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Sacred Geometry: Does mathematics hold a case for intelligent design?

Sacred Geometry: Does mathematics hold a case for intelligent design?

A rather factual and equally amusing retort by atheists on the argument of their lack of faith goes, “There have been 10,000 gods throughout his­tory. You reject 9,999 of them. I just go one further.”

By David Jacklin

Sunday 14 April 2019, 10:00AM

The Vitruvian Man. Image: Eric S / Flickr

The Vitruvian Man. Image: Eric S / Flickr

As a damned non-believer of our world’s major religions, I personally find it bizarre that a grown-up can seri­ously consider that there’s an all-pow­erful creator just waiting to evaluate your end-of-terminal report to see if you made the grade.

It’s certainly a risky line of think­ing, and I’ll accept I’ll look pretty darn stupid if I’m wrong. If I’m right, I don’t even get the chance to see the opposi­tion lose face. It’s a bum deal all round.

But to doubt is to be human, and we all have our moments. For my grand­father it was the taste of an onion. He was a strange chap. But then again, over the past 40 years I’ve come to consider that if there is a creator, she’s pretty odd too. Surprisingly for me, numbers can raise a rather profound spiritual dilemma.

Our universe is determined by cer­tain mathematical constants which express themselves in the form of pat­terns and cycles in nature. So precise and extraordinary are the formulae that it certainly presents itself as an argument for intelligent design in our creation.

The blueprint of these mathemati­cal designs can be found in religious doctrine, signage and imagery since the earliest of times. From the spiral­ling galaxies, the symmetry within flora to the humble snail shell, math­ematical constants are woven into our fabric and presented all around us.

Scientifically, we believe that ge­ometry was the art of the Greeks. But long before this complex geometric de­sign was present in the construction of sacred spaces from races as diverse as the Minoans, Sumerians, Egyptians, Indus Valley, Chinese, Phoenicians and the curators of Megalith rock for­mations across the Western European countryside. Thai sacred geometry is inherent in the Sak Yant tattoo, where geometric design is incorporated with Buddhists psalms and magical formu­las to invoke elements and powers of protection and blessings.

But just how were ancient civilisa­tions able to mimic the natural ob­servations around them into complex symbolic design? It all starts with the humble circle.

All other geometric shapes can be determined from a circle with the use of only a compass (or string) and a ruler (straight edge).

By starting with the vesica piscis (a shape formed by the intersection of two circles with the same radius, intersect­ing so that the centre of each circle lies on the perimeter of the other) one can produce an equilateral triangle, hexa­gon, pentagon and square.

The exterior angle of the Great Pyr­amid of Giza, built over 4,500 years ago, can be calculated with the vesica piscis. The figure of Pi is equally to be found in the dimensions of the Great Pyramid several times, including the height/perimeter ratio of the pyramid itself.

Egyptian mathematicians recorded The Sacred Mean (Phi), presenting a figure of 3.16 in the Rhind Papyrus, which was written 600 to 800 years later and was far cruder than the pre­cise ratio the Great Pyramid architec­turally presents.


More sophisticated use of the vesica piscis led to the ad-triangulum, a system of Masonic Geometry in use throughout the Middle Ages into Re­naissance times, and used to design many of Europe’s greatest cathedrals.

The Sacred Mean (also known as the Golden Ratio or The Divine Propor­tion) is a mathematical constant which is visible across the spectrum of the natural world. It defines that there is a constant ratio between measurable quantities of any kind. Leonardo Da Vinci used these principles to produce his famous image of the Vitruvian Man, sectioning the human form into a measurement of ‘cubits’ which are related. For example, while the body is four cubits high, it can be seen on the same body that one cubit is both the length from shoulder to shoulder and from elbow to fingertips. The same rules apply throughout the dimensions of the human body.

One of the mathematical products of this mean is the spiral, again found throughout nature. The Sacred Mean is also observed in the geometry of the pentagram and its associated penta­gon, where the ratio between the sides of the pentagon and its extension into the pentagram also demonstrate a ratio of Pi. The design has been used in ancient times as a Christian sym­bol for the five senses, or of the five wounds of Christ, and also in witch­craft as a symbol of spiritual shielding.

Further sophisticated play with the humble circle produces ‘The Flower of Life’ symbol, a geometrical figure com­posed of multiple evenly-spaced, over­lapping circles. They are arranged to form a flower-like pattern with a six-fold symmetry, similar to a hexagon. The centre of each circle is on the cir­cumference of six surrounding circles of the same diameter. The Flower of Life is considered to be sacred among many cultures around the world. It can be found in architecture through the ages, in the Kabbalah’s ‘Tree of Life’, through to the dimensions of the Stonehenge prehistoric monument in Wiltshire, England, dated to 3000 BC.

And from the Flower of Life symbol 3D form or ‘solids’ can be generated. Extending from the exact same shape and angle, one can create the star tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron, col­lectively known as the Platonic solids. The Greeks taught that these five sol­ids were the core patterns of physical creation, and are now realised to be intimately related to the arrangements of protons and neutrons in the ele­ments of the periodic table.

From the micro to the macro, ge­ometry is inherent. The mathematical harmony of the universe is visible in the proportions of the planets of our own solar system. The diameter of the sun is the same as the perimeter of the square of the moon.

The ratio of the Sacred Mean can also be seen in the rotations of Venus and the Earth around the Sun so that for each five years that Earth rotates around the Sun, Venus manages to orbit it eight times. The result of this motion is that Venus ‘draws’ a penta­gram around the sun with its orbit­ing meeting points with the Earth. Spooky, huh?

Well, yes and no. In the debate of whether or not an all-powerful creator exists, it could easily play into both camp’s debate. It would seem reason­able to an atheist that our life is due to no more than a strict set of mathemati­cal rules, and yet the sheer beauty and complexity borne out of such simple founding ratios cannot help but make us wonder on the possibility of con­scious intelligent design.

For many this is the observation of the god that is nature, and it’s the only one in my canon.

One thing’s for sure. Any secret, villainous plans I had to become the powerful ruler of my very own uni­verse has been well and truly scup­pered. I was always shockingly abys­mal at maths.

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BosysurfNaiHarn | 14 April 2019 - 14:16:09

A very fun read. Thank you, David. One small correction though...rotate means to spin on one's axis. Both the earth and venus REVOLVE around the sun.

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