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Early humans preferred the Golden Ratio too?

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Golden ratio? 1.618

From 1.5 million to 200,000 years ago, called the Acheulian period

From Lithic Studies: Pattern Recognition of Universal Mathematical Constants in Acheulean Biface Formats by Alan Edward Cannell

See also:What we know about human evolution

What we know about the human mind

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Here’s the abstract:

The similar design formats of many Acheulean bifaces has prompted several studies into the use of ‘mental templates’, leading to controversial claims that there may be a relation between length and width equal to the Golden Ratio. To avoid subjectivity, these studies have used aggregate data from assemblages that, by definition, mask the individuality of each tool, its material, any retouching and the original imposed design. Visual pattern recognition is widely used in psychological research and some branches of engineering and a similar technique is presented to highlight the formats of two samples of the Boxgrove assemblage (one random) and examine the
presence of universal mathematical constants. A probabilistic analysis suggests that the repeated use of the numbers 2, Pi and Phi and the relationship between them could not have been produced by chance. These relationships appear to be constant over very long time periods and are still used today in modern gemstone design. Pdf here.

One Reply to “Early humans preferred the Golden Ratio too?

  1. 1
    bornagain says:

    A few related notes:

    The golden ratio is found throughout nature and has often been referred to as ‘the fingerprint of God’:

    Nature by Numbers – The Fingerprint of God – video

    From the shape of some galaxies to quantum mechanics, the golden ratio is found throughout nature

    Do We Live in a “Golden Ratio” Universe? – December 2, 2014
    *The curl of an elephant tusk
    *The shape of a kudu’s horn
    *Hurricane spirals
    *The distribution of planets in the solar system
    *A biological species constant, T
    *The spiral structure of the cochlea ear-bone in a fossil hominin
    *The logarithmic spirals of galaxies
    *The structure of DNA
    *The growth of many plants (phyllotaxis)
    *The Periodic Table of the Elements
    *Spiral shells of certain mollusks, like snails
    *Spiral shells of living and extinct ammonites
    *Stress patterns in nanomaterials
    *The stability of atomic nuclides
    *The topology of space-time

    What is sculpting the Milky Way into its beautiful spiral shape? In the following article it is claimed that ‘the topology of space-time’ itself is based on the golden ratio and, as such, could be very instrumental in explaining why the Milky Way forms such a beautiful spiral shape:

    Number theory and the unity of science – 2014
    Excerpt: We suggest that there is a strong case that this so-called ‘Golden Ratio’ (1.61803…) can be related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time.,,,

    As well, the golden ratio is found on the quantum scale:

    Golden ratio discovered in quantum world: Hidden symmetry observed for the first time in solid state matter – January 7, 2010
    Excerpt: For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture.” Radu Coldea is convinced that this is no coincidence. “It reflects a beautiful property of the quantum system — a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material,” he explains.

    ‘Fibonacci quasiparticle’ could form basis of future quantum computers – Dec. 15, 2014
    Excerpt: “The Fibonacci anyon is a non-Abelian anyon whose quantum dimension is the golden ratio (1.617…), and is the simplest anyon capable of performing universal quantum computation,” Vaezi explained. “Using the fusion rule of Fibonacci anyons, it can be shown that the degeneracy of the ground state in the presence of n well-separated Fibonacci anyons on a sphere is the nth number in the Fibonacci sequence.”
    notes: In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than fermions and bosons;,,,
    ,,,the Nth Number is some arbitrary positive integer in a sequence.

    DNA also has the beauty of the golden ratio embedded within it:

    DNA spiral as a Golden Section
    Excerpt: The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339.
    DNA in the cell appears as a double-stranded helix referred to as B-DNA.This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms.
    ,,, a cross-sectional view from the top of the DNA double helix forms a decagon:
    A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon.
    The ratio of the diagonal of a pentagon to its side is Phi to 1. So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!

    Cross section of DNA compared to the Rose window at York Minster (the largest Gothic cathedral in northern Europe) – picture

    various google Images for cross section of DNA

    The golden ratio is not only beautiful to look at but it even sounds beautiful when put to music

    What Phi (the golden ratio) Sounds Like – music


    Exodus 25:10
    “Have them make a chest of acacia wood-
    two and a half cubits long,
    a cubit and a half wide,
    and a cubit and a half high.”

    The ratio of 2.5 to 1.5 is 1.666…, which is as close to phi (1.618 …) as you can come with such simple numbers and is certainly not visibly different to the eye. The Ark of the Covenant is thus constructed using the Golden Section, or Divine Proportion. This ratio is also the same as 5 to 3, numbers from the Fibonacci series.

    In Exodus 27:1-2, we find that the altar God commands Moses to build is based on a variation of the same 5 by 3 theme:

    “Build an altar of acacia wood, three cubits high; it is to be square, five cubits long and five cubits wide.”

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