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Re: [sl] #'s & planets-- the larger picture

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  • mikebispham@cs.com
    In a message dated 01/12/00 03:18:45 GMT Standard Time, canuck@comco.ne.jp ... I think its worth looking at the Vesica Piscis as a bare schema that displays
    Message 1 of 2 , Dec 1, 2000
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      In a message dated 01/12/00 03:18:45 GMT Standard Time, canuck@...
      writes:

      > >I'm thinking along the lines of
      > >1=God=Unity; 2=Intellect=Universal Architype=Pattern; 3=Incarnated World,
      > >article. Again 'point, line, surface, solid' seems to feature large in
      > >various esoteric strands. And 1) Father/Pattern, 2) Mother/Matrix 3)
      > >Child/Birth/Becomming/Being.
      >
      > This is exactly along the lines of thought I wish to develop.

      I think its worth looking at the Vesica Piscis as a bare 'schema' that
      displays this idea, unifying a number of interpretations. Father/mother,
      Spirit/(primary)matter is the basis, quite which depends on whose looking -
      the principle is the same. The *result* in all cases is a
      birth/child/incarnation/substance/3 dimensional being. In the geometric
      traditions, this diagram unites the geometry with the number mysticism, as
      well as the message of origins. Some folks read the circles that Plato
      begins with in the Timeaus as the VP. In the Christian Neoplatonic
      tradition, this geometric/mathmatical/metaphysical version was united with
      the Christian revelatory text, Genesis, giving a unified
      'scientific'/revelatory account of creation. Euclid starts with a vp,
      building an equilateral triangle, and ends, after 13 books of divine
      mathematics, at the moment of birth, the regular solids. His books are
      called 'The Elements'.

      I think this is a complex picture we're trying to divine, because it ranges,
      changes through time, develops and turns back again; and is presented
      differently by different traditions. But I think an account of the physical
      nature of being, and its spiritual (or non spiritual - see Democritus)
      origins is the *basis* upon which *everything else* is built in *most*
      traditions. The Vesica has survived as a great way to express the essential
      'facts' of several competing accounts.

      > >The number systems involving the elements might also be worth bearing in
      > >mind.
      > >
      > >'Primary' elements
      > >Fire 8 (2*2*2)
      > >Earth 27 (3*3*3)
      > >
      > >'Reconciling' elements
      > >Air 12 (2*2*3)
      > >Water 18 (2*3*3)
      >
      > Where do these numbers come from?
      >
      > -Chris

      My source is Richard Foster's 'The Hidden meaning of the Great Pavement of
      Westminster Abbey' (Thanks again Barry!). The math is found in numerous
      diagrams from around the 12th and 13 C.s - and perhaps other periods. (If
      anyone comes across any of these elemental schemas, or texts explaining them,
      I'm collecting examples : ).

      I've swiped Foster's text below, and you can find this and an image of the
      Oxford Bible Manuscript schema he's referring to on my website, on 'The
      Elements' page; http://www.fupro.com/plat - page down a couple of screens,
      take the 'all other pages' link and look for 'Medieval Atoms: The Elements'.

      __________________

      Foster's Text
      "The relationships between Fire, Air, Water and Earth were a popular theme
      among the devisers of schemata, and provided the intellectual scaffolding
      upon which more comprehensive concepts were built.

      Empedocles, the Greek philosopher of the early fifth century b.c., is usually
      credited as the originator of the theory of four Elements which come together
      under the influence of `love' and disintegrate under the influence of
      `enmity' in a cycle that forms the material diversity of the created world.
      The four are related together by two pairs of opposing qualities: Fire is Dry
      and Hot; Air is Hot and Moist; Water is Moist and Cold; Earth is Cold and
      Dry. Each Element, therefore, shares a quality with two of the others.
      Elements with a common quality are obviously more capable of combination,
      thus Earth and Water may be more readily combined than Fire and Water.
      Elements sharing a quality may also be transmuted one into the other by the
      replacing of the quality which differs between them. Thus Water (Moist and
      Cold) may become Air (Moist and Hot) by replacing Cold with Hot, that is
      heating it so that it becomes vapour. The primary purpose of any schema of
      the four Elements was to demonstrate this double set of reconciled opposites.

      The reconciliation of opposites was a dominating principle that lay at the
      heart of medieval philosophical speculation. The opening sentence of Abbot
      Suger's description of the rebuilding of his church of Saint-Denis during the
      twelfth century presents a resounding verbal image of the harmonising of
      opposites as the paramount act of Divine creation:

      "The awesome power of one sole and supreme Reason reconciles the disparity
      between all things of Heaven and Earth by due proportion: this same sweet
      concord, itself alone, unites what seem to oppose each other, because of
      their base origins and contrary natures, into a single exalted and well-tuned
      Harmony."

