Re: Non-linear / full-2d writing systems?

On Sat, May 07, 2005 at 06:22:22PM +0100, Ray Brown wrote:
> As Sai & Teoh make some similar points, I'll try a joint reply    :)
Ditto, to prevent clutter.


[...]
> [ALL WRITING IS 2D]
> H. S. Teoh wrote:
> >On Fri, May 06, 2005 at 07:25:03PM +0100, Ray Brown wrote:
> >>_All_ writing systems surely have to be fully 2d otherwise we'd not be
> >>able to see the darn things? Sure, things like radio and electronic
> >>transmissions are not 2d - but *writing*?
> >
> >I think what is meant is a writing system that is not confined to a
> >single dimension in its extension.
>
> Sure - but arguably this applies to abugidas, to the Korean writing system,
>  Egyptian hieroglyphics to some extent and to Mayan hieroglyphics to a
> greater extent. What I guess I was trying to get at is: "What are the two
> extensions?"
I would still consider Korean as linear, because the second extension
is finite. The other extension is (potentially) infinite, which is
what qualifies it as linear (1D) as opposed to 0D. Or, in English, :-)
there is only a limited number of symbols you can stack, before you'd
have to move on to the next symbol. I consider these stacked symbols
as units, so essentially it doesn't matter what you can do inside each
unit; you could consider each Chinese character, for example, as a 2D
composition of various kinds of strokes. But these units, once
composed, can only be strung together in a linear fashion. To me,
that's what defines whether the writing is linear or not. Yes, within
each unit ("character") there is certainly a 2D organization, but at
the top-level, they are merely units which are still strung together
in a linear fashion. Therefore, the writing system is essentially
linear.

The first step towards getting away from this inherent linearity is to
make the structure branching as opposed to linear: i.e., the top-level
units (which may be composed of multiple "atoms" of whatever
dimensionality) can be strung together not only along a line, but they
can branch, and each branch can have a (potentially) unlimited
extension.

A further step would be to allow not only branching, but also
arbitrary interconnections between units, like a graph (in the sense
of nodes and edges). This does not mean literally drawing circles
representing nodes and lines representing edges; it means that the
units of the writing system are such that they can be composed with
each other in such a way that you can have complex inter-relationships
between them. As a contrived example, you may have a crescent-shaped
symbol around which other symbols may be juxtaposed, and each
juxtaposition carries a particular meaning.

I'm not sure how close this is to Sai's idea of a "fully" 2D writing
system, but I'd say any writing system that purports to be 2D must
have at least this level of expressivity before it can be considered
as such.


> ==================================================
>
> [3D WRITING]
[...]
> H.S.Teoh wrote:
> >If you meant writing in 3D characters, that'd be right up the alley of
> >a conlang spoken by 4D beings. :-)
>
> But why couldn't 3d beings use 3rd characters? But I thought Sai was
> envisioning something that was not just made up of characters.
Because even though we are 3D beings, we are more familiar with 2D
surfaces (which may be curved in 3D, but are nevertheless still only
2D in topology). A true 3D writing would distinguish, for example,
between a hollow sphere and a solid sphere, or concentric spheres. It
would also distinguish between the internal grain (wood grain, if the
letters were made of wood) of the letters.

Our limitation comes from the fact that our eyes really only see 2D
projections of 3D objects, even though we exist in 3D. As such, we
don't "really" see 3D objects in their full 3D-ness. Even though our
mind is quite capable of inferring 3D depth, we nevertheless think of
3D objects mainly in terms of their 2D surfaces.

In order to deal with a fully 3D writing system, one would have to be
able to see a 3D object in its entirety: not only its surfaces, but
also every internal point simultaneously. This can only be feasibly
handled by a 4D being, who has the advantage of being "outside" the 3D
space it is looking at, and therefore its line of sight is not
obscured by the surfaces of the objects it sees.


> Elsewhere H.S.Teoh wrote:
> >How about a description of carvings on a long totem pole?
>
> Yes, and a totem pole, whether short or long, is a 3d object   :)
> As Sai suggested above, it could be _sculptural_ which is what a totem
> pole is.
>
> If we 3d creatures can play 3d chess & other 3d games, then some 3d
> written system should be possible. I am not saying that I am advocating it
> - but it might be fun to try  :)
But see, our idea of 3D is still only based on the *surfaces* of 3D
objects. A real 3D writing would take advantage of the additional
dimension to represent different glyphs. For example, consider the
letter O and the Greek letter theta. If you were a 2D creature, both
would appear identical to you, because you could only see the outer
surface. But as 3D beings, we can see that the former is completely
hollow inside, whereas the latter has a stroke through its middle.
Similarly, a 3D writing could have such characters as a hollow sphere,
or a sphere with something inside. We can, of course, use various
methods such as transparency in order to be able to see what's inside,
but only a 4D being could truly appreciate the entire shape of such a
character.


