[sugar] Defining Collaboration

[Michael Stone]

Michael Stone wrote:

> While informative, these descriptions of some known means of
> collaborating fail to pierce to the heart of what collaboration is. More
> abstraction seems to be required in order to get a useful handle on the
> whole situation. Hence, I propose that:
> 
> 1. A `collaboration' as a connected surface (i.e. a connected
>    topological 2-manifold) parameterized by time. The points of this
>    surface represent or can be mapped to some atomic notion of local
>    state that cannot be further subdivided, i.e. an opaque integer.

Oops. I found a slight bug. While one time dimension and only one "space"
dimension works for three people collaborating because they can arrange
their overlaps in any desired fashion on the surface of a cylinder, it
doesn't work for more than three people. In effect, only one space
dimension doesn't give you enough wiggle room for more than three people
to fragment and recombine into network islands in any fashion they wish.
Solution: tack on another space dimension and it all works fine.

Just imagine that collaborations look coral growing upwards from a flat
base. The coral has lots of holes in it because it branches and rejoins
in multiple directions.

In this image, people are now like little subcolonies of coral that have
grown together and then grown apart. Documents are invisible lines that
twist and turn and sometimes join and split as they run upwards through
this knarled block of coral.

Michael

(P.S. - If you want to really blow you brain, ask yourself what the reef
is... then notice, that it's just a big block of coral. :)