Changes

====1.2.1.  Functions of Observation====

====1.2.1.  Functions of Observation====

An observation preserved in a permanent record marks the transience of a certain compound event, the one that an observational account creates in conjunction with the events leading up to it.  If an observation succeeds in making an indelible record of an event, then a certain transient of the total system has been passed.  To the extent that the record is a lasting memory there is a property of the system that has become permanent.  The system has crossed a line in state space that it will not cross again.  The state space becomes strictly divided into regions the system may possibly visit again and regions it never will.  Of course, an equivalent type of event may happen again, but it will be indexed with a different count.  The same juxtaposition of events in the observed system and accounts by the observing system will never again be repeated, if memory faithfully serves.

An observation preserved in a permanent record marks the transience of a certain  

compound event, the one that an observational account creates in conjunction  

with the events leading up to it.  If an observation succeeds in making an  

indelible record of an event, then a certain transient of the total system has  

been passed.  To the extent that the record is a lasting memory there is a  

property of the system that has become permanent.  The system has crossed a line  

in state space that it will not cross again.  The state space becomes strictly  

divided into regions the system may possibly visit again and regions it never  

will.  Of course, an equivalent type of event may happen again, but it will be  

indexed with a different count.  The same juxtaposition of events in the  

observed system and accounts by the observing system will never again be  

repeated, if memory faithfully serves.

But perfect observation and permanent recordings are seldom encountered in real  

But perfect observation and permanent recordings are seldom encountered in real life.  Therefore, informational content must be found in the distribution of a system's behavior across the whole state space.  A system must be recognized as informed by events whenever this distribution comes to be anything other than uniform, or in relative terms deviating from a known baseline.  As to what events caused the information there is no indication yet.  That kind of decoding requires another cycle of hypotheses about reliable connections with object systems and experiments that lay odds on the systematic validation of these bets.  The impressions that must be worked with have the shape of probability distributions.  The impression that an event makes on a system lies in the difference between the total distribution of its behavior and the distribution generated on the hypothesis that the event did not happen.

life.  Therefore, informational content must be found in the distribution of a  

system's behavior across the whole state space.  A system must be recognized as  

informed by events whenever this distribution comes to be anything other than  

uniform, or in relative terms deviating from a known baseline.  As to what  

events caused the information there is no indication yet.  That kind of decoding  

requires another cycle of hypotheses about reliable connections with object  

systems and experiments that lay odds on the systematic validation of these  

bets.  The impressions that must be worked with have the shape of probability  

distributions.  The impression that an event makes on a system lies in the  

difference between the total distribution of its behavior and the distribution  

generated on the hypothesis that the event did not happen.

A system of observation constitutes a projection of the object system's total  

A system of observation constitutes a projection of the object system's total behavior onto a space of observations, which may be called the space of observing or observant states.  The object system's total state space is not necessarily a well-defined entity.  It can only be imagined to lie in some unknown extension of the observing space.  How much information a system may have is defined only relative to a particular system of observation.  It is often convenient to personify all the various specifications of observational systems and spaces under a single name, the observer.  Every bit of information that a system maintains with respect to an observer constrains the system's behavior to half the observed state space it would otherwise have.  When designing systems it is preferred that this bit of information reside in a  

behavior onto a space of observations, which may be called the space of  

well-defined register, a localized component of anatomical structure in a designed-to-be-known decomposition of the intelligible object system.

observing or observant states.  The object system's total state space is not  

necessarily a well-defined entity.  It can only be imagined to lie in some  

unknown extension of the observing space.  How much information a system may  

have is defined only relative to a particular system of observation.  It is  

often convenient to personify all the various specifications of observational  

systems and spaces under a single name, the observer.  Every bit of information  

that a system maintains with respect to an observer constrains the system's  

behavior to half the observed state space it would otherwise have.  When  

designing systems it is preferred that this bit of information reside in a  

well-defined register, a localized component of anatomical structure in a  

designed-to-be-known decomposition of the intelligible object system.

that may be driving the process.

In order to assess the purpose and object of an information process, it is  

However, the kind of direct product decomposition that would make this feasible is not always forthcoming.  When investigating a system of unknown design, it cannot be certain that all its information is embodied in localized components.  It is not even certain that a given observation system is detecting the level, mode, or site in which the majority of its information is stored.  Even when it is found that a system occupies a small selection or a narrow distribution of its possible states and increases its level of informedness with time, this may yield a quantitative measure of its determination and progress but it does not offer a motive, neither a reference to the objects nor a sense of the objectives that may be driving the process.

measure of information might receive.  A first employment scales the information

that an object system possesses by virtue of being in a certain state, as among

the possibilities envisioned by an observer.  A second grades the information

that a state in a sign system provides to reduce the uncertainty of an

interpreter about the state of an object system.  A third weighs the information

that a self-informed intelligent system can exercise with respect to the control

of its own state transformations.