> ======================================
> [LINEARITY]
> Sai:
> >Surely you take my point about nonlinearity, though - writing now is
> >2d in its symbols, yes, but not in anything else (e.g. syntax or
> >flow).
>
> Yes.
Which is why I was attempting, in my writing-on-the-wall example, to
illustrate how one might begin to transcend linearity: by introducing
branching and joining of the symbols.


[...]
> H.S. Teoh:
> >But the point is, it doesn't *have* to be linear in order to be
> >understandable. Take for example, the description I gave in my post a
> >few days ago, of a "writing" on the wall which describes the story of
> >a hero who slays a beast:
> >
> >The entire story is written as a very large, and very complex 2D
> >diagram comprising of interconnected parts.........
>
> Yes, I read your "writing on the wall" description and was going to reply
> to it. This is all very well, but two points occur to me:
> 1. Having something that takes up so much space it needs a whole wall is a
> bit inconvenient. We need something that is going to fit onto a reasonable
> size sheet of paper or VDU (with sensible resolution) IMO.
It doesn't have to be on a wall. I used the wall example just to prove
that it is indeed non-linear; it can be projected on a wall without
such devices as line-wrapping, which would betray its actual
linearity.


> 2. How would you deal with something like J.R.R. Tolkien's "Lord of the
> Rings"? Six walls? In what case the walls would be read linearly.
Whether they are read linearly or not, to me, is beside the point.  A
human reader, bound by time and limited mental capacity, would
necessarily process the information linearly in one way or another.
Therefore, what decides whether the writing is 2D or not is whether it
is confined to a fixed *order*. (After all, what defines linearity is
that there are only two directions: forwards and backwards, which also
implies that there is a unique beginning and a unique ending.) A
non-linear writing would not have a fixed linear order: there would be
more than merely 2 opposite directions, and there would be no unique
beginning and ending points.

To answer your question, I'd say that the writing system must be such
that you can excise one sub-diagram from the whole and put it on its
own page, and so forth; but the resulting set of pages would have no
fixed order in which you must read them. They would be related to each
other by complex interrelationships. Most likely, one would use
"anchor symbols" (or symbols/sub-diagrams that recur on two separate
pages) to reference each other and establish an interrelationship.
What order you read the pages in would be irrelevant; if you read
through all the pages, presumably you would be able to piece them all
together in your mind into the wall-sized writing.


[...]
> H.S.Teoh continued:
> >take a look at Pinuyo if you
> >haven't already --- it expresses complex concepts by
> >arbitrarily-complex layouts of pictograms, in 2D. You can potentially
> >write an extremely complex "sentence" in Pinuyo, involving nested
> >boxes of every sort at every point, and it will still constitute a
> >"single sentence". This can obviously be linearized (as with anything
> >else), but it is much easier to "read" in its 2D form.
>
> I have - quite literally - taken a look at Pinuyo; maybe I should look
> more closely. I am sue Sai want to express concepts (not words) in layouts
> which would, I guess, necessarily be complex. But _arbitrarily_ complex?
[...]

I think the crux of the issue is linearity. Complexity does not
necessarily indicate non-linearity; what defines non-linearity is the
lack of a fixed forwards/backwards direction in the text, and the lack
of a unique beginning and a unique ending. What makes Pinuyo
non-linear, at least within a single "sentence", is that you can read
the elements in any order and it conveys the same thought. There is
more than one way you can read it, and it doesn't have to be
top-to-bottom, left-to-right. There is no unique starting/ending
element. You could very well start in the middle and scan
circumferentially, or start at an arbitrary corner and proceed
radially, etc..


On Sat, May 07, 2005 at 06:15:18PM -0000, Joseph Bridwell wrote:
> > > If you meant writing in 3D characters, that'd be right up the
> > > alley of a conlang spoken by 4D beings. :-)
> >
> > But why couldn't 3d beings use 3rd characters? But I thought
> > Sai was envisioning something that was not just made up of
> > characters.
>
> I don't know about the others, but I'm a 4D being - I have height,
> with, depth and I exist in time.
[...]

Well, that depends on how you define 4D. :-) I am speaking not of 4D
as in 3 dimensions of space plus 1 dimension of time, but rather *4*
dimensions of *space*. If you like, consider it as 5D (4 spatial
dimensions + 1 temporal dimension).


T

--
Always remember that you are unique. Just like everybody else. -- despair.com

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