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Blak Holes

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  • starbirdgarden
    Hi Maurice, how goes the world with you? Last night I was re-reading the print our of your first post. I had = not read it carefully enough at the
    Message 1 of 7 , Jul 30, 2003
      Hi Maurice, how goes the world with you?
      Last night I was re-reading the print our of your first post. I had =
      not read it
      carefully enough at the time, because my attention had been on family matte=
      rs. So I
      have recently taken it up again. So much is there, so many seed thoughts, =
      so many
      directions one could take.
      As I am, very sadly, not learned in mathematical-scientific concepts, I h=
      ave to
      struggle, so I hope you are patient! To begin at the beginning with Newton=
      .
      Apart from a very basic everyday knowledge of Newton, I have previousl=
      y been
      interested in him as a member of the Baconian Royal Society, and the more e=
      soteric
      Invisible College. I know masons still involved with this. Some say he was=
      Grand
      master of the Prieure de Sion, from which, maybe indirectly, still come som=
      e very
      interesting books and articles, promoting the idea of the blasphemous so ca=
      lled
      `blood-line' of Jesus/Magdalene into certain royal families today and the i=
      dea of
      reinstating a new King from this `line'.
      One of the books outlining the death of Diana is definitely coming fr=
      om this
      direction. (Jon King) And there is actually a King in waiting.
      I do not know if Newton was the Grand master of this Order or not, but=
      his
      connection with the royal Mint also interested me. His portrait still appe=
      ars on our
      banknotes. Materialistic science is always intimately linked with money. A=
      hriman
      seems to gobble it up. Stony Bread!
      He was more involved with forgers than was purely professional, it se=
      ems, and
      formed associations with spies and informers in his pursuit of them. He al=
      so devised
      new tortures and methods of execution for those he caught. Is there an ana=
      logy here
      with the Netonian concepts you quoted ? It seems that Blake thought so. H=
      is
      painting seems also to link Newton with the Masonic idea of God as Architec=
      t, and
      shows the symbol of the compass, and a threatening movement from light to d=
      ark,
      although I suppose that can also be read the other way. Paradox.

      "Nature and nature's laws lay hid in night. God said, Let Newton be! And =
      all was
      light!" Pope - with tongue in cheek

      Your post led me back to Steiner's lecture series on The fourth dimension,=
      which
      interests me a lot, but I have a hard time with parts of it. Incidentally I=
      met Coleridge
      again there, in the intro by David Booth. Speaking of the mathemetician W=
      illiam
      Rowan Hamilton, he says

      " While he was studying at university, Hamilton fell under the influenc=
      e of the
      Tractarian movement that sought to revitalize religion from it's spiritual =
      content. He
      was influenced in this by the more radical subjective branch of the movemen=
      t that
      was inspired by the philosophy of Samuel Taylor Coleridge. Driven, perhaps=
      , by
      Coleridge's notion of Algebra as the science of time, Hamilton discovered a=
      four
      dimensional manifold of numbers, the `quarternions' – usually called hyperc=
      omplex
      numbers today." End of quote

      As I say, it is a struggle for me, but I read the lectures anyway, and=
      get glimpses
      here and there, which is the best I can do. The following few lines from S=
      teiner
      reminded me of Daniel's poem about the shadow.

      Steiner - "Now that we have admitted the possibility that a four-dimens=
      ional world
      exists, we may wonder whether we can observe a four dimensional object with=
      out
      being clairvoyant. A projection of sorts allows us to do so. We can turn =
      a plane
      figure until the shadow it casts is a line. Similarly the shadow of a line=
      can be a point,
      and the shadow image of a solid three dimensional object is a two-dimension=
      al plane
      figure. Thus, once we are convinced of the existence of a fourth dimension,=
      it is only
      natural to say that three-dimensional figures are the shadow images of four=

      dimensional figures." End of quote.

      This is extremely interesting. I trust that if I live into these conce=
      pts, the organ for
      better understanding will be formed! May have to await next life.......
      Your words on the black hole also remind me of the exercise in higher =
      Worlds of
      suggesting away the physical object. From the little I know of black holes=
      I believe
      the idea of wrinkles in time and the popular parallel universe also pertain=
      . Any
      comments?
      Was it Olive Whicher who, speaking of levity, commented on Newton's d=
      iscovery
      occasioned by the apple falling, and that nobody asks how it got up there i=
      n the first
      place?
      Sorry these are such fragments. I have been reading and re-reading your=
      post. It is
      the most valuable part of this whole forum-interchange for me, that there i=
      s so much
      to absorb and learn from so many people!
      Jan
    • snowplank
      Hi guys, Sorry to interrupt but I was reminded of a physics lecture at school when Jan quoted Steiner thus: Thus, once we are convinced of the existence of a
      Message 2 of 7 , Jul 30, 2003
        Hi guys,

        Sorry to interrupt but I was reminded of a physics lecture at school
        when Jan quoted Steiner thus:

        "Thus, once we are convinced of the existence of a fourth dimension,
        it is only natural to say that three-dimensional figures are the
        shadow images of four dimensional figures."

