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help me remember this non-linear language from years back

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  • Alex Fink
    When Sai or myself (but he particularly) are discussing UNLWS we often like to cite precedents. There is one conlang in particular I remember from this list,
    Message 1 of 19 , Aug 25 3:06 AM
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      When Sai or myself (but he particularly) are discussing UNLWS we often
      like to cite precedents. There is one conlang in particular I
      remember from this list, years ago -- before 2009? but surely after
      2004 when I joined -- which was a nonlinear language on the
      nodes-and-connections model, "fully 2D" in Sai's sense, but I've never
      been able to re-find it. Its words looked something like this
      *
      *
      * * *
      *******
      * * *
      *******
      * *
      * *
      but drawn more caligraphically, and with the vertical lines a little
      bit concave (and quite possibly in red, or red shadow, on the
      documentation webpages). Sentences were tree-like; the legs at the
      bottom of the glyph could be connected to the lines at the top of its
      arguments.
      Can anyone help me track this language down?

      I did turn up a few dead links: one of Rémi Villatel
      https://listserv.brown.edu/archives/cgi-bin/wa?A2=conlang;55b6b829.0505C
      and one which Sai found but didn't even state the name of *glare* and
      has now fallen off the ZBB
      https://listserv.brown.edu/archives/cgi-bin/wa?A2=conlang;d8ec9da5.0607B .

      The post Sai was just composing was at
      http://www.reddit.com/r/conlangs/comments/2dimz9/what_are_some_writtenonly_conlangs/
      which I would modify by saying
      - Shaquelingua is Rémi's principal language but I doubt it's the
      nonlinear one above
      - the only scripts of Pehrson that I've ever seen him describe the
      workings of are phonetic, or phonetic with logographic elements,
      arranged caligraphically but linearly.

      Alex
    • And Rosta
      ... What is fully 2D? What is partially 2D? (I mean, please remind what the terms mean.) I m guessing a musical stave, bounded in one dimension and unbounded
      Message 2 of 19 , Aug 25 7:30 AM
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        On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
        >
        > There is one conlang in particular I
        > remember from this list, years ago -- before 2009? but surely after
        > 2004 when I joined -- which was a nonlinear language on the
        > nodes-and-connections model, "fully 2D" in Sai's sense,

        What is fully 2D? What is partially 2D? (I mean, please remind what the
        terms mean.)

        I'm guessing a musical stave, bounded in one dimension and unbounded in the
        other, would count as partially 2D and full 2Dness requires unboundedness
        in both dimensions. If so, is there an identifiable taxonomy of fully 2D
        types, such as the node--connector systems, the grid system, and so forth?

        And
      • Thomas Ruhm
        Donkey Kong Country and Odd World where partially 3D.
        Message 3 of 19 , Aug 25 8:15 AM
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          Donkey Kong Country and Odd World where partially 3D.

          > On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
          >>
          >> There is one conlang in particular I
          >> remember from this list, years ago -- before 2009? but surely after
          >> 2004 when I joined -- which was a nonlinear language on the
          >> nodes-and-connections model, "fully 2D" in Sai's sense,
          >
          > What is fully 2D? What is partially 2D? (I mean, please remind what the
          > terms mean.)
          >
          > I'm guessing a musical stave, bounded in one dimension and unbounded in the
          > other, would count as partially 2D and full 2Dness requires unboundedness
          > in both dimensions. If so, is there an identifiable taxonomy of fully 2D
          > types, such as the node--connector systems, the grid system, and so forth?
          >
          > And
        • Sai
          To me, fully 2D means that the syntax is two-dimensional — i.e. it is not comprised of potentially two-dimensional components or morphology that are
          Message 4 of 19 , Aug 25 8:16 AM
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            To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
            is not comprised of potentially two-dimensional components or
            morphology that are arranged according to a one-dimensional (or free)
            syntax.

            I don't know whether the cartouche-based ornamental script for
            Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
            description of its grammar.

            Musical notation is not, in my opinion, 2D at all, any more than
            Hangul. It is a one-dimensional script with many parallel
            articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
            etc), and various other (syntactically linear) articles (e.g. key
            signature, time signature, D.C. / repetition marks, etc).

            If you don't analyze it this way, then you would have to consider e.g.
            French to be "2D" because it has semantically meaningful diacritics,
            and that's just silly.

            Likewise, "linear" can be arranged in various ways (e.g.
            boustrophedon) without changing that it is linear. And elements can of
            course have two-dimensional structure (every writing system I know of
            does, other than Morse code).

            I would say that sign languages are partially two-dimensional, to the
            extent that they use visuo-spatial grammar (e.g. the ASL for "the car
            veered wildly and hit a tree" is far richer than can be conveyed).
            However, they aren't syntactically two-dimensional — at least, not in
            the same sense — because their syntax is embedded in time (which is
            one-dimensional).


            As one test: musical notation can be written, with no loss whatsoever,
            in one dimension — e.g., ABC notation.

            A fully 2D language cannot be expressed in one dimension without
            significant alteration of meaning and/or a significant increase in the
            amount that must be expressed (in order to state the two-dimensional
            relationships).

            Though one certainly *could* write down a traversal of UNLWS or Ouwi
            in one dimension, and include enough information to fully resconstruct
            the original, such a conversion would necessarily alter the meaning,
            e.g. by *adding* pragma related to the traversal order chosen by the
            transcriber that is not present in the original.


            I'm not sure I could a full taxonomy, since there are so few examples,
            and my imagination is limited.

            As far as I know, there are only two top level classes:
            * extremely fusional
            - I know of no actual examples of this; Heptapod B in Ted Chiang's
            Story of Your Life is a hypothetical example.

            * node-and-connections
            - grid-based
            -- 2d Livagian (… if it's a language?)
            -- Pinuyo

            - freely connecting
            -- Ouwi
            -- UNLWS


            I'm not sure what else there would be or where it'd fit, and I suspect
            that there isn't a strict taxonomy anyway, so much as family
            resemblance.

            - Sai

            On Mon, Aug 25, 2014 at 3:30 PM, And Rosta <and.rosta@...> wrote:
            > On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
            >>
            >> There is one conlang in particular I
            >> remember from this list, years ago -- before 2009? but surely after
            >> 2004 when I joined -- which was a nonlinear language on the
            >> nodes-and-connections model, "fully 2D" in Sai's sense,
            >
            > What is fully 2D? What is partially 2D? (I mean, please remind what the
            > terms mean.)
            >
            > I'm guessing a musical stave, bounded in one dimension and unbounded in the
            > other, would count as partially 2D and full 2Dness requires unboundedness
            > in both dimensions. If so, is there an identifiable taxonomy of fully 2D
            > types, such as the node--connector systems, the grid system, and so forth?
            >
            > And
          • Jeffrey Brown
            ...but could a spoken language be 2D, given the one dimensionality of time? On Mon, Aug 25, 2014 at 8:16 AM, Sai
            Message 5 of 19 , Aug 25 8:24 AM
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              ...but could a spoken language be 2D, given the one dimensionality of time?



              On Mon, Aug 25, 2014 at 8:16 AM, Sai <
              000000400d74820a-dmarc-request@...> wrote:

              > To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
              > is not comprised of potentially two-dimensional components or
              > morphology that are arranged according to a one-dimensional (or free)
              > syntax.
              >
              > I don't know whether the cartouche-based ornamental script for
              > Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
              > description of its grammar.
              >
              > Musical notation is not, in my opinion, 2D at all, any more than
              > Hangul. It is a one-dimensional script with many parallel
              > articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
              > etc), and various other (syntactically linear) articles (e.g. key
              > signature, time signature, D.C. / repetition marks, etc).
              >
              > If you don't analyze it this way, then you would have to consider e.g.
              > French to be "2D" because it has semantically meaningful diacritics,
              > and that's just silly.
              >
              > Likewise, "linear" can be arranged in various ways (e.g.
              > boustrophedon) without changing that it is linear. And elements can of
              > course have two-dimensional structure (every writing system I know of
              > does, other than Morse code).
              >
              > I would say that sign languages are partially two-dimensional, to the
              > extent that they use visuo-spatial grammar (e.g. the ASL for "the car
              > veered wildly and hit a tree" is far richer than can be conveyed).
              > However, they aren't syntactically two-dimensional — at least, not in
              > the same sense — because their syntax is embedded in time (which is
              > one-dimensional).
              >
              >
              > As one test: musical notation can be written, with no loss whatsoever,
              > in one dimension — e.g., ABC notation.
              >
              > A fully 2D language cannot be expressed in one dimension without
              > significant alteration of meaning and/or a significant increase in the
              > amount that must be expressed (in order to state the two-dimensional
              > relationships).
              >
              > Though one certainly *could* write down a traversal of UNLWS or Ouwi
              > in one dimension, and include enough information to fully resconstruct
              > the original, such a conversion would necessarily alter the meaning,
              > e.g. by *adding* pragma related to the traversal order chosen by the
              > transcriber that is not present in the original.
              >
              >
              > I'm not sure I could a full taxonomy, since there are so few examples,
              > and my imagination is limited.
              >
              > As far as I know, there are only two top level classes:
              > * extremely fusional
              > - I know of no actual examples of this; Heptapod B in Ted Chiang's
              > Story of Your Life is a hypothetical example.
              >
              > * node-and-connections
              > - grid-based
              > -- 2d Livagian (… if it's a language?)
              > -- Pinuyo
              >
              > - freely connecting
              > -- Ouwi
              > -- UNLWS
              >
              >
              > I'm not sure what else there would be or where it'd fit, and I suspect
              > that there isn't a strict taxonomy anyway, so much as family
              > resemblance.
              >
              > - Sai
              >
              > On Mon, Aug 25, 2014 at 3:30 PM, And Rosta <and.rosta@...> wrote:
              > > On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
              > >>
              > >> There is one conlang in particular I
              > >> remember from this list, years ago -- before 2009? but surely after
              > >> 2004 when I joined -- which was a nonlinear language on the
              > >> nodes-and-connections model, "fully 2D" in Sai's sense,
              > >
              > > What is fully 2D? What is partially 2D? (I mean, please remind what the
              > > terms mean.)
              > >
              > > I'm guessing a musical stave, bounded in one dimension and unbounded in
              > the
              > > other, would count as partially 2D and full 2Dness requires unboundedness
              > > in both dimensions. If so, is there an identifiable taxonomy of fully 2D
              > > types, such as the node--connector systems, the grid system, and so
              > forth?
              > >
              > > And
              >
            • Sai
              No. A spoken language can have *co-articulation* (just like music), but it can t be two-dimensional in any grammatically significant way. Note that the
              Message 6 of 19 , Aug 25 8:34 AM
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                No. A spoken language can have *co-articulation* (just like music),
                but it can't be two-dimensional in any grammatically significant way.

