ERIC ED462408: The Information in the Folds of the Complex Adaptive Landscapes of a Verbal Expression.

32 Pages·2002·0.5 MB·English

by  ERIC

DOCUMENT RESUME
TM 033 670
ED 462 408
Bierschenk, Bernhard
AUTHOR
The Information in the Folds of the Complex Adaptive
TITLE
Landscapes of a Verbal Expression.
Lund Univ. (Sweden). Cognitive Science Research.; Copenhagen
INSTITUTION
Cognitive Science Research.
Univ.
(Denmark) .
No-82
REPORT NO
ISSN-0281-9864
ISSN
2002-00-00
PUB DATE
31p.; Portions of the paper presented at the Herbstakademie
NOTE
on Self-Organization of Cognition and Applications to
Psychology (9th, Ascona, Switzerland, October 25-28, 2000)
and at the Meeting of the Swedish Group of Cognitive
Psychology (Vaxjo, Sweden, May 7-8, 2001).
Speeches/Meeting Papers (150)
Reports Descriptive (141)
PUB TYPE
MF01/PCO2 Plus Postage.
EDRS PRICE
Biological Influences; *Cognitive Processes; *Text
DESCRIPTORS
Structure; *Translation; *Verbal Communication
*Natural Language
IDENTIFIERS
ABSTRACT
This paper advances the bio-kinetic hypothesis that the
Agent-action-Objective (Aa0) axiom constitutes the only valid foundation for
a behavioral expression of the informational dimensions contained in natural
language. Based on the bookkeeping capacity of the discovered Aa0 mechanism,
it is shown that this mechanism can capture emergent (Aa0) units and track
their growth in complexity. Through individual variations in the growth of
the components as well as the variations in nesting, it is demonstrated that
structural stability and textual morphogenesis generates corresponding
informational invariants. Furthermore, on the basis of the translation
function, it is shown that a sequential translation of an original text to
Swedish and from Swedish to Italian produces the condition for an effective
and textual objectives (0)
control of interplay between textual agents
(k.)
within a system of language specific coordinates. Based on coordinated
structural invariants, it is shown that convoluted structures are pointing
toward the presence of a biologically determined interplay between a produced
perspective and stated objectives. (Contains 10 figures and 13 references.)
(Author/SLD)
Reproductions supplied by EDRS are the best that can be made
from the original document.
ISSN 0281-9864
The Information in the Folds
Landscapes
of the Complex Adaptive
of a Verbal Expression
Bernhard Bierschenk
Department of Psychology
Lund University
No. 82
2002
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The Information in the Folds
Landscapes
of the Complex Adaptive
of a Verbal Expression
Bernhard Bierschenk
Department of Psychology
Lund University
No. 82
2002
Cognitive Science Research
Lund University
University of Copenhagen
Editorial board
Bernhard Bierschenk (editor), Lund University
Copenhagen
Inger Bierschenk (co-editor), University of
Copenhagen
Ole Elstrup Rasmussen, University of
Helge Hehnersson (adm. editor), Lund University
Education
JOrgen Aage Jensen, Danish University of
Adm. editor
Cognitive Science Research
Helge Helmersson
Copenhagen Competence
Dep. of Business Adm.
Research Center
Lund University
University of Copenhagen
P.O. Box 7080
Njalsgade 88
S-220 07 Lund
DK-2300 Copenhagen S
Sweden
Denmark
2
Abstract
bio-kinematic hypothesis that the Agent-action-Objective
The present article is advancing the
foundation for a behavioural expression of the
(Aa0) axiom constitutes the only valid
language. Based on the bookkeeping capacity
informational dimensions contained in natural
it is shown that this mechanism can capture emergent
of the discovered Aa0-mechanism
Through individual variations in the growth
[AaO] units and track their growth in complexity.
in nesting, it is demonstrated that structural
of the components as well as the variations
corresponding informational invariants.
stability and textual morphogenesis is generating
it is shown that a sequential translation
Furthermore, on the basis of the translation function,
for an
Swedish to Italian is producing the condition
of an original English text to Swedish and
(A) and textual objectives (0) within
effective control of the interplay between textual agents
structural invariants, it is
specific coordinates. Based on coordinated
a system of language
toward the presence of a biologically
shown that convoluted structures are pointing
perspective and stated objectives.
