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

From: Sai Emrys Tuesday, May 10, 2005, 13:46
```Here's my uber-compiled response thread, since that seems to be the

H.S. Teoh:
---
Even where time is involved, there's no need to constrain the
representation to linearity. One could, conceivably, have a noun at
the center of a circle, with lines connecting it to sub-diagrams (in
my diagram-writing system :-P) laid out around the circle, each
connected to a modifier node that indicates time (not necessarily in
increasing/decreasing clockwise/anti-clockwise sequence). In fact, it
doesn't have to be connected to the same central noun at all. With
time specification modifiers, things can appear anywhere in the
interconnected whole.
---

Definitely an interesting idea. Metaphors for time, anyone? It would
be interesting to work out a system of describing temporal events
that's based on a "time is cyclical" metaphor, or perhaps "time is
wheels within wheels [...]" one.

I suspect that random occurance, however, would be moreorless
impossible to parse into a sequence-of-events, and that would screw
with us. We need sequence in order to determine causality; merely
having each event be tagged with its time, in no particular order,
would nullify that.

---
How about a description of carvings on a long totem pole? Of course,
you don't *need* to use a linear description, but if you wanted to
thoroughly describe it, a linear approach would seem to be the easiest
choice.
---

Why? If you're aiming at *transcription*, then yes, you'll need at
least some sort of spatially-mapped equivalent, but I don't see a need
for that aside from special uses. If you want *translation*, then you
could have linearity being an optional, designatable thing, if it's
important to the source. But if you're going for *interpretation* -
that is, conveying the same general idea in what is potentially a
completely different form - I suspect even that would be unnecssary.

---
Perhaps using directions to represent different syntactic roles? E.g.,
symbol X on top of symbol Y means X owns Y; whereas X to the left of Y
means X is the cause of Y, etc.
---

Probably too limiting / redundant / inapplicable to have that be so
for everything. I think that core juxtaposition 'slots' would need to
be one of the most overloaded / dense / efficiently used things in the
language, given that they're omnipresent; wouldn't want to waste it on
implausible or infrequently-used relations (e.g. do you need to have a
slot for what owns an instance of the action of eating?)

FWIW, this also reminds me of another point - one I dislike in Pinuyo:
drawing little frames or whatnot around atoms is silly and wasteful. I
can't see this plausibly being used in something that would be so core
and so frequent; it needs a more elegant approach.

---
We're aiming at representing semantics, not syntax, I'd hope! (And
especially not syntax of a natlang!)
---

Let's hope. ;-)

---
The atoms-and-relations idea isn't as dull as you might think... for
example, in existing (linear) writing, one often finds that repeated
units over time tends to get shortened because people get tired of
writing long strings of the same thing over and over. Over time, you
get abbreviations that eventually turn into first-class citizens
(e.g., much computer acronyms turning into verbs, such as "can you FTP
that file to me?"). In non-linear writing, sub-graphs could get
simplified over time, and become calcified graphical units get reused
in brand new ways. Eventually, they *become* the atoms of the writing.
---

I'm not saying it's dull, just that ultra-fusion is more intriguing
because it's even more difficult to conceptualize. :-P I tend to like
thinking about things I can't quite figure out how to think about.
Dig?

Agreed on the need for proforms and 'lexicalization' (or however that
would be called in its equivalent... sematization?). I wonder how one
would do the latter, though. The former is simple enough.

Perhaps you'd simply create new atoms for the meta-idea expressed in
the subtree? (Something like "person who teaches" -> "teacher", except
on crack. :-P)

---
> Mm. Ideographic I think would be limiting, but obviously whatever it
> is, it would need to encode purely meaning. (I don't know of any
> ideographic writing systems that do so; all the ones I know have at
> least some phonetics in them, like Chinese.)
Why does it have to encode meaning directly? It can have idioms too,
like the symbol for a horse combined on its bottom-right stroke with
the symbol of a frog being an idiom meaning "it is going to rain". It
can also have such features as indicating focus: say you're describing
a story, and you'd use a particular decoration on the symbol for the
hero to indicate that it's an important figure.
---

Sure, sure. But that's all meaning, ya? I don't think you're actually
disagreeing with me here.

Let me clarify that: "encode meaning exclusively" as opposed to e.g.
Mandarin, which encodes both meaning and rhyme (moreorless) into a
typical character.

Quite agreed on the desirability of idiom and profiling, though.

(That brings up another question: Color as another dimension? Could be
used to make things pop much better, and to make meta-relations
obvious even when physically far apart. Viz. the various uses of color
on maps, email programs like Gmail, etc., to profile certain
patterns.)

---
Affixes would simply generalize to ... sub-symbols in some sort of
geometric relation with the main symbol. E.g., symbol X with a small Y
on top means something, symbol X with a small Y below means something
else, symbol X with a small Y to the left means a third thing. They'd
still be affixes, except you can attach them to a LOT more than just
two ends of a "word".
---

Agreed. Dunno if I would want to encode on a particular orientation,
though I can see benefits to it. It would make for problems of space
limitation and aesthetics, though, unless very cleverly designed
indeed.

Damian Yerrick:
---
I think Toki Pona, though it is a spoken or linearly written language,
is small enough to analyze nearly exhaustively for necessary
relationships.
---

Mind pointing me to this?

---
Anyone want to see an example of such a diagram of a sentence
with English words?
---

... please for the love of sanity no?

---
> But whichever approach is used, one cannot, as far I can see, avoid some
> linearity/serialization.
> Even if whole sentences are depicted as a single symbol construct
> (glyph/frame/ or whatever) the sentences will surely follow sequentially
> or linearly.
Especially given that at least to human observers at classical-mechanical
scales, cause and effect is the dominant feature of time, and a "linear"
path can always be traced from a cause to its effect.
---

*nodnod* It would be interesting to use this as a vehicle for
low-level-encoding (or prompting) a different conception of time /
causality, though. Viz. "Story of your life" again.

---
How about spatial relationships, such as that things are physically laid
out in a given order?  H. S. Teoh pointed out the example of a totem
pole.  Or given the theoretical equivalence of space and time, is that
---

I hadn't thought of space/time as being relevant here, since our
consciousness is generally locked into one directionality on that. :-P

Nah, see above - transcription, yes; translation, maybe; interpretaion, no.

Simon Clarkstone:
---
And what about the mutations?  There are so many possibilities (as
a start, consider the mutations that are used for the radicals in
Chinese characters).  A symbol could be rotated, flipped, skewed,
squashed, stretched, bent, abbreviated (in some symbol-specific way),
or the core lines could be changed to double lines, or it could gain a
"siamese twin", or ... !
---

Indeed! And this is where the 'uberfusion' idea comes in... ;-)

Ray Brown:
---
> 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 see this as still chunked-linear, just with more complexity in the
chunks. Korean is pretty trivial in this respect, and trivially (and
one-to-one) serializable. Don't know enough about Egyptian/Mayan to
comment on those.

---
But why couldn't 3d beings use 3rd characters? But I thought Sai was
envisioning something that was not just made up of characters.
---

For one, whateverthehellweare *can* use 3d characters. Easy: just make
a unique sculpture for each letter of the alphabet and put them in
sequence. That's the ultratrivial version of course, but it just goes
to show that atoms at least are obviously encodable as a 3d object.
Would pose certain difficulties, perception-wise, and you would need
extreme skill or computers (holograms?) to be able to add a time
dimension to it (rather than just putting discrete 3d objects next to
each other).

---
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  :)
---

Probably would be. But I agree with the post below - probably best to
pause this one until we solve the oh-so-much-easier *cough cough*
problem of a merely 2d system. ;-)

---
Yes, the sentence is probably to restrictive, but ......
---

But?

---
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.
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.
---

1: Depends how much you want to encode, obviously. :-P

2: *nod* See my clarification in above reply about that being chunking
rather than linearity.

---
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?
---

Explain what you mean by "arbitrarily complex", here?

---
I don't know any reference to expanded version of it on the Net, i'm
afraid. It was certainly far more developed than Leibnitz's attempts. But
we would find all these 17th century attempts somewhat quaint as they
embody scientific & other knowledge as understood at that time.

This, it seems to me, is the problem with trying to derive a written form
that expresses concepts. thoughts or whatever, independently of natural
language (whether spoken or otherwise signed). What we will IMO finish up
doing is finding a way of expressing in graphic (or sculptural) form the
way we conceptualize the world/universe in the early 21st century.

But on second thoughts that might not be so bad. It would provide
amusement for people in centuries to come, but by seeing how we have moved
on from the earlier efforts, they can improve and by a process of Socratic
dialectic better & better systems might be developed  :)
---

*grin* At least it would be one step more meta on the self-awareness scale. ;-)

But yeah, I fully agree that this leads in very few steps (if any) to
being an exercise in figuring out how we think (omg, a cogsci major
saying that?) and how one can encode worldviews and suchlike.
Otherwise, how can you possibly try to make a system that attempts
accurately reflect your 'native' thoughtprocesses? :-P

Joseph Bridwell:
---
I keep coming back to ASL. Many ASL signs change/morph. That
requires a way of projecting 4D onto 3D, or a medium in which the
morphing can be actively shown.
---

Trivial: map time onto linearity.

Ray Brown:
---
Sai's idea, as I understand it, is to represent whole complex _meaning(s)_
in a some graphic form without any relation the linear way in which we
order the natlang representations. I think Sai is right that the concept
of affixation is meaningless or at least significantly different in such a
context.
---

Bingo.

I should point out, though, that this is an assertion of intuition; I
can't as yet actually support it. I'm not even sure what the proper
questions would need to be to figure that out.

(For that matter, at what point do you chunk a single "meaning"? Can
it be arbitrarily complex and still be "one" item?)

Remi Villatel:
---
So here came my idea. Whenever a non-linear writing system should be
invented, why should it absolutely reproduces all the flaws of the linear
system? Our visual cortex is capable of deciphering more that a word at a time.

A non-linear system could use this ability to present us several words in a
semagram which would induce a mental image. In a linear text, there are a
lot of tiny words that we don't actually need to read in order to
understand, like most of the articles, some redundant pronouns, the
prepositions, and other non-essential bits. These "useless" words shouldn't
be used in a non-linear system, unless really necessary, for example to
connect logically two semagram.
---

*nodnod* I wonder how you could take advantage of psych / cogsci /
perception research to optimize for this...

Ideas?

---
So, a semagram is no more than a few words the one above the other which can
be read at once, almost like a picture, as a whole. Thus, the semagrams are
the symbols and the words are their atomic components. We don't need more.
No line, no arrows, no other symbol, except maybe a frame around the
semagrams to separate them.
---

Strongly *dis*agreed. "A few words one above the other" is an
extremely linear concept. If you're going to treat them as a whole,
why not fuse them 2d, or even in a completely overlapping /
integrating fashion? Why keep the bounds of the constituent atoms and
then string those along?

---
If you haven't room enough, you just add a third dimension thanks to a
hyper-semagram... well... a hyperlink just like on any HTML page. (We're
living in a computerized world, ain't we?)
---

Mm. I find that such things tend to be difficult for me to parse /
chunk, though - ones that rely on hyperlinks. Tend to get lost and not
have a sitemap, nor the ability to have a "zoomed-out" view of the
situation.

---
BUT this is no kind of writing system that can you read aloud. You can only
only one dimension so any non-linear writing system can logically only have
an indirect relation with it.
---

Not really. Any graph or tree can be linearized; it's just a
one-to-many relation. You'd also have to add salt in order to recover
the broken links, but that's doable. Probably not in a cognitively
easy way for a human, though, so you could consider that to be
effectively lost data.

That does beg the question, though, of how much you could screw with
it so as to render it not just nonlinear, but *nonlinearizable*...
*hmmmmmmmm*...

(Your story, btw, showed in my gmail [via both Firefox and IE] as a
formatted table, but without lines of any kind - just cells. Was that
the intended appearance?)

Ray Brown:
---
> I wrote a little 2D fairytale to illustrate my purpose. (I hope that the
> list allows an attachment. It's only HTML.)
I like it - but then, I like crossword puzzles   :-)

Please, don't get me wrong. I think your idea is an interesting one - and
unlike most systems, your lines do go in different directions and do make
more use of 2d space than most writing systems. Egyptian hieroglyphics
(and, I believe, the Mayan glyphs) certainly made use of both rows and
columns - but not in the ingenious way that you do  :)

However something tells me it's not what Sai has in mind. I would call
this a 'full-2d linear writing system'.
---

I would agree.

H.S. Teoh:
---
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.
---

Agreed, per my comment above. However, you could deal with this.

Option A: Limit certain relations, like semantically relevant things
being in a visually obscured position (e.g. hollow-vs-not sphere).
Call this the equivalent of phonology - there are some things you just
can't pronounce / perceive accurately due to biological limitations.

Option B: Tech that's capable of overcoming this visually. Holograms
or selective transparency again, and physical movement with respect to
it? (Something like walking through / amidst the writing...)

Option C: Call it a limitation of perception - an ambiguity that's
dependent on where you stand. So if you want the 'full picture',
you'll have to walk around, per above. ;-)

---
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.
---

*nod* Also keep in mind that it could be "dangled" in lots of
different ways, depending on how interconnected it is, and how
strongly encoded the links are wrt orientation & distance.

---
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.
---

*nodnod* The question of how to excise, though, is a tricky one in
itself. What exactly do you choose to chunk? And at what LOD(s)?

Can you retain scalability of detail (and presence/accessibility of
all LODs simultaneously) after this sort of a chunking operation?

(One throwaway suggestion would be to have the excised one have
"ghost" versions of their immediate structure and the overall
structure into which they fit [that is, very attenuated versions of
1-2 steps up and down in the LOD chain]...)

... there, all caught up. Now on to studying some more for that NTL
final... *procrastinate procrastinate*

- Sai
```

### Replies

 Sai Emrys Sai Emrys Remi Villatel Damian Yerrick