Re: Conjoinment (was: User semantics for dimensions / sug'd guidelines

[Mark-Jason Dominus <mjd@xxxxxxxxxx>]

> This "conjoinment" may be a good term.  I have
>  been noticing that you generally want new dimensions
>  in pairs in just this way,
> d.inside / d.contents
> d.mark / d.marklist (tells what cells are part of
>  "the same mark")

That's what I was thinking.  Any time someone is going to want to have
a relationship that is one-to-many, they will need to do this.

> "Transitive" means that ordering is important. 

Not exactly.  Order can be important wihout being transitive.

Consider:

	---> d.ancestor

	A--B--C

Here you want --- links to express `ancestry'.
A is the ancestor of B, and B is the ancestor of C.
But it is transitive, so A is also the ancestor of C.

	---> d.child

	A--B--C

Here you want --- links to express a parent-child relation.
A is the parent of B, and B is the parent of C.
But is is *not* transitive, so A is *not* the parent of C.

The two pictures look exactly the same, so if ZZ is going to
understand the difference between these two pictures, there will have
to be an explanation somewhere else.

> See my paper on Preflets

Where?

> I think 1 and 3 come from somewhere else
>  (as you see, I'm no mathematician) and may not 
>  have meaning or relevance.  Hey, I'm open--

I wrote them down because I ran into examples where they were
important. 

Symmetric means that in A---B, A is related to B in the same way that
B is related to A.  If you hop A over B and make it B---A, the meaning
does not change.  Example: d.contents is symmetric.  d.inside is not.

If ZZ is going to do things like selecting and gathering cells
automatically, it will have to understand something about the meaning
of the structures you build.  Symmetry and transitivity are both
important here.

In an earlier message, I suggested that there could be an operation
for automatically alphabetizing cells:

	---> d.sex
	MALE   -- Homer -- Bart -- Ned -- Barney -- Moe -- Snake

You'd put the cursor on MALE, press the button, and the structure
would become

	MALE   -- Barney -- Bart -- Homer -- Moe -- Ned -- Snake

In order to do this, ZZ must know that d.sex is symmetric and
transitive.  Otherwise it should give you a warning first, because
what you are asking for makes no sense, and if you try to alphabetize
in a dimesion that is not symmetric or transitive, you will change the
meaning of the structure:

	---> d.son
	Grandpa -- Dad -- Ted

	||   Alphabetize
	\/

	Dad -- Grandpa -- Ted        (ooops)

> >There were a couple of others I thought of, but my notebook is
> >downstairs.
> 
> Uh-oh.  You DEFINITELY are one of us.

My notebook is now in the compuiter, so beware.