Sunday, January 29, 2006
Generative Methodology Glass Bead Games
possibility of complexity arising in grid computing
[368] ß [comment on four issues
(Richard Ballard)
[367] ß [Four Issues facing
Ontological Modeling (Paul Werbos)
[371] ß [Discussion about founding
the Second School (Paul Prueitt)
[151] ß [Comment by Paul Werbos on
invariance of natural laws
[152] ß [Continuing discussion
between Peter Krieg and Judith Rosen
Communication
to part of the SOA Blueprint Technical Committee (at OASIS) à [144],
Note from Judith Rosen, regarding the nature of Shannon’s information theory,
Addressed to Dr Richard Ballard
Shannon's Information Theory pertains to a specific type of information, leaving all other types of information (particularly the biological, causally active types) out. Therefore, what is learned about the larger subject of information and all of its causal potential is a tiny, fractionated subset of the whole. Therefore, it would logically be unwise to rely on Shannon-based Information Theory as your sole source for that aspect of your work. I will quote for you a passage from "Anticipatory Systems" which can describe this situation in far more concrete terms than I...
On page 406, Robert Rosen wrote:
We shall introduce the rather wide-ranging considerations
that follow with a discussion of the concept of information and its role in
scientific discourse. Ever since Shannon began to talk about "Information
Theory" (by which he meant a probabilistic analysis of the deleterious
effects of propagating signals through "channels"; cf. Shannon, 1949)
this concept has been relentlessly analyzed and re-analyzed. The time and
effort expended on these analyses much surely rank as one of the most
unprofitable investments in modern scientific history; not only has there been
no profit, but the currency itself has been debased to worthlessness. Yet, in
biology, for example, the terminology of information intrudes itself
insistently at every level; code, signal, computation, recognition. It may be
that these informational terms are simply not scientific at all; that they are
an anthropomorphic stopgap; a facon de parler which merely reflects the
immaturity of biology as a science, to be replaced at the earliest opportunity
by the more rigorous terminology of force, energy, and potential which are the
province of more mature sciences (i.e. physics) in which "information is
never mentioned. Or, it may be that the informational terminology that seems to
force itself upon us bespeaks something fundamental: something that is missing
from physics as we now understand it. We shall take this latter viewpoint and
see where it leads us.
In human terms, information is easy to define; it is anything
that is or can be the answer to a question. Therefore, we shall preface our
more formal considerations with a brief discussion of the status of interrogatives,
in logic and in science.
The amazing fact is that interrogation is not ever a
part of formal logic, including mathematics. The symbol "?" is not a
logical symbol, as for instance are "v", [and several other
notation symbols that my keyboard doesn't have; an upside down v, a backwards
capital E and an upside down capital A]; nor is it a mathematical symbol. It
belongs entirely to informal discourse, and as far as I know, the purely
logical or formal character of interrogation has never been investigated. Thus,
if information is indeed connected in an intimate fashion with interrogation,
it is not surprising that it has not been formally characterized in any real
sense. There is simply no existing basis on which to do so.
I do not intend to go deeply here into the problems of
extending formal logic (always including mathematics in this domain) so as to
include interrogatories. What I want to suggest here is a relation between our
informal [natural language-based] notions of interrogation and the
familiar logical operation "=>" ; the conditional, or the
implication operation. Colloquially, this operation can be rendered in the form
"If A, then B". My argument will involve two steps. First I will
argue that every interrogative can be put into a kind of conditional form
If A, then B?
(where B can be an indefinite pronoun like
"who", "what", etc., as well as a definite proposition).
Second and most important, I will argue that every interrogative can be expressed
in a more special conditional form, which can be described as follows. Suppose
I know that some proposition of the form
If A, then B
is true. Suppose I now change or vary A; i.e. replace A
by a new expression which I will call *A.
[Note; about *A... I have to improvise a symbol to substitute for the
odd little notation (looks like an upside down tadpole with a bent tail) my
father used in his book, so just pretend the * (asterisk) is one of those
jobbies...]
<continuing>
The result will be an interrogative, which I can
express as
If *A, then *B?
Roughly, I am treating the true proposition "If A,
then B" as a reference, and I am asking what happens to this proposition
if I replace the reference expression A by the new expression *A. I could of
course do the same thing with B in the reference proposition; replace it by a
new proposition *B and ask what happens to A. I shall assert that every
interrogative can be expressed this way, in what I shall call a variational
form.
The importance of these notions for us will lie in
their relation to the external world; most particularly in their relation to
the concept of measurement, and to the notions of causality to which they
become connected when a formal or logical system is employed to represent what
is happening in the external world; i.e. to describe some physical or biological
system or situation.
