# IT, Phase space

Tom Bourbon [931227.1213]

[Martin Taylor 931221.1400]

Martin, in your post on "IT, dynamics, PCT," you used the example of a
phase-space analysis of the momenta and locations of a ball in a bowl to
illustrate basic concepts in dynamical analysis and information theory. To
test my understanding of your presentation, I am trying to convert your
discussion to one of (what else?) the position of a cursor relative to that
of a target. Before I proceed, would you consider it appropriate for me to
think of the phase-space in terms of (x) displacement of the cursor from the
target and (y) velocity of change in displacement? For example, if the
cursor is suddenly displaced positively on the axis x to point A relative to
the stationary target, the cursor accelerates in y, then decelerates, while
moving back to the position of the target in x; similarly for a sudden
negative displacement of the cursor to point B on the axis x. In either
case, the cursor "ends up" at the position (in x) and velocity (in y) of
the stationary target. (In the plot below, the locations in phase-space of
the cursor in example A are shown as periods; those for example B, as zeros;
and the point of 0-displacement and 0-velocity [when the cursor matches the
target] as @, to represent both a period and a zero. Would you consider the
point @ to represent a "point attractor?")

y
>
> .
B | . .
-x --0-------@------.--- +x
0 0| A
0 |
>

(Time runs from A to the left, back to the @; for B, time runs to the right,
to the @.)

If this rendering of a phase-space analysis for control of a simple cursor-
target relationship seems acceptable to you, I will finish my attempt at a