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BAA. STRUCTURE OF MIND
NOTE: neologies and ambiguous terms clarified in GLOSSARY
are marked "[G]".
Summary
The structure of Mind defined and justified in the body
of the present chapter may appear rather complex.
It seems therefore advisable to limit the first reading
to this summary and to return to the chapter after having
read at least
PREFACE ,
OUTLINE OF FIRST AND SECOND ENLIGHTENMENT
The structure of Mind is defined in terms of following domains
and faculties:
-Domain "Sensorium" comprising Sensations.
-Domain "Imagery" comprising continuous 3D space "Images",
reciprocally bounded and structured as recursive "Patterns"
ordered by Causality and Encompassment ( CAUSALITY ).
As Image is an elementary, but full fledged Pattern, we
shall below use "Patterns" in the double sense of "Images"
and their structures.
Patterns evolve continuously in time. Thus, Imagery is a
4D time/space, affine (incommensurable) between 1D time and
3D space components.
In the context of scientific Models Imagery may be called
"Phenomenon #Space[G]"(PS).(see PRIMACY OF CONTINUUM below)
Patterns appear to Awareness as "real objects". Mistaking
this appearance for transcendental "Reality" underlies
the "Naive View", or "Naive Realism".
-Faculty "Morphogenesis" which maps Sensations to Imagery
and constructs of them affine 4D Patterns.
-Domain "Symbolics" or "Abstract #Space[G]" (AS), is a
discrete map of continuous Imagery. Image Patterns map to
abstract, symbolic Entities. Recursive Pattern Orderers ,
Causality and Encompassment are imaginary representations
of abstract Implication Relations, which structure Entities
within symbolic "Entity-Relation (ER) Networks".
-Faculty of "Reflection", aka "Lateral Thinking" consisting
of reciprocal, two-way mapping between Imagery and Symbolics:
1."Symbolizing" or Mapping Patterns into symbolic,
(or "abstract") ER Structures.
2."Understanding", or regressing symbolic Structures to
Patterns of Imagery, which embody their "Meaning" and that
of their Implications.
In the previous paragraph we defined PS Orderers "Causality"
and "Encompassment" as imaginary representations of abstract
Implications. In the terms of Reflection we may say that
abstract Implication may be imagined (ie. understood) as
Causality or Encompassment.
Allegory of the Cave
At the very origins of our rationality we notice, in Ancient
Greece, some theories and concepts which remain foundations
of contemporary reason, as fresh today as they were at their
origins.
We find the Heraclit/Democrit dichotomy in Continuity/
Discreteness topologies, in chaos/order, in integral/
differential calculus, in Einstein's Field Theory/Planck's
Quanta. And Plato's Allegory of the Cave resurrects today,
after millennia of idle transcendental speculations, as a
genial foresight of one of most advanced branches of
Science, the Morphogenetics.
In his famous Allegory Plato depicts slaves born and chained
in a cave so that they are perpetually facing the rear wall
and turning their backs to the entrance. Objects of the outer
world project their shadows on the rear wall. These shadows
are the only aspects of "reality" which the slaves may
observe: vague, two-dimensional, flat forms contingent and
chaotic, arising, vanishing and changing without any apparent
reason. (For "reality" in inverted commas see GLOSSARY ).
Lacking other communication with the outer world, the slaves
tend to confuse projections with their source, to believe
that the shadows are themselves the actual "reality", a
"reality" entirely contingent, chaotic and meaningless.
However, as all humans, the slaves have the faculty of
imagination, the gift of interpreting their observations.
They can imagine external objects and interpret the shadows
as their rudimentary aspects, as their projections.
In other terms, they can build an imaginary model and use it
to represent and to predict the "reality".
Nevertheless, only very few will have the courage to carry
out this endeavor which indeed raises enormous difficulties.
It is certainly simple to project 3D objects upon a plane.
The relation is unique and exact: an object may project only
one, exactly determined 2D aspect-shadow upon a specific
projection plane.