        The lecture described the search for the "Grail" of physics - the
        unified field theory. When trying to understand the possibility of
        other dimensions it used an analogy which I found very thought
        provoking and I believe marries up very well with Steiner quote above.
        Picture a matchstick man drawn on a piece of paper. He has no
        concept of a thrid dimension i.e. depth. To an observer from the
        third dimension, he is clearly visible, but not vice versa. His
        dimension stretches to infinity in two directions along an
        infinitesimally narrow piece of paper (our third dimension being
        infinitesimally wide). Now picture the observer from the third
        dimension poking a pen through the piece of paper. Our matchstick
        friend get's quite a shock. A hole suddenly appears in front of him.
        He has no idea where it came from because he is unable to perceive
        the three dimensional pen which made it.

        If one extends this idea to the line of inquiry started by Daniel, I
        believe one is on the right lines in trying to understand the black
        hole phenomenon.

        Paul



        --- In anthroposophy@yahoogroups.com, "starbirdgarden"
        <starbirdgarden@b...> wrote:
        >
        > Hi Maurice, how goes the world with you?
        > Last night I was re-reading the print our of your first post.
        I had =
        > not read it
        > carefully enough at the time, because my attention had been on
        family matte=
        > rs. So I
        > have recently taken it up again. So much is there, so many seed
        thoughts, =
        > so many
        > directions one could take.
        > As I am, very sadly, not learned in mathematical-scientific
        concepts, I h=
        > ave to
        > struggle, so I hope you are patient! To begin at the beginning with
        Newton=
        > .
        > Apart from a very basic everyday knowledge of Newton, I have
        previousl=
        > y been
        > interested in him as a member of the Baconian Royal Society, and the
        more e=
        > soteric
        > Invisible College. I know masons still involved with this. Some say
        he was=
        > Grand
        > master of the Prieure de Sion, from which, maybe indirectly, still
        come som=
        > e very
        > interesting books and articles, promoting the idea of the
        blasphemous so ca=
        > lled
        > `blood-line' of Jesus/Magdalene into certain royal families today
        and the i=
        > dea of
        > reinstating a new King from this `line'.
        > One of the books outlining the death of Diana is definitely
        coming fr=
        > om this
        > direction. (Jon King) And there is actually a King in waiting.
        > I do not know if Newton was the Grand master of this Order or
        not, but=
        > his
        > connection with the royal Mint also interested me. His portrait
        still appe=
        > ars on our
        > banknotes. Materialistic science is always intimately linked with
        money. A=
        > hriman
        > seems to gobble it up. Stony Bread!
        > He was more involved with forgers than was purely
        professional, it se=
        > ems, and
        > formed associations with spies and informers in his pursuit of them.
        He al=
        > so devised
        > new tortures and methods of execution for those he caught. Is there
        an ana=
        > logy here
        > with the Netonian concepts you quoted ? It seems that Blake thought
        so. H=
        > is
        > painting seems also to link Newton with the Masonic idea of God as
        Architec=
        > t, and
        > shows the symbol of the compass, and a threatening movement from
        light to d=
        > ark,
        > although I suppose that can also be read the other way. Paradox.
        >
        > "Nature and nature's laws lay hid in night. God said, Let Newton
        be! And =
        > all was
        > light!" Pope - with tongue in cheek
        >
        > Your post led me back to Steiner's lecture series on The fourth
        dimension,=
        > which
        > interests me a lot, but I have a hard time with parts of it.
        Incidentally I=
        > met Coleridge
        > again there, in the intro by David Booth. Speaking of the
        mathemetician W=
        > illiam
        > Rowan Hamilton, he says
        >
        > " While he was studying at university, Hamilton fell under the
        influenc=
        > e of the
        > Tractarian movement that sought to revitalize religion from it's
        spiritual =
        > content. He
        > was influenced in this by the more radical subjective branch of the
        movemen=
        > t that
        > was inspired by the philosophy of Samuel Taylor Coleridge. Driven,
        perhaps=
        > , by
        > Coleridge's notion of Algebra as the science of time, Hamilton
        discovered a=
        > four
        > dimensional manifold of numbers, the `quarternions' – usually called
        hyperc=
        > omplex
        > numbers today." End of quote
        >
        > As I say, it is a struggle for me, but I read the lectures
        anyway, and=
        > get glimpses
        > here and there, which is the best I can do. The following few lines
        from S=
        > teiner
        > reminded me of Daniel's poem about the shadow.
        >
        > Steiner - "Now that we have admitted the possibility that a
        four-dimens=
        > ional world
        > exists, we may wonder whether we can observe a four dimensional
        object with=
        > out
        > being clairvoyant. A projection of sorts allows us to do so. We
        can turn =
        > a plane
        > figure until the shadow it casts is a line. Similarly the shadow of
        a line=
        > can be a point,
        > and the shadow image of a solid three dimensional object is a
        two-dimension=
        > al plane
        > figure. Thus, once we are convinced of the existence of a fourth
        dimension,=
        > it is only
        > natural to say that three-dimensional figures are the shadow images
        of four=
        >
        > dimensional figures." End of quote.
        >
        > This is extremely interesting. I trust that if I live into
        these conce=
        > pts, the organ for
        > better understanding will be formed! May have to await next life.......
        > Your words on the black hole also remind me of the exercise in
        higher =
        > Worlds of
        > suggesting away the physical object. From the little I know of
        black holes=
        > I believe
        > the idea of wrinkles in time and the popular parallel universe also
        pertain=
        > . Any
        > comments?
        > Was it Olive Whicher who, speaking of levity, commented on
        Newton's d=
        > iscovery
        > occasioned by the apple falling, and that nobody asks how it got up
        there i=
        > n the first
        > place?
        > Sorry these are such fragments. I have been reading and
        re-reading your=
        > post. It is
        > the most valuable part of this whole forum-interchange for me, that
        there i=
        > s so much
        > to absorb and learn from so many people!
        > Jan
      • Maurice McCarthy
        Dear Jan and Paul The Oort Cloud was first discovered, if memory serves, in the 1930 s by the Dutchman of that name. It is supposed to be an invisible cloud of
        Message 3 of 7 , Jul 31, 2003
          Dear Jan and Paul

