‘Let no-one ignorant of geometry enter here.’ These are the famous words said to have been inscribed over the door of Plato’s Academy in ancient Athens. Not many people these days would think to have such words written over their own front door. We might be more disposed to have something simpler like ‘welcome’ or ‘home sweet home’, and rather than it being written over the entrance it is more likely that our welcome will be written on a door mat. Be that as it may, why was geometry so important for Plato, and is it relevant for the modern home? Let’s have a brief philosophical diversion to find out.
The universe is all mathematics and geometry
Although many of us will have been happy to see the study of mathematics disappear into the rear vision mirror of our lives once we left school, we may never have seen it for the fascinating thing that it is. This is probably more an indictment on the way it is taught than it is on the subject of mathematics itself. Mathematics is interesting because the universe is interesting, and the universe is interesting in large part because it is mathematical. This was as obvious to the ancient Greeks as it has been to modern-day scientists from Albert Einstein to Stephen Hawking.
What is meant when we say that the universe, or nature if you prefer that term, is mathematical? It means that the physical laws which govern the universe — such as electricity, gravity, sound, quantum physics — are mathematical and defined by mathematical equations. The most famous equation is probably E=MC2 but there are hundreds of others. It also means that mathematical proportions and relationships are always expressing themselves through nature. Music is moving mathematics, while geometry is mathematics applied to the three-dimensional world and the link between music, harmony and the universe has fascinated scientists for centuries.
The term ‘geometry’ is made up of two Greek words for ‘earth’ and ‘measurement’. It is a branch of mathematics concerned with the shape, size, relative position and the properties of space. Thus, the universe is not just mathematical but it’s also geometrical. There is no need to get too esoteric or to go into this in much greater depth here, other than to give a few examples from nature to illustrate the point. See, for example, the geometry of a snowflake or of seashells. For this reason the world’s great wisdom traditions look at the universal creative process as being highly intelligent, organized, lawful and mathematical.
The golden mean
Whether or not we believe in God doesn’t change the fact that, from the smallest to the largest scale, the universe is mathematical and geometrical. One particular aspect of geometry that occurs again and again throughout nature, and which was used at length by sacred geometers and architects, was what is called ‘the golden mean’ or ‘the golden ratio’, and this can give us a reference point when designing the proportions of our home. Mathematically the golden mean is approximately 1:1.618. What is special about this ratio? Well, it occurs all around us whether it be in the geometry of the nautilus shell, a galaxy or a flower.
The golden mean is also the basis of what is called the Fibonacci series. In this series, first take a rectangle of the proportions of the golden mean. Now divide off a square within it and then a rectangle of the same proportions appears again. You can then divide off yet another square to produce another rectangle, then another and so on in an infinite series. What you trace out is a spiral, the same spiral that is represented in the nautilus shell and many other works of nature.
The mathematics of this series is both intriguing and complex and since ancient times many forms of architecture have been based on these same proportions. One famous example is the Parthenon in Greece. The great cathedrals of mediaeval Europe such as Chartres and Salisbury are other famous examples. Architects in times past, from East and West tended to have a strong grounding in mathematics, aesthetics and, indeed, the arts more generally. Before being let loose to design a building the architect needed to have an understanding of beauty so that they would build a beautiful building. Such beauty is both appealing to the senses but also to the emotions and intellect. Unfortunately, these days the love of beauty and proportion have been largely ignored or treated as an indulgence in the face of a utilitarian approach to architecture.
In the modern day there is a movement called New Classical Architecture that is combining the modern advances in design and sustainability with classical forms and styles.1 Although it is an approach that has largely been used for contemporary public buildings, the influence of such architecture can also be expressed in homes. New Classical Architecture sometimes only utilizes decoration styles seen in classical buildings, such as columns, but the ones that take it more seriously also take proportion into far greater consideration.
We know it when we see it. When something is beautifully proportioned it just looks right although we may not be able to say why, at least not mathematically. Conversely, when something is out of proportion it looks odd, awkward and out of place. Some would say this is just a result of what we have been conditioned towards as a culture, but those with an interest in the mathematics of nature would answer that we have this geometry in our DNA, literally and metaphorically. The golden mean or ratio has an aesthetic about it, which is why it is represented all around us in ways we may never have realized, from the dimensions of credit cards and playing cards to the proportions of standard photos and widescreen televisions.2
In buildings geometry matters too. This is not to say that every wall, window or roofline needs to be based on the golden mean, but it is worth taking proportion into account when designing or buying a building. Although an architect may not have been trained in sacred geometry, they will often have an intuitive aesthetic awareness that reflects itself in the buildings they design. Before engaging an architect look at their other work. Have a conversation with them about their thinking on proportion and balance.