Unfortunately, MODELING requires the inverse operation:
ascending from shadows towards their source-objects. Now
this operation is neither unique nor exact. Indeed, a 2D
projection admits infinity of 3D projectors.
Let's imagine in the 3D #Space a sphere S and a thin coin C
in a "source" plane parallel to the projection plane (cave's
wall), both of the same radius. Perceived aspects
(projections) of S and C are identical and there is no
reason to associate them with different 3D objects: it's
impossible to create a model on the base of a single
observation.
Let's now suppose the coin rotating around a diameter in the
source plane. Consecutive observations of its aspects
(projections on the projection plane or caves wall) will
deliver circle, thick ellipse getting thinner and becoming
a line, getting in turn ellipse and circle.
It doubtless takes a genius, but now it is not impossible to
create a model. A genial slave may CONCEIVE a 3D #Space
transcending his given 2D, as well as a 3D object-coin
rotating in this #Space.
Membrane Analogy. Sensorium and Imagery.
Plato's Allegory is amazingly similar to Membrane Analogy, an
introductory example of Morphogenetics, whether Thom's Theory
of Catastrophes, or Haken's Synergetics.
Let us consider an elastic membrane framed with a rigid frame.
We shall call 'Observation Plane' or 'SENSORIUM' the plane
passing par the frame and delimited by its internal contour
(Fig.1). The membrane is sensitive to temperature, the frame
totally insensitive. At a given temperature the membrane is
flat. Its surface which we shall call the 'Imagination
Surface' is a plane coinciding with the observation plane
(Fig. 1).
We warm the system up. The frame stays unchanged, but the
membrane's surface extends. It "grows out" of the frame,
cannot stay flat and develops hills and valleys, or "basins"
(Fig. 3). Imagination surface does not coincide more with
the observation plane, but intersects with it along the
Observation configuration composed for instance of square
Forms (Fig. 2). Square configuration is the simplest, but
not the only possible one. Imagination surface may intersect
with observation plane along any configuration of convex
polygons. It is interesting to note that the basins interact
among each other. If a hill disappears as result, for
instance, of being pushed down by some external force, the
whole pattern will change: some of the basins whether close
to the disturbance, or remote, will change their size and
form, or vanish entirely, while others will appear. The
interaction is of the type local to global: a local change
of one basin may modify the whole pattern. We recognize here
the basic morphogenetic principle asserting that emergence
of Order and Forms from Chaos results from competition and
struggle between Attractors. And, as we rooted Morphogenesis
in "deplatonized" Plato, so we may root this principle in
Heraclit's: "It's to be known that conflict is universal,
that justice is but struggle and that all things are
engendered following struggle and necessity."
(Our translation).
Let's note that basins may be either neighbors "at the same
level", or encompass one another at various "levels". A
single basin resembling the crown of a bowler hat may under
a force pushing it down take the creased crown form of an
"Eden hat", encompassing three basins: two elevations and a
crease. We shall say that the basin "Eden hat" encompasses
basins "brim" and "crown", which encompasses in turn two
elevations and a crease. Let us note that all basins are
encompassed by some more general ones, at the limit by the
most general, the Imagery itself. Due to the competition of
Attractors, the basins are structured by encompassment,
juxtaposition, unification, intersection, exclusion and
negation.
We shall show in subsequent paragraphs on the domain
"Symbolics" and the faculty "Reflection" that this
structure of Imagery underlies the Phenomenal Logic.
The imagination surface itself, it is no more a plane,
it became a curved 2D surface immerged in a 3D Imagination
#Space or Imagery. Basins may be considered as volumes,
imaginary 3D Patterns in the imagination #Space delimited on
the one hand by the imagination surface and, on the other
hand by the observation plane. Observation configuration may
be now considered as projection of a Pattern of Images from
the imagination #Space upon the observation plane (Fig 3).
