The geometry of the planets

A Personal Journey: Ann Hechle

The Journal ‘Figures of Speech’ is not a book but the publication of a personal diary (in words and drawings) which was written over some years. The original idea to write it was inspired by a commission associated with an exhibition of calligraphy. It was suggested then that I might take the creative process as my theme. The symbolic language of Sacred Geometry arose quite early on in my researches. I had been interested in this subject before and knew it captured certain situations and processes in a very fundamental way. Essential to these understandings was enactment: that in the practice of drawing out these archetypal shapes with a sharpened attention, one perceived their meaning with the whole self – body, mind and spirit. Being engaged in this way I found very moving, it was like being directly in touch with the workings of the universe!

This is not really surprising, as in creating a piece of work, the maker inevitably engages with fundamental issues that underly the surface marks: the necessity of process, hierarchical decisions, functional requirements; harmony, balance, proportion. All these belong equally to marks made on a page as well as to the deeper laws of nature - and as earlier traditions would say, to philosophical meaning.

Furthermore, as as we touch paper with pen and ink, a certain poise of mind - between engagement and detachment - becomes crucial. If the focus is too close, too much on the particular, this interrupts the flow and the whole is lost. Conversely if too much detachment, there is a diminishing of personal investment, and the work loses quality and identity. The paradox of engagement and detachment has resonances in other performance art-forms, and in many spiritual practices.

Not being a mathematician, I found extending my knowledge quite difficult; so over one whole winter I put myself through a rigorous course of basic geometry and maths using two excellent books: Sacred Geometry: Philosophy and practice by Robert Lawlor; and The Elements of Dynamic Symmetry by Jay Hambidge.

When I started, I knew very little of my subject matter: what areas it might cover or where it might lead. However there is one great advantage in knowing nothing; it is that if out of a mass of information gathered you repeatedly trip over something, you know it must be meaningful. This freshness of approach is important, because recognition of a significant connection can bring together quite different and surprising elements, whereas learning in a more formal way tends to box information into separate categories.

There are now many brilliant books written by scientists for the general public, and I read lots of them: biology, general physics, chaos theory, and the strange twilight world of quantum physics where paradox and ambiguity play such an important role. I had noticed that a scientific description could also find an echo in the philosophical world, and began to wonder whether the mathematics were not the drivers but the expressions of the deeper principles at work in the universe; and if they were, these principles might also be present in Myth - the great stories of mankind. This idea was followed up at the end of the book.

So in ignorance I just started on page one focusing on an aspect that interested me, and let the book unfold from there. During the time spent researching and writing it over the years, page by page, topic by topic, I gradually became aware of certain recurring themes whereby elements were held together. These appeared to be different versions of Sameness and Difference - such as variations on a theme and cyclical repetition; though these variants were often hidden as they came to light in unexpected forms and were masked by altered contexts. In retrospect, the themes appeared to run throughout the book, and I wondered if they formed not only the major substance of it, but were also the hidden guiding force driving the whole narrative, though this was not obvious at the time. This all went on for some 17 years; the book gathered momentum, and the coincidence of the practical and philosophical content became more evident.

The Paradox of Sameness and Difference.

As a practicing calligrapher, I often find myself struggling to bring all the different visual elements together into harmony on the page, so that every item has its appropriate placing and significance. I became aware that every mark has two aspects: what it is, and how it is behaving in a particular context. For instance, take a piece of green paper, cut it into two and put each piece on a different coloured background, the green paper will remain the same yet the colour of green will appear to be altered. This paradox of two facets: substance and activity held together is inherent in every mark that we make on the paper in relationship to all the other images. So each word or mark can have its own identity as well as the flexibility to negotiate with other elements; integrity is then maintained and the design problems flow more easily. So the crucial task in resolving harmony in a piece of work is the finding of relationships. Music has the same inbuilt concept: F sharp will sound assonant when played in the scale of G major, but dissonant in other settings. Robert Lawlor adds another musical offering: ‘…..This quality of perceiving sameness and difference is part of the poise of mind that Sacred Geometry means to cultivate, one which is precisely discerning and harmoniously integrating.

The paradox of sameness and difference is an important finding in any circumstance: think of a human being in society, we are essentially ourselves yet we have sub-selves, we adapt and behave differently to every other individual person: family, friends, strangers - smoothing the path towards a more harmonious community. To make a connection between the very different examples of a green paper, a person and how they adapt to their surroundings may seem fanciful, but in principle it is the same concept. So as I grapple with putting letters and images together on a page, I am unknowingly using strategies that belong to a much larger and grander world.

