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:

seq∈IN

→ M, IN

= {i∈IN: 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

 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.

ICINCO 2006 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

188

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→∞

)∈IN→IQ }. 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

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,

Niculiu, T., 2002. Hierarchical Intelligent Simulation,

Matrix Publ. Bucuresti.

ICINCO 2006 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

190