                Note that the "2d"-ness of music notation is also not grammatically
                significant. Things' placement with respect to each other has no
                meaning. They're just articulated *in parallel*, with restricted
                placement, and a few things being bound to some cluster (e.g. time and
                accent marks bound to the chord they modify).

                To be 2D in the sense I mean, there must actually be a semantic
                meaning, text-wide, to the use of two dimensions. (Super/sub script
                does not count, nor Hangul's within-character ordering, nor staff
                notation placement, nor the 'kinetic typography' video type
                arrangement of words*.)

                Of course, others are free to have their own definitions which differ
                from mine. I'm hardly the One True Authority on it. :-P

                - Sai

                * … because it has no syntactic meaning. A word arrangement of this
                sort *could* potentially be 2D in my sense if the arrangement was
                actually dictated by grammar, not just artistic choice.

                On Mon, Aug 25, 2014 at 4:24 PM, Jeffrey Brown <jrbrown0@...> wrote:
                > ...but could a spoken language be 2D, given the one dimensionality of time?
                >
                >
                >
                > On Mon, Aug 25, 2014 at 8:16 AM, Sai <
                > 000000400d74820a-dmarc-request@...> wrote:
                >
                >> To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
                >> is not comprised of potentially two-dimensional components or
                >> morphology that are arranged according to a one-dimensional (or free)
                >> syntax.
                >>
                >> I don't know whether the cartouche-based ornamental script for
                >> Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
                >> description of its grammar.
                >>
                >> Musical notation is not, in my opinion, 2D at all, any more than
                >> Hangul. It is a one-dimensional script with many parallel
                >> articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
                >> etc), and various other (syntactically linear) articles (e.g. key
                >> signature, time signature, D.C. / repetition marks, etc).
                >>
                >> If you don't analyze it this way, then you would have to consider e.g.
                >> French to be "2D" because it has semantically meaningful diacritics,
                >> and that's just silly.
                >>
                >> Likewise, "linear" can be arranged in various ways (e.g.
                >> boustrophedon) without changing that it is linear. And elements can of
                >> course have two-dimensional structure (every writing system I know of
                >> does, other than Morse code).
                >>
                >> I would say that sign languages are partially two-dimensional, to the
                >> extent that they use visuo-spatial grammar (e.g. the ASL for "the car
                >> veered wildly and hit a tree" is far richer than can be conveyed).
                >> However, they aren't syntactically two-dimensional — at least, not in
                >> the same sense — because their syntax is embedded in time (which is
                >> one-dimensional).
                >>
                >>
                >> As one test: musical notation can be written, with no loss whatsoever,
                >> in one dimension — e.g., ABC notation.
                >>
                >> A fully 2D language cannot be expressed in one dimension without
                >> significant alteration of meaning and/or a significant increase in the
                >> amount that must be expressed (in order to state the two-dimensional
                >> relationships).
                >>
                >> Though one certainly *could* write down a traversal of UNLWS or Ouwi
                >> in one dimension, and include enough information to fully resconstruct
                >> the original, such a conversion would necessarily alter the meaning,
                >> e.g. by *adding* pragma related to the traversal order chosen by the
                >> transcriber that is not present in the original.
                >>
                >>
                >> I'm not sure I could a full taxonomy, since there are so few examples,
                >> and my imagination is limited.
                >>
                >> As far as I know, there are only two top level classes:
                >> * extremely fusional
                >> - I know of no actual examples of this; Heptapod B in Ted Chiang's
                >> Story of Your Life is a hypothetical example.
                >>
                >> * node-and-connections
                >> - grid-based
                >> -- 2d Livagian (… if it's a language?)
                >> -- Pinuyo
                >>
                >> - freely connecting
                >> -- Ouwi
                >> -- UNLWS
                >>
                >>
                >> I'm not sure what else there would be or where it'd fit, and I suspect
                >> that there isn't a strict taxonomy anyway, so much as family
                >> resemblance.
                >>
                >> - Sai
                >>
                >> On Mon, Aug 25, 2014 at 3:30 PM, And Rosta <and.rosta@...> wrote:
                >> > On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
                >> >>
                >> >> There is one conlang in particular I
                >> >> remember from this list, years ago -- before 2009? but surely after
                >> >> 2004 when I joined -- which was a nonlinear language on the
                >> >> nodes-and-connections model, "fully 2D" in Sai's sense,
                >> >
                >> > What is fully 2D? What is partially 2D? (I mean, please remind what the
                >> > terms mean.)
                >> >
                >> > I'm guessing a musical stave, bounded in one dimension and unbounded in
                >> the
                >> > other, would count as partially 2D and full 2Dness requires unboundedness
                >> > in both dimensions. If so, is there an identifiable taxonomy of fully 2D
                >> > types, such as the node--connector systems, the grid system, and so
                >> forth?
                >> >
                >> > And
                >>
              • MorphemeAddict
                In the story referenced earlier, the spoken language was a simple version of the the actual language, which was written. stevo
                Message 7 of 19 , Aug 25 8:35 AM
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                  In the story referenced earlier, the spoken language was a simple version
                  of the the actual language, which was written.

                  stevo


                  On Mon, Aug 25, 2014 at 11:24 AM, Jeffrey Brown <jrbrown0@...> wrote:

