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Hi Tim,
Interesting post. Sorry it's taken me so long to respond.
I think it would definitely be worth writing up and posting on your
website. I have been finding more and more, lately, that this issue
(measurement) tends to come up all the time. It's worth a few general
comments in addition to the issues you raised in your post...
The concept of a meter, which any form of measurement or assessment
represents, and the effect of applying any meter to a system-- which
is then part of the resulting observation (measurement)--
is precisely what Einstein was on about. If we sacrifice the
relation, and with it all the information contained by it, then our result
will be anomalous. There is a second problem now, in science: I suspect
that the meters/modes of measurement we have created (in
physics) are specifically designed to give the "right" answer in spite of
this missing information. In other words, people take a set of values
produced by measurements and create "transformation" equations which make that
set of measurements agree with a known end sum. Then, the transformations are
applied to all measurements, under the assumption that we have accurately
figured out how to deal with this "measurement problem"...... But we're missing
critical information. The meters don't register it because they were not
designed to and the transformations are simply modes of making two sets of
numbers agree with each other, as pure syntax.
In a sense, I think that this whole phenomenon is also what
frustrated Einstein in his search for a Unified Field Theory. He found that you
can make certain specific measurements obtained via Relativity
Theory "agree" with measurements taken via Quantum Theory, but the solution
(the set of transformations) won't apply in all cases of measurement
comparisons. So, each meter requires different transformations, to make
measurements obtained via the two disciplines agree with each
other.
In any case, I think your post spotlights one of the biggest
sources of trouble in science right now, namely; complexity in systems on one
side and tools conceived around simplicity on the other side. Even if one
doesn't presume simplicity, the tools and techniques (including the "scientific
method") do. The current scientific notions
of measurements-as-numbers/increments are based on presumptions
of simplicity. As it happens, such numbers may be very useful in
local, transient, specific situations, but the type of information
that is specific, in nature, is usually different from the kind
that is systemic, and vice versa. Increments and numbers tend to
obscure that fact.
We see this happening in the field of medicine all the
time. It's common, in medical studies, to extrapolate back up to
larger systems from smaller ones, using results obtained via reductive means.
But we've lost information by those reductive means, which is missing also in
the extrapolation. For example, drug trials done on men
will yield results which are not necessarily applicable to female
physiology because the measurements all include hidden information specific to
men. Drug trial results on adults are not necessarily applicable to infants or
children, for the same reason. There are times when drug trials conducted on
laboratory animals may not be applicable to human physiology... Specificity
and genericity...
I have to wonder: What if we have rejected the "magic bullet"
cancer drug (or something like it), because it killed the laboratory rats when
it was administered to them? We automatically assume that something which is
toxic to rats will be toxic to us, as well. But this is not always the
case: If we had tested chocolate on dogs before we had ever eaten it, we
would consider it poisonous and it would be banned by the FDA. Their physiology
can't handle it-- it's lethal to them, but not to us.
I see a lot of medical studies which cite tons of numbers, often
with .001 level of exactitude.... I would laugh if it wasn't deadly serious. But
I don't understand how they can take it seriously: Exact numbers are almost
never what they seem, even with simple systems. Even if it were
possible to get exact numbers in measurements, there's a tendency in
humans, when reading a number registering on some meter, to round up or
down, to the nearest increment. ("Is that line closer to the six or the seven?"
Squint...) Then there's the fact that our various measuring equipment
has a tendency to malfunction and/or to be somewhat idiosyncratic in its
calibration. And we have a tendency to not notice. On top of these
considerations, there is the fact that choices have to be made about what mode
of measurement to employ in every measurement situation and that involves
foresight and judgment in the chooser-- which may or may not be reliable for the
task (especially because schools generally teach from the reductionist
mindset).
Clearly, all of the above adds to the Einsteinean findings, proving
that the act of measurement is going to add information to any
measurement and-- it can also be subtracting information as
well.
Judith
----- Original Message -----
Sent: Saturday, June 25, 2005 3:52
PM
Subject: [ROSEN] Rosennean Complex
Systems as Classifiers
The following is
something I've been thinking about for awhile. Maybe I'll write it up more
completely and add it to my website....
One of the
central concepts in Rosen's Fundamentals of
Measurement is that of the meter. A meter does at least
two things: 1) it interacts in particular modes with other systems,
and 2) it can discriminate and classify those interactions. Those
classifications can be described in formal terms as partitioning into
equivalence classes the entire set of the range of possible induced
responses to interactions. Each of those equivalence classes is then a
possible value of a meter reading. When a meter generates a
value, these values are then imputed back to observables of the system
which induced the response by the meter.
In FM, Rosen
utilizes the concept of meters along with his formalism to explore the idea of
measurement and the interactions of dynamical systems
generally. This idea was also explored in (at least) two earlier papers
by Rosen, "Autonomous State Classification by Dynamical Systems" (BMB 1972,
14:151-167) and "Further Comments on Autonomous State Classifiers and an
Application to Genetics" (BMB 1972, 14:305-310).