These distinctions can be traced back through the ideas of pragmatism to a

In order to assess the purpose and object of an information process, it is important to examine and distinguish several applications that the common measure of information might receive.  A first employment scales the information that an object system possesses by virtue of being in a certain state, as among the possibilities envisioned by an observer.  A second grades the information that a state in a sign system provides to reduce the uncertainty of an interpreter about the state of an object system.  A third weighs the information that a self-informed intelligent system can exercise with respect to the control of its own state transformations.

couple of distinctions made by Aristotle in the first textbook of psychology. 

things the factors of form and matter.  In regard to animate creatures Aristotle

divines that the actuality of their intelligence is found in their form while it  

is the potentiality of mind that is embodied in matter.  The form and actuality

of mentality is like the edge of an implement that makes it effective in its

intended purpose.  The formal aspect is an organic shape impressed upon and

infused within the material substrate of life.  The matter of the mind merely

supplies a medium for the potentiality of mental functioning.  Subsequently

Aristotle divides the form of actuality into two senses, exemplified in turns by

the possession and the exercise of knowledge.  Can such distinctions, devices of

ancient pedigree on fields of patent verdigris, bring a significant bearing to  

the conduct of modern inquiries in applied AI?  This question is considered

among the topics of (Awbrey & Awbrey, 1990).

At this point the notion of observation put forward above would seem identical

These distinctions can be traced back through the ideas of pragmatism to a couple of distinctions made by Aristotle in the first textbook of psychology.  In Aristotle's ''Peri Psyche'' or ''On the Soul'' he discerns in the essential nature of things the factors of form and matter.  In regard to animate creatures Aristotle divines that the actuality of their intelligence is found in their form while it is the potentiality of mind that is embodied in matter.  The form and actuality of mentality is like the edge of an implement that makes it effective in its intended purpose.  The formal aspect is an organic shape impressed upon and infused within the material substrate of life.  The matter of the mind merely supplies a medium for the potentiality of mental functioning.  Subsequently Aristotle divides the form of actuality into two senses, exemplified in turns by the possession and the exercise of knowledge.  Can such distinctions, devices of ancient pedigree on fields of patent verdigris, bring a significant bearing to the conduct of modern inquiries in applied AI?  This question is considered among the topics of (Awbrey & Awbrey, 1990).

to the notion of representation that is usual in AI in cognitive science.  But

mathematicians and physicists reserve the status of representation to maps that  

are homomorphisms, in which some measure of structure preservation is present.   

And if these two notions are confounded, what sort of observation would enable

the detection of whether maps preserve structure or not?  Therefore it seems

necessary to preserve a more general notion of observation which permits

arbitrary transformations, not just the linear mappings or morphisms that

properly constitute representations.

At this point the notion of observation put forward above would seem identical to the notion of representation that is usual in AI in cognitive science.  But mathematicians and physicists reserve the status of representation to maps that are homomorphisms, in which some measure of structure preservation is present.  And if these two notions are confounded, what sort of observation would enable the detection of whether maps preserve structure or not?Therefore it seems necessary to preserve a more general notion of observation which permits arbitrary transformations, not just the linear mappings or morphisms that properly constitute representations.

an isomorphism is almost totally useless for the purposes that motivate

representation and that a single representation is hardly ever enough.   

Representations are exactly analogous to coordinate projections or spectral

coefficients in a fourier analysis.  It is a necessary part of their function to

severely reduce the data, and this engenders the complementary necessity of  

having a complete set of projections in order to reconstitute the data to the

extent possible.

The extent to which a representation found embodied in a system is an isomorphic

It has been appreciated in mathematics and physics for at least a century that an isomorphism is almost totally useless for the purposes that motivate representation and that a single representation is hardly ever enough.  Representations are exactly analogous to coordinate projections or spectral coefficients in a fourier analysis.  It is a necessary part of their function to severely reduce the data, and this engenders the complementary necessity of having a complete set of projections in order to reconstitute the data to the extent possible.

representation of its object system is the extent to which that information has

form of representation can supply grist for the mill that applies rational

itself does not exist in the analyzed form created by a system of representation  

is like objecting to changing the form of bread in the process of digesting it.   

It is only necessary to remember that representations are supposed to be

different from the realities they address, and that the nature of one need not

existentially conflict with the nature of the other.

In exception to the general rule, some work in AI and cognitive science has  

reached the verge of applying the homomorphic idea of representation, although  

 

in some cases the arrows may be reversed.  Notable in this connection is the  

In exception to the general rule, some work in AI and cognitive science has reached the verge of applying the homomorphic idea of representation, although in some cases the arrows may be reversed.  Notable in this connection is the concept of structure-mapping exploited in (Gentner & Gentner, 1983) and (Prieditis, 1988) and the notion of quasi-morphism introduced in (Holland, et al., 1986).  One of the software engineering challenges implicit in this work is to provide the kind of standardized category-theoretic computational support that would be needed to routinely set up and test whole parametric families of such models.  An off-the-shelf facility for categorical computing would of course have many other uses in theoretical and applied mathematics.

concept of structure-mapping exploited in (Gentner & Gentner, 1983) and  

(Prieditis, 1988) and the notion of quasi-morphism introduced in (Holland, et  

al., 1986).  One of the software engineering challenges implicit in this work is  

to provide the kind of standardized category-theoretic computational support  

that would be needed to routinely set up and test whole parametric families of  

such models.  An off-the-shelf facility for categorical computing would of  

course have many other uses in theoretical and applied mathematics.

=====1.2.1.1.  Observation and Action=====

=====1.2.1.1.  Observation and Action=====