[From Bill Powers (2010.09.05.0152 MDT)’
Martin Taylor.2010.08.31.19.25 --
The point is that the
need for
PCT can be derived from the basic laws of physics with no need
for any
model fitting.
This is hard for me to understand because PCT is a specific theory
of how
specific systems of one kind are organized. We can show that there
are
similar systems with physically identical components but different
properties, systems that are organized only slightly differently
and are not control systems. Consider a (former) control system
that
simply has the sign of one of its functions reversed or a time
delay in a
function somewhat extended (an oscillator) or with a missing
environmental feedback function or one with a very small
multiplier (an
S-R system), or one with a missing perceptual input function ( a
central
pattern generator, for instance). In most model diagrams the
actual
system parameters are neither shown nor mentioned, yet the
magnitudes or
signs of those parameters can critically determine what kind of
system is
present. And all of those other kinds of system may be found among
natural systems. They all work by doing something.
What is a "basic law" of physics? Is conservation of momentum
one of them? If so, then how is the theory of a gyroscope “derived
from” conservation of momentum? Many systems with and without
wheels
demonstrate conservation of momentum, and by that token can’t be
related
to each other just by sharing that property. Conservation of
momentum is a generalization from observations of the behavior of
specific systems; it says there is some variable that is not
affected by
changes in the values of certain system variables; if one variable
changes, there are others that will also change in specific ways,
as
angular velocity changes when linear dimension changes, leaving
momentum
alone. From that alone you could never deduce that there will be
any
planet going around any star in a elliptical orbit – even if very
nearly
all observed planets are doing so. Nothing says any planet at all
MUST go
around a given star, or that a skater has to spin.
So it seems to me that universal laws say only that certain
organizations
can exist, not that they must, nor do they offer classifications
that
show categorically different types of organized behavior that
come
out of subtle changes in the details. It is the details, not the
generalizations, that determine what kinds of systems will
emerge.
I am reminded of Ashby's "Law of requisitive variety." On the
surface this looks like a deep and subtle law, yet all it says is
that
every working control system succeeds because it can vary its
outputs
along sufficient degrees of freedom to oppose all physical
disturbances
sufficiently well. From this requirement alone nobody could ever
develop
a successful design for a brain, or any kind of control system.
The
critical information still missing is HOW this requirement can be
met;
that is almost the whole ball game, but not quite. WHY must also
be
specified – the purpose being satisfied.
Going up a level leaves no trace about the pathway; it can never
be
uniquely retraced since in a many-to-one function, one set of
variables
is represented by a far smaller number of variables. Inevitably
someone will mention a set of variables, or properties of
collections of
such variables, that seems to explain why a set of lower-order
variables
behaves as it does. On closer examination the multiple-valued
relationships are discovered.
This has confused many scientists ( like Michael Turvey, about
whom David
Goldstein can tell you much concerning Turvey’s views of control
theory).
If one configuration of an arm can place the hand at a certain
distance
above the terrain, while many other configurations with different
joint
angles can place it at exactly the same distance above the
terrain, how
can we ever determine how an observed distance above the terrain
is
actually caused? From the bottom-up divergent point of view, which
is
emergentism, the question can’t be answered because the same
causes can
have different effects, and neither can it be explained from the
top-down, convergent point of view, precisely because of this
convergence
and divergence; the same effects can have different causes. The
possible
number of variables to be explained is different from the possible
number
of variables available to explain them. Either you have
indeterminate
degrees of freedom left unexplained, or you have too many
different
explanations for the same variables and no way to explain why they
are
different (wave and particle, for example) so there are no unique
solutions. David, is this how he actually put the problem? Any old
class
notes you could share?
Only when the loop is closed do you find that the convergences and
divergences can be properly matched even if the numbers of
variables are
different. Nature allows indeterminate solutions with unspecified
degrees of freedom. If you translate Pluto along its orbit by a
few
years, it will not necessarily split into two Plutos to satisfy
the new
values of the variables, nor will it stop obeying the Newtonian or
Einstenian laws of motion. Something will happen, like emission of
a
gravity wave or some loss of structural integrity, and anyone
navigating
by observing Pluto may be a bit lost until rediscovering where
Pluto now
is, but the navigator will learn to deal with the new behavior, or
even
perhaps even shovel it back the way it was.
Maxwell's Demon was struck down by the Second Law, but had there
been a
successful design for Maxwell’s Demon, the Second Law would not
have been
struck down; the relationship between the two ideas is not rigid
and
prescriptive, it is merely hierarchical. Any violation can be
corrected
by a control system of proper design, or caused the same way.
Control
systems can cause an object to rise when dropped, since the
desired
result is defined first, and then a way to achieve it is found or
invented. Put wings on it, or tie it to a helium balloon, or shape
it
like a kite, or drop it in your briefcase and take it with you.
The arm can be held a specific distance above the terrain by
specifying
what distance is wanted and what distance is observed and then by
manipulating all variables that affect the distance until the
error is
corrected, near enough. It doesn’t matter if the values needed for
this
are unpredictable and not repeatable as long as they are feasible;
this
system is purpose-driven, any combination of lower-order values
that does
the job being as acceptable as any other. We are not proposing to
control the position by setting the variables to the required
values –
we can’t, because there are no required values. We are proposing
to vary the variables until the desired position occurs, then
keep
varying them as necessary to maintain the position. We hope the
pilot
does that, too. We raise the arm above the ground in Newark and
set
it down again in Manchester… We don’t need to know in advance
what those
values will be. No ceterus paribus required. That is what
confused
Turvey as I understand his problem. If you can cause the arm to be
in any
desired position, but don’t know the values of the variables on
which
those positional variables will depend today, and proceed to do
the task
anyway, what has happened to causation itself? Can the job ever be
done?
PCT has created, as Gavin Ritz had recently noted, a new physics
by
removing some of the old boundaries. Control systems are not
operated by
causes in the environment, nor do they act as predictable causes
of the
environment. They override local physics by taking advantage of
unused
degrees of freedom – sticking the newspaper under the arm while
using
the hand on the same arm to rotate the key in the lock. We seldom
use up
the arm’s degree of freedom completely.
I have more thoughts on this that are of personal concern to me
right
now, thoughts about life and death. There is already some extra
equipment
in the spare bedroom and a lot of new chemistry in the
refrigerator.
Smelly. Inconvenient. most expensive. Have I been panicked into
forgetting PCT? Probably somewhat. It’s hard to resist the
certainty with
which charismatic and intelligent people – smarter than I am –
make
their cases, considering that they could be right and more
particularly
that they are in a position to make themselves right by refusing
to
consider certain alternatives. This may take some sorting out
before I
can know what to do. Better not to move too fast despite good
reasons for
wishing I could.
All helpful comments accepted, if not believed.
Best,
Bill P.