                  > ...but could a spoken language be 2D, given the one dimensionality of time?
                  >
                  >
                  >
                  > On Mon, Aug 25, 2014 at 8:16 AM, Sai <
                  > 000000400d74820a-dmarc-request@...> wrote:
                  >
                  > > To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
                  > > is not comprised of potentially two-dimensional components or
                  > > morphology that are arranged according to a one-dimensional (or free)
                  > > syntax.
                  > >
                  > > I don't know whether the cartouche-based ornamental script for
                  > > Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
                  > > description of its grammar.
                  > >
                  > > Musical notation is not, in my opinion, 2D at all, any more than
                  > > Hangul. It is a one-dimensional script with many parallel
                  > > articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
                  > > etc), and various other (syntactically linear) articles (e.g. key
                  > > signature, time signature, D.C. / repetition marks, etc).
                  > >
                  > > If you don't analyze it this way, then you would have to consider e.g.
                  > > French to be "2D" because it has semantically meaningful diacritics,
                  > > and that's just silly.
                  > >
                  > > Likewise, "linear" can be arranged in various ways (e.g.
                  > > boustrophedon) without changing that it is linear. And elements can of
                  > > course have two-dimensional structure (every writing system I know of
                  > > does, other than Morse code).
                  > >
                  > > I would say that sign languages are partially two-dimensional, to the
                  > > extent that they use visuo-spatial grammar (e.g. the ASL for "the car
                  > > veered wildly and hit a tree" is far richer than can be conveyed).
                  > > However, they aren't syntactically two-dimensional — at least, not in
                  > > the same sense — because their syntax is embedded in time (which is
                  > > one-dimensional).
                  > >
                  > >
                  > > As one test: musical notation can be written, with no loss whatsoever,
                  > > in one dimension — e.g., ABC notation.
                  > >
                  > > A fully 2D language cannot be expressed in one dimension without
                  > > significant alteration of meaning and/or a significant increase in the
                  > > amount that must be expressed (in order to state the two-dimensional
                  > > relationships).
                  > >
                  > > Though one certainly *could* write down a traversal of UNLWS or Ouwi
                  > > in one dimension, and include enough information to fully resconstruct
                  > > the original, such a conversion would necessarily alter the meaning,
                  > > e.g. by *adding* pragma related to the traversal order chosen by the
                  > > transcriber that is not present in the original.
                  > >
                  > >
                  > > I'm not sure I could a full taxonomy, since there are so few examples,
                  > > and my imagination is limited.
                  > >
                  > > As far as I know, there are only two top level classes:
                  > > * extremely fusional
                  > > - I know of no actual examples of this; Heptapod B in Ted Chiang's
                  > > Story of Your Life is a hypothetical example.
                  > >
                  > > * node-and-connections
                  > > - grid-based
                  > > -- 2d Livagian (… if it's a language?)
                  > > -- Pinuyo
                  > >
                  > > - freely connecting
                  > > -- Ouwi
                  > > -- UNLWS
                  > >
                  > >
                  > > I'm not sure what else there would be or where it'd fit, and I suspect
                  > > that there isn't a strict taxonomy anyway, so much as family
                  > > resemblance.
                  > >
                  > > - Sai
                  > >
                  > > On Mon, Aug 25, 2014 at 3:30 PM, And Rosta <and.rosta@...> wrote:
                  > > > On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
                  > > >>
                  > > >> There is one conlang in particular I
                  > > >> remember from this list, years ago -- before 2009? but surely after
                  > > >> 2004 when I joined -- which was a nonlinear language on the
                  > > >> nodes-and-connections model, "fully 2D" in Sai's sense,
                  > > >
                  > > > What is fully 2D? What is partially 2D? (I mean, please remind what
                  > the
                  > > > terms mean.)
                  > > >
                  > > > I'm guessing a musical stave, bounded in one dimension and unbounded in
                  > > the
                  > > > other, would count as partially 2D and full 2Dness requires
                  > unboundedness
                  > > > in both dimensions. If so, is there an identifiable taxonomy of fully
                  > 2D
                  > > > types, such as the node--connector systems, the grid system, and so
                  > > forth?
                  > > >
                  > > > And
                  > >
                  >
                • Sai
                  Actually, it isn t. Quoting the relevant part of the story (as ... Gary frowned. “So their writing constitutes a completely separate language from their
                  Message 8 of 19 , Aug 25 8:41 AM
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                    Actually, it isn't. Quoting the relevant part of the story (as
                    academic fair use):

                    ---

                    "Gary frowned. “So their writing constitutes a completely separate
                    language from their speech, right?”

                    “Right. In fact, it'd be more accurate to refer to the writing system
                    as ‘Heptapod B,’ and use ‘Heptapod A’ strictly for referring to the
                    spoken language.”

                    “Hold on a second. Why use two languages when one would suffice? That
                    seems unnecessarily hard to learn.”

                    “Like English spelling?” I said. “Ease of learning isn't the primary
                    force in language evolution. For the heptapods, writing and speech may
                    play such different cultural or cognitive roles that using separate
                    languages makes more sense than using different forms of the same
                    one.”

                    He considered it. “I see what you mean. Maybe they think our form of
                    writing is redundant, like we're wasting a second communications
                    channel.”

                    “That's entirely possible. Finding out why they use a second language
                    for writing will tell us a lot about them.”

                    “So I take it this means we won't be able to use their writing to help
                    us learn their spoken language.”

                    I sighed. “Yeah, that's the most immediate implication. But I don't
                    think we should ignore either Heptapod A or B; we need a two-pronged
                    approach.” I pointed at the screen. “I'll bet you that learning their
                    two- dimensional grammar will help you when it comes time to learn
                    their mathematical notation.”

                    ---

                    - Sai

                    On Mon, Aug 25, 2014 at 4:35 PM, MorphemeAddict <lytlesw@...> wrote:
                    > In the story referenced earlier, the spoken language was a simple version
                    > of the the actual language, which was written.
                    >
                    > stevo
                    >
                    >
                    > On Mon, Aug 25, 2014 at 11:24 AM, Jeffrey Brown <jrbrown0@...> wrote:
                    >
                    >> ...but could a spoken language be 2D, given the one dimensionality of time?
                    >>
                    >>
                    >>
                    >> On Mon, Aug 25, 2014 at 8:16 AM, Sai <
                    >> 000000400d74820a-dmarc-request@...> wrote:
                    >>
                    >> > To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
                    >> > is not comprised of potentially two-dimensional components or
                    >> > morphology that are arranged according to a one-dimensional (or free)
                    >> > syntax.
                    >> >
                    >> > I don't know whether the cartouche-based ornamental script for
                    >> > Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
                    >> > description of its grammar.
                    >> >
                    >> > Musical notation is not, in my opinion, 2D at all, any more than
                    >> > Hangul. It is a one-dimensional script with many parallel
                    >> > articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
                    >> > etc), and various other (syntactically linear) articles (e.g. key
                    >> > signature, time signature, D.C. / repetition marks, etc).
                    >> >
                    >> > If you don't analyze it this way, then you would have to consider e.g.
                    >> > French to be "2D" because it has semantically meaningful diacritics,
                    >> > and that's just silly.
                    >> >
                    >> > Likewise, "linear" can be arranged in various ways (e.g.
                    >> > boustrophedon) without changing that it is linear. And elements can of
                    >> > course have two-dimensional structure (every writing system I know of
                    >> > does, other than Morse code).
                    >> >
                    >> > I would say that sign languages are partially two-dimensional, to the
                    >> > extent that they use visuo-spatial grammar (e.g. the ASL for "the car
                    >> > veered wildly and hit a tree" is far richer than can be conveyed).
                    >> > However, they aren't syntactically two-dimensional — at least, not in
                    >> > the same sense — because their syntax is embedded in time (which is
                    >> > one-dimensional).
                    >> >
                    >> >
                    >> > As one test: musical notation can be written, with no loss whatsoever,
                    >> > in one dimension — e.g., ABC notation.
                    >> >
                    >> > A fully 2D language cannot be expressed in one dimension without
                    >> > significant alteration of meaning and/or a significant increase in the
                    >> > amount that must be expressed (in order to state the two-dimensional
                    >> > relationships).
                    >> >
                    >> > Though one certainly *could* write down a traversal of UNLWS or Ouwi
                    >> > in one dimension, and include enough information to fully resconstruct
                    >> > the original, such a conversion would necessarily alter the meaning,
                    >> > e.g. by *adding* pragma related to the traversal order chosen by the
                    >> > transcriber that is not present in the original.
                    >> >
                    >> >
                    >> > I'm not sure I could a full taxonomy, since there are so few examples,
                    >> > and my imagination is limited.
                    >> >
                    >> > As far as I know, there are only two top level classes:
                    >> > * extremely fusional
                    >> > - I know of no actual examples of this; Heptapod B in Ted Chiang's
                    >> > Story of Your Life is a hypothetical example.
                    >> >
                    >> > * node-and-connections
                    >> > - grid-based
                    >> > -- 2d Livagian (… if it's a language?)
                    >> > -- Pinuyo
                    >> >
                    >> > - freely connecting
                    >> > -- Ouwi
                    >> > -- UNLWS
                    >> >
                    >> >
                    >> > I'm not sure what else there would be or where it'd fit, and I suspect
                    >> > that there isn't a strict taxonomy anyway, so much as family
                    >> > resemblance.
                    >> >
                    >> > - Sai
                    >> >
                    >> > On Mon, Aug 25, 2014 at 3:30 PM, And Rosta <and.rosta@...> wrote:
                    >> > > On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
                    >> > >>
                    >> > >> There is one conlang in particular I
                    >> > >> remember from this list, years ago -- before 2009? but surely after
                    >> > >> 2004 when I joined -- which was a nonlinear language on the
                    >> > >> nodes-and-connections model, "fully 2D" in Sai's sense,
                    >> > >
                    >> > > What is fully 2D? What is partially 2D? (I mean, please remind what
                    >> the
                    >> > > terms mean.)
                    >> > >
                    >> > > I'm guessing a musical stave, bounded in one dimension and unbounded in
                    >> > the
                    >> > > other, would count as partially 2D and full 2Dness requires
                    >> unboundedness
                    >> > > in both dimensions. If so, is there an identifiable taxonomy of fully
                    >> 2D
                    >> > > types, such as the node--connector systems, the grid system, and so
                    >> > forth?
                    >> > >
                    >> > > And
                    >> >
                    >>
                  • MorphemeAddict
                    Okay, thanks for the correction, clarification, and excerpt. stevo On Mon, Aug 25, 2014 at 11:41 AM, Sai
                    Message 9 of 19 , Aug 25 10:16 AM
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                      Okay, thanks for the correction, clarification, and excerpt.

                      stevo


                      On Mon, Aug 25, 2014 at 11:41 AM, Sai <
                      000000400d74820a-dmarc-request@...> wrote:

