[sci.virtual-worlds] The semantics of multidimensional space

gbnewby@rodan.acs.syr.edu (Gregory B. Newby) (08/19/90)

My dissertation involves building a prototype information retrieval
system making use of "information space."  Users will navigate through
the space, choosing what's of interest to them.  I'll also be developing
the theoretical justification for choosing such a representation and
display scheme.

I've been working with multidimensional scaling, a social-science 
visualization technique, for several years.  Here's a few bits of 
"insight" and some other comments:

1.  When you talk about "dimensions" of space, don't get confused between
dimensions and the orthogonal coordinate system on which they are mapped.

In other words:  yes, you have  X, Y, Z, etc. axes for drawing stuff on.
However, you can associate more traits than the number of dimensions
with the space.

For instance, one region of the space can be "good," another can be "complex,"
and another can be "colorful."  You can imaging putting quite a large
number of these "dimensions" in a space with a small number of axes.
The extent to which any item in the space is close to these various
qualities reflects the extent to which they have these quantities.

You have more power when projecting a high-D space onto only three
axes -- the space need not be euclidean or even isomorphic.

2.  I've seen these kinds of "dimensions" emerge from every dataset
I've analyzed using multidimensional scaling (MDS).  The thing is:
the "meaning" is there in the space ("good," "complex," "colorful,"
whatever is relevant for the chosen domain).

The neat part is:  these "dimensions" emerge from the data -- they were
NOT part of the original input.  Without going into details on MDS,
what I mean here is that you choose your concepts to map in the space.
These emergent dimensions were NOT part of the set of concepts which
were measured, but they are clearly there.

3.  I'm working on a chapter of my diss titled as the subject line
above (will distribute it when completed -- don't rush me).  It's clear
to me that a space with only a few axes can represent a rich amount
of "meaning."  The key is to measure the object under study in such a
way as to make that meaning accessible.  

Then, I need to represent the MD-space using a limited coordinate
system (3 or 4 orthogonal axes).  I also plan on inserting "sign posts"
so that people can see which direction to go in for a particular
"information trait."

4.  A few more details on the prototype project:  using Usenet,
and word cooccurrence data to build a space based on statistical
information in the words.  Using a Silicon Graphics IRIS workstation to 
display the data on a monitor.  (I'm working on a grant proposal to try to 
get a datavisor/dataglove/etc setup.)

All this stuff is pretty new for Information scientists -- I've seen
nothing that approaches the implementation I'm planning, although there's
plenty of discussion of "space" in the field.  The visual interface is the
real clincher, from my point of view.

5.  If you want to know more about MDS, pick up any intermediate-level
statistics or social science methods book.  Sage puts out a great social
science series, and the MDS book there is quite good.  I am affiliated
with the Galileo method for MDS (See Joseph Woelfel and Edward Fink (1980),
_The measurement of communication processes_, New York:  Academic Press.),
which has some important differences from other methods, but not important
to the novice.

6.  I'd appreciate any leads to people working on information space for
information retrieval.  The information field is decidedly devoid of such
work.

7.  Sorry this message is so long...

-- Greg Newby
   School of Information Studies	gbnewby@rodan.acs.syr.edu
   Syracuse University			gbnewby@sunrise.bitnet
	"Curiouser and curiouser"  -Alice