Now, let us imagine two-dimensional beings living in the
Euclidean #Space coinciding with the observation plane. They
would observe discrete, ordered polygons emerging in the
continuous, i.e. chaotic observation plane as consequence
of temperature increase. As long as their imagination does
not transcend the 2D Euclidean #Space of their praxis, they
will be unable to find for this phenomenon any reasonable
interpretation. They will see no way to understand this
emerging of Order from Chaos.
However, once freed from the "common sense" restricting them
to their 2D praxis space, they may transcend it and conceive
the membrane model, which interprets simply the phenomenon.
Nevertheless, such a model, though simple for us, would
require from them extreme creativity, imagination and
intellectual courage. They would have to transcend the
dimensionality of their praxis, conceive a 3D imaginary
#Space, immerge in it a 2D imagination surface such that it
would intersect with the 2D observation plane along the
observed configuration. Like some exceptionally creative
slaves of the cave they will interpret the observed forms as
projections of imaginary Patterns such as membrane basins.
Apparently contingent and meaningless behavior of the
observed configuration, when interpreted as projection of
meaningful and meaningfully ordered patterns will become
itself ordered and meaningful.
Apparently arbitrary and meaningless appearences become in
the light of Imagery ordered and meaningful. ORDER and
MEANING of Image Patterns are generated in Imagery along
with Patterns themselves. Patterns are essentially Ordered
and Meaningful. The concept of Order is discussed in the Part
CHAOS AND ORDER
We shall mention here by anticipation that the Orderer of
Imagery is the Causality Relations ( CAUSALITY ).
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Entire human behavior is determined and controlled by a model
whose principles are illustrated in a very general and
simplified way by Plato's Allegory and Morphogenetic Membrane
Analogy. Our short discussion pointed out superficially the
complexity of such a model. Its most general idea is
conceivable only to people with some basic intellectual
training and experience. Its theoretical details, let alone
its eventual realization, exceed the capabilities of most
talented humans by orders of magnitude.
Nevertheless, everybody uses it in every instance of his
life and "simple" people use it often much more efficiently
than sophisticated intellectuals.
Fortunately, basic modeling problems, those determining our
very survival have been solved for us by evolution: indeed,
human brain is essentially a modeling device of enormous
scope and efficiency. It performs modeling procedures
concerning the daily routine often without involving the
consciousness. We are under the impression of dealing with
"reality", without being aware of actually dealing with
Patterns created in Imagery by the modeling activity performed
by our Mind. This level of genetically determined modeling
may be called instinctive or subconscious. Besides it, we may
distinguish another level, involving conscious reasoning,
which endeavors to improve some areas of instinctive modeling
with respect to its conformity, scope, depth, or precision.
We shall discuss it in the next paragraph.
Network Analogy, Symbolics.
Sensations and Images appear with respect to Sensorium and
Imagery, which are, consequently, their respective
Referentials.
We are going to introduce now the third basic Referential,
SYMBOLICS.
Each of the basins of the example discussed above may be
associated with an optimum (maximum, or minimum) point or
ATTRACTOR (Fig. 3A). Projecting Attractors on the Observation
Surface (Fig. 4) and connecting them with links representing
adequate integrals of involved basin volumes we obtain a
network structure whose vertices and edges are respectively
Attractor projections and their links (Fig. 5).
The multilevel Pattern of basins maps into a multilevel
network structure: the vertex "Eden hat" will encompass
vertices "brim" and "crown", encompassing in turn three
vertices, two "sources" (corresponding to elevations) and
a "sink" (corresponding to crease). Within this structure,
the connecting edges get the meaning of Encompassment.
It may be shown that for a multitude of physical phenomena
(particularly for those involving, like our Membrane,
potential fields) it is possible to map a given Pattern to
an equivalent network. As examples of such phenomena let us
mention the flow of viscous fluid through permeable and
porous media, the flow of heat, the deformation of
construction elements under given stress conditions, the
electric flow in a medium with continuous distribution of
resistance and capacity. Continuous aspects of these
phenomena are described by partial differential equations,
whose solutions represent the mapping of continuous Patterns
into a discrete network. In the case of electric flow the
involved network is associated with the name of Kirchhoff.