          The Oort Cloud was first discovered, if memory serves, in the 1930's by
          the Dutchman of that name. It is supposed to be an invisible cloud of
          dust and ice surrounding the solar system. Usually we think of space
          existing whether or not there is something in it but it could not exist
          at all unless there were two or more things to separate. And conversely
          there would not be physical objects without space (and time). From our
          viewpoint on Earth space must cease to exist at a certain distance from
          the Earth because there is nothing to be separate from - paradoxical, I
          know, but RS mentions that between the galaxies is non-space 'occupied'
          by the Seraphim and Cherubim, keeping the galaxies in respective
          position. Similarly our solar system must have its spatial limit. At
          this limit physical matter ceases to exist so that the comets have to
          materialise. Beyond the limit is spiritual communion which forbids the
          kind of spatial relations that we know. The plot thickens with light
          from other galaxies, of course - what does it mean for this light to
          cross non-space? How now the red-shift? To understand it seems like
          having to remove your entire head and start all over again!

          >
          > Hi Maurice, how goes the world with you?


          My mind's been a bit lazy of late, but thanks for asking. I know little
          of Newton's involvement with the esoteric but it is fitting that he did
          lean this way as he must have felt dreadful at banishing the soul from
          reality. Feelings for the soul were very much more alive then.


          > He was more involved with forgers than was purely professional, it
          > seems, and formed associations with spies and informers in his pursuit
          > of them. He also devised new tortures and methods of execution for
          > those he caught. Is there an analogy here with the Newtonian concepts
          > you quoted ? It seems that Blake thought so. His painting seems also
          > to link Newton with the Masonic idea of God as Architect, and shows
          > the symbol of the compass, and a threatening movement from light to
          > dark, although I suppose that can also be read the other way. Paradox.


          What struck me about the painting was the power in the rippling muscle,
          the right-angle of the visible leg, the way his being rests upon rock
          yet the left foot has to emerge from under the rock as if it were
          necessary for the rock to be supported! I found that delightful. Maybe
          it can be seen as analogous.

          >
          > ... Samuel Taylor Coleridge. Driven, perhaps by Coleridge's notion of
          > Algebra as the science of time, Hamilton discovered a four dimensional
          > manifold of numbers, the `quarternions' - usually called hypercomplex
          > numbers today." End of quote


          I've searched and searched for Coleridge's philosophy on the net but its
          just not there. Literary stuff only. I do not know of quarternion's and
          it mystifies me as the Gauss Theorem is supposed to prove that there are
          no more possible numbers after the complex.

