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Weekly Theme for Contemplation: The Divine Proportion

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  • #7261

    ModeratorTN
    Keymaster

    Weekly Theme for Contemplation: The Divine Proportion

    “There is within the empyrean an archetypal conception of an ideal society, a
    divine proportion, the kingdom of God on earth, heaven in time. “

    — Aquarian Almanac

     

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Weekly Theme for Contemplation: The Divine Proportion


  • Grace Cunningham
    Participant
    Grace Cunningham

    Does anyone know the math behind the divine proportion? Can someone explain it in simple terms for the mathematically challenged?


    • Peter
      Moderator
      Peter

      I’ve inserted a couple of small pictures in my post below but I’m not sure how well they will come out. The may not display properly in messages sent from the list and only appear properly (if at all!) in the online post. Here goes:

      The ‘divine proportion’ is also referred to in mathematics as the the golden mean or golden ratio. The use of the term proportion refers to the ratio between two sets of numbers, or lines, or areas etc. For example: the ratio between 27 and 9 is the same as the ratio between 9 and 3.

      Here’s what it means in words without the numbers: take a line divided into two parts, a long part ‘a’ and a short part ‘b’. We have at least two ratios to consider. The ratio of the long part ‘a’ to the short part ‘b’ and the ratio of the total length of the line (i.e. ‘a+b’) to the long part ‘a’. In the golden mean the ratio of total length of the line (‘a+b’) to ‘a’ is the same as the ratio of ‘a’ to ‘b’.

      This can be expressed as a+b/a = a/b.

      For the golden mean that ratio number turns out to be 1.618 represented by the greek letter phi. (It’s actually has a infinite number of numbers after the decimal point eg. 1.6180339887498948….)

      If ‘a+b’ = 100 then:
      ‘a’ = 61.8
      ‘b’ = 38.2

      When a rectangle (say a picture frame or size of a building) is made up of, say, the size 100 to 61.8 (width and height or vice versa) then that reflects the divine proportion or golden mean. Obviously, the actual lengths of height and width can vary so long as the proportion between them of 1.618 remains.

      ~~


      • Peter
        Moderator
        Peter

        I’m not sure I’ve put it very well and the above may not be clear.

        The ratio between 27 and 9 is the same as the ratio between 9 and 3 because the ratio is 3 in each case. This is just an example showing how the ratio between two sets of numbers can be the same. It’s not the divine proportion.

        In the divine proportion the ratio is always 1.618, represented by the greek letter phi ‘φ’ .

        In the line ‘a + b’ (see previous post) where a + b = 100 the only way to divide the line into two segments that reflect the divine proportion is when:
        a = 61.8
        b = 38.2

        The ratio of 100 to 61.8 = 1.618*
        The ratio of 61.8 to 38.2 = 1.618

        (*Actually, to get 100 rather than 99.99 you need to multiply 61.8 by the full number of phi which is 1.6180339887498948….)

        To put it slightly differently: in a divided line where ‘a’ is the longer (greater) part and ‘b’ is the smaller (lesser) part then divine proportion is said to occur when the relationship between the whole and the greater is the same ratio as that between the greater and the lesser.

        ~~


        • Kirk Marzulo
          Participant
          Kirk Marzulo

          “The whole nature of man must be used wisely by the one who desires to enter the way.” -Light on the Path

          There are many layers to be unfolded here. According to Kepler and a long line of mathematicians, scientists and geometricians since Euclid, among the most valued and studied of the Pythagorean/Euclidean proofs was this “division of a line into extreme and mean ratio.” As many know, along with many other fascinating mathematical features of this proportional series, it is that found throughout the plant, animal and human kingdoms. It is found in the logrithmic spiral of the nautilus shell and ammonite, the pattern of scales on the rind of a pineapple, the distribution of seed points on a pine cone, on the face of a sunflower, as well as in spiral galaxies and hurricanes. It is also the basic proportional series found in the primary relationships between parts of the human body. We might therefore suppose that it represents a fundamental proportional keynote in nature connected with the steps of harmonic growth where each movement forward in an evolutionary series is in right relation to the part or parts which precede it, as well as to the whole of which it is a part.