      This short but triumphant passage, redolent with the neo-Platonic imagery
      that had long been absorbed into Christian philosophy, conjures up the
      breadth and majesty of the Divine order that the designers of schemata sought
      to encapsulate in their work.

      In the process of harmonising neo-Platonic teaching with that of the Bible,
      the Church Fathers had identified the caelum et terram created by God in the
      opening words of Genesis with the Elements of Fire and Earth: `In the
      beginning God created the heaven and the earth.' In the Timaeus, Plato
      describes Fire and Earth as the first two Elements to be created, an opposing
      pair which were then reconciled by the creation of two intermediary Elements,
      Air and Water. The reconciliation of the four Elements was achieved not only
      by the qualities of Hot, Cold, Dry and Moist, but also quantitatively by
      giving them numerical values.

      The numerical treatment of the theme of the four Elements plaited together
      strands from both the Pythagorean and the Platonic traditions. Being primal,
      the Elements must be represented by, or derive from, the simplest numbers.
      Since I was reserved for the divine unity of God, the first two numbers that
      could possibly be used to represent the first two Elements to be created,
      Fire and Earth, were 2 and 3. However, these numbers were not considered
      adequate in themselves. A simple number can represent only one dimension, in
      visual terms, a line. By analogy, a square number, for example 4 (2 x 2), may
      represent a surface area, that is, a plane figure. But for material and
      spatial existence, three dimensions are necessary. Theon of Smyrna, the Greek
      mathematician, wrote that 3 `is the first bond and power of the solid; for in
      three dimensions is the solid conceived'. Thus the appropriate numbers for
      the first two Elements had to be the cubes of the first two available
      numbers, 2 and 3. So Fire was assigned the number 8 and Earth the number 27.

      The extremes of Fire and Earth, 8 and 27, then had to be reconciled by bonds
      which were sufficiently strong, in the numerical sense, to hold together the
      whole of the created world. Between two square numbers (those representing
      plane figures) a single mean is sufficient, but for cube numbers (solid
      figures) two means are needed. These means are 12 (2 x 2 x 3) and I8 (2 x 3 x
      3). So the intermediary Elements of Air and Water received the mean numbers
      of 12 and 18 respectively. The numbers of the Elements, therefore, form a
      progression in which each individual Element is bound to its neighbour by the
      ratio of 2:3, one of the favourite harmonic ratios of the Pythagoreans, known
      as the sesquialter, the sixth of the proportions described by Nicomachus of
      Gerasa in his Introduction to Arithmetic, c. ad 100. In this way the Elements
      that `seem to oppose each other' were united into a stable and `well-tuned
      harmony . As Plato summarised it in his Timaeus:

      "Having bestowed upon them so far as possible a like ratio one towards
      another - air being to water as fire to air, and water being to earth as air
      to water - he joined them together and constructed a Heaven visible and
      tangible. For these reasons and out of these materials such in kind and four
      in numbers, the body of the Cosmos was harmonised by proportion and brought
      into existence."

      As well as assigning numbers to the four Elements, in the Pythagorean and
      Platonic traditions each had its own regular geometric solid. Pythagoras is
      generally credited with having discovered the five regular solids: the cube,
      with square faces; the tetrahedron, octahedron and icosahedron, with
      triangular faces; and the dodecahedron, with pentagonal faces. The
      tetrahedron was associated with Fire, the octahedron with Air, the
      icosahedron with Water, and the cube with Earth. The fifth solid, the
      dodecahedron, was taken to represent the heavens as a totality.

      To the primary qualities of Hot, Cold, Dry and Moist six more subtle
      secondary qualities were added: Fire is sharp, tenuous and mobile; Air is
      sharp, mobile and weighty; Water is mobile, blunt and weighty; Earth is
      blunt, weighty and immobile.

      In the attempt to harmonise all aspects of the world around them, the
      philosophers also related the four Elements to the four human Temperaments.
      Four bodily fluids, or `humours', were believed' to govern the constitution
      of the body and mind: blood, phlegm, black bile and yellow bile. An excess of
      one humour gave an individual a particular temperament. Blood made a man
      sanguine; phlegm, phlegmatic; black bile, melancholic; and yellow bile,
      choleric. This theory had been suggested first by Hippocrates, the `Father of
      Medicine'. The fiery choleric temperament became associated with Fire, the
      breezy sanguine with Air, the dissipated phlegmatic with Water, and the heavy
      melancholic with Earth.