          >
          >
          > As I say, it is a struggle for me, but I read the lectures anyway, and
          > get glimpses here and there, which is the best I can do. The following
          > few lines from Steiner reminded me of Daniel's poem about the shadow.
          >
          > Steiner - "Now that we have admitted the possibility that a
          > four-dimensional world exists, we may wonder whether we can observe a
          > four dimensional object with out being clairvoyant. A projection of
          > sorts allows us to do so. We can turn a plane figure until the shadow
          > it casts is a line. Similarly the shadow of a line can be a point, and
          > the shadow image of a solid three dimensional object is a
          > two-dimension al plane figure. Thus, once we are convinced of the
          > existence of a fourth dimension, it is only natural to say that
          > three-dimensional figures are the shadow images of four dimensional
          > figures." End of quote.


          p225-230 Goethean Science, Mercury Press seems to refute the notion that
          space can have more than 3D. The reason is that space, as defined by RS
          but only implicit in Goethe, is the idea of separation between
          *independent* existents. (Leibniz in his letters to Clark has a less
          accurately expressed but similar notion of space as relative to the
          existents.) Independent means that if one is annihilated then the other
          remains unchanged, the existence of one is independent of the other. The
          development is to consider only two existents and how the idea of space
          (and only space) proceeds between them. It leads to the realisation that
          independence in existence is not compatible with more than 3D. So we have

          1. the bare notion of separation as such
          2. the separation of two real existents = 1D

          (if 1D were a human being there would be a real existent in each hand)

          Adding a 3rd existent does NOT qualitatively alter the dimension. In
          Cartesian geometry, in fact all spatial geometry (excludes projective)
          the second and subsequent dimensions are of the same kind as the first.
          However this erroneous dimension is made by adding a third real point,
          altering the terms of reference to more than pure space only. You can
          reduce it back to two existents by, for example, imagining two of the
          points removed but the centre point of the line between them remaining

          3. the separation of a real and an ideal or virtual point = 2D

          This is qualitatively different. If the measure of 1D is distance then
          now it is angle. The second dimension is delimited by the centre real
          point and the line at infinity - the ideal line - this is the totality
          of the plane. Contact is only just maintained with reality in the second
          'existent' in that it "points to" the original real existents which have
          been abstracted away in thought. ("Points to" is a nebulous philosophic
          phrase without a precise meaning.)

          4. 3D now has to be the separation of two ideal points.

          But now we have totally lost contact with reality and returned to the
          bare notion of separation. Therefore 3D *completes* the idea of space
          and there cannot be a fourth dimension *retaining independent
          existents*. The measure of 3D is space itself.


          > ... Was it Olive Whicher who, speaking of levity, commented on
          > Newton's discovery occasioned by the apple falling, and that nobody
          > asks how it got up there in the first place?


          It is very often indeed a crunch question, "How did you arrive at the
          presuppositions or theory?"

          Maurice

          >
          >
        • jan
          On 31/7/03 1:06 pm, Maurice McCarthy wrote: Hello Maurice, If this is your mind when lazy, what¹s it like when exercised!?
          Message 4 of 7 , Jul 31, 2003
            Re: [anthroposophy] Blak Holes On 31/7/03 1:06 pm, "Maurice McCarthy" <maurice.mccarthy@...> wrote:
                 



                   Hello Maurice,  If this is your mind when lazy, what’s it like when exercised!?
                   About to print out.  It will certainly turn my head inside out, but I’ll try my best!
                   Interestingly, a member of The Royal Society spoke on the radio news this
                   morning, don’t know if you heard it.  He was suggesting a double helix or
                   something similar to stand on the empty  plinth in Trafalgar Square to
                   commemorate Crick and the Roslin Institute.  As the alternative seems to
             be the Queen Mother, I think the double helix wins!  I would like to
             leave it empty, and think the double helix into movement, a supersensible sculpture!
            Thanks, Jan
            PS Paul, you can come round and explain it to me!

