Tuesday, January 23, 2018

The Pinecone and the Golden Spiral

In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. Golden spirals are self similar. The shape is infinitely repeating when magnified. (source)

The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence), as originally shown by Kepler: Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ (source)

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. (source)
The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.

In the case of tapered pinecones or pineapples, we see a double set of spirals – one going in a clockwise direction and one in the opposite direction. When these spirals are counted, the two sets are found to be adjacent Fibonacci numbers. (source)

 
The source for the 2 images above and their respective text can be found here.

Related esoteric topics:

THE PINEAL GLAND
Diagram of the operation of the pineal gland for Descartes in the Treatise of Man (figure published in the edition of 1664)

The pineal gland, also known as the conarium or epiphysis cerebri, is a small endocrine gland in the vertebrate brain. The pineal gland produces melatonin, a serotonin derived hormone which modulates sleep patterns in both circadian and seasonal cycles. The shape of the gland resembles a pine cone, hence its name. The pineal gland is located in the epithalamus, near the center of the brain, between the two hemispheres, tucked in a groove where the two halves of the thalamus join.


René Descartes believed the pineal gland to be the "principal seat of the soul". Academic philosophy among his contemporaries considered the pineal gland as a neuroanatomical structure without special metaphysical qualities; science studied it as one endocrine gland among many. However, the pineal gland continues to have an exalted status in the realm of pseudoscience.

In the late 19th century Madame Blavatsky (who founded theosophy) identified the pineal gland with the Hindu concept of the third eye, or the Ajna chakra. This association is still popular today.

Rick Strassman, an author and Clinical Associate Professor of Psychiatry at the University of New Mexico School of Medicine, has theorised that the human pineal gland is capable of producing the hallucinogen N,N-dimethyltryptamine (DMT) under certain circumstances. In 2013 he and other researchers first reported DMT in the pineal gland microdialysate of rodents. (source)
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