                      > Actually, it isn't. Quoting the relevant part of the story (as
                      > academic fair use):
                      >
                      > ---
                      >
                      > "Gary frowned. “So their writing constitutes a completely separate
                      > language from their speech, right?”
                      >
                      > “Right. In fact, it'd be more accurate to refer to the writing system
                      > as ‘Heptapod B,’ and use ‘Heptapod A’ strictly for referring to the
                      > spoken language.”
                      >
                      > “Hold on a second. Why use two languages when one would suffice? That
                      > seems unnecessarily hard to learn.”
                      >
                      > “Like English spelling?” I said. “Ease of learning isn't the primary
                      > force in language evolution. For the heptapods, writing and speech may
                      > play such different cultural or cognitive roles that using separate
                      > languages makes more sense than using different forms of the same
                      > one.”
                      >
                      > He considered it. “I see what you mean. Maybe they think our form of
                      > writing is redundant, like we're wasting a second communications
                      > channel.”
                      >
                      > “That's entirely possible. Finding out why they use a second language
                      > for writing will tell us a lot about them.”
                      >
                      > “So I take it this means we won't be able to use their writing to help
                      > us learn their spoken language.”
                      >
                      > I sighed. “Yeah, that's the most immediate implication. But I don't
                      > think we should ignore either Heptapod A or B; we need a two-pronged
                      > approach.” I pointed at the screen. “I'll bet you that learning their
                      > two- dimensional grammar will help you when it comes time to learn
                      > their mathematical notation.”
                      >
                      > ---
                      >
                      > - Sai
                      >
                      > On Mon, Aug 25, 2014 at 4:35 PM, MorphemeAddict <lytlesw@...> wrote:
                      > > In the story referenced earlier, the spoken language was a simple version
                      > > of the the actual language, which was written.
                      > >
                      > > stevo
                      > >
                      > >
                      > > On Mon, Aug 25, 2014 at 11:24 AM, Jeffrey Brown <jrbrown0@...>
                      > wrote:
                      > >
                      > >> ...but could a spoken language be 2D, given the one dimensionality of
                      > time?
                      > >>
                      > >>
                      > >>
                      > >> On Mon, Aug 25, 2014 at 8:16 AM, Sai <
                      > >> 000000400d74820a-dmarc-request@...> wrote:
                      > >>
                      > >> > To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
                      > >> > is not comprised of potentially two-dimensional components or
                      > >> > morphology that are arranged according to a one-dimensional (or free)
                      > >> > syntax.
                      > >> >
                      > >> > I don't know whether the cartouche-based ornamental script for
                      > >> > Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
                      > >> > description of its grammar.
                      > >> >
                      > >> > Musical notation is not, in my opinion, 2D at all, any more than
                      > >> > Hangul. It is a one-dimensional script with many parallel
                      > >> > articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
                      > >> > etc), and various other (syntactically linear) articles (e.g. key
                      > >> > signature, time signature, D.C. / repetition marks, etc).
                      > >> >
                      > >> > If you don't analyze it this way, then you would have to consider e.g.
                      > >> > French to be "2D" because it has semantically meaningful diacritics,
                      > >> > and that's just silly.
                      > >> >
                      > >> > Likewise, "linear" can be arranged in various ways (e.g.
                      > >> > boustrophedon) without changing that it is linear. And elements can of
                      > >> > course have two-dimensional structure (every writing system I know of
                      > >> > does, other than Morse code).
                      > >> >
                      > >> > I would say that sign languages are partially two-dimensional, to the
                      > >> > extent that they use visuo-spatial grammar (e.g. the ASL for "the car
                      > >> > veered wildly and hit a tree" is far richer than can be conveyed).
                      > >> > However, they aren't syntactically two-dimensional — at least, not in
                      > >> > the same sense — because their syntax is embedded in time (which is
                      > >> > one-dimensional).
                      > >> >
                      > >> >
                      > >> > As one test: musical notation can be written, with no loss whatsoever,
                      > >> > in one dimension — e.g., ABC notation.
                      > >> >
                      > >> > A fully 2D language cannot be expressed in one dimension without
                      > >> > significant alteration of meaning and/or a significant increase in the
                      > >> > amount that must be expressed (in order to state the two-dimensional
                      > >> > relationships).
                      > >> >
                      > >> > Though one certainly *could* write down a traversal of UNLWS or Ouwi
                      > >> > in one dimension, and include enough information to fully resconstruct
                      > >> > the original, such a conversion would necessarily alter the meaning,
                      > >> > e.g. by *adding* pragma related to the traversal order chosen by the
                      > >> > transcriber that is not present in the original.
                      > >> >
                      > >> >
                      > >> > I'm not sure I could a full taxonomy, since there are so few examples,
                      > >> > and my imagination is limited.
                      > >> >
                      > >> > As far as I know, there are only two top level classes:
                      > >> > * extremely fusional
                      > >> > - I know of no actual examples of this; Heptapod B in Ted Chiang's
                      > >> > Story of Your Life is a hypothetical example.
                      > >> >
                      > >> > * node-and-connections
                      > >> > - grid-based
                      > >> > -- 2d Livagian (… if it's a language?)
                      > >> > -- Pinuyo
                      > >> >
                      > >> > - freely connecting
                      > >> > -- Ouwi
                      > >> > -- UNLWS
                      > >> >
                      > >> >
                      > >> > I'm not sure what else there would be or where it'd fit, and I suspect
                      > >> > that there isn't a strict taxonomy anyway, so much as family
                      > >> > resemblance.
                      > >> >
                      > >> > - Sai
                      > >> >
                      > >> > On Mon, Aug 25, 2014 at 3:30 PM, And Rosta <and.rosta@...>
                      > wrote:
                      > >> > > On 25 Aug 2014 11:06, "Alex Fink" <000024@...> wrote:
                      > >> > >>
                      > >> > >> There is one conlang in particular I
                      > >> > >> remember from this list, years ago -- before 2009? but surely after
                      > >> > >> 2004 when I joined -- which was a nonlinear language on the
                      > >> > >> nodes-and-connections model, "fully 2D" in Sai's sense,
                      > >> > >
                      > >> > > What is fully 2D? What is partially 2D? (I mean, please remind what
                      > >> the
                      > >> > > terms mean.)
                      > >> > >
                      > >> > > I'm guessing a musical stave, bounded in one dimension and
                      > unbounded in
                      > >> > the
                      > >> > > other, would count as partially 2D and full 2Dness requires
                      > >> unboundedness
                      > >> > > in both dimensions. If so, is there an identifiable taxonomy of
                      > fully
                      > >> 2D
                      > >> > > types, such as the node--connector systems, the grid system, and so
                      > >> > forth?
                      > >> > >
                      > >> > > And
                      > >> >
                      > >>
                      >
                    • Herman Miller
                      ... Well, each part of a musical score could be represented in 1D, sure. But in the same way, a frame of a TV picture can be represented as a series of 1D
                      Message 10 of 19 , Aug 25 6:09 PM
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                        Sai wrote:
                        > To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
                        > is not comprised of potentially two-dimensional components or
                        > morphology that are arranged according to a one-dimensional (or free)
                        > syntax.
                        >
                        > I don't know whether the cartouche-based ornamental script for
                        > Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
                        > description of its grammar.
                        >
                        > Musical notation is not, in my opinion, 2D at all, any more than
                        > Hangul. It is a one-dimensional script with many parallel
                        > articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
                        > etc), and various other (syntactically linear) articles (e.g. key
                        > signature, time signature, D.C. / repetition marks, etc).

                        Well, each part of a musical score could be represented in 1D, sure. But
                        in the same way, a frame of a TV picture can be represented as a series
                        of 1D lines. The only difference is the number of lines. Representing a
                        musical score as a set of independent linear parts would be impossible
                        for a conductor to keep track of. So it's easier to think of it as a 2D
                        notation, even though one dimension has a smaller practical limit.
                      • Sai
                        That s not quite the same. The second dimension in musical notation has no syntax; something s vertical placement relative to another thing, except where it is
                        Message 11 of 19 , Aug 25 8:27 PM
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                          That's not quite the same. The second dimension in musical notation
                          has no syntax; something's vertical placement relative to another
                          thing, except where it is fixed and context-free (e.g. a note
                          placement), is completely meaningless. (E.g. note tails / length bars
                          can go either up or down from the note body, with no difference.)

                          I see a very significant difference here.

                          There are many cases of *parallel articulation* within a linear
                          syntax. Vocal prosody, for instance. But those parallel articulations
                          don't *interact*; they don't have meaning more than the sum of their
                          parts. Nor is there any *meaning* in a conductor's score to the
                          (song-wide) choice of how to order the staves for different
                          instruments.

                          To qualify as 2D writing for my meaning, it cannot be reduced to a
                          string of arbitrary symbols — even symbols that have a high number of
                          parallel articulations.

                          I'm making a semantic/syntactic distinction here. Like I said, of
                          course if it is written, it probably is two-dimensional in *form*
                          (excepting Morse code), and that's not interesting as a distinction to
                          make. (Is it reasonable to consider French or Pinyin-written Mandarin
                          Chinese to be "two dimensional" because they have character-bound
                          suprasegmentals? I think not — no more than it is reasonable to
                          consider the written vocal parts in a duet to be "two dimensional"
                          because they are arranged vertically with respect to each other. The
                          second dimension is not syntactically semantic.)


