MODEL OF MIND
---------------------
ALLEGORY OF THE CAVE
At the very origins of our
rationality we remark, in Ancient Greece,
some models and theories whose general concepts
remain foundations of contemporary reason,
as fresh today as they were at their origins.
We find the Heraclit/Democrit dichotomy in
continuous/discrete topology, in chaos/order,
in integral/differential calculus, in Einstein's
Field Theory/Planck's Quanta. And Plato's
Allegory of the Cave which after thousands
of years of idle, transcendental speculations
resurrects today as introductory version
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 the reality which the slaves may
observe:
vague, two-dimensional, flat forms
entirely
contingent and chaotic, arising, vanishing
and changing without any apparent reason.
Lacking other communication with the
reality,
the slaves tend to confuse the observation
with its 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, to explain
and to predict the reality.
Nevertheless, only very few will have
the
courage to undertake this enterprise
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.
Lets imagine in the 3D space a sphere
S and
a thin coin C in a 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 turning.
Consecutive
observations of its aspects (projections
on the projection plane or caves wall)
will
deliver circle, thick ellipse getting
thinner
and becoming a line, becoming 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
turning in this space.
MEMBRAN ANALOGY. SENSORIUM and IMAGERY.
Plato's Allegory is amazingly similar
to Membran Analogy, an introductory example
of Morphogenetics, whether Thos Theory of
Catastrophes, or Haken's Synergetics.
Let us consider an elastic membran
framed
with a totally rigid frame. We shall
call
'Observation Plane' or 'SENSORIUM'
the plane
passing par the frame and delimited
by its
internal contour (Fig. 1). The membran
is
sensitive to temperature, the frame
totally
insensitive. At a given temperature
the membran
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 membran'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 recognise 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
juxtaposed
"at the same level", or encompass
one another in various "levels".
Thus, 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"
encompasss
basins "brim" and "crown",
which encompasss in turn two elevations
and
a crease.
As for 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 patterns or IMAGES
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 euclidian 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 euclidian 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 membran model, which interprets
simply
the phenomenon. Nevertheless, such
a model,
though simple for us, would require
from
them a great deal of 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 membran basins. Apparently contingent
and meaningless behavior of the observed
configuration, when interpreted as
projection
of meaningful and meaningfully ordered
images
will become itself ordered and meaningful.
Apparently contingent and meaningless
phenomenon
appears in the light of imagination
as ordered
and meaningful. ORDER and MEANING are
effects
of imagination. We shall discuss in
detail
the concept of Order in future chapters.
Let us mention here by anticipation
that
1. Order of Imagery is causal,
2. in case of Perception (mapping of
Sensorium
to Imagery), causality is effective,
3. in case of Action (mapping of Imagery
to Sensorium), causality is final.
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 Membran
Analogy.
Our short discussion pointed out very
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
"objects
of reality", without being aware
of
actually dealing with Images created
in Imagery
by the modeling activity performed
by our
brain. 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 section.
NETWORK ANALOGY, SYMBOLICS.
--------------------------- Sensations
and
Images appear in context of, or with
respect
to, respectively 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 encompassing 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 "encompass"
relations.
It may be shown that for a multitude
of physical
phenomena (particularly for those involving,
like our Membran, 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. All these
phenomena
are described by partial differential
equations,
which usually represent the mapping
of a
continuous pattern into a discrete
network.
In the case of electric flow the involved
network is associated with the name
of Kirchhoff.
This last case semms particularly significative,
as it points to electric stimuli in
neural
networks.
A PATTERN of ATTRACTORS and BASINS
may be
mapped into a NETWORK of respectively
VERTICES
and EDGES, or, in logical terms, ENTITIES
and RELATIONS.
However, this mapping holds only for
one
given SCHEMA or particular structure
of vertices
and edges. Within this schema the network
is capable of simulating the dynamics
of
the model, i. e. the changes of potential
at the attractors and the corresponding
reactions
of the basins (shrinking and expansion)
respectively
with help of similar changes of potential
at the vertices. The mapping is reversible:
a given pattern determines a specific
unique
network structure, a given network
structure
determines a specific unique pattern.
To resume: an imaginary pattern may
be uniquely
mapped into a ER (Entity / Relation)
Network
structure whose Vertices (Entities)
represent
Image Attractors. We may say that Entities
SYMBOLIZE Images and that their structure,
the ER Network, provides a referential
supporting
symbolic forms of thinking. We shall
call
this referential SYMBOLICS.
Let us mention by anticipation, as
we did
in the section on Imagery, that
1. order of Symbolics is logical,
2. Causality of Imagery maps into Necessity
in Symbolics,
Our model of Mind encompasses three
basic
Referentials: SENSORIUM, IMAGERY and
SYMBOLICS.
Human Reason encompasses Lateral Thinking
or Reflection consisting of two basic
faculties:
1. Symbolizing, or mapping Imagery
to Symbolics
2. Understanding, or mapping Symbolics
to
Imagery.
