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Re: [sl] Indian magic squares

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  • Dan Washburn
    Bravo, Mark! This sounds like a fantastic find. You are certainly filling in all sorts of gaps in our knowledge of the history of the squares. When I think
    Message 1 of 3 , Mar 8, 2001
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      Bravo, Mark!

      This sounds like a fantastic find. You are certainly filling in all
      sorts of gaps in our knowledge of the history of the squares. When I
      think back to what we knew when you first started and what we know now,
      I am totally impressed with the mega leaps that have ocurred. Please
      torment us on the list as much as possible with your continuing
      fascination with the squares.

      I know that the squares research is part of a broader inquiry into the
      relation of mathematics and the sense of the sacred. Any preliminary
      intuitions you would like to share with us on that topic?

      In the Taliban correspondence we have been talking about spiritual
      emptiness, the lack of a firm root in the sense of the sacred. Its my
      feeling that the west won't recover from grieving for the death of god
      until mathematics and mysticism are united in marriage. So I'm
      interested in any thoughts you have on the subject.

      Dan W.

      Mark Swaney wrote:
      >
      > Hey folks,
      >
      > In spite of my intense desire to inflame the sensibilities of every
      > normal thinking person on this list with my searing radical opinions
      > about the Taliban (I hate 'em - but then I don't like any
      > self-righteous religious killer scum and blah blah blah) anyway, I got
      > this new great information and I can't stand not to talk/write about
      > it, and since nobody in the actual FLESH every speaks to me, I am
      > blessed, as they say down here in the Bible-Belt, to have my friends
      > on the SL list to drive nuts with my peculiar fascinations.
      >
      > It seems that in 1993 a certain Takanori Kusba, then a candidate
      > for a PhD in the History of Science residing at Brown University,
      > wrote for his PhD thesis "Combinatorics and Magic Squares in India - A
      > Study of Narayana Pandita's Ganitakaumundi, Chapters 13 & 14"
      >
      > And yesterday I finally got my grubby little hands on the
      > delectable goodies.
      >
      > Two volumes worth, including the original text of the Chapters of
      > the Ganitakaumundi (published in India 1356 AD), in Sanskrit, AND the
      > English Translation! The whole effort is about 562 pages of the best
      > information available on Indian magic squares! Now this thing is
      > beautiful, Narayana Pandita was an artist as well as a mathematician -
      > the book is LOADED with magic squares and diagrams and also a fair
      > amount on the *applications* of the magic squares.
      >
      > Kusuba also surveys the whole history of Indian magic squares,
      > giving in particular the magic squares of the Kaksaputa , a mysterious
      > work on divination ascribed to the Indian alchemist, Nagarjuna, as
      > well as the early work of Varahamihira. Kusuba establishes that
      > Varahamihira published the earliest known magic square of 4 in 550 AD
      > in India, in a book on astronomy an divination called the
      > Brhatsamhita, consisting of 106 chapters of which one describes a
      > method of mixing perfume, or incense, according to proportions given
      > by a magic square. The interesting aspect of this is that
      > mathematically the first published magic square of 4 is also
      > pandiagonal. That has implications for the history of combinatorics
      > in as much as pandiagonal magic squares are more advanced than
      > ordinary magic squares and imply the further knowledge of Latin
      > Squares, cousins of the magic squares, and which are important to
      > modern combinatorics.
      >
      > But further and on to Narayana Pandita himself, he will speak to
      > you now from 14th century India, and quoting from the Ganitakaumundi;
      >
      > "Now the rules concerning the net of numbers
      >
      > 1) I will briefly describe the net of numbers which causes
      > enjoyment for mathematicians, in which those who are jealous,
      > depraved, and poor mathematicians fall down.
      >
      > 2) It is applied to dance and music, medicine, garland-making, and
      > mathematics as well as architecture. Knowledge of these subjects is
      > indeed acquired by means of the net of numbers"
      >
      > The net of numbers refers to the Indian study of arranging objects
      > in specific fields in specific orders and the combinations and
      > permutations of these arrangements. The rules of this practice deal
      > with the short and long syllables in metrics (poetry), notes and beats
      > in music, tastes in medicine, and windows in architecture. Narayana
      > generalized these rules in the theory of ankapasa, the Net of Numbers.
      >
      > So I'll be having a lot of fun with this for a while, there is a
      > ton more juicy stuff that is in this work I don't have time to go into
      > now, but I will put it into the HIstory of magic squares that I am
      > preparing for Dan's web page.
      >
      > Mark
      >
      > --
      > Please address any e-mail to my new address: mswaney@...
      >
      > Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
    • Mark Swaney
      ... Well, ok, but most of the work will have to wind up on your web page, where we will organize the research findings to date, and post them as a finished
      Message 2 of 3 , Mar 9, 2001
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        Dan Washburn wrote:
        Bravo, Mark!