determined interplay between a produced
3
articulation" during text production synthesising
In the context of "angular
unique behavioural outcome of a biological system,
information will be presented as the
capability. All forms of supporting production
which has the writing-reading-rewriting
examples of complex self-organisation. When the
activities, e.g. the verbal flow dynamics, are
particular writing-reading-rewriting activities, then an
verbal flow dynamics is coupled with
of
point of view becomes manifest in the development
important ability from the evolutionary
exist in the brain
the perspective and the structure of a complete text cannot
a perspective. But
the
during text production. This implies the coupling of
in latent form. Both must be built up
language
flow dynamics within the context of a continuous
structure of a text with verbal
the Gestalt-space of the
dimensionality (= infiniteness). Figure 1 illustrates
space of unknown
involved evolutionary dynamics.
String production rests on the realisation of
The sequencing space of string dynamics.
of
becomes evident through the interaction of two kinds
kinetic energy. Most of its production
of information either in the form of virtual strings
strings. Individual strings appear as carrier
produced kinetic energy is
Hence, when the textual surface is altered,
or as material strings.
dynamics.
forming the sequencing space of the string
The formation of patterns of strings is not
The production of a concentration space.
requires the concept of self-reference as
only the result of self-organising processes but
self-organisation can be observed in the
information synthesising mechanism. While
self-reference mechanism is pushing
neighbourhood of a thermodynamic equilibrium, the
variable symmetry at the kinematic level. This
toward equilibrium and thereby producing
point of
until all parts are in balance from a thermodynamic
process of equilibration continues
distance from the thermodynamic equilibrium
view. The involved phase-transitions are at a
dependent on non-linear and dissipative operating processes.
operating processes of self-reference
The Functional Clause (FC). The dissipative
Functional Clause (FC), which is capturing the
and self-organisation are confined through the
following Expression:
produced pattern dynamics according to the
(1)
SM
verb
SM
FC =
I
ivi
0-field
A-field
lal
spherical property. In order to be able to
The borders (I) of its A- and 0-field embrace a
determine the intersections. In (FC)
observe the movement of a text segment, it is necessary to
is the 0-
alongside of the border of the A-field. The other
appears the first component
border. The dorsal-ventral and the A/O-intersections
component, which appears at the lower
(0) are
have contrasting functions. But when placeholders
appear always in pairs. Both
and downward for (A), while substitution
needed, their substitution is carried out from the top
down and proceeds upward. Furthermore, it has
of the placeholders for (0) is initiated from
that the operations proceed counter-
been made evident that the cyclic processing requires
clockwise.
continues until all A's and 0' s are
The Flow-fields. The process of equilibration
and complementary operation in the
dependent on each other. This explains their pair-wise
specific equations of text production have
establishment of unity. Whenever the language
emerging structure.
been resolved, their evolutionary property is observable as
Figure 1.
Evolutionary Language Dynamics
Concentration Space
Sequencing Space
A-field
Movement of
Functional
Text Segments
Clause
0-field
s'ss, Fitness Values
(0-1 Matrices)
VERTEX
PERTEX
Angular
Surface-related
Articulation
Pattern Processing
5
has reached a "Flidgleichgewicht", i.e.
This means that the process of equilibration
analysis of
language specific equation is observable through an
symmetry. The resolution of a
produced space. Since dissipative operating
the anti-symmetries and symmetries in the
through
dynamics can be captured in the movement of text segments
processes are open, their
of
become enclosed through the operational closure
the flow-fields. Hence the patterns, which
emerging solutions. The operational closure of FC is
(FC), lead to qualitative statements about
in
conceived phenomenon, which becomes enclosed
determining that part of the perceived or
difference between the AaO's, conceived as
the closure of FC. This process is producing a
non-equilibrium
AaO's conceived of as a configuration of
systems, and their environments.
driving forces are maintaining their dynamical
and equilibrium states, imply that internal
provides the conditions (resources) for the maintenance
states. The rest is environment, which
self-organisation is possible only in a structured
of the non-symmetry condition. Hence,
environment.
