Posts Tagged Golden Mean

The Logoi’s Creating in the Physical world and the Fibonacci Sequence

The Golden Mean as the Key to the Universe

From I was a young and hopeful mathematician I have been fascinated by the Golden mean and the Fibonacci Series, with its connection to plants and animals, but I lacked a good explanation for why it was found in all of nature, in all of the universe.

Plato said that the Golden Mean, Phi, is key to the universe. It has puzzled me over time as the interesting and beautiful structures following the Fibonacci numbers in nature aren’t explanation enough, there has to be a spiritual background. If the Golden Mean is the key, the Golden Triangle is the door. So, what is the spiritual explanation behind?

Fibonacci RoseThe Creating Trinities

The Fibonacci Series

The formula for the Fibonacci series is

Fi+1= Fi + Fi-1, where the initial conditions are i= 1, F0= 0, F1= 1

where the subscript describes the position in the sequence.

Notice that the new value depends on the previous two! This is the principle behind all creation. If it only depended on the foregoing, it would be a repetition, like the propagation of single-celled organisms producing copies of itself, but here the the growth factor is phi, the golden mean.

This means we get a sequence that looks like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Growth from point to point in the sequence approaches a fixed value the further we get and this growth factor is phi= Fi / Fi-1 (~1.6180), which we also know from the golden section.

The growth is large, in mathematical language we call it exponential, which can be displayed graphically:The formula is connected with growth, both with physical growth of plants, animals, planetary systems, galaxies, but also in breeding, sexual reproduction, see Fibonacci Numbers and Nature with many good examples and descriptions.

The Fibonacci Spiral

One of the most characteristic forms is the Fibonacci curve, occurring everywhere:

FibonacciSpiral

And the following two pictures show impressing examples.

A hurricane:

And a galaxy:
fibonaccimessier51

Plant Growth

What’s makes the formula interesting is that the next value depend on the two preceding values, not the last alone, this explains the growth in plants, where each step always builds on the already existing, and the new is not just a repetition of the previous, it’s bigger and better, with a factor of Phi, the Golden Mean.Here an example of plant growth with the number of leaves produced:flower8

Here a collage with many examples on Fibonacci grows:fractalcollage

The Fibonacci Series and Reincarnation

I read a Theosophic text some years ago where it was stated that man through each incarnation spiritually was growing with the factor Phi. It sounded very interesting, but there was no explanation for why it was that way, but I remembered it, one day I might find out.

One day I found out that the Fibonacci series also described the sexual reproduction, and that was the beginning of the understanding.

The Fibonacci formula tells that one incarnation builds on the two previous incarnations, which following Steiner should be one female and one male incarnation. It sounded reasonable.

Hegel’s dialectic described as thesis plus antithesis, resulting in the synthesis, or with his own concepts: abstract, negative and concrete. You start with the abstract and put it up against its opposite, the negative and from these are the concrete formed:

thesis_antithesis_synthesis

So we have

Fi+1= Fi + Fi-1        where Fi-1= Thesis, Fi = Antithesis,  Fi+1= Synthesis

If we look at the incarnations of a person, a is the first incarnation as a woman, b is the next incarnation as a man, it will be followed by a second incarnation c as a man, the synthesis of the previous two. Next incarnation d are as a woman and also the next incarnation e and as all incarnations hereafter will be between d and e, they will no longer alternate between the sexes, but all subsequent incarnations will be as a woman:fibonacci-split

The Three Logoi

This is a definition by Rudolf Steiner on the three creative principles in the universe, also called the Logoi’s:

Here we have three definitions of Beings who bring about, who underlie a planetary chain. They are called the three Logoi.

1. The Third Logos produces by means of combining.
2. When out of one substance something else having new life comes into being, this is brought forth by the Second Logos.
3. Everywhere, however, where we have to do with a coming forth out of nothing, we have the First Logos.

This is why the First Logos is also often called the One who is immanent in things, the Second Logos the One who in the quiescent substance in things creates life out of the living, the Third Logos the One who combines everything existing, who puts the world together out of things.

TheThreeLogoi2Drawing by Steiner             

These three Logoi always manifest in the world in and through one another.

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The Third Logos in spiral form, Sam Tageuk or Gankyil:

sam-tageuk.png

See much more on this here: The Logos Walks the Earth

Here

Fi+1= Fi + Fi-1        where Fi-1= First Logos, Fi = Second Logos,  Fi+1= Third Logos.

