A short piece on the Tree of Life and the Structure of the Solar System

Or a Mathematical Derivation of the Tree of Life

I have been working for a few years at expressing some of the structure of the Tree of Life from the perspective of mathematics and the measurable properties of the Solar System. In some ways it should be offered at the outset that the Tree of Life and its Spheres are, for some people, things that have no correlation to one object or even one celestial body as fully representative of the nature of its Spheres of Influence. The traditional model of the Tree of life comes in many slightly varied forms, and yet it also comes in some other ways as a curiously unaltered diagram of Perennial Wisdom and Practice. Some factors in its transmission as a diagram for spiritual progress and learning make it particularly difficult to talk about and explain. One of these factors is that it has been used to understand and remember many different types of things — some of which are very much about Spiritual Wisdom, Consciousness, and Angelic Beings and some of which are about processes and principles that govern the world around us and hold together the very building blocks of all matter in the universe.

It isn’t too strange to think that some of the earliest uses and developments of the Tree of Life consisted in thought experiments very much like what Einstein and many other physicists and scientists undergo to arrive at some understanding of a particular aspect of Nature which is out of reach. So if we are to construct a thought space of the Solar System conveyed in the form of a diagram how might we go about it?

For the purposes of this article I will concentrate on the Solar System and its structure to arrive at the very self same diagram of the Tree of Life. I don’t necessarily believe that this is somehow new information or that I alone have discovered it — mainly because I don’t believe that ideas come from individuals alone but from collective effort — -even when we are alone. To be sure I have never read an exposition of the type I am making, but I don’t claim that one doesn’t exist either. So for the purpose of clearly delineating a connection between Spirit and Science in a culture which has found it so very difficult… here goes something….

Orbits and Octaves

The most relevant aspect of the intersection of spiritual and scientific practice as regards the Tree of Life is the orbital distance of each of the planets as they cycle around the Sun.

Above I have included the basic data set of Orbital Distances of the Planets as compiled from the Information that NASA freely shares on their website. The strategy we will use here to make sense of this data is the musical concept of Octaves.

In music a note like A or C may be played in multiple registers. Usually they are numbered as in C1 or C2, etc. The idea is that even though the pitch isn’t the same because one C note is lower or higher than another C note, yet they have a certain resonance and harmonic which reinforces the one with the other and amplifies the signal in combination. It is important to note that each note must be played either at the same time or in phase with each other to get that amplifying and satisfying effect of harmony that we are all familiar with as chords.

In the solar system I am not sure that the “notes” have ever started off or played at the same time, but in terms of orbital distance the notes are always unchangingly and unceasingly “played” even though they certainly do waiver to various degrees in each case. One must realize as well that Western music is often cited as originating in and created as a mirror of the Solar System. Each key has 7 notes, and yet there are 12 notes in the range of an octave. This is very harmonic with the solar system as it was known classically as a 7 body system framed by 12 constellations.

If you take a look at the data offered above you see a figure for the average distance from the sun of each planet under its name at the top — as well as the closest distance each planet gets (perihelion), and the farthest distance (aphelion). These last figures are important to include because it shows how much a planet actually overlaps with the key or note of the rest of them, without needing to worry over how close each average is to the octave structure which runs through it.

For example, Mercury is shown to be somewhere around 58 million km from the Sun on average. Even so, Mercury’s orbit varies quite a bit more than many of the others. Yet the most relevant point here is the octave structure. To find this we must use a simple rule of math and musical structure: to find the octave frequency of any note’s higher or lower register (C1 to C2, say) you simply times or divide that frequency by 2. For 440Hz, or an A note, we have 220Hz as the lower register of A and 880 as the higher register of A. Applying this same rule you can arrive at the harmonic structure of the Solar System as expressed by Orbital Distance.

A basic map is this:

50–100–200–400–800–1600–3200–6400–12800

If you correlate the above numbers to the chart you can immediately see the overlap. It isn’t quite perfect as a first attempt as Venus, the Earth, Saturn, Uranus and Neptune stand outside the perfect octave, yet they are quite close in even the most clumsy attempt to put them all in an octave structure.