            Dear Jan and Paul

            The Oort Cloud was first discovered, if memory serves, in the 1930's by
            the Dutchman of that name. It is supposed to be an invisible cloud of
            dust and ice surrounding the solar system. Usually we think of space
            existing whether or not there is something in it but it could not exist
            at all unless there were two or more things to separate. And conversely
            there would not be physical objects without space (and time). From our
            viewpoint on Earth space must cease to exist at a certain distance from
            the Earth because there is nothing to be separate from - paradoxical, I
            know, but RS mentions that between the galaxies is non-space 'occupied'
            by the Seraphim and Cherubim, keeping the galaxies in respective
            position. Similarly our solar system must have its spatial limit. At
            this limit physical matter ceases to exist so that the comets have to
            materialise. Beyond the limit is spiritual communion which forbids the
            kind of spatial relations that we know. The plot thickens with light
            from other galaxies, of course - what does it mean for this light to
            cross non-space? How now the red-shift? To understand it seems like
            having to remove your entire head and start all over again!

            >
            > Hi Maurice, how goes the world with you?


            My mind's been a bit lazy of late, but thanks for asking. I know little
            of Newton's involvement with the esoteric but it is fitting that he did
            lean this way as he must have felt dreadful at banishing the soul from
            reality. Feelings for the soul were very much more alive then.


            > He was more involved with forgers than was purely professional, it
            > seems, and formed associations with spies and informers in his pursuit
            > of them. He also devised new tortures and methods of execution for
            > those he caught. Is there an analogy here with the Newtonian concepts
            > you quoted ? It seems that Blake thought so. His painting seems also
            > to link Newton with the Masonic idea of God as Architect, and shows
            > the symbol of the compass, and a threatening movement from light to
            > dark, although I suppose that can also be read the other way. Paradox.


            What struck me about the painting was the power in the rippling muscle,
            the right-angle of the visible leg, the way his being rests upon rock
            yet the left foot has to emerge from under the rock as if it were
            necessary for the rock to be supported! I found that delightful. Maybe
            it can be seen as analogous.

            >
            > ... Samuel Taylor Coleridge. Driven, perhaps by Coleridge's notion of
            > Algebra as the science of time, Hamilton discovered a four dimensional
            > manifold of numbers, the `quarternions' - usually called hypercomplex
            > numbers today." End of quote


            I've searched and searched for Coleridge's philosophy on the net but its
            just not there. Literary stuff only. I do not know of quarternion's and
            it mystifies me as the Gauss Theorem is supposed to prove that there are
            no more possible numbers after the complex.

            >
            >
            > As I say, it is a struggle for me, but I read the lectures anyway, and
            > get glimpses here and there, which is the best I can do. The following
            > few lines from Steiner reminded me of Daniel's poem about the shadow.
            >
            > Steiner - "Now that we have admitted the possibility that a
            > four-dimensional world exists, we may wonder whether we can observe a
            > four dimensional object with out being clairvoyant. A projection of
            > sorts allows us to do so. We can turn a plane figure until the shadow
            > it casts is a line. Similarly the shadow of a line can be a point, and
            > the shadow image of a solid three dimensional object is a
            > two-dimension al plane figure. Thus, once we are convinced of the
            > existence of a fourth dimension, it is only natural to say that
            > three-dimensional figures are the shadow images of four dimensional
            > figures." End of quote.


            p225-230 Goethean Science, Mercury Press seems to refute the notion that
            space can have more than 3D. The reason is that space, as defined by RS
            but only implicit in Goethe, is the idea of separation between
            *independent* existents. (Leibniz in his letters to Clark has a less
            accurately expressed but similar notion of space as relative to the
            existents.) Independent means that if one is annihilated then the other
            remains unchanged, the existence of one is independent of the other. The
            development is to consider only two existents and how the idea of space
            (and only space) proceeds between them. It leads to the realisation that
            independence in existence is not compatible with more than 3D. So we have

            1. the bare notion of separation as such
            2. the separation of two real existents = 1D

            (if 1D were a human being there would be a real existent in each hand)

            Adding a 3rd existent does NOT qualitatively alter the dimension. In
            Cartesian geometry, in fact all spatial geometry (excludes projective)
            the second and subsequent dimensions are of the same kind as the first.
            However this erroneous dimension is made by adding a third real point,
            altering the terms of reference to more than pure space only. You can
            reduce it back to two existents by, for example, imagining two of the
            points removed but the centre point of the line between them remaining

            3. the separation of a real and an ideal or virtual point = 2D

            This is qualitatively different. If the measure of 1D is distance then
            now it is angle. The second dimension is delimited by the centre real
            point and the line at infinity - the ideal line - this is the totality
            of the plane. Contact is only just maintained with reality in the second
            'existent' in that it "points to" the original real existents which have
            been abstracted away in thought. ("Points to" is a nebulous philosophic
            phrase without a precise meaning.)

            4. 3D now has to be the separation of two ideal points.