First Logos gives the idea, Second Logos gives life and Third Logos gives the resulting form.

Video on the Golden Key

This is a beautiful video made on the Golden Mean and the Fibonacci series by Jonathan Quintin:

References:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html

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A non-Euclidean tiling of the disc by regular heptagons.
Image created by David Wright.

Non-Euclidean geometry and Indra’s pearls

Self-similar syncopations
picture2012
The flower of life 

Pythagoras and harmonic notes in music..

Pascals Triangle.

Two dimensional geometry and the Golden Section.

The Golden Section.

Some beautiful Math:).

A little history.

2000px-golden_triangle_and_fibonacci_spiral-svg

The Logoi of the different hierarchies as genders.

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rosecroix

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All Creation Happens Through the One Becoming Two…

All creation happens through the one becoming two, and all creations ends through the two becoming one.

The one is the two genders combined creative force, by splitting them they become weak, but the contrast between them creates a strong field of development.

This field exist not only between man and woman, also when we change sex between our incarnations, or the differences between physical and etheric body.

It’s also permeates all of nature.

Sexual reproduction increases the development speed enormously. It’s speed is described through the Fibonacci series, and phi the golden mean, the key of the universe.

Nearly everything in nature follows the Fibonacci series or spiral, plants or galaxas. It reflects the three creative powers, the three Logoi : Father, Mother and Son.

It was necessary for us to enter deeply into the physical, as creators we should understand the created fully, master it fully, for that the masculine was needed.

To come up again the female part is needed, to direct the powers of the masculine upward again, only together can humanity get up from materialism.

See The Logoi’s Creating in the Physical world and the Fibonacci Sequence

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Esoteric Picture Collections with References and Texts

I believe that one picture replaces many words, so I have made some picture collections where I try to show the relationship between different religious and esoteric traditions. The following collages are entries into these collections. Most pictures both contains texts and references.

Variations around the Trinities

In all religions and esoteric traditions we have the three creative powers of the Trinity more or less hidden. These three powers are also known through their colors, with Red for the Father, Blue for the Mother, and typically Yellow for the Son, symbolizing all colors. The picture and label link to the collection:


See Variations around the Trinities

This is the main theme of this blog, and the most central texts are:

  • The Art of Asha, an Analysis
    “The Art of Asha” are the origin of chess and was introduced by Zarathustra as a kind of teaching aid describing the spiritual powers or hierarchies behind the physical world. But the spiritual background was lost, and here I regain it.
    Johfra’s Libra – an Analysis
    I had some years ago an inspiring idea exchange on Johfra’s beautiful picture
    Libra, and I bring it here as it was very illuminating, and a good example showing that it is possible to work together, instead of the usual fights between different opinions.

The World Egg and the Zodiac

The World Egg is the most universal symbol we have, and the Zodiac is the most developed form of it, but it’s everywhere, we just don’t recognize it as representing the world egg.

We can find the history of the zodiac in the four heavenly beasts, Eagle, Lion, Ox and Man; they were the first members of the Zodiac, first later came the Cardinal signs, and later again the mutable, they came when man began developing these qualities, just as the outer planets first became visible when they became influential. In the bible we find it in The Sons of Jacob and the Zodiac.

I have made a collection of pictures with text and references:


See The World Egg and the Zodiac

I have made “Creation of the Sun System and the Zodiac” for an illustrated overview of what was created, with the following extract as basis:

“The egg of Amma was closed, but made of four parts called ‘clavicules,’ themselves ovoid and joined as if they had extruded one from the others. Amma is four joined clavicules; it is only these four clavicles.” (Marcel Griaule & Germaine Dieterlen, Le renard pâle)

The sun system is ‘Amma’s Egg’ [the Zodiac], not the whole universe. Within his egg, Amma began spinning around, forming the po seed. The po is the smallest invisible seed at the center.

Amma then placed seven ‘words’ [Planets] in the po, which began to vibrate strongly within the seed. The spiraling vibrations caused four clavicles to grow forth from the po. These were the four heavenly beasts, the fixed star signs. These four Androgyne beings split into four male and four female, the cardinal and fixed star signs.

