Nature is Mathematics patent. Mathematics is Nature latent. Mathematics is primal. Nature is produced.

The modern academic study of phenomena (curriculum) grew helter-skelter from a four-part curriculum developed in the Greek cultural areas during the 4th and 5th Centuries BCE. That curriculum was called Quadrivium. It was used throughout the Mediterranean world, including to North and East Africa, which were Greek areas long before Alexander's time. Roman teachers subsequently amended Quadrivium to seven parts, calling their configuration Septivium. By custom, Quadrivium is attributed to quasi-Pythagoreans, Plato and others. But this is a careless attribution. Pythagoreans of that era were both reticent and renowned for setting decoys to draw the curious into fruitless endeavor -- away from themselves. Quadrivium was developed by pseudo-Pythagoreans, whose number included Plato, not by quasi-Pythagoreans.

Pythagoreans were monastics religious. They were private and vegetarian. Silent. They established the principles of the professions (law, medicine, priesthood) and of the arts (engineering, music, drama, iconography). They collated and preserved the Sacred Scriptures.

Pythagoreans supported those they taught or treated and, on principle, took no compensation for teaching or curing them. They attended only those determined to learn, and these they accepted regardless of their condition of birth.

On principle, a monastic propagates wisdom freely, without charge, so confident are they of their holding. This principle is illustrated by the Hippocratic Oath, which is the Pythagorean formulation of the medical profession. (This Oath, incidentally, prohibits iatrogenic abortion and euthanasia.)

Pythagoreans were not academicians per se, although they engaged in academic activities. Academicians, such as Plato, admired them and relied on them for curriculum content. However, academicians are not monastics. They are not seasoned and deepened by renunciation as monastics are.

The Pythagorean study of phenomena (curriculum) was expressed by the Star Pentagram, the emblem of the Order. It was a five-fold study reflecting the five-fold nature of the Universe, which is combinations and permutations of the five Elemental Principles: Ether, Air, Fire, Water, Earth.

Pythagoreans placed before academicians, such as Plato, a decoy called Quadrivium. This was a curriculum of four-fold nature, reflecting four Elementals, Air, Fire, Water, Earth, and absenting the first one, Ether. The ruse worked.

Plato, following 'Pythagorean tradition,' calls Ether the Fifth Essence (Quintessence) and takes it for the logical type, Unity. That is, he takes Ether for a logical type different from that of the other four Elementals -- Air, Fire, Water, Earth. In fact, all five Elementals, including Ether, are of the same logical type, Multiplicity. Plato takes Ether as superior to the Elementals, as of the logical type, Unity. He takes the mundane for something it is not -- the supra-mundane (Unity). He is followed in this error by many Alchemists and Freemasons.

This error of systematization or construction signals the presence of a grave defect in Platonic epistemology, a defect that we should expect will deform Platonic philosophy in toto. It does.

Ether is the first essence (Elemental), not the fifth. It is of the same logical type as the other
Elementals, namely, Multiplicity.

Ether has been mis-taken, by Plato and others, both cosmologically (male aspect) and ontologically (female aspect). Endless confusion and perfidy have gone down through the ages as a result. We may assert that Pythagoreans intended as much!

Over the centuries, Quadrivium has undergone scission motivated by hope of supplying its deficiency. The result is an omnium gatherum without hope of integration because Quadrivium, Itself, is an inadequacy.

Behind any discussion of education reform is this matter of correcting the structure of the study of phenomena by reinstating its first element, Ether. This is a quid pro quo. In place of the Pythagorean decoy, we could employ the Pythagorean Archetype, which is Five-ness.

It is called Quintivium: The Integration of Inquiry. Quintivium is the correct study of phenomena reflecting accurate cosmology and ontology and being appropriate for all grades and manner of student. Quintivium is a reacquisition of archetypal Indo-European structure through a study of phenomena, through empirical study.

Quintivium embodies the five Elemental Principles, Ether, Air, Fire, Water, Earth. It embraces the five essential activities of culture, Seeing, Teaching, Guarding, Producing, Crafting. Its comprehension declares the great principle of the Universe: Non-Dualistic Philosophy. It asserts that all beings are brothers and sisters in the same family, belonging to God the Father and Nature the Mother.