                          By contrast to music notation, where ABC notation is a totally
                          readable equivalent, there is (to my knowledge) no way to transform a
                          two-dimensional *image* — even a very simple one like a line drawing —
                          into a one-dimensional form without obliterating its structure and
                          meaning.

                          However, images' 2D-ness is not *syntactic* — they have
                          two-dimensional *semantics*, yes, but that structure is not
                          linguistic.

                          (And Mayan hieroglyphs are not 2D in my sense either. Individual
                          glyphs are 2D, yes, just like all graphemes — but there's not even any
                          meaning within that 2Dness, and considered as arbitrary symbols, there
                          is no other 2Dness of semantic significance to be had.

                          Could the same superficial *form* in fact be 2D in my sense? Certainly
                          — e.g. it could be using a matrix based syntax, or using the relative
                          positioning of various within-grapheme or inter-grapheme elements
                          semantically [e.g. using eye gaze for indexing]. But they don't.)


                          It's the *meaningful* use of two-dimensional syntax that I consider
                          criterial — not merely whether a thing happens to be have
                          two-dimensional *form*.

                          This very email has two-dimensional form (and is composed of
                          two-dimensional graphemes), but it is in no way "2D" in the sense I
                          mean.

                          - Sai


                          On Tue, Aug 26, 2014 at 2:09 AM, Herman Miller <hmiller@...> wrote:
                          > Sai wrote:
                          >>
                          >> To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
                          >> is not comprised of potentially two-dimensional components or
                          >> morphology that are arranged according to a one-dimensional (or free)
                          >> syntax.
                          >>
                          >> I don't know whether the cartouche-based ornamental script for
                          >> Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
                          >> description of its grammar.
                          >>
                          >> Musical notation is not, in my opinion, 2D at all, any more than
                          >> Hangul. It is a one-dimensional script with many parallel
                          >> articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
                          >> etc), and various other (syntactically linear) articles (e.g. key
                          >> signature, time signature, D.C. / repetition marks, etc).
                          >
                          >
                          > Well, each part of a musical score could be represented in 1D, sure. But in
                          > the same way, a frame of a TV picture can be represented as a series of 1D
                          > lines. The only difference is the number of lines. Representing a musical
                          > score as a set of independent linear parts would be impossible for a
                          > conductor to keep track of. So it's easier to think of it as a 2D notation,
                          > even though one dimension has a smaller practical limit.
                        • And Rosta
                          ... I see. So whereas in spoken lgs syntax specifies how phrases phonological forms concatenate in one dimension, in a fully 2D lg, syntax specifies how
                          Message 12 of 19 , Aug 26 5:51 AM
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                            Sai, On 25/08/2014 16:16 & Sai, On 26/08/2014 04:27:
                            > To me, "fully 2D" means that the syntax is two-dimensional — i.e. it
                            > is not comprised of potentially two-dimensional components or
                            > morphology that are arranged according to a one-dimensional (or free)
                            > syntax.

                            I see. So whereas in spoken lgs syntax specifies how phrases' phonological forms concatenate in one dimension, in a fully 2D lg, syntax specifies how phrases' phonological forms concatenate in two dimensions. That description applies to Pinuyo and 2D-Livagian, at least if we replace "phrase" by "word" (or whatever our term for minimal syntagmatic unit is). It's not clear to me it applies to UNLWS, since in UNLWS all that matters is what connects to what, regardless of how it is distributed in 2D-space. But I suppose that in the case of UNLWS the 2Dness results from mathermatical properties of the graph rather than from the syntax imposing any ordering constraints.

                            > It's the *meaningful* use of two-dimensional syntax that I consider
                            > criterial — not merely whether a thing happens to be have
                            > two-dimensional *form*.

                            That's not really true of UNLWS. Rather, the structure of logical forms is essentially 2D. 1D lgs therefore have to have strategies for linearizing logical forms. UNLWS, being 2D, simply needs no such strategy. But UNLWS doesn't make meaningful grammatical use of any spatial relation other than contiguity. 2D-Livagian, by contrast, relies on rows and columns. And Pinuyo consists of natlang-like clause structure with 2D phonology that makes use of the relative positioning of contiguous elemments.

                            > Musical notation is not, in my opinion, 2D at all, any more than
                            > Hangul. It is a one-dimensional script with many parallel
                            > articulations (e.g. chords), suprasegmentals (e.g. accent, forte,
                            > etc), and various other (syntactically linear) articles (e.g. key
                            > signature, time signature, D.C. / repetition marks, etc).

                            It seems to me that for ordinary music the minimal syntagmatic unit is the note. Notes are distinct in time or in pitch-space. Pitch-space is represented by the vertical dimension and time-space is represented by the horizontal dimension.

                            > As one test: musical notation can be written, with no loss whatsoever,
                            > in one dimension — e.g., ABC notation.

                            ABC notation won't work when there are many notes simultaneously, unless the ABC notation is augmented by punctuation to mark simultaneity.

                            You could also linearize musical notation -- very counterintuitively -- by representing every note as a pair of numerical time indices, for start and end of the note, and then order the pairs linearly by pitch.

                            > The second dimension in musical notation has no syntax; something's
                            > vertical placement relative to another thing, except where it is
                            > fixed and context-free (e.g. a note placement), is completely
                            > meaningless. (E.g. note tails / length bars can go either up or down
                            > from the note body, with no difference.)

                            Relative position in the horizontal dimension represents notes' relative position in time, and relative position in the vertical dimension represents notes' relative position in pitch.

                            > I see a very significant difference here.
                            >
                            > There are many cases of *parallel articulation* within a linear
                            > syntax. Vocal prosody, for instance. But those parallel articulations
                            > don't *interact*; they don't have meaning more than the sum of their
                            > parts. Nor is there any *meaning* in a conductor's score to the
                            > (song-wide) choice of how to order the staves for different
                            > instruments.

                            Your distinction is valid, but in the case of the vertical position of notes, the vertical ordering does matter.

                            > As far as I know, there are only two top level classes:
                            > * extremely fusional
                            > - I know of no actual examples of this; Heptapod B in Ted Chiang's
                            > Story of Your Life is a hypothetical example.

                            Isn't fusionality independent of dimensionality?

                            > * node-and-connections
                            > - grid-based
                            > -- 2d Livagian (… if it's a language?)
                            > -- Pinuyo
                            >
                            > - freely connecting
                            > -- Ouwi
                            > -- UNLWS

                            Pinuyo is not grid-based, I would say, but is sensitive to directionality/ordering, within each dimension, of contiguous elements, whereas UNLWS is insensitive to directionality and is sensitive only to contiguity (via connectors). I haven't got my head round how Ouwi works.

                            I dimly recall discussion of a grid based conlang during the earliest discussion of nonlinear conlangs, but I wasn't paying careful attention at the time, and can't remember anything more.

                            > I'm not sure what else there would be or where it'd fit, and I suspect
                            > that there isn't a strict taxonomy anyway, so much as family
                            > resemblance.

                            Maybe not a strict taxonomy, but still a potentially clearly articulable quality space.

                            --And.
                          • Sai
                            ... Replace concatenate with some generic term (e.g. are arranged ) and I d agree. ... I use node , though word is not too horrible (except for an
                            Message 13 of 19 , Aug 26 6:42 AM
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                              On Tue, Aug 26, 2014 at 1:51 PM, And Rosta <and.rosta@...> wrote:
                              > I see. So whereas in spoken lgs syntax specifies how phrases' phonological
                              > forms concatenate in one dimension, in a fully 2D lg, syntax specifies how
                              > phrases' phonological forms concatenate in two dimensions.

                              Replace 'concatenate' with some generic term (e.g. 'are arranged') and
                              I'd agree.

                              > That description
                              > applies to Pinuyo and 2D-Livagian, at least if we replace "phrase" by "word"
                              > (or whatever our term for minimal syntagmatic unit is).

                              I use 'node', though 'word' is not too horrible (except for an
                              ultrafusional language, where one wouldn't be able to easily
                              distinguish glyph boundaries…)

                              > It's not clear to me
                              > it applies to UNLWS, since in UNLWS all that matters is what connects to
                              > what, regardless of how it is distributed in 2D-space. But I suppose that in
                              > the case of UNLWS the 2Dness results from mathermatical properties of the
                              > graph rather than from the syntax imposing any ordering constraints.

                              UNLWS doesn't just have graph (as in math) constraints.

                              Even if it did, I would still consider it to be 2D (IIRC Ouwi falls
                              into this category) because a (nontrivial) graph cannot be reduced to
                              one dimension without some sort of distortion (such as choosing a
                              traversal order).