The pertinent point is: Is there a single figure that integrates so simply the whole solar system into the octave structure? I don’t know if there is. But I don’t think so, or at least I don’t find that as interesting as the way the Solar System actually functions in a musical manner.

Mercury exists in octave alignment with all the other planets listed except Neptune and the Earth. In fact, each of the planets except the Earth and Neptune reinforce the Octave of each other in the changes of their orbital distance through time. The other quite interesting thing is the way that the Earth and Neptune both are the perfect fifth to the Octave of the rest of this list of planets. This means that both the Earth and Neptune exist at the halfway point in the solar octave and that in some sense the Solar System plays the Primal power chord of harmony in its structure!

This is not to say that Mercury is the only one that unifies the Octave structure of the Solar system — also do Mars, Pluto and Eris — but it also points to the fact that there is no one point or figure that defines Stellar harmony in every case. Perhaps we are encouraged instead to regard that the Music of the Stars is just as organically created as life on Earth.

Music and Mapping

So what does this have to do with the Tree of Life?

If you look closely at the diagrams to the left you might see a very regular and geometric structure at work. Each of the circles exist in a regular grid structure, and yet there are 4 circles which exist in an in-between space compared to the 6 circles on the grid at the edges. The four which run through the middle are often attributed to Earth, Moon, Sun and the highest circle on the map was left unattributed classically because it takes a very good telescope to see past Saturn, which is the furthest planet visible in the night sky with the naked eye.

If you haven’t already guessed it, I would submit to place Neptune at the top as one of the bodies that do not orbit in the octave structure of the rest of the planets. The other question which you may be asking is: Why would the Sun be in that list of planets or bodies which aren’t a part of the one note scheme of the rest of the planets? The answer is because the sun is the center point of the system and is therefore at zero (or not a part of the scale) but reinforcing the harmonic of them all.

The other question which may be lurking in the shadows here is why put the planets in such a strange pattern? They certainly don’t configure in this way physically judging by the history of human experience, so why the weird diagram? One answer has to do with conveying the structure of the Solar System: even if it is impossible to convey the sizes and distances in a true to form relation to one another on a printed page, we can still try to convey some of the structure and harmony involved in stellar motions and distances.

The idea here is that the limitation of the printed page made for a special case of solution where the roughly circular nature of the orbits of the planets wasn’t adequate to the task of conveying something about their nature in printed form. Aside from that, there is a serious difficulty in mapping the solar system to scale in any art form that i know of. The reason has more to do with the vast differences of scale and the very much more vast distances involved even in our little neck of the cosmic woods. The Sun is approximately 1.5 million km in diameter, yet the distance to Mercury is roughly 50 to 60 times that. Mercury itself is but a fraction of either of those huge figures at 4879km in diameter. So if you set up a page to illustrate the scale and distances of the Solar system you wouldn’t even be able to see the planets or the Sun for that matter — they would be smaller than a dot from any ordinary pen or pencil you might find to use.

The tree of life might be described mathematically as a concept diagram (or group theory map) made to be of the order of a “graceful graph” (a graph that is capable of being legibly labeled) and in many versions it is also a “complete graph” or a graph where each pair of vertices is connected by a line or edge.

To clarify, the Tree of Life is a diagram that illustrates the structure of the known Solar System in a compacted and ingenious form. Each of the six spheres or points on the tree that run along the outer grid structure are part of the harmonic structure of the solar system which exists as a repeating and yet somewhat organic octave of the same note. Neptune and the Earth in the central column are the part of the Solar system which plays the other big note of the whole — the perfect fifth of the Solar octave. To be sure, Mercury and Mars change their tones more so than the others. But I don’t think it strange that they are known for being akin to the forces we work with daily to harmonize the chaos of life within our daily lives. Even though Mars is associated with War and aggression, he is also associated with acting through force of will in alignment with our highest values.

Hope you enjoyed this little run through of the geometric and mathematical aspects of the tree of life. I plan on adding to this as time permits. This is part of a series of writings and art on the intersection of scientific and spiritual traditions as a part of the Perennial Wisdom.