TIME & HPCT - RKC

[From Bob Clark (930509.1520 EDT)]

···

*************
I've spent much of my "spare" time this past week writing and re-writing
the following ( some six drafts). I still don't like it in some ways -- it
seems a bit "disconnected." But I've just now been going through some 40 of
the posts that have accumulated, and I think I might as well send it. And
see what happens. I'm planning to start reporting my application of PCT to
City Government -- with some success to date.
*************

WHY "TIME?"
Time must be considered in HPCT in several respects: underlying independent
variable; stability; perception; time scales; selection among levels of
control systems; engineering analysis; analysis of interacting levels;
analysis of interacting hierarchies (people, governments); operation of
memory; planning/scheduling; anticipation; etc etc

TIME DEFINED
My Webster's Unabridged Encyclopedic Dictionary of the English Language,
1989 includes:
"time, n, 1. the system of those sequential relations that any event has
to any other, as past, present, or future; indefinite and continuous
duration regarded as that in which events succeed one another. 2.
duration regarded as belonging to the present life, as distinct from the
life to come or from eternity; finite duration. 3. a system or method of
measuring or reckoning the passage of time; 4. a limited period or
interval, as between two successive events."

TIME AS INDEPENDENT VARIABLE
In working with any changing phenomenon, especially in areas of physics and
engineering, the underlying Independent Variable is Time. Other Variables
are Parameters of the System. Of course the Parameters can also be treated
as Variables, with resulting changes in the Temporal Characteristics of the
System.

Time derivatives and integrals are also important concepts throughout this
changing world. But both derivatives and integrals use two variables, at
least. In addition to the variable of differentiation/integration, there
is the dependent variable, itself a function of time. These general
concepts can be applied to time elements of any size.

STABILITY
In BCP, Appendix, p 273f, Bill concludes with a discussion of
"Stability," in which he demonstrates the results of tracing events
around the loop -- when internal time delays are omitted. As he
notes, p 282, "The more sensitive the control system, the smaller
fraction of the calculated correction must be permitted on each round
of calculation and the more slowly must the system change its output
if stability is to be maintained. This is how time can be taken into
account in a sequential-state analysis of a control system. When
time is properly taken into account, the sequential analysis gives
the same steady-state result as the continuous-variable (algebraic)
analysis."

These observations apply to EACH SYSTEM INDIVIDUALLY. In addition,
as we observed years ago, stability requires lower order systems to
complete their actions before higher order systems introduce further
changes. Thus temporal relations throughout the hierarchy cannot be
ignored.

PERCEPTION OF TIME
It has been pointed out that we have no "Time Sensor" in the sense that we
have taste, smell, touch, etc. However, those senses are each quite
distinct from each other, and some degree of time sense seems to be very
widespread. Perhaps we don't know where to look for the Time Sensor. That
time is recognized as somehow perceptible is suggested by the dictionary:

Higher Order Perceptions are conceived as combinations of Lower Order
Perceptions. Thus an "object" is a "configuration" of perceptual
variables. To perceive an object as changing, moving, etc, requires an
additional perceptual variable: time. Examples, a cube rotating, a balloon
being inflated, a ball being thrown, a ball bat being swung. Such
perceptions depend on which Time Scale is applied.

TIME SCALES
Time Scale is defined in terms of the duration of its time intervals. A
"Fast" Time Scale uses short intervals, and a "Slow" Scale, longer
intervals. To observe the details of an event, the swing of the bat, a
Fast Scale is needed. On a Slow Scale, the bat is a blur. These relations
are well known, and frequently used.

Time Scales apply throughout the levels of Hierarchical Perceptual Control
Systems. The perceptual variable of concern determines the Time Scale to
be applied. If the details of the internal operation of the relevant
system are of interest, a Fast Scale is needed. This Scale should be fast
enough that changes in the related Reference Level can be neglected. On
the other hand, if the system is to be perceived as a Control System, the
Scale should be slow enough that the internal details of the system are
de-emphasized while the changes in Reference Level are emphasized.

SELECTION AMONG LEVELS OF CONTROL SYSTEMS
HPCT is frequently treated in static terms, as though time plays no part in
the operation of Control Systems.

This may have resulted from Bill's excellent discussion of the operation of
a Control System where he pointed out, p 275, "These equations represent
steady-state conditions of the variables ... and that transient effects
die out rapidly to zero."

This steady-state treatment of the hierarchy as a whole seems to have been
widely accepted among PCTers. However, at most, it applies directly only
to a SINGLE SYSTEM.

Each of the levels of the Hierarchy has its own typical range of Time
Scales, although it appears there can be some over-lap if the
perceptual variables are otherwise independent.

For lower levels, suitable Time Scales are suggested by the "Reaction
Time" of the Perceptual Variable of interest. Our early work on this
subject was presented at the American Psychological Association
Meeting of August 30, 1958. Our estimates for the first four orders
(as then conceived) were: First - 0.06 sec; Second - 0.20 sec; Third
- 0.22 sec; Fourth - 0.63 sec. N was small, but the data were quite
distinct. Further study is certainly desirable, especially for
Higher Orders. Informal observation suggests similar "Reaction
Times" apply to Higher Order Systems. Measurements may be difficult
because attention easily and rapidly shifts among perceptual
variables leading to mixed results.

Discussions of interactions involving more than one or two levels of the
hierarchy require suitable selection of time scale -- what works for one
level may be improper for another. This is because the lower level is
following the Reference Level set by the higher -- and the higher is
working to control its own perceived variable on its own time scale.

For interpersonal interactions, this is even more critical because more
than one set of hierarchical systems is interacting -- usually at more than
one level! This is what I am attempting to deal with in the local
government.

THE ENGINEER'S TIME SCALE
For the Engineer, the emphasis is on the events within the lowest loop,
with its Reference Level unchanging. The Time Scale must be fast enough to
distinguish the internal events. It also must be fast enough that the
Reference Level does not change as the internal events are observed.
Otherwise the relation between an Environmental Event and the later Action
of the Output Function could be modified by intervening changes of the
Reference Signal. For the Engineer, a single variable is considered as it
passes around the loop and interacts with the components of that system.

This Viewpoint is concerned with the properties of each of the following,
both individually and in combination:
1) Feedback Function: a one-to-one amplitude converter from one physical
form to another;
2) Neurons: passive and unidirectional conductors;
3) Comparator: a fixed off-set when the Reference Level is unchanging;
4) Output Function: a "Power Amplifier" rather than just a magnitude
amplifier
5) Environment: with properties fixed by the physical surroundings

THE ENGINEER'S ANALYSIS
This viewpoint includes band-width, internal delay times, the nature of
signals being transmitted, linearity, time derivatives and time integrals
etc. These are appropriate for this fast Time Scale. Changes in R, were
they to occur, can readily be included in this analysis.

INFORMATION THEORY ANALYSIS
The IT posts also imply that the Reference Level remains constant. No
changes of R are considered in the discussions. This is also an
Engineering viewpoint. If changes in R occurred, what would be the IT
analysis?

SUMMARY
In HPCT it is necessary to include TIME explicitly at many points. For
some limited purposes of exposition, it can be assumed in the form of an
underlying independent variable. But temporal considerations are critical
in working with combinations of levels and interpersonal interactions.

Time Scales must be selected that are appropriate for the specific selected
Perceptual Variables and the corresponding Systems. If more than one
person is involved, interacting Systems from more than one level in each is
likely. Thus it will be necessary to pay attention to several Time Scales,
shifting from one to another as conditions may require.

Regards, Bob Clark