CONSCIOUSNESS FOR MODELING INTELLIGENCE
Simulating the Evolution by Closure to the Inverse
Tudor Niculiu
University POLITEHNICA Bucuresti, Dept. Electronics, Telecommunications, and IT
Cristian Lupu
Romanian Academy, Center of New Electronic Architectures
Sorin Cotofana
TU Delft, Electrical Engineering, Mathematics, and Computer Science
Keywords: Intelligent Simulation of Intelligence, Hierarchy Types, Divide et Impera et Intellige.
Abstract: Intelligence = Consciousness × Adaptability × Intention and Faith = Intuition × Inspiration × Imagination,
are the complementary parts of human mind. Conscience = Consciousness × Inspiration is the link between.
The subtitle refers to an interpretation of Way, Truth, and Life. It is a strategy of development. Conscience
simulation demands transcending from computability to simulability, by an intensive effort on extensive
research to integrate essential mathematical and physical knowledge guided by philosophical goals. A way
to begin is hierarchical simulation. Coexistent interdependent hierarchies structure the universe of models
for complex systems, e.g., hardware - software ones. They belong to different hierarchy types, defined by
simulation abstraction levels, autonomous modules, classes, symbols, and knowledge abstractions.
Applying Divide et Impera et Intellige to hierarchy types reveals their importance for intelligent simulation.
The power of abstraction is the real measure for the human mind. Turning the abstraction into
comprehensive construction could be the aim of humanity, the unique God for different cultures of free
humans. The way to freedom is by understanding necessity. We have to recall our conscience, to reintegrate
our mind, and to remember that society has to assist humans to live among humans, not to consider that
they only have to work for it. An operating system serves the autonomous programs, both for the function
of the hard and for development of the soft. The society has to be reasonable, to assure health and education
for every human, and to encourage search and research for every conscient human.
1 FUNCTION STRUCTURE
To begin was the word. Words enable us to express
ourselves, to be humans among humans. The
expression is complex, so it has to be hierarchical in
order to be comprehensible. Words are sequences of
letters, sentences are sequences of words, and texts
are sequences of sentences. The hierarchy is not
necessary linear. The basic hierarchical type is tree-
like, to optimally represent the generic strategy of
Divide et Impera et Intellige, or even graph-like, in
order not to constrain the links between levels. The
sequence is an ordered set, i.e., a function that
applies the first n natural numbers on the set M:
seqIN
n
M, IN
n
= {iIN: 1 i n}. If n is finite,
it is the number of sequence elements. Not. card M
= n.
Class, concept, term are aspects (syntax,
semantics, pragmatics) of the expression. Class is a
primitive notion. Set is a class that belongs to
another class. The set operations are paradigmatic:
serial (), parallel (×), hierarchical ( - set of all
parts). The possible expressions form a language.
Syntax, semantics, and pragmatics define any
language; the rules of each of the former defining
components refer, respectively, to correct
construction, interpretation, and application.
The syntax is determined grammatically:
187
Niculiu T., Lupu C. and Cotofana S. (2006).
CONSCIOUSNESS FOR MODELING INTELLIGENCE - Simulating the Evolution by Closure to the Inverse.
In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics, pages 187-190
DOI: 10.5220/0001203701870190
Copyright
c
SciTePress
grammars are of different types that can build a
hierarchy that corresponds to the reciprocal
inclusion of the defined languages. Grammar is a
language that refers to the language that grammar
defines, i.e., is beyond the defined language – a
metalanguage. This is another hierarchy type than
modularization (of a text) or inclusion (of the
languages due to the stronger rules of the defining
grammar). Its definition is based upon the principle
that each level is a metalevel of its inferior ones.
Further, the language can be symbolic, and symbols
can symbolize other symbols, what reveals another
hierarchy type.
We classified, we symbolized, we divided into
modules, and we reflected an inferior level
(language) on a higher one (grammar). Grammar is a
language, so it has a grammar, which, if isomorphic
to the initial grammar or to the language itself,
would mean that we obtained a reflexive language,
i.e., capable to express itself. Classes, symbols, and
modules permit the construction of a system that
structurally implements a function expressed in a
language, i.e., behavior (Niculiu, 2002). In the same
way, with classes, symbols, and modules, the
behavior of a structurally described system can be
determined. Another hierarchy type, simulation
hierarchy, orders the variety of languages that
describe function and structure. It assists the passing
from the goal function (constrained by functional
parameters) to the structural form, and inversely, to
determine the mathematical function/ physical
behavior of a system (characterized by structural
properties).
Simulation is the relationship between function
and structure. Researching intelligence by
simulating it, to enable intelligent simulation,
demands the study of combined essential
mathematical structures (algebra, order, topology),
to understand the different hierarchy/ abstraction
types. Because it is a hierarchical relation between
static and dynamic structures, and even between
structural and functional, the simulation can
contribute essentially to understand the human mind.
A multihierarchical representation for complex
systems can be formalized in the theory of
categories, object-oriented expressed, symbolically
interpreted, and structurally approached.