In the first of
these papers, Rosen discusses the general requirements and principles involved
necessary for some system, like a meter, to act as a classifier of its
own states based on its intrinsic autonomous dynamics (hence the name,
autonomous state classifier). Thus, a meter
is mainly a discriminator of its own states ; that those
states are induced by another system (i.e., the system being measured) is
what allows the imputation of the classified value back to the observable of
the system being measured. As Rosen notes, this concept of classifiers
applies to many areas, including measurement, pattern recognition,
psychophysical discrimination, and self-organization (pattern recognition
therein).
In this
treatment, Rosen utilizes a formalism whereby dynamics of the classifier
system are thought of in terms of trajectories and
attractors. That is, as dynamics are induced on a classifier system,
the result will be dynamics in the classifier which will follow some
trajectory toward some attractor. Each of these attractors is thus an
equivalence class. (Intuitively, one can think of a trajectory toward an
attractor as an analog meter needle moving toward some particular value
and then remaining fixed there, and not jumping around randomly. All the
possible induced dynamics which result in the meter needle pointing to that
same value are thus members of that same equivalence
class.)
In the second
treatment, Rosen discusses a modified approach in which an interaction is
not tied to corresponding fixed trajectories, but rather is tied to
rates of change in the classifier. Thus, a classifier system of this
kind may operate such that its initial state is not specifically relevant to
how it classifies, but its initial dynamics is.
I suspect this
could approach be iterated, such that classification occurred based on
rates of rates of change and so on. Or, more generally, that there
are a myriad of possible similar and unique approaches. The key idea
that I come away with is that there are many ways in which a system
may implement the role of classifier.
If we consider
classifiers as members of the general class of systems, then it occurs to me
is that there is no requirement that the classifier rely specifically on
states (or their changes). Put another way, if state-based models do not
exhaust the description of a Rosennean complex system, then state-based
treatment of classifiers does not theoretically exhaust the set of
classifiers possible in a Rosennean complex system.
It
seems that such classifiers that could be left untreated
in state-based approaches would include those classifiers whose
equivalence classes are partitions of a set of organizations
which admit a relational description, but not necessarily a
correspondings dynamical description. That is, an interaction with
another system would not result in a classification based on the dynamics
of the classifier; but rather, based upon the kind of organization that
resulted. For example, perhaps such a classifier could be one which generates
different active sites. Or, psychophysically, classifiers might
operate by generating particular select organizations of neuronal
activity.
What is
important in either the state-based approach or the relational approach, is
that the system can reliably classify what is induced by the
interaction. Regardless of how it classifies, it is necessary that the
classifier be able to partition its responses into the same equivalence
classes repeatedly. A classifier is competent if it can do
so. (Intuitively, a voltmeter which reads 5 volts at one time and then 3
volts at another time, when the induced value is actually the same, is an
incompetent meter - we would consider it defective.)
More generally, though, if
neither state-based or relational-based models alone suffice to fully
describe a Rosennean complex system, then it may well be that a
complex system could be a perfectly competent classifier, yet seem quite
incomprehensible to us. This apparent incomprehensibility would be further
compounded because of the inability to apply the notion of algorithms
to such a system. [see Essays p. 2-3] What this means in this arena is
that if a complex classifier were classifying based upon multiple
observables, it is quite possible that we would be unable - even in principle
- to create a list, a set of conditions, which would specify what
particular combinations of what particular values of individual observables
correspond to a classification into a given equivalence
class.
This result
seems to me to be a possible reason for our inability to codify many
"subjective" criteria into a list of conditions. What is beauty, what is
good art, what is love, etc., may be things which we can each classify for
ourselves yet be quite unable to describe to anyone precisely what are our
rules for making such classifications. Natural language has remained quite
immune to such codifications, despite many attempts, yet this does not impede
our ability to use, comprehend, and extend natural
languages.
It may also be
that complex classifiers on a biological level are at work, perhaps
partaking in the process of things such as guiding self-organization, and
metabolic regulation. Just as, for example, Chomsky's transformational
grammar codifies some useful portions of language structure, so too might we
well be able to successfully codify portions of those aforementioned
processes. But if these processes involve complex classifiers, then such
successes in partial codification do not point to our being able
to asymptotically achieve a complete codification.
This would also
indicate that diagnosis would be sometimes confounding. A system
which contains a complex classifier which is no longer competent may be
very difficult to diagnose since the classification scheme it
should have may not be possible to delineate in a list of
conditions and accordingly, it could be difficult to identify any deviations
from its normal classification scheme, much less correct
them.
There
are other ramifications of this line of thought, but this post is long
enough already....
Regards,
Tim
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