of a latticed (i.e. regular
0-1-matrices. The generation of the regulatory power
it
of (0-1) matrices. In the set-up of the matrices
patterned) text space refers to the generation
the unit of length for the measuring of distance.
has been useful to define a Block-variable as
the
Euclidean properties of physical space. However,
This procedure is consistent with the
frozen at the textual level through the
produced thermodynamic movements become
Text Analysis (PTA) is the method that
processing of the surface-related pattern. Perspective
of pattern movement. Computer routines in the
has been developed for efficient processing
Bierschenk, & Helmersson, 1996) consist of a
form of the PERTEX package (Bierschenk,
needed trajectories for adding positive charges
number of procedures, which are establishing
developed AaO's. During original
(= supplementations) to sequences of imperfectly
evolving text, but in operation extracted from
production these sequences are embedded in an
principle, the grouping of the A's and O's is an
their embeddings and made complete. In
trajectory. However, when the co-
indispensable step in the generation of a thermodynamic
running A- and 0-strands, time is only
ordinated A's and O's are sequenced as parallel
the other hand, traditional routines for the
indirectly related to the measure of distance. On
resistant to severe shear and strain
establishment of the corresponding concentration space are
at their space-time axes.
distance and its
In contrast. the VERTEX-approach to structural
Fitness values.
articulation, which is the only way to achieve
foliation builds on the discontinuities in angular
of the strict dependency in the working of the
perfectly reliable observations. Further. because
incompleteness problem in a constructive
Aa0-mechanism, it has been possible to solve the
precise
stated that the only necessary tool for exact and
way. As a result, it can be
time-sensitive foliation procedure. Basically,
reconstruction of structure is an efficient and
change in the articulation of a variable. At the
such a procedure concerns the degree of
latticed
of a particular text satisfies the condition of a
moment when the textured surface
of grouping of a- and
be made the foundation for the operations
space, measured distance can
of
variance-invariance relationship, governing the process
13-variables. To determine the
in successions, requires that a change is
producing "branches" and their arrangement
the "groupoid". A groupoid (G) consists of a set
producing a convolution, which is based on
operation, whose domain is all of (G). Hence (G)
of variables that is closed under a binary
of the kind of order parameters that
will be made the foundation for the manifestation
convolution. Therefore, (G) is replacing the classical
generate the dynamic aspect of the
taxonomic approaches, and is computed
frequency group, which has been dominating the
7
6
basis of a complex-valued function. In changing from
when regular latticed spaces form the
function of Connes (1994), (G) will play a crucial
this kind of functions to the operator-valued
when a natural language expression is treated
role in the "foliation" of dynamical states. So,
limit of its states is determined through the "Connes-fusion".
as system, the thermodynamic
through self-organisation and self-
Morphogenesis. The establishment of the Aa0-system
follows that only certain conditions, namely
reference requires a structured textual context. It
supporting the differentiation of the
those, which provide the texture of the context, are
Hence, the generation of
dynamical states and the morphogenesis of state attractors.
of the surrounding textual
informational invariants become determined by the structure
textual segments, which are mediated through
context. Context structures are producing the
non-equilibrium properties through symmetry-
the flow-fields of (FC). Maintenance of its
reflect the structure of the context
breaking operations in text production allows the system to
self-referential property of the Aa0-system is
together with its own internal dynamics. But the
producing a manifold of novel
integrating the context into the mechanism and thereby
attractor states.
Analysis
Foliation as Prerequisite for Structural Distance
"classification" or grouping of sets of
In the PERTEX-system the "categorisation" and
that identified patterns are treated as
empirical data, i.e., grapheme patterns, has required
this process, mutually exclusive
categories, which can be clustered (Anderberg, 1973). In
frequently resulting in hierarchically
categories are used directly and their representation is
this kind of configuration precludes a
organised trees of clusters (Sokal & Sneath, 1963). But
cluster-tree from accurate reconstruction. Moreover,
test of divergence of a particular
algorithm, assume that the data entries of
conventional cluster techniques, like Ward's (1963)
For any clustering procedure,
corresponding matrices consist of dissociated categories.
foundation.
