So, for example, I like the above analogy of the fountain, with the water flowing trough each sephiroth ... but does that explain the sephiroth themselves ... and WHY each one has the function it does.
I might depart from Jewish Kabbalah a bit and get into some ' number concept progression - another , more 'mathematical way' way of looking at it.
Lets just see the Sephiroth as their numbers ( Kether 1, Chokmah 2, etc )
(this is a cut and paste from a longer post I put up elsewhere here somewhere. ) .
In some traditions numbers are not just symbols that tell us how many of a particular thing there are but can be seen as divine emanations.
In simpler form it goes something like this;
1. The original primal unity. Some call it God - at the stage of God before creation.
Others call it pure Self or pure Being. In cosmology it represents the singularity before the ‘Big Bang’. In geometry, it is represented by the ‘point’. (In the Thelemic/Thoth system {which uses Ancient Egyptian Gods and symbols as metaphors} this is symbolised by the point or disc i.e. the Sun or Hadit.)
2. There doesn’t seem to be much of a definition so far, as definition has not come into being. Concepts like self or even God require some level of awareness of the self or being, that is, it is postulated that being or self will have self-awareness.
This concept or awareness of the self or being, is a little different from the idea of self on its own. The idea of self, on its own, ‘implies’ awareness of self, one has within it the potential for two, duality, i.e. the self 'itself' and the contemplation of or awareness of self.
Now we have two concepts; the self and the self’s idea of itself. Subjective and (to an extent) objective. To contemplate the self requires one to ‘step outside’ of the self and ‘look back’ at the self. In geometry this is symbolised by ‘the line’. [This ‘dimension’ is perhaps the basis of the components of matter and energy; In the 1980s, a new mathematical model of theoretical physics called string theory emerged. It showed how all the particles, and all of the forms of energy in the universe, could be constructed by hypothetical one-dimensional "strings", infinitesimal building-blocks that have only the dimension of length, but not height nor width. (In the Thelemic system this process is seen as a moving point, and symbolised by the winged disc)
3. As one implies two, two implies three. Via the process in 2 a new view is formed, a ‘new’ view of the self as gained by contemplation or awareness of the self. [Or the vibration of the ‘string’ forms a ‘particle’ or ‘energy field’.] Something has been gained, even if it is ‘just’ internal experience.
In geometry this is symbolised by the concept of ‘surface’. It is also represented by the triangle. The triangle represents structure, order and form, definition and rigidity. It represents either; Singularity further explained by its polarities or a mediating ‘middle path’ between two polarities. With 3 ‘space’ has been created; up/down, left/right, forwards/backwards. But it is still a 'concept' in the ideal world.
Now we begin to see how maps of 3 can be useful; The three Gunas – rajas, satvas and tamas, the three alchemical principles – sulphur, salt and mercury, The Holy Trinity – Father, Son, Holy Spirit, the three primary colours – red blue yellow and many other things like; Yin, Yang, Tao, even in electricity – positive, negative and current or temperature, moisture, light or Mother Father Child (to cut through all the mythic terminology).
(In Thelema the ‘product’ of Hadit and Nuit {who represents zero or the circle – whose radius is infinite as Hadit represents the point or centre of the circle, which is located everywhere} is Ra Hoor Khuit; motion or ‘force’. See The Aeon Card )
But with three we are still in the realm of idea, or the ideal world. It is a little beyond our normal comprehension and experience (which is why people have always used symbols, like maps or hieroglyphs or gods). Next we cross the Abyss, from this triangular relationship of 'ideal' or divinity .
On the Tree of Life of the Qabbalah this ‘Supernal Triad’ lies above the ‘Abyss’.
Energies ‘travelling’ into manifestation pass through the third Sphere, Binah and become formulated, solidified, restricted and directed to become further manifest in the fourth realm. Alternatively, energies travelling ‘up’ the Tree, towards duality, unity and beyond, become liberated from form and restriction and Binah becomes a realm of liberation. [In the realm of physics this is the 3-D world of matter.]
4. Basically, 4 , Chesed / Jupiter is an expansion - not of everything, but of the things formulated by 3 / Binah. As two implied three, three implies four. The energies manifesting in four take on the ‘principles of four’ and are able to operate in a word of ‘double duality’ (2 x 2).
Although many systems use the map of 4 it has its roots in 3 and extensions to 5. In four we have the map of the 4 elements; fire, water, air, earth, the four suits of the Tarot, the four worlds of the Kabbalah and many more .
Four brings the concept of space from the 3 (up-down, left-right, forwards-backwards) which define space. The 4 is the result, ‘space’ itself. In physics it represents the concept of time.
5. Five moves more into the world of action ( or Chesed - 'force' ) . One analogy is the pyramid; the four sides can be extended up into the point. We can get the idea of motion and action. It can also relate to the pentagram; the four elements and spirit. Some traditions have 5 elements, either including ‘spirit’ as an element or adding an element such as wood or metal. In physics this is the idea of motion.
6. Six solidifies the manifestation of the second triangle. It can be represented as the hexagram; two superimposed triangles, one pointing up, the other down. It can represent the four elements and spirit, with spirit in its duality of active and passive, or the four elements, their origin in spirit and their connection to ‘earth’.
[ “Height, width, and length constitute three-dimensional space, and time gives a total of four observable dimensions; however, string theories initially supported the possibility of ten dimensions – the remaining six of which we cannot detect directly. This was later increased to 11 dimensions based on various interpretations of the ten dimensional theory that led to five partial theories ... Super-gravity theory also played a significant part in establishing the necessity of the 11th dimension.” (Wikipeadia). The relationship of this model to the Qabbalistic model of 10 spheres of Creation (with an 11th and ‘hidden’ sphere – Daath, situated in the ‘Abyss’) and its manifestation through the 5 elements is an interesting correlation but beyond the scope of this post.]
One thing to point out is, so far, I have been quiet lineal. There are concepts that relate to reflection (or refraction), that is, the Supernal Triad on the Tree of Life reflects through (or on the waters of) the Abyss and makes another downward pointing triangle (the first triangle implies a second, as 1 implies 2) and of course this requires a third triangle, and all three come together in the manifest realm, to make the 10th sphere of the Tree of Life.
But there is also the idea (of lineal manifestation) within this system of the Lightning Flash, where the energy travels from 1 – 10.
[ The article then goes back to examine these numbers in greater detail - concentrating on the move from 3 to 4 .... the crossing of the Abyss, the 'ideal' manifesting towards 'the real' . ]