            But now we have totally lost contact with reality and returned to the
            bare notion of separation. Therefore 3D *completes* the idea of space
            and there cannot be a fourth dimension *retaining independent
            existents*. The measure of 3D is space itself.


            > ... Was it Olive Whicher who, speaking of levity, commented on
            > Newton's discovery occasioned by the apple falling, and that nobody
            > asks how it got up there in the first place?


            It is very often indeed a crunch question, "How did you arrive at the
            presuppositions or theory?"

            Maurice

            >
            >



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          • Maurice McCarthy
            http://www.princeton.edu/~his291/Newton.html http://www.artmagick.com/paintings/enlarge.aspx?pid=2221&path=blake/blake7 Are two of the larger images of Blake s
            Message 5 of 7 , Jul 31, 2003
              http://www.princeton.edu/~his291/Newton.html
              http://www.artmagick.com/paintings/enlarge.aspx?pid=2221&path=blake/blake7

              Are two of the larger images of Blake's Newton available online. I've
              never actually seen the real thing, which I think is at the Tate
              Gallery. If it is true to the original you can see what I meant about
              the foot emerging from the rock.

              Missed the Royal Society spokesman though.

              Maybe we live in a plum pudding universe with islands of physical
              reality surrounding each star in the life-sea of the spirit. At the
              level of number theory Chaitin has worked out that there are only
              islands of rational mathematics in the sea of random numbers.

              http://www.cs.umaine.edu/~chaitin

              See the interview for Channel 4, London about half way down the page.

              Maurice.
            • jan
              On 31/7/03 3:50 pm, Maurice McCarthy wrote: The picture is interesting in lots of ways. The rock seems organic, at least
              Message 6 of 7 , Jul 31, 2003
                Re: [anthroposophy] Blak Holes On 31/7/03 3:50 pm, "Maurice McCarthy" <maurice.mccarthy@...> wrote:

                        The picture is interesting in lots of ways.  The rock seems organic, at least overgrown with mosses and leafy forms in an integral way, as if it is not purely mineral, and definitely not inert.
                Near to the foot, which can also be seen as emerging out of the rock, are winglike leafy forms.
                The scroll, some kind of material, rolled out, being measured or geometrised, ends in a Keely like spiral, as if the etheric works into it, or as if the scroll itself is a picture of life, rolled out. It almost seems to roll away from him. The gave is focused and concentrated downward.
                     The scroll-folds appear to issue from the figure, as if it is his own life which is being measured and mapped.  The hand holding the compass is out of proportion, much larger than the other. It is actually like a figure in two halves, the left (compass holding) hand and foot seeming not to belong to the figure at all.
                     Another interesting thing was that Newton moved currency from silver to gold.
                     I have been having another look at what you wrote.  It is easier for me to understand the indications given about time and space and dimension in the many cosmology lectures where he speaks of the Heirarchies. Those I love, and seem to assimilate more easily. I don’t know whether it is a result of not having any kind of education other than reading, or whether I just can’t understand maths and don’t have the head for it. (although I play around with projective geometry to try to get the concepts)  When I was a child I got hold of an old maths book and tried to teach myself but did not get very far.
                    I’ve been reading a wonderful play about Keely, “Amplitude of Force” by Martha Keltz.  There are many pertinent thoughts in it, but I love this hopeful piece.

                           Let a crowd of men
                          Generate so dark a dissonance
                          And hatred is augmented.
                          The amplitude of force
                          Is precisely proportionate
                          To the number of units vibrating
                          At that particular pitch.
                          But a far smaller degree
                          Of sympathy, of love
                          Can counter this force,
                          And Charles is full of goodwill
                          For earnest seekers of truth,
                          Of which there must have been
                          One or two in that crowd.
                          Thereby was he protected
                          From more serious effects.......

                      Thank you for patiently explaining.  I’ve always found in my life that the struggle for things I can’t do has been more important than those I can!
                Jan


                http://www.princeton.edu/~his291/Newton.html
                http://www.artmagick.com/paintings/enlarge.aspx?pid=2221&path=blake/blake7

                Are two of the larger images of Blake's Newton available online. I've
                never actually seen the real thing, which I think is at the Tate
                Gallery. If it is true to the original you can see what I meant about
                the foot emerging from the rock.

                Missed the Royal Society spokesman though.

                Maybe we live in a plum pudding universe with islands of physical
                reality surrounding each star in the life-sea of the spirit. At the
                level of number theory Chaitin has worked out that there are only
                islands of rational mathematics in the sea of random numbers.

                http://www.cs.umaine.edu/~chaitin

                See the interview for Channel 4, London about half way down the page.

