A Paridgm Shift
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, … (each number is the sum of the previous two).
Named after Leonardo Fibrinocci who traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation)
Pascal’s Triangle and Fibonacci Numbers
The triangle was studied by B. Pascal, although it had been described centuries earlier. (about 500 years earlier)
Pascal’s Triangle is described by the following formula:
The “shallow diagonals” of Pascal’s triangle
sum to Fibonacci numbers.
Amazingly the Fibonacci numerical patterns occur frequently in nature
(flowers, shells, plants and leaves, just to name a few) that this phenomenon appears to be one of the principal “laws of nature”. Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern early in the morning and the design of a pine cone. In addition, many claims of Fibonacci numbers or golden sections (1.618 ) in nature are found in popular sources, e.g. relating to the breeding of rabbits, the spirals of shells, the curve of waves and most importantly, the galaxy, where stars are created.
Makes some wonder………
Above: A baby in creation in compairison to stars in creation.
“You are the light of the world. A city on a hill cannot be hidden. Neither do people light a lamp and put it under a bowl. Instead they put it on its stand, and it gives light to everyone in the house. In the same way, let your light shine before others, so that they may see your good works and give glory to your Father who is in heaven.”
“Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of men. The light shines in the darkness, but the darkness has not understood it.”
“While I am in the world, I am the light of the world.”
It is hard to find any more of a beautiful explanation and example of the true meaning of the Fibrinocci other then that done by Rock Band Tool, titled: “Lateralus.”
A term denoting a structure situated farther from the median plane of the body or the midline of an organ.
The lyrics are arranged in ascending then descending order of the Fibonacci sequence, which is 1,1,2,3,5,8, based on their syllables. For instance,
(2) white are,
(3) all I see,
(5) in my infancy,
(8) red and yellow then came to be,
(5) reaching out to me,
(3) lets me see.
(2) There is,
(2) more and
(3) Beckons me,
(5) to look through to these,
(8) infinite possibilities.
(13) As below so above and beyond I imagine,
(8) drawn outside the lines of reason.
(5) Push the envelope.
(3) Watch it bend.
And so on.
(Native American Medicine wheel in reference to Maynard’s opening lyrics.) “Black and white are all I see, in my infancy, red and yellow then came to be, reaching out to me, lets me see, there is so much more and beckons me.”
As the lyrics continue, the sequence then goes backwards and then forwards again.
The Fibonacci sequence shares a relationship with the Golden Spiral (1.618)mentioned over and over in the song.
Even further, the syllables length itself spirals-in and spirals-out on the sequence: 1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 8, 5, 3.
Maynard James Keenan (Tools’ band leader) begins singing at 1:37 into the song. 1 minute 37 seconds, or 97 seconds, is approximately 1.618. 97 seconds is 1.61666…or 1.618 of a minute. This happens to be the Golden ratio, which is also closely related to the Fibonacci sequence.
A combination of these references can be found in the line “to swing on the spiral of our divinity”, as the golden ratio is also often referred to as the divine proportion or Golden ratio. (1.618)
~The title, the fibrinocci sequence, the message within and the golden ratio makes for one of the most beautiful explanations, examples and displays ever created by man.~