We removed a section of the new floor, and used red silk ribbon to mark out aspects of the geometry of the arched doorway. This elegant archway springs from principles established by the ancient Greeks, when grammar, logic and rhetoric; mathematics, geometry, music and astronomy were developed in close relation to each other.

The arch is a semicircle; an intersection of material experience and conceptual thought. Imagine a square. Join the mid point of its base to one of its top corners to make a right triangle. The hypotenuse is the radius of the semicircle. Where the radius touches the base, draw perpendicular lines upwards. Extend the top of the square as a horizontal line, till it touches these perpendiculars to complete a root five rectangle: the height is taken to be a unit of one, and the length is the square root of five.

The square plus one of the adjacent rectangles is a Golden Section, an aspect ration in which ‘the smaller part is to the larger as the larger is to the whole’. Held up for centuries as the paragon of universal harmony, the Golden Section was widely used in architecture, art and craft, including the Parthenon, Leonardo Da Vinci’s painting of the Last Supper, and the curve of a classic ship’s anchor.

Right triangles within the Golden Section give rise to the whirling square construction and logarithmic spiral structure found in nature at every order of magnitude, from sea shells to hurricanes, the relative positions and movements of the planets and the spiral galaxy of the milky way.

‘Fire Down Below’ is a novel by William Golding, which follows an epic sea voyage in the last days of sail. A momentous struggle unfolds between an experienced mariner and an enterprising officer, in which hope, tempered by patience and rectitude, collides with a sense of adventure born of curiosity and self-regard.