ONT Re: Extension x Comprehension = Information
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Note 85
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Tom,
I am still a few hypotheses shy of an explanation of all that
our Mister Tuesday Afternoon was saying just now, or a little
while ago, about icons and indices, and their symmetries, but
I am under the perhaps too facile impression that I have long
understood the gist of it, by dint of the particular examples
that arise in my application to systems theory, many of which
seem to fit the pattern of what Peirce seems to be describing.
And so, here for comparison is the picture of an iconic sign:
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| q o |
| ·· |
| · · |
| · · |
| · · |
| · · |
| · · |
| · · |
| · · |
| · v |
| · o u |
| · / |
| v / |
| x o------@ |
| \ |
| \ |
| o v |
| |
o-----------------------------------------------------------o
| Sign u is an Icon of Object x by Virtue of Property q |
o-----------------------------------------------------------o
And here is the putatively dual figure of an indexical sign:
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| o u |
| / |
| / |
| x o------@ |
| ^ \ |
| · \ |
| · o v |
| · ^ |
| · · |
| · · |
| · · |
| · · |
| · · |
| · · |
| · · |
| ·· |
| t o |
| |
o-----------------------------------------------------------o
| Sign v is an Index of Object x by Virtue of Instance t |
o-----------------------------------------------------------o
The reason that the indexical style of picture appears almost immediately
recognizable in a systems-theoretic context is because the state space of
a complex dynamic system is a setting in which "objects have instances".
In effect, an object is an abstract unity that comprises a collection of
components and connects a sequence of state points in an orbit over time.
Now, an "abstract unity" is a funny sort of thing -- it is partly a whole
and wholly a part, in other words, a whole in its own right that is merely
a face of some more complete and full-bodied whole. What this means in the
present setting is that we can view the whole system and the temporal state
of the whole system as objects, the latter being an "instant" of the former.
For example, two people in a dialogue may be viewed as a "dyadic system",
and each person's experience of the interaction is a facet of the whole.
One's experience is an index of the other's experience, and vice versa,
by virtue of their actual connection in the instantaneous state of the
whole system. And if one of them points to a common object, to which
the other independently or by dint of that pointer attends, then each
of their experiences, in that moment, becomes an index of that object.
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o