The Dogon call these beings the Nommo Anagonno, ‘The Word (Nommo) that Became Fish-Man’ (Anagonno). The male and female got a son, and the mutable star signs was created.

There are two levels of understanding, the macrocosmic, as mentioned above, but also the microcosmic:
“Hence, the eight ancestors were taken to heaven with the Nummo to learn the skills of civilisation. Later, each was given one of the eight grains of heaven, with which they returned to live with men, civilising them. They thus became the “civilising deities”, the Dogon equivalent of the Apkallu, or Seven Sages.” See The Old Granary.

This description of the Earth creation is only part of another greater history, the creation of man, which started long before Earth. In Esoteric History of Man I give a short overview of the path man has followed since the initial seed of man was created.

Nidanas and the Zodiac

WheelOfLife-2

I have looked at the Nidanas in relation to the Zodiac. The twelve Nidanas are the karmic powers keeping man reincarnating on the Earth. The twelve Nidanas consists of three groups, the first group of four is the Cardinal signs, the next group are the Mutable and the last group are the Fixed star signs. In the following tables and zodiac I have placed the Nidanas on the zodiac following these principles. See Astrology, Karma & Nidanas

Lucifer – Shiva and Krishna

Another entry into the history of humanity is through Lucifer, the lightbringer, see The Origin of Lucifer – Shiva

Shiva

The Earth evolution started within the existing universe, with center in the sun, and on the planet Earth was constructed a crucible where the seed to the new universe was constructed.

Shiva, the Luciferic powers, were the creators of the old universe; together with Brahma and Vishnu they were the old universe. See also The Origin of Lucifer – Shiva.

In the crucible the new began to take form, Krishna, the transformed Lucifer, became stronger and stronger and the old Lucifer, Shiva became smaller and smaller, through the development of man. See Krishna as Teacher of Love

When the new universe was developed far enough, the transformed gods died in the old universe, and they resurrected/incarnated into the new universe, from being outside the physical body of man, they became soul and spirit in man, what we see outside is the dead body of the gods, the new universe is inside man.  See Krishna and the Holy Spirit

Francis Bacon and the American Project

What happens in the world have always been prepared from the spiritual world through highly developed people. In the time before Christ it was kings and priests who led the development, after Christ it was more incognito, but they were great personalities within all aspects of the society ingeniously infusing new ideas and changing the power structures from country to country op through Europe as the point of focus changed.

The American adventure wasn’t just a random thing, it was prepared through hundreds of years, but now the ideas behind have worn down, something new is needed.

I have collected some material behind the American project here, includes many pictures, texts, and references:


See Francis Bacon and the American Project

The driving force of history have always been a pair, the Hero and the Teacher as Alexander the Great and Aristotle. Was Francis Bacon the Teacher and King James I the Hero? Benjamin Franklin the Teacher and George Washington the Hero.

Description of the work done under the auspices of Francis Bacon:

  1. To develop and improve the English language for future use so it could become an instrument for a new world of universal values across national borders, with America as a pilot project.
  2. To formulate a renewed spiritually grounded whole philosophy of the future, uniting the physical, mental and spiritual, and built bridges between faith and enlightenment.
  3. Providing for publication of books in England and in continental Europe, and in general to stimulate learning, study, individual discernment and human integrity.
  4. To use theater and art as cultural and spiritual tool and through entertaining creativity to promote the formation, life-insight and consciousness transformation.
  5. To launch scientific research on a group basis, with special focus on promoting new, empirical discovery methods, the reader universe laws.
  6. Working in a ritual community for spiritual elevation, as has occurred in the helmet or the Knights of Solomon House, the Rosicrucian, Masonic work.
  7. To tell about it for posterity and hide it in cryptographic codes, so it little by little would be possible for people to see and understand the work and be encouraged to continue development.

From Søren Hauge: Shakespeare Mysteriet

Pythagoras et al

Much of modern esoteric knowledge goes back to Pythagoras, but what we know about his teachings are mostly through indirect sources.

I have collected a number of pictures, texts and references here:


See Pythagoras et al

One of the most interesting topics, but least understood, is the Golden Mean which Plato said was the key to the universe: “Golden Mean, Key to the Universe?“.

I have written a note on “Origin of the usage of Left Path and Right Path“, as it has been misused in various discussions, but it goes at least back to Pythagoras.

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