Shapes and Sequences as Families of Numbers

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Most people are familiar with the idea of "reducing" a number to a single digit to find what number-family it belongs to.

For example 597 reduces to (5+9+7) 21, the 21 reduces to (2+1) 3. So 597 belongs to the family of the 3, within the sub-group of the 21.

That gives us a general classification for any number, showing a broad environment in which we can do a specific interpretation of the unique higher number.

There are other families of numbers which have stronger bonds than simple reduction. These strong families are derived from geometric shapes and mathematical sequences.

Last month we looked at the traditional "secret keys", which are based on what mathematicians would call the triangular sequence. In the context of their secret-key function, we found that their position within the triangular sequence was fundamentally important. That same concept applies to all sequences. Within that triangular sequence of: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105 - the fact that 10 is in the 4th position gives it a 4-ness which it will share with any number which is in the 4th position of any other sequence.

So let's have a look at some other sequences.


If we build a solid of triangular layers we will create a tetrahedron


The number of units in each layer will be the triangular sequence, but the accumulating total will give us the tetrahedral sequence.

Layers of 1, 3, 6, 10, 15, 21, 28 accumulate to progressive totals of 1, 4, 10, 20, 35, 56, and 84.

So the tetrahedral family within the Aura-Soma Equilibrium Bottles is:

Bottle 1 Bottle 4 Bottle 10 Bottle 20 Bottle 35 Bottle 56 Bottle 84

Tetrahedra are sometimes seen as symbolising the triangular relationship between the animal, vegetable, and mineral kingdoms - together with the higher spirit echoes of those three. The tetrahedron is the simplest three-dimensional shape with straight sides. It is symmetrical from all viewpoints, and it will fit perfectly into a sphere. The ancient Greeks associated it with the fire element.


Forming progressively growing squares of 1x1, 2x2, 3x3, etc will give us the square sequence: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. This sequence will have an innate 4-ness in the same way that the triangular sequence had a three-ness because of its shape.

The four and the square shape symbolise stability, the four elements, materialism, structure, tradition, orthodoxy, organisation, order, routine, logic, definition, reason, convention, protection, and practicalities.

So we should look for how those qualities manifest within the relevant Aura-Soma Equilibrium Bottles.

Bottle 1 Bottle 4 Bottle 9 Bottle 16 Bottle 25 Bottle 36 Bottle 49 Bottle 64 Bottle 81 Bottle 100


We can build layers of squares into a pyramid in the same way we built triangles into a tetrahedron. The square sequence gives us the measure of each layer, and the accumulating totals give us the pyramid sequence itself.

1, 5, 14, 30, 55, 91

Bottle 1 Bottle 5 Bottle 14 Bottle 30 Bottle 55 Bottle 91

Let's have a look at this one in detail, and bear in mind that the great pyramid was a sacred place of initiation (not a burial place), and pyramids are said to embody the concept of the whole earth.

Bottle 1

At the top is Equilibrium Bottle 1 - where the Magician stands on the peak of the pyramid; his pure blue conscious floating on the magenta vision of infinity in his subconscious.

Bottle 4 Bottle 5

In the next layer we have 4 units within the layer, giving us an total of 5 in the pyramid so far.

Now the 4 shows us the square of the four elements, and 5 shows us the 5th element of aether (or azoth, or pranah, or love) beyond and throughout the other four. There is colour harmony in B4 being B5 with less red in the base. Perhaps the pyramid B5 tells us of the need for energy and grounding if we are to find the golden wisdom (B4) in this layer. The 4 is the number of stability, and 5 the number of communication.

The Magician in the first layer now stands on a carpet of Sunlight to become the Teacher.

Bottle 9 Bottle 14

The third layer is 9, making a total of 14 so far. Remember B9 returns as B87. Bottles 9 & 87 colour-add energetically to clear over pale gold, showing colour harmony with B14. The 9 is the number of mystery, and (2x7=) 14 shows us 2 aspects of each of our 7 chakras. These are likely to be male and female rather than conscious and sub-conscious as the mystery of the 9 is that such a male number reveals a totally female interior.

We go into the Crystal Cave to find the Wisdom.

Bottle 16 Bottle 30

Fourth layer where the accumulated B30 will shake to the B16 of the individual layer.

Putting on the Violet Robe of responsibility enables Bringing Heaven to Earth.

Bottle 25 Bottle 55

The fifth layer is violet and magenta (25) convalescence suggesting the ongoing care after the initiation. Now (5x5=) 25 shows us two versions of the 5 coming together in an intense relationship, whereas in the accumulated 55 they are standing side-by-side in companionship.

The 55 is the secret key to the 10, and the 10 is the secret key to the 4, and it was the 4 in the second layer which defined the shape of the pyramid. So at this level we find that the hidden heart of the pyramid is the green of a B10 locked between 4 and 55.