        This sounds like a fantastic find. You are certainly filling in all
        sorts of gaps in our knowledge of the history of the squares. When I
        think back to what we knew when you first started and what we know now,
        I am totally impressed with the mega leaps that have ocurred. Please
        torment us on the list as much as possible with your continuing
        fascination with the squares.
        Well, ok, but most of the work will have to wind up on your web page, where we will organize the research findings to date, and post them as a finished work, Revision "A" as we say in the engineering world, complete with diagrams and illustrations.  Let's get together on the update project.
        I know that the squares research is part of a broader inquiry into the
        relation of mathematics and the sense of the sacred. Any preliminary
        intuitions you would like to share with us on that topic?
        Nothing that I would call wild or wonderful, however the catalog of religious reverence for the mathematics of the magic squares alone, include, Daoism, Confucianism, the Jains, the Sufis and Islam, the Hindus, the Hebrews, and the Christians.  An impressive total for the proposition that there is in fact some connection between what people consider "Sacred" and mathematics.  The real result is the ability to demonstrate forcefully that such a connection does in fact exist.  It will then become necessary for folks smarter than me to flesh out the nature of the links. 

        My bet is that it has to do with the way information is organized in the brain.  This emphasis on information is important for a radical theory of physical existence that requires that the Universe be actually observed before it can in fact exist.  Compare to the theories on the Birth of the Universe of the Kabbalists.  The meaning of the name of god IHVH, means "I Am" - the radical statement of existence.  Information implies consciousness, and has implications stemming from the second law of thermodynamics, which as you know is highly relevant to the essence of "time" as we experience it, and therefore to our awareness, to our very existence.
        In the Taliban correspondence we have been talking about spiritual
        emptiness, the lack of a firm root in the sense of the sacred. Its my
        feeling that the west won't recover from grieving for the death of god
        until mathematics and mysticism are united in marriage. So I'm
        interested in any thoughts you have on the subject.
        Well that's a dramatic way of putting it, but I see a solution (I imagine!) to the science/religion quandary, to the old war between the Dualist and the Materialist viewpoints.  In my way of thinking, the Dualist can have whatever they want, because the experience of the Sacred is not affected in any way by the synthesis between the thesis (dualism) and the antithesis (materialism).  Nor are moral values, ethics, consequences, laws, rules, etc. as well as the mystical visionary experiences and profound compassion of the Saints of all religions.  Lets call the synthesis Meta-Materialism, or just M&M for short.  No relation to the music star.  According to M&M theory, the Sacred is just as real, and for essentially the same reasons, as it is in the Dualist system.  In the M&M view the Sacred, just as we experience it, just as we feel it, is in fact, *real*, precisely because it is based on a Unified Definition of Reality which is the unity, the totality of the "material" - or as I would describe it, the meta-material world, that is everything that is around us in all it's forms from dung to gold, from star dust to the pyramids.  This view is to my mind not very different from the system as propounded by the mystics of the Spanish Kabbalists schools in the emanationist theory.
        Mark
        -- 
        Please address any e-mail to my new address:  mswaney@...

      • datki90
        greeting, I was reading the posting below. Does anyone know where I can find the book Ganita Kaumudi ? Thanks in-advance, Dimitri Atkins ... I ... now, ...
        Message 3 of 3 , Jun 4, 2003
        • 0 Attachment
          greeting,

          I was reading the posting below. Does anyone know where I can find
          the book "Ganita Kaumudi"?