This last case seems particularly significant, as it may
point to electric stimuli in neural networks.
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A Pattern of Attractors and Basins may be mapped respectively
into a Network of Vertices and Edges, or, in logical terms,
the "ER" structure of Entities and Implication Relations.
Abstract Entities point back to Pattern-Basins and Implications
to Encompassment and Causality (see CAUSALITY )
In the Summary we defined Reflection as the faculty of
Symbolizing (mapping Imagery Patterns to Symbolics ER Networks)
and Understanding (mapping ER Networks to Patterns).
In those terms, Entities are understood as Patterns and their
Implications - as Causality or Encompassment.
Reflection is defined in more detail in REFLECTION SPIRAL
and ER Network in the chapter CCA.COGNITIVE NETWORK , which
presents it as support of rational, phenomenal Logic.
Recollection and (Re)Cognition
-Recollection: Patterns are memorized. Previously observed
ones may be Recalled to Awareness.
-(Re)Cognition: A Pattern may be Recognized as homomorphic
with a Recalled one. Recognition underlies Cognition:
a Pattern is known when it's recognized.
Brain-Mind Interface
The present chapter deals with Mind and its structures such
as emerge from psychological and introspective inquiry.
Yet, an attentive reader may object that the continuous
Phenomena of Imagery lack an interface with physical Events
and appear to the Awareness like Deus ex Machina. The
receiver of physical Events is of course the Brain, which
transfers them to the conscious Mind via the Brain-Mind
Interface. Although the existence of this Interface appears
to be certain, its fabric stays entirely unknown, in spite of
numerous investigations. The state of the art sees it as a
black box with a discrete port to Brain and a continuous to
Mind's Imagery. We discuss it in C.MIND AND BRAIN
We show there that the discrete Brain alone would need more
that the age of Universe to coordinate a few simple movements
of an advanced organism and that the Continuous Mind's Imagery
appears as Evolution's device making viable advanced forms
of life.
Impulses received by the Brain map via Interface and Sensorium
to Points of Imagery Continuum symbolized as "Events".
Events represent the bottom level of recursive ER network
superficially defined above, whose vertices are Entities and
edges - Implications.
Primacy of Continuum
It seems essential to stress the primacy of Continuum over
Discreteness in the Structure of Mind. Imagery consists of
Continuous Patterns bounded by their intersections.
Discretization is performed by mapping Singularities of Imagery
Patterns (Attractors) into discrete Networks of Symbolics.
Awareness of Imagery precedes the language, or any other sort
of symbolizing, which justifies our ontological equivalencies
Subject-Continuum and Object-Discreteness
INTRODUCTION TO RELATIVISTIC PHENOMENOLOGY .
On the other hand, abstract Entities, whether symbols, language
expressions of mathematical formulas get meaning only by reduction
to Continuum of Imagery, which justifies our basic requirement
for Models to be founded in Continuum.
In that light we shall consider Phenomenon as an understood
Entity coupled with the Imagery Pattern which embodies its
Meaning. Primacy of Imagery justifies it homonym "Phenomenal
#Space". Phenomena are not directly observable, but "given"
by their lower ER neighbors, or "Aspects", thus, recursively
by the ultimate bottom Aspects or Events.
Postface
We shall consider our Structure as one of axiomatic
Foundations of Relativistic Dialectic, which we justify in
two ways.
1.Comparing it with Mind's physical counterpart, the Brain.
Our Structure founded in psychological observations matches
within acceptable precision the structures of Brain
determined by biological approach.
We find this correspondence in Popper and Eccles "The Self
and Its Brain" (Springer International) Page 327, Fig E5-7,
where
World 1 corresponds to our Sensorium
World 2 - to Imagery
World 3 - to Symbolics
All subsequent references to World 1,2,3 confirm this
correspondence.
2.Showing pragmatically, a posteriori, the adequacy of our
Structure as support of Reason and Logic.