                              However, UNLWS has several grammatical features that are actually
                              spatial, such as:

                              * which (rotational) side of a connecting line a glyph is placed on

                              * a whole system for indicating location and movement, where (locally):
                              - the page can be given a 'gravity-wards' direction
                              - location-related glyphs are located in relation to each other based
                              on how they are actually located on the page
                              - portions of the movement glyph indicate velocity, acceleration,
                              rotational velocity, and acceleration of rotation by the relative
                              position and orientation of two curved lines with respect to both
                              their base glyph and each other
                              - a glyph for indicating three-dimensional size using relative line
                              lengths, which is 2D oriented within the local context (e.g. with
                              respect to gravity)

                              * embedded *graphs* (as in two-dimensional sparklines and
                              scatterplots), which have meaning with respect to the 1D *or* 2D axes
                              that are established, which can also optionally indicate the size of
                              one unit

                              * containment within a two-dimensional cartouche (which can have
                              exclaves) — which can be incompletely drawn, relying on relative
                              location of glyphs in 2D to indicate which ones are included in the
                              implied full cartouche)

                              * analog-variable glyphs, which have graphemic features (such as line
                              length or angle) to indicate degree (e.g. hot-cold, asleep-awake, etc,
                              though those are 1D)
                              - these can also describe analog *ranges* of values within their
                              gamut, and the gamut itself can be used as a referent
                              - arguably the location system above is a 2D exemplar

                              > It seems to me that for ordinary music the minimal syntagmatic unit is the
                              > note. Notes are distinct in time or in pitch-space. Pitch-space is
                              > represented by the vertical dimension and time-space is represented by the
                              > horizontal dimension.

                              If you take that line of argument, then it would seem to follow that
                              e.g. super/subscript, diacritics (especially for tone, more especially
                              the wacky IPA symbol that allows insertion of an arbitrary
                              tone-graph), etc., would also be "2D" — which I think is at best not a
                              very useful definition, and at minimum does not describe the same
                              *kind* of thing as happens with the things I call 2D writing systems.

                              There is no interrelationship between the notes in pitch-space (except
                              perhaps indication of which ones are played by which hand or voice).
                              Each grapheme (note) simply happens to have a different, fixed
                              position on the staff.

                              One could equivalently make a "font" for English where e.g. vowels a e
                              i o u are represented by a pixel at the top, mid-top, mid, mid-bottom,
                              and bottom of a single character respectively. Does this use a
                              vertical dimension semantically? Yes, barely. Does it use it
                              syntactically? No. Can it be collapsed without loss to an arbitrary
                              symbol in one dimension? Yes.

                              >> As one test: musical notation can be written, with no loss whatsoever,
                              >> in one dimension — e.g., ABC notation.
                              >
                              > ABC notation won't work when there are many notes simultaneously, unless the
                              > ABC notation is augmented by punctuation to mark simultaneity.

                              It is. http://abcnotation.com/wiki/abc:standard:v2.1#chords_and_unisons

                              > You could also linearize musical notation -- very counterintuitively -- by
                              > representing every note as a pair of numerical time indices, for start and
                              > end of the note, and then order the pairs linearly by pitch.

                              You could, and yes that would be a very distorted re-linearization.
                              However, my test was not whether there exists a distorted
                              linearization, but rather whether there *doesn't*.

                              A fully 2D system *cannot* be linearized without significant
                              distortion, any more than a n-dimensional object can be projected into
                              n-1 dimensions without distortion. (Cf.
                              https://www.youtube.com/watch?v=zBFY6_RDPVs)

                              > Your distinction is valid, but in the case of the vertical position of
                              > notes, the vertical ordering does matter.

                              Not quite. The *ordering* does not matter; there *is* no order of
                              notes with respect to each other (except hand/voice indication). The
                              *placement* matters, but that's only because the glyph for each tone
                              happens to have a form that has a vertically distinct placement, to
                              accommodate a lot of parallel articulation.

                              I should add that musical notation is (or at least is intended to be)
                              directly isomorphic, without loss, to the actual sounds produced — and
                              I think that there is no such thing as a two-dimensional [in my sense]
                              vocalization (with the possible exception of extremely contrived
                              examples, such as embedding images in spectrographs of specially made
                              sounds).

                              >> As far as I know, there are only two top level classes:
                              >> * extremely fusional
                              >> - I know of no actual examples of this; Heptapod B in Ted Chiang's
                              >> Story of Your Life is a hypothetical example.
                              >
                              > Isn't fusionality independent of dimensionality?

                              Yes. These are just two top-level classes within 2D writing systems.

                              There is also 1DWS fusionality to some extent (e.g. Arabic). I'm not
                              sure whether all 1DWS features can be mapped to 2DWS ones. I'm fairly
                              certain that at least some 2DWS features *cannot* be mapped to a 1DWS
                              feature.

                              > Pinuyo is not grid-based, I would say, but is sensitive to
                              > directionality/ordering, within each dimension, of contiguous elements,

                              I would still call this grid-based; it just uses relative ordering
                              within the grid, rather than specific placement, for its semantics.

                              That is, it uses a highly restricted two-dimensionality, permitting
                              only orthogonal relationships.

                              > whereas UNLWS is insensitive to directionality and is sensitive only to
                              > contiguity (via connectors)

                              Not so, as above.

                              >> I'm not sure what else there would be or where it'd fit, and I suspect
                              >> that there isn't a strict taxonomy anyway, so much as family
                              >> resemblance.
                              >
                              > Maybe not a strict taxonomy, but still a potentially clearly articulable
                              > quality space.

                              That would certainly be interesting to have, especially if it can
                              imply potential areas for new development that haven't yet been
                              explored.
                            • John Q
                              ... An explanation of the basic principles of the ornamental script can be found here:
                              Message 14 of 19 , Aug 26 10:09 AM
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                                Sai wrote:
                                >
                                >I don't know whether the cartouche-based ornamental script for
                                >Ithkuil/Ilaksh fits this definition or not, as I haven't seen a
                                >description of its grammar.
                                >
                                --------------------------------------------------------

                                An explanation of the basic principles of the ornamental script can be found here:

                                http://web.archive.org/web/20110605210044/http://ithkuil.net/ilaksh/images/script_diagram.gif

                                Not sure whether this meets Sai's definitional requirements or not.

                                --John Q.
                              • Sai
                                ... Given that you say that the relative horizontal and vertical position of glyphs is morphologically relevant, as well as possibly the *third* dimension of
                                Message 15 of 19 , Aug 26 10:15 AM
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                                  On Tue, Aug 26, 2014 at 6:09 PM, John Q <Jquijada21@...> wrote:
                                  > An explanation of the basic principles of the ornamental script can be found here:
                                  >
                                  > http://web.archive.org/web/20110605210044/http://ithkuil.net/ilaksh/images/script_diagram.gif

                                  Given that you say that the relative horizontal and vertical position
                                  of glyphs is morphologically relevant, as well as possibly the *third*
                                  dimension of stacking order, I believe so — though it's hard to tell,
                                  and I'd be very interested to read a more thorough explanation. ;-)

                                  - Sai
                                • And Rosta
                                  ... It does look to be 3D, doesn t it. I wonder: given that 3D can be represented in 2D (by complicating the edges of contiguous 2D shapes to simulate
                                  Message 16 of 19 , Aug 26 12:16 PM
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                                    Sai, On 26/08/2014 18:15:
                                    > On Tue, Aug 26, 2014 at 6:09 PM, John Q <Jquijada21@...> wrote:
                                    >> An explanation of the basic principles of the ornamental script can be found here:
                                    >>
                                    >> http://web.archive.org/web/20110605210044/http://ithkuil.net/ilaksh/images/script_diagram.gif
                                    >
                                    > Given that you say that the relative horizontal and vertical position
                                    > of glyphs is morphologically relevant, as well as possibly the *third*
                                    > dimension of stacking order, I believe so — though it's hard to tell,
                                    > and I'd be very interested to read a more thorough explanation. ;-)

                                    It does look to be 3D, doesn't it. I wonder: given that 3D can be represented in 2D (by complicating the edges of contiguous 2D shapes to simulate overlap), can 2D be represented in 1D by similar means? My debile mind lacks the powers of geometrical reasoning to address this question.

                                    --And.
                                  • Sai
                                    ... Yes; this is called projection. See the video I linked earlier. - Sai
                                    Message 17 of 19 , Aug 26 3:30 PM
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                                      On Tue, Aug 26, 2014 at 8:16 PM, And Rosta <and.rosta@...> wrote:
                                      > It does look to be 3D, doesn't it. I wonder: given that 3D can be
                                      > represented in 2D (by complicating the edges of contiguous 2D shapes to
                                      > simulate overlap), can 2D be represented in 1D by similar means? My debile
                                      > mind lacks the powers of geometrical reasoning to address this question.

                                      Yes; this is called projection. See the video I linked earlier.