Function is a transformation that can be
mathematically formalized, or physically
instantiated as temporal behavior. Structure is a set
of properties that characterize a mathematical or
physical space. The properties can be constant or
variable in time, reflecting static or dynamic
structures. Simulation is the relation between
function and structure. Structured set = (Set,
structure). Language/ system is a generic form of a
mathematical/ physical model. Model results of an
inversion-able representation of the simulation
object. Abstraction is a human defining capacity that
enables him to think. Hierarchy is a functional/
structural concept that fulfils mathematically/
physically the concept of abstraction. Hierarchy is
syntax of abstraction. Intelligence and faith, like any
dichotomy, can converge to integration or can
destroy one another if not associated by Conscience.
God is in us - as the faith is part of our
definition, with us - by the others, and for us – by
the spiritual evolution, that is first conditioned, then
assisted, to be followed by the social one. To
prevent the danger of dichotomy, we concentrate in
three different ways on the unique Reality (Plato):
Art for the art - to look for the essential Way;
Science with God’s fear - to search the existential
Truth; Engineering-technology - to understand the
Being and to concentrate more on the Spirit in our
Life.
The power to abstract is the crucial difference
between human end any other natural being. Divide
et Impera et Intellige applies the hierarchical
expressed abstraction. The abstraction can be
simplifying or reflexive. Intelligent simulation
results by integration in the hierarchical simulation
of the associated knowledge hierarchy, which
represents a reflexive abstraction that converges to
self-awareness of the adaptable intentional
simulation.
2 HIERARCHY TYPES
By a self-aware simulation, we get self-control of
the simulation process. Therefore, we build a
knowledge hierarchy corresponding to the
simulation hierarchy. Then, by expressing both
simulation and knowledge hierarchies in the
reference system of the basic hierarchy types
(classes, symbols, modules), we create the context
for a self-organization of the simulation (Figure 1).
The triad of the basic hierarchy types corresponds to
the fundamental partition of the real life (beauty-
arts, truth-science, good-engineering), that has to be
continuously integrated by philosophy (essence,
existence, being). The absolute functionality is
symbolized by yin-yang, while the waves suggest
hierarchical levels that are increasingly structured
for simulation and knowledge.
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Hierarchy consists of a net that can represent any
type of mathematical structure (algebraic,
topological, order). The different hierarchy types
correspond to the kind of abstraction they reflect:
Class hierarchy (concepts) // abstraction goal
Symbol hierarchy (metaphors)
Module hierarchy (strategies)
Construction hierarchy (simulation)
Knowledge/ consciousness hierarchy (theory)
reflexive abstraction, each level aiming to
know all inferior levels, including itself; it is the
first step to model the Conscience.
Figure 1: Extended H-diagram.
3 DIVIDE. IMPERA. INTELLIGE
Philosophy is not a specialty but a human right.
There have to be schools to prepare the teachers of
philosophy for the other humans. These schools
have to develop also respect for those that look for
the Way on one of the three alternative paths that
correspond to the fundamental partition (arts,
science, engineering). Because recently the essential
Divide et Impera do not Intellige, the only
philosophers are the masters in:
Arts – especially great mathematicians, and
those, aware or not, compose mathematically
Science – physicists, and those that do not
forget their science is a chapter of physics
Engineering – mostly those working in
domains that attain the limits of the pure
Reason.
Each of the nondeterministic separated
complementary pairs is functionally structured like
(interface, kernel, ambassador of the complement).
The yin-yang model was not randomly selected: it is
formed of three tangent circles emphasizing the
centers of the inner ones. It retains only the essence
of a dichotomy symbol that suggests a complete
integration of the parts without loss of autonomy,
realized by vicinity and pointing one to another. The
Chinese symbol reflects the importance of
something else, reminding of creation as love for
something else. Three circles, each tangent to the
others, models a partition of something to be
understood in order to get further, says the center of
Europe. Circle is cerc only in our mother tongue, a
perfect expression: Cer (sky) is the infinite, cerc is
the finite representation of the infinite, by the
permanent link from the (never)begin to the
(never)end. π is the most famous real number
(Pitagora), followed by e (existence). And research
is cercetare.
The religion had to learn us about God's
existence in our being. The philosophy has to learn
us about essence, existence, and being. Our
conscience is our representation of the essence of
our existence as being, i.e., God is in ourselves, for
ourselves, and among ourselves. We have to be to
search our essence researching our existence.
Divide et Impera et Intellige has three parts as
alle guten Dinge sind drei of the most philosophic
European people. Mathematics develops by 3 basic
structure types, integrating them. We divide our
Universe in 3 worlds: essence, existence, and being.
We divide our existence in three interdependent
components: arts, science, and engineering,
corresponding to our beauty-loving ideas, our truth-
searching efforts, and our good-oriented
constructions - presently exaggerated to exclusivity.
As the Reality contains abstract ideas, even if
physics could explain everything as being discrete,
the power of continuum can not be forgotten.
