#### Sacred Geometry and the Golden Proportion.

It’s not just St. Mary’s. It could just as easily be St. George’s, St. Michael’s, or any other church you care to name. Indeed, there is an indefinable ‘something’ about many of our older churches and cathedrals, especially the great Gothic cathedrals of the middle Ages. But what exactly is that ‘something’? What is it that makes a structure a good place for spiritual working? What gives it that numinous quality that leads us to define the space as sacred?

Any dowser will tell you that almost all of our sacred structures, from the megalithic to the Gothic, are sited over confluences of underground water flows and lines of subtle energy – rising vortices of earth energy called ‘power centres’. These natural telluric hotspots can be harnessed by the geomancer and used to power the space. But that’s just the start of the story. A suitable container needs to be constructed to shape and tune the energies, and the form and proportion of the final edifice can have a dramatic effect on the ‘feel’ of the space. Specific numbers and geometric ratios are employed to impart a subtle, yet palpable, resonance to the structure. These ratios are not simply human-made mathematical constructs designed to solve a particular problem; rather they are universal principles and natural constants, the very building blocks of creation that can be found by anyone who cares to look for them. Early philosophers discovering these numbers and ratios in nature believed they were seeing evidence of a divine hand in action; hence the study and utilisation of these archetypal patterns became known as *sacred geometry.*

The forms of sacred geometry naturally produce subtle energy fields that can be detected by dowsers. It makes no difference if it’s a chalk circle on your living-room carpet or the dizzying architecture of a Gothic cathedral; the principles are exactly the same. The spaces are designed to resonate on a subconscious level in such a way that the possibility of a spiritual connection is maximised.

At the heart of any structure incorporating sacred geometry is the principle of *incommensurability*. The irrational numbers generated by the geometric ratios employed in the construction are dimensions that can never be precisely measured but only expressed though geometry. By definition, an irrational number is one that cannot be expressed as a fraction * p/q* for any two integers

*and*

**p***. Irrational numbers have infinitely long, non-repeating decimal extensions. Mathematically, it is impossible therefore to precisely measure something like the diagonal of a square; rather like Achilles trying to catch the tortoise in Zeno’s famous paradox, the decimal part recedes infinitely into the distance. This is why irrational numbers are so fascinating to the geometer; they cannot ever be expressed as a*

**q***quantity*, they can only be appreciated as

*qualities*. They are the inner, esoteric face of number, their presence detectable only in the relationships between parts, like cracks between the paving stones of reality. They manifest the infinite in the finite, bridging Spirit and Matter via the Universal framework that is sacred geometry.

To the masons who raised the great Gothic cathedrals and other places of worship, sacred geometry was also of paramount importance to the actual construction. Lacking our modern knowledge of materials science and load-bearing calculations, they relied on the use of harmonious proportions to build balanced structures that could support themselves without collapsing; so in a very practical sense it is this geometry that holds up the soaring vaulted ceilings of the cathedrals, not engineering science.

An impressive side effect of sacred geometry is that many of these structures possess extraordinary acoustic properties, a result of the inter-related harmonic structure behind both music and geometry. Certain types of music (e.g. Bach) were designed to be sacred geometry you can hear, so it is little wonder the buildings resound with it.

Perhaps the best-known ratio of sacred geometry is the Golden Mean or Golden Proportion, also known as the Divine Proportion because it appears so frequently in natural systems. Mathematically, it approximates as 1.618033… and is represented by the Greek letter Phi (Φ). Two quantities are said to be in golden proportion if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. This sacred ratio has long fascinated artists as well as mathematicians, as it seems that we are genetically programmed to accept things that are in golden proportion relationship as most harmonious to our eyes – be it a building façade or a human face. Entire volumes have been written about the Golden Ratio, and in his book of the same name, mathematician Mario Livio explains it thus: “Early mathematicians assumed that, if you have two line segments, one of which is longer than the other, then you can always find some smaller unit of measure so that the lengths of both segments will be exact whole-number multiples of this smaller unit. For instance, if one segment is precisely 21.37” long and the other is 11.475” long, then we can measure both of them in units of 1/1000 of an inch, so the first one will be 21,370 units and the second 11,475 units. So in theory finding such a common measure is just a matter of patient search. But the discovery of irrational numbers and incommensurability means that for the two segments of a line divided in Golden Ratio, such a common measure *can never be found*.”

The Golden Proportion usually manifests in nature as a numerical sequence called the Fibonacci sequence, where each term is the sum of the two preceding numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34… etc. Dividing each term by the one before it approximates to the Golden Mean number of 1.618…, and this approximation gets closer and closer to Φ the higher the numbers become in the sequence. If you plotted these numbers on a graph, you would get a wildly oscillating waveform that would fairly quickly settle down to a smaller and smaller wiggle around the line of Golden Mean.

The Fibonacci sequence is the governing factor of natural growth systems and can be found everywhere; from the distribution of leaves on plants and trees, growth patterns in a nautilus shell, the breeding patterns of rabbits, the spacing of atoms on the DNA molecule, the proportions of the human body – even the orbital distances of the planets.

Perhaps this explains why the Golden Proportion is so favoured by artists and architects; because of its ubiquity in both plant and human biology, structures involving this proportion naturally provide the perfect container for the harmonious integration and enhancement of the living systems within.

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