                                      - Sai
                                    • And Rosta
                                      ... [...] ... I agree (of course), but your original characterization of Full 2Dness had seemed to me not to cover this case. ... I d forgotten some of these.
                                      Message 18 of 19 , Aug 26 5:26 PM
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                                        Sai, On 26/08/2014 14:42:
                                        > On Tue, Aug 26, 2014 at 1:51 PM, And Rosta <and.rosta@...> wrote:
                                        >> I see. So whereas in spoken lgs syntax specifies how phrases' phonological
                                        >> forms concatenate in one dimension, in a fully 2D lg, syntax specifies how
                                        >> phrases' phonological forms concatenate in two dimensions.
                                        [...]
                                        >> It's not clear to me
                                        >> it applies to UNLWS, since in UNLWS all that matters is what connects to
                                        >> what, regardless of how it is distributed in 2D-space. But I suppose that in
                                        >> the case of UNLWS the 2Dness results from mathermatical properties of the
                                        >> graph rather than from the syntax imposing any ordering constraints.
                                        >
                                        > UNLWS doesn't just have graph (as in math) constraints.
                                        >
                                        > Even if it did, I would still consider it to be 2D (IIRC Ouwi falls
                                        > into this category) because a (nontrivial) graph cannot be reduced to
                                        > one dimension without some sort of distortion (such as choosing a
                                        > traversal order).

                                        I agree (of course), but your original characterization of Full 2Dness had seemed to me not to cover this case.

                                        > However, UNLWS has several grammatical features that are actually
                                        > spatial, such as:
                                        >
                                        > * which (rotational) side of a connecting line a glyph is placed on
                                        >
                                        > * a whole system for indicating location and movement, where (locally):
                                        > - the page can be given a 'gravity-wards' direction
                                        > - location-related glyphs are located in relation to each other based
                                        > on how they are actually located on the page
                                        > - portions of the movement glyph indicate velocity, acceleration,
                                        > rotational velocity, and acceleration of rotation by the relative
                                        > position and orientation of two curved lines with respect to both
                                        > their base glyph and each other
                                        > - a glyph for indicating three-dimensional size using relative line
                                        > lengths, which is 2D oriented within the local context (e.g. with
                                        > respect to gravity)
                                        >
                                        > * embedded *graphs* (as in two-dimensional sparklines and
                                        > scatterplots), which have meaning with respect to the 1D *or* 2D axes
                                        > that are established, which can also optionally indicate the size of
                                        > one unit
                                        >
                                        > * containment within a two-dimensional cartouche (which can have
                                        > exclaves) — which can be incompletely drawn, relying on relative
                                        > location of glyphs in 2D to indicate which ones are included in the
                                        > implied full cartouche)
                                        >
                                        > * analog-variable glyphs, which have graphemic features (such as line
                                        > length or angle) to indicate degree (e.g. hot-cold, asleep-awake, etc,
                                        > though those are 1D)
                                        > - these can also describe analog *ranges* of values within their
                                        > gamut, and the gamut itself can be used as a referent
                                        > - arguably the location system above is a 2D exemplar

                                        I'd forgotten some of these. Interestingly they go beyond an encoding of predicate--argument structure. In some of the cases, tho, I wonder if they mightn't count, in your terms, as internally-complex nodes that don't in themselves yield full 2Dness. For example, if I had a written conlang written in linearly-ordered ideograms, with some ideograms looking like your embedded graphs or some of the glyphs you describe, would you consider that conlang Fully 2D?

                                        >> It seems to me that for ordinary music the minimal syntagmatic unit is the
                                        >> note. Notes are distinct in time or in pitch-space. Pitch-space is
                                        >> represented by the vertical dimension and time-space is represented by the
                                        >> horizontal dimension.
                                        >
                                        > If you take that line of argument, then it would seem to follow that
                                        > e.g. super/subscript, diacritics (especially for tone, more especially
                                        > the wacky IPA symbol that allows insertion of an arbitrary
                                        > tone-graph), etc., would also be "2D" — which I think is at best not a
                                        > very useful definition, and at minimum does not describe the same
                                        > *kind* of thing as happens with the things I call 2D writing systems.
                                        >
                                        > There is no interrelationship between the notes in pitch-space (except
                                        > perhaps indication of which ones are played by which hand or voice).
                                        > Each grapheme (note) simply happens to have a different, fixed
                                        > position on the staff.

                                        I am supposing that the note graphemes have no intrinsic pitch. Their placement upon a 2D grid indicates their position in time and pitch-space. The relation between two notes in the same column is simultaneity. What the 2Dness affords is a natural unmarked way to represent simultaneity. A 1D version, as we have noted, requires a special additional notational device.

                                        > One could equivalently make a "font" for English where e.g. vowels a e
                                        > i o u are represented by a pixel at the top, mid-top, mid, mid-bottom,
                                        > and bottom of a single character respectively. Does this use a
                                        > vertical dimension semantically? Yes, barely. Does it use it
                                        > syntactically? No. Can it be collapsed without loss to an arbitrary
                                        > symbol in one dimension? Yes.

                                        I see this, but this is not analogous to the music case. In the music case, there can be as many simultaneous notes as there are discrete pitches, and the two dimensions of the notation represent the two dimensions of the representatum.

                                        >> You could also linearize musical notation -- very counterintuitively -- by
                                        >> representing every note as a pair of numerical time indices, for start and
                                        >> end of the note, and then order the pairs linearly by pitch.
                                        >
                                        > You could, and yes that would be a very distorted re-linearization.
                                        > However, my test was not whether there exists a distorted
                                        > linearization, but rather whether there *doesn't*.
                                        >
                                        > A fully 2D system *cannot* be linearized without significant
                                        > distortion, any more than a n-dimensional object can be projected into
                                        > n-1 dimensions without distortion.

                                        What counts as a significant distortion? For example there are several ways to linearize 2D-Livagian, but all involve the addition of extra notational devices to compensate for the loss of a dimension, and some involve schemes for chopping up the grid row by row or column by column and then concatenating them linearly.

                                        > (Cf. https://www.youtube.com/watch?v=zBFY6_RDPVs)

                                        This is exactly the sort of geometryry that boggles my mind. When in 1995 I met Richard Kennaway, one of the earliest creators of a website on conlanging, and the first conlanger to appear on TV talking about conlanging (reciting 'Shall I compare thee to a summer's day' in Klingon, iirc), he spent ages failing to succeed in getting me to understand the notion of a two-dimensional shadow of a four-dimensional cube (or summat like that).

                                        >>> As far as I know, there are only two top level classes:
                                        >>> * extremely fusional
                                        >>> - I know of no actual examples of this; Heptapod B in Ted Chiang's
                                        >>> Story of Your Life is a hypothetical example.
                                        >>
                                        >> Isn't fusionality independent of dimensionality?
                                        >
                                        > Yes. These are just two top-level classes within 2D writing systems.
                                        >
                                        > There is also 1DWS fusionality to some extent (e.g. Arabic). I'm not
                                        > sure whether all 1DWS features can be mapped to 2DWS ones. I'm fairly
                                        > certain that at least some 2DWS features *cannot* be mapped to a 1DWS
                                        > feature.

                                        Whereas 1DWSs mostly represent phonologies, a 2DWS is a phonology, so the 1D counterpart of a 2D phonology is properly an ordinary 1D phonology. Ergo, 1D fusionality is ordinary common-or-garden morphological fusion. Just as Fusional is not a primary classification of 1D-phonology grammars, so -- it seems to me -- it is not a primary classification of 2D-phonology grammars.

                                        >> Pinuyo is not grid-based, I would say, but is sensitive to
                                        >> directionality/ordering, within each dimension, of contiguous elements,
                                        >
                                        > I would still call this grid-based; it just uses relative ordering
                                        > within the grid, rather than specific placement, for its semantics.
                                        >
                                        > That is, it uses a highly restricted two-dimensionality, permitting
                                        > only orthogonal relationships.

                                        It would, I think, not be possible to write Pinuyo, without further adaptation, by first imposing a grid upon the page and then placing nodes in the cells. If there is a grid, then every node creates its own mini grid, comprising the positions contiguous to it, but mini-grids needn't align and can't always align. This is quite different from 2D Livagian, which does divide the page into rows and columns and then places nodes in cells.

                                        (Incidentally, I think Pinuyo is an excellent conlang, the paradigm example of a naturalistic grammar with a graphical phonology.)

                                        >> Maybe not a strict taxonomy, but still a potentially clearly articulable
                                        >> quality space.
                                        >
                                        > That would certainly be interesting to have, especially if it can
                                        > imply potential areas for new development that haven't yet been
                                        > explored.

                                        An obviousish approach that I've not seen taken is a 2DWS that simply represents in a dendritic diagram ordinary natlangoid syntax, i.e. a 2DWS that reflects what can loosely be termed the meronomic structure of syntax. (Pinuyo doesn't, I think, preserve syntax meronomy.)

                                        --And.
                                      • Sai
                                        ... It s rather hard to give a formal specification. :-P If you like, you could say that the syntax can t be embedded (in the mathematical sense) in less
                                        Message 19 of 19 , Aug 27 4:02 AM
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                                          On Wed, Aug 27, 2014 at 1:26 AM, And Rosta <and.rosta@...> wrote:
                                          > I agree (of course), but your original characterization of Full 2Dness had
                                          > seemed to me not to cover this case.

                                          It's rather hard to give a formal specification. :-P

                                          If you like, you could say that the syntax can't be "embedded" (in the
                                          mathematical sense) in less than two dimensions, perhaps? I believe
                                          this covers nontrivial graphs.