Art has sometimes been referred to as a way of knowledge, and it is interesting to note that in various traditions the same word ( for instance the ‘Tao’ and ‘Dharma’ in the East) is used for both meanings: the Way and the way things are - the path to follow as well as the underlying order of things. The implication is that these two meanings can come into alignment and work together. So, though we work intuitively in placing the elements on our canvas, we unknowingly enact these deeper universal laws of which we are part - though implemented through the specific vocabulary of our particular art form.

The Philosophy of Number

Absolute Unity, Oneness, the hidden underlying foundation of the whole creative experience is not static but seething with infinite potential. Scientists are becoming increasingly aware that mind and matter are intimately connected, so how we engage with our material, how we perceive and how we select, crucially shapes what what is created. The maker’s mind and subject matter are all part of an undivided continuum; see for example David Bohm’s Wholeness and the Implicate Order. One - Absolute Unity is self-contained, self complete; so in order procreate, it must divide into Two within itself to create the Other: difference, dynamic - and diversity.

Contemplating this step away from One to Two, I remembered reading about the early Greek philosophers and their ideas about Number. Pythagoras, and later Plato believed that Numbers were not just quantities, but they also had qualities that operated on the archetypal level as universal patterns and processes. For instance Two was expressed as Twoness, representing the principle and active power of duality. So Twoness could become a container which would include a whole range of noun/verbs such as pairing, opposition, exchange, alternation, reciprocation, paradox. These attributes could be unpacked still further: for example alternation would include our heartbeat, our breath, our walking; exchange recalls Einstein’s equation of energy and matter: (e=mc squared); and reciprocity is to be found in the musical octave where half the length of the string gives double the vibrational frequency (1/2 x 2/1=1). All this information then could be gathered together under one label, mediating appropriately between the archetypal and factual levels. Thus complexity on the factual level, in its many varied guises, could be traced back to very simple beginnings. At the heart of all creation there is a profound simplicity.

In this context,

The gateway from the One to the Many is through Two; and the importance of paradox.

Twoness has a special significance as it is the first step away from One which represents wholeness, completeness and the symbolic source of all creation; and that first step away brings its own responsibilities and also the hazards of separation and strife. The paradox of self-similarity heals that separation.

The One creates the Other, and the Other is also the One. Everything is honoured, nothing is wasted: a both/and situation rather than an either/or.

Below are two versions describing the primal division of Unity, and how that separation is healed. The line that connects the centres unites and divides. In the Yin and Yang symbol duality is embraced by the encompassing circle. 

Many mystics of the past have told us, and today some quantum scientists now believe:

All is One

We suggest the reader first browse the full book  HERE

the golden proportion

The links below allow access to further reading on the content of individual pages.

Pages 1–11
Peter Rogers Extract: A Painter’s Quest  + The Way of Life: Lao Tsu      

Pages 12–13
The Circle and the Square

Pages 14–17
The Study and Practice of Contemplative Geometry

Pages 18–19  
The Primal Act: The Division of Unity

Pages 20–21  
Relationships between the Changing and the Unchanging   

Pages 22–23  
Pattern: The Universal language

Pages 24–25  
The Cosmic Connection

Pages 26–27  
The  Circle and Shapes That Arise   

Pages 28–29   
All is One - One is All

Pages 30–31   
The Square and √2, and the Principle of Growth and Transformation     

Pages 32–33   
The Root Rectangles, and the One and the Many

Pages 34–35   
Diagonal, Reciprocal and Root Rectangles

Pages 36–37   
Seeking the Root

Pages 38–39  
Music: Vibration and Key Relationships

Pages 40–41  
Expressions of Reciprocity,  Mediation and Alternation  

Pages 42–43  
The Golden Proportion (Extract by Robert Lawlor)

Pages 44–45   
The Geometry of the Planets

Pages 46–47   
The Golden Proportion  (extract by Robert Lawlor)

Pages 48–49    
The Golden Proportion: The Golden Proportion in line, square and curve. The Ubiquity of ⏀

Pages 50–51   
The Golden Proportion: The Star and 5. The Divisions of ⏀

Pages  52–53   
The Golden Proportion: Carpet pages: ⏀ in All Things 

Pages 54–55  
Three that is Two that is One

Pages  56–57   
Constancy in Change

Pages 58–59   
God  in All Worlds

Pages 60–61    
Complex Structures and Organisation, and Visual Vocabulary

Page 62–63
Myths to live by: An introduction. Freud and Jung, The Fig. √3

Pages 64–65
Myths. The Primal Division of Unity, and √3

Pages 66–67
Myths. Death and Resurrection, and √2

Pages 68–69
Myths.The Macrocosm, Man, The Microcosm, and ⏀ the Golden Proportion

Pages 70–71
Paradox: some thoughts and reflections

Pages 72
The Circle of Eternity. Text from Four Quartets by T.S. Eliot.