          The renaissance mathematician, Lucas Pacioli wrote in his treatise on The Divine Proportion, “From the human body derive all measures by which God reveals the innermost secrets of nature.” The famous drawing by Leonardo da Vinci called “The Vitruvian Man” which accompanied this treatise was derived from the writings of Vitruvius Pollio, the Roman author, architect and engineer, “an initiate” who (in his 10 books on Architecture) hinted at the lost canons of proportion once taught in the mystery schools of antiquity. (per H. P. B., Vol 1, p 209 fn). The harmonic proportional series of the Golden Mean, is also found in numerous line and form relationships created in the five pointed star, the symbol of the Pythagorean school and (per H. P. B.) was also the symbol for the 10th sign of the Zodiac: Capricorn or Makara in Sanskrit. What became the crocodile associated with Makara, was originally the “Dragon of Wisdom,” connected with the Kumaras “the mind born sons of Brahma,” and the Human Soul. H. P. B. also mentions in one of her articles that the symbol of the pentagram within the six-pointed star is the same as that of the Theosophical seal, linking the microcosm and macrocosm, a symbol so rich with occult meaning that volumes would be needed to explain it. In reference to one of its meanings, she says the five points of the pentagram represent the five limbs of man through which “stream most powerfully” the force once called ‘Mesmerism.’ She also says the inverted pentagram is the symbol of Kali Yuga, the inversion of values and the use of divine energies for personal benefit. At the individual ethical level many questions thus arise: What aspect of Manas are we allowing to rule the kingdom? For what purpose are we putting the energies loaned to us by great nature? Is thought and action performed out of service to the whole and in right proportion to the whole, or in service of self? If we would have our words, our hands and our feet be blessings rather than weapons, a re-alignment of thought in harmony with Brotherhood and non-violence may be needed.


      • Grace Cunningham
        Participant
        Grace Cunningham

        This is wonderful Peter and many thanks. And I suppose it is Divine because of what Kirk is sharing, namely that it is constant pattern used in Nature.


  • ModeratorTN
    Keymaster
    ModeratorTN

    July 21, 2018 Weekly Theme for Contemplation: The Divine Proportion

    Four blessings come to the person who respects the elders and practises
    reverence — length of days, beauty, happiness and strength. — BUDDHA


  • ModeratorTN
    Keymaster
    ModeratorTN

    July 22, 2018 Theme for Contemplation: The Divine Proportion

    We should take care that the movements of the different
    parts of the soul should be in due proportion. — PLATO


  • ModeratorTN
    Keymaster
    ModeratorTN

    July 23, 2018 Theme for Contemplation: The Divine Proportion

    How can we etherealize ourselves? By studying the action of Causes
    and Effects and acting accordingly. — D. K. MAVALANKAR


  • Gerry Kiffe
    Moderator
    Gerry Kiffe

    Does the golden measure have an ethical corollary? Or how about an ethical application or ethical relevance?


  • ModeratorTN
    Keymaster
    ModeratorTN

    July 24, 2018 Theme for Contemplation: The Divine Proportion

    A due measure is excellent. — PYTHAGORAS


  • ModeratorTN
    Keymaster
    ModeratorTN

    July 25, 2018 Theme for Contemplation: The Divine Proportion

    We would willingly have others perfect, and yet we amend not our own faults.
    We will have others severely corrected, and will not be corrected ourselves.
    — THOMAS à KEMPIS


  • ModeratorTN
    Keymaster
    ModeratorTN

    July 26, 2018 Weekly Theme for Contemplation: The Divine Proportion

    There are two tragedies in life. One is to lose your heart’s desire.
    The other is to gain it. — GEORGE BERNARD SHAW

    We can only love what we know, and we can never know
    completely what we do not love. — ALDOUS HUXLEY


  • ModeratorTN
    Keymaster
    ModeratorTN

    July 27, 2018 Weekly Theme for Contemplation: The Divine Proportion

    Give thy thoughts no tongue,
    Nor any unproportion’d thought his act.
    — WILLIAM SHAKESPEARE

© 2017 Universal Theosophy

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