disjoint sets of categories constitute the accepted
categories is taken as the proportional
It follows that the distance between any two
the expression
Its behavioural expression, and consequently
measure of "structural" distance.
in all branches of the established tree-
of all rates of change, is assumed to be the same
by means of the axiom of
configuration. In addition, its theoretical basis is established
Furthermore, aggregation is made
association and consequently the premise of randomness.
data entries. However, especially critical
dependent on the assignment of polarity (0-1) to the
(1996, p. 106), the absence of criteria for
for the classical approach is, according to Raff
reconstruction. Trees with large numbers of
testing the "goodness of fit" of an achieved
incompleteness" in a produced
terminal states may appear as a result of "polynomial
observations are
discussion to "phylogenetic categories", but his
sequence. Raff refers in his
for clustering are applied.
valid in all cases where classical procedures
dissociated elements recent developments
In the comparison and classification of
partly on the
partly on non-linear geometric approaches,
propose a modelling based
pair-wise
In the latter case, the need to estimate
measurement of locally linear embeddings.
is circumvented. But Principal Component
distances between widely separated data points
of "non-linear dimensionality reduction"
Analysis and Multidimensional Scaling as a measure
the listed shortcomings. Likewise,
(Tenenbaum, de Silva & Langford, 2000) cannot remove
non-linear structures from locally linear fits"
the geometric approach for recovering "global
time dimension and insensitive to the
(Roweis & Saul, 2000) is independent of any
incompleteness problem.
generated, which means that the speed in
In the VERTEX-system pairs of values are
enveloped by an operation that is closing all open
the clocking mode of a component becomes
inserting a zero
the initial variable is, closing is realised by
sets. No matter what the value of
7
certain
fourfold table. In applying this technical operation,
value in the upper left cell of the
the distance (A) is half the difference between the
magnitudes are united. At every moment,
left cell), resisting or non-resisting an operator value
effects of a reference value (in the upper
taken as basis for fusion.
(in the lower right cell), which is
its validity. At the beginning, all fractions
It follows that the classical certainty has
As a consequence of this requirement, any
within a particular period must contain closed sets.
values. Since the contrasting value is
individual variable value will be wrapped by zero
all other cells of the resulting connection (C) matrix
always inserted in the lower right cell,
second fourfold table appear the values, which may or may
have to be filled with zeros. In a
is accounting for the
like (,). Thus, a second connection (C) matrix
not follow a clause marker
and third value.
absolute difference between the second
consists of the ordinary space-time product,
Hence, the employed (Al2) operator
(Connes, 1994, p. 176), which is
manipulated by a very tiny discrete two-point space
is emphasising the central role of the (Al2)
superimposed. As a result, the process of fusing
that
of calculation, the procedure may produce a structure
operator. However, at the first step
consider a second step, and hence the possibility
is trivial. Though, it is always instructive to
The
ring and for that reason at least one invariant.
that the set of fractions may contain a
contains the values, which are governing a
corresponding second-order fourfold table
fourfold table refers to a T-matrix, which demonstrates
foliation over borders. A second-order
simple C-matrices.
the fact that the concentration space develops on two
C 0 C] as fusion process. The
Foliation appears immediately in the T-matrix [T =
resulting directly from the interaction of the
superimposed second-order fourfold table is
value. This space corresponds to the
rearranged reference value with the rearranged operator
foliation and branching. As a sequence, textual
discovery of a progressive discontinuation in
from the restrictions of the active control parameter,
segments are repeatedly disconnected
In overcoming the "borders", constituted by
which are the periods and fractions of periods.
folding is proceeding effectively and apparently
the markers of periods and fractions, the
concretely, this means that foliation and
resulting in an overall integration effect. Quite
operations.
branching must begin with interval-sensitive
interval do not depart beyond the stated
As long as the pairs of values within each
reflecting a continuous system. A smooth attractor
criterion value (0> coAl2 < 1), foliation is
Although
which is locally continuous (Connes, 1994, p. 11).
state is a special case of a space,
individual rotations and fluctuations in one or the
af3-strands are by definition symmetric,
and
concerning a component's acceleration in speed
other can exhibit striking differences
concluded that the breaking of evenness must
establishment of distance. In addition, it can be
pairs of values both within and between components.
