Of the seven liberal arts and sciences, Geometry holds a singular position in Freemasonry: it is not merely one of seven equals but the supreme science, the foundation on which the entire superstructure of the Craft rests. The Fellow Craft lecture states it directly: "Geometry, the first and noblest of sciences, is the basis upon which the superstructure of Freemasonry is erected." Every Masonic symbol is a geometric symbol. Every working tool is a geometric instrument. Every lodge is a geometric space. The letter G that hangs in the east of every lodge — above the Worshipful Master's chair, within the blazing star — stands simultaneously for Geometry and for God: because in the Masonic tradition, these two words point to the same reality. The universe is a geometric construction, and the mind that understands Geometry is approaching the mind of the universe's architect.
The letter G suspended in the east of the lodge — within or adjacent to the blazing star, always in the most honoured position in the room — carries three simultaneous meanings that Masonic tradition weaves together deliberately:
Geometry — the mathematical science of form, proportion and spatial relationship that is both the operative craft's primary tool and the speculative Craft's primary symbol. Without Geometry, no building can be designed or constructed. Without Geometry, no Masonic symbol can be correctly understood. The letter G marks Geometry as the centre of the lodge's intellectual programme. God — the Supreme Being whose existence Masonry requires of every candidate, regardless of which religious tradition that belief takes form in. The lodge is not a church and takes no position on theology, but it insists that the Mason acknowledge a higher power. The G in the east places that acknowledgment at the centre and highest point of the lodge's visual field. Grand Architect of the Universe — the specifically Masonic title for the divine: not the God of any particular tradition but the cosmic intelligence that designed and built the universe — understood, in the Masonic framework, as a geometer, a builder, a craftsman who worked according to mathematical principles. The Grand Architect title, introduced into Masonic use by Elias Ashmole in the 17th century and borrowed from Calvin's earlier theological usage, expresses the Masonic conviction that the universe is a designed artefact and that its design is geometrical.
The Blazing Star: the blazing star in which the letter G is often displayed is one of Masonry's most ancient and multi-layered symbols. At its simplest, it represents the sun — the source of light and life, the master luminary that governs the lodge's orientation (East, where the sun rises, is where the Worshipful Master sits). In higher-degree Masonry, the blazing star is associated with the star Sirius — the star whose heliacal rising marked the beginning of the Egyptian year and the annual Nile flood; the star associated with Isis and with the divine knowledge that descends to humanity. In still other interpretations, the blazing star is the five-pointed star — the pentagram of the Pythagoreans, the geometric form produced by the golden ratio, the symbol of the human body in Leonardo's Vitruvian Man. All of these interpretations converge on the same point: the blazing star marks the presence of cosmic order — geometric, astronomical and divine — at the centre of the lodge.
The Compasses — one of the three great lights on the altar, the jewel of the Senior Grand Warden — are Geometry's working tool and one of Masonry's most immediately recognisable symbols. The operative compasses were used to draw circles, to transfer measurements and to describe arcs: the fundamental geometric operations of design. The speculative meaning extends this practical function into a complete moral philosophy:
The Compasses circumscribe a circle — they define a boundary, marking out a specific area from the infinite space available. In Masonic teaching, the Compasses symbolise the moral boundary that the Mason draws around his desires and ambitions: "to circumscribe our desires and keep our passions within due bounds" is the explicit Masonic teaching associated with the Compasses. The person who can draw a circle — who can define a clear boundary between what is within and what is outside — is the person who can define the limits of acceptable conduct and maintain them under pressure. Geometry's circle is Ethics made spatial.
The Compasses and Square together — combined in the central Masonic emblem visible on every lodge building, every apron and every ring — represent the integration of Geometry and Logic: the science of form (Compasses) combined with the instrument of right angle (Square). Together they produce the complete working toolkit: the ability to design and the ability to build truly. Together they also represent the integration of heaven and earth, spiritual aspiration (the Compasses describe the arc of the sky) and material rectitude (the Square confirms the earth's perpendicularity). The central Masonic emblem is Geometry meeting Logic at the point where design becomes construction.