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

[Ted Nelson <ted@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")
various other examples I forget at the moment.

The other relations you mention--
>	1. Symmetric (positive and negative are the same, as you said)
>	2. Conjoined to other dimensions
>	3. Reflexive (A cell is considered to be related to itself)
>	4. Transitive (If A-B and B-C, then A is considered to be
>	   related to C even though there is no explicit link)
>	5. Disordered (I think this turns out to be the same as
>	   symmetric + transitive.)

... I'll have to think about.  

"Transitive" means that ordering is important.  See my paper
 on Preflets (the long proposal for Slices, ca. July 15) for
 a proposed way of representing transitive relations so that
 slices can come and go with cells appearing and disappearing
 consistently within that sequence.

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--

>There were a couple of others I thought of, but my notebook is
>downstairs.

Uh-oh.  You DEFINITELY are one of us.

Best, Ted


At 11:01 AM 10/26/98 -0500, you wrote:
>
>> Hi Mark-Jason--
>> 
>> >If the existing contents system is going to work at all, users must be
>> >able to provide their own semantics for dimensions.  
>> 
>> Definitely!
>> 
>> My intention (and I'm way behind) has been to provide
>>  about sixteen predefined dimensions, and suggested guidelines
>>  for how to extend.
>
>I hope you won't mind if I expand on my ideas a little.  
>
>Your plan is for d.inside and d.contents to be closely related to each
>other, so that neither one has a real meaning without the other.
>
>Suppose I am using ZigZag, and I want to create my own pair of
>dimensions that are related int the same way that d.inside and
>d.contents are, to serve an analogous but separate purpose.  For
>example, suppose I am doing a geneological chart, and I want to
>capture the idea of `ancestry'.  I will have two dimensions, d.parent
>and d.sibling:
>
>
>	A-B-C    +--> d.parent
>          | |    |
>          D E    v d.sibling
>
>A is the parent of B, who is the sibling of D and the parent of C and E.
>
>As far as `ancestry' goes, this is almost exactly the way d.contents
>and d.inside work:
>
>	A-B-C    +--> d.inside
>          | |    |
>          D E    v d.contents
>
>A holds B and D, and B holds C and E, so that C and E are also
>considered to be inside of A.
>
>If I want ZigZag to be able to do appropriate computations with
>ancestor charts, I will need to be able to tell ZigZag that d.parent
>and d.sibling are associated dimensions, that they go together in the
>way that d.inside and d.contents do.  In my notes I called this kind
>of association a `conjoinment'.  (I think `conjoinment' is as
>absolutely awful name.)  d.inside and d.contents are conjoined.
>
>Conjoinment is one of the kit items I was thinking about. When I
>create a new dimension, I should be able to say whether it is
>conjoined to other dimensions.  
>
>Similarly, the chart above has exactly the same *meaning* as if I had
>built it this way:
>
>	A-D      +--> d.parent
>          |      |
>          B-C    v d.sibling
>            |
>            E
>
>I would like ZigZag to understand that.  So when I create d.sibling, I
>would like a way to say `The order of the cells in a group doesn't
>matter, and positive and negative directions are the same.'
>
>This `disorderment' property is closely related to conjoinment, but I
>haven't figured out the details yet.  `Disordered' is another item in
>the kit.  When I create a new dimension, I should be able to say that
>in this dimension, the order of cells in a group is unimportant as
>long as they are all linked in a line.  (I called a line of linked
>cells in one dimension a `pier', but maybe you have a different name
>for it.)
>
>> Interesting point.  Except users might want to add some
>>  meaning to the direction of a dimension whose general
>>  meaning is predefined without direction.  
>
>Just so.  Dimensions express relations between things.  In forming
>relations, they might have any, all, or none of the following properties:
>
>	1. Symmetric (positive and negative are the same, as you said)
>	2. Conjoined to other dimensions
>	3. Reflexive (A cell is considered to be related to itself)
>	4. Transitive (If A-B and B-C, then A is considered to be
>	   related to C even though there is no explicit link)
>	5. Disordered (I think this turns out to be the same as
>	   symmetric + transitive.)
>
>There were a couple of others I thought of, but my notebook is
>downstairs.
>
>
>
>
____________________________________________________
Theodor Holm Nelson, Visiting Professor of Environmental Information
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"The most incomprehensible thing about the universe is that it is
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