The Garn Goch Golden Ratio

The Golden Ratio is said to be 'the divine proportion', and has fascinated philosophers, mathematicians, artists and architects for millennia. It is found in leaves and flowers, at the atomic scale, in the design of the Egyptian pyramids (built around the same time as Stonehenge), in Leonardo's famous Vitruvian Man (roughly), and in Le Corbusier's 20th century architecture.

The Ratio, simply stated, is one thirds - two thirds, but strictly it is a formula that today we know is 1.618, but the designers of Garn Goch made it 1.5. Not bad for 'Stone Age people'.

Specifically, when a line (or a distance between stones) is split into two sections, short and long, and when the long section divided by the short section equals the whole length divided by the long section, then that is the Golden Ratio. 

Above you can see it graphically with Garn Goch measurements, and you might argue this is coincidence, luck or divine intervention, but it has to be said that the lengths are compellingly precise when using the Google maps measuring tool. Surely, it argues convincingly that the site's designers not only had a plan, but also had precise measuring instruments?

Logically, it also argues not only that Goch's Cairn predated the assembly of the linear stones, but also that the stones were laid in reference to the Cairn. If the Cairn is religious, then so are the lines of stones.

Given that such large stone monuments were exclusively Neolithic, and Garn Goch follows Neolithic long cairn designs found in Wales and western England, we can be confident that Garn Goch is Neolithic. (We'd like to say indisputably Neolithic, but there's always someone who wants to dispute!)

In a philosophical and religious context, the Golden Ratio becomes the Golden Mean, which is essentially about moderation, balance, and avoiding extremes. It was much discussed by Plato and Socrates, and the temple at Delphi had written above its entrance 'Nothing In Excess'. Buddha and Hinduism teach the middle way. Judaism and Islam frequently promote the idea of moderation, and Thomas Aquinas says 'moral virtue observes the mean'.

There is, then, a religious perspective and significance to the Golden Mean/Golden Ratio, and its universality and longevity suggested by those examples encourages the idea that for the Neolithics too proportionality and balance were important in both architectural design and religious belief (but, later, not so much in the design of forts).

Left: Le Corbusier Pavilion, Zurich. Middle: Gizah pyramids. Right: Stonehenge. See copyrights.