While 4320 is different numerically from 4321, the 1 and the 0 were understood as equivalent. They represent the duality of manifest and unmanifest – two phases of one principle underlying. In Buddhism, sunyata or the Void is the source of all things. It is mysterious to us and looks like nothing, a void, 0. But it is teeming with potential forms and from it comes all that is manifest, a quantity, 1.

4321 manifests in the Hindu system via the division of the caturyuga by dividing it by ten and then multiplying that quotient by 4, 3, 2 and 1.

Amazingly, the Pythagorean tetraktys is numerically represented as 4321. Geometrically, it is ten points arranged in an equilateral triangle – a bowling pin arrangement as seen from above. What does it mean?

There were four levels of study of the tetraktys that was popular during the Renaissance called the Quadrivium.

Level 1 of the quadrivium is arithmetic. 1+2+3+4=10 and 10 encompasses all numbers from 0 to 9. Buddhism has a doctrine called the 10 Worlds and there are 10 sephira on the Qabalistic Tree of Life.

Level 2 of the quadrivium is music. 4321 describes several important musical intervals. 1:2 is the octave. 2:3 is the perfect 5th. 3:4 is the perfect 4th.

Level 3 of the quadrivium is geometry. 1 is the point—dimensionless, infinitely small. 2 such points can be connected by a line. 3 points form the simplest plane which is the triangle since a plane cannot be drawn with less that 3 points. 4 points constitutes the simplest volume which is a tetrahedron. A tetrahedron is essentially a pyramid composed of identical equilateral triangles making 3 sides and a base. It is the most surface area enclosing the least amount of space. Our simplest molecules, for examples, are tetrahedronal. R. Buckminster Fuller in his book, Synergetics calls the tetrahedron universal and all-space filling. Science uses the cube to fill space (hence "cubic" space) but the tetrahedron actually works better (e.g. renders Planck's Constant as an integer). Tetrahedrons are far more stable than cubes.

Level 4 of the quadrivium is astronomy/physics. 4321 represents the dimensions we occupy. 1 dimension is the same as no dimensions because 1 and 0 in this system are equivalent. 1 is the potential of motion. 2 dimensions is motion on a flat surface where "up and down" do not exist. 3 dimensions is motion within space. 4 dimensions represent time which is motion along the time axis of the space-time coordinate system. 4321 also represent the four primal elements of earth, wind, fire and water. Level 4 is a unity of the other three with the addition of temporal motion (time).

The 4 levels culminated in a 5th more esoteric level (think of a pentagram where the 4 lower points are the elements and the 5th upper point is quintessence or spirit). This level is called dialectic. 1 is the Monad, the indivisible. 2 is multiplicity, the Dyad which represents the duality of existence. 3 is the Triad representing the 3rd agent that arises to harmonize the duality. 4 is the Tetrad representing stability, solidity and matter. At this level, we are being given a layout of the universe we build within when we take in data from the external world and synthesize it into a worldview. 1 is the raw sense data we take in without judgments, 2 is the inevitable split into duality that is a result of our consciousness which is itself a duality of perceiver and perceived, 3 is the harmonizing of the duality in an attempt to understand the world, 4 is the mental creation of the world of matter that we see around us.

But the shape of the tetraktys is the triangle, of the many signs of the Triad to be found among ancient societies and spiritual systems the world over. The triangle depicts two descending from the One. The Dyad from the Monad. All three are united forming the Triad. The Triad is the harmonizer. Indeed the 3 uniting the 2 gives us our familiar 3:2 ratio of the perfect 5th, the ultimate basis of all harmony, of all music. If geometry is frozen music as the Pythagoreans stated, then music is liquid geometry.

The 4321 arrangement of the tetraktys is the physical manifestation of existence but its triangular shape is the hidden pattern underlying. The very heart of the Mystery.