The Quadrivium, a fundamental component of the Seven Liberal Arts, encompasses four key disciplines: Mathematics and Science, expressed through Geometry, Music, Cosmology, and Pure Number. Rooted in the teachings of eminent philosopher Plato, this ancient concept emphasizes the importance of studying numbers as a means to unravel the hidden principles that govern our universe. In this article, we will explore the fascinating interconnections between these disciplines and their profound implications.


The Quadrivium consists of Mathematics and Science through Geometry, Music, Cosmology, and Pure Number. These subjects were considered essential by Plato to understand the Universe. Geometry describes numbers in space, while music reveals the harmony of numbers in time. Cosmology explores the relationship between numbers and planetary motion, and pure number forms the basis of all natural laws. These studies were believed to have divine origins and offer insights into the nature of reality.

Geometry: Numbers in Space

Geometry, derived from the Greek words for “earth” (Geo) and “to measure” (metri), holds the key to understanding numbers in space. Originally practised by using sticks and strings to create perfect circles in the sand, modern geometry now employs precise tools such as the drawing compass and straight edge. The application of geometry extends beyond measurement; it reveals inherent relationships and ideal archetypes that transcend scale. These concepts, often termed Sacred Geometry, hint at the intrinsic interconnectedness of all things.

Music: Numbers in Time

Unlike geometry, music unfolds in the dimension of time and is perceived through the sense of hearing. The harmonious arrangement of musical scales is closely linked to geometric principles. Nature’s cycles, from birth to decay, echo the concept that all emerges from the harmonious relationships of numbers. Simple numerical ratios, such as the division of length producing octaves or fifths, define the pitch of musical notes. By understanding these foundational principles, we gain insight into the underlying rhythm of the universe.

Musical keyboard and the fractal geometry of the square and triangle

As we can see from the images above, music and geometry are intimately connected. Nested triangles generate the octave and musical 4th, whereas nested square produce the musical 5th. From these divisions, the 12 notes of the musical scale are created. The notion of 7 white note and 5 black notes on the musical keyboard are also represented by the number of circles found in these 2 nested shapes.

In the Geometric Universe of this concept of music is found to structure light, and the periodic table. Thus, it is so great significance in resolving the most challenging scientific paradoxes of our modern age.

The concept of geometry and time is unified further when we consider forms in the 4th dimensions and above. This produces the notion of 4D time, expressed by the rotation of a higher dimensional polytope on its time (w-axis). Key examples are the torus field and 4D hypercube, or Tesseract.

horn torus
tesseract rotation

Through our examination of 4D forms, we have produced an alternative solution to the Ultraviolet Catastrophe, and Photoelectric Effect, which paves the way for a new geometric understanding of time, and reveals how we are able to extract free energy from the vacuum of space.

Numbers in Space-Time

Whilst the notion that time and space are inseparable phenomena is often attributed to Minkowski at the beginning of the 1900s, ancient texts, including the Vedic scriptures, reveal this same truth. The interplay of planetary motion and time-space cycles showcases the intricate connection between numbers and the fabric of the universe. Plato himself associated time with the motion of celestial bodies. Through the study of cosmology, or Solar Geometry, we can unveil universal truths about the nature of reality, deeply embedded in the movements of heavenly bodies. In more recent time, Johannes Kepler through his exploration of planetary motions suggested that their spacing can be ascribed to nested sets of Platonic solids. Whilst discredited by modern science, due to the elliptical nature of their orbits, we find that by taking the mean orbit a very close match is produced. The theory of Solar Geometry thus offer a fresh comprehension of the nature of gravity, that can be extended into both the galactic and quantum worlds, where present gravitation theory fails.

Explore the theory of Solar Geometry and Geo-gravitation

Pure Number: Unveiling Divine Origins

Pure Number, the most mysterious aspect of the Quadrivium, eludes the grasp of our senses and lacks direct appearance. Yet, it serves as the foundation upon which all laws of nature are expressed. Modern mathematicians and scientists often perceive numbers as human constructs. However, ancient philosophies considered mathematical objects to possess divine origins, independent of human conceptualization

At the foundations of the Geometric Universe is our new theory of number. Geometric Maths resolves for the first time the problem of the Continuum Hypothesis, which radically shifts the axiomatic foundations of mathematics, by resolving the paradoxes of infinity expressed in the nature of set theory. This leads to a new comprehension of numerical space, which is able to solve the most challenging problem of mathematic in the present age, the Reimann Hypothesis.

Solving Infinity

A new mathematical theory that revolutionises the concept of number, resolving its infinite nature

The study of Pure Number surpasses mere arithmetic, delving into a contemplative realm that reveals profound insights about our existence as part of a unified whole, yet endowed with individual free will.



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The Quadrivium, encompassing Geometry, Music, Cosmology, and pure Number, opens the gateway to understanding our universe through the mystical language of numbers. By exploring the mathematical underpinnings of various disciplines, we uncover the interconnectedness of all things. As Plato postulated, the study of number leads us to the essential principles of reality. Embracing the Quadrivium equips us with a profound perspective, fostering a deeper appreciation for the awe-inspiring wonders that surround us.

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Metaphysics is a branch of philosophy that deals with the fundamental nature of reality, including the relationship between mind and matter, the nature of consciousness, the existence of free will, and the ultimate nature of the universe. It attempts to answer questions about the nature of reality that go beyond the physical and empirical realms of science.

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