                Maurice.




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              • snowplank
                Hi guys,Just back from a weekend festival so playing catch up with the list. I have heard about the quaternions that Maurice mentioned before. It was in an
                Message 7 of 7 , Aug 5, 2003
                  Hi guys,

                  Just back from a weekend festival so playing catch up with the list.
                  I have heard about the quaternions that Maurice mentioned before. It
                  was in an article written by Richard Hoagland's lot from the
                  Enterprise Mission;

                  see http://www.enterprisemission.com/hyper1.html

                  It is quite a long article and I NEVER take anything at face value fro
                  m this website as there is a plethora of deliberately misleading junk
                  therein. However I printed out this article as it contained some
                  'mind candy' in the form of hyper-dimensional physics. It seems that
                  A.S. Hathaway wrote a paper entitled "Quaternions as numbers of
                  four-dimensional space".

                  Anyway, I hope you enjoy the article.

                  Paul




                  --- In anthroposophy@yahoogroups.com, jan <starbirdgarden@b...> wrote:
                  > On 31/7/03 1:06 pm, "Maurice McCarthy" <maurice.mccarthy@n...>
                  > wrote:
                  >
                  >
                  >
                  >
                  > Hello Maurice, If this is your mind when lazy, what¹s it
                  like when
                  > exercised!?
                  > About to print out. It will certainly turn my head inside
                  out, but
                  > I¹ll try my best!
                  > Interestingly, a member of The Royal Society spoke on the
                  radio news
                  > this
                  > morning, don¹t know if you heard it. He was suggesting a double
                  > helix or
                  > something similar to stand on the empty plinth in Trafalgar
                  Square
                  > to
                  > commemorate Crick and the Roslin Institute. As the
                  alternative seems
                  > to
                  > > be the Queen Mother, I think the double helix wins! I would like to
                  > > leave it empty, and think the double helix into movement, a
                  supersensible
                  > > sculpture!
                  > > Thanks, Jan
                  > > PS Paul, you can come round and explain it to me!
                  > >
                  > > Dear Jan and Paul
                  > >
                  > > The Oort Cloud was first discovered, if memory serves, in the
                  1930's by
                  > > the Dutchman of that name. It is supposed to be an invisible cloud of
                  > > dust and ice surrounding the solar system. Usually we think of space
                  > > existing whether or not there is something in it but it could not
                  exist
                  > > at all unless there were two or more things to separate. And
                  conversely
                  > > there would not be physical objects without space (and time). From our
                  > > viewpoint on Earth space must cease to exist at a certain distance
                  from
                  > > the Earth because there is nothing to be separate from -
                  paradoxical, I
                  > > know, but RS mentions that between the galaxies is non-space
                  'occupied'
                  > > by the Seraphim and Cherubim, keeping the galaxies in respective
                  > > position. Similarly our solar system must have its spatial limit. At
                  > > this limit physical matter ceases to exist so that the comets have to
                  > > materialise. Beyond the limit is spiritual communion which forbids the
                  > > kind of spatial relations that we know. The plot thickens with light
                  > > from other galaxies, of course - what does it mean for this light to
                  > > cross non-space? How now the red-shift? To understand it seems like
                  > > having to remove your entire head and start all over again!
                  > >
                  > >> >
                  > >> > Hi Maurice, how goes the world with you?
                  > >
                  > >
                  > > My mind's been a bit lazy of late, but thanks for asking. I know
                  little
                  > > of Newton's involvement with the esoteric but it is fitting that
                  he did
                  > > lean this way as he must have felt dreadful at banishing the soul from
                  > > reality. Feelings for the soul were very much more alive then.
                  > >
                  > >
                  > >> > He was more involved with forgers than was purely professional, it
                  > >> > seems, and formed associations with spies and informers in his
                  pursuit
                  > >> > of them. He also devised new tortures and methods of execution for
                  > >> > those he caught. Is there an analogy here with the Newtonian
                  concepts
                  > >> > you quoted ? It seems that Blake thought so. His painting seems
                  also
                  > >> > to link Newton with the Masonic idea of God as Architect, and shows
                  > >> > the symbol of the compass, and a threatening movement from light to
                  > >> > dark, although I suppose that can also be read the other way.
                  Paradox.
                  > >
                  > >
                  > > What struck me about the painting was the power in the rippling
                  muscle,
                  > > the right-angle of the visible leg, the way his being rests upon rock
                  > > yet the left foot has to emerge from under the rock as if it were
                  > > necessary for the rock to be supported! I found that delightful. Maybe
                  > > it can be seen as analogous.