Before doing this, I want to motivate the two
assertions made above regarding the expression of arbitrary interrogatives in a
kind of conditional form. I will do this by considering a few typical examples,
and leaving the rest to the reader for the moment.
Suppose I consider the question; "Did it rain
yesterday?"
First I will write it in the form "If (yesterday),
then (rain)?"
Which is the first kind of conditional form described
above. To find the variational form, I presume I know that some proposition
like "If (today), then (sunny)" is true. The general variational form
of this proposition is
"If *(today), then *(sunny)?".
In particular, then, if I put *(today) = (yesterday),*(sunny)
= (rain)
I have indeed expressed my original question in the
variational form. A little experimentation with interrogatives of various kinds
taken from informal discourse (of great interest are questions of
classification, including existence and universality) should serve to make
manifest the generality of the relation between interrogation and the
implicative forms described above; of course this cannot be proved in any
logical sense, since as noted above, interrogation sits outside logic.
It is clear that the notions of observation and
experiment are closely related to the concept of interrogation. That is why the
results of observation and experiment (i.e. data) are so generally regarded as
being information. In a formal sense, simple observation can be regarded as a
special case of experimentation; intuitively, an observer simply determines
what IS, while an experimenter systematically perturbs what is, and then
observes the effects of his perturbation. In the conditional form, then, an observer
is asking a question which can generally be expressed as: "If (initial
conditions = 0), then (meter reading)?
In the variational form, this question may be
formulated as follows
Assuming the proposition "If (initial conditions =
0), then (meter readings = 0)" is true-- which establishes the reference,
and corresponds to calibrating the meters-- our question becomes:
"If *(initial conditions = 0), then *(meter readings =0)?
where simply *(initial conditions =0) = (initial
conditions) and *(meter readings =0) = (meter readings).
The experimentalist essentially takes the results of
observation as his reference, and thus, basically asks the question which in
variational form is just "If *(initial conditions), then *(meter
readings)?"
The theoretical scientist, on the other hand, deals
with a different class of question; namely, with the questions which arise from
assuming a *B (which may be B itself) and asking for the corresponding *A. This
is a question which an experimentalist cannot approach directly, not even in
principle. It is mainly the difference between the two kinds of questions which
marks the difference between experiment and theory, as well as the difference
between the explanatory and predictive roles of theory itself; clearly, if we give
*A and ask for the consequent *B, we are predicting, whereas if we assume a *B
and ask for the antecedent *A, we are explaining.
It should be noted that exactly the same duality arises
in mathematics and logic themselves; i.e. in purely formal systems. Thus a
mathematician can ask (informally): If (I make certain assumptions), then (what
follows)? Or he can start with a conjecture, and ask; If (Fermat's Last Theorem
is true), then (what initial conditions must I assume to explicitly construct a
proof)? The former is analogous to prediction, the latter to explanation.
When formal systems (i.e. logic and mathematics) are
used to construct images of what is going on in the world, then interrogations
and implications become associated with ideas of causality. Indeed, the whole
concept of natural law depends precisely on the idea that causal processes in
natural systems can be made to correspond with implication in some appropriate
descriptive inferential system (a model).
But the concept of causality is itself a complicated
one; this fact has been largely overlooked in modern scientific discourse, to
its cost. That causality is complicated was already pointed out by Aristotle.
To Aristotle, all science was animated by a specific interrogative: Why? He said
explicitly that the business of science was to concern itself with "the
why of things". In our language, these are just the questions of
theoretical science: If (B), then (what A)? and hence we can say B because A.
Or in the variational form *B because *A.
But Aristotle argued that there were four distinct
categories of causation; four ways of answering the question Why? [all of
which can be answered with information that is "correct"]. These
categories he called material cause, formal cause, efficient cause, and final
cause. These categories of causation are not interchangeable. If this is so
(and I will argue below that indeed it is), then there are correspondingly different
kinds of information, associated with different causal categories. These
different kinds of information have been confused, mainly because we are in the
habit of using the same mathematical language to describe all of them; it is
from these inherent confusions that much of the ambiguity and murkiness of the
concept of information ultimately arises. [underlining, mine] Indeed,
we can say more than this: the very fact that the same mathematical language
does not (in fact, CANNOT) distinguish between essentially distinct categories
of causation means that the mathematical language we have been using is in
itself fundamentally deficient, and that it must be extended by means of
supplementary structure to eliminate those deficiencies.
End excerpt.
OK , now this really is getting to be a long letter. Time for coffee.
Judith
Web address: http://www.rosen-enterprises.co
BioTheory: An electronic journal of general science based on the Relational (Rosennean) Complexity Paradigm