Bottle 10

Note that Bottle 10 returns as 88 which in turn reduces to B16 which we found making the pervious layer here.

Bottle 36 Bottle 91

In layer six we find B36, a carpet of kindness being laid under the pervious structure. This accumulates a total of 91 illustrating feminine leadership.

The number 36 is the secret key to the 8 which is the number of the law (law of karma, and law of "As above so below", and law of the structure of the spiritual universe). With the 6x6 = 36 showing us the number of love (6) intensified by its squaring, and the violet under the pink of B36 showing us that this takes the love to a higher level in faith, hope, & Charity.

The 91 is the secret key to the 13 which is the number of change. B91 is the return of B13 so this a lock-off. And 91 is also 13x7, so it show change in all 7 chakras or all 7 levels in the Tree of Life.

Bottle 49

If we go one step beyond the present bottle range, the New Messenger rides out to lay a 7x7 layer of turquoise and violet. Notice that this bottle is B5 seen through a blue filter.

Bottle 14

The total accumulated is 140, which is a meditation on the 14. The 14 was the third pyramid number, being the accumulated total of the first three layers. Bottle 14's second name is "a butterfly" - because it is the inversion of B73 Chuang Tsu ("Am I Chuang Tsu who dreamed I was a butterfly, or am I a butterfly now dreaming I am Chuang Tsu?"). In Bottle 14 we see the butterfly of the new aeon wisdom emerging from the chrysalis of the old age wisdom.

Bottle 105

The secret key to the 14 is 105 where the 14's gold has transmuted to another form and moved into the conscious. Now the Archangel Azreal (whose traditional role is helping people out of one level of existence into the next) helps the butterfly to emerge from the chrysalis and fly.


Although the Fibonacci sequence can make the shape of a spiral, this sequence is more associated with the proportions of natural growth. The sequence is made by starting with 1 and 1, then adding each current number to its immediate predecessor.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

Bottle 1 Bottle 1 Bottle 2 Bottle 3 Bottle 5 Bottle 8 Bottle 13 Bottle 21 Bottle 34 Bottle 55 Bottle 89

If we divide any number in this sequence by its immediate predecessor, as we go higher up the sequence we get progressively closer to the golden mean proportion of "phi" 1.618033988749894848 used in classical architecture.

So in these bottles we should look for expressions of natural growth and awareness of proportion.

Doubling Sequence

1, 2, 4, 8, 16, 32, 64

Bottle 1 Bottle 2 Bottle 4 Bottle 8 Bottle 16 Bottle 32 Bottle 64

This sequence is about structure. The 1 and 2 gave birth to all other numbers. The 4 is stability and 8 is the law. Then the 16 is "the structure which is not the real structure" (as illustrated by the collapse of the Tower in the taro) warning us that we are chasing an illusion. The 32 is verity - perhaps as the "real" structure - and 64 as the 8th square and the 4th cube shows that a single entity can operate in different dimensions simultaneously.

Prime Numbers

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103

Mathematicians would not include the 1 here, but it is included by numerologists. The definition of a prime number is "a number which can be integer divided only by itself and one". The 1 obeys the rule, but mathematicians would see its inclusion as tautological, whereas a numerologist would see the 1 as the source of all - so should begin any sequence where possible.

Prime numbers stand alone because they do not have an internal relationship with any other number. This can be interpreted as an integrity which they share with the one itself.

Any other shape or sequence will show us an equivalent family of numbers.

Positions within Sequences

Having said that position within any sequence is important, lets have a look at an example of the 7th members of various sequences to see how they show their seven-ness. Obviously we must start with the 7 itself as the 7th of all numbers. Then:

13 is the 7th Fibonacci (spiral) number
13 is also the 7th prime
28 is the 7th triangular number
49 is the 7th square
84 is the 7th tetrahedral number
140 is the 7th pyramid number
343 is the 7th cube
Conversely, the 7 itself is the 5th prime.

Notice that the 13 occurs twice, indicating a particularly well-locked relationship between 13 (change) and 7 (triumph of spirit over matter).

Bottle 7 Bottle 13 Bottle 13 Bottle 28 Bottle 49 Bottle 84

We could then use B14 for the 140 as 140 is a meditation on the 14 as well as being double 7 itself.

Bottle 14

Using B10 for 343 would seem unhelpfully over-simplistic, so it would probably be more useful to look at the relationship between bottles 3 and 4 - especially as these two add to the 7.

Bottle 3 Bottle 4 Bottle 3

Next month we will look at the names of the numbers and the extended grid.

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This month's question is:
What do you see in either the tetrahedral sequence or the Fibonacci sequence?

Send your answer to if you would like to. A future feature will publish some of the answers of the widest general interest- with your name credited to honour your copyright.