The Quadrivium accounts for 4 of the 7 Liberal Arts, representing Mathematics and Science through Geometry, Music, Cosmology and pure Number. According to the great philosopher Plato, the study of number was considered essential to understand the Universe, a divine language through which the hidden principles of reality could be uncovered.
Geometry Numbers in Space
The word Geometry has its root in Ge-meaning earth and metri which translates into to measure. Prior to the modern drawing compass, two sticks connected with a piece of string could be used to create a perfect circle. One end was hammered into the Earth and the other rotating around it, making a circle in the sand. The practice of Geometry was considered to describe numbers in space. Modern geometry uses a drawing compass and straight edge, that provides much greater accuracy at smaller scales.
In nature, we find patterns, designs, ratios, and structures that inevitably follow ideal geometrical archetypes. Similarly, the geometric principles create form without measurement, but instead manifest an intrinsic relationship that stays the same regardless of scale. This idea contains the seed that suggests everything is relative, which presents the underlying metaphysical principle of interconnectedness. That’s why, in modern times, it is often referred to as Sacred Geometry.
Music Numbers in Time
The construct of modern musical scales also have analogies in geometry. However, as music is sound organised in time, that we perceive through hearing and not with sight, it is less tangible, similar to time itself. Nature provides a constant repetition found in the cycles of life, that are created, sustained and then decay, through time. The central idea was that all arises from harmony of numbers, which provide the background for these cycle to be enacted. Harmony is composed of a set of frequencies that form simple numerical ratios. The pitch of a musical note is inverse to the proportion of the length of the string that produces it, e.g. the octave is expressed through halving, while a division into three creates the musical fifth. Understanding these foundations of music, is a valuable tool that enables us to conceptualise the underlying rhythm of the Universe.
Cosmology Numbers in Space-Time
The study of planetary motion is related to numbers in time-space. Long before the notion of time-space appears in Western Science, the notion that time and space are inseparable phenomena is found in ancient Vedic texts. Described as Yugas and Kalpas, time and space are enacted through cycles that repeat themselves at different scales of reality. The Greek philosopher Plato identified time with the period of motion in space of the heavenly bodies. Through the study of cosmology, we also term Cosmic Geometry, the heavenly bodies can revel Universal Truths about the nature of reality.
As the most elusive aspect of the Quadrivium, pure number avoids the detection of the five senses, and has no direct appearance by which it can be appreciated. Yet, it forms the basis through which all laws of nature are expressed. Most mathematicians and scientists today see numbers solely as a construction of the human mind. However, according to the ancient Greeks, Vedas, and other philosophical thought, mathematical objects exist independently of our being able to conceptualise them and were considered to be of divine origin. The study of Pure Number transcends the idea of Arithmetic. Within this study, we find a contemplative aspect that looks deep into our very being. Similar to Buddhist and New Age spiritual thought that declares, We are all ONE, and yet at the same time we are separate from each other as individuals who can act in accordance with our own free will.