked more spacious than the original sculpture. This fascinated me no end. How is it possible that a two- dimensional thing could be more spacious than a three-dimensional one?

(This, evidently, is hard to illustrate with pictures.)


In a way, this goes for 3-dimensional ‘descriptions’ as well. In particular, the works made of welded steel rods are decidedly looking less spacious than, for instance, the solid form. Why, then, do I make such rod pieces more and more often? I am in doubt. Because you probably expect me to come up with an answer, I am inclined to classify my sculptures in a systematic way. In fact it is quite simple to order them when I think of the adagium “less is more”, which is especially relevant to constructive art. With this in mind, one could say there are minus, zero and plus works. The zero pieces are the nice sculptures which are easy on the eye. The minus pieces are the ones where something is left out. The plus pieces are the airy, complicated, pieces made of rods. I awarded this code to every one of the pictures.

The translation of the zero pieces in sheet metal are the minus ones. A clear example is the sculpture “Strength”. The basic form you see in figure 5: a shape originally made in black granite. In the sheet metal version (figure 7), all the contours of the form are visible, but certain surfaces are missing. The sculpture is more spatial than it’s zero mother. The sheets are fixed by very tiny welding points. The observer has to fill in the missing surfaces to see the relationship with the solid shape of figure 5. Figure 8 shows another ‘description’ of the Strength form, decidedly looking less “spatial” then the painting (Figure 6)





figure 6 strength painting
Figure 6 ‘Strength’ painting.
Figure 7 Strength minus form
Figure 7 ‘Strength’, a minus form

Meanwhile, my methods have changed as well. In former days, the invention of new work was done by sketching, mostly after long nights of thinking “in the air”. Nowadays new works are growing by thinking but also by cutting elements from polystyrene foam (EPS), which I find a much more adequate way of experimenting. Yet, let me be clear about this: the first design will always be a zero piece, the basic shape. Whether I make it in wood, cast it in bronze or develop it no further than the polystyrene foam model. The sheet and rod pieces (minus and plus) are works sprouting from the basic shape.

Figure 8 Strength plus form
Figure 8 ‘Strength’, a ‘plus’ form

My latest work I gave the title ‘Interaction 2’ (Figure 9). One could conceive of this work as being made from a slice of a cylinder, 5 units in diameter, the thickness of the slice being, of course, 1 unit. Then a hole is made in the middle, 1 unit in diameter.

Then a larger circle is cut out, 3 units in diameter. Now we have 2 rings, each with a square cross-section of 1×1 unit. These are cut in half, so we have 4 half-circles. The picture (Figure 9) shows how these are glued together to make this form, which I named ‘Interaction’ since the form escapes and then kind of reverts back on itself. (Obviously, I did not really use the ‘construction method’ as described above, if only because the width of the saw slot would spoil everything.) I think this form is less ‘solid’ than the Borsalino or the zero form of ‘Strength’ and clearly shows the ‘idea’. The sculpture depicted here, by the way, has an outer diameter of 15cm, but I dream of seeing it in a park at least 3m high.



But in fact, the aluminum solid form was not the first realisation of the basic form; I first made it from steel rods, with red enamel (Figure 10). I regard it more as interesting then as a real beauty. After launching my way of cataloguing my work in minus, zero and plus, I realise some inconsistencies in my assertions. Indeed, after first emphasizing the importance of three-dimensionality, I admit being fond of my ‘wire’- sculptures where hardly any plasticity is observed.

According to my simple system, I would have to give the rod-form a double minus, since even more surfaces are left out. But this doesn’t sit well with my intuïtive feeling, since the result does not look simpler, but, on the contrary, more complex. Although this description offers the possibility to read the complete ground-plan, it is actually harder to do so, or even to recognize the basic simple form. Thus, I’m inclined to give these incarnations of the basic form a ‘plus’ for presenting a more complex picture. Note the striking absence of 3-dimensionality, even when photographed in a garden; no doubt because there are no shadows stressing the basic form; it’s just a bit of confined air.


Obviously, my preferences are still developing; it might even be that I am less sensitive to the temptations of that devil that makes me strive for beauty





Figure 10 open interaction 2
Figure 10, Open Interaction 2


The sculpture ‘Rondeau’ (Figure 11) is based on the same form as ‘Interaction 2’, but half-circles are added; the picture does not fully show it but it has no ‘end’ anywhere, it is a ‘closed’ form. Although it is tempting to describe ‘Interaction 2’ as being derived from ‘Rondeau’ by leaving some parts out, the funny thing is that it did not happen that way: I first conceived of the ‘Interaction 2’ form and only later realised I could add a few half-circles to ‘complete’ the form. That is why I described extensively the mental construction of Interaction 2: it is the ‘basic form’ as it can be cut from one slice of a cylinder. To realise ‘Rondeau’ an additional slice has to be cut, most of which is discarded. ‘Rondeau’ looks beautiful (and is very sellable), but in a way it does not satisfy me as much as the ‘Interaction 2’ form with it’s simple ground-plan.


The pictures of ‘Interaction 2’ as shown here demonstrate clearly how the work is constructed, especially the form constructed of red rods (Figure 10). Yet in reality, the views are sometimes confusing. By walking round the sculpture, one has to discover the interesting viewpoints and/or discover the ‘ground-plan’. In other words: the observer has to make an effort. I think it is this aspect which fascinates me: a sculpture should be like a woman: visibly appealing but above all particularly interesting.



Henk van Putten

Reprinted from the periodical ‘Symmetry: Culture and Science’, VOL. 16, NO.1 by The Art Stable Gallery, Amsterdam,