(Marcus, 2000) Consequently, the analog
engineering has not to be neglected in modeling and
simulation. Physics permanently uses as dichotomy
the discrete-continuous, while the engineering just
adapts intuitively (as a primitive life form) to the
requests of a consumption-oriented society
(characteristic for primitive life). The reason is that
presently the engineering escaped of the control of
the inspiring arts, as of the consciousness for the
science that conditions its existence.
For physical or philosophical orientation, we
need cardinal points. To inspire ourselves of the
most pure of the arts, we learn about cardinal
numbers (although, being sincere, mathematics leads
the way to show that nothing is pure, so without
leaving anything behind the Way has to be followed
further). Cardinal numbers are just numbers of
elements in a set, but also for infinite sets. The
Nature demands the least infinity and is defined by
modules
pragmatics
technology
good
order
classes
syntax
arts
beauty
algebra
symbols
semantics
sciences
truth
topology
intelligent
simulatio
CONSCIOUSNESS FOR MODELING INTELLIGENCE - Simulating the Evolution by Closure to the Inverse
189
(0, successor, induction). Adding is in Nature’s
definition. However, the inverse operation,
subtraction, needs negative numbers. We close
mathematically the Nature to an Integer that opens
the physics for recognizing the limits of Reason
(electrons), in the meanwhile, attracting marvelous
engineering solutions for different technologies.
Electronics is among the most advanced engineering
sciences (Lupu, 2004); therefore, it has to be
practiced by the most conscient human beings.
Recurrent addition is multiplication, a most
important parameter for the Nature. Mathematics
closes the integers to the multiplication inverse,
defining the rational numbers. These are not more
than the naturals, but we can do many useful things
with the Reason, from strategy to computer. So
"what else do we need?" say too many, forgetting
that the limits of the, so-called, pure Reason are
caused by the fact that it bounds itself to close the
Adaptability to (discrete) sequential operations.
Thanks God, neither the mathematicians, nor the
physicists do accept the all-happiness. They discover
in three ways (order, algebra, analysis), which
assisted all of them together to think, the power of
continuum and that of the patience.
The Reality does not reduce to Nature, as card
IN is strictly inferior to card IR. The Reason is the
closure of the Nature relative to the primary
operations, as IQ is the closure of IN to the inverse
operations of addition and multiplication. However,
the Reason is dense in Reality – as the reals are the
analytical closure of the rationals, IR = {lim
n→∞
(q
n
):
(q
n
)INIQ }. The Reality extends beyond Nature
and Reason, not just for the quality of the quantity,
but also regarding the power of transforming
operations. IR closes IQ to the inverse of power
rising – the last arithmetic operation resulted by
recurrence of the prior one, which can be pursued by
Reason. Further, closing to the inclusion order, the
set of all subsets of IN, Z/ , IQ , or in general, of
countable sets, is the uncountable IR, the power of
continuum. To get to complex numbers is a matter
of Imagination. Reason closes the Nature to the
inverse of natural operations. Reality is the closure
of the Reason to the inverse of artificial operations,
or to the reasonably deducted infinite, or to an order
over the Being itself. We know that if there were no
cardinal number between the natural/ integer/
rational discrete and that of the real continuum, then
the logic would include the principle of the excluded
tierce. This, pure and simple, hurts the Human, who
is fond of nuances. Therefore, we can prove that
there is an intermediary level between Reason and
Reality (nonconstructive). There are angels between
Human and God, said the wise.
The density of Reason into Reality means that
every real is the limit of a sequence of rationales.
Therefore, we hear nowadays that if we master the
Reason, Reality becomes a complexity problem, i.e.,
speed of convergence. The density of IQ in IR shows
that between any two real there is a rational numbers
one. Therefore, Reality is much more than Reason
can even imagine but something reasonable exists
between any two real objects (nonintuitive).
Neither Intuition nor Reason arrives to
something that mathematics proves elementary. As
any true art or beautiful Science of the ideas or the
phenomena, mathematics does not limit itself to
either Intuition or Reason, allowing them to
collaborate by Conscience.
4 CONCLUSIONS
Conscience = closure to (knowledge o simulation)
-1
of
Conscience
Note: initially Conscience = Consciousness
The essential limit of discrete computability,
inherited by the computational intelligence, is
generated by the necessity for self-reference to
integrate the level knowledge with metalevel
knowledge in Conscience modeling. A hierarchical
type expressing reflexive abstraction can represent
the conscient knowledge. The aspects of the Reality,
and of the human mind reflecting it, have not to be
neglected, although they are neither constructive nor
intuitive. A way from Reason to Intelligence is to
integrate Consciousness and Intention, then to
integrate Intelligence and Faith to Reality-
awareness.
God is the absolute abstraction
the evolution goal for faith-assisted intelligence
REFERENCES
Lupu, C., 2004. Interconnection. Locality and Symmetry
in Orthogonal Computer Nets, Technical Publ.
Bucuresti.
Marcus, S., 2000. From Real Analysis to Discrete
Mathematics and Back, Real Analysis Exchange. 25,
2.
Niculiu, T., 2002. Hierarchical Intelligent Simulation,
Matrix Publ. Bucuresti.
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