This blog examines the role harmonic physics plays in biology, cosmology, human perception and social development.
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Turtles all the way down

Posted: August 14, 2009

The popular phrase 'Turtles all the way down' refers to the infinite regression theory of the cosmos, otherwise known as 'the fractal universe.' It is a modern retelling of the ancient fable that the world is borne on the back of one or more enormous animals, such as the turtle in Native American creation myth. It begs the question, 'Upon what is the turtle standing on?'


Of course, first cause cannot be answered simply by declaring it's 'turtles all the way down.' In fact, it can't be answered by an infinite number of anything. This is because infinity is by definition nothingness and non-physical. The last turtle isn't standing on anything at all - it's standing on an idea.

Consider for a minute the following comparison between the shell pattern of a tortoise and the patterns created by vibrating sand at specific frequencies on an oval plate. Clearly, there is a match between the shell pattern and the cymatic patterns, overlapping as harmonic standing waves inside the shell. In effect, the tortoise is 'standing on' electromagnetic waves resonating as cymatic patterns through every cell in his body. But given this, what can we say the waves themselves are 'standing on?'


Well, when we get down to the last turtle and turn him over we find that he is standing on nothing but empty space. That is, harmonics are 'standing' on the space that lies in between the waves. We see this in the above cymatic pattern where the sand comes to rest in the calm negative space between the resonating harmonic waves. This dead space is created by enharmonic waves that cancel each other out. This is known as harmonic damping.

As it occurs at all levels of nature, harmonic damping occurs near proportions of the golden ratio (a.k.a. 'divine proportion') of about 1.618033. Since this is an infinite number, it can only be approximated in nature as a Fibonacci spiral, usually in the range 21:13 (1.61538) to 13 : 8 (1.625), increasing in deadness as it converges to the golden ratio. This damping range works so well in canceling unwanted echoes and feedback that rectangular speakers and auditoriums are often built using the dimensions of 0.62 X 1.0 X 1.62. Standing waves and whole number harmonics simply cannot reflect or be sustained in proportions any where close to the golden ratio. This is true for every kind of standing wave, always suppressing fractional waves and enabling the 'sympathetic' formation of harmonic structures in atoms, solar systems and all living creatures.

Yet in spite of the fact that the golden ratio is such a perfect damping proportion, it remains an infinite, intangible and irrational nothing that simply cannot exist in a finite physical world. It represents perfect nothingness even while it gives rise to all things. We might call it an imaginary something.

In this way, the golden ratio - able to mirror only itself - functions as the matrix of all things. It is the labyrinth of Minos, the lotus of Brahma, the very mind of God. Just as the ancients believed, material structure is a creation of an imaginary something, nothing more than a dream. The turtle must first dream itself, then dream the world so we can dream it back. So it is that we live in an endless fractal dream of nothing imagining that it is something.

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RE: Turtles all the way down
By: sleuthold - August 17, 2009 04:54 PM MST
It always fascinates me how everything comes back to being an illusion - a dream. Through observation, possibilities are created. If one of us ponders a concept, an idea, that one of us creates the possibility for all of us. It is an infinitely expanding awareness. No?
RE: Turtles all the way down
By: gtarrant - September 16, 2009 02:59 PM MST
The Lo Shu story tells of the founding of the 3x3 magic square on the shell of a turtle. A turtle shell was used by the gods(+) and demons(-) to bring forth Amrit(Ambrosia, Manna, etc..) from the salts of the earth in the depths of the ocean.
The Hopi call the planet the "Great Turtle". A turtle shell is almost a perfect golden elipse in design.
Just some comparisons.
RE: Turtles all the way down
By: Richard Merrick - September 21, 2009 12:27 PM MST
Wasn't aware of these relations of the turtle, thanks George. Also, the golden ellipse aspect I wasn't aware, but it now makes sense. Bones and shells are damping regions in living creatures where resonance crystallizes the most. Thus, it makes perfect sense that the golden ratio would be involved in the turtle shell ellipse. Maybe we should check the orbital ellipses to see how golden they are too.
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