We SYMBOLIZE by mapping Patterns and
Images
of Imagery into Entity/Relation network
structures
of Symbolics which we may express with
Statements
(or Propositions) and Symbols of our
languages.
We UNDERSTAND ER network structures
as well
as linguistic Statements and Symbols
by imagining
them, by mapping them to Imagery, which
confers
on them signification and meaning.
MODEL AS ONE OF FOUNDATIONS OF RELATIVISTIC
DIALECTIC
-----------------------------------------------------
Membran analogy is not an exact Model
of
Mind. but a simple schematic illustration
of extremely complex structure and
interrelations
of Sensorium, Imagery and Symbolics.
With
its help we may better understand following
axiomatic assertions:
Imagery consists of 3D Images which
may be
called Basins in topological context.
Each Image-Baisin is a potential form
created
by a construct called Attractor, or,
more
precisely by competition among all
Attractors
of Imagery Pattern.
Continuous Pattern of Images maps into
discrete
Network Structure in Symbolics. Attractors
map to Vertices and Basins into Edges
consisting
of inegrated characteristics of neighboring
Basins.
The 3D structure of Imagery admitts
any number
of neighbors in each dimension and,
consequently,
maps to nD symbolic network where n
is unlimited.
Network dimensionality is defined for
each
Vertex as number of Edges connecting
it with
related Vertices.
We shall consider the Model as one
of axiomatic
Foundations of Relativistic Dialectic,
which
we justify in two ways corresponding
to our
definition of Axiom (see Dogma and
Axiom).
1. Comparing the Model with biological
foundations
of Mind. Our model resulting from purely
morphogenetic and topological considerations
matches within acceptable precision
the structures
of Mind 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 model as support of
human
reason.
MODEL AS ONTOLOGICAL FOUNDATION OR
REFLECTION
---------------------------------------------
In "Foundations in Ontology"
we
postulate that the ontological foundation
of RD, Awareness is never empty, that
it's
thematic and that its theme or "Reflection"
consists strictly of some "present"
substructure of the structure of Mind,
as
defined in the present chapter.
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 Membran Analogy.
Our short discussion pointed out very 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 "objects of reality",
without being aware of actually dealing with
IMAGES created in Imagery by the modeling
activity performed by our brain. 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 section.
NETWORK ANALOGY, SYMBOLICS.
Sensations and Images appear in context of,
or with respect to, respectively 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 encompassing adequate integrals of
involved basin volumes we obtain a network
whose vertices and edges are respectively
Attractor projections and their links (Fig.
5). It may be shown that for a multitude
of physical phenomena (particularly for those
involving, like our Membran, potential fields)
it is possible to map a given Situation 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.
All these phenomena are described by partial
differential equations, which usually represent
the mapping of a continuous Situation into
a discrete network. In the case of electric
flow the involved network is associated with
the name of Kirchhoff. This last case is
particularly interesting for us, as it encompasses
electric stimuli in neural networks.
A SITUATION of ATTRACTORS and BASINS may
be mapped into a NETWORK of respectively
VERTICES and EDGES. However, this mapping
holds only for one given SCHEMA or particular
distribution of vertices and edges. Within
this schema the network is capable of simulating
the dynamics of the Situation, i.e. the changes
of potential at the attractors and the corresponding
reactions of the basins (shrinking and expansion)
respectively with help of similar changes
of potential at the vertices. The mapping
is reversible: a given Situation determines
a specific unique network, a given network
determines a specific unique Situation. To
resume: an imaginary Situation may be uniquely
mapped into a network whose vertices represent
Image Attractors. We may say that vertices
SYMBOLIZE images and that their structure,
the network, provides a referential supporting
symbolic forms of thinking.
We shall call this referential SYMBOLICS.
Let us mention by anticipation, as we did
in the section on Imagery, that 1.order of
Symbolics is logical, 2.Causality of Imagery
maps into Necessity in Symbolics, Our model
of Mind encompasses three basic Referentials:
SENSORIUM, IMAGERY and SYMBOLICS. Human Reason
encompasses Lateral Thinking consisting of
two basic faculties: 1.Symbolizing, or mapping
Imagery to Symbolics 2.Understanding, or
mapping Symbolics to Imagery. We SYMBOLIZE
by expressing Situations and Images with
Statements (or Propositions) and Symbols
of our languages. We UNDERSTAND Statements
and Symbols by imagining them, by getting
their meaning, by mapping them to Imagery.
MODEL AS AN AXIOM OF RELATIVISTIC DIALECTIC
We shall consider the Model as one of axioms
of Relativistic Dialectic, which we justify
in two ways corresponding to our definition
of Axiom (see Dogma and Axiom). 1.Comparing
the Model biological foundations of Mind.
Indeed our model resulting from purely morphogenetic
and topological concepts corresponds within
acceptable precision to structures of Mind
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 model as support of human
reason. ===================================================
|
Evans Experientialism 
Relativistic Dialectics