          Thanks in-advance,
          Dimitri Atkins




          --- In sacredlandscapelist@yahoogroups.com, Dan Washburn <danw@n...>
          wrote:
          > Bravo, Mark!
          >
          > This sounds like a fantastic find. You are certainly filling in all
          > sorts of gaps in our knowledge of the history of the squares. When
          I
          > think back to what we knew when you first started and what we know
          now,
          > I am totally impressed with the mega leaps that have ocurred.
          Please
          > torment us on the list as much as possible with your continuing
          > fascination with the squares.
          >
          > I know that the squares research is part of a broader inquiry into
          the
          > relation of mathematics and the sense of the sacred. Any
          preliminary
          > intuitions you would like to share with us on that topic?
          >
          > In the Taliban correspondence we have been talking about spiritual
          > emptiness, the lack of a firm root in the sense of the sacred. Its
          my
          > feeling that the west won't recover from grieving for the death of
          god
          > until mathematics and mysticism are united in marriage. So I'm
          > interested in any thoughts you have on the subject.
          >
          > Dan W.
          >
          > Mark Swaney wrote:
          > >
          > > Hey folks,
          > >
          > > In spite of my intense desire to inflame the sensibilities of
          every
          > > normal thinking person on this list with my searing radical
          opinions
          > > about the Taliban (I hate 'em - but then I don't like any
          > > self-righteous religious killer scum and blah blah blah) anyway,
          I got
          > > this new great information and I can't stand not to talk/write
          about
          > > it, and since nobody in the actual FLESH every speaks to me, I am
          > > blessed, as they say down here in the Bible-Belt, to have my
          friends
          > > on the SL list to drive nuts with my peculiar fascinations.
          > >
          > > It seems that in 1993 a certain Takanori Kusba, then a
          candidate
          > > for a PhD in the History of Science residing at Brown University,
          > > wrote for his PhD thesis "Combinatorics and Magic Squares in
          India - A
          > > Study of Narayana Pandita's Ganitakaumundi, Chapters 13 & 14"
          > >
          > > And yesterday I finally got my grubby little hands on the
          > > delectable goodies.
          > >
          > > Two volumes worth, including the original text of the Chapters
          of
          > > the Ganitakaumundi (published in India 1356 AD), in Sanskrit, AND
          the
          > > English Translation! The whole effort is about 562 pages of the
          best
          > > information available on Indian magic squares! Now this thing is
          > > beautiful, Narayana Pandita was an artist as well as a
          mathematician -
          > > the book is LOADED with magic squares and diagrams and also a fair
          > > amount on the *applications* of the magic squares.
          > >
          > > Kusuba also surveys the whole history of Indian magic squares,
          > > giving in particular the magic squares of the Kaksaputa , a
          mysterious
          > > work on divination ascribed to the Indian alchemist, Nagarjuna, as
          > > well as the early work of Varahamihira. Kusuba establishes that
          > > Varahamihira published the earliest known magic square of 4 in
          550 AD
          > > in India, in a book on astronomy an divination called the
          > > Brhatsamhita, consisting of 106 chapters of which one describes a
          > > method of mixing perfume, or incense, according to proportions
          given
          > > by a magic square. The interesting aspect of this is that
          > > mathematically the first published magic square of 4 is also
          > > pandiagonal. That has implications for the history of
          combinatorics
          > > in as much as pandiagonal magic squares are more advanced than
          > > ordinary magic squares and imply the further knowledge of Latin
          > > Squares, cousins of the magic squares, and which are important to
          > > modern combinatorics.
          > >
          > > But further and on to Narayana Pandita himself, he will speak
          to
          > > you now from 14th century India, and quoting from the
          Ganitakaumundi;
          > >
          > > "Now the rules concerning the net of numbers
          > >
          > > 1) I will briefly describe the net of numbers which causes
          > > enjoyment for mathematicians, in which those who are jealous,
          > > depraved, and poor mathematicians fall down.
          > >
          > > 2) It is applied to dance and music, medicine, garland-making,
          and
          > > mathematics as well as architecture. Knowledge of these subjects
          is
          > > indeed acquired by means of the net of numbers"
          > >
          > > The net of numbers refers to the Indian study of arranging
          objects
          > > in specific fields in specific orders and the combinations and
          > > permutations of these arrangements. The rules of this practice
          deal
          > > with the short and long syllables in metrics (poetry), notes and
          beats
          > > in music, tastes in medicine, and windows in architecture.
          Narayana
          > > generalized these rules in the theory of ankapasa, the Net of
          Numbers.
          > >
          > > So I'll be having a lot of fun with this for a while, there is
          a
          > > ton more juicy stuff that is in this work I don't have time to go
          into
          > > now, but I will put it into the HIstory of magic squares that I am
          > > preparing for Dan's web page.
          > >
          > > Mark
          > >
          > > --
          > > Please address any e-mail to my new address: mswaney@e...
          > >
          > > Your use of Yahoo! Groups is subject to the Yahoo! Terms of
          Service.
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