                                          > In some of the cases, tho, I wonder if they
                                          > mightn't count, in your terms, as internally-complex nodes that don't in
                                          > themselves yield full 2Dness. For example, if I had a written conlang
                                          > written in linearly-ordered ideograms, with some ideograms looking like your
                                          > embedded graphs or some of the glyphs you describe, would you consider that
                                          > conlang Fully 2D?

                                          Certainly, some of them would not count in isolation. For instance, I
                                          can embed a sparkline here, by saying for instance "my daily
                                          wakefulness over the last week has been ▃▂▅▁▄▁▂".

                                          However, that's not really grammatically integrated or licit in
                                          English, so that doesn't really count.

                                          Now, we could certainly make a normal (1D) writing system in which
                                          suffixing a sparkline to an adjectival root *is* the primary,
                                          grammaticalized, morphological means of indicating its state or
                                          variation over time.

                                          This would potentially be *morphological* 2Dness. However, it's not
                                          *syntactically* 2D, because (unlike UNLWS), a 1D writing system would
                                          be unable to bind directly (in space) to e.g. the "▅" or "▄" points of
                                          the graph above.

                                          I can't think of a way to replicate e.g. our path/location system in a
                                          1D-syntax / 2D-morphology system. (If you can, feel free to
                                          demonstrate.) I *think* that it is intrinsically not projectable
                                          (without significant distortion) into a 1D system, because of how
                                          extensively it relies both on (a) graphemes that are morphologically
                                          two dimensional, and (b) the grammaticalized 2D spatial
                                          interrelationship of glyphs in a local area.

                                          I'm less sure about (a) — maybe if you have four freely variable
                                          components over a very wide range which you can use morphologically,
                                          you could do so — but (b) I'm pretty sure is impossible.

                                          FWIW, in the simplest case of an isolated movement glyph, it consists
                                          of a circle two successive arcs next to it, like comics' movement
                                          lines. The arcs vary as follows:
                                          * first arc's distance from base: speed (farther = faster)
                                          * second arc's distance from first arc, relative to first one's (more
                                          = higher acceleration)
                                          * first arc's radial placement on base: direction (with respect to
                                          some local area of other spatially grammatical glyphs, like the
                                          gravity-is-this-way symbol)
                                          * second arc's radial placement with respect to the circle, compared
                                          to first arc: turning (in the direction given by drawing a line
                                          through the centers of the second arc, first arc, and circle body)
                                          * second arc's radial placement with respect to the second arc:
                                          acceleration-of-turning (implying a sort of spline in the curve above)

                                          E.g. as a rough sketch*, supposing we put it on graph paper with a
                                          unit circle in the middle (x,y: 0,1 - 1,0 - 0,-1 - -1,0), if the
                                          gravity symbol is nearby pointing downwards (towards y=-inf); first
                                          arc is at 2,3 - 3,2 (with same curve with respect to 0,0); and the
                                          second arc is at 4,2 - 3,1 (with the same curve with respect to the
                                          center of the first one's arc), then the object has roughly:
                                          * velocity down-left at ~2 units [unit can be specified but isn't by
                                          default] (distance from first arc center to center of circle)
                                          * acceleration ~1/2 (distance from second arc center to first arc
                                          center divided by above)
                                          * rotation counterclockwise (radial location of second arc center with
                                          respect to first arc center)
                                          * accelerating rotation (radial location of second arc's
                                          spherical-center [i.e. the way it points] with respect to the circle
                                          center, compared to the rotation)

                                          (I think we may have at some point specified jerk (the derivative of
                                          acceleration, second derivative of velocity, third derivative of
                                          position) using relative arc-length, but I don't remember.)


                                          * Which Alex is welcome to correct, since I'm not the math guy amongst us. :-P

                                          > I am supposing that the note graphemes have no intrinsic pitch. Their
                                          > placement upon a 2D grid indicates their position in time and pitch-space.
                                          > The relation between two notes in the same column is simultaneity. What the
                                          > 2Dness affords is a natural unmarked way to represent simultaneity. A 1D
                                          > version, as we have noted, requires a special additional notational device.

                                          You could also think of the graphemes as having intrinsic pitch and
                                          fixed vertical location.

                                          Simultaneity is an extremely weak relation — weak enough that I don't
                                          consider it adequate.

                                          If you didn't do so, then e.g. overlapping speech (as indicated by
                                          e.g. parallel lines of written lyrics) would be "2D".

                                          I think you need to make a distinction between parallel articulation
                                          and 2D syntax proper. The former is not, to me, 2D at all — any more
                                          than speaking over each other verbally is "2D". Compare to e.g. a sign
                                          language description of where people are seated around a table and
                                          where they're facing; the latter has something the former plainly
                                          lacks.

                                          If you can come up with a better formal description of what that thing
                                          is, feel free, but this is the best I have so far.

                                          >> One could equivalently make a "font" for English where e.g. vowels a e
                                          >> i o u are represented by a pixel at the top, mid-top, mid, mid-bottom,
                                          >> and bottom of a single character respectively. Does this use a
                                          >> vertical dimension semantically? Yes, barely. Does it use it
                                          >> syntactically? No. Can it be collapsed without loss to an arbitrary
                                          >> symbol in one dimension? Yes.
                                          >
                                          > I see this, but this is not analogous to the music case. In the music case,
                                          > there can be as many simultaneous notes as there are discrete pitches, and
                                          > the two dimensions of the notation represent the two dimensions of the
                                          > representatum.

                                          People are capable of at least two-tone simultaneous articulation (cf
                                          Tuvan throat singing); groups of people would be capable of multi-tone
                                          simultaneous articulation. A non-human with multiple vocal apparatus
                                          could plausibly have significantly more parallel articulation than we
                                          do, and one could make a conlang which incorporates non-vocal phonemes
                                          (such as finger snaps).

                                          Merely increasing the number of parallel articulations does not
                                          increase its 2D-ness to me; there has to be real, complex,
                                          grammaticalized structure to the second (or further) dimension(s) that
                                          is the same kind of structure given to the first dimension.

                                          (Besides which, music [as in tones] is not, in the first place,
                                          *linguistic* — so this comparison is flawed at root, because there is
                                          no clear *semantics* to any of it.

                                          As I mentioned for e.g. Mayan hieroglyphics, something that looks the
                                          same might or might not have 2D-ness in my sense, and the difference
                                          hinges on semantic use of 2D syntax, which TTBOMK Mayan does not
                                          have.)

                                          > What counts as a significant distortion? For example there are several ways
                                          > to linearize 2D-Livagian, but all involve the addition of extra notational
                                          > devices to compensate for the loss of a dimension, and some involve schemes
                                          > for chopping up the grid row by row or column by column and then
                                          > concatenating them linearly.

                                          I'm not sure I can give a formal answer to that — but I think we would
                                          agree that e.g. the projection of a cube into two dimensions
                                          introduces significant distortions (as well as an extra aspect that
                                          could potentially be seen as meaningful which is not present in the
                                          original and purely the creation of the person doing the projection).

                                          Whatever that is, that's the sort of distortion I mean.

                                          >> I would still call this grid-based; it just uses relative ordering
                                          >> within the grid, rather than specific placement, for its semantics.
                                          >>
                                          >> That is, it uses a highly restricted two-dimensionality, permitting
                                          >> only orthogonal relationships.
                                          >
                                          > It would, I think, not be possible to write Pinuyo, without further
                                          > adaptation, by first imposing a grid upon the page and then placing nodes in
                                          > the cells. If there is a grid, then every node creates its own mini grid,
                                          > comprising the positions contiguous to it, but mini-grids needn't align and
                                          > can't always align. This is quite different from 2D Livagian, which does
                                          > divide the page into rows and columns and then places nodes in cells.

                                          I didn't know that. In that case, it's less restricted than I thought
                                          — but still fairly highly, in that there are only four directions
                                          available for relationship, rather than the full 360° worth.

                                          (This also seems to still preclude equal-status n-ary predicates of
                                          order >4, which UNLWS can handle just fine. Cf.
                                          http://s.ai/poetry/st_francis — the glyphs around the left and and
                                          right arcs are n-ary predicates [2n-ary in the left side] of the
                                          glyphs binding to those arcs and [for the left side] of the two
                                          [triangular] pronouns at the bottom left.

                                          Their radial placement, however, is only artistic / pragma, not
                                          semantic per se.)

                                          >>> Maybe not a strict taxonomy, but still a potentially clearly articulable
                                          >>> quality space.
                                          >>
                                          >> That would certainly be interesting to have, especially if it can
                                          >> imply potential areas for new development that haven't yet been
                                          >> explored.
                                          >
                                          > An obviousish approach that I've not seen taken is a 2DWS that simply
                                          > represents in a dendritic diagram ordinary natlangoid syntax, i.e. a 2DWS
                                          > that reflects what can loosely be termed the meronomic structure of syntax.
                                          > (Pinuyo doesn't, I think, preserve syntax meronomy.)

                                          Could you give or sketch an example?

                                          - Sai
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