      These then were the `facts' of the four Elements that the geometry of
      schemata was called upon to summarise. There were two basic approaches: a
      linear diagram which tended to emphasise the numerical relationship between
      the Elements, and a square or circular diagram which was more useful for
      showing their qualitative connections and also had the advantage of
      expressing their cyclic nature."
    • Pam Giese
      It s interesting to note that this is similar to the values given Yin and Yang in the I-Ching. Similar but opposite since in I-Ching
      Message 2 of 2 , Dec 1, 2000
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        It's interesting to note that this is similar to the values given Yin and
        Yang in the I-Ching. Similar but opposite since in I-Ching
        Earth/Yin/Female/Receptive qualities are given as 2 while the
        Heaven/Yang/Male/Active priniciples are given 3 .Typically 3 coins are
        shown, the "yin" sides being given values of 2 and "yang" sides given values
        of 3. This creates the following possibilities:

        Old Yin (6)
        - -
        - -

        Old Yang(9)
        ___
        ___

        Young Yin(7)
        __
        - -

        Young Yang(8)
        - -
        __


        Pam
        pgiese@...
        http://www.snd.softfarm.com/pws/pgiese

        "Blessed are the cracked, for they shall let in the light..."
        > > >The number systems involving the elements might also be worth bearing
        in
        > > >mind.
        > > >
        > > >'Primary' elements
        > > >Fire 8 (2*2*2)
        > > >Earth 27 (3*3*3)
        > > >
        > > >'Reconciling' elements
        > > >Air 12 (2*2*3)
        > > >Water 18 (2*3*3)
        > >
        > > Where do these numbers come from?
        > >
        > > -Chris
        >
        > My source is Richard Foster's 'The Hidden meaning of the Great Pavement of
        > Westminster Abbey' (Thanks again Barry!). The math is found in numerous
        > diagrams from around the 12th and 13 C.s - and perhaps other periods. (If
        > anyone comes across any of these elemental schemas, or texts explaining
        them,
        > I'm collecting examples : ).
        >
        > I've swiped Foster's text below, and you can find this and an image of the
        > Oxford Bible Manuscript schema he's referring to on my website, on 'The
        > Elements' page; http://www.fupro.com/plat - page down a couple of screens,
        > take the 'all other pages' link and look for 'Medieval Atoms: The
        Elements'.
        >
        > __________________
        >
        > Foster's Text
        > "The relationships between Fire, Air, Water and Earth were a popular theme
        > among the devisers of schemata, and provided the intellectual scaffolding
        > upon which more comprehensive concepts were built.
        >
        > Empedocles, the Greek philosopher of the early fifth century b.c., is
        usually
        > credited as the originator of the theory of four Elements which come
        together
        > under the influence of `love' and disintegrate under the influence of
        > `enmity' in a cycle that forms the material diversity of the created
        world.
        > The four are related together by two pairs of opposing qualities: Fire is
        Dry
        > and Hot; Air is Hot and Moist; Water is Moist and Cold; Earth is Cold and
        > Dry. Each Element, therefore, shares a quality with two of the others.
        > Elements with a common quality are obviously more capable of combination,
        > thus Earth and Water may be more readily combined than Fire and Water.
        > Elements sharing a quality may also be transmuted one into the other by
        the
        > replacing of the quality which differs between them. Thus Water (Moist and
        > Cold) may become Air (Moist and Hot) by replacing Cold with Hot, that is
        > heating it so that it becomes vapour. The primary purpose of any schema of
        > the four Elements was to demonstrate this double set of reconciled
        opposites.
        >
        > The reconciliation of opposites was a dominating principle that lay at the
        > heart of medieval philosophical speculation. The opening sentence of Abbot
        > Suger's description of the rebuilding of his church of Saint-Denis during
        the
        > twelfth century presents a resounding verbal image of the harmonising of
        > opposites as the paramount act of Divine creation:
        >
        > "The awesome power of one sole and supreme Reason reconciles the disparity
        > between all things of Heaven and Earth by due proportion: this same sweet
        > concord, itself alone, unites what seem to oppose each other, because of
        > their base origins and contrary natures, into a single exalted and
        well-tuned
        > Harmony."
        >
        > This short but triumphant passage, redolent with the neo-Platonic imagery
        > that had long been absorbed into Christian philosophy, conjures up the
        > breadth and majesty of the Divine order that the designers of schemata
        sought
        > to encapsulate in their work.
        >
        > In the process of harmonising neo-Platonic teaching with that of the
        Bible,
        > the Church Fathers had identified the caelum et terram created by God in
        the
        > opening words of Genesis with the Elements of Fire and Earth: `In the
        > beginning God created the heaven and the earth.' In the Timaeus, Plato