If we only look for utilitarian functionality in a building without consideration for the aesthetic then we will be the poorer for it. Yes, a house needs to be functional, but not just functional. Although we need functionality we are not enriched by it. Its a little like a doctor being medically proficient without the bedside manner to match. It doesnt leave your heart warmed, uplifted or comforted.
At home we built a straw-bale calligraphy studio for Deirdre where an old garage used to be. It was a simple rectangular space and we designed the building based on the simple harmonic proportions of the golden mean: the height of the building to its width, or the length of the building to the width, or the proportions of the alcoves carved into the walls, were all based on those proportions. Apart from the quiet and cool atmosphere created by the wide, rendered straw-bale walls, the proportions and the pitched cathedral ceiling give the building excellent acoustics and a meditative and tranquil atmosphere that many first-time visitors notice and comment on. A building can help or hinder us in our search for peace, but ultimately we have to go there ourselves.
THE MINDFUL BUILDING
There is no one thing we can point to and say that it represents the ‘typical mindful building’ or is the ‘mindful style of architecture’ — at least not yet. The point here is to emphasize the importance of stopping to look; to be mindful when we look at, choose or design a building to live in. What is the effect a building has on us aesthetically and emotionally? What does it communicate to us and the world? What do we want to communicate? How does it sit within itself and with its surroundings? If we don’t pay attention we may not know and our choices wont be informed or conscious ones.
Harmony
Harmony is another word derived from Greek — from harmos, meaning to join. It carries the sense of things fitting or joining together, being in agreement or concord. When the individual elements of a thing fit together well, as if they are meant to be with each other, they add value to each other, express harmony and create an aesthetically pleasing effect. Harmony is often associated with beauty. Without harmony there was no beauty according to Plato, and where there is no beauty love does not follow. In music, when notes go with each other according to the laws and proportions governing the musical scale they create a kind of harmony. When they don’t go together we hear discord. In medicine, harmony is associated with health and disharmony with illness.
Many cultures have reflected on the importance of buildings being harmonious within themselves and with their environments. The ancient Chinese discipline of feng shui could be considered both an art and a science. Although one may be more or less interested in the metaphysical explanations for it, clearly many of the precepts of feng shui are based on common sense and astute observation. There are principles for the alignment of the house, the use of light, the layout of the floor plan, garden design and the placement of water features, the choice of colours and the placement of furniture, among other things.
In a building, when the various elements work harmoniously together the whole is far more than the sum of its parts. In a village, when the various buildings complement each other, together they create a cohesive atmosphere and a sense of an interconnected community. One only has to go to the beautiful French or Italian countryside or to a village on a Greek island to have a sense of what this means.
On the other hand, in these days of postmodern architecture this harmonizing could be seen as conformity — a thing to be avoided at all costs. The main things that are communicated in the postmodern world of architecture and design are not so much the harmony of the thing within itself and its surroundings, but rather making a statement, novelty, size, utilitarianism, cost, individuality and, oftentimes, discord. It could be said that postmodern architecture, like postmodern music, philosophy or art, reflects the values and discord of the modern world. Often there is a desire to shock. It may or may not be right, or even possible, to say that postmodernism is or isn’t mindful. The point is that just as we want harmony within our body, which we can equate with good health, so we want harmony within the mind, which equates with mental health or happiness. In order to foster this it is useful to surround ourselves with objects and an environment that makes this easy rather than difficult.
The aim here is not to say that there is only one kind of architecture that works or is beautiful. There are so many examples of beautiful buildings and towns from every culture throughout history. The aim is rather that we take the time to stop and be mindful of the home we live in or the home we are considering buying. Does it communicate beauty and harmony to us? Do we even value beauty and harmony? If the building was a representation of the mind, is it a mind we would like to inhabit? If you are looking at the home you already live in and it doesnt communicate harmony to you, perhaps either move house or make whatever changes you can to produce an aesthetic you feel enriched by and at peace with.