appear with respect to
implies a transition from enveloping Step
On the other hand, whenever the calculation
established intervals are transcended, and new
(1) to enveloping Step (2), the borders of the
second
When the deviation in a particular pair at the
pairs of neighbouring values are formed.
respond in
it can be concluded that a system begins to
step exceeds the criterion value,
shown that subtle discontinuities in speed of
discontinuous manner. As a result, it can be
by this simple procedure for calculating
rotational pattern dynamics can be captured
level. In overcoming the "borders", constituted
symmetry-breaking behaviour at the kinematic
Thus,
is binding participating variables effectively.
by the clause markers, the folding process
p-dimensional space becomes available,
when length no longer is connected arc-wise, a
with the Euclidean space.
which is leaving behind all connections
Bifurcation
Topological Representation of Linkage and
illustration of the process of fusion
The computed quantities that will be used in the
(Bierschenk, 2001, p. 13) The first step in the
and branching have been presented previously
8
only
particular interval. As stated previously, if there is
folding is to identify the values in any
trivial fusion,
period, then this first step is always resulting in a
one value in an interval or a
corresponding trivial configuration. But this does not
which must lead to the generation of a
there still might be a specific set of intervals, which
tell anything about the possibility that
Therefore, it may be instructive to consider the
encircles a more extensive discontinuity.
particular singularity, and thus that the entire
possibility that the intervals of a period contain a
stability.
period posits the property of thermodynamic
topological configuration is to rule a co-
A convenient device for visualising a
its holotopic trajectory. This operation
ordinated grid on the source space and to examine
specificity of the
rotation dynamics, which is generating the
opens a new perspective on the
flowing information is manifested in
information in the folds. Since the dynamics of
have constraining effects. The latter indicate
continuous and discontinuous branching, both
the
itself around the corresponding trajectory so that
that an evolving helical curve is winding
the point of destination. Based on the variable
defining thermodynamic path develops toward
possible to capture the point of destination
configuration, established in Figure 2, it becomes
informational invariant through the name of the
through the final state attractor and the
attractor.
required a novel way of varying. Non-
Variations in a holotopic evolution must have
kinematic path is a definite demonstration of
change in a particular segment of an evolving
thermodynamic description of text means an
existing contextual constraints. It follows that a
properties. In focusing on the specification of the
alternative description through its holotopic
have been attracted by a holotopic
locations where the variables of the 0-component
basis of unit distance. By localising
singularity, space and time can be formalised on the
simply counting the number of
informational invariants in the latticed space, and
determine holotopic length. If a counting of nodes
neighbouring nodes, it becomes possible to
of
distance, then distance becomes visible as length
is regarded as expression of topological
concerning the establishment of a
the trajectory, which has empirical implications
synthesising outcome.
has a length of one-step. The necessary net would
A trajectory can be imagined, which
if a path is imagined, which consists of two
then consist of nine nodes. On the other hand,
reproduced
be involved. The structures, discovered and
state attractors, at least 12 nodes must
scientific concern, since the established singularities
in Figure 2, are of a most fundamental
configuration is characterised by at least one
(0-ri, OT2) have made evident that each
significant change of a previously formed
significant discontinuity. A discontinuity suggests a
and the establishment of the ring-
invariant, and is thereby contributing to development
information. Hence the foliation
relations, which are carrying the ecologically significant
properties, which can be used in the specification and
process is producing topological
studying the structure of a profile from a
description of an evolving information profile. In
configuration and the significance of its shape as
macroscopic point of view, its convoluted
the kinematic level.
well as its dimensions can be established at
Coupling of the 0- with the A-component
relation, it has been necessary to treat the
In order to obtain a perspective depth
has to be taken, if a perspective rotation
variables as autonomous units. Thus, one more step
translations. This step consists in the coupling
shall be capable of manifesting corresponding
the coupling can give expression to their
of the trajectories at the kinematic level, so that
running trajectories means a reworking that
coordinative co-operation. Coupling of differently
degree of abstraction. The necessary function concerns
generates information of a still higher
by means of cyclic swinging operations
the naming of the attractor states of the A-component
performed on the 0-component.
1 0