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

translation of your examples into a series of PCT tracking tasks.

Until later,

Tom