Pythagoras did not consider numbers as preparatory for study of Spirit; he regarded numbers as Spirit-in-itself. Here we see how a point replicates itself to gain dimension through relationship.
Geometry
The Division of Unity
The Principle of Alternation
The Golden Spiral
The Divine Proportion can create infinite diversity at all levels of the cosmos and accommodate growth without changing shape. It can be observed in physics, botany, entomology, zoology, anatomy and the double-helix of DNA. Artists and architects frequently use it in their work.
The Creation of Form
The Origin of Anthropos
Nature is a repeating pattern; human evolution includes all previous stages of incarnation, from geometry in conception and physical proportion, through the structures common to fish and birds during the embryonic stage, to the fully developed form which in its elemental composition and psychic realization is a microcosm of the universe: minerals as bones, vegetative life as sensation, animality in emotions, and the uniquely human thinking processes and creative soul potential.
Endless Cycle of Phenomenal Appearances
Brahman (Spirit) is the elements, which in their various arrangements give rise to all forms; Brahman never dies and never changes, although the atoms belonging now to an apple will soon become part of my body and in breathing out carbon dioxide released in digestive processes, it will later be absorbed in a tree and recycled into another fruit. Therefore, there is only changeless change and multitudes coming into Life for a moment of eternity then passing away. Only Brahman is Real.
Astronomy
The Elements
Beginning with vibration and resonance, "electrons" unite with "protons" to form atoms, which unite to form molecules, which eventually become tissues, organs, organisms, and the material cosmos. The Elements can be categorized into many different chemicals and minerals based on wave-frequency, but in alchemical spirituality, it is easiest to think of them as five: Ether (which is Space itself) and the four Elements that derive from it: air, fire, water, and earth.
The Planets
In classical philosophy, only the planets visible with the naked eye were considered part of the Solar System, but since the invention of powerful telescopes, the modern scientists include Uranus, Neptune, and sometimes Pluto. Through thousands of years of correlative witness, each of the planets and astronomical bodies has been ascribed attributes and effects in personal and social life depending on its movements and comparative position. Though some skeptics are quick to dismiss such observations, consider the moon's power in ocean tides and fertility cycles. The links between stellar activities and life on Earth is undeniable; in fact, the ancient astrologers were among the elite of society and often served in the secret councils of kings.
The Zodiac
Over long periods of time (almost 26,000 years), the sun's position appears to change position in the sky due to the angle of Earth's rotation. This is called the Precession of the Equinoxes. An annual calendar has been linked to this phenomenon, and like the planets, correlations with constellations have been observed with effects in personal and social life. The ancient scientists concealed their knowledge and wisdom in myths based on the relationships they witnessed in the heavens.
Music
The phenomenal cosmos functions by sympathetic vibration; thus, the science of sound is useful in unveiling the mechanics of Creation. In nature, music is evident in circadian rhythms, bird calls, whale songs, and even in the harmonic arrangement of the planets around the sun (the music of the spheres). Language has its origins in song.
The functions of music in society: 1) emotional expression; 2) aesthetic enjoyment; 3) entertainment; 4) communication; 5) symbolic representation; 6) enforcing conformity to social norms; 7) validation of social institutions and religious rituals; 8) contribution to the continuity and stability of culture (through persuasion of norms); and 9) contribution to the integration of society (definition of group boundaries and coordination).
Music helps to: 1) control aggression; 2) facilitate courtship; 3) display identity; 4) relieve anxiety; 5) promote co-operation; 6) hype. Music can be an effective healing therapy.
The culture industry uses music as a tool of mass deception. By selling trivial escape fantasies and exploiting neurotic stupidity, the entertainment business takes away the authentic voice of the people and commands obedience to the patterns of aesthetically-degraded mass society.