Proportion, Theta and the Pentacle Star

What is Proportion? We learn to keep a ‘sense of Proportion' in daily life meaning that without out a sense of this we are in danger of not seeing the world in a balanced way but only from a narrow perspective. Living as we do in an age when there is so much opinion that we are exposed to through various forms of printed and electronic media it is vital that we maintain a broad perspective to counteract partial and limited interpretations of events both local and global.

Another way to maintain a sane sense of proportion is to cultivate a sense of humour which in one sense is the ability to see a situation from a different perspective and often this means one can see the absurdity of a given situation when looked at differently.

Thinking about the what we mean by Proportion philosophically it is useful to review what the Classical thinkers thought about it. In ancient Greece ‘Ratio’ was a simple difference between two things and is the fundamental basis of conceptual judgement., a : b. For example comparing an orange to an apple and defining their various qualities and properties.

‘Proportion’ is more complex as it is a relationship of equivalency between two ratios and was called also called Analogy. 

Esoteric knowledge requires us to use our abstract thinking to try and understand concepts and ideas presented to us. Using analogy can help us make an abstract idea more real. For example the process of the unfoldment of consciousness in a human can be likened to a lotus flower which is rooted in the earth and blossoms in the light of the radiant sun. This analogy helps us to relate to this abstract process by relating it to something in our daily experience.

A distinction was made between Discontinuous Proportion, described as particular knowledge related to the concrete mind whereas Continuous Proportion was described as knowledge that flowed and can be seen as connected to the higher abstract mind. Both these forms of knowledge are part of the Law of Correspondences.

For example a four term ratio, or discontinuous proportion is such that a Father is to his son as a Mother is to her daughter, the comparison is approximate but communicates a general concept in words.

A three term ratio, or ‘continuous proportion’, is for example, my child is to me as I am to my father. So the ‘me’ is the middle term and bridges between the extremes of the child and the grandfather. The person hearing this analogy can imagine them self to be the middle character and can therefore participate in the analogy subjectively relating to both extremes and also sensing the Generational Unity of all 3 terms in relationship. A sense of ‘flow’ is thereby established between the elements and also between the objective and subjective experience of the person involved.

An example of a 4 term proportion is therefore where the yellow rectangle A / B is related to blue rectangle C / D, fig 1, with a common diagonal axis - thus A: B as C: D

An example of a 3 term proportion, fig 2, is where the green square can be subdivided along a common diagonal such that square B is half the size of square A and double the size of square C - thus A: B  as B: C, the relationships are more intimate.

THE GOLDEN PROPORTION

There is only one example of a 2 term proportion which brings the observer even closer into relationship with Unity or Wholeness and this is the ratio of theta in the Greek alphabet, numerically 1.6128 and this is called the ‘golden proportion’ such that

A : B   as    B: A + B

graphically we can see this in the proportions of the human body, fig 3, such that 

the measurement from the top of the head to the navel (A) 

is to the navel to the feet (B) 

as the navel to the feet (B) is to the the entire height of the person (A + B) = 1 (Unity), 

Please try this out with a tape measure yourself  later as there is nothing like measuring your own body to really get a grasp of this concept. 

Therefore: measure your full height  X

multiply X by 0.388 (crown of head to navel)

multiply X by 0.6128 (navel to feet)

and then check those calculations by measuring yourself to see if they tally. There will always be some variation in the measurements as the human form is only an approximation of a Divine Idea but they should be generally correct.

An example of this is in the act of bowing, we bend from this waist point in the body and therefore this is a physical enactment of this division of Unity.

There are also many other relationships in the physical body which demonstrate an associated set of proportions called the Fibonacci Series, where 1🔢3:5:8…adding the preceding two terms together to make the next term. These proportions can also be found in many natural forms and systems from the Nautilus Shell to a Galactic spiralling star cluster.

We can also see this primary golden proportion geometrically in the unfolding construction of an expanding rectangle, fig 4.

Taking an initial red rectangle and by adding a blue square to the side of the red rectangle we create another rectangle in the same proportion as the smaller one. Thus we can keep adding a proportional square to the side of each larger rectangle and keep growing the rectangle in the same ‘golden’ proportion and we can draw a spiral using larger and larger quarter circles as it grows.

So we can say that this proportional system expresses both ‘sameness’, i.e. all rectangles are in proportion to each other but also ‘differentness’ in terms of their increasing sizes and alternating orientations.

This beautifully and simply demonstrates the principle of ‘Unity in Diversity’.

THE PENTACLE STAR

The 5 pointed Pentacle star which derives from the Pentagon, is the only regular polygon to have within its geometric structure these special ‘golden proportion’ properties. And in this illustration, fig 5, we can see how these relationships in the star relate back to human proportion.

We see these proportions in each arm of the star. There is a relationship between Unity (1) and Theta (1.6128) and its related fractions, we don’t need to understand the mathematics to intuitively grasp the flowing unity of the whole.

As an example of how we can apply this knowledge, if we take the 5 cities which we are told in the Alice Bailey teachings are planetary inlets for spiritual energy, we can visualise them as represented by the 5 points of a pentacle star. If one imagines drawing this star shape with a continuous line, one is entering into these relationships intimately through the geometric construction. 

Therefore we get a sense of interconnection of these centres in relation to the geometry of the star as it unfolds in Time and Space, fig 6.

This is my conjecture of how this sequence might go, following the sequence of the unfolding sepals of a rose flower.

From London to Darjeeling to New York to Geneva to Tokyo and back to London. 

To conclude returning to the basic premise of the golden proportion, such that 

A : B   as    B : A+B

Thus theta divides Unity into two unequal parts but it paradoxically also unites these two parts as Unity through this unfolding and enfolding Proportional system.

Here follows an animated presentation with a song to try and capture something of this elusive subject,

   James Mills