        > describes Fire and Earth as the first two Elements to be created, an
        opposing
        > pair which were then reconciled by the creation of two intermediary
        Elements,
        > Air and Water. The reconciliation of the four Elements was achieved not
        only
        > by the qualities of Hot, Cold, Dry and Moist, but also quantitatively by
        > giving them numerical values.
        >
        > The numerical treatment of the theme of the four Elements plaited together
        > strands from both the Pythagorean and the Platonic traditions. Being
        primal,
        > the Elements must be represented by, or derive from, the simplest numbers.
        > Since I was reserved for the divine unity of God, the first two numbers
        that
        > could possibly be used to represent the first two Elements to be created,
        > Fire and Earth, were 2 and 3. However, these numbers were not considered
        > adequate in themselves. A simple number can represent only one dimension,
        in
        > visual terms, a line. By analogy, a square number, for example 4 (2 x 2),
        may
        > represent a surface area, that is, a plane figure. But for material and
        > spatial existence, three dimensions are necessary. Theon of Smyrna, the
        Greek
        > mathematician, wrote that 3 `is the first bond and power of the solid; for
        in
        > three dimensions is the solid conceived'. Thus the appropriate numbers for
        > the first two Elements had to be the cubes of the first two available
        > numbers, 2 and 3. So Fire was assigned the number 8 and Earth the number
        27.
        >
        > The extremes of Fire and Earth, 8 and 27, then had to be reconciled by
        bonds
        > which were sufficiently strong, in the numerical sense, to hold together
        the
        > whole of the created world. Between two square numbers (those representing
        > plane figures) a single mean is sufficient, but for cube numbers (solid
        > figures) two means are needed. These means are 12 (2 x 2 x 3) and I8 (2 x
        3 x
        > 3). So the intermediary Elements of Air and Water received the mean
        numbers
        > of 12 and 18 respectively. The numbers of the Elements, therefore, form a
        > progression in which each individual Element is bound to its neighbour by
        the
        > ratio of 2:3, one of the favourite harmonic ratios of the Pythagoreans,
        known
        > as the sesquialter, the sixth of the proportions described by Nicomachus
        of
        > Gerasa in his Introduction to Arithmetic, c. ad 100. In this way the
        Elements
        > that `seem to oppose each other' were united into a stable and `well-tuned
        > harmony . As Plato summarised it in his Timaeus:
        >
        > "Having bestowed upon them so far as possible a like ratio one towards
        > another - air being to water as fire to air, and water being to earth as
        air
        > to water - he joined them together and constructed a Heaven visible and
        > tangible. For these reasons and out of these materials such in kind and
        four
        > in numbers, the body of the Cosmos was harmonised by proportion and
        brought
        > into existence."
        >
        > As well as assigning numbers to the four Elements, in the Pythagorean and
        > Platonic traditions each had its own regular geometric solid. Pythagoras
        is
        > generally credited with having discovered the five regular solids: the
        cube,
        > with square faces; the tetrahedron, octahedron and icosahedron, with
        > triangular faces; and the dodecahedron, with pentagonal faces. The
        > tetrahedron was associated with Fire, the octahedron with Air, the
        > icosahedron with Water, and the cube with Earth. The fifth solid, the
        > dodecahedron, was taken to represent the heavens as a totality.
        >
        > To the primary qualities of Hot, Cold, Dry and Moist six more subtle
        > secondary qualities were added: Fire is sharp, tenuous and mobile; Air is
        > sharp, mobile and weighty; Water is mobile, blunt and weighty; Earth is
        > blunt, weighty and immobile.
        >
        > In the attempt to harmonise all aspects of the world around them, the
        > philosophers also related the four Elements to the four human
        Temperaments.
        > Four bodily fluids, or `humours', were believed' to govern the
        constitution
        > of the body and mind: blood, phlegm, black bile and yellow bile. An excess
        of
        > one humour gave an individual a particular temperament. Blood made a man
        > sanguine; phlegm, phlegmatic; black bile, melancholic; and yellow bile,
        > choleric. This theory had been suggested first by Hippocrates, the `Father
        of
        > Medicine'. The fiery choleric temperament became associated with Fire, the
        > breezy sanguine with Air, the dissipated phlegmatic with Water, and the
        heavy
        > melancholic with Earth.
        >
        > These then were the `facts' of the four Elements that the geometry of
        > schemata was called upon to summarise. There were two basic approaches: a
        > linear diagram which tended to emphasise the numerical relationship
        between
        > the Elements, and a square or circular diagram which was more useful for
        > showing their qualitative connections and also had the advantage of
        > expressing their cyclic nature."
        >
        >
        >
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