# Posts Tagged 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?

The 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:

And the following two pictures show impressing examples.

A hurricane:

And a galaxy:

### 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:

Here a collage with many examples on Fibonacci grows:

### 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:

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:

### 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.

Drawing by Steiner

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

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

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

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

Non-Euclidean geometry and Indra’s pearls

The Logoi of the different hierarchies as genders.

### Why are there so much pain on Earth?

It’s a question often asked by atheists, and a good one too, but they use it as an excuse to set themselves out on the sidelines yelling at those who try to make the world a better place.

God didn’t create our paradise, he created a paradise, the beautiful Earth, and gave it to us. We have the responsibility for the Earth, and it’s not better than we make it. It’s so to speak our apprenticeship what we do with ourselves and the Earth, we are a unity.

## Suffering, the short story

Why do people suffer as they do? The short answer is that they have created the situation themselves, that they had acted in a way so they needed to experience the situation seen from the other side. As everywhere else, there are exceptions.

It’s not God or gods who punish the sinners, we create the situation ourselves.

We should of course help each other, it’s not punishment, it’s teaching, and being helped and being a helper is part of the teaching, Love is the primary goal of the teaching on Earth.

If we have Hell in our inner when we die, it follows us into the afterlife and when born again, the new life is created based on our inner.

If Vishnu/God had been the only creator, mankind would have been a beautiful creation, a beautiful robot, acting as the gods decreed, but Shiva/Lucifer gave man the ego so we became independent. We were still only animals with egotism, we weren’t truly independent, we acted fully following the rules of Karma.

Prometheus/Lucifer stealing the fire of knowledge
from the gods to give to humankind.

At a certain time where the body was ready, the outer gods died and was reborn into the inner of man. Man got a soul with an I, the I AM entered the body. The I was like a rider taming a horse, the ego. Now humanity began changing from tribe mentality to individuals.

This is where we are now. The karma you see is where the bodies with their ego have brought them, their soul have a strong fight getting the body and ego out of the misery.

## Life, Death and Compassion

The Earth has a beautiful geography kept alive through movements in the underground, earthquakes and volcanic activity, giving new minerals for plant life to work on.

The Earth is covered with a diverse flora transforming the Earth to a place for life to live and a varied fauna lives in this garden of Earth.

The Earth is beautiful, but Earth has no compassion, every being fight for their place, although so wisely that it makes room for all.

Life dies in this struggle for a place in the world, or they die when earthquakes or fires roams the land, creating new worlds and new life.

Death is no exception, it’s a path out when life has no purpose any more.

To create compassion something new had to happen, and out of the animals was the best suitable selected for developing a being having compassion.

It’s of course a painful process. To develop compassion we need to give the animal an ego, a stepping stone to something higher, but in the process egotism gives many problems.

## Is compassion worth the painful process?

God is not a magician, he can’t create something as precious as love by a magical invocation, it has to be created by individual beings who develop love in freedom. And we can’t develop love in a paradise, we can only develop love where people are depending on each other to live.

We are in the last third of that process, and we are in a situation where things are going to change for the better.

Materialism is the last great teaching, we should understand that material things is not making us happy, that it’s really slavery for all.

## All development happens through correcting errors.

Errors are build into the system. Just look at nature, there is always exceptions that are corrected. Karma is the mechanism behind the process, orchestrated by the Zodiac.

So of course there are injustice, but they become corrected sooner or later. Black magic is a way to make it later.

The strongest power on Earth is karma. Black magic is manipulating the power of karma, using karmic beings, and in some cases being used by something much worse. It’s really nasty.

## The Creators – the Logoi

All creation is defined through three powers, called the three Logoi, but each religion have their own names for them.

They are also called Father, Mother and Son, but each are both genders.

Their work in the creation can be seen through the Fibonacci series, everything from the smallest to galaxies are formed after the Fibonacci series. It also describes sexual reproduction and the development through reincarnation.

It says the new is the result of the two previous instances/incarnations. Creation equal form + idea.

We also have it described in Hegel’s synthesis = thesis + antithesis.

This is the most optimal and simple algorithm for creation where there is only one god.

The Logoi is different consciousnesses in God, every being in God act God’s will, they don’t think independently about what they do, they can’t modify the creation if something goes wrong, so the correction is build into the creation. Or so it was!

In the Bible God sees at the end of the day that the creation is good, it was not possible while creating. The beings of God is to him as our organs is to us, we really don’t know what they do until they fail.

Our creation is different from earlier, except the prototype(s) in whose picture we are created. When we are fully developed we can instantly correct new creation where it goes wrong, and thereby avoid pain.

It is said that this creation is the most painful of all as it’s the most complicated. To create individuals is complicated.

It is said that God before he started, asked the potentially created humanity if it was worth it and we answered yes. First then started the creation.

### 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.