                  > >
                  > >> >
                  > >> > ... Samuel Taylor Coleridge. Driven, perhaps by Coleridge's
                  notion of
                  > >> > Algebra as the science of time, Hamilton discovered a four
                  dimensional
                  > >> > manifold of numbers, the `quarternions' - usually called
                  hypercomplex
                  > >> > numbers today." End of quote
                  > >
                  > >
                  > > I've searched and searched for Coleridge's philosophy on the net
                  but its
                  > > just not there. Literary stuff only. I do not know of
                  quarternion's and
                  > > it mystifies me as the Gauss Theorem is supposed to prove that
                  there are
                  > > no more possible numbers after the complex.
                  > >
                  > >> >
                  > >> >
                  > >> > As I say, it is a struggle for me, but I read the lectures
                  anyway, and
                  > >> > get glimpses here and there, which is the best I can do. The
                  following
                  > >> > few lines from Steiner reminded me of Daniel's poem about the
                  shadow.
                  > >> >
                  > >> > Steiner - "Now that we have admitted the possibility that a
                  > >> > four-dimensional world exists, we may wonder whether we can
                  observe a
                  > >> > four dimensional object with out being clairvoyant. A projection of
                  > >> > sorts allows us to do so. We can turn a plane figure until the
                  shadow
                  > >> > it casts is a line. Similarly the shadow of a line can be a
                  point, and
                  > >> > the shadow image of a solid three dimensional object is a
                  > >> > two-dimension al plane figure. Thus, once we are convinced of the
                  > >> > existence of a fourth dimension, it is only natural to say that
                  > >> > three-dimensional figures are the shadow images of four dimensional
                  > >> > figures." End of quote.
                  > >
                  > >
                  > > p225-230 Goethean Science, Mercury Press seems to refute the
                  notion that
                  > > space can have more than 3D. The reason is that space, as defined
                  by RS
                  > > but only implicit in Goethe, is the idea of separation between
                  > > *independent* existents. (Leibniz in his letters to Clark has a less
                  > > accurately expressed but similar notion of space as relative to the
                  > > existents.) Independent means that if one is annihilated then the
                  other
                  > > remains unchanged, the existence of one is independent of the
                  other. The
                  > > development is to consider only two existents and how the idea of
                  space
                  > > (and only space) proceeds between them. It leads to the
                  realisation that
                  > > independence in existence is not compatible with more than 3D. So
                  we have
                  > >
                  > > 1. the bare notion of separation as such
                  > > 2. the separation of two real existents = 1D
                  > >
                  > > (if 1D were a human being there would be a real existent in each hand)
                  > >
                  > > Adding a 3rd existent does NOT qualitatively alter the dimension. In
                  > > Cartesian geometry, in fact all spatial geometry (excludes projective)
                  > > the second and subsequent dimensions are of the same kind as the
                  first.
                  > > However this erroneous dimension is made by adding a third real point,
                  > > altering the terms of reference to more than pure space only. You can
                  > > reduce it back to two existents by, for example, imagining two of the
                  > > points removed but the centre point of the line between them remaining
                  > >
                  > > 3. the separation of a real and an ideal or virtual point = 2D
                  > >
                  > > This is qualitatively different. If the measure of 1D is distance then
                  > > now it is angle. The second dimension is delimited by the centre real
                  > > point and the line at infinity - the ideal line - this is the totality
                  > > of the plane. Contact is only just maintained with reality in the
                  second
                  > > 'existent' in that it "points to" the original real existents
                  which have
                  > > been abstracted away in thought. ("Points to" is a nebulous
                  philosophic
                  > > phrase without a precise meaning.)
                  > >
                  > > 4. 3D now has to be the separation of two ideal points.
                  > >
                  > > But now we have totally lost contact with reality and returned to the
                  > > bare notion of separation. Therefore 3D *completes* the idea of space
                  > > and there cannot be a fourth dimension *retaining independent
                  > > existents*. The measure of 3D is space itself.
                  > >
                  > >
                  > >> > ... Was it Olive Whicher who, speaking of levity, commented on
                  > >> > Newton's discovery occasioned by the apple falling, and that nobody
                  > >> > asks how it got up there in the first place?
                  > >
                  > >
                  > > It is very often indeed a crunch question, "How did you arrive at the
                  > > presuppositions or theory?"
                  > >
                  > > Maurice
                  > >
                  > >> >
                  > >> >
                  > >
                  > >
                  > >
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