Descartes' Church - Sold
405 x 405 mm
Archival Ink on Textured Fine Art Paper

How does the physical structure of a church connect with the human soul?

This question formed the basis for the paintings in this body of work.

Descartes' Church

The Greek mathematician and philosopher Pythagoras is well noted for his quote "God is ever a geometer".

It is this consideration that has drawn many minds to reflect upon the connection between the spiritual and the physical. In 1638 Descartes first described the logarithmic, or equiangular spiral by the equation r = ka which relates the polar co- ordinates of any point in the spiral and expresses an exponential growth pattern. In nature it is usually associated with the growth of dead tissues forming structures like the shells of many invertebrates, corals and several horns found in mammailian species.

Question: Is a church like a beautiful nautilus shell in that its architecture may arise from some sacred geometric design?

The painting Descartes Church arose from considering how the structure of a hollow nautilus shell might reflect the empty murmurings and hypocritical posturing of people who enter the skeletal structure of a church. Pythagoras and his Order, and later, Plato and his Academy, raised geometry to a sacred science of discovering the nature of reality and through it the Deity. Plato is quoted in the statement "Geometry rightly treated is the knowledge of the eternal" and "Geometry must ever tend to draw the soul towards the truth". These ancient philosophers considered geometry to have the power to lead the mind from the world of appearances to the contemplation of the Divine Order. It is this thinking that is behind Descartes' Church

Euclid's Flower  NZ$990
405 x 405 mm
Archival Ink on Textured Fine Art Paper

Euclid's Flower

This painting has its roots in an investigation of geomancy, or gematria, the science of using the ancient method of feeding our planet with the life giving influences of cosmic forces.

From the building of the old testament tabernacle, to the pyramids of Egypt, from the prehistoric massive structures of South America to the laying out of the sacred sites such as Glastonbury Abbey and the stone circles such as Stonehenge, a question arises about their designers possession of a science that is now almost completely denied to us. Geomancy is a seeing of numbers in relation to letters, and a working out from this the sonic power structure of the universe. It involves the concept that numbers are not just separate amounts but when certain numbers are combined with certain others a power is released - a kind of cosmic engineering if you wish. This method was the essence of Pythagorean law, and this is why mathematics was considered a sacred art.

Pythagoras considered five to be the number of man, because of the fivefold division of the body, and the ancient Greek division of the soul. According to Pythagoras, the five points of the pentagram each represent one of the five elements that make up man: fire (energy), water (fluid), air (breath, earth (matter) and psyche (mind). Pythagoras chose the five-pointed star, the pentagram, as the emblem for his fraternity. At each point of the star was a Greek letter which all together spelled a Greek word meaning "health" (ugitha).

Now enters Euclid and his systemically presented knowledge of geometry in his work "Elements", beginning with five unproved principles about lines, angles, and figures, which he called postulates. These five postulates became the foundation for plane geometry, the study of any flat surface that extends in all directions.

Postulate 1: Any two points can be joined by a straight line. Could this mean that two people separated by race, religion, age, sex or culture can be directly connected and share an understanding of each others position, recognizing their own individual point of view yet realizing that we are connected to all other points, or people.

Postulate 2: Any straight line segment can be extended indefinitely in a straight line. Could this mean that our life span here on earth is like a line segment, just a tiny fragment of eternity, which allows us to be connected to divine time and truth.

Postulate 3: Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as centre. Could it be that if our life span is represented by the line segment then the prescribed circle defines our lifetime and all we put into it. Considering the idea that a line segment can extend indefinitely in a straight line, then just how big can we make our lives?

Postulate 4: All right angles are congruent. If two shapes have the same shaped and size, but are in different positions they are still deemed congruent. That is, one can be transformed into the other by moving, rotating or flipping it. Congruency has its counterpart in the equality of numbers. The number 5 is still the same whether it is written as 4 + 1 or 3 + 2 or any other infinite combination of numbers. Could it be that all the people on earth are congruent with respect to equality for a number. Could all our various parts and differences simply be the fractional parts of the same number. What if that number was God? 

Postulate 5: The famous Parallel Postulate. If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. Put another way, (with reference to the diagram), for two dimensions, that given a line L, there is exactly one line through P that does not intersect L. That is to say it is parallel to L
For two thousand years, many attempts were made to prove the parallel postulate using Euclid's first first postulates. The main reason that such a proof was so highly sought after was that the fifth postluate wasn't self-evident, unlike the other postulates.

In mathematics, hyperbolic geometry is a non-Euclidean geometry, and has been used to demonstrate that the parallel postulate of Euclidean geomety has been replaced.

In hyperbolic geometry it has been shown that here are at least two distinct lines through P which do not intersect L, so the parallel postulate is false. Models have also been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid.

To the ancients, the parallel postulate seemed less obvious than the others (verifying it physically would require inspecting two lines to check that they never intersected, even at some very distant point, and this inspection could potentially take an infinite amount of time).

What all this implies is that mankind has spent much time and thought on trying to apply logic and reasoning to something that perhaps steps outside these parameters. Maybe, at this point, we enter the realm of eternal truths and begin to know the wisdom that has been given to us from other realms. Opening this book of knowledge is not chosen by all.

Parting on the Square  NZ$990
405 x 405 mm
Archival Ink on Textured Fine Art Paper

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Parting on the Square

This painting is the result of thinking about how symmetry and proportion are fundamental elements of geometry and to the architects who use them. The ancient Roman architect, Marcus Vitruvius, believed that builders should always use precise ratios when constructing temples. In his famous treatise De Architectura he wrote, "For without symmetry and proportion no temple can have a regular plan". The proportion Vitruvius recommended was modelled after the human body. He observed that all human beings are shaped according to a ratio that is astonishingly precise and uniform. Eg. Vitruvius found that the human face equals one tenth of the total body height. The foot equals one sixth of the total body height and so on. Scientists and philosophers later discovered that the same ratio Vitruvius saw in the human body, 1 to PHI (1.618), exists in every part of nature, from swimming fish to swirling planets. This ratio became known as the "Golden Ratio" or "Golden Rule".

Leonardo de Vinci studied Vitruvius' writings and made his famous "Vitruvian Man" sketch. He believed the workings of the human body to be an analogy for the workings of the universe. It is also believed by some that Leonardo symbolized the material existence by the square and spiritual existence by the circle. Thus he attempted to depict the correlation between these two aspects of human existence. The drawing itself is often used as an implied symbol of the essential symmetry of the human body, and by extension, to the universe as a whole. 

  The Medieval Master Masons who built the great structures of stone, the Gothic cathedrals, applied these ratios to their work. Interestingly these sites were imbibed with a feeling of peace long before Christianity designated these buildings as holy houses of God. Stone is the material of sacred buildings, and links to the concept that stone is the ancestor of all - but that is another story.

These great structures were based upon the builders working tool - the square. The square represents perfection. When the angles and sides are equal to each other there exists a perfect balance in all directions. When we feel a balance in our lives there is a harmony between our physical, mental and spiritual aspects - a sense of stability and strength exists, a foundation upon which we know we can build on.

The number four is associated with the square. The image of the square can be overlaid with eternal rhythms: the four seasons, the four cardinal directions and the four cardinal virtues of justice, fortitude, prudence and temperance. All of these give a stable measure and guide to help perfect our physical interaction with the world.

The painting "Parting on the Square" draws upon this background and from Freemasonry's belief that when we part upon the square, we go in different directions, but in full knowledge that our courses in life will be going according to the angle of the square (which means the right direction), until we meet again.