RM: Actually, I still have no idea what the law means in terms of the variables in a control loop. I don’t think this law has anything to do with PCT becuase I have never seen any need to take this law into account when I build models of or do research on control systems. And Powers never mentions this law in his descriptions of PCT. Actually, I do think Powers referred to the law of requisite variety in discussions on the CSGNet so someone who can look through the archives might like to see what he had to say about it (and about Ashby as well). As I recall Bill criticized both the law of requisite variety (and Ashby’s whole approach to control theory) in his usual diplomatic way. But I would like to see what Bill actually did say about it.
First we describe the tracking task. Let's take the simplest one, a
pursuit task in which the subject uses a mouse to move a visible
cursor so that it lines up with a disturbed target. The subject can
perceive differences as small as one pixel between the two
In the usual tracking task, the subject can move the mouse so that
the cursor can be placed to one pixel accuracy, and the cursor
location can be altered 60 times per second. There is requisite
variety all around the loop, to permit perfect control, so the only
limit on the actual control is the subject’s ability to perform the
task. That limit is determined by several factors, among which is
the loop transport lag. But we ignore that, and consider a
ridiculous extreme case in the other direction – or rather, a
parallel set of extreme cases, in which somewhere in the loop there
may be insufficient variety. In each of these illustrative cases,
the conditions are normal except for the change indicated.
Case 1: The mouse does not influence the cursor. In other words,
there is zero variety available from the output to the environmental
variable, the cursor. We call this “open-loop”.
Case 2: The mouse moves the cursor normally, but the subject cannot
see what it did until two minutes later. If the disturbance changes
by only a pixel every few minutes, control could be perfect, but if
the disturbance influence changes by a few pixels per second, there
is no control, and the situation is effectively open-loop, though
the loop is actually closed. There is requisite variety in the
spatial domain, but not in the temporal domain. The limit in this
case is in the path from the display to the controlled perception.
Case 3: The mouse moves the cursor and the perception is immediate,
but the mouse can only move the cursor to places separated by 10
pixels (e.g. to pixel …120, 130, 140, … from the edge of the
screen). The output variety is reduced by a factor of 10. The
subject could do nothing about an error that might be as much as 5
pixels. Control still occurs and is fast, but control is not as good
as it would be if the output had requisite variety.
Case 4: Exactly as in case 3, except that the disturbance now only
moves the target in 10 pixel increments, to locations …, 120, 130,
140,… from the screen edge. Control can be perfect, within the
limitations of the subject’s ability. The output variety hasn’t
changed, but the reduced variety of the disturbance has changed the
variety that is requisite around the loop. (If the target moves to,
say, …122, 132, 142,… There will be irreducible but constant
error. This is not a question of “requisite variety”, because the
error enforced by the offset doesn’t change).
Case 5: Everything as normal, except that the mouse is sampled and
moves the cursor only once per two seconds instead of 60 times per
second, to a new location determined in the normal way by how much
the mouse moved between sample moments. The disturbance moves the
target smoothly, as normal, and the subject perceives the
cursor-target difference normally, but control is poor because the
cursor only moves in a series of two-second-long steps. There is
insufficient variety in the temporal domain.
Case 6: Same as case 5, except that the disturbance moves the target
only once in ten seconds, with the steps synchronized with the mouse
sample moments. Control can be perfect, within the limits of the
subject’s ability. The variety around the loop is the same as in
case 5, but the requirement is less. There is requisite variety all
around the loop.
I hope these extreme cases give an idea about what is meant by
“requisite variety” in the context of simple tracking. At a much
more complex level, a novice chess player does not have sufficient
variety in her perceptions of winning and losing positions on the
board to win against a chess master who has been learning these
positions for a couple of decades and has dozens if not hundreds of
them in mind. “Requisite variety” applies to any and every part of a
control loop, but what is “requisite” depends on how good control
must be and on the variety in the disturbance. In case 3, for
example, if control is good enough with error as high as 6 pixels,
then the loop has “requisite variety”, but it doesn’t if pixel-level
control is wanted.
Nicholas has been writing as though "requisite variety" referred to
the number of different environmental feedback pathways through
which the control unit’s output might influence the environmental
variable. That kind of variety is important when we use PCT in
social analysis, because the more ways you can influence your
perception, the less likely it is that someone else’s side-effects
will block your ability to control. To be useful, however, each of
these different environmental paths of influence must individually
allow “requisite variety” of the Ashby kind.
terms of a simple control task, like the tracking task.
The law of requisite variety is not a concept that is part
of PCT or control theory, for that matter.