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--- In [log in to unmask], Patrick Littell <puchitao@G...> wrote:
>On 1/30/06, tomhchappell <tomhchappell@y...> wrote:
>>Do you mean by that, that you can throw in a finite, 

[actually it turns out there can be arbitrarily many]

>>suitably sparse set of exceptional "tiles" with more than 6 
>>neighbors? In fact, some bathroom floors are tiled with octagons 
>>and "diamonds" (tilted squares), the octagons having 4 octagonal 
>>neighbors horizontally and vertically, and 4 diamond neighbors 
>>diagonally; every diamond having 4 octagonal neighbors. This graph 
>>is not regular, however.
> 
>That's a good point, Tom;

Thanks!

>it makes me wonder... what's special about regularity for this sort 
>of project? 

Me too.

>Do we gain anything from having all our "tiles" the same size and 
>shape and having (the possibility of) the same number of neighbors?

Actually you can have up to any number of tiles of any "arity", 
provided no tile has more than 6 neighbors with "arity" more than 6.

Jefferson Wilson was putting together elementary symbols 
(representing something like "distinctive features") into "glyphs", 
which were something between syllabary-members and logograms-
ideograms, representing something between words and phrases.

For such a purpose, regularity is probably an advantage.

As far as stringing the glyphs together to make an entire compound-
complex sentence (something between a sentence and a paragraph, I 
think), regularity would not serve such a purpose; and Jefferson's 
glyphs are not, in fact, regular, some being composed of two "simple" 
glyphs, which can be joined in several different ways, leading to 
sizes from 7 to 18 "elementary symbols", with a variety of shapes.

> After all, not every word is going to allow the same semantic
> connections... it doesn't lose us anything if not every sort of word
> allows us every possible connection.  What's the Agent of "cat"?

Damn good question, and it puts me in mind of a question I asked on 
the list once.
"What, besides verbs, can have more than one dependent?"
The answers seemed to be something like this;
1) In natlangs, only verbs are attested with more than two 
dependents; and none of them have more than five _core_ terms, in any 
known natlang.
2) In natlangs, there are attested a few words of a few other lexical 
categories that do have two dependents; they may be conjunctions, or 
prepositions, or adverbs, or adjectives, for example.  But they are 
generally a (or a few) closed class(es), in each such natlang.
 
>Having some tiles with eight neighbors and some with only four 
>doesn't seem to be a big problem, if for some reason we decide six 
>isn't enough for all cases.

That's how I see it; or, some with 12 and some with 3, for instance.

>One more question: the "game", as it's shaping up, seems to involve 
>adjacency being the marker for... whatever we're putting 
>these "tiles" together for. Some sort of semantic connection 
>therebetween. 

At least, the way Jefferson was doing it.

>Anyway, how is purposeful adjacency distinguished from accidental 
>adjacency, since (in the hexagonal grid) a fully "saturated" center 
>tile will lead to six further adjacencies between its "arguments", 
>not all of which are going to make sense.  

This was one of the problems Jefferson was working on the last time I 
read an update of his "Glyphica Arcana".

He was also working on a problem he considered one degree more urgent 
than that one; namely, when you have two "adjacent" glyphs, and you 
do mean one to be a semantic dependent of the other, how do you tell 
which one is the head and which one is the dependent?

>And what happens when, say, the north hex is already in use and you 
>need to place something there?

While this is a problem in such a NLF2DWS, it is also a problem in 
spoken language.  What do you do when you want to put a subject in a 
clause that already has a subject?
Attested natlangs have basically two answers;
1) "here's how"
or
2) "you don't".

>I figure drawing lines all over the place would solve all of this, 
>but once we start connecting things with lines we don't really 
>*need* adjacency any more.

If the lines aren't allowed to cross each other, the problem is 
isomorphic to the adjacency problem.

If there are absolutely no restrictions on the lines crossing each 
other, the possibility of a "spaghetti-gram" arises; something which 
is incomprehensible, in spite of being grammatical, because of the 
limitations on human sensory and processing abilities.

Also; Even if the lines aren't allowed to cross each other, they 
should indicate _direction_, as well as connection.  (Which one is 
the dependent and which one is the head?)

Also; Maybe some nodes can have more than one line running out of 
them; but these lines could come in kinds ("colors"), so that no node 
could have more than one line of each color running out of it.

Also; In attested natlangs, it seems to be accepted by theorists that 
no node has more than one line running _in_ to it (as opposed to 
_out_ of it).  That would make the diagram tree-like, and wouldn't 
allow cycles and/or loops.  Sai seems to want a conlang a little 
unlike any attested natlang, that would allow a non-treelike diagram; 
perhaps a single word could be dependent on more than one head, or, A 
could depend on B which could depend on C which could depend on A (a 